THE UNIVERSITY OF MICHIGAN INDUSTRY PROGRAM OF THE COLLEGE OF ENGINEERING ANALYSIS AND DIGITAL SIMULATION'QF-CARBURETOR METERING David -L. Harrington A dissertation submitted in partial fulfillment of the requirements for the degree of Doctor of Philosophy in The University of Michigan 1968 December, 1968 IP-825

O David Lee Harrington 1968 All Rights Reserved ii

ACKNOWLEDGMENTS I wish to express my appreciation to all of the members of the Doctoral Committee for their assistance and advice during this entire project. Special thanks are due to Professor Jay A. Bolt who provided leadership and inspiration in the course of countless project discussions. I also owe special thanks to Dean Gordon Van Wylen for his special support and counsel. The financial support of the United States Public Health Service is gratefully acknowledged. Without this support, this project could not have been completed. The financial support of the Cummins Engine Co., through their Fellowship in the Mechanical Engineering Department, is also appreciated. The assistance of Mr. Stephen Derezinski in obtaining accurate flow model data is greatly appreciated. In addition, his numerous comments and suggestions were invaluable in developing the over-all simulation program. Acknowledgment is also made of the assistance given by Mr. Robert Olree, now of the Ethyl Corporation, in instrumenting and obtaining engine test data. Thanks is also due to the various carburetor groups of the Ford Motor Company for providing numerous test carburetors, specification sheets, and road load curves. The valuable assistance of Mrs. Joan Neagli and Miss Ruth Howard in preparing the original manuscript is gratefully acknowledged. Thanks is also due to the personnel of the Office of Research Administration at The University of Michigan for their assistance in preparing this document. iii

TABLE OF CONTENTS PAGE LIST OF TABLES viii LIST OF ILLUSTRATIONS x NOMENCLATURE (non-computer) xv CHAPTER I INTRODUCTION 1 A. General 1 B. Reasons for Developing the Simulation 3 C. Overall Scope and Limitations of the Simulation 5 D. Brief Description and Goals of the Simulation 8 II. THEORETICAL ANALYSIS OF COMPRESSIBLE MIXTURE FLOW 11 A. Background 11 B. Mathematical Model of the Compressible Flow Path 15 C. Thermodynamic Properties of the Compressible Mixture 18 D. Throttle Plate Flow 21 E. Analysis of Total Mixture Flow and Engine Parameter Effects 25 F. Analysis of Compressible Flow Through Multiple Venturii 44 G. Analysis of Fuel Atomization and Spray Vaporization 50 III. FUEL FLOW THROUGH ORIFICES 66 A. Reasons for Orifice Flow Work 66 B. Background 67 C. Analysis and Correlation of Orifice Flow 76 D. Correlation of Fuel Properties 86 E. Results of Orifice Flow Bench Tests 90 F. Application of Orifice Coefficient Data to Actual Flow Situations 106 iv

TABLE OF CONTENTS (continued) PAGE IV. THEORETICAL ANALYSIS OF FUEL AND AIR BLEED FLOW 116 A. Background 116 B. Fuel Channel Model 121 C. Criteria for Solution 124 D. Pressure Losses in Fuel Channel Elements 127 E. Fuel Channel Iterative Technique 137 V. ENGINE AND VEHICLE ANALYSIS 142 A. Reasons for Relating The Engine and Vehicle to the Carburetor 142 B. Requirements For Road Load Carburetor Analysis 143 C. Vehicle Road Load Relationships 144 D. Correlation and Prediction of Engine Performance 148 E. Summary of Engine Data Correlation Technique 161 F. Iterative Technique For Obtaining Road Load Operating Points 164 VI. ON-ENGINE CARBURETOR TESTS 167 A. Reasons for Tests 167 B. Background 168 C. Experimental Equipment and Conditions 171 D. Carburetor Performance Over The Entire Operating Range 177 E. Special Experimental Programs 188 1. Suction profiles within the boost venturi 188 2. High speed movies of fuel discharge 190 3. Transient and pulsating flow study 195 v

TABLE OF CONTENTS (continued) PAGE VII. LUCITE FUEL CHANNEL MODEL TESTS 206 A. Reasons for Fuel Channel Model Tests 206 B. Lucite Fuel Channel Model 206 C. Flow Model Test Stand 211 D. Advantages of Using the Flow Model and Test Stand 216 E. General Test Techniques and Conditions 217 F. Results of Fuel Channel Flow Tests 221 G. Two-Phase Flow Observations 239 H. Comparison With Predictions of Subroutine FLOW 243 VIII. OPERATION OF THE COMPLETE SIMULATION 246 A. General Description 246 B. Required Input Data 248 C. Basic Iterative Scheme 251 D. Carburetor Analysis At Constant Engine Speed or Constant Throttle Angle 255 1. Simulation predictions 255 2. Carburetor - engine operating map 260 3. Accuracy of the simulation predictions 262 4. Available computer plots 263 E. Carburetor Analysis At Road Load Operating C onditions 268 F. Carburetor Analysis With Production Variations In Dimensions 274 G. Auxiliary Subroutine Printouts 280 H. Computer Times Required 282 IX. APPLICATIONS OF THE COMPLETE CARBURETOR SIMULATION 283 A. General Applications 283 B. Single Variable Effects 283 C. Additional Applications 284 D. Examples of Single Variable Effects 285 vi

TABLE OF CONTENTS (continued) PAGE X. RECOMMENDATIONS 296 APPENDICES A. ADDITIONAL SIMULATION PREDICTIONS 298 B. THROTTLE FLOW AREA 304 C. IDLE NEEDLE FLOW AREA 311 D. THERMODYNAMIC PROPERTIES OF AN AIR, WATER VAPOR, AND FUEL VAPOR MIXTURE 314 E. EXPLANATION OF SUBROUTINES 319 F. MULTI-PURPOSE INTERPOLATION SUBROUTINE 326 G. GENERAL CONVERrGENCE TECHNIQUE 330 H. ANALYTICAL PREDICTION OF FUEL VAPORIZATION WITHIN THE CARBURETOR 333 I. LISTING OF MAIN COMPUTER PROGRAM 340 J. LISTING OF SUBROUTINES 363 K. ADDITIONAL FLOW MODEL CURVES AND DATA UTILIZED WITHIN THE SIMULATION 407 L. EXPLANATION OF SYMBOLS USED IN THE SIMULATION 417 BIBLIOGRAPHY 439 vii

LIST OF TABLES TABLE TITLE PAGE I. Specifications of Test Orifices 92 II. Computed Results For A Typical Flow Bench Test 94 III. Orifice Cd Data Used In The Simulation 105 IV. The Percentage Of The Static Pressure Differential That Is Irrecoverable 112 V. Head Loss Values For Non —Uniform Flow 133 VI. Fuel Channel Analysis Results 140 VII. Equipment Utilized in On-Engine Carburetor Tests 172 VIII. Ranges Of Variables In Carburetor Tests 176 IX. Reduced Data For On-Engine Carburetor Tests At Constant Engine Speed And Variable Throttle Angle 178 X. Reduced Data For On-Engine Carburetor Tests At Constant Throttle Angle And Variable Engine Speed 181 XI. Listing Of Fuel Channel Flow Tests 218 XII. Typical Data Sheet For A Lucite Fuel Channel Flow Test Using Gasoline 222 XIII. Reduced Data For A Lucite Fuel Channel Flow Test With Air Bleeds 224 XIV. Reduced Data For A Lucite Fuel Channel Flow Test Without Air Bleeds 225 XV. Required Input Data 249 XVI. Simulation Predictions For A Constant Engine Speed - Variable Throttle Angle Analysis 256 XVII. Simulation Predictions For A Constant Throttle Angle Analysis (Closed Throttle) 258 viii

LIST OF TABLES (continued) TABLE TITLE PAGE XVIII. Simulation Predictions For A Constant Throttle Angle Analysis (26~) 259 XIX. Simulation Predictions For Carburetor Operation At Road Load Conditions 270 XX. Engine Input Data For Road Load Analysis 271 XXI. Vehicle Input Data For Road Load Analysis 272 XXII. Simulation Predictions For The Effects Of Production Tolerances On Carburetor Performance 276 XXIII. Computer Prediction Of Main And Boost Venturi Parameters 281 XXIV. Required Computer Times (Approximate) 282:XXV. Simulation Predictions For Carburetor Performance at Altitude 286 XXVI. Simulation Predictions For Carburetor Performance With Reduced Ambient Temperature 292 XXVII. Simulation Predictions For The Effects of Production Tolerances on Carburetor Performance (Ford C4AFB-91 Carburetor) 300 XXVIII. Reduced Data For A Lucite Flow Model Test Using Hot Mineral Spirits 408 XXIX. Reduced Data For A Lucite Flow Model Test Using Cold Mineral Spirits 409 XXX Specifications and Experimental Values For A Typical Test Carburetor 413 XXXI. Viscosity Conversions Utilized in The Simulation 415 XXXII. Constants Utilized In The Simulation 416 ix

LIST OF ILLUSTRATIONS FIGURE TITLE PAGE 1 Basic Model of the Compressible Flow Path 17 2 Computer Model of the Compressible Flow Path 19 3 Throttle Plate Discharge Coefficient Values 24 4 Illustration of Local P0 and To Values 29 5 Simultaneous Solution of Exhauster and Nozzle Equations 40 6 Computer Model Parameters for Boost Venturi 47 7 Methods of Illustrating Drop Size Distributions 53 8 Drop Size Distribution with Two Preferential Sizes 58 9 Illustration of Drop Vaporization Regimes 61 10 Variation in Ultimate Cd with L/D Ratio 73 11 Boundary Layer Development within an Orifice 77 12 Ideal Flow in an Orifice 79 13 Nomenclature for Common Orifice Types 83 14 Iso-Octane Property Variations with Temperature 89 15 Specific Gravity Variations of Test Fuels 89 16 Schematic Diagram of Orifice Flow Bench 91 17 Gasoline Flow Rate vs. Pressure Drop for F-50 Orifice 96 18 Cd vs. Pressure Drop for F-50 Orifice 97 19 Characteristic Discharge Coefficient Curve for F-50 Orifice 99 x

LIST OF ILLUSTRATIONS (continued) FIGURE TITLE PAGE 20 The Effect of Fluid Type on the Discharge Coefficient 100 21 The Effect of L/D Ratio on the Orifice Characteristic Curve 102 22 Pressure Variations in the Vicinity of An Orifice 108 23 Typical Fuel Channel Geometry Near Air Bleed Well 119 24 Computer Model of Complete Carburetor Fuel Channel 121 25 Nodal Points in the Fuel Channel Flow Network 124 26 Total and Static Pressure Variations Within a Simple Fuel Channel 128 27 Dependence of the Engine IHP on the Air Mass Flow Rate 150 28 Slope of the IHP Curve as a Function of Fuel-Air Ratio 152 29 Constant Air Flow Curves for Varying Fuel-Air Ratios 154 30 Three-Dimensional Operating Surface for an Engine 155 31 FMEP Variations with Engine Speed and Intake Manifold Vacuum 159 32 Applications of Constant Air Mass Flow Rate Curves 163 33 Equipment Utilized in On-Engine Carburetor Tests 174 34 Equipment Utilized to Control and Monitor Carburetor Variables 175 35 Variations in Intake Manifold Vacuum With Throttle Angle and Engine Speed 182 36 Effect of Measured Air Flow Rate on The Metering Signal 184 37 Total Pressure Loss Through Venturi 185 xi

LIST OF ILLUSTRATIONS (continued) FIGURE TITLE PAGE 38 Brake Specific Fuel Consumption Curves For Various Engine Speeds 186 39 BSFC Variations At Constant Throttle Angle and Constant Engine Speed 187 40 Suction Distribution in Inches of Water Within A Typical Boost Venturi 189 41 Equipment Utilized in Obtaining High Speed Movies of Fuel Discharge 192 42 High Speed Photographs of Fuel Discharge Within The Boost Venturi - Low Fuel Flow 193 43 High Speed Photographs of Fuel Discharge Within The Boost Venturi - High Fuel Flow 194 44 Equipment Utilized in Obtaining Pressure - Time Traces Under Transient and Pulsating Conditions 196 45 Pressure Transients Within A Carburetor During A Sudden Throttle Opening 197 46 Pressure Transients Within A Carburetor During A Sudden Throttle Closing 198 47 Mean and Alternating Components of The Metering Signal At Various Operating Points 200 48 Waveforms For The Boost Venturi Suction And Main Metering Orifice Pressure Drop For Highly Pulsating Air and Fuel Flow 201 49 Effective Metering Signal For Pulsating And Steady Flow Conditions 204 50 Lucite Flow Model Of Complete Carburetor Fuel Channel 207 51 Cross-Section of Lucite Flow Model 209 xii

LIST OF ILLUSTRATIONS (continued) FIGURE TITLE PAGE 52 Flow Model Test Stand 210 53 Relative Position of The Lucite Flow Model On The Test Stand 212 54 Schematic Flow Diagram Of Fuel Channel Model Test Stand 214 55 Manometer Bank Utilized To Obtain The Static Pressure Distribution With The Fuel Channel 220 56 Experimental Values of Gasoline Flow Rate As A Function Of The Metering Signal 227 57 Log-Log Plot Of Total Gasoline Flow Rate Versus The Metering Signal 228 58 Measured Air Bleed Flow Rate As A Function Of The Metering Signal 230 59 Mass Flow Rate Of Cold Gasoline As A Function Of The Metering Signal 231 60 The Effect Of Numerous Operating Variables On The Mass Flow Rate of Mineral Spirits 233 61 The Effect Of Fluid Temperature On The Mass Flow Rate of Mineral Spirits 234 62 Illustrations Of The Rapid Change In The Main Channel Discharge Coefficient At Small Metering Signals 236 63 Air Bleed Flow Rate Variations For One And Two Operating Bleeds 237 64 The Effect Of Fluid Temperature On The Air Bleed Mass Flow Rate 238 65 High Speed Photographs Of Two-Phase Flow Within The Lucite Model 240 66 Total Pressure Loss Variations For Two-Phase Flow Within The Carburetor 242 xiii

LIST OF ILLUSTRATIONS (continued) FIGURE TITLE PAGE 67 Comparison Of The Flow Rate Predictions Of Subroutine FLOW With Actual Fuel Channel Data 244 68 General Procedure Utilized In The Basic Iterative Scheme 252 69 Carburetor - Engine - Vehicle Operating Map 261 70 Predicted Fuel-Air Ratio Variations 265 71 Predicted Main Fuel Flow Rate Variations 266 72 Carburetor - Engine - Vehicle Operating Map With Expanded Scale 267 73 Predicted And Experimental Road Load Fuel Economy Values 273 74 Carburetor - Engine - Vehicle Operating Map At Altitude 290 75 Carburetor - Engine - Vehicle Operating Map For Reduced Ambient Temperature 295 76 Simulation Predictions Of Main Fuel Flow Rates 299 77 Variables In The Throttle Plate Flow Analysis 305 78 Idle Needle Flow Area Variables 312 79 Sample Difference Table Using Actual Square-Edged Orifice Data 327 80 Illustration Of The Newtonian Iteration Technique 330 81 Illustration Of Generalized Convergence Technique 331 82 Fuel Mass Flow Rate As A Function Of The Main Metering Orifice Pressure Differential In The Lucite Flow Model 410 83 Main Fuel Channel Discharge Coefficient Curve 411 84 Mass Flow Rate Of Hot Test Fluid Within The Lucite Flow Model 412 xiv

NOMENCLATURE SYMBOLS (NON-COMPUTER) A = Area C = General constant Cd = Discharge coefficient C = Constant pressure specific heat C, = Constant volume specific heat CC = Vena contracta coefficient CR = Engine compression ratio d = Throttle shaft diameter D = Diameter or engine speed Dv = Mass diffusion coefficient E = Error f( ) = General functional relationship fd = Darcy friction factor gc = Mass conversion factor h = Fuel hydrostatic head H = Enthalpy of combustion H = Lower heating value of fuel c K = Specific heat ratio * K = Cavitation number KL = Head loss factor L = Length m = Mass xv

NOMENCLATURE (continued) m = Mass flow rate M = Mach number n = Number of moles N = Engine speed N = Number of engine cylinders c cb Ncy= Number of strokes in an engine cycle Nth = Number of threads per inch on idle needle Nu = Nusselt number P = Pressure q = Moment of the drop size distribution 4 = Volume flow rate R = Gas constant R = Universal gas constant Re = Reynolds number S, = Schmidt number t = Time T = Temperature V = Velocity V = Swept volume of engine cylinder W = Molecular weight x = Drop diameter or a general abcissa variable x = Mean drop diameter xvi

NOMENCLATURE (continued) xvs= Sauter mean drop diameter y = Mole fraction or a general ordinate variable z = Distance traveled by a fuel drop Z = General error parameter = Included angle of idle needle screw, or interpolation argument parameter /9 = Expansion ratio of venturi 8S = Air compressibility factor, or Sterling's divided difference = Iterative error or surface roughness = Finite increment - = General throttle plate angle -G = Completely closed throttle plate angle y7 = Vehicle drive train efficiency ^ = Relative humidity f.[ = Bend radius to channel radius ratio = Density 9' = Pulsation factor T = Surface tension or standard deviation of dimensions. = Summation / = Absolute viscosity V = Kinematic viscosity O = Mass ratio of water vapor to air xvii

NOMENCLATURE (continued) SUBSCRIPTS a = Air amb = Ambient b = Air bleed system cl = Clearance volume corr = Corrected to zero approach velocity e = Enrichment system f = Fuel fa = Fuel and air h20 = Water i = Inlet or ith component or idle system j = Main metering orifice (jet) flow I = Local m = Main system man = intake manifold mix = Mixture of air, fuel vapor, and water vapor n = Idle needle or normalized distribution o = Stagnation conditions r = Residual gases rel = Relative s = Static or surface surf = Drop surface surr = Surroundings xviii

NOMENCLATURE (continued) t = Total flow or total (stagnation) conditions th = Venturi throat v = Fuel vapor voo = Fuel vapor at infinity 1 = Fuel vapor or orifice approach channel 2 = Air or orifice 3 = Water vapor 9 = Surface tension (o = Infinity ABBREVIATIONS A/F = Air-fuel ratio BHP = Brake horsepower BMEP = Brake mean effective pressure BSFC = Brake specific fuel consumption C = Degrees Centigrade cm = Centimeter R-55 = Rochester main metering orifice of 0.055 inch diameter cps = Cycles per second OF Degrees Fahrenheit FHP = Friction horsepower FMEP = Friction mean effective pressure F/A = Fuel - air ratio F-50 = Ford main metering orifice of 0.050 inch diameter xix

NOMENCLATURE (continued) ft = Feet gm = Grams in = Inches IHP = Indicated horsepower IMEP = Indicated mean effective pressure ISFC = Indicated specific fuel consumption lbf = Pound force Ibm = Pound mass MPG = Miles per gallon MPH = Miles per hour psi = Pound force per square inch psia = Pound force per square inch absolute RPM = Engine revolutions per minute OR Degrees Rankine S-E = Square-edged orifice SG = Specific gravity TORQB = Brake torque TORQF = Friction torque TORQI = Indicated torque VACMAN = Intake manifold vacuum xx

CHAPTER I INTRODUCTION A. GENERAL The modern carburetor is a complex assembly of subsystems, each with its specific function. The simple "ideal carburetor" as presented for analysis in textbooks bears little resemblance to the true hardware in either theory or operation. The theoretical analysis of carburetors is, in the case of textbooks, so greatly oversimplified that the resulting equations are of little or no value in predicting the operation of an actual carburetor. Even the published papers and theses in the field are very restrictive in terms of the assumptions made. These include: 1. assuming incompressible air flow 2. assuming constant coefficients of discharge for all orifices 3. ignoring viscous pressure losses in the fuel channels 4. ignoring the presence of the throttle plate and shaft 5. ignoring enrichment and idle systems 6. neglecting air bleed systems 7. ignoring engine parameter effects 8. ignoring heat and mass transfer effects in the vaporization of the fuel droplets. 1

2 In addition, the simplified analyses invariably predict a carburetor parameter such as total fuel flow as a function of air flow. This ignores the fact that any air flow is the result of a certain engine speed and throttle opening and that there are an infinite number of combinations of the two which will give a specified air flow. Each combination will have a different intake manifold vacuum and thus a different total fuel flow. Therefore the simplified analyses are quite erroneous in assuming that if a total air flow is specified, the other carburetor parameters can be obtained. This concept has its corollary in the standard carburetor flow box test. This test presents the fuel-air ratio as a function of air flow and wculd seem to convey the fact, as mentioned above, that the fuel flow is fixed for a given value of air flow. This error is the result of neglecting the infinite number of engine speed-throttle opening combinations. As will be shown later, an accurate, comprehensive carburetor simulation must include, in addition to many other items, the interrelationships between the carburetor and the engine. In the past, the theoretical analysis of carburetor operation has been hampered by the fact that closed form solutions were sought. An example of this type of solution is:70 * F/A = Ajet Cjet 1 /fuel AvenCven p/air The closed form solutions are obviously easy to work with but it should be evident that, in order to obtain a closed form equation describing a process which involves many interacting variables, a large number of * Superscript numbers refer to listings in the bibliography (Pages 439-444).

3 simplifying assumptions must be made. However, if the numerous complex relationships describing each variable are utilized in an iterative solution, numerical values may be obtained without oversimplifying. The analogy to this is the solution of an nth degree polynomial equation. For small n, closed form algebraic solutions of a general nature can be obtained, (such as the familiar quadratic formula) but for large n this becomes impossible. Yet numerical values can be obtained for large n by iterative techniques. B. REASONS FOR DEVELOPING THE SIMULATION Most of the simplifying assumptions mentioned above were made because little is known of the complex interactions within and between carburetor systems. Thus, the analyses based on these assumptions yield predictions which do not correlate well with actual carburetor data. Therefore, one of the important reasons for developing a comprehensive simulation is to understand the complex phenomena that are known to occur during the operation of the carburetor. For example, it is known that carburetors deliver a richer mixture as altitude increases and as fuel temperature is decreased. Almost every other carburetor variable from the main metering jet diameter to the throttle plate shaft diameter will affect the mixture ratio delivered to the engine. Since the fuel-air ratio is one of the most important variables in internal combustion engine work, accurate metering is extremely important. Numerous other variables, such as engine thermal

4 efficiency, unburned hydrocarbon emission, maximum brake mean effective pressure, rate of pressure rise, and dissociation losses are greatly influenced by this ratio. Many practical problems in internal combustion engine work, such as combustion instability under lean operation can be traced to variations in metering the fuel to the air. Also, the growing importance of the vehicle air pollution problem has given new and urgent incentives to improve all aspects of automotive carburetor and induction system performance. Foremost among these incentives is the desire for more precise carburetor metering under all engine and ambient conditions. This can only be accomplished if the metering processes are analyzed and understood more completely. Another incentive for developing the carburetor simulation is based on economic considerations. If it is considered that millions of carburetors are manufactured annually and are used to meter billions of gallons of fuel, then the possible economic gain through more precise metering becomes evident. Another economic factor is related to the fact that there is still a great deal of art inherent in the design of carburetors. It is generally conceded that a great deal of practical carburetor experience and system prototype testing are required in the development of a new 52 carburetor. In fact Stoltman made the statement in a recent paper that.... the carburetor has more engineering hours per cubic inch than the majority of automotive components." This trial and error design, construction, and testing is expensive and time consuming,and the more

5 evaluation that is done by computer analysis, the less will be the trial and error design cost. This points up the final reason for developing a comprehensive simulation and that is; to provide the engineer with an evaluation tool. If the simulation is accurate enough to replace some of the prototype construction and testing, the engineer can rapidly evaluate numerous proposed designs and can discard those that are unsuitable before they are constructed. Coupled with rapid computer plotting, the entire range of variables could be investigated and the simulation could be used to optimize systems and determine the effect of variables which would be too expensive to determine by actual test. An example of this might be; the effect of the fuel channel dimensional tolerances on the fuel-air ratio spread among hundreds of carburetors. C. OVERALL SCOPE AND LIMITATIONS OF THE SIMULATION The purpose of this thesis was to perform a theoretical analysis of an actual carburetor, analyzing each system and phenomenon in terms of the fundamentals of fluid mechanics and thermodynamics and to combine these analyses into a comprehensive digital computer simulation. As few simplifying assumptions as possible were made and the following quantities were analyzed and incorporated into the simulation:

6 1. variations in ambient pressure, temperature, and humidity. 2. a fuel flow network containing main, idle, and a vacuum sensitive enrichment system. 3. variations in fuel specific gravity, viscosity, surface tension, and molecular weight with fuel type and temperature. 4. compressible flow of an air, fuel vapor, and water-vapor mixture through a primary and boost venturi in parallel. 5. variation in orifice coefficients of discharge with orifice type, L/D ratio, flow rate, and fuel properties. 6. effects of multiple air bleeds in both main and idle systems. 7. variations in operation due to mating with different engines and vehicles. 8o. multiple passages which allow air to bypass the throttle plate. 9. flow of a wet mixture across a throttle plate (variable geometry throat) with a finite shaft size. 10. atomization of the fuel at discharge and vaporization of the fuel droplets in the air stream. For reasons of maximum applicability and program readability, the simulation was written in the language most familiar to engineering groups in the industry, FORTRAN II. This was thought by the author to be a consideration outweighing the greater flexibility and ease of programming of FORTRAN IV and MAD. (The CALCOMP plotting subroutine is, however, written in the MAD language as will be seen later.) Although more statements are required to accomplish a given task in FORTRAN II

7 than in the newer, more flexible languages, it was the author's opinion that user adaptation should prevail over ease of programming. The simulation was written for an air-bled, boost venturi carburetor with an enrichment valve which is sensitive to intake manifold vacuum. Each component of the compressible mixture (air, water vapor, and fuel vapor) was assumed to be an ideal gas and the equations describing the dynamics and thermodynamics of the compressible mixtuire were obtained by assuming one-dimensional, steady flow. (A pulsation parameter will be discussed later). Thus the simulation is not intended for transient air or fuel flow conditions such as occur with sudden throttle openings and closings or rapid engine speed increases or decreases. The fuel channel flow was analyzed on the basis of steady, incompressible flow in a branching network. Since no correlations existed for two-phase flow through orifices and since the standard two-phase pipeline pressure drop correlations gave very erroneous predictions, the air bleed system pressure drop was based on the average velocity of the fuel-air mixture foam in the passages. This velocity was based on the relative proportions of fuel and air by volume in each passage. The simulation as written is essentially a comprehensive analysis of a carburetor barrel containing a primary and a secondary (boost) venturi. No air cleaner or choke is included, but as will be seen later, these devices could be included quite easily if desired, since their function can be described simply by a reduction in the incoming stagnation pressure.

8 In addition, the simulation as written is for two main fuel system air bleeds and two idle system air bleeds. However, as will be explained more fully in chapter eight, the program is flexible enough to account for variations in these numbers by a change in the input data. Many of the computer runs were for input data corresponding to a two-barrel carburetor with two main metering jets,because a significant portion of the experimental data used to verify the simulation accuracy was taken on carburetors of this type. D. BRIEF DESCRIPTION AND GOALS OF THE SIMULATION For a specified carburetor geometry, fuel, ambient conditions, engine, and vehicle, an analysis is made of the iteractions between the various systems (taking into account the 10 items mentioned earlier) and values for nearly all important operating variables are calculated. One of the most important goals of this simulation was to accurately predict, for any carburetor geometry, fuel type, fuel temperature, ambient conditions, engine, vehicle, and operating point, most of the significant carburetor, engine, and vehicle variables. Some of these variables are: 1. total engine air flow 2. main system fuel flow 3. idle system fuel flow 4. enrichment system fuel flow 5. main and idle system air bleed flow

9 6. intake manifold pressure 7. boost and primary venturi signals 8. road load intake manifold pressure and throttle angle 9. vehicle miles per gallon 10. engine bhp, ihp, bsfc, and isfc The road load and vehicle parameters were incorporated into the simulation because one of the original goals of the simulation was to analytically relate the carburetor, engine, and vehicle variables and to provide for computer evaluation of carburetor operation on a road load basis. This expands the usefulness and applicability of the simulation enormously. For example, any carburetor parameter can be varied over its limits and its effect on the road load miles per gallon predicted. The method of obtaining the large amount of engine data needed and the method of analytically predicting the road load throttle angle and air flow will be discussed in detail later. Another goal of the simulation was to arrange the resulting computer predictions in such a way that many trial and error design tests could be eliminated. In other words, to have the computer predict the results of the test just as if it had been performed. This is applicable in many cases such as flow box tests and proving ground mileage tests where definite quantities are measured and recorded, but tests involving such subjective variables as "driveability" can obviously not be eliminated. However,

10 if the simulation is to eliminate a trial and error design test, it must produce as its output the accurately predicted values for all of the variables which would have been determined in the test. Also, if it is to evaluate any or all possible carburetor-engine-vehicle operating points, it must predict or calculate from the engine and vehicle input data nearly all the significant engine and vehicle parameters along with the carburetor values. This includes all the items listed on the previous page. Thus the simulation and the computer plotting were developed with carburetor design and application in mind; that is, to assist the engineer in answering the inevitable questions which arise in design and operation: 1. How will a change in parameter "A' affect parameter "B"? 2. How will the operating variables such as ambient or fuel temperature affect the overall performance of the carburetor? 3. How will a particular carburetor design perform on a particular engine or engine-vehicle combination? 4. How do variations in carburetor dimensions due to production tolerances affect the metering?

CHAPTER II THEORETICAL ANALYSIS OF COMPRESSIBLE MIXTURE FLOW A. BACKGROUND The analysis of the compressible flow of air, water vapor, and fuel vapor is an extremely important part of the over-all simulation. This is because all later fuel flow calculations are dependent upon the pressure losses and metering signals obtained from the compressible flow analysis. The literature which exists on compressible flow through carburetors is mainly experimental in nature. That portion which is analytical involves, for the most part, many simplifying assumptions which results in an inadequate description of actual carburetor behavior. Dodson, Booth, and Metsger experimentally investigated the metering signals produced by double venturii combinations of various geometries. An analysis of the throttle plate flow was not made nor was the compressible air flow related to engine operation. Variations in metering signal with altitude were obtained experimentally and an altitude enrichment was calculated. This was not done by actually flowing fuel into the boost venturi but by describing the fuel flow as; mf uel Constant / P boost This is an extremely simplified description of the fuel flow, thus the resulting extension of measured boost venturi suctions to fuel flow rates could be significantly in error. The chief contribution of 11

12 this work was the determination of the effect of geometry on the metering signal of double venturii. Rogowski9, and Taylor and Taylor 70 gave analyses of compressible mixture flow which are suitable as an introduction to carburetor metering but which involved too many simplifying assumptions to give an accurate prediction of carburetor performance. The analyses involved only a single venturi with no throttle plate. In addition, the compressible mixture properties were assumed to be constant rather than varying with mixture ratio. In addition, the independent variable was the total air flow rather than engine speed and throttle angle. The errors associated with this assumption were stated in chapter one. A very thorough experimental evaluation of nozzle and venturi design parameters was given by Shaffer.SO This work represented an optimization of a triple venturi design. Various diameters, lengths, and profiles of primary, secondary, and tertiary venturii were used with the goal of obtaining a large, stable metering signal. Complete venturi drawings and test data were given for each series. The metering signals were obtained with long hypodermic needles inserted in the direction of flow. Some of the important conclusions were: 1. The maximum signal occurred near the inside wall of the boost venturi. 2. The signal was relatively insensitive to axial location within the throat of the primary venturi. 3. The signal was sensitive to throttle opening for low air flow and large throttle openings.

13 4. The maximum signal multiplication for the final triple venturi arrangement was 6.4 A few of the references on compressible mixture flow were concerned with the very involved phenomenon of pulsating air flow. Prien8 reported an experimental study to determine the effect of air pulsations on metering. The metering device was a single venturi and nozzle system which was connected to a CFR engine. Steady flow tests were performed by drawing air through the engine cylinder with the valves open. Data on venturi suction, fuel flow, and air flow were taken. The pulsating air flow was obtained both by motoring and firing the engine. The results showed that the fuel/air ratio remained constant with increasing air flow for the steady flow case and increased with engine rpm for the pulsating case. Due to the complexity of the problem, no theoretical explanation of the data was given. Another discussion of the difficulties encountered in pulsating air flow was given by Earles.33 The main consideration of this paper was the measurement of the instantaneous mass flow rate for various pulsation waveforms. The data were correlated approximately by dimensionless groups involving the frequency and amplitude of the pulsations. The application of pulsating flow measurement to engine air flow determination was discussed by Fries, et al.2 This work was concerned with experimental techniques,and the theoretical analysis of pulsating air flow was not discussed.

14 Literature surveys related to the compressible mixture flow in the carburetor and induction system were given by Mirsky and Bolt5, and Oppenheim and Chilton.7 Mirsky and Bolt were concerned with surveying a broad range of subjects dealing with the induction process in a spark ignition engine while Oppenheim and Chilton were concerned with the more specific problem of surveying the literature on the measurement of pulsating flow. Hwa4 reported a study of compressible flow through double venturis. This involved an experimental as well as an analytical investigation of the metering characteristics of the system. A onedimensional compressible flow analysis was used with the additional restrictions of constant thermodynamic properties and no total pressure loss across the system. The following equation was derived for the velocity at the secondary venturi throat in terms of the system variables: (2cPi / K {.. Pth ]K- i vth 1 At21 -a ti 2 / The system was examined analytically and experimentally for nine combinations of area ratio and for two expansion angles. The important conclusions were: 1. A secondary venturi gave a lower over-all pressure loss for the same metering signal. 2. The experimental metering signal multiplication rose rapidly with increasing air flow up to a value of 5.0 where it leveled off. This was in all cases lower than the theoretical values.

15 3. The actual mass flow rate through the secondary venturi was less than predicted for all area ratios tested. The general problem of compressible flow through restrictions was discussed by Greenland.34 He classified the various types of flow as venturi, smooth orifice, and sharp-edged orifice and derived typical flow equations for each type. Also shown were coefficient of discharge curves and pressure versus length diagrams for various types of nozzles. Fundamental relationships providing a foundation for the analysis of compressible mixture flow in the carburetor were given by Shapiro. 0 This included the thermodynamic and fluid mechanics aspects of steady, one-dimensional, compressible flow under various conditions of total pressure and total temperature change. The variations in the thermodynamic properties of air with temperature and pressure reported by Gerhart, et al.3 indicate that, for the normal range of values encountered in the carburetor and induction system, the specific heats and specific heat ratio of the air can be considered constant. Also,the assumption of ideal gas behavior is seen to be very good over the pressure and temperature ranges encountered in carburetor work. B. MATHEMATICAL MODEL OF THE COMPRESSIBLE FLOW PATH In order to accurately simulate the complex behavior of an actual carburetor, an accurate mathematical model of each system must be obtained. To be able to adequately predict the mixture flow rates,

16 pressures, temperatures, and Mach numbers within the carburetor, the geometric flow path of the compressible mixture must be described accurately. This means that each flow path in the actual carburetor must have its counterpart in the model. Thus, if the carburetor has multiple venturii and bypasses around the throttle plate, these must be accounted for in the model. The basic model of the compressible flow path consists of two fixed geometry converging-diverging nozzles in parallel,and in series with a variable geometry converging nozzle. The operating conditions within this system of nozzles is controlled by a variable rate exhauster acting on an outlet plenum. The back pressure on the system is related to the exhauster flow and the throat area of the variable geometry nozzle. The correspondence of this model with the actual carburetor is as follows: (See Figure 1) The two fixed geometry converging-diverging nozzles correspond to the primary and secondary (boost) venturi in an actual carburetor. This type of nozzle was chosen because the pressure recovery or conversion from static to total pressure in the expanding portion of the venturi is very high in typical carburetors. This is related to the expansion angle of the nozzle which is generally small. The variable geometry converging nozzle corresponds to the throttle plate. The variable geometry feature was incorporated to account for the large variation in throttle flow area with throttle angleand the converging nozzle was chosen as the model because laboratory tests verified that the pressure recovery downstream of the throttle plate was

1' AR FLOW ___ _ MixTTRE TO VARIAIBL PLmOW RA1E EXMMBTER Figure 1. Basic model of the compressible flow path

18 very poor. This should be evident from the geometric arrangement of a typical throttle plate which is a complex sharp-edged restriction. The conversion of total to static pressure as the flow area decreases on the upstream side of the throttle plate is very good,but the expansion angle is much too great to permit good conversion of static to total pressure after the throttle plate minimum area. Thus the logical model is a converging nozzle with the throat area corresponding to the minimum throttle flow area. The plenum chamber corresponds to the intake manifold,and the back pressure acting on the nozzle system is the intake manifold pressure. The variable rate exhauster is the engine. The basic model of the compressible mixture flow path is still inadequate for numerous reasons. These include the facts that bypasses exist around the throttle, fuel may be introduced at two places,and that the mixture properties are changing as it moves through the system. Thus the system must be divided into stations, which are the important points where areas must be calculated, pressures known, flow rates determined, or mixture properties evaluated. The numbering of these stations for the main venturi is shown in Figure 2. The boost venturi stations will be illustrated in Section 2-F. C. THERMODYNAMIC PROPERTIES OF THE COMPRESSIBLE MIXTURE Any analysis of the compressible flow in carburetors will involve the thermodynamic properties of the mixture of air, water vapor, and fuel vapor. These properties include molecular weight, constant pressure and constant volume specific heats, and specific heat ratio. Since, in

1-9 / _ MOIST AIR FLOW (MEASURED FLOW) _AIR. 1 VAPOR... -..,.m,, A D S A4_ VALVE PV XXA^ U I^?^r^^lb^~^ MAIN FUEL FLOW IDE FUEL FLOW TsI~OTTLE ^ N PLATE V^ *\TRANSFER TUBE FLOW HOKNTAKE \ ACOLD TOTAL MIXTURE FLOW _ U|~ \I~~ N^ ~TO ENGINE \ Figure 2. Computer model of the compressible flow path

20 general,ve the relative proportions of each component in the mixture will be changing as the mixture flows through the carburetor, general equations must be obtained for each property in terms of the individual component properties and the relative proportion of each in the mixture. This can be done by assuming that the mixture is composed of ideal gas components. Over the typical temperature and pressure ranges encountered in carburetors, this is an excellent assumption for the air. Also, since the partial pressures of the water vapor and fuel vapor in the mixture are almost always very low, the assumption of ideal gas behavior is justified for these components. A complete derivation of the equations expressing the thermodynamic properties of the mixture is given in Appendix D. The final relationships in terms of the local fuel-air mass ratio (F/A) and waterair mass ratio (CO) are: Molecular weight W: Wm 1 + F/A 0C) EQN 2.1 vmix F/A + 1 + + fuel air WH 0 Specific Heats: 1 + t) + F/A C = air+ ) H2O F/A fuel vaporEQN 2 P mix 2EQN 2. 2~. 1 + L) + F/A 0v mix Cvair (v H20 + F/ (Cv)fuel vapor EQN 2.3 v+ W9+

21 Specific Heat Ratio: Kmx = Cp mix = (Cp) air +o(Cp) H20 + F/A(Cp)fuel vapor Cv mix (C) air +A (Cv) H20 + F/A (Cv)fuel vapor EQN. 2.4 It should be emphasized that the local values of W and F/A (at each station) are used to calculate the local thermodynamic properties. D. THROTTLE PLATE FLOW The throttle plate is an extremely important item in the compressible flow path. Under typical road load conditions about 95% of the total pressure loss occurs across the throttle plate. It usually provides the minimum flow area in the entire system although this area range is quite large, varying typically from about 0.010 to well over 1.0 square inches per barrel. This will obviously give a very large range in mixture flow rate through the throttle restriction. As mentioned earlier, the model of the throttle plate was chosen to be a converging nozzle of varying throat area. This, however, creates the problem of calculating this flow area for any throttle plate and shaft size and for any throttle angle. There are four additional practical considerations which cannot be avoided in a comprehensive simulation. These are: 1. The throttle plate shaft is almost always of significant diameter and must be considered. 2. To prevent binding in the throttle bore the throttle plate is, in most cases, completely closed at some angle to the

22 horizontal (usually 5 to 150) 3. The coefficient of discharge of the throttle plate will be lower than that of a smoothly converging nozzle at the same pressure ratio. This coefficient will be a function of the throttle angle. 4. Due to the manufacturing tolerances involved, there is some minimum leakage area even at completely closed throttle. This leakage area becomes important at small throttle angles. The above four considerations complicate the calculation of the throttle flow area and flow rate significantly, but ignoring them would result in an inaccurate simulation. In Appendix B, a complete analysis of the throttle flow area is given. This analysis includes 1 and 2 above and the following equation for the throttle flow area was obtained by evaluating an elliptic integral: Aflow -1 cos d D2 co2 G d2 co D2 cosG sin r dcos - d 2 2 D sin d + 2scos n ~ L] D -d + 2 dsin + cos L D cos -GJ s EQN 2.5 where: d is the throttle shaft diameter is the minimum closing angle Go is the throttle plate angle This complex relationship is easily evaluated as a computer subroutine for any value of the parameters. Item number 3 above was evaluated by actual engine tests. For numerous throttle angles, the values of air mass flow rate and pressure

23 ratio were determined with all throttle bypasses plugged. Equation 2.5 was used to calculate the throttle flow area corresponding to a given throttle angle. The coefficient of discharge was then calculated as the ratio of the actual flow rate to the ideal flow rate based on the flow area and pressure ratio. The throttle plate discharge coefficient values are shown in figure 3. Note that the discharge coefficient is lowest at the completely closed position as might be expected since the throttle plate is simply a sharp edged restriction. At greater throttle openings the coefficient rises, reaching a maximum at 900 from the horizontal, the point of minimum throttle turbulence. This data was incorporated into the simulation program and used to calculate accurate mass flow rate values for any operating point. Item number 4 above was accounted for quite well by allowing {o, the completely closed throttle angle, to be slightly smaller than the actual value. In other words, since there is some small leakage area Al at the actual closed throttle angle, say 5.00, then if we let as used in the calculation be slightly smaller, (for example 4.00) then when the throttle angle is completely closed at 5.0, the area calculated by equation 2.5 will be the actual leakage area. Thus what is needed is a relationship between o) actual and O as used in the program to accurately account for the leakage area. This relationship was determined empirically on the basis of measurements on numerous carburetors and is: (eO) = (od) - 3.800~- 0.100() EQN 2.6 pseudo / actual actual

H-t 1.0 LLJ 0j0.9 0 0 0,7 C 0.8 C) 5 05 ~- ~ * High Air Flow -J o^0 Low Air Flow Median Curve - 00 10 20 30 40 50 60 70 80 90 (e-o) THROTTLE PLATE OPENING IN DEGREES Figure 3. Throttle plate discharge coefficient values

25 This relationship is valid for completely closed throttle angles from 5.0~ to 15.0~. E. ANALYSIS OF TOTAL MIXTURE FLOW AND ENGINE PARAMETER EFFECTS The flow of the compressible mixture in an actual carburetor is a very complex phenomena. The mass flow rate is determined by an engine volumetric flow rate and the density of the fuel-air mixture in the cylinder when the intake valve closes. This density is mainly a function of the ambient conditions, total pressure loss across the throttle plate, and the fuel-air ratio being delivered. Additional factors which affect this density are total pressure losses in the venturi section, air bypasses around the throttle, total pressure losses across the intake valve, heat addition in the intake manifold, and the mixing of hot residual exhaust gases with the incoming fuel-air mixture. The relative importance of these additional factors is directly related to the amount of throttling which occurs at the throttle plate. Thus, as will be shown in equation form later, the main variables determining the operating conditions in a carburetor are the engine volumetric flow rate and the amount of throttling present. This of course is directly related to the engine speed and throttle angle. What are the goals in analyzing the compressible mixture flow and why is it of primary importance to the simulation? To answer this question one has only to consider the logical order of events in the actual carburetor: the mixture mass flow rate through the carburetor and

26 to the engine is established by engine speed and throttle angle (along with many secondary factors.) This flow rate is a value that will satisfy the throttle flow equations for the given area and pressure ratioand will also satisfy the engine (exhauster) flow relationships. Once the total mixture mass flow rate has been calculated, the pressure distribution within the venturi section can be analyzed and the metering signals determined. Since the total fuel rate (the sum of the main and idle fuel flow rates) is a function of the boost venturi suction and the intake manifold vacuum, the following air flow parameters must be determined before any fuel rate interations are performed. 1. Total air flow rate 2. Main venturi flow rate 3. Boost venturi flow rate 4. Venturi Mach numbers 5. Throttle plate Mach numbers 6. Intake manifold pressure 7. Boost venturi throat pressure Thus the total mixture flow rate is given by the simultaneous (and iterative) solution of the flow equations for the throttle and the engine. General relationships will now be derived which describe the flow in each element. The physical meaning of these equations is as follows: The relationships describing the throttle plate flow correspond to flow at constant engine speed and variable throttle angle. That is, the exhauster conditions are fixed and the minimum area of the converging nozzle is changing. The relationships describing the engine flow correspond to flow at constant throttle angle and variable engine speed. That is, the minimum area of the converging nozzle is constant but the exhauster

27 volumetric flow rate is changing. These are very distinct relationships because a variable flow area nozzle with fixed exhauster volume flow rate will have greatly different operating characteristics than a fixed geometry nozzle with variable exhauster conditions. The latter is much easier to visualize since the flow rate will be increased as the back (downstream) pressure is lowered, finally choking at some low back pressure and high mass flow rate. However, the variable geometry nozzle with fixed exhauster volume flow rate operates in a much more complex manner. The main variable is flow area at the throat and the flow is choked for very low flow rates. As the flow area increases, the flow rate and back pressure increase. Thus, let us consider an extremely small flow area with the downstream plenum connected to a constant volume flow rate pump. There will be a large pressure drop associated with this small flow and the flow will be choked. If the flow area is now made quite large, the pressure ratio will be small, the flow rate large, and the flow will be non-choked for that particular area, These equations will yield distinct curves, the intersection being the correct value of intake manifold vacuum (which controls idle flow) and air mass flow rate (which can be related to boost venturi suction). Thus for the throttle plate flow with: A = Flow area in square inches PO = Local stagnation pressure in lbf/in2 To = Local stagnation temperature in ~R R = Universal gas constant = 1545.4 ft lbf gc = 32.174 ft lbm lbm mol ~R Ibf sec2 W = Molecular weight Ibm Ibm mol

28 m = Mass flow rate in ibm/Hour M = Mach number where area is A K = Specific heat ratio of mixture P = Local static pressure in lbf/in2 T = Local static temperature in OR /l = Local fluid density in Ibm/Ft3 Starting with the 1 dimensional, steady, compressible flow of an ideal gas mixture, the following equation can be easily obtained:l0 Ammi =(3600.o)P R KqW M 1 + K-l)M EQN 2.7 This equation is actually the continuity relationship for the above assumptions and does not involve the assumption of isentropic flow. Now to eliminate P in terms of Po, the isentropic relationship must be used: k P -To kl i =(-) 1 or P T) EQN 2.8 When equation 2.8 is substituted into equation 2.7, the following relationship results for the mass flow rate through an area A: mix(36000 )A P Kgc W IM EQN 2.9 m RTo [ K-l M W2 (k-1) The isentropic assumption is not as restrictive as it might seem because the flow can be evaluated from a point just ahead of the throttle plate to the point of minimum throttle flow area. In other words, by saying that there is some Po loss in the carburetor (due to friction and turbulence) up to station X* (see Figure 4),and that there is some To loss in the carburetor due to fuel vaporization, the isentropic relations can

29 AMBIENT CONDITIONS POO To O 0^&OI^ A _ BOOST VENTURI THROAT -- PoLOSS P (Psooo p) )____ __ --- MAIN VENTURI -------- THROAT Ii | \ POSSIBLE To REDUCTION (Tco - To*) X Po,1 v T (MAIN STATION 5) aim8:^^-/ ^ _ + THROTTLE PLATE \ \ T j —:Pt PLANE X (THROAT) Figure 4. Illustration of local Po and TO values

30 still be used with little error between X* and X throat if the values of Po and To are the values at X*. Thus what is needed in conjunction with the flow equations is the relationship between (Po) local and (PO) ambient as well as (To) local and (To) ambient. These can be easily obtained in terms of the total mixture flow rate and the amount of fuel vaporized up to a given station, The statement that there is very poor pressure recovery after the throttle restriction is equivalent to saying that the intake manifold pressure is the pressure at the throat of the converging nozzle. Note that the driving force for flow in the nozzle is the pressure ratio, p —,For throttle flow it is much more convenient to work with the equao tions in terms of the pressure ratio rather than the Mach number. Thus let us eliminate the Mach number in terms of the pressure ratio across the nozzle Pthroat Pi P K ( 2; ] 0 - [l.I )M2] K-i Now noting that X is merely a substitution variable; Thus let: X - 1 K-I 2 M2 Then Po K/K2 p X or X = K-K also M2 = 2 (X-1) K-l or M = 2 (X-l K-1 Now eliminate M from equation 2.9: K-l ri mix 3600.00 W (Aflow) Po - l V i' o K-.P... LBM HP \ K+l Hour 2K EQN 2.1

31 The throttle plate Mach number is thus given by: I.-, I K-l M throttle XMACH K - 1 EQN 2.11 and the throttle plate flow will be critical (choked) when Po P 2i[ ] at which point the throttle plate Mach number will be unity. The flow rate under this condition will be given by: mix = (3600.0) Afow P~ T T [K_ W1 EQN 2.12 mix fl ow 0 T0 K;11 (K E 2 For the special case of dry air (K = 1.40) the choked flow rate will be given by: mix = (1913.1) Aflow Po m ix It should be emphasized t that since this is a variable throat area nozzle, the choked flow value does not indicate the flow capacity of the throttle but only the maximum flow for the current area. It will turn out that the throttle plate mach number is 1.0 only for very low mass flow rates which correspond to very small flow areas. Another useful relationship is obtained by introducing the intake manifold vacuum, VACMAN. VACMAN = Ambient pressure - intake manifold pressure or VACMAN = P - P Ooo

32 thus Poo = Pooo P Pooo - VACMAN In terms of the throat Mach number instead of the nozzle pressure ratio, the special cases of equation 2.9 are: For the special case of air only: K = 1.400 W= 28.95.mol lb. mol m pure A Po (.9189) _ M (3.) pure 3 air To + M.. L ~5~J air "".r [ l M2] 3 For the special case of a stoichiometric air-gasoline vapor mix: K = 1.35 W = 30.3 ibm b. mol m = (3324.0) 0Po M mix 0 + M V 3 7l 3]57 C8 H17 L 5.715 Next, the flow relationships for the engine must be obtained. This will relate the engine variables to the mixture flow rate. The throttle and engine relationships will be coupled by means of the pressure ratio. This is because the pressure on the downstream side of the throttle (exhauster side) is controlled by the exhauster. The pressure may be less than, equal to, or greater than the critical pressure, depending on

33 the exhauster flow. If the exhauster volume flow is such that the downstream (manifold) pressure is critical (.528 Po for air alone), the Mach number at the throttle plate will be unity and the maximum mixture mass flow rate will exist for that particular flow area. If the exhauster volume flow rate is then increased, as by increasing engine speed, the downstream pressure will drop (manifold vacuum will increase) but the mass flow rate will not change significantly. (Slight changes in mass flow rate can occur even under choked conditions as a result of fuel-air ratio changes which affect the thermodynamic properties of the mixture.) Thus many values of manifold vacuum may exist for the same throttle setting and air mass flow rate. To analytically predict the value of this downstream pressure, the exhauster flow must be analyzed. Now if we let: N b = number of cylinders per carburetor barrel N = engine revolutions per minute Nc = number of cylinders in engine P0 = atmospheric pressure lbf/in2 POHG = atmospheric pressure in inches of mercury Vs = swept volume of cylinders - in3 D = displacement of engine - in3 V = clearance volume - in3 cl CR = compression ratio of engine Tcl = temp. of mixture in clearance volume - ~R Tman = temp. of mixture in intake manifold ~R

34 P = pressure of mixture in clearance volume - lbf/in2 cl Pmn= pressure of mixture in intake manifold - lbf/in2 Wm = mixture molecular weight - Ibm/lb mol Vtotal = total volume of cylinder - in3 VACMAN = manifold vacuum in inches of mercury m = mass of mixture inducted into cylinder - Ibm The mass of mixture added per intake stroke will be: total mass mass in clearance madded = in cylinder - volume when exhaust when intake valve closes valve closes however, the mass may be expressed as: PVW mn =_ RT therefore: madded (0.4912) Pcyl VtotalWmix - (0.4912) PclVcl Wc (12.0) R Tfina (12.0) R Tcl Tfinal is the absolute temperature of the mix (~R) in the cylinder at the end of flow into the cylinder and results from a mixing of the hot residual gases with the cool intake gases. Inherent in this formulation is the assumption that the mass of mixture which enters the cylinder and immediately exits through the exhaust valve is insignificant. If, in a

35 particular engine, this is known to be significant, as in engines with large valve overlap at high loads, then an additional lost mass term would have to be included in the above equation. The pressure in the cylinder when the inflow of fresh mixture ceases is the intake manifold pressure minus a pressure differential which is related to the average intake valve flow area and the mass flow rate of the mixture over the intake stroke. The clearance volume pressure at the end of the exhaust stroke is the ambient pressure plus a pressure differential which is related to the average exhaust valve flow area and mass flow rate of the exhaust gases over the exhaust stroke. These pressures, in equation form, are given by: cyl = Pman - P l = o + Pex The pressure differentials are complex functions of valve design, valve timing, and mixture instantaneous velocity. Fortunately, under most operating conditions, these pressure differentials are on the order of a few inches of water and may be neglected in the expressions for Pcyl and Pcl (For example, Po is typically on the order of 400 inches of water.) Thus the following equation is obtained for the mass added per intake stroke; (the pressure units will be carried as lbf/in2 until the final equation is obtained.)

36 madded = P V W P V W added man total mix o _ 0 cl cl (12) R Tfinal (12) R TCl EQN 2.13 But Vtotal = Vs + Vcl and Pmn = P - VAC MAN man o Thus: madded = (Po-VACMAN) (Vs + Vcl) Wm PoVc1Wc (12) R Tfinal (12) I Tc EQN 2.14 Now, for convenience, let us define C5 as the ratio of the absolute temperature of the mixture in the cylinder when mixture inflow ceases, to the absolute intake manifold temperature. Let us also define C6 as the ratio of the absolute temperature of the gases in the clearance volume when exhaust outflow ceases, to the absolute intake manifold temperature.

37 or in equation form: C5 = Tfinal OR TmanOR C6 = Tcl OR Tman OR Substituting these definitions into equation 2.14 and factoring, the following equation is obtained: madded = 1_ pF - VACMAN) (Vs + Vcl) Wm PoVd (12) RT Tmanc5 0 1. EQN 2.15 Now let us eliminate the cylinder volumes in terms of the common engine variables. Note that: R = Vtotal =Vcl +Vs EQN 2.16 Vcl Vcl D but: Vo = Nc thus: Vcl - D EQN 2.17 Nc(CR-1) Substituting equation 2.16 into equation 2.15 and noting that Wcl differs very little from Wm, the resulting relationship is: madded = Vcl Wm P - VACMAN) (CR) _ P (12) R Tm a n (12) TmanL C5 C6 or by rearrangement: mdded _Vcl Wm(CR) POCR - 5/C - VACMAN (12)(C5) R Tman CR -

38 Now eliminate Vcl by using equation 2.17: added (12) (C5) N man CR-1 L o CR EQN 2.18 This is, of course, the mass of mixture added per intake stroke. Of greater and more practical interest is the total mixture mass flow rate. This mass flow rate is related to the mass added per intake stroke by: ^ LBM ^/ LBM /intake s Hour iaddd intake Hour and: intakes = Revs intake30 NN H~our\ M inute Hour 2 Rev / c CRN'' CRC J r(12) (C5)., Tmanp CR- liCR or further simplifying:. LBM = DN _ PfOHG (CR- C5/C6j- VACMAN m Hour ( 0.40)(C5) R Tman (CR-1) -~ CR Wm (CR)(0.4912) EQN 2.19 Where the 0.4912 enters if POHG and VACMAN are in the common units of inches of mercury. Substitution of typical values shows that the ratio of C5/C6 does not exert a great influence on the result, thus a sophisticated theoretical cycle analysis is not justified to obtain this ratio. The technique was to analyze various fuel-air cycles by means of the combustion charts and obtain reasonable correlations for the clearance volume and final temperature variations as a function of the fuel-air ratio. These correlations, in

39 piecewise form over various fuel-air ratio ranges, are listed in subroutine AIRMAS. It should be emphasized that the variables which greatly influence the mass flow rate are the engine displacement and speed and the intake manifold pressure. The engine compression ratio and the various temperature ratios have a much smaller influence on the mixture flow. (For hand calculations C5 can be taken as approximately 1.2 and C6 can be taken as about 2.4). Thus we have obtained a theoretical equation relating the exhauster (engine) flow rate to the manifold vacuum in terms of ambient pressure, mixture properties, engine rpm, displacement, and compression ratio. When a correlation of all the engine data taken in the carburetorengine tests was attempted, the agreement with this theory was found to be excellent. The resulting theoretical equation for the values; P0 = 29.00 "Hg. CR = 8.5 D = 289.0 in.3 T = 600 OR R = 1545.4 ft.lbf. C5/C6 = Tfinal/T =1/2 Ibm OR /cl W = 30.3 LBM/LB MOL is the following: albm = N m hr 95= 0N [27.26 -Vacman] When this theoretical exhauster analysis is coupled with the throttle flow area analysis;

40 w Hr R 2f2 NOZZLE EQUATION ERROR.J3 2 I) PARAMETER U): UJ ^X ~~~~~~~~~~~~~~~~~~~~~~~~~~~I I 0 MAN ITER 00o INTAKE MANIFOLD PRESSURE Figure 5. Simultaneous solution of exhauster and nozzle equations

41 nexhauster = fl (VACMAN, PO, D, N, Wm, CR) rthrottle = f2 (VACMAN, Po, Aflow, K, Wm, To) The simultaneous solution will be the intersection of the two curves as shown schematically in Figure 5, with the result being an accurate prediction of mixture flow rate and intake manifold vacuum. The importance of this result is that: 1. Engine-carburetor variables are mated theoretically. For example, this indicates the quantitative effect of engine displacement, speed, and compression ratio on the carburetor air flow. 2. All engine-carburetor operating points (combinations of engine speed and throttle angle) can be shown on a single graph as opposed to a standard carburetor flow box curve which does not directly involve the engine variables. This analysis can also be utilized to determine the dilution of the fresh fuel-air mixture by the exhaust residual gases. The fractional dilution is defined as: mass of residual gases _= cl dilution fraction = total mass in cylinder mCl + madded when intake valve closes But the mass of the residual gases in the clearance volume and the total mass of the mixture in the cylinder are given in equation 2.13. Substituting these relations into the expression for the dilution fraction, the following equation is obtained: PoVcl wc (12) R Tl dilution fraction = - V A _ Pmdilution fraction an totalWmix - PoVcl Tfinal (12) R Tfinal J PmanVtotal Tcl

42 Now noting that Tfinal/Tcl is defined as C5/C6, that Vtotal/Vcl is the compression ratio of the engine, and that the intake manifold pressure may be expressed as Po - VACMAN, the above expression may be written as: dilution fraction = Po (C5/C6) CR (Po - VACMAN) EQN 2.20 where the ambient pressure, Po, and the intake manifold vacuum, VACMAN, are both in inches of mercury. This equation predicts the effects of ambient pressure, engine compression ratio, intake manifold vacuum, and fuel-air ratio on the dilution fraction. (The fuel-air ratio effect is given by the variation in C5/C6, which is small under steady firing conditions.) The most influential variable in affecting the dilution fraction is the intake manifold vacuum. The magnitude of this effect is tabulated below for the following variables: P0 = 29.00 "Hg. CR = 8.5 (i = 0.5 \C6/ dilution VACMAN fraction 0.00 "Hg 0.0588 5.00 0.0708 10.00 0.0863 15.00 0.1215 18.00 0.1545 23.00 0.2833 27.28 (max) 1.0000 Note from the above values that the dilution fraction will be unity (100% dilution) when the intake manifold vacuum has the following value:

43 VACMAN (max.) = VACMAN (for 100%) = PF CR - (C5/C6) dilution CR this value of intake manifold pressure corresponds to zero fresh mixture added to the cylinder. This can be verified by substituting the above expression for VACMAN into equation 2.19. This is theoretically the maximum intake manifold vacuum and, under these conditions, the intake stroke consists of the expansion of the hot exhaust residual gases from the clearance volume to the total volume. At this point the pressure has been reduced from slightly over one atmosphere to the kr value; Po (1/CR), where kr is the specific heat ratio of the residual gas mixture. No fresh mixture flows into the cylinder because the cylinder pressure during the intake stroke is always greater than the intake manifold pressure. This means that the same residual gases are continuously being compressed, expanded into the intake manifold through the intake valve, drawn back into the cylinder, and recompressed. Since no combustion is occuring under these maximum dilution conditions, the value of C5/C6 will be given by: rk- I kr -1 (\ = /Tf ina V C1 C6 motoring \ Tcl 1l krt l For a compression ratio of 8.5 and a specific heat ratio of 1.40, the minimum value of C5/C6 for these high dilution (non-firing) conditions is 0.427. In operation the theoretical maximum intake manifold vacuum is not obtained, due to the fact that the mass of mixture added is never

44 zero. Since there is a throttle plate leakage area and bypasses around the throttle, the mixture mass flow rate will be small at the closed throttle position, (25 to 45 Ibm/hour) but never zero. This means that the dilution is never 100% and that the intake manifold vacuum is always less than the theoretical maximum even at closed throttle. All of the foregoing results and relationships were incorporated into subroutine AIRMAS which accurately predicts, for any combination of variables, the intake manifold vacuum and mass flow rates of each mixture component. F, ANALYSIS OF COMPRESSIBLE FLOW THROUGH MULTIPLE VENTURII After the total dry air and water vapor flow rates have been predicted for any specified operating condition, the next problem is to analyze the manner in which this flow passes through the main and boost venturii and to determine all significant pressure parameters. The questionsto be resolved analytically include:

45 1. What fraction of the total flow passes through the boost venturi? 2. What are the metering signals at the throats of the main and boost venturii? 3. How does the introduction of fuel into the boost venturi air stream affect the metering signal? The fraction of the total moist air flow that passes through the boost venturi is extremely important since the boost venturi throat depression (or metering signal) is very sensitive to air mass flow rate. The first step in the analysis of flow through nozzles in parallel is to establish the criterion for flow division. This criterion is that the static pressure at the outlet of the boost venturi be equal to the static pressure at the corresponding position in the main venturi. If we then define a parameter XF as the fraction of the total moist air flow that passes through the main venturi, we have a very convenient iteration parameter. X F = Primary venturi mass flow rate. PVFLO Total venturi mass flow rate VENFLO For a given value of total moist air mass flow rate (resulting from subroutine AIRMAS) and an assumed XF value, the flow rates through each venturi are specified. With this known, a compressible flow analysis can be performed on each venturi and the Mach numbers at each station calculated. This analysis will be for moist air only in the main venturi, and for a changing mixture of air, water vapor, and fuel vapor in the boost venturi. The static pressures at the boost venturi outlet and at

46 the corresponding main venturi position can thus be determined. They should be equal but,if XF is too high, the flow rate through the main venturi will be too great a fraction of the total flow and the boost outlet pressure will be greater than the corresponding main venturi pressure. (note that as the flow rate increases, the pressure at each station decreases.) Thus, a convenient error parameter for use in the generalized convergence technique (Appendix G) is: Iterative error parameter = El = PB5W - PM4W EQN 2.21 where: PB5W = Boost venturi pressure at boost station 5 PM4W = Main venturi pressure at main station 4 The main venturi stations were shown earlier in Figure 2 and the corresponding boost venturi stations are shown in Figure 6. Note that boost station 5 is at the outlet and that main venturi station 4 corresponds to the annular flow area in the plane of the boost venturi outlet. Note also that boost venturi station 3 is the throat of the converging - diverging nozzle and that fuel is discharged at 4. This means that the suction at boost station 4 is the metering signal. Thus, if the value of XF is continuously adjusted at each iteration until the error parameter El becomes very small, the resulting flow rate in the boost venturi can be used to calculate a pressure at boost stations 2, 3, 4, and 5. Recall that the compressible flow rate equation obtained earlier (equation 2.9) was:

47 -DBV( I )| - -0 -DBV( 2'~ | —-_-DBV DBV(4 XBV _MB DBV(5)-*-j DBV(6) Figure 6. Computer model parameters for boost venturi

48 m = (3600.0) A P / K gc W M To [1 + K- M] K+ Thus if m, A, Po, To, K, and W are specified, it should be possible to to calculate the mach number M. However, the equation is not explicit in M, thus a direct solution is not obtainable. The Newton-Rhapson method may be employed to iteratively obtain the Mach number for any combination of variables. This technique may be written 69as: Mi 1 = M - f(Mi) EQN 2.22'1 1 f'(M.) where: K- 1 (Mi) = m l -L i M+(K1)2 EQN 2.23 d Mi (3600.0) A Po g EQN 2.24 By assuming an initial guess for the mach number Mi, the values of f(Mi) and f'(Mi) can be calculated. The Newton-Rhapson iteration formula can then be used to calculate the next guess Mi.on- These equations as well as all of the other compressible flow relationships for isentropic, Fanno, and Rayleigh type flow have been incorporated into subroutine SOLVE. This subroutine performs the desired analysis by making a proper initial guess, performing the iterations, checking for

49 stability and errors, and returning the pressure, temperature, density, and Mach Number. The initial guess (for the isentropic case),and a check to see if the specified mass flow rate exceeds the maximum are made by noting that: m max = (3600.0) A Po Kg W 1.0 EQN 2.25 R To K+1 rK+ 2K- 1) and that a logical initial guess is: L 2-J Minitial = (3600.0) A Pol K gc W K+'..0 + m~ 2(KR To 2 1.0+mmax EQN 2.26 Once the Mach number has been calculated for the given conditions, the mixture density, temperature, pressure, and suction are calculated from the following relationships: loocal (P) local EQN 2.27 [1+ K1 M2 Plocal (o) local T,_ ~= (To) local EQN 2.29 local K-1 M2]- K Tlocal - (To) local EQN 2.29 local local (Po) - (P)local = (P -(Po) - suction / ambient local ab Po local (P0 )amb.J

50 The distinction between local and ambient total pressures and temperatures must be made because of Po losses due to friction,and To decreases due to fuel vaporization. For example, if the dry air flow rate through the boost venturi is m b,the main system fuel flow rate is m f, and the fraction of fuel that has vaporized up to the station being analyzed is FRACTB, then the fuel-air ratio at that station is: boost fuel-air ratio = BFA = (mf) (FRACTB) / nb EQN 2.30 The total temperature of the mixture at that station is given by: (T)local OR = (To) ambient + BFA* HVAPOR / (Cp)mix (To7local ) o ambient P mix EQN 2.31 where HVAPOR is the enthalpy of vaporization or latent heat of the fuel and (Cp) mix is the constant pressure specific heat of the mixture at that station. Subroutine SIGNAL contains the venturi flow analysis and iterates on XF for any venturi geometry, atmospheric conditions, fuel type, and total air flow rate. It calls on subroutine SOLVE at each main and boost station to obtain the flow parameters. When XFhas converged to the proper value for the specified conditions, these flow parameters will represent the predicted performance of the main and boost venturi system. G. ANALYSIS OF FUEL ATOMIZATION AND SPRAY VAPORIZATION The extremely complex processes of fuel atomization and spray vaporization were analyzed for two basic reasons. The first reason is that we would like to determine which variables affect these processes and to what extent. The second reason is that the thermodynamic properties

51 of the flowing mixture will be changing as the liquid fuel vaporizes. Thus the mixture flow will be affected by the vaporization rate within the carburetor. This effect will turn out to be slight because the relative amount of fuel in the air is small,thus the mixture properties will vary only slightly from those of pure air. It should be emphasized that we are concerned only with vaporization within the carburetor, from the point of main fuel introduction (boost venturi) to the throttle plate minimum area. This is the section of the carburetor where the thermodynamic properties of the mixture are utilized in the compressible flow analyses, and vaporization after the throttle plate (which is the bulk of the vaporization) does not affect the mixture properties within the carburetor. The amount of fuel vaporized after the throttle plate minimum area is important for other considerations such as unburned hydrocarbon emissions but will have little influence on the flow within the venturi and throttle sections. However, the vaporization equations which were derived could be extended to encompass this additional vaporization even though it was not necessary for this simulation. First let us categorize the analyses to be performed. The atomization analysis, which logically must precede the vaporization analysis, is basically a droplet size distribution study. The problem is one of predicting parameters which will adequately describe the characteristics of the spray in terms of the system variables.

52 The vaporization analysis consists fundamentally of predicting the mass and heat transfer between the droplets and the gaseous stream,taking into account the acceleration of the droplets in the stream (which affects the droplet Reynolds number.) Let us first consider the atomization process in the carburetor. The fuel stream in the typical carburetor is drawn into a high velocity air stream by means of a slightly reduced air pressure at the throat of the boost venturi. This fuel stream is then broken into many droplets by the relative motion of the air stream. This type of atomization is termed "pneumatic atomization"18 and the drop size distributions resulting from this method have been investigated experimentally by various workers. One other type of atomization occurs to a very slight degree in carburetors and that is "impingement atomization" which is the breaking up of a fuel stream by the action of fuel striking an object in the flow path (the throttle plate.) This has been studied very little and was not analyzed in this simulation. Before discussing the investigations of pneumatic atomization, a few definitions and concepts basic to drop size distribution studies must be introduced. Figure 7 shows four curves which can be used to describe the distribution of droplet sizes within the spray. Curve 7a is a droplet size frequency curve and indicates the number of drops of a given diameter Xd. Curve 7 is the normalized frequency curve which is obtained by dividing the number of drops of a given diameter by the total number of

53 DROP SIZE FREQUENCY CUMULATIVE DISTRIBUTION DISTRIBUTION CURVE CURVE T MAX Frequent XMAX XMAX DROPLET DIAMETER X —-- (A) (B) NORMALIZED FREQUENCY NORMALIZED CUMULATIVE CURVE DISTRIBUTION CURVE Figure 7. Me s of i n diNote:I -C I ZI I I V'4- / I \'-,o / I'AX l Most / YMAX =fN (x)dx1.0O FrequentMAX xMAX XMAX x X ---- (C) (D) DROP SIZE DISTRIBUTION CURVES Figure 7. Methods of illustrating drop size distributions

54 drops in the spray n max Curve 7b illustrates another technique for describing the distribution. This is denoted as the cumulative distribution curve and represents the number of drops having a size less than Xd. Note that there is always a maximum droplet size in the practical case. (It will be seen that many of the mathematical approximations to the distribution curves will not predict any maximum droplet size.) Curve 7d is the normalized cumulative distribution curve and is probably the most useful representation of the droplet sizes. The various moments of the normalized frequency distribution curve (7c) have important physical meanings: Xmax moment q = / X fn(X) dx 0 The spray volume is proportional X max to the 3rd moment with 1/6 being Sr X3 fn(X) d 6 J the proportionality constant: The spray surface area is propor- Xmax 1Ir X2 f (X) dx tional to the 2nd moment: X2 (X) d The Sauter volume -surface Xmax mean diameter is given by the X3 (X) d Xv s ~o X3n (X) dx Xvs ratio of the 3rd moment to the Xmax 15 /' X2fn(X)dx 2nd moment: EQN 2.32

55 Thus Xvs represents a droplet diameter which has the same ratio of volume to surface area as the total spray (when the proportionality factor of 1/6 is introduced.) This parameter is very important in calculating rates of evaporation. Thus: spray volume = Xs microns EQN 2.33 spray surface area 6 Nukiyama and Tanasawa 19 studied the pneumatic atomization of alcohol-glycerine mixtures in air nozzles. They developed an empirical equation correlating the effects of the operating variables on the Sauter mean droplet size. This may be used where an experimental frequency distribution curve is not available, although the experimental data should be used if available. X = 1410..O' + 191.0? 1000.0 QL V_____ + VYA j EQN 2.34 where: Xvs Sauter mean drop diameter (microns) Vs dvnes -T = liquid surface tension in contact with air cm. P = liquid viscosity in centipoise ft VA relative velocity between air and liquid - A sec P = liquid density LBM /ft3 Q./* = ratio of liquid volume flow rate to air volume flow rate A

56 This equation is applicable to the atomization of a liquid by a high velocity air stream when the liquid properties are in the following range: A/ 43 to 75 LBM/FT3 ~v 19 to 75 Dynes/cm PL 0.3 to 50 centipoise VA up to sonic In addition they proposed an empirical frequency distribution correlation of the form: 2 -cx f (x) = dn = b x e EQN 2.35 dx Where b and c are constants to be experimentally determined for a given geometry and fluid. Their distribution correlation has not found wide acceptance but their empirical relationship for the Sauter mean droplet diameter is used extensively. It was used in the atomization and vaporization analyses in this simulation. From the available literature, the accuracy of the Sauter mean diameter predicted with the N-T equation is probably about + 20 % for hydrocarbons in air. However much larger errors have occurred for gases other than air and for more viscous liquids.l5 Some final comments on droplet size frequency distribution equations are justified when one considers the maximum drop size. Note that equation 2.35 predicts a decreasing frequency of occurence as the drop size goes to infinity. Thus the frequency of occurence is very small but non-zero for all huge drops. A more involved though physically more

57 realistic distribution function is the upper limit log normal distribution as 21 discussed and utilized by Rice.21 This predicts a limiting maximum droplet size as opposed to the Rosin-Rammler1 and Nukiyama-Tanasawa19 relations which do not limit the maximum droplet size. 12 Benson, 1et al, state, on the basis of their work in determining droplet size distributions, that the assumption of a smooth curve having a single maximum may not be valid in all instances. This means that there may be, in some nozzles, preferential clustering of droplet sizes at two or more sizes, yielding a curve as shown in Figure 8. This complicates the analytical determination of mean droplet parameters to the point where numerical integration of the experimental distribution data would be the most accurate technique. %MlAX or: X = OX fn(X) AX EQN 2.36 vs X^2 X fn () AX 0o where f(X) is obtained by interpolation from the experimental frequency curve. The evaporation of the fuel droplets in the air stream is an extremely complex process. Each droplet diameter will have its own drag coefficient and mass and heat transfer rates. The acceleration of each droplet will be different and the time required to travel a distance downstream, or residence time, will be different for each droplet size. In addition, from studies of pneumatic atomization it may be stated that the droplets are not

58 fn(x) I-I x1 X2 Xmax DROP DIAMETER x - Figure 8. Drop size distribution with two preferential sizes Figure 8. Drop size distribution with two preferential sizes

59 spherical but are actually highly irregular in shape. 15, 18 These facts should indicate that a mathematic description of the process is nearly impossible unless certain simplifying assumptions are made. The droplet vaporization studies reported in the literature consist of experimental investigations of vaporization rates from single droplets and sprays,and analytical work on the heat and mass transfer rates from a single droplet. Bahrl reported an experimental investigation of the vaporization of isooctane sprays. The isooctane was injected under a pressure of 25 to 85 psia into a moving air stream. The air velocity was varied from 100 to 350 feet per second. The effect of the system variables on the per cent vaporized was indicated by the exponents in the correlating equations. The per cent vaporized was found to vary as: Air Temperature to the + 4.40 power Air velocity to the + 0.80 power Air pressure to the - 1.20 power Injection pressure to the + 0.42 power Distance downstream to the + 0.84 power The injection pressures were much higher than occur in typical carburetors (55 psia as compared to 25 inches of water) thus the data have little application to fuel vaporization within carburetors. The work of Ingebo16 was performed at conditions more related to those in carburetors. Isooctane sprays were investigated at room temperature and pressure. Vaporization rates and droplet velocities were obtained by high speed photography. The

60 analytical portion of the study was based upon vaporization from a single spherical droplet of a mean diameter. An excellent discussionof the experimental and analytical work that has been done was given by Graves and Bahr. 15 They described the problems and reviewed the existing literature extensively. They began their chapter on the evaporation of sprays by stating; "Extension of single drop data to sprays is difficult, since both drop-size distribution of the spray and relative velocities between the air and the drops must be known. In addition, there are such complicating factors as drop distortion, unsteady state vaporization, and interactions between drops. " The vaporization of a liquid drop in the absence of relative motion with the surroundings is basically a diffusional mass transfer problem. The driving force for mass transfer will be the concentration gradient of the component comprising the droplet. The vaporization process will consist of two distinct portions, the relative importance of which will depend upon the initial difference between the droplet temperature and that of the surroundings. The quantitative variation in temperatures for the droplet (fuel) and the infinite, stagnant, surrounding medium (air) is illustrated inFigure 9. Note that the initial vaporization occurs with unsteady heat and mass transfer, that is, the droplet temperature is changing rapidly with time. This will continue until the droplet temperature reaches an equilibrium value slightly lower than that of the surroundings. This occurs at time t+C as shown in the figure. This portion of

61 A /TSURR -- X C TDROP <. t UNSTEADY HEAT PSEUDO STEADY HEAT H I MASS TRANSFER AND MASS TRANSFER O t" tMAX TIME t - Curve A Initial drop temperature greater than TSurr Curve B Initial drop temperature equal to Turr Curve C Initial drop temperature less than Turr ~Figur 9 llsrain frpaorztinsuregime Figure 9. Illustration of drop vaporization regimes

62 the vaporization process is important in cases where the droplet is part of a liquid that is sprayed into surroundings which are at a much higher temperature, as in diesel engine injection. Due to the large changes in droplet temperature/the specific heats of the liquid fuel and fuel vapor become significant. The same is true for the upper curve which shows the case of initial droplet temperature much greater than that of the surroundings. However, if the initial temperatures of the droplets and the surroundings do not differ greatly, the time t will be a small portion of the total vaporization time, tmax, anrd the unsteady portion can be neglected with little error. Such is the usual case in carburetor work where the fuel temperature does not differ greatly from the air stream temperature. The pseudo steady portion of the vaporization is characterized by a relatively constant droplet temperaturewith the energy transferred to the droplet (by means of the temperature difference) being equal to the enthalpy flux of the vapor leaving the droplet. In the actual situation, the surroundings are not infinite, thus the temperature of the surroundings (air temperature) must decrease as energy is supplied to the droplets. This would give a slight downward trend to the curves rather than a constant temperature. The analysis of droplet vaporization is based upon the mass transfer from a single spherical droplet of an initial diameter equal to the Sauter

63 mean diameter. The equations are derived and the variables and units listed inAppendix H. Only the important results will be shown here. First, for the diffusion of a vapor, v, through a non-diffusing gas from a spherical droplet, the following equation for the rate of mass transfer was obtained: mv = (12192.0) 2 Dv Wf (P - P ) LBM EQN 2.37 A RT d sec ft f f Equation 2.37 expresses the mass transfer rate only for zero relative motion between the droplet and the surrounding medium. The droplet diameter at a time t after vaporization begins was obtained in terms of the system variables: d2 = d (12192)(304,800) 8 Dy Wf (Ps - PO, ) t microns f sauter /' Tf EQN 2.38 For mass transfer with relative motion between the drop and the surrounding medium, the vaporization equations must be modified by the mass transfer Nusselt number. On the basis of their investigations on the 20 evaporation of water drops in air streams, Ranz and Marshall proposed the following correlation for the Nusselt number: (N) = 2.0 + 0.60 (Re) (S) EQN 2.39 where Re is the droplet Reynolds number and Sc is the Schmidt number. (See Appendix H) This resulted in the following equation for vaporization

64 with relative motion: mv = (12192.0) Dv Wf (Ps -P 20 + 0.60 (Re) ____f2.0 sur 0.60 (Re c A R Tf df EQN 2.40 By introducing the Sauter mean diameter as a description of the atomization that occurs, the single drop equations were extended to obtain relationships describing the vaporization of the entire spray. If m spray is the total mass flow rate of the spray, the spray surface area being formed can be expressed as: Aspray = (304,800) (6) mspray ft2 EQN 2.41 /rf d sauter sec For small changes in drop diameter and thus for only the first 20 to 25% of the spray vaporization, the fraction of the spray vaporized in At seconds was found to be: FRACT = (6)(12192)(304800)( ds w a r(P - P (Nu) At e R Tf ( dsauter) EQN 2.42 It was found to be quite useful and informative to express the vaporization fraction in terms of downstream distance in the carburetor, A Z,rather than in terms of time. This was an additional complexity since the droplet velocity is constantly changing and is related to the droplet diameter and Reynolds number. The result of this analysis was

65 the following equation, again valid only for the first 20 to 25% of the spray vaporization: FRACT= (12192) 304,800' [Dv Wf (Ps -Pv) (Nu) /ff dsauterAZ (fR Tf (dsauter)2 /air (Vrel) Cdrag EQN 2.43 Any extension of the equations to encompass the entire vaporization process would have to account for the droplet diameter decreasing significantly, with correspondingly large changes in Reynolds number and drag coefficient.

CHAPTER III FUEL FLOW THROUGH ORIFICES A. REASONS FOR ORIFICE FLOW WORK The analysis of orifice flow is extremely important to the overall carburetor simulation. This is true because of the large number of orifices in series and parallel within the typical carburetor and the control they exert over the main and idle fuel flows. The air bleed orifices are also extremely important in influencing the pressure losses within the fuel channels. If the coefficients of discharge of the orifices are assumed to be unity (or any constant value) then a very inaccurate description of fuel flow will result. A comprehensive simulation must determine the pressure drop across any orifice in terms of the orifice geometry, fluid properties, and fluid mass flow rate. This is equivalent to saying that the true variation in discharge coefficient with geometry, fluid properties, and flow rate must be known for each orifice in the carburetor. Since the purely theoretical prediction of orifice discharge coefficients is a nearly impossible task, (as will be discussed in section 7c) each orifice type must be tested on an orifice flow stand over a wide flow rate range. Then the flow data must be correlated in a reasonable manner to facilitate the calculation of the coefficient of discharge for any operating conditions. 66

67 B. BACKGROUND There are numerous papers in the literature concerned with fluid flow through orifices. In general they are concerned with one or more of the following problems: 1. The experimental determination of orifice discharge coefficients 2. Correlation techniques for orifice Cd data 3. The effect of cavitation and fluid properties 4. The effect of orifice L/D ratio Some of the literature on orifice flow is related to the calibration of standard orifice meters for pipe line flow measurement and does not have a direct bearing on carburetor fuel flow. Thus, the papers which are discussed here are, for the most part, concerned with the discharge characteristics of small, submerged orifices. Bond32 determined the variation in discharge coefficient with fluid properties and mass flow rate for a thin square-edged orifice with an L/D ratio of 0.051. Various mixtures of glycerine and water were used to obtain the effect of fluid properties. The data points were plotted as a function of(R and illustrated the fact that Cd reached a maximum value of 0.69 at a Reynolds number of about 180, then dropped slightly to a constant value of about 0. 66 for higher Reynolds numbers.

68 The experimental work of Spikes and Pennington41 was related to the variation in discharge coefficient with L/D ratio and with cavitation. The Reynolds number range investigated was generally higher than that encountered in carburetor fuel flow. The L/D ratios studied were from 0. 142 to 2.00 and it was concluded that L/D ratios of about 1/2 gave Cd values which oscillated markedly with Reynolds number. It was also concluded that the discharge coefficient was constant for L/D ratios of 0. 142 and less. (This would be true for the Reynolds number range investigated, which was from about 7000 to 40,000 but in the typical carburetor flow range from about 500 to 9000 this is not necessarily true.) In addition, the method of plotting the discharge coefficient data leaves much to be desired in this paperas well as in numerous other orifice papers. The plot size, axis scales, and axis parameters used in many reports make it extremely difficult to read Cd values or distinguish different data sets. 43 Zucrow reported the results of an extensive test program to study the variation in discharge coefficients of submerged orifices. The only fluid used was Benzol, however many orifices were tested with various L/D ratios, chamfer angles, chamfer depths, and mass flow rates. The Reynolds number range was fairly limited but was within the region of interest for carburetor orifice flow. Zucrow claimed that by plotting the coefficient of discharge against the orifice Reynolds number, a characteristic curve would be obtained for each orifice which would be independent

69 of fuel properties. This would be true if the only important variables were the ones involved in the Reynolds number, however there are many other factors which influence orifice flow and it has been found by numerous workers, including the author, that the Reynolds number does not completely correlate the fluid properties. Three additional variables which probably influence the flow are; the fuel surface tension in contact with the orifice material, the orifice surface roughness, and small cavitation bubbles at the leading edge of the orifice. These would tend to give different orifice performance even for the same Reynolds number. Mirsky and Bolt 9reported test results and a photographic flow study of a metering rod orifice system. They performed an inlet chamfer angle study and reported that a 40 included angle gave the optimum discharge coefficient. (Spikes4 reported 50~ and Zucrow3 showed a peak in the coefficient of discharge at 400 to 600.) Mirsky and Bolt correlated the flow data by means of dimensional analysis parameters and did not show coefficient of discharge values directly. 25 Ishikawa25 attempted to find an orifice configuration which would compensate for changes in air and fuel temperature. This is admittedly an extremely difficult problem and could only be accomplished on an approximate basis. This was done by assuming the air flow was incompressible, the fuel kinematic viscosity decreases linearly with temperature, and that the viscous pressure loss in the fuel channel does not

70 change with flow rate. An orifice having a specific decrease in the coefficient of discharge with Reynolds number was needed and various configurations were tested until the desired characteristics were obtained. This study illustrates an important point: the manner of change in the orifice discharge coefficient is one of the controlling factors in the variation of the F/A ratio due to changes in fuel and ambient conditions. The flow characteristics of short capillary tubes were studied by Kreith and Eisenstadt.37 They were concerned with pressure drops and flow rates for small diameter tubes of varying L/D ratios. The interesting fact about this study is the variation in the flow exponent "n" in the equation: Q = constant (AP) n It was known that for orifices (very low L/D values) the value of n was 1/2 and for flow in pipes (very large L/D values) the value was 1. The L/D range from 0.50 to 20.0 was investigated and the n value plotted versus L/D. A pressure drop correlation was found by using the dimensionless variable L/D which was first suggested by Langhaar.7 (Re) 36 Kastner and McVeigh were chiefly concerned with investigating the discharge coefficients of orifices in the Reynolds number range below 5000. Their Reynolds numbers were based upon the upstream pipe diameter rather than the orifice diameter. This is usually done in pipeline metering

71 work but since the pipe Reynolds number loses its significance when the orifice flow area is much smaller than the pipe flow area, the orifice Reynolds number is much preferred for carburetor work. They tested square-edged orifices with L/D ratios from 0.267 to 2.67 and all having a nominal orifice diameter of 0.375 inch. The fluids utilized in their investigation were water, oil, and air. Since the ratio of the orifice flow area to the upstream pipe flow area was 0.035,the conversion of their pipe Reynolds numbers to the more meaningful orifice Reynolds numbers will be: (Re) orifice p= 5.33 (Re) pipe 0.035 Since their reported data for square -edged orifices was over the pipe Reynolds number range from 150 to 3000, the corresponding orifice Reynolds number range was 800 to 16,000. Since there are significant Cd changes at orifice Reynolds numbers less than 800, ( Cd will go to zero at zero Reynolds number) the results are only partially applicable to carburetor work. 38 Lichtarowicz, Duggins, and Markland gave an excellent review of the literature on square-edged orifice studies. They also presented discharge coefficient data for L/D ratios from 0.50 to 10.0 over an orifice Reynolds number range from 1 to 10,000. Because these are the ranges of interest in carburetor work, this paper is a valuable reference. The coefficient of discharge curve for an L/D ratio of 0.50 was of an

72 oscillatory nature with a peak value of 0. 72 at a Reynolds number of about 700. This phenomenon was also mentioned by Spikes and 41 Pennington although their curves did not clearly show it. The Cd data in the paper by Lichtarowicz was plotted on semi-log coordinates with the x axis as the logarithm of the orifice Reynolds number. The data points of numerous other workers were also plotted, which gave an indication of the magnitude of the scatter. A plot of the ultimate coefficient of discharge, Cdu versus L/D ratio was also given. (The ultimate Cd value is the asymptotic value at high Reynolds numbers.) This data is of interest because it provides an easy check of any experimental results, and because the orifices with small L/D values reach their ultimate Cd values at low Reynolds numbers, after which the coefficient of discharge is constant. Figure 10 illustrates the variation in Cdu with L/D ratio for square -edged orifices. Both the data points of various workers as plotted in reference 38 and the data points obtained in this project are shown. Note that the maximum value of Cdu occurs at an L/D ratio of about 2.0, and that Cdu is 0.61 for very thin orifices. Empirical relationships which fit the experimental Cd data have 40 been proposed by various workers. Nakayama,4 on the basis of his experiments on 24 square-edged orifices with L/D ratios from 0.799 to 16.520, suggested the following relationship for the ultimate coefficient

.95 _ _ LJ.90.85 -1r U) Empirical Relationship (I *801 I~ *, d= 0.827 -O.0085(L/D) -.8O LJ..75 ~ ~' LL * IL O 0 0 UJ.70._ _ _ _ <0 o 1~ *Data of Various Workers L///////ZZZZZZZ2 as Shown in Reference 38 tV D — o Data Points Obtained.65 _______ in this Study:.65 * **0 00 ~ t ~* 0 I 2 3 4 5 6 7 8 9 10 SQUARE-EDGED ORIFICE LENGTH TO DIAMETER RATIO Figure 10. Variation in ultimate Cd with L./D ratio

74 of discharge: Cdu = 0.868 -0.0425 D' EQN 3.1 He also proposed an empirical equation for the coefficient of discharge in general. This would be suitable for use where specific test data for a given square - edged orifice are not available. This relationship is: Cd ( Re)/ EQN 3 2 17.11 (L/D) +1.65 (Re)O~ An accuracy of 2.8% is claimed over an L/D range of 1.5 to 17.0 and a Reynolds number range of 550 to 7000. Another empirical relationship for Cdu was proposed in reference 38 and is plotted on figure 10. This equation is: Cdu = 0.827 - 0.0085 (L/D) EQN 3.3 One of the few papers dealing with the theoretical analysis of the 35 flow through square-edged orifices was given by Hall.5 He analyzed the flow in terms of a developing turbulent boundary layer within the orifice and included the effect of a stable separation region near the inlet. In the model, the separation region results in a boundary layer which is thicker than it would be without the recirculation near the inlet. Hall proposed the concept of a virtual origin or a point upstream of the orifice from which the boundary layer would reach the given thickness. He then analyzed the movement of the virtual origin as a function of the Reynolds number based on orifice length. (The distance from the

75 leading edge of the orifice is the logical choice for the significant length in the Reynolds number. This is because the boundary layer thickness is related to the distance from the point of development, which in this case is the distance from the inlet to the orifice.) The result of this analysis was the following equation for the coefficient of discharge as a function of L/D ratio and Reynolds number based on orifice diameter: Cd = 1.0 -0 0.1 LI1 0.2 5 0.80 (R*)0 2 [/D- 1.0 + 1.11 (Re)0-25] (Re) L0 e' EQN 3.4 While many simplifying assumptions had to be made in the analysis, this work was certainly an initial step toward predicting the behavior of orifices. 42 Starrett, Halfpenny, and Nottage were concerned with the effects of various approach conditions on the coefficients of discharge of standard metering orifices. While these standard pipe orifice plates are not important for the carburetor simulation, this paper was included because it illustrates the factors which may affect the coefficient of discharge when the orifice is in place (in the fuel channel.) When conditions are not exactly the same as the orifice flow stand, the Cd value may be affected to some degree. An example of this might be that the surface roughness of the fuel channel could be different from the inlet tube of the orifice flow stand. This could result in a different Cd value in the carburetor than in the flow stand. The paper of Starrett,

76 et al, examined the relative effects of various nonstandard approach conditions on the Cd values. These conditions were: 1. different approach area 2. different upstream velocity profile a. swirl introduced by upstream elbows b. skewed profile introduced by upstream obstructions 3. different upstream wall roughness The effects of nonstandard approach conditions would be very difficult to evaluate for carburetor work (except for number one above) but the possibility of uncorrelated Cd variations due to these conditions should be kept in mind. The magnitude of these variations can be obtained only by testing the entire fuel channel and determining the discharge coefficient of each orifice in place. C. ANALYSIS AND CORRELATION OF ORIFICE FLOW The general problem of the evaluation of the coefficient of discharge for any orifice configuration, fluid, and mass flow rate is, as stated earlier, a very important part of the overall simulation. However, while it is possible to analyze and predict the compressible flow through variable geometry nozzles in terms of fundamentals, the general problem of fluid flow through orifices is much more involved. The theoretical prediction of the fluid mass flow rate, pressure drop, and velocity distribution in an orifice is an exceedingly involved if not impossible task. This would involve the solution of the boundary layer equations with complex

77 exit conditions and with an increasing main stream velocity. The main stream velocity increases with orifice length because the annular boundary layer increases in thickness along the orifice. Continuity thus requires that the inner core of fluid increase in velocity as the boundary layer thickness increases. (The mass flow rate at any x must be the same as is shown below in Figure 11. ) I LT*RAnON l _ ro L L/ =0 NO EXlr _i E rrFFcCtmS L/D.05 TO 25.0 Figure 11. Boundary layer development within an orifice One complication is that the increase in the boundary layer thickness depends upon the variation in main stream velocity with x, and this variation depends upon the thickness of the boundary layer. This problem has been solved theoretically for the special case of laminar flow in the inlet to an infinite pipe connected to a reservoir. It is a most involved solution consisting of the simultaneous solution of two infinite series with unknown coefficients. The correct coefficients yield the main stream velocity variation, the transition length required for fully developed parabolic flow, and the pressure variation with length.

78 Any attempts to extend this type of theoretical analysis to orifice flow, even for the simple geometry of the square edged orifice, soon encounter the fact that the flow never becomes fully developed. Thus the mating of two series at the point of parabolic velocity profile is meaningless. Added to this is the fact that there is a sudden expansion at a point where the boundary layer is only partially developed and that the velocity profile at the exit plane of the orifice is dependent on the L/D ratio and the Reynolds number. When it is also considered that boundary layer separation and cavitation occur in many orifice flow situations, it should be obvious that the theoretical prediction of orifice performance is nearly impossible. We are thus faced with utilizing a more simplified flow situation in conjunction with experimentally determined coefficients. (Even this one-dimensional orifice flow model will become quite complex in the actual application of predicting pressure losses as will be seen later.) The experimental coefficients are referred to as discharge coefficients and they indicate the deviation from performance based on steady, onedimensional, inviscid flow. Figure 12 illustrates an orifice flow situation with this type of flow, that is, the ideal conversion of pressure head to velocity head. Since there are no energy losses between 1 and 2 in the ideal case, we may write Bernoulli's equation between those two points assuming steady, one dimensional, incompressible flow. Z1 + P1 +V = Z2 + P2 + V22 f 2gc igf 2gc

79 1 2 I I ORIFICE FLOW DIRECTION ORIFICE VELOCITY APPROACH VELOCITY Figure 12. Ideal. Flow in an Orifice

80 By noting that Z 1 is equal to Z2 and that the head of a fluid is related to the pressure by: Head = h = P of we obtain: 22-V1 12 = - Ah 2gc f By utilizing continuity, V1 and V2 are found to be related by A1V1=A2V2, thus the ideal velocity is given by: V (ideal) = 2g (P//f)l = 2gc (Ah) EN -',.............. EQN 3.5 1 (A2 1 - 2 A2/A1)2 Since the mass flow rate through the orifice is given by m = (fA2 V2, the following equation may be written for the ideal case: rh (ideal) = /f A2 2g Pf EQN 3.6 1 2 1) at this point the definition of the discharge coefficient is introduced. This coefficient, which is denoted as Cd, is an experimentally determined parameter which compares the actual flow situation to the ideal case;that is: Cd = m (actual) or: (actual)= (Cd) n (ideal)EQN 3 7 m (ideal)

81 if the units are as follows; = lbm/ft3 A2 = inches gc = ft lbm/lbf sec2 A h = inches of fluid V = ft/sec = lbm/hour then the expression for the actual mass flow rate becomes: i (actual) = 3600.0 /9f A2Cd\ 2 g Ah/121 2..... r EQN 3.8 144.0 1 -(A/A hr The static pressure differential across the orifice is given by substituting equation 3.7 into equation 3.6 and converting to the desired units. The resulting equation for this pressure differential in inches of water is:.2 (3600.0) (3600.0) (14.696) 2gc A2 Cd 1 (A2/A) inches H20 EQN 3.9 Note that the complex flow effects have not been evaluated by introducing Cd. This has merely transferred the problem to one of determining the variation in Cd with fuel type, mass flow rate, and orifice type. As previously mentioned, this must be done experimentally by measuring the fluid mass flow rate and the pressure differential across the orifice.

82 Since the coefficient of discharge represents all deviations from ideal flow, we might expect that Cd would be influenced by many factors. This is in fact the case. The coefficient of discharge is affected to some extent by the following variables: 1. Fluid mass flow rate 2. Orifice L/D ratio 3. Orifice to approach area ratio 4. Fluid specific gravity 5. Fluid viscosity 6. Fluid surface tension 7. Orifice surface area 8. Orifice surface roughness 9. Orifice inlet and exit chamfers The problem of correlating coefficient of discharge data is one of accounting for these effects experimentally and obtaining parameters from which Cd values can be predicted for other orifices of different geometries or fluids. It should be obvious that the correlation of all nine operating variables listed above would be exceedingly difficult. Fortunately, some of the variables are much less influential than others in the actual flow situation. This permits us to correlate only the most important variables and still obtain an accurate value for the discharge coefficient for nearly all operating conditions. There are two distinct methods which can be used in correlating orifice discharge coefficient data. The first is to obtain a generalized correlation for all orifices of a given type. Ten common orifice types are shown in Figure 13. (The types of greatest interest in carburetor fuel channel flow analysis are 1, 2, and 6.) This correlation for an orifice type such as 1, the square-edged orifice, would be of the form:

83 Ji 1 U V i U_ n a in A n la lb 2 3a 3b 4 TL ____ 5a 5b 6 7a 7b flow direction 8 9 10 la square-edged (small L/D) 5b quadrant facing downstream lb square-edged (large L/D) 6 complex 2 chamferred 7a conical facing upstream 3a sharp-edged facing upstream 7b conical facing downstream 3b sharp-edged facing downstream 8 re-entrant (Borda mouthpiece) 4 semi-circular 9 double bevel 5a quadrant facing upstream 10 venturi Figure 13. Nomenclature for common orifice types

84 Cd (type 1) = f (mf, L/D, f, //^f, Vff, A1/A2, Asurf, ) The second technique involves a correlation for each orifice of a given geometry. More correlations are needed but they are of a simpler form. For example, consider the coefficient of discharge of a square-edged orifice with an L/D ratio of 3.63. The orifice geometry is fixed (except for the approach area), thus the correlation does not involve the L/D ratio. If the orifice for which a Cd value is to be predicted is geometrically the same as the orifice from which the correlation was obtained, then the surface area and roughness are not variables. This correlation is of the form: Cd (specific geometry) = f (f, f,,, A1/A2) The second method is useful for carburetor fuel channel analysis. The application of this method is to obtain a correlation of the above form for each orifice in the fuel channel. This correlation is then used to obtain the coefficient of discharge for any fuel property values, mass flow rate, and approach area. This will be discussed in detail in Section 3f. In obtaining the correlation from the experimental discharge coefficient data, the use of dimensional analysis has been found to be quite useful. Zucrow43 was one of the first to propose a coefficient of discharge correlation utilizing the orifice Reynolds number,Re: Re = UfVD = VD = 4fn 7tf _r/Off X~~f \)f,r D?f

85 where D is the orifice diameter in inches and )f is the fluid kinematic viscosity in centistokes. In these units the orifice Reynolds number is given by: Re = (12.0)(92903.0) (4.0) 1m EQ 3.10 R(3600.0) - [D f310 The use of the Reynolds number as a correlation parameter accounts for the effects of rhm'f, and/If to a good first approximation. Since the Reynolds number represents the ratio of the inertial forces to the viscous shear forces, and these forces are based upon the shear of a Newtonian fluid, the Reynolds number does not completely correlate orifice flow. This will be obvious when actual Cd data are shown in Section 3e. The orifice surface area and fluid surface tension in contact with the orifice material are not accounted for by the Reynolds number. These variables can be included in the dimensional analysis, resulting in the dimensionless number /OfV2D/. This number represents the ratio of the inertia forces to the capillary or surface tension forces and is known as the Weber number, W. An additional dimensionless number, known as the cavitation number, should be included if the orifice pressure drop and fuel vapor pressure, Pfv, are such that cavitation is likely. This number, K* is given by: PI - P K = - Pfv Since cavitation does occur under most normal fuel channel operating conditions, the cavitation number can usually be excluded. However,

86 cavitation effects can occur under conditions of high flow rates with hot fuel of low Reid vapor pressure. Thus, the correlation of discharge coefficient data for a given orifice is of the form: Cd (specified geometry) = f(Re, W, A1/A2) The Weber number effect was found to be very small for typical fuels and orifice sizes, exerting only a slight influence at very low flow rates. Fuel surface tension was found to exert a significant effect on the fuel discharge orifice pressure drop (where fuel is drawn into the air stream) and was included in that case. For other orifices,the final form of the Cd correlation becomes: d Cd (specified geometry) = f (Re, A1/A2) iD. CORRELATION OF FUEL PROPERTIES It has just been shown that the correlation of orifice discharge coefficient data is very dependent on fuel property values. These values must be known for each possible fuel over a wide temperature range. This includes absolute viscosity, kinematic viscosity, density, and surface tension in contact with air. In addition, from the compressible mixture flow analysis in chapter two, it was found that numerous fuel property values were needed including specific heats, specific heat ratio, latent heat of vaporization, and molecular weight. Thus, the

87 goal of the fuel property correlation work was to provide all needed values for many possible fluids. This was accomplished by putting all values and correlations in a subroutine called FPROP. This subroutine may be called for a specified fuel type and temperature any time fuel properties are needed. Numerous fluids are listed in this subroutine including ASTM Iso- octane, ethyl alcohol, mineral spirits, four brands of gasoline, and water. The experimental work on fuel properties consisted of determining kinematic viscosity and specific gravity variations with temperature for each of the fuels. The kinematic viscosity measurements were obtained with Cannon-Fenske capillary viscometers in conjunction with a Neslab constant temperature bath. A typical temperature range was 10~ F to 110~ F in 10~ F incrementswith three viscosity measurements made at each temperature. The experimental Kinematic viscosity data was correlated by an equation of the form: V = A + - C centistokes T+C Where T is the temperature in degrees Fahrenheit and A, B, and C are constants to be determined for the best data fit. The correlating equation for the Kinematic viscosity of Standard regular gasoline was, for example: = 0.0830 + 135.79 centistokes EQN 3.11 T+ 132.5 The specific gravity tests were run just after the viscosity tests for each fluid. In this manner all necessary test data were obtained for a given

88 temperature before the bath temperature was changed to a new value. The specific gravities of all fluids were determined with calibrated H-B Instrument Company hydrometers. The bath temperature was held to the nominal value - 0.1 F in all cases. The values of surface tension in contact with air were taken from the literature (chiefly from references 66 and 67). The variation in surface tension with temperature of a pure liquid can be adequately described by a correlating equation of the form; 11/9 N= T (1 - T/T ) dynes/cm EQN 3.12 Where T is the liquid temperature and T is the critical temperature, both in degrees Rankine, and GO is an empirical constant to be determined from the data. The conversion factor of 1 ibm/foot = 14550.0 dynes/cm must be used when substituting surface tension values into equations with English units. The surface tension of most hydrocarbons (in the presence of air at one atmosphere) was found to lie between 16.0 and 23.0 dynes per centimeter at 70 F. A typical variation in surface tension with temperature is that of normal octane which decreases from 23.7 at 320 F to 19.8 dynes per centimeter at 104~ F. The effect of temperature on specific gravity, kinematic viscosity and surface tension is shown in Figure 14 for ASTM iso-octane. The gravity and viscosity data were obtained in this project and the surface tension values were obtained from reference 67. Similar curves exist for each fuel type. The important thing to notice is that significant

89 1.4 24.0 1.2 22.0 C,) w o z I.- 0 20.00 C,) 1.0 z 0.8 ------- z^ —-_ 180 z 0.6 - 16.0 | > DATA OBTAINED IN THIS PROJECT Fiur 0 DATA FROM ROSSINI (REF 67) -- CORRELATING EQUATIONS 0 0.~4 14.0 U< IZ~~~~~~~~:3^~~~~~~~~~ 0.2 - - - - 12.0 0 20 40 60 80 100 120 FLUID TEMPERATURE IN DEGREES F Figure 14. Iso-Octane Property Variations With Temperature 0.780 --- 0.760 0.740 0 w 0.720 0.700 - -$ - - U. 0) 0.680 0.660 0 20 40 60 80 100 120 FLUID TEMPERATURE IN ~F Figure 15, Specific Gravity Variations of Test Fuels

90 variations in these properties occur over the normal range of fuel temperature. In addition, the experimental data indicate that significant differences in kinematic viscosity and specific gravity can occur among various brands of gasolines, even at the same temperature. This is illustrated in Figure 15 which is a plot of the gravity data for three pump gasolines and ASTM iso-octane. The numerical values for liquid specific heat, vapor specific heats, vapor specific heat ratio, latent heat of vaporization, lower heating value, and molecular weight were also obtained from the literature. These values, as well as the experimental correlations, are listed under each fluid in subroutine FPR!DP, in Appendix J. E. RESULTS OF ORIFICE FLOW BENCH TESTS A large scale orifice testing program was carried out on an orifice flow bench. The goal of this testing program was to provide accurate correlations of orifice discharge coefficients for use in the simulation. Approximately 100 tests on numerous orifice configurations were run on the flow bench using iso-octane, mineral spirits, and various gasolines as test fluids. A schematic diagram of the experimental apparatus is shown in Figure 16. The static pressure difference across the orifice was measured with a vernier manometer, accurate to within 0.02 inches of the fluid. The downstream pressure tap essentially measured the static pressure at the exit plane of the orifice. Test runs consisted of approximately 35 points taken over a pressure drop range

91 MERIAM VERNIER MANOMETER -- - -FUEL SUPPLY TANK AP INCHES OF FLUID NEEDLE VALVE -:, ORIFICE FILTER THER MOCOUPLE - RESERVE TAN K SCALES [ SUPPLY PUMP Figure 16. Schematic diacramC of orifie fl w oe:-T'.hi

92 of 0.20 to 55.0 inches of fluid. Most of the orifices were tested for each fluid at various temperatures. This provides a check on the validity of the Re correlation. A description of all of the orifices used in the tests is given in Table I. Note that typical automotive main metering jets were tested as were square-edged orifices with an L/D range from 0.100 to 7.230. TABLE I ORIFICE TEST INFORMATION O ORIFICE I DIAMETER LENGTH NUMBER TYPE inches inches L/D RATIO REASON FOR TESTING 1i Ford 0.0502 0.1837 3.660 F-50 2 Ford 0.0514 0.1837 3.574 to obtain Cd curves F- 51 for typical main metering orifices 3 Roch. 0.0553 0.1765 3.191 R-55 4 Square 0.0518 0.0052 0.100 edged (Brass) 5 Square 0.0518 0.0319 0.616 edged (Brass) 6 Square 0.0518 0.1880 3.630 to obtain characteristic edged curves for orifices we (Brass) various L/D ratios 7 Square 0.0518 0.3745 7.230 edged (Brass) 8 Square 0.1015 0.0625 0.616 to determine the effect edged of orifice surface area (Brass) (compare with orifice 5) 9 Square 0.0506 0.0323 0.638 to determine the effect edged of orifice material. (Teflon) (compare with orifice 5) In Section 3C the discharge coefficient correlation for a given orifice was found to be of the form; Cd (specified geometry) = F (R,, A2/A1) where A2 is the orifice flow area and AL is the approach area. The

93 experimental data in these tests consisted of mass flow rate and static pressure differential values (in inches of test fluid) for a specified orifice and fluid. The Reynolds number was obtained by utilizing the relation: Re = 394.2 e f - EQN 3.13 The observed coefficient of discharge can be calculated from the following equation: Cd (observed) m actual (144.0) EQN 3.14 rm ideal (3600.0),f A2 \ 2gch/12' E The effect of the finite approach area A1 may be correlated by multiplying the observed coefficient of discharge by the factor 1 -(A2/A1)2 This yields a discharge coefficient which is corrected to zero approach velocity. Thus: Cd (corrected) =1 - (A/A1) Cd (observed) EQN 3.15 since the diameter of the approach channel in the flow bench was 0.375 inch, and the flow diameter of the orifices was about 0.051 inch, the velocity of approach correction factor was very nearly unity. - 1(A1/A2)2 - 1 -(D1/D = 1 - (0.136)4 - 1 The corrected Cd data is then plotted as a function of the orifice Reynolds number. (Note that the orifice diameter is used as the characteristic dimension in the Reynolds number.) The resulting curve of C versus R for a specific orifice will be referred to as the d e "Characteristic Curve" for that orifice. If the orifice Reynolds number

94 TABLE II RESULTS OF A TYPICAL ORIFICE FLOW STAND TEST TEST NUMBER: 914661 ORIFICE: FORD F-50 MAIN METERING JET FLUID: STANDARD REGULAR GASOLINE AT 77~F P lAP Fluid Orifice Ideal Run Inches of Inches of Flow Rate Reynolds Cd Flow Rate Number Fluid Water Ibm/hr. Number lbm/hr. 1.030.022.329 99.8.3643.903 2.080.058.717 217.6.4858 1.475 3.120.088.877 266.8.4855 1.806 4.210.154 1.302 396.2.5448 2.389 5.300.220 1.651 502.8.5781 2.856 6.400.293 2.003 615.5.6079 3.295 7.500.367 2.259 695.6.6134 3.684 8.590.433 2.502 770.6.6252 4.001 9.700.514 2.779 856.6.6377 4.358 10.790.580 2.987 920.6.6451 4.630 11.940.690 3.275 1009.4.6484 5.050 12 1.040.764 3.499 1078.6.6587 5.312 13 1.520 1.116 4.531 1395.7.7055 6.422 14 2.050 1.506 5.346 1645.8.7167 7.459 15 2.520 1.851 5.997 1842.6.7250 8.271 16 2.990 2.196 6.603 2027.7.7329 9.010 17 3.650 2.681 7.518 2305.7.7552 9.955 18 4.040 2.968 7.918 2423.7.7559 10.475 19 4.500 3.306 8.418 2576.9.7614 11.055 20 5.030 3.695 9.043 2768.3.7737 11.688 21 5.520 4.055 9.540 2920.5.7792 12.244 22 6.050 4.444 10.197 3121.5.7955 12.819 23 6.540 4.804 10.574 3236.8.7934 13.328 24 7.000 5.142 11.058 3385.1.8020 13.789 25 7.530 5.532 11.499 3520.1.8041 14.301 26 8.100 5.951 12.076 3696.7.8142 14.832 27 8.390 6.164 12.213 3731.5.8089 15.098 28 8.910 6.546 12.749 3893.0.8194 15.559 29 9.530 7.001 13.147 4012.0.8170 16.092 30 9.520 6.994 13.238 4034.7.8230 16.085 31 10.020 7.362 13.585 4135.1.8231 16.504 32 11.120 8.170 14.485 4406.3.8331 17.387 33 12.070 8.868 15.138 4604.9.8357 18.114 34 13.030 9.573 15.734 4786.2.8360 18.821 35 14.060 10.330 16.425 4993.2.8401 19.552 36 15.060 11.065 17.085 5190.7.8443 20.236 37 16.050 11.793 17.696 5372.7.8470 20.891 38 17.080 12.550 18.327 5557.3.8503 21.553 39 18.050 13.263 18.853 5709.6.8508 22.159 40 19.050 13.998 19.420 5874.1.8530 22.766 41 20.040 14.725 19.940 6027.4.8539 23.352 42 26.450 19.483 22.828 6885.8.8620 26.531 43 29.620 21.766 24.647 7426.6.8680 28.396 44 35.210 25.874 27.094 8143.3.8750 30.966 45 40.510 29.769 29.131 8749.9.8770 33.216 46 45.170 33.194 30.902 9270.2.8810 35.078 47 50.000 36.745 32.524 9738.0.8811 36.911 48 54.840 40.303 34.275 10243.0.8866 38.661 49 58.040 42.655 35.264 10524.9.8865 39.777

95 completely correlated the flow, the test data for all fluids would lie on the same curve. This claim was made by Zucrow when he proposed the Reynolds number correlation/but subsequent investigations, including the orifice work in this project, have shown that Cd data for different fluids, or for a given fluid at various temperatures, do not always lie on the same Cd versus Re curve. This is likely due to phenomena which are not accounted for in the orifice Reynolds number correlation such as surf-ace tension effects, non-Newtonian flow, boundary layer separation (w hich should be correlated with distance from the inlet edge of the orifice), and cavitation. It will be seen, however, that for the oi-i-fico-s, fuels, and flow rates normally encountered in carburetor work, the orifice Reynolds number does an adequate job of correlating fuel property and mass flow rate effects. It should be emphasized that the effects which have been neglected may be of great significance and could, in fact, predominate in other orifice flow situations. All test data were reduced by a digital computer program and the resulting values were plotted on a CALCOMP plotter. Table 2 shows the test results for a typical run (number 914661) which was an orifice flow bench test of a Ford F-50 main metering jet using Standard regular gasoline as the fluid. The important parameters from this test are plotted in Figures 17 through 21. (computer plots of this type were obtained for each test). The variation in gasoline flow rate with static pressure differential across the orifice is shown in Figure 17. Note that this flow rate rises smoothly with pressure differential, yielding a

36.0 32.0 28.0 cr I I I I IDEAL FLOW i9 C D= 1.0 24.0 -- co y^ ^ Experimental Flow Curve For: -tI 1 I I Ford F-50 Metering Jet z Standard Regular Goso ne at 77~ F -J z 16.0 W20 z 12 0 cn 8.0 4.0 (O 4.0 8.0 12.0 16.0 200 240 28.0 32.0 36.0 PRESSURE DROP ACROSS JET-INCHES OF WATER figure 1.7. Gasoline flow rate vs. pressure drop for F-5O orifice

Ln:So REGULA GASOL UC- -__ __-___ co r oo I^l.N AT 77o F UJ'C) o 1 0ORD F-50 MAIN METNG LO ~00 1.00 2.00 3.00 4.00 5.00 6.00 7.00 8.00 9.00 10 m PRESSURE DROP RCROSS JET-INCHES OF WRTER Figure 18. Cd vs. pressure drop for F 50 orifice

98 mass flow rate of 16.20 Ibm/hour at a AP value of 10.0 inches of water. Figure 18 illustrates the variation in the coefficient of discharge with the static pressure differential across the orifice. The important fact shown on this graph is that significant changes in the orifice discharge coefficient do occur over the normal operating range of pressure drops. For this particular orifice, the operating discharge coefficient will vary between 0.63 and 0.84. This verifies the statement made earlier that large errors in predicting fuel flow rates can result from assuming the discharge coefficient to be constant. The characteristic or correlated curve for the orifice is shown in Figure 19. In this curve the orifice discharge coefficient is represented as a function of orifice Reynolds number. Note that the discharge coefficient rises smoothly with Reynolds number which is the usual case for orifices with L/D ratios greater than about 2.0. This data was obtained for a specified orifice (Ford F-50) and a specified fluid and temperature (Standard regular gasoline at 77~ F.) If Figure 19 is actually a characteristic curve for that orifice, thlat is, if the Re correlation is exact, then the discharge coefficient data for all other fluids and for Standard regular gasoline at other temperatures would lie on the same curve. Since many tests were performed on each orifice using fluids of various viscosities and densities, all that was required to check the validity of the Reynolds number correlation was to plot Cd curves for various fluids on the same grid. A typical set of these curves is shown in Figure 20. Note that the orifice Reynolds number

.85 ---- Orifice Number I,Ford F 50 Main f.8o0 Metering Jet.80 0 Le.70 0 i.65 0 11-.50 I.50 i_______ ____ _ ----------------------.00 1.0 2.00 3.00 400 5.00 600 7oo 8.00 O OO REYNOLDS NUMBER OVER ONE THOUSAND ---.'w".gu' I. QC haracrter..stic r'`-charge coefficirnt curve for F 50 orifice

.. —OC ^-0^^^ -0-c.85 -- -__ _ ____ _ ____ __ —-.8o ^ y^J~ t,~~~~~~P" /Ford F-50 Main Metering Jet r;75 _____ __ y^_ ____ A Shell Mineral Spirits at 750F < o ASTM Isooctane at 800F I o o Standard Regular Gasoline at 770 F 07 0 U0 z Lu) O.65 Li 0 L60 I:.55 I.50.00 1.00 2J0 300 4.00 500 600 Oo0 8.00 9.00 REYNOLDS NUMBER OVER ONE THOUSAND ---- Figure 20. The effect of fluid type on the discharge coefficient

101 did not completely correlate the data because different Cd values were obtained at the same value of Re (for Re less than 5000). The higher Cd values were obtained with fluids of higher viscosity and surface tension. For this particular orifice, the spread between the curve for Standard regular gasoline and Shell mineral spirits at a Reynolds number of 1000 was 0.10 (0.55 to 0.65). The spread among gasoline brands was much smaller, being 0.64 to 0.67. For orifice Reynolds numbers greater than 5000, the discharge coefficient was correlated to within + 1% for all fluids tested. One of the important reasons for conducting the orifice flow tests was to obtain accurate data on the manner in which the characteristic curve is affected by orifice L/D ratio. Another reason was to compare the characteristic curves of various square-edged orifices with those of typical main metering orifices. This information can be ascertained by inspecting Figure 21 which contains the characteristic curves for three square-edged orifices and one main metering orifice. Notice that the L/D ratio exerts a large influence on the shape of the characteristic curve. The coefficient of discharge variation for orifice number four, with an L/D ratio of 0.100, is very similar in form to that of a sharp-edged orifice. This type of orifice yields a Cd value which reaches a maximum at a low Reynolds number (less than 1000) and then remains relatively constant or decreases slightly as the Reynolds number is increased. This similarity in performance is due to the fact that the square-edged orifice geometry approaches that of the sharp

Fluid: ASTM Isooctane at 72~F.85 Orifice Number 2 0-0F 10 Ford F-51 L/D= O3574 ~.80 Iee::ao —- - eo —---- Iu r,,,Orif ice Number 6 r0 r S.E. L/D = 3.630 T.75.7 O z Orifice Number 5 _d._,o/ -N S.E. L/D =0.616 -L.65 LL uJ'""'""'"-e' —Orifice Number 4 ~~~~O I IP I I ~~~~~~~S.E. L/D =0.100 LLJ.60.50.50 ------- - - - -.00 1.00 2.00 300 400 5.00 6.00 ZOO0 8.00 9.OO REYNOLDS NUMBER OVER ONE THOUSAND Eimure 21. The effect of L/D ratio on the orifice characteristic curve

103 edged orifice as the length becomes very small. Note that flow instabilities are inherent in orifice number 5, which has an L/D ratio of 0.616. The instability of square-edged orifices with L/D ratios between 0.25 and 1.0 has been noticed by numerous workers as mentioned previously. This instability is most predominate at L/D ratios near 0.50 and orifice Reynolds numbers greater than 800, and is characterized by difficulties in obtaining steady mass flow rates and pressure differentials during a flow bench test. These parameters tend to undergo step changes at various times during a flow test, indicating that the instabilities may result from a detachment and reattachment of a separation bubble near the upstream edge of the orifice. Square-edged orifices with L/D ratios greater than about 1.0 yield a discharge coefficient which increases smoothly with Reynolds number as illustrated by orifice numbers 2 and 6 in Figure 21 (there is always a positive slope to the characteristic curve.) The ultimate value of the discharge coefficient for these orifices is reached, for all practical purposes, at Reynolds numbers in the 8000 to 10,000 range. The value of Cdu decreases slightly as L/D increases because the viscous dissipation within the orifice is increasing. In fact, this is the predominate mechanism for total pressure losses as the L/D ratio approaches 40 (approximately), which is the beginning of the pipe flow regime.

104 The data points describing the characteristic curves of the orifices are listed in Table III. These points were read in as data for use by the interpolation subroutine STERL. The data for all L/D ratios which were previously listed in Table I were obtained in this project. The data for the remaining L/D ratios were obtained by reducing and plotting the original data of Zucrow.43

Table III Orifice Cd data used in the simulation INPUT DATA FOR ORIFICE COEFFICIENTS OF DISCHARGE POINT RE F-50 0.100 0.616 1.426 3.629 4.726 7.230 10.58 }LJwg O RE F-50 L 1 0.000.000.000.000.303.000.000.000 0.000 2 500.577.663.690.737.674.623.570.525 13.361 3 1000.656.665.720.766.715.580.647.620 33.467 4 1500.702.654.677.770.739.710.688.660 330.513 5 2000.734.648.668.774.759.727.711.685 400.550 6 2500.761.644.700.788.768.741.724.703 500.577 7 3000.783.641.675.790.772.750.729.712 6)3.597 8 3500.804.638.677.790.776.756.730.720 7)3.614 9 4000.820.635.675.793.779.751.734.726 8)).629 13 4500.832.633.670.796.781.764.739.729 900.643 11 5030.840.631.678.798.783.766.743.732 1030.656 12 5500.848.629.698.800.785.768.746.734 1100.665 13 6000.854.627.686.802.786.770.747.736 12).675 14 6500.860.626.676.804.787.771.749.737 13) 3.684 15 7000.865.625.713.805.788.772.751.738 14)0.693 16 7500.869.624.705.806.789.773.753.739 15)0.73? 17 8000.873.623.700.807.790.774.755.740 1600.739 18 8500.876.622.690.808.791.775.757.741 1700.716 19 9000.879.621.682.809.792.776.759.742 1830.722 20 9500.881.620.680.810.793.777.760.743 19)).728 21 10000.883.620.680.810.793.778.761.743 2030.734

106 F. APPLICATION OF ORIFICE COEFFICIENT DATA TO ACTUAL FLOW SITUATIONS The preceding sections have been devoted to methods of formulating and obtaining orifice flow correlations. Even after this has been accomplished, many questions must be answered in connection with the application of orifice flow stand data to actual flow situations. These questions are: 1. How can the total and static pressure differentials across an orifice be calculated from its characteristic curve? 2. How can orifice performance be predicted when using fluids and approach area geometries which differ from those used to obtain the characteristic curve? 3. How can the pressure differentials be calculated for an orifice with an L/D ratio for which a characteristic curve has not been obtained. These questions arise because the typical carburetor fuel channel contains numerous orifices of various types (square-edged, chamferred, and complex) and L/D ratios. The properties of the fluid flowing through these orifices will vary over a wide range due to variations in fuel brand and ambient temperature. In addition, the orifices will be installed in fuel channel branches having various diameters, giving various approach area ratios. The characteristic curve for a particular orifice is, as mentioned in the previous section, a plot of the discharge coefficient (corrected to zero approach velocity) versus the Reynolds number based on orifice diameter. Once this has been obtained for a particular orifice type and L/D ratio, the discharge coefficient and pressure differentials can

107 be obtained for any mass flow rate by the following technique: A mass flow rate, fuel type, and fuel temperature will be specified. (The mass flow rate is the iteration variable in the fuel channel analysis as will be explained in the next chapter.) Subroutine FPROP is called and the fuel properties determined. The orifice Reynolds number can then be calculated by using the relationship: Re 4 r (309.6) re r /,P D The coefficient of discharge is obtained by interpolation within the characteristic curve. This is accomplished by the multi-purpose interpolation subroutine, STERL (Appendix F). The characteristic curve for the given orifice is supplied to the subroutine by reading in the Cd and Re values. For example, for a square-edged orifice with an L/D ratio of 3.630, twenty Cd versus Re points were obtained by a flow stand data reduction program. These points were read in and stored for use by the interpolation subroutine. Whenever a Cd value is required for this orifice at a certain Re argument, subroutine STERL performs an th accurate n- degree iterpolation on the data. Briefly, this is accomplished by generating a difference table from the data points and using Sterling's interpolation technique, which is a combination of the Gauss forward formula and the Gauss backward formula. This Cd value is one which corresponds to zero approach velocity, as would be obtained in an orifice at the exit of a reservoir. In the general case of a fuel channel orifice, there is a finite approach area which will vary with the channel diameter. This must be taken into

108, /// //_//_///A I \// ORIFICE / u FLUID FLo H @ _; c, 2 _,,- a - CLJQI,I I w p.V2 29c LENGTH Figure 22. Pressure Variations in the Vicinity of an Orifice

109 consideration in utilizing flow stand data to calculate orifice pressure differentials. Figure 22 illustrates the areas involved in the approach velocity correction as well as a schematic representation of the static and total pressure variations in the vicinity of the orifice. It should be realized that the calculation of the coefficient discharge is only an intermediate step in the analysis of orifice flow. The parameters of greatest interest are actually the static and total pressure differentials across the orifice as installed in the fuel channel. Note that areas A1 and A3 will, in general, be different from those of the orifice flow stand, and that only the static pressure differential is measured, although the total pressure differential is a more significant parameter in the analysis. Thus, expressions for these pressure differentials will now be obtained. Let us define the following additional variables: Pit = total pressure at station 1 in inches of water P2t = total pressure at orifice exit in inches of water Pls = static pressure at station 1 in inches of water P^ = static pressure at orifice exit in inches of water total presure differential acrs orifice in inches of water APt = static pressure differential across orifice in inches of water APs - static pressure differential across orifice in inches of water A1 = approach area in square inches (in this case the cross-sectional area of the fuel channel containing the orifice.) A2 = orifice flow area in square inches The total and static pressure differentials may be written as: Pit P2t + (APt)-2 and Ps = P + (AP) It 2t 1-2 Is 2s s 1-2 But the relationships between the static and total pressures are: lt = Pls + C*OV21 and P 2 2s P +CV 2 EQN 3.16 2gc 2gc

110 where C* is a units conversion factor of 406.62/2116.6. Now eliminating the total pressure values Plt and P2t, and factoring out the term C*o /2gc, the following equation is obtained. (ls -P2s) = C*p (V2 -V2 ) + (^Pt) EQN 3.17 2gc but, from the continuity equation for one-dimensional, steady, incompressible flow (which is the flow situation upon which coefficient of discharge analyses are based); bmh (25.0) A1V = (25.) A2V2 or V2 = (A2/A )2V2 EQN 3.18 Eliminating the approach velocity in the fuel channel, V, the following relationship is obtained: V - 2=, Z (P s - P s) - (^Pt) 1-2 2 C*o 1 (A/A 1- EQN 3.19 If there is no total pressure loss between 1 and 2 (ideal flow), then (APt) -2 is zero and the discharge velocity would be the theoretical maximum for the particular value of static pressure differential: or: (V2)2 (theoretical) = 2c 1 - P) C*[1 - (A2/A1)z] EQN 3.20 For an actual orifice, the coefficient of discharge represents the efficiency of converting pressure (potential) energy to velocity (kinetic) energy. That is: Cd = V2 (actual) or V2 = Cd (V2) theor EQN 3.21 V2 (theoretical) Thus the fluid mass flow rate may be written as: Ib (25.0)A2C (V)theor = (25.0) A C' d2g (Pls - P2s) EQN 3.22

111 or, solving equation 3.22 for the static pressure differential; (Pls - P) (406.62) r2 [1 - (A2/A1)2] (2116.6) 2gc/A2 C2 (625.0) EQN 3.23 Now an expression for the static pressure differential has been obtained in terms of the installed approach area ratio, A2/A1, and the interpolated flow bench data, Cd. To obtain an expression for the total pressure differential, equation 3.23 may be substituted into equation 3.17 to give: t - P2t) = C*2 1 -(A2/A1)2] _ (V22 - 2 ) 2gc A22 C d (625.0) 2gc EQN 3.24 Eliminating V1 by using equation 3.18 and factoring out/O/2gC and the area ratio term, the following relationship is obtained: (Plt 2t) =cP [C 1 (A2/A1)2 ]2 - V }2 2g,. I -A2I 2 C2 2 - V2 ~~2gc A 2 d (625.0) EQN 3.25 Next let us eliminate V, by using the continuity equation, then factor out an additional r2/o 2A22C2d term to obtain: (Plt - P2) 406.62) 2 2 (2116.6) 2gcfAz2C (625.0) 2/A - EQN 3.26 Thus, the total (irrecoverable) pressure loss for the orifice has been obtained as a function of the interpolated flow bench data, fuel channel geometry, and fluid mass flow rate. Note that from equations 3.23 and 3.26, the relationship between the static and total pressure differentials for the orifice can be written as: (AP)total = ( AP)static [1 - Cd2] EQN 3.27

112 Therefore, the coefficient of discharge indicates the fraction of the static pressure differential that is irrecoverable (cannot be reconverted to total pressure.) This ratio is tabulated in Table IV for various values of the discharge coefficient. TABLE IV THE PERCENTAGE OF THE STATIC PRESSURE DIFFERENTIAL THAT IS IRRECOVERABLE C- A Pt/ P % IRRECOVERABLE 0.00 1.000 100.0% 0.25 0.875 87.5% 0.50 0.750 75.0% 0.75 0.438 43.8% 0.80 0.360 36.0% 0.90 0.190 19.0% 1.00 0.000 0.0% It should be emphasized here that all of the fuel properties will have some effect on the static and total pressure differentials, although only the fuel density appears in equations 3.23 and 3.26. The viscosity influence will occur by virtue of changing the Reynolds number for a given flow rate, resulting in a different Cd value. The magnitude of the viscosity effect will depend upon the shape of the characteristic curve for a particular orifice. The fuel surface tension exerts an effect which is related to the orifice surface to volume ratio, and to the fuel mass flow rate. As mentioned earlier this effect was found to be very slight for typical carburetor orifices over normal flow rate ranges, and

113 was therefore not included in the orifice flow correlation. Next let us direct our attention to the problem of predicting the performance of an orifice with an L/D ratio for which no characteristic curve was obtained. This, for example, might be a square-edged orifice with an L/D ratio of 6.232. In the case of square-edged orifices, characteristic curves were obtained for many L/D ratios from nearly zero to over 10.0. Thus, a fairly accurate Cd value can be obtained by interpolating between the L/D ratios (on either side of the desired value) for the specified Reynolds number. This was the technique utilized in the simulation for any specified L/D ratio and Reynolds number. Similarly, each chamfered fuel channel orifice should be tested if possible. If this cannot be done, a reasonable approximation to their characteristic curves will be given by the Cd versus R plot for the square-edged orifice with an L/D ratio of 7.230. These chamferred orifices generally have smoothly increasing Cd versus Re curves with approximately the magnitude of the above orifice. If the orifice is of complex profile, a characteristic curve must be obtained if accurate pressure differentials are to be predicted. This is especially true for main metering orifices, whose characteristic curves exert a substantial effect on the flow characteristics of the fuel channel. A final question related to the selection of orifices for use in actual flow channel flow situtations will now be discussed, This question may be stated as;what is the optimum shae for an orifice characteristic curve? This will depend upon the criterion for which

114 optimization is desired, such as minimizing fuel property variation effects. Stable orifice operation that is unaffected by variations in fuel properties will be obtained when the two following criteria are satisfied: 1. The orifice has a smoothly increasing mass flow rate versus pressure differential curve. 2. The orifice mass flow rate at a given pressure differential is the same for all fuel brands and fuel temperatures. The above criteria immediately rule out square-edged orifices with L/D ratios between 0.25 and 1. 00. Orifices with nearly constant coefficient of discharge values (L/D ratios less than 0.25) are also ruled out by the following reasoning: Since it is desired to maintain the fuel mass flow rate constant (for a given pressure differential) as the fuel density and viscosity change, the coefficient of discharge must also change. This should be obvious from the expression for the fuel mass flow rate through the orifice as a function of the operating variables, with the pressure differential in inches of water: hourb = 93.90 C D2 / P EQN 3.28 hour d 2 or for fixed values of D and AP, the variation in the coefficient of discharge required to maintain a constant mass flow rate is: -0.5 Cd (required) - constant (/f) EQN 3.29 therefore, the orifice coefficient of discharge must increase as the fuel density decreases. The orifice Reynolds number is given by equation

115 3.13, which is rewritten here for reference: Re = 394.2 D] The characteristic curve shape required to eliminate the effect of variations in fuel properties must be one in which Cd increases with Re. Let us consider an example of this, an increase in fuel temperature. As the temperature of a given fuel increases, its density and viscosity decrease. This increases the orifice Reynolds number and, from equation 3.28, woulddecreasethe mass flow rate if Cd did not change. However, if Cd increases in the manner given by equation 3.29, the orifice flow will be unaffected by changes in fuel temperature. The locus for all values of pressure differential will yield the Cd versus Re curve shape for minimal fuel property variation effects. The exact shape will depend upon the fuel viscosity and density variations with temperature, but for typical gasoline brands the squareedged orifice with an L/D ratio of 7.230 showed very little effect of fuel properties. Thus, for this type of fuel, the characteristic curve for this orifice is very near to the required curve.

CHAPTER IV THEORETICAL ANALYSIS OF FUEL AND AIR BLEED FLOW A. BACKGROUND The multiplicity of analyses presented in the preceding chapters has resulted in equations which predict the intake manifold vacuum and venturii pressures for a wide range of operation. The next step in obtaining a comprehensive simulation of the air bled, boost venturi carburetor is to predict the fuel and air bleed flow parameters for the fuel channel. This includes the fuel and air bleed flow rates in the idle, main, and enrichment system branches of the fuel channel. In order to predict these variables accurately, the entire fuel channel must be analyzed as a Reynolds number dependent flow network, taking into account the interactions between individual branches. The driving force for flow in each branch will be the pressure differential acting on that branch, which can be related to the intake manifold vacuum and boost venturi suction. There is very little published information concerning the analysis of actual carburetor fuel channels. There are, of course, textbook analyses in which the main metering orifice is the entire fuel channel and its discharge coefficient is assumed to be constant.9,70 This neglects the pressure losses due to the numerous other elements of the fuel channel, the effects of other systems, such as enrichment and idle, and the effects of air bleeds. One of the few references which considered some of the complexities of carburetor fuel channel analysis 116

117 30 is that of Ting. He analyzed fuel channel models which contained only a main system (no enrichment or idle system) but which contained an air bleed at various locations downstream from the main metering orifice. For that particular geometry, he obtained equations which expressed the fuel flow rate as a function of the fuel properties, pressure differential, and air bleed orifice diameter. The pressure loss for the two-phase flow downstream from the air bleed was calculated by assuming one-dimensional flow and using the average density and velocity of the fuel-air foam. A study not directly related to carburetion, but which has some application to fuel channel air bleeds was conducted by 31 Weir. He measured the mass flow rates and pressure differentials associated with sonic air flow through various square-edged orifices. Schlieren photographs were also obtained for the flow in the vicinity of the orifice. Although the flow rates and Reynolds numbers were higher than those encountered in carburetor air bleed flow, this study does provide limiting discharge coefficients for various L/D ratios. Ishikawa and Ito25 were concerned with minimizing the effects of fuel property variations on fuel channel flow by optimizing the main metering orifice design. However, their fuel channel model did not include air bleeds, idle, or enrichment systems, which would make the extension of their results to an actual carburetor a large extrapolation. (In fact, they reported that a main metering orifice which has a coefficient of discharge that decreases with Reynolds number in a specific manner would compensate for fuel property variations. It was found in this

118 project that the effect of variations in fuel properties was minimized with an orifice in which Cd increased smoothly with Reynolds number.) There are numerous references dealing with the analysis of twophase flow in long pipes. The analyses of Baker22, Lockhart and Martinelli28, and Huey and Bryant24 were concerned with methods of predicting the pressure drop in a pipe under various two-phase flow conditions. These conditions, or flow regimes, are related to the relative mass velocities and fluid properties of each component, and are denoted as bubble, stratified, spray, slug, wave, and plug flow. Since these methods and correlations were intended for use in long pipes, (pipelines in many cases) they yielded very erroneous pressure drops when applied to the very short, bending, small diameter passages of the carburetor. This will be discussed in more detail in section 4c. Fundamental relationships describing the pressure losses in conduits, orifices, bends, sudden expansions, and sudden contractions were 23 Kay26 and Streeter29 stated by Daily and Harleman, Kay, and Streeter. Streeter also gave an excellent discussion of the solution of complex pipe network problems which was quite applicable to the analysis of the carburetor fuel channel. The application of these relationships allow one to divide the fuel channel into discrete elements and determine the contribution of each element to the overall pressure differential of a given branch. These equations will be given in section 4c for each channel type and flow situation.

119 — FIXED IDLE ORIFICES \\ I IDLE AIR BLEED \ ASPn O1D~~LC~ \ 2'rMAIN 2~ iDLE AIR BLEED IRv~ BLEEDy ^s-KX ~ (UPPER) MAIN FUEL \DL F NOFLOW IDLE FLOW - _ MAIN I A t' MAIN AIR BLEED (LOWER) IDLE DISCHARGE \ PORT AIR BLEED WELL THROTTLE /I TB \ PLATE: \ ~n l /// //yD — -IDLE TUBE IDLE PORT SCREW Figure 23. Typical Fuel Channel Geometry Near Air Bleed Well

120 B. FUEL CHANNEL MODEL From a fluid mechanics standpoint, the typical carburetor fuel channel is geometrically very complex. A portion of one of these channels is shown in figure 23. (The main metering orifice and enrichment systems have been omitted for clarity.) Note that there are numerous drilled passages of various diameters, giving rise to sudden expansions and contractions as well as bends and elbows. Also note that there are many fixed and variable area orifices installed in these passages. The enrichment valve and idle needle screw represent orifices in which the flow area may change. Another complexity is introduced by the fact that the fuel may or may not flow in different branches of the fuel channel, depending on the engine speed and load conditions. For example, at wide open throttle, fuel will flow in the enrichment system but not in the idle system. When the throttle is nearly closed, just the opposite is true. Further complexity is encountered due to the addition of air to the flowing fuel by means of multiple air bleeds. These bleed orifices typically supply ambient air to the main (boost venturi) and idle fuel flows, resulting in two-phase flow in that portion of the channel downstream from the initial bleed. In order to accurately predict the operation of the fuel channel as one portion of the overall simulation, a model must be chosen which considers all of the above factors and yet is amenable to analysis. Such a computer model was constructed and is illustrated in Figure 24. The important thing to note is that each element of the actual fuel

0........ *** ------ U LJ ~~~~~~~~~~"Itr 24~ ~fU ^M~l N||~2~5 IDLE SYSTEM FLOW INAK FUEL I - 16 INTAKE HEOT~ADn ~ 10. ----- r~~~~~~~~~~MANIFOLD H";" 15TD 18192 VACUUM (VACMAN) 15 $1..i S M 2 a z "/iE ~" I1 1 1 *ft *^n IlBOOST ~~~6 F==J~ a 9 W ~ 1 12 fZ VENTURI 7 ------- SUCTION TOTAL FUEL FLOW INssT F (BVSUC);T;Mt 1. MAIN METERING ORIFICE 14. IDLE TUBE 2. DELIVERY CHANNEL 15. FIRST IDLE SYSTEM ORIFICE 3. ENRICHMENT VALVE INLET NEEDLE (VARIABLE) 16. IDLE SYSTEM PLENUM CHAMBER 4. ENRICHMENT VALVE INTERNAL CHAMBER 17. IDLE SYSTEM INTERMEDIATE TUBE 5. ENRICHMENT VALVE OUTLET ORIFICE 18. SECOND IDLE SYSTEM ORIFICE 6. ENRICHMENT SYSTEM PLENUM CHAMBER 19. IDLE SYSTEM DELIVERY TUBE 7. ENRICHMENT SYSTEM METERING ORIFICE 20. IDLE NEEDLE ORIFICE (VARIABLE) 8. DELIVERY CHANNEL 21. FIRST MAIN AIR BLEED ORIFICE 9. AIR BLEED WELL (BELOW IDLE TUBE) 22. EMULSION TUBE ORIFICE 10. ANNULUS BETWEEN IDLE AND EMULSION TUBES 23. SECOND MAIN AIR BLEED ORIFICE 11. AIR BLEED WELL PLENUM CHAMBER 24. FIRST IDLE AIR BLEED ORIFICE 12. MAIN FLOW DISCHARGE TUBE 25. SECOND IDLE AIR BLEED ORIFICE 13. MAIN FLOW DISCHARGE ORIFICE FIG. 24 COMPUTER MODEL OF COMPLETE CARBURETOR FUEL CHANNEL

122 channel has its counterpart in the model which means that each orifice, sudden expansion, and bend can be accounted for in the overall pressure distribution. In addition, each fuel channel system (or branch) in the actual carburetor has its equivalent in the model. These are: 1. Main system 2. Idle system 3. Enrichment system 4. Main air bleed system 5. Idle air bleed system Each passage and orifice is numbered according to the numerical iteration sequence beginning with number 1, the main metering orifice. Each element has a length, diameter, manufacturing tolerance, angle from the preceding element, and type code which is read into the computer. The type code indicates the type of analysis that is to be applied to that particular element to determine the pressure and flow rate parameters. If the element is a drilled passage, the analysis will be different from that used for a square-edged orifice. Thus, an L/D ratio and a random passage diameter can be calculated for each element. A sudden expansion or contraction can be accounted for by comparing adjacent elements such as 8 and 9. If the diameter of element 9 is greater than the diameter of element 8,then a sudden expansion exists and the appropriate equations can be utilized. In an actual carburetor, the enrichment system operation is related to the engine load, and the idle system operation may be adjusted by means of the idle needle screw. This is accounted for in the model by allowing the flow area of element 3 to be a function of intake

123 manifold vacuum and by obtaining the flow area of element 20 as a function of the idle needle geometry and the number of turns (See Appendix C.) The idle needle parameters, as well as the intake manifold vacuum at which the enrichment valve begins to open, are read in as data. One final item to notice concerning the flow channel model is that the flow potentials for the network are provided by the boost venturi suction and the intake manifold vacuum, as is the case in the actual carburetor. If the boost venturi suction is high and the intake manifold vacuum is low, (as with large throttle openings) then most or all of the flow will pass through the main system. As the intake manifold vacuum increases and the boost venturi suction decreases, more and more fuel will pass through the idle system and the main fuel flow will go to zero. The values of boost venturi suction and intake manifold vacuum must be determined before a fuel channel analysis can be performed. This is accomplished by calling on subroutines THROTL and AIRMAS. C. CRITERIA F1OR SOLUTION The next consideration after the establishment of a geometric and iterative model is that of determining the criteria for obtaining the correct fuel flow rates in each system. These criteria are based upon the conservation of mass and energy and the relationship between the total and static pressure at a point in a moving fluid. Referring again to Figure 24, it is obvious that there are 5 distinct fuel mass flow rates, 4 air bleed mass flow rates, and 4 total mass flow rates to consider in

124 the model. These are as follows: 1. mj The main metering jet (orifice) mass flow rate 2. me The enrichment system mass flow rate 3. mt The total fuel mass flow rate 4. mm The main system fuel mass flow rate 5. mi The idle system fuel mass flow rate 6. rmbl The first main air bleed mass flow rate 7. rmmb2 The second main air bleed mass flow rate 8. mibl The first idle air bleed mass flow rate 9. rhib2 The second idle air bleed mass flow rate 10. ml The total flow rate between idle bleeds 1 and 2 11. mrl The total flow rate between main bleeds 1 and 2 12. mint The total main system flow rate (fuel + air) 13. mit The total idle system flow rate (fuel + air) Note in figure 25 below that there are six nodal points, or intersections of two or more network branches, in the total flow network.' — ~ — ~- rr^. u i l Ti b 2 rfiibl rii r it rj ~- - Tl --- mt N mt l N5 N6 N1 ) - N2 N mll N3 N4 mre i t l f n mt Fiur5.Nda oit miembl c mmb2 n Figure 25, Nodal points in the fuel channel flow network

125 The application of the continuity equation to each node yields the following relationships: Node 1 mj + me - mt = o EQN 4.1 Node 2 rt - mrm - t = EQN 4.2 Node 3 mm + mni - il o EQN 4.3 m mbl ml Node 4 rim + m ml- rm = EQN 4.4 Node 5 mi + rfiibl - mil= EQN 4.5 Node 6 mi + fmil - mit = EQN 4.6 The above relationships control the iterative flow rates within the program, thus assuring that the 13 values currently being evaluated satisfy continuity at every nodal point. This avoids additional iterations on the mass flow rates to satisfy these criteria. There are an infinite number of flow rates that will satisfy continuity for a given flow network, but only one set of these will also satisfy the energy requirements. These requirements may be generally stated as; the sum of total pressure losses of each element in a branch, plus the net fluid velocity head and height change between the inlet

126 and exit to the branch, must be equal to the imposed pressure differential across that particular branch. A specific example of this,for the carburetor fuel channel modelis that the sum of the total pressure losses for elements 1, 2, 8, 9, 10, 11, 12, and 13, plus the velocity head of element 13, plus the height change between the fuel bowl level and the outlet of element 13, plus the pressure differential at the outlet of element 13 due to the fuel surface tension, must be equal to the boost venturi suction. (With all units converted to inches of water.) In equation form, with BVSUCW meaning the boost venturi suction (metering signal) in inches of water, SPILL1 denoting the height differential discussed above, which is commonly referred to as the spill point of the carburetor, and VHEADW(I) and DELPTW(I) denoting the velocity head and total pressure loss in the It element; z DELPTW (I) 4 VHEADW(1I3) 4 SPILL1 - A -I BVSUCW =E (r) EQN 4.7 where I takes on the values 1, 2, 8, 9, 10, 11, 12, and 13. The symbol AP. denotes the pressure differential due to surface tension, and E (m) is the iterative error parameter which is a function of the iterative flow rates. (When the 13 fuel and air bleed flow rates approach the correct values, the error parameters become very small.) It should be obvious from equation 4.7 that, for a specified value of BVSUCW, values of, tand m which are too large will result in a large system pressure loss and give a positive erromt system pressure loss and give a positive error term.

127 Equations similar in form to that of equation 4.7 can be written for each branch of the network. For example the relationship for the enrichment system can be expressed as: DELPTW (I) + VHEADW (7) -ZDELPTW (I) - VHEADW (2) = E(r ) I=3, 4, 5, 6, 7 1=1, 2 EQN 4.8 In this case the enrichment system flow rate, fm is adjusted e iteratively while the main metering jet flow rate, mj, is held constant at its current value. This is continued until equation 4.8 is satisfied, which means that the correct relationship between rm1 and rm has been ] e obtained. This means that each time the main metering jet flow rate is changed iteratively, a new iteration must be performed on mi. It should be noted here that enrichment flow exists, and the enrichment iteration is performed, only if the specified intake manifold vacuum is less than the value at which the enrichment system begins to operate (commonly 6 to 7 inches of mercury.) Otherwise the flow area of element number 3 is zero and rfi is zero. e D. PRESSURE LOSSES IN FUEL CHANNEL ELEMENTS The foregoing equations express the interrelationships among the various energy quantities but they do not relate the pressure terms to the physical channel variables such as mass flow rate, element diameter, and element length. The evaluation of these pressure terms will now be considered. The evaluation of the pressure versus distance traveled along the

128 TOTAL't FU \ VELOCITY _ * _ HEAD i -c G)O I w 0 SE I~ ISTA IC: r:> FUEL _ __ AIR I Z//A MAIN DISCHARGE METERING ORIFICE ORIFICE Figure 26. Total and Static Pressure Variations Within a Simple Fuel Channel

129 fuel channel must take into consideration both the static and total pressure changes. These values are not only required for the flow channel evaluation but are very useful in comparing the predicted fuel channel pressures to actual model test data, where the pressure taps measure the static pressure at various points in the fuel channel. Figure 26 is a schematic representation of the total and static pressure variations in the fuel flowing through a simple main fuel system with 1 air bleed and 5 elements (from main metering orifice to discharge into the boost venturi.) Note that the difference between the total and static pressure at any point within the fuel channel is denoted as the velocity head and is related to the density and velocity of the fuel (or fuel-air mixture) at that point. The total pressure decreases continuously along the fuel channel while the static pressure decreases and increases at numerous points in the flow path. The static pressure will decrease markedly wherever the fluid encounters a decrease in flow area such as an orifice. Air that is bled into the flowing fuel stream will both decrease the average density of the stream and increase the velocity. This will increase the velocity head and also result in an increased slope for the total pressure curve (a greater energy loss per unit length of fuel channel.) The static pressure at the channel outlet will be the pressure that exists in the boost venturi at that position, minus the pressure differential required to lift the fuel up to the spill point which is, in inches of water, the spill point height multiplied by the fluid specific gravity. Figure 26 clearly illustrates how static pressure measurements

130 at various positions in a actual carburetor fuel channel can yield widely fluctuating values that should be corrected for local velocity effects. The velocity in channel element I will be given by: (144) m V() = (143600) ft/sec EQN 4.9 V (I) (3600)QA The velocity head of the fluid in channel element I, in inches of water, may be expressed as; VHEADW (I) = (C3)/[V(I 2 EQN 4.10 where the units conversion constant is given by: 0C3 = 4 06.406.62 (2116.6) (2.0) (32.174) The pressure losses associated with fuel flow within the carburetor are a function of element type, as well as fuel properties and mass flow rate. Within FLOW, which is the subroutine that evaluates the fuel channel flow network for any specified conditions, the type of channel element is designated by the variable CTYPE(I). This designation is as follows: C TYPE (I) = 0.0 A simple drilled passage C TYPE (I) = 1.0 A standard carburetor main metering orifice C TYPE (I) = 2.0 A square-edged orifice C TYPE (I) = 3.0 A variable area orifice For example, C TYPE (7) = 2.0 indicates to subroutine FLOW that channel element number 7 is a square-edged orifice. Thus the correct analysis

131 can be applied to that element during the iteration. For the simple passage,the total pressure loss may be divided into distinct quantities. These quantities are: 1. Entrance Losses a. Sudden contraction b. Sudden expansion c. Bends 2. Viscous Dissipation Losses a. Laminar Flow b. Turbulent Flow t Thus the total pressure loss for the I element, AP (I), may be written as: tP ( =AP AP + AP t area Pdirection friction EQN 4.11 change change One point that should be mentioned here is that sudden expansion or contraction and bend losses are systematically accounted for in this program as entrance losses. Thus the total pressure loss due to the difference in diameter between elements 8 and 9 (refer to Figure 24) is evaluated in subroutine FLOW as an entrance loss for element 9. Once it has been determined that element I is a simple passage with a given length and diameter, the entrance losses can be evaluated by using the following relationships, in which the variables have the meanings: DPENTR = Entrance loss (total) in inches of water DPW = Frictional loss (total) in inches of water CC - Vena contracta coefficient Fl = Sudden expansion or contraction factor F2 = Bend loss factor FDARCY = Darcy friction factor The total entrance loss is given by:

132 DPENTR = C3 (F1 4 F2) [V (I-)] 2 EQN 412 where the relationship for Fl is: if A(I) > A(I-1) Sudden expansion F- [1- A(I-I) 2 F1 = A(I) EQN 4.13 if A(I) < A(I-1) Sudden contraction C C ) A(I) 2 EQN 4.14 Where the vena contracta coefficient, CC, has been experimentally determined23 as: CC = 0.62 + 0.38[ A(I EQN 4.15 The value of F2, the bend loss factor may be determined by curve fitting, as a function of angle, the experimental data for KL in the equation: AP = K V 2/2gc Ad c 29 This data is available in numerous references, such as Streeter Some of the more applicable values for K are listed below in table 5, withA denoting the ratio of the bend radius to the element radius.

133 TABLE V HEAD LOSS FACTORS FOR NON-UNIFORM FLOW TYPE OF FLOW KL Smooth Bend (l = 15) 450 90~ 180~ 0.18 0.28 0.52 Smooth Bend (A = 5) 0.26 0.50 0.96 Right angle bend 1.10 Sudden expansion - A (I-1)/A(I) 2 Sudden contraction (1/cc) - 1 Standard Tee 1.5 to 1.8 Standard Elbow 0.7 to 1.0 The viscous dissipation in the passage of length L and diameter D may be obtained by evaluating the general pressure loss equation involving the Darcy friction factor. This relationship, which is actually a definition of the friction factor, is as follows: Pt d ( D) [D 2gc EQN 4.16 or in computer nomenclature, with the total pressure loss in inches of water: DPW = FDARCY * XLD (I) ][ VHEADW(I)] EQN 4.17 The value of FDARCY is dependent upon the element Reynolds number based on the diameter, D: R = 92903DV e 12) EQN 4.18

134 Where D is in inches, V in feet per second, and i is in centistokes. For element Reynolds numbers in the range from zero to approximately 2100 (the laminar range), the Darcy friction factor may be obtained 23 analytically by considering the Hagen-Poiseuille equation. This equation can be rearranged to express the mass flow rate as a function of the system variables; Ibm 3600 7T / D AP hr 128 U L EQN 4.19 This relationship can be combined with the definition of the Darcy friction factor, equation 4.16, to obtain: for R < 2100 e FDARCY = f = 64/Re EQN 4.20 d e for element Reynolds numbers greater than 2100, the friction factor must be obtained from empirical relationships. The correlating equation chosen 23 for this turbulent flow regime is: for R > 2100 e n 25 FDARCY 0.3164/(R )0 e EQN 4.21 The pressure differential across a fuel drop due to surface tension must be considered at fuel discharge points. This may be expressed in terms of the element diameter in inches, D, and the surface tension of the fuel in contact with air, X, in dynes per centimeter. Or in the usual pressure units of inches of water: A Pw = 0.000634 V /D inches of water EQN 4.22 If the element is not a simple passage, but is an orifice of some

135 type, the analysis utilized in subroutine FLOW is based upon the equations obtained in Chapter 3. Subroutine STERL is called to interpolate on the characteristic curve of the orifice for the particular element Reynolds number. After the interpolated value for Cd has been obtained, the approach area factor, which is denoted by ADUM within subroutine FLOW, is obtained in terms of the orifice flow area and the element area immediately upstream from the orifice. If A(I) is the flow area of the orifice under consideration: ADUM = 1.0 - [A(I)/A(I-1)] 2 EQN 4.23 An additional factor that is evaluated is the relationship between the total and static pressure differentials across the orifice. This factor was obtained in chapter 3 and, in computer nomenclature, may be expressed as: CDUM = 1.0 - C 2 EQN 4.24 Thus the total pressure differential for any orifice under any flow condition may be written as; DELPTW(I) = (C4) (m) (ADUM) (CDUM) DELPTW (I) 2 inches of 0p Cd w(I) water EQN 4.25 where C4 is a units conversion constant given by: C4 = (406.62) (144) (3600) (3600) (14.696) (2) (32.174) Note that this is the only equation that must be evaluated if element I is an orifice, since all pressure loss factors are included in the

136 coefficient of discharge value. The final item to be considered in evaluating the pressure losses in fuel channel elements is that of two-phase flow. This type of flow exists in the fuel channel at all points downstream from the first main or idle system bleed. The two-phase flow in the channel, as will be discussed in chapter 6, is usually in either the stratified or bubble regime. The standard correlations for predicting pressure losses with these flow types gave very erroneous values. This is in all probability due to the geometry of the channel. The short, bending passages of small diameter differ significantly from the long, large diameter pipelines from which much of the correlated data was obtained. The two alternative procedures were to utilize experimental flow channel date (which, of course, would be valid only for the geometry being used) or to use the equations presented earlier in this section, based on an average fuel-air mixture density and velocity. Since the first alternative also has the disadvantage of using data from the device that is being simulated, and thus detracts from the value of the computer predictions for other geometries, the second alternative was tried. (This method of evaluating the simultaneous flow of fuel and air was utilized by Ting in his analysis of air bleed flow.) For a given element downstream from an air bleed, such as elements 11, 12, 13, and 16 through 20 in Figure 24, the iterative mass flow rates of fuel and air were utilized to obtain a weighted average for the mixture velocity and density. The density is given by;

137 mf + ma 3 0~fa =f mi lbm/ft EQN 4.26 f + _a Of /?a and the velocity is given by: V = 144 (mf 4- ma) ft/sec EQN 4.27 fa 3600/fa A When these weighted averages were utilized in conjunction with equations 4.10 through 4.25, the resulting pressure predictions agreed surprisingly well with actual flow model data. Thus, it was not necessary to incorporate two-phase flow data into the simulation. E. FUEL-CHANNEL ITERATIVE TECHNIQUE The general iterative scheme utilized in subroutine FLOW is closely related to the actual flow situation in the fuel channel. The subroutine is called with the following quantities specified: 1. Number of elements and their type code. 2. Length, diameter, and angle of each element. 3. Fuel type and temperature. 4. The spill point and enrichment valve parameters. 5. Boost venturi suction and intake manifold vacuum. 6. Reasonable initial guesses for all system flow rates with continuity satisfied at every node point. The initial guesses are obtained by calling subroutine ASSUME (Appendix E ) with the given values of boost venturi suction and intake manifold vacuum, and are very helpful in reducing the number of iterations required. On the basis of the assumed system flow rates, the average densities, velocities, mass flow rates, Reynolds numbers, etc., can

138 be calculated for each element. The boost venturi suction is then checked to ascertain if it is sufficient to lift the fuel from its level in the air bleed well to the main system discharge point. This height is always greater than or equal to the spill point height. (With zero idle flow, the fuel level in the air bleed well is a maximum, and as the idle flow increases, this level is lowered). This means that a larger boost venturi suction is required to initiate flow in the main system. If the boost venturi suction is less than this minimum value, the fuel and air bleed flow rates in the main system elements 10, 11, 12, 13, 21, 22, and 23 are set to zero (no main flow.) It should be mentioned at this point that back flow is not considered in subroutine FLOW. This complex phenomena can occur in carburetor fuel channels under certain operating conditions, and consists of air (no fuel) flowing in the idle or main system in a direction opposite to that of normal fuel flow. After determining whether main flow exists, the next step is to check the intake manifold vacuum and determine the enrichment valve opening, A(3). If the intake manifold vacuum is greater than the opening value then the flow rates in elements 3, 4, 5, 6, and 7 are set to zero (no enrichment flow.) If the intake manifold vacuum is less than the opening value, then the enrichment valve flow area is calculated from its geometry and opening rate, and the flow rates in elements 14 through 20, plus elements 24 and 25 are set to zero. The initial guesses are then adjusted such that continuity is satisfied at every node point. The network analysis utilized in subroutine FLOW, in

139 which the iterative flow rates are always chosen to satisfy continuity, is based upon the Hardy Cross method.29 The pressure losses for each element are evaluated utilizing the equations in the preceding section. The error terms are evaluated for each system, and new values are assumed for the 13 system mass flow rates on the basis of these terms. New velocities, Reynolds numbers, densities, coefficients of discharge, and friction factors are then computed for the elements. The iterations continue until all error terms are negligibly small. At this point, all of the important fuel channel parameters have been predicted for the specified values of boost venturi suction and intake manifold. This includes: 1. The pressure loss contribution of each element. 2. The fuel flow rates in each element and system. 3. The flow rate for each air bleed. 4. The velocity, Reynolds number, friction factor or coefficient of discharge value for each element. In addition, the main and total (main + idle) fuel-air ratios can now be calculated since the air flow rates were previously determined by subroutine AIRMASand the main and idle fuel flow rates are known. The fuel channel parameters calculated for various values of boost venturi suction and intake manifold vacuum are shown in Table 6. Note that the idle flow rate is zero for the first two cases, (VACMAN = 0.22 and 0.78) and that the enrichment flow rate is zero for the last two cases.

140 TABLE EI FUEL CHANNEL ANALYSIS RESULTS INITIAL SPILL POINT = 0.30 INCHES IDLE NEEDLE SCREW TURNS = 1.25 ENRICHMENT VALVE OPENING = 6.00 INCHES HG. FOR: BVSUCW 14.19"H 20 VACMAN =0.22" HG. ELEMENT iA LBM P VELOCITY R VELOCITY DIAMETER L/D HR HEAD e 1 17.61?..4. 463 5551.4 7.94. 002 3.64 54 2 17.661 7.2~q.044 1490.3.57.IP?7 1.66A4 3 9R.14.3.27.2'- 15R.? 1.41.)810 1.'308 4 ~ I 4'4 2 21- 41 4 r. l 4.11.? q09.3125.4nn 5 8.14.41.c019 923.6.3.A 1I60?.5s0c 6 8.143.C-3.34 951 7.51.l 5C 1.52 9 7 4.071 4. 28 4.647 2?94.4 5,8.20 4. 546 R 21.732 2.551.174 2332.8 1.14.1470 6.3776 9 21.732.185.11 1178.4.29.2910.R591.1?1.73?2 1.8i..131 2170.4.99.4158 6.3 29.1 11 71.o64.l 2.121 9037.1 2.64.2700 1.;593 12 22.267.439 2.123 35763.2 16. 5.1600 5.0795 13??.267.2e1.543 lOOC.0 8.12.2250.6000n 14.%(: *.?C 0'".0.0(.0061') 31.6393 15. 0..CO.0.00.0. 00).0260 3.A077 16.OCC., O.COn.0 -."r.. 14C9 5.r'429 17.'CC.0 0..0.00 0. C 8. 2979 18.'r..'"). 0.C.0420 2.5238 19.n0.C.0.o..040 21. 7~76' 20.00r. n. C Cr. 0f.009.orC4?97.0645 21.'32 9.757 3.1 2 2145.5 122.47 r037n 3.3784 22.232 4.149 1.43 1779.9 84,2.0446.6996?3.302 14.9r9 5.366 2799.5 159.9 0.0370 3.7~38?4.o"C.'Cq.C C *..n.0280 4.4643 25. C?.00'.nr.0.no.029??.6301 FOR: BVSUCW = 9.04" H 20 VACMAN 0.78" HG. 1 13.896 1. 07 g.239 4367.8 6.25.050? 3.I 444 2 13.806 4.514.027 1172.5.45.1870 1.66a4 ___ 3 _.4P.9. 1 I8 1263.9 1.1?.nPIO 1.3 R6 4 5.498.1 47.0r 1 327.6.r.3125.O40 5 6.418.n 12. 012 656.2.31.1560?. 50r0 6 6.488.00.0?22 759.3.4 o.l50 1.525O 7 3.244 3.'.5 2.5T:) 182P.1 4.59.028s ~4.4643 8 17.140 1.613.1r8 1830.A.ot.&1470.3 776 9 17.149.115.CC7 920.4.74.2910.8591 10 17.14Cr.`47.OPI 1711.7.7P.1C8) 6.?3791 11 17.324., ^e.~76 7 00.2 2.10.770C 10. 5?q 12 17.555.?P4 1.3322 2 3144.7 12.77.16,00 5.0757 13 1.5,.17A.3C1 l C.I I C0.46.7250,.0 14.0 C *t ln:)'If 0.Io10 31.6!Ql 15.O"._ O. -n`...'.?6O 1 6177 16.Cr C" VIP * C,.C14... 00. 17."".* 0..n."n^40.S297t 17.C..0n.. 420? 2.5ZqR 19.''C.,0'.<..0 *."." (A) l.?77', 22.119., 94L 1416.o ]o.1.08.004 23 -.?41 C 0 I O?"t7..1?7.1_~.77 1.7aq 24.O' r.'.^.*') ~ 4. 4641 25.0(^ * * "~'.rr'.0.*."'O? ^.^ l 2

141 TABLE i (Continued) FUEL CHANNEL ANALYSIS RESULTS INITIAL SPILL POINT a 0.30 INCHES IDLE NEEDLE SCREW TURNS - 1.25 ENRICHMENT VALVE OPENINGs 6.00 INCHES HG. FOR: BVSUCW 5.04"H2 0 VACMAN ~ 7.78" HG. ELEMENT M-R P HEAD R VELOCITY DIAETER L/D 1 11.21 1.5. 41! 3?.? 5.. 2',. 4SO.0504JL 2 11.21 2.941.^1 94f.3 3..11TO 1.664 3.rr. "'^<".r 172??2.r.' I l7 1? 1 4. C.^1C C^ 19? 25.4 S.(OU.^')5."' 394.5.n5.*'^ 7?. S^" 6.~''0 *..C,' 444 3.0).l[ C 1.S?)t 7 71'( r*.^',I 1"71.2 * v * t 4. - 44 3 11.215.C`.'4 17'. - 8 5o.1471,. 37?) 9 11.21.21 4n.^03 6.1 l 2910.49l 10 9.042.22. 9.03..41.l P F 6..l 92? 3.?."?3 *33:. 9 1.74.7 1'.;5' 12.4 1.13.r 4 "47.5 1^" 7.1600 5.?s' 13 Q 410."^q.l 13C^" ^.".4.2?5.S^ 14 2.173.2'4.C 567.1. * 1 l 3361.'393 15 2.173 1.792 1.7' 131R.7 3.64 23260 3.,77 16?.17 3.? ^.0:C2 744.9 13 14 5.'4s9 17 )2 299.11.465 154"?.4 11.77.,^44 8.979 i 2.209 1 11.C; q.1.677 ln'r.O R.O4? 2.?39? 19 2.557'.6' 1.561 46491." 35e.r'94r 1.?766 20 2 557 4r.779 4.?4 1 n'). 0 iP..n 41 7 2.541'?1.161 3.^91 1.514 14 37.? 94.99.C37 3.37R4 22.161 1.464.717 1)33. R.P4?. 446,604 23.2"7 5.139 2.517 1917.4 1"9.4i.4C'7 7 3.7893 24.126 6. 30 2.7. a 1521.7 114.79. I2R? 4.4043?5.25 P 23.139 1".0or 3n16.7?1. 1 2 -?a 3.631n FOR: BVSUCW 0.47"HaO VACMAN 21.78" HG. I 4.1 1.37n.467 1304.7 1.7. 5 n2 3.64,54 72 4. 11.4^3. C2 3e5.3.13.1870 1.66R4.3. P.r.'.r -.n 71722.2."?. r'4 297. 64' 4 r.r...^192.0..312.F)k 5.0C.^"'.Cr' 3R4.5.0 ).1r6) 2.50"' a * r.^*'.,r^ 444.3..1359 1. i2Q 7.*^ >," *, 1.0 71. 2.R.C24 4.464? s. 151.)6.C6 445.6.2.1470 6.3776 9 4. 51i. 7.^"' 225.1..2915.so91 10.Cf0 * ".0"" 93.5.03.15O0 6.3291 11.'0r. 0o.r r,- 2 996. 2.0. 7700 1.2593 12 *'I.0, 2 I799.2 ^.160 * C073I 13 r~^ r ^ ^ r r. f.' 7679 4.4 22. O9'0 14 4.151./-4.214 1"73.7 1 312.010 16393 15 4.151 h6. 54?.4c7 2519.1 6.9?. 6"' 3.677 16 4.151 1.94o.r'- 4 467.q.24.l&4O's44'9 17 4 2'P? 257 1.174?0 QC.C l. O7.0)940 ).29q7 18 4?. 2?q.43P 2o.42 1'OC.O 7 Q 2'42^ 2. 73 1 46.,?? 7. 69^ 4.'1 76Z'3.5 5Al 47.C4, )? 71.7 2n A llC 14 9. 57n l.4.q6 7 7^C. 9l6 274 I'7l? 21.,!,.r'cO 7r55.3.r. ^^ 3 3374q.0'~~t7 nr 5S. 3 ~ 4,IS 6% qe 73."'r.e'l. "'. 9'..6 (370 3 7',R8 24.117 7.7''?.6?7 14?.q Itl.6.^?qO9 4. 4,4 2'.3 5,.0^? 7 16. t ^ 9" q0.4 2 7.'."?9? 7.,3o1

CHAPTER V ENGINE AND VEHICLE ANALYSIS A. REASONS FOR RELATING TIE ENGINE AND VEHICLE TO THE CARBURETOR In this chapter the engine and vehicle parameters related to the operating point of the carburetor will be analyzed. There are sound reasons for performing this type of analysis within the framework of a carburetor simulation. The first reason is that carburetor operation is directly related to certain engine parameters, as was discussed in Chapter 2. Thus, in the rigorous sense, the carburetor must be analyzed with these interrelating engine parameters taken into consideration. Another important reason for relating the engine and vehicle to the carburetor is that the value and application of the simulation is greatly extended. This results from the fact that in numerous tests, carburetor performance is evaluated on the basis of engine or vehicle data such as brake specific fuel consumption, fuelair ratio, and miles per gallon. Therefore, it would be very advantage - ous to be able to predict many of the important engine and vehicle parameters along with those associated with the carburetor It should be obvious that the carburetor simulation program would represent a much more powerful evaluation tool if the effect of any one carburetor variable on the engine brake specific fuel consumption or the vehicle miles per gallon could be predicted analytically, 142

143 This would allow the simulation program to evaluate a proposed carburetor design on the basis of predicted results for numerous standard tests. The engineer would then be able to evaluate the design not simply on how it will perform at various air flow rates, but also on the basis of what specific fuel consumptions and miles per gallon would be expected over a wide engine or vehicle speed range. B. REQUIREMENTS FOR ROAD LOAD CARBURETOR ANALYSIS The key to relating the engine and vehicle to the operation of the carburetor is to relate the respective operating points. The vehicle operating point may be based on many considerations, the most important of which is probably that of road load operation. This is defined as vehicle operation under conditions such that vehicle speed is maintained at a specified velocity, V, on a level roadway with no prevailing wind. These conditions are then referred to as those corresponding to the road load at the velocity, V. One of the most important operating lines to consider is that given by the locus of all vehicle road load operating points, which is the road load curve for a given carburetor or engine parameter. The basis of this importance is that the carburetor-engine operating points (which are combinations of throttle angle and engine speed) will be on or near the road load operating curve the majority of the time. In order to evaluate carburetor performance at points which correspond to operation along the road load line for a given vehicle and

144 engine, the vehicle velocity must first be related to the carburetorengine operating point. This means that the engine speed and throttle angle corresponding to a given vehicle velocity, V, must be ascertained before road load carburetor operation can be simulated. Obtaining the engine speed in terms of the vehicle parameters is reasonably simple, but determining the throttle angle corresponding to road load operation for a specified vehicle velocity is much more involved,as will be evident later in this chapter. C. VEHICLE ROAD LOAD RELATIONSHIPS In the relationships presented in this section, the following variables are defined as: V Vehicle velocity in miles per hour Af Vehicle frontal area in square feet ROLL Rolling resistance coefficient DRAG Drag resistance coefficient WEIGHT Vehicle weight in lbm BHP Required engine brake horsepower RHP Road (rear wheel) horsepower N Engine speed in revolutions per minute Ntire Tire revolutions per mile Gd Differential gear ratio Gt Transmission gear ratio C1,2,3 Correlation constants Ad Total drive train efficiency In terms of the specified vehicle parameters, including the differential and transmission gear ratios along with the tire revolutions per mile, the engine speed is; N = Ntire Gd GtV/60.0 EQN 5.1 therefore the engine speed corresponding to any vehicle velocity may be obtained by using the above equation. The road or rear wheel

145 horsepower that is required for a specified vehicle at a velocity, V, may be obtained by a suitable correlation of vehicle proving ground data. There are numerous forms of this correlation available, and the relationship utilized in this simulation is: RHP = (ROLL'WEIGHT + DRAG * A V2) (V/375) EQN 5.2 The rolling and drag resistance coefficients are obtained by curve fitting actual vehicle road horsepower data. Representative values for a typical American sedan are: ROLL = 0.0150 DRAG = 0.00125 These values could be used as an approximate representation of the road horsepower requirements for a vehicle if actual proving ground data were not available. The engine brake horsepower that is required at any vehicle speed is a function of the road horsepower and the total drive train efficiency. This efficiency, expressed as a fraction, indicates the fraction of the input power that is dissipated in the entire drive train as a function of the vehicle velocity. This must also be obtained by correlating actual vehicle data for these power losses. The correlating equation used to describe the drive train efficiency of any vehicle is of the form: fd = C1 - V/C2 + V2/3 EQN 5.3 Typical values for the three constants in the above correlation are: C1 = 0.86 C2 = 1210.0 C3 = 333300.0

146 Thus the brake horsepower output (of any engine) that is required to maintain a specified vehicle velocity may be written as: REQUIRED ENGINE BHP = ROADHP/qd EQN 5.4 The engine speed and required engine brake horsepower have now been expressed for any vehicle velocity in terms of the vehicle parameters only. (No engine or carburetor parameters involved.) The next step in the analysis, that of determining the specific operating point of a certain carburetor and engine that corresponds to the above vehicle velocity, is a complex one. There are an infinite number of combinations of throttle angle, engine air flow, and fuel-air ratio that will satisfy the vehicle road load requirements (a specified engine brake horsepower output at a specified engine speed). The complexity of this situation can be illustrated by considering the throttle angle required to produce 20 engine brake horsepower at a vehicle velocity of 25 miles per hour. (Assuming for the moment that this is the road load requirement for the specified vehicle.) The engine speed is therefore fixed and is related to the vehicle speed, tire revolutions per mile, differential gear ratio, and transmission gear ratio. The required engine air flow and throttle angle will be very dependent on the particular carburetor geometry and the manner in which the performance of the particular engine that is being used is affected by the overall fuel-air ratio. If the specified carburetor geometry is such that the fuel-air ratio curve is generally very rich, (as would occur if the main metering orifice diameter were large) and the engine

147 performance was poor at these overall fuel-air ratios, then a large air flow, low manifold vacuum, and hence a large throttle angle would be required. If the carburetor design, as specified by all the dimensions on the input data cards, were such that the resulting fuel-air ratio curve was in the range which yields high engine thermal efficiency values, then the required engine air flow and carburetor throttle angle would be much less. If the carburetor design being evaluated produced fuel-air ratios that were outside the flammability limits of the engine (richer than the rich limit or leaner than the lean limit) then the engine brake horsepower would be zero or negative for all air flow values. In this case even wide open throttle angles would be insufficient and road load operation could not be maintained. The above examples were cited to illustrate that the road load operating parameters will be affected by a large number of vehicle, engine, carburetor, fuel, and ambient variables. Each proposed carburetor design and fuel type will result in a particular set of fuel-air ratio values. Each engine will utilize these fuel-air ratio values in a different manner, producing a particular set of brake specific fuel consumption curves and exhibiting a variation in performance with fuel-air ratio and speed that is particular to that engine. The road load requirements themselves will vary with the particular set of vehicle variables that are being used. Thus the complete simulation results for a road load carburetor analysis apply to one particular carburetor-enginevehicle combination. This is especially valuable for evaluating

148 variations in carburetor operation due to mating with various combinations of engine and vehicle. D. CORRELATION AND PREDICTION OF ENGINE PERFORMANCE It is evident from the above discussion that in order to analyze carburetor operation at road load operating points, the brake horsepower output, as well as numerous other engine operating parameters, must be known for any engine speed, throttle angle, air flow, mainfold pressure, and fuel-air ratio. This would obviously involve the determination of a tremendous amount of actual engine data if a universal correlation were not utilized. In addition, it would be quite advantageous to obtain most of the engine brake, indicated, and friction variables during the road load analysis. These important engine parameters are listed below with their corresponding symbols. IHP Indicated horsepower BHP Brake horsepower FHP Friction horsepower IMEP Indicated mean effective pressure in psi BMEP Brake mean effective pressure in psi FMEP Friction mean effective pressure in psi ISFC Indicated specific fuel consumption in lbm/IHP hr BSFC Brake specific fuel consumption in lbm/BHP hr THERMI Indicated thermal efficiency in % THERMB Brake thermal efficiency in % TORQI Indicated torque in foot pounds TORQB Brake torque in foot pounds TORQF Friction torque in foot pounds One important goal in finding a universal engine data correlation technique was to be able to determine all of the above parameters for a particular engine for any engine speed, intake manifold pressure, air

149 mass flow rate, and fuel-air ratio, without conducting the hundreds of dynamometer tests that would be required. It was felt that in order to make the road load carburetor analysis feasible in an actual case, not over 2 dynamometer tests should be required to generate all of the needed data. No suitable correlation technique could be found in the literature, therefore a significant effort was expended to develop a method which would enable the computer to develop complete engine data maps from the results of two dynamometer tests. This technique was successfully developed and is based upon the following logic: It is well known that, all other quantities being equal, the indicated horsepower of an engine is proportional to the air mass flow rate supplied to that engine. This is illustrated very well in figure 27, which is a plot of the results of approximately fifty engine tests for a specific engine (Ford 289 cubic inch V-8) over a wide range of speed and load conditions. The indicated horsepower is linearly related to the air mass flow rate by means of the slope of the line. A very important point to emphasize here is that the fuel-air ratio for these runs was always near stoichiometric. If the fuel-air ratio were to nominally be some other value, there would be no reason to expect the slope to remain the same. In fact, if the fuel-air ratio supplied to the engine were to be outside its particular flammability limits for spark ignition, the indicated horsepower would be zero for all values of air flow. (This is what occurs during a motoring test.) In those cases the proportionality constant would be zero. For fuel-air ratios near the

C O~~~~~~~ a gs 0 / w Ia: (3L'-.8 S".____ _____ -_____ ___ ___ eJ J *.00 50.00 100.0 li0.0 150.00 200.0 ~ 0.0 300.G 36i0.00 400.00 450.00 500.00 550.00 600.00 650.00 700.00 MERSUAiEDRIRFLOWRATEINLBM/HQUR _ Figure 27. Dependence of the Engine IHP on the Air Mass Flow Rate cccv C:oJotCo3 ^ g, ___ ___ ------------------------ y L —----------------------------------------------- CE ~y U —^ —-- S IT ^ - -^ —----------- - 8 _ _ _ _ _ _ _ _ _ _____________ s-7^ —----------— MO,.00 50.00 100.00 150.00 200.00 250. 00 300.00 360.00 400.00 450.00 500.00 550.00 600.00 650.00 700 MEAlSURED AIR FLOW RATE IN LWMHOUR Figure 2 7. Dependence of the Engine IHP on the Air Mass Flow Rate

151 maximum power value of approximately 0.085, the slope will be a maximum, indicating that the greatest indicated horsepower per unit air mass flow rate is being obtained. For all other fuel-air ratios, both richer and leaner the slope will be less, finally reaching zero at the lean and rich limits. Since this suggested a possible technique for correlating engine data on the effect of fuel-air ratio, many engines tests were conducted at various nominal fuel-air ratios to determine the variation in this slope. Some of these test results are plotted in Figure 28, which has precisely the same coordinates as Figure 27. These curves were obtained by overriding the normal operation of a carburetor by applying an artificial pressure or vacuum to the float bowl until any desired fuelair ratio was obtained. (The test equipment and procedures will be discussed in Chapter 7. This discussion will only be concerned with testing relevent to the development of the engine data correlation.) Note that the slope of the curve for a fuel-air ratio of 0.061 is very close to that in Figure 27, since 0.061 is also near stoichiometric. The fuel-air ratio of 0. 080 yields a significantly greater slope than the test series conducted with the 0.061 fuel-air ratio. It is also evident that the rich (0.103) and lean (0.054) fuel-air ratios resulted in much lower slopes than those of the tests utilizing fuel-air ratios near the power ratio and stoichiometric. At fuel-air ratios richer than 0.103, and leaner than 0.054, the slope decreased rapidly. The significance of this slope becomes evident if one considers a constant air flow value.

.8_ -MEA SRED FUEL AIR'R'' 1 00 Vol CIaU''.00 50.00 100.00 150.00 200.00 250.00 300.00 O. 00 400.00 450.OC 500.00 550.00 600,00 650.00 700,00 MEASURED RIR FLOW RATE IN LBM/HOUR Figure 28. Slope of the IHP Curve as a Function of Fuel-Air Ratio

153 If the air mass flow rate to the engine is maintained constant in some manner while the fuel-air ratio is varied from zero to a value greater than the rich limit, the indicated horsepower will increase from zero, reach a maximum at the power ratio (which changes with air flow rate), and then decrease to zero again. The exact manner in which this occurs is particular to a given engine. If many such tests are conducted at various nominal air flow values, the results will be as shown in Figure 29. Note that the indicated horsepower decreases rapidly at fuel-air ratios less than 0. 050, indicating a lean ignition limit of around 0. 040. (This will in fact be a slight function of the air mass flow rate.) The curves also tend to flatten out for the lower air flow values, indicating less of an effect of fuel-air ratio on engine operation. If Figures 28 and 29 are studied carefully, it will become evident that each is merely a cross section of a general 3-dimensional plot which describes the entire operation of the engine. An approximate sketch of this general plot is given in Figure 30. Note that Figure 28 may be generated by taking cross-sections of this volume at various fuel-air ratios, and that Figure 29 may be generated by taking cross sections at various air mass flow rates. The importance of this concept, along with the linearity of the indicated horsepower versus air mass flow rate curves, is that only two dynamometer tests need be run to establish the entire surface of Figure 30 which represents the variation in indicated horsepower (for that particular engine) for all possible fuel-air ratios and air flow rates. These two tests consist of two con

g ~1 —- _____ _____ _________________ COh STANr cg aS2~'. ~ ~ ~~~~~~~~~~~~~~~2 I / - 8 200 *.00 10 0, 30.40,50.60,70.80.0 1.00 1.10 1 1.20 1.40 OVERFiLL FUEL-AIR RFiTIO iXO1 Figure 29. Constant air flow curves':'-or varying fuel-air ratios

155 IHP -^.../3.AIR FLOW V\^~ — I M ~ iT,''LEAN 1/Figure 3. Three-dimensional opeRIating surface for a engine 2 L'IMT Figure 30. Three-dimensional operating surface for an engine

156 stant air mass flow rate tests such as the 200 and 432 brrm/hour curves shown in Figure 29. After the fuel-air ratio has been varied over the entire range from the lean to the rich limit and the indicated horsepower has been determined at each fuel-air test point, the IHP can be calculated for any other fuel-air ratio and air mass flow rate. This is accomplished by first supplying the computer with the IHP versus F/A data points for both air mass flow rate values, (two data sets) which will be denoted by AIRFL1 and AIRFL2. Then the indicated horsepower corresponding to each air flow rate for the desired fuel-air ratio is determined by calling the generalized interpolation subroutine STERL for each data set. These two indicated horsepower values corresponding to the desired fuel-air ratio will be denoted as XIHP1 and XIHP2. Since the curves are linear for all air flow rate values, the slope may be calculated by utilizing the following equation: SLOPE = XIHP2 - XIHP1 EQN 5.4 AIRFL2 - AIRFL1 It was not found necessary to restrict the IHP versus air flow rate curve to pass through the origin. (In much of the data,the curves tended to intersect the air flow axis at small positive values such as +20 Ibm per hour.) Thus the IHP relationship was left in the more general form; ~ Ibm mair our + IHP/SLOPE EQN 5.5 where A0 represents the air flow rate at which the curve would intersect the axis if extended. This value may be expressed as:

157 Ao = AIRFL2 - XIHP2/SLOPE EQN 5.6 For any desired air mass flow rate value, denoted as AIRFLO, the corresponding indicated horsepower value is given by the relationship: IHP = (AIRFLO - AO) (SLOPE) EQN 5.7 Once the indicated horsepower has been determined for a specified fuel-air ratio and air flow rate, all of the other indicated engine parameters can be readily obtained. If the engine speed in revolutions per minute is denoted by N, the displacement in cubic inches is D, and the fuel mass flow rate in Ibm per hour is rmf, the indicated torque, specific fuel consumption, and mean effective pressure are; IMEP = (5252.0)(150.8) IHP/(N)(D) psi EQN 5.8 ISFC = [mf/IHP] lbm/BHP hr EQN 5. 9 TORQI = (IMEP)(D)/150.8 ft lbf EQN 5.10 where the fuel mass flow rate is given by: nf = (AIRFLO)(F/A) lbm/hr EQN 5.11 The engine friction and brake values must now be obtained in terms of the indicated values and the friction parameters for any engine that is being utilized. The important point to note here is that the friction values (torque, horsepower, and mean effective pressure) are functions of the engine speed and intake manifold pressure for a given engine. The variation in these frictional values must be correlated for all possible engine speeds and intake manifold vacuums, since any combination might have to be evaluated during a carburetor simulation run. The goal of this study was to find a correlation technique that

158 could be easily implemented using friction data obtained from a simple test or tests, preferably tests that could be performed during the IHP tests discussed previously. A successful technique was found to simply correlate the variations in engine friction with intake manifold pressure (pumping work variations) and with engine speed. This correlation can be obtained from two simple motoring tests on the dynamometer, and is conducted in the following manner. With the engine at a normal operating temperature, the engine is motored with the throttle wide open to give a very low intake manifold vacuum and consequently a minimum pumping work situation. The engine speed is varied from zero to the upper limit of the operating range, with friction load values recorded at suitable speed increments such as 500 RPM. This test run is then repeated with the throttle plate completely closed, which provides a maximum intake manifold vacuum and maximum pumping work situation. When the friction data are converted to mean effective pressure values by using the equation; FMEP = (150.8)(TORQF)/D psi EQN 5.12 the values for a particular engine are as shown in figure 31. The lower curve, which corresponds to the minimum pumping work situation, is denoted as the FMEP1 data set, and the upper curve is the FMEP2 data set. All possible friction values will lie on or within the region bounded by the two curves. If the intake manifold vacuum is increased as the engine speed is kept constant, the friction mean effective pressure

159 -W.- -F - -~ ~ ~~~. --- -, -U i. - ~ ~ I T - -~ -,- it ~ 4 i 4 414 4+ j~''I-,',-" —7 i I —-I - " -- —!- 11 —, - -~ 1,I'4-'I''- -I-H r-1 j-t 14-i- -1i 14" 4 1~- " 1- 441 - I -- 4 4 i-~7I I i7 I4- -1 —4 —-" I. "' ---. I~i -, - - ~'-.j4-t''iL''-__'-:I -4 ti'-4- 1 41 -i - I - i 1; 1,,k,~ ~ ~ ~ ~ ~ ~~~~~~~~~~~~~~~~~i'''' - 4 -'I i 7- i - -1 i',;T -, I - -I _ K I 1 2! L K - ~II 1 U' ~ 4- - I2ii: Ij~I - I. — I'' -- UTT7IL;~~~~~~~4 ~ 1 U ~TI1 4'Ii:I 4 j~ 4 44"- 1:- 241 4 - 44 V - ~ ~ -.- A'4'I I.4} %4I 1,. 44'' A —~ -Iii, i -- - - -- N i, - -- " 2 41 i' 4- - I 4-,IT f -. ~ _ _ I I 4 4 I I' -4 I' - 1 1 1 B'f I i t A N 4 I -.I- 4 44!- 1 & " 5 44-4 + j — >I I iI —ft4, -, i i ~.. I-i,- ~.,j 1 ". t-'-""4'~I l44 j4P~ I ~- ~,-i -:~~~,4-4,tj'q''-ti LI4 V 11 -.- A- -I 1I'1- 1' 4-~~~1.- I.~~~~' - -— ~ ~ ~ ~ ~ ~ ~~~~~,-.~~~~~ ~~~~ —1 - ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ -. III~~~I -t Fi ur 3IM E V r at o n it e g n e sp e 7TI-rt~..IIand intake manifold vacuum

160 will move from the lower curve value toward the upper curve. The determination of the engine frictional values is quite similar in form to that utilized in obtaining the indicated values. If the engine speed and intake manifold vacuum are specified, the generalized interpolation subroutine STERL is called to return the upper and lower curve values for the given RPM, which are denoted as FMAX and FMIN. Then the FMEP corresponding to the actual intake manifold vacuum is obtained by noting that the pumping work will be proportional to the intake manifold vacuum at a given engine speed. or: VACMAN p FMEP = FMIN + (FMAX - FMIN) [POHG - 3.0 EQN 5P 13 EQN 5.13 In equation 5.13 the symbol POHG denotes the atmospheric pressure in inches of mercury, and the value 3.0 represents a very good approximation to the absolute intake manifold pressure (in inches of mercury) when the throttle is completely closed. Once the friction mean effective pressure has been obtained, all of the important friction and brake values can be calculated from the following equations: FHP = (TORQF)(N)/5252.0 EQN 5.14 BHP = IHP - FHP EQN 5.15 BMEP = IMEP - FMEP psi EQN 5.16 BSFC =[mf/BHP] lbm/BHP hr EQN 5.17 THERMI = 2545.0/(ISFC)H, EQN 5.18 THERMB = 2545.0/(BSFC)Hc EQN 5.19

161 Where H is the lower heating value of the fuel being utilized. By c utilizing the above relationships in conjunction with the carburetor analysis, nearly all of the'important operating variables of numerous standard tests can be predicted. E. SUMMARY OF ENGINE DATA CORRELATION TECHNIQUE An accurate method of correlating numerous engine operating parameters on the basis of two simple dynamometer tests was developed for utilization within the simulation program. This correlation technique is not an engine simulation, but merely provides a method for efficiently employing actual engine data for the particular engine that is being used. Strictly speaking, the actual engine IHP data should be obtained using the same fuel, fuel temperature, and inlet air temperature as will be specified in the carburetor simulation. In the practical sense however,it was found from numerous engine tests that the indicated horsepower curves for a given engine are affected only slightly by variations in fuel and air temperature and gasoline brand. Thus, unless the fuel to be specified in the simulation differs markedly from that used to obtain the IHP data, or unless the temperature values to be specified differ greatly from those of normal test cell conditions, the IHP curves may be used as a good approximation of engine performance under many specified simulation conditions. The FMEP curves are are affected even less than the IHP curves, therefore they may be used for all simulation runs.

162 Four parameters must be specified with this method in order to obtain values for all of the engine operating parameters listed in the preceding section. These are: 1. Engine speed 2. Dry air mass flow rate 3. Intake manifold vacuum 4. Total fuel-air ratio This corresponds very well with the carburetor simulation since subroutine AIRMAS predicts all mixture flow rates and the intake manifold vacuum. Then, after the carburetor parameters have been analyzed and predicted in the simulation (including the total fuel-air ratio), the analyses presented in the preceding sections are utilized to determine how a particular engine would perform for the predicted carburetor behavior. The method of acquiring data along constant air flow rate curves with varying fuel-air ratio, and the general correlation technique both have numerous other applications within the automotive industry. Figure 32 illustrates the significance of lines and points when the indicated (or brake) horsepower data are obtained along constant air mass flow rate lines and are plotted on the coordinates shown. Note that the fuel rate will be exactly linear and that a straight line through the origin that is tangent to the IHP (or BHP) curve, as denoted by point A, will be tangent at the point of minimum indicated (or brake) specific fuel consumption. Any other straight line through the origin will intersect a constant air flow rate at points of equal specific fuel

163 IHP (OR BHP) CURVE FOR A CONSTANT AIR FLOW RATE HORIZONTAL TANGENT LINE/_ D S.//! ^^^ ^^j~~ POINT A IS 0X: ^^ / ^^ \ ~~TH4E MINIMUtM Soa~~~~~ <y / \ISFC (OR BSFC),/ MAX. MAX. \ / /' / ECONOMY POWER RATIO RATIO.00.02.04.06.08.10.12.14.16 FUEL-AIR RATIO Figure 32. Applications of constant air mass flow rate curves

164 consumptions, as shown by points B and C. A horizontal line that is tangent to the curve (point D) will do so at the fuel-air ratio which represents the maximum power ratio for that particular engine and air flow rate. The general data correlation analysis has application wherever numerous engine parameters must be known over the entire operating range. F. ITERATIVE TECHNIQUE FOR OBTAINING ROAD LOAD OPERATING POINTS The engine data correlation technique, when combined with the road load considerations of the vehicle, makes possible the analysis of the carburetor at operating points which correspond to road load conditions for the particular carburetor, engine, and vehicle combination. Since the carburetor design is analyzed on the basis of specified operating points which are determined by engine speed and throttle angle, these parameters must be specified before the carburetor analysis is performed. The engine speed corresponding to any vehicle velocity may be calculated directly by means of the equations in section 3c, but the throttle angle corresponding to a given road load situation is much more difficult to obtain. This throttle angle is the one which will yield the fuel-air ratio, intake manifold vacuum, and air mass flow rate that results in the required brake horsepower. Therefore,the following iterative technique is utilized in obtaining the correct throttle angle and the resulting analysis for the road load conditions:

165 1. The vehicle velocity is specified and the corresponding engine speed and required engine BHP are calculated. 2. A reasonable initial guess is made for the throttle angle, thus the operating point is specified. 3. A complete carburetor analysis is performed utilizing all the relationships presented in the preceding chapters. This results in an air mass flow rate, intake manifold vacuum, and total fuel-air ratio. 4. Now the four parameters needed for the complete engine data calculations are known. Therefore all of the engine parameters presented in this chapter may be calculated, including the brake horsepower output. 5. If the engine BHP output for the assumed throttle angle is not equal to the required road load BHP value, a new throttle angle is assumed according to the general convergence technique (Appendix G) and the magnitude of the difference. 6. Another complete carburetor analysis is performed and the new engine brake horsepower output is calculated. This continues until convergence is obtained or the iterative throttle angle exceeds 90~. The later indicates that the given carburetor-engine combination cannot provide the road load requirements of the specified vehicle and velocity. This procedure can be applied over the entire velocity range from zero to the maximum value. In the carburetor simulation, if an analysis is requested under road load operating conditions, the above procedure is utilized at 5 miles per hour increments until the maximum vehicle velocity is reached, which corresponds to a throttle angle of 90~. Typical IHP, FMEP, and vehicle input data, as well as the computer output for a road load analysis will be presented in Chapter 8. Once the throttle angle iterations have converged to the road load value, the vehicle miles per gallon can be calculated for each

166 velocity from the equation; MPG = (231.0) Av EQN 5.20 (1728.0) (BSFC) (BHP) thus, for any proposed carburetor design, the results of steady speed fuel economy tests can be predicted, as well as the results of numerous engine tests.

CHAPTER VI ON-ENGINE CARBURETOR TESTS A. REASONS FOR TESTS Numerous dynamometer tests were performed on specific carburetor-engine combinations during this project. These tests were carried out for many important reasons, the first of which was to obtain a general understanding of the processes that occur within the carburetor over a wide range of operation. Another basic reason for conducting the on-engine carburetor tests was to obtain precise data for use in developing the engine data correlation technique which was presented in the previous chapter. One of the most important reasons for conducting these tests was to obtain accurate data on the performance of individual carburetor systems. These data, such as the variation in metering signal with air mass flow rate, the choked mixture flow rates at various throttles angles, and the minimum air flow values for completely closed throttle angles, were necessary to check the analytical predictions of individual computer subroutines, as well as the complete simulation. Thus, it was possible to debug each subroutine separately and to assure that the analytical predictions were in good agreement with actual data before combining all subroutines into one carburetor simulation. 167

168 B. BACKGROUND Some experimental data on the effect of specific carburetor operating variables may be found in the literature. The data that have application to the overall computer simulation and the associated carburetor-engine test program will now be discussed. In the area of overall carburetion, the problems of enrichment with altitude, variation in fuel/air ratio with fuel properties, and enrichment under deceleration are of current interest. This is mainly because of the air pollution problem and the relation between variations in mixture ratio and the emission of unburned hydrocarbons. Bolt and Boerma44 studied the effect of altitude on the mixture ratio delivered by three different carburetors. They showed a definite enrichment of the mixture with a decrease in ambient pressure, amounting to a 30% enrichment at an inlet pressure of 18.0 inches Hg. absolute. They also derived a theoretical enrichment equation: F/A* i P a F/A* ^ I/ air JrF/A* - * V /~aiEQN 6.1 F/A = /Oair where S is a compressibility parameter and the * superscript denotes the reduced pressure conditions. This equation gives a reasonable correlation of the experimental data down to inlet pressures of 20 inches of mercury absolute. In the derivation of the equation, some terms had to be neglected due to lack of information. This included the manner in which fuel channel frictional pressure losses vary with flow rate and the variation in the main metering orifice discharge coefficient as a

169 result of changes in venturi suction. Wahrenbrock56 discussed the effect of fuel density variations on carburetion. The actual test data involved on-engine determinations of the fuel-air ratio for ten different fuel types. These fuels ranged from toluene to catalytically cracked fuels, and represented a density range from 31.6 to 71.9 A.P.I. degrees. Two carburetor types were tested at various throttle settings. The data showed an increase in the fuel-air ratio for increasing fuel density, however the effect was not large and the scatter was quite pronounced. A very simple analytical equation, relating the fuel-air ratio to the fuel specific gravity, was obtained for the special case of constant air mass flow rate: F/A = constant SGful EQN 6.2 However, the assumption of constant coefficients of discharge with increasing fuel flow rate, and the fact that the constant in equation 6.2 involves many complicated factors, reduces the validity of the equation. Also neglected was the fact that all of the metering signal is not lost across the main metering orifice in an actual carburetor. The analyses presented in the preceding chapters should convey the fact that the fuel-air ratio cannot be expressed simply as a function of specific gravity alone. Numerous other factors such as the viscosity of the fuel must be considered since the viscous pressure losses in the fuel channel are related to viscosity. In fact, for a given fuel,a decrease in specific gravity due to a temperature increase will be accompanied

170 by a reduction in viscosity. Thus, an important effect that is not considered in equation 6.2 is the change in the coefficient of discharge of the main metering orifice with viscosity. The experimental data due to Goetsch, et al,47 provided a useful reference because the carburetor used in the study was one of the types used in this experimental program (Ford C4AF-DE). The data included fuel-air ratio versus air mass flow rate, as well as pressure differentials at various locations in the carburetor fuel channel, including: 1. boost (secondary) venturi 2. main metering orifice 3. fuel discharge nozzle The fuel specific gravity and viscosity were not given, nor was the fuel temperature, nevertheless the experimental trends shown in the report provided useful comparisons with the data obtained in this project. Additional experimental data on the effect of fuel type on overall carburetion was given by Smith.51 The tests were concerned with the separate effects of changes in specific gravity, viscosity, and vapor pressure. The results were as follows: 1. Increasing the fuel specific gravity from.70 to.74 increased the fuel mass flow rate 2.7%, and decreased the fuel volume flow rate 2.7%. 2. Increasing the kinematic viscosity from 0.582 to 2.35 centistokes by using eight different fuels gave a fuel mass flow rate decrease of about 1.0% per 0.1 centistoke increase. By using fuels with the same specific gravity but viscosities from.730 to 8.30 centistokes, a mass flow rate decrease of 0.4% per 0.1 centistoke change was obtained.

171 TABLE VII EQUIPMENT UTILIZED IN ON-ENGINE CARBURETOR TESTS CARBURETORS Ford C6AFB-C6FC 2-barrel Ford C6AF-9510-B 2-barrel Rochester 2MV 2-barrel Rochester 4MV quadra et model 7027135 Ford C4AF-9510-DE 2-barrel Ford C7AF-9510-BZ 2-barrel Carter YF single barrel ENGINES 1966 Ford 289 cubic inch V-8 1967 Chevrolet 283 cubic inch V-8 INSTRUMENTATION General Electric dynamometer model 26G51 Meriam micromanometer (10 inch) model A-750 Meriam manometer (30 inch) model 30W King manometer (6 tubes-60 inch) model ASC 6FF30 Honeywell 8 channel Visicorder model 508 General Motors standard air orifice plate (5 hole) Hewlett-Packard automatic fuel burette system model 521A Neslab constant temperature bath model PBC-5 Statham strain gage pressure pickups (~ 2.5, ~ 5.0, O 15.0 psi) Beckman-Whitley movie camera (3000 frames/sec) Brown Instruments multi-point potentiometer model Y156X62-P18 Carrier strain gage amplifiers Tectronix dual beam oscilloscope 502A Honeywell galvanometer amplifier

172 The viscosity effect seemed to be reduced at higher orifice pressure differentials but this was not investigated in detail. The test procedures, engines, carburetors, and orifice types were not given, thus the value of the data is significantly reduced. It may be that for a different orifice type the trend would be just the opposite. C. EXPERIMENTAL EQUIPMENT AND CONDITIONS The on-engine carburetor test program was conducted at the University of Michigan Automotive Laboratory. A large number of tests were made utilizing various test conditions, carburetors, fuels, and engines. The bulk of the tests were performed on two-barrel, airbled, fixed venturi carburetors using gasoline as the fuel. However other carburetor types and fuels were also tested. The equipment and instrumentation used in these tests consisted of the items listed in Table 7. Note that in addition to the normal air rate, fuel rate, and load measuring devices, numerous special items such as strain gage pressure transducers, a high speed movie camera, and a constant temperature bath were utilized to obtain additional information on carburetor operation. Tests were performed on both a 1966 Ford 289 cubic inch V-8 engine and a 1967 Chevrolet 283 cubic inch V-8 engine, with the majority of the tests being run on the Ford engine. Various standard and modified carburetors were tested on these engines. The modifications consisted of such items as:

173 1. Internal pressure transducers installed 2. Enrichment system made inoperative 3. Idle system and air bleeds plugged 4. Float chamber pressurized 5. Choke and acceleration pump removed 6. Part of main and boost venturi cut away One or more of these modifications were made for a given test in order to obtain information on specific carburetor variables. For example, modification number 4 was used in a test to determine the effect of fuel flow rate on the reduction in boost venturi suction. An overall view of the equipment used for many of the tests is shown in Figure 33. Note that the air flow rate is measured by calibrated orifices and a micromanometer, and that the fuel flow rate is obtained by an automatic burette system. Figure 34 shows the carburetor pressure chamber and the protractor used to accurately position the throttle plate at any desired angle. The pressure chamber was used only for those tests with reduced carburetor inlet pressure (simulated altitude). For all other runs it was removed. A constant temperature bath provided a controlled fuel temperature over a wide range of values. A liquid nitrogen bath was used in conjunction with the constant temperature bath whenever very cold fuel temperatures were desired. This system was capable of holding the fuel temperature at any value down to the freezing point of the fuel being used. The types of tests run were: 1. constant engine speed, varying throttle angle 2. constant throttle angle, varying engine speed 3. constant air flow rate, varying fuel flow rate 4. varying fuel type and temperature 5. varying inlet air pressure 6. tests with no idle, enrichment, or air bleed flow

A """4/" "'"4' "44 "4,">' /4/p #" 44/4>'> 4' 444' Picure 2 2curr frj7/>- carburetor tes

A:' i::z: Fgure 3.Equimentutilized to cnrtol and monirtor crrLr variable

176 7. tests with engine motoring (no fuel flow) The ranges of the important variables in these tests are listed in Table 8. Note that the humidity was measured for each test but was not controlled. TABLE VIII RANGES OF VARIABLES IN CARBURETOR TESTS VARIABLE RANGE Throttle Angle Completely Closed to Fully Opened Engine Speed 500 to 4500 RPM Ambient Pressure 24.00 to 29.86 inches of mercury Ambient Temperature 70.0 to 100.0 0 F Fuel Type 3 gasoline brands and isooctane Fuel Temperature 0.0 to 120.0 0 F Relative Humidity 25 to 90% (uncontrolled) The data obtained in these tests included all important variables related to the carburetor analyses and the engine data correlation. Some of these variables are: 1. engine speed 2. throttle angle 3. intake manifold vacuum 4. air mass flow rate 5. total fuel mass flow rate 6. carburetor air inlet pressure 7. brake, indicated, and friction torque, mean effective pressure, and horsepower 8. brake and indicated specific fuel consumption and thermal efficiency 9. primary and secondary (boost) venturi suctions 10. temperatures of the inlet air, fuel bowl, throttle plate, and intake manifold (inlet and outlet) The throttle angle was obtained by fitting each throttle shaft with a protractor and pointer. The pointer was set in each case such that 90~ corresponded to the venturi axis. This pointer was also equipped

177 with a special lever to allow the throttle plate to be set and locked in any desired position. The carburetor air inlet pressure for simulated altitude runs was obtained from the pressure differential between the ambient and the inside of the chamber surrounding the carburetor. Both the chamber and the throttle angle lever are shown in Figure 34. D. CARBURETOR PERFORMANCE OVER THE ENTIRE OPERATING RANGE Series of tests were conducted with the engine speed held constant and the throttle angle varying in small increments from completely closed to wide open. The series was then repeated with the throttle angle held constant, while the engine speed was varied from 500 to 4500 RPM. Typical results from these test series are presented in Tables 9 and 10. Note that the test data have been reduced by a digital computer, and that all of the important variables have been tabulated. From these (and additional) results the next five figures were obtained. Figure 35 illustrates the observed variation in intake manifold vacuum with throttle angle for various engine speeds. Since the intake manifold vacuum was previously shown to be one of the controlling factors in determining both the idle and enrichment system flow rates, its relationship to the operating point variables is quite important. Plots of data illustrating the relation between air flow, intake manifold pressure, engine speed, and throttle angle will be presented in Chapter 8, where they can be compared to the simulation predictions.

TABLE IX REDUCED DATA FOR ON-ENGINE CARBURETOR TESTS AT CONSTANT ENGINE SPEED AND VARIABLE THROTTLE ANGLE CATA REDUCTION PROGRAM FOR ENGINE TESTS **** PROGRAM RESULTS FOR THIS TEST **** THE TEST NUMBER IS 16 TO 2. ENGINE: FORD 28f V- THE TEST DATE IS 91766 TO i0i547 CARBURE-ORS: VARIOUS FORD, THE AMBIENT AIR DENSITY IS.0716 TO. OG LfW/FT ROCHES CARMR THE SAE CORRECTION FACTOR IS 1.010 TO 1.02. FUEL:0 SAWARD -RE~v. 6ASOWNE THE ENGINE DISPLACEMENT IN CUBIC INCHES IS 288.52 RUN RPM SCALE PNAN BFP FHP RATEF RATEA F/A BSFC EFFVOL THERMB 1 1195.0 27.5 9.8 6.28 6.35 7.215 92.91.0777 1.1492 21.61 11.55 2 1 20 2.7 46.8 11.7 10.72 6.18 7.932 117.99.0672.7401 27.36 17.93 3 1194.1 73.5 15.1 16.72 5.82 9.605 158.B5.0605.5745 37.08 23.10 4 1200.5 104.5 18.7 23.89 5. 53 12.121 204.24.0593.5074 47.45 26.15 5 1189.4 150.5 25.3 34.08 4.87 16.437 282.91.0581.4823 66.34 27.52 6 1226.3 179.5 28.8 41.91 4.67 18.520 312.75.0592.4419 71.13 30.03 7 1195.6 21.0 8.9 4.78 6.31 f6.957 86.03.0809 1.4553 20.07 9.12 8 1197.8 44.0 11.1 10.03 6.18 7.817 113.50. 0689.7790 26.43 17.03 9 1198.8 73.0 14.6 16.66 5.91 9.690 157.77.0614.5815 36.71 22.82 10 1195.6 110.0 19.3 25.13 5.48 12.750 215.64.0591.5074 50.13 26.15 11 1202.1 155.0 25.4 35.48 4.92 16.943 290.38.0583.4776 67.37 27.79 12 1201.1 183.0 28.7 41.85 4.57 19.100 322.15.0593.4564 74.81 29.07 13 1588.9 23.0 9.1 6.96 9.20 1.682 112.06.0686 1.1041 19.67 12.02 14 1595.8 45.2 11.4 13.73 8.93 9.610 15492.0620.6997 27.08 18.96 15 1603.7 71.0 14.6 21.64 8.53 12.477 208.02.0600.5766 36.24 23.01 16 160 3.4 117.0 19.2 3 5. 72 7.97 17.152 286.63.0598.4802 49.86 27.6310 17 1602.5 140.5 22.0 42.87 7.60 19.984 330.89.0604.4662 57.59 28.47 18 1603.5 2C3.5 28.5 62.13 6.72 27.826 443.91.0627 4479 77.21 29.63 19 1595.9 18.0 8.3 5.48 9.32 7.543 105.05.0718 1.3757 18.31 9.65 20 1602.4 54.0 12.4 16.48 8.85 10.678 176.20.0606.6481 30.67 20.47 21 1600.2 70.0 14.0 21.733 8.62 12.345 202.55.0609.5789 35.30 22.9? 22 1598.0 103.0 17.3 31.34 8.18 15.591 259.72.0600.4975 45.33 26.67 23 1603.6 139.0 21.7 42.44 7.66 20.048 334.66.0599.4724 58.20 28.09 24 1600.4 200.0 28.5 60.94 6.70 26.713 436.95.0611.4383 76.15 30.27 25 2001.3 20.5 8.7 7.81 12.57 8.946 140.82.0635 1.1452 19.63 11.59 26 1598.3 44.5 11.2 16.93 12.21 11.968 197.94.0605.7068 27.63 18.77 27 2001.1 73.0 14.3 27.81 11.81 15.808 263.03.0601.5683 36.66 23.35 28 2001.4 118.0 17.9 44.97 11.36 20.491 334.66.0612.4557 46.64 29.12 29 2000.0 139.0 21.6 52.93 10.85 24.627 416.54.0591.4653 58.09 28.52 30 2002.5 208.0 28.2 75.31 9.91 35.147 547.26.0642.4432 76.22 29.94 31 212561 8.0 7.2 3.24 13.43 8.316 123.49.0673 2.5689 16.21 5.17 32 2100.8 24.0 8.9 9.60 13.20 9.958 155.58.0640 1.0373 20.66 12.79 33 2016.5 55.0 12.3 21.75 12.34 13.941 231. 83.0601.6411 31.14 20.70 34 2104.6 81.0 14.1 32.46 12.38 16.943 279.76.0606.5220 37.07 25.42 35 2115.1 116.0 18.4 46.71 12.12 22.685 364.94.0622.4856 48.12 27.33 36 2152.6 148.0 22.3 60.66 11.89 27.627 451.54.0612.4554 58.50 29.14 37 2146.2 206.0 28.1 84.18 10.71 36.946 577.36.0640.4389 75.03 30.23 38 2503.2 21.0 7.0 10.01 17.87 11.437 185.64.0616 1.1426 20.68 11.61 39 2502.2 47.0 11.7 22.39 17.25 15.808 259.72.0609.7060 28.95 18.80 40 2502.8 74.0 14.5 35.26 17.01 20.152 330.10.0610.5714 36.79 23.22 41 2500.0 111.5 18.5 53.08 16.57 26.658 436.95.0610.5023 48.75 26.42 42 2504.7 138.0 21.7 65.81 16.26 30.913 517.28.0598.4697 57.60 28.25 43 2505.5 195.0 27.9 93.03 15.46 40.981 647.67.0633.4405 72.10 30.12

TABLE IX (continued) 44 1213.6 26.5 9.3 6.12 6.47 7.300 91.75.0796 I'.1920 21.09 11. 13 45 1199.9 47.5 11.3 10. 85 6.21 7.974 118.80.0671.7348 27.61 18.06 46 1203.1 71.5 14.4 16.38 5.96 9.450 156.07.0606.5770 36.18 23.00 47 1201.3 116.0 19.6 26.53 5.49 13.211 219.87.0601.4979 51.05?6.65 48 1204.7 141.0 23.5 32. 33 5.11 15.719 269.37.0584.4862 62.39 27. 29 49 1?I-0 183.0 28.7 42.17 4.61 19.193 325.15.0590.4552 74.93 29.15 50 1605.7 25.0 8.8 1.64 9.32 8.111 116.89.0694 1.0612 20.30 12. 50 51 1605.2 48.5 11.6 14. 82 8.96 10.007 163.43.0612.6751 28.40 19.66 52 1602=8 80.0 14.8 24.41 8.58 13.479 217.22.0621.5521 37.80 24. 04 53 1605.0 107.5 17.7 32.85 8.22 16.411 269.13.0610.4995 46.77 26. 56 54 1601.1 135.0 20.9 41. 16 7.74 19.593 320.94.0610.4761 55.91 27.87 55 1605.0 200.5 28.5 61.27 6.72 26.535 438.22.0606.4331 76.15 30.64 56 120S.2 24.5 9.8 5.64 6.40 7.422 92.30.0804 1.3158 21.29 10.09 57 1205.9 62.8 13.5 14.42 6,02 9.344 140.24.0666.6480 32.44 20.48 5K 1205.6 97.5 17.8 22.34 5.74 12.314 191.16.0644.5513 44.22 24.07 59 1205.0 130.5 22.6 29.94 5.23 15.894 249.71.0637.5309 57.80 25.00 60 1200.1 178.0 28.4 4C.67 4.64 20.085 321.68.0624.4938 74.76 26.87 61 1602.5 101.5 17.1 30.97 8.24 16.263 252.12.0645.5251 43.88 25.27 2 1600.8 171.0 25.2 52.12 7.28 24.396 384.28.0635.4681 66.95 28.35 RUN IMEP TCiSCF TORQI BMEP IHP 8HPC IHPC SG A/F ISFC THERMI 1 28.90 27.80 55.3C 14.37 12.62 6.41 12.75.7247 12.88.571 23.22 2 38.57 2i.00 73.80 24.46 16.90 10.89 17.07.7243 14.88.469 28.27 3 51.80 25c60 99.10 38.42 22.54 16.95 22.77.7243 16.54.426 31.14 4 67.27 24.20 128.7C 54.62 29.42 24.19 29.72.7243 16.85.412 32.21 5 89.90 21.50 172.30 78.66 38.95 34.48 39.35.7258 17.21.422 31.45 6 104.27 20.00 199.50 93.82 46.58 42.38 47.05.7262 16.89.398 33.38 25.45 27.70 48.7C 10.98 11.09 4.89 11.20.7254 12.37.628 21.15 8 37.16 27.10 71.IC 23.00 16.22 10.20 16.38.7254 14.52.482 27.53 9 51.69 25.90 98.90 38.15 22.57 16.89 22.80.7258 16.28.429 30.91 10 70.04 24.00 134.00 57.49 30.61 25.44 30.92.7262 16.91.417 31.86 11 92.25 21.50 176.50 81.01 40.40 35.89 40.81.7265 17.14.419 31.64 12 106.10 20.00 203.30 95.65 46.42 42.32 46.90.7265 16.87.411 32.25 13 27.91 30.40 53.40 12.02 16.15 7.12 16.32.7251 14.59.476 27.90 14 38.99 29.40 74.60 23.62 22.67 13.96 22.90.7262 16.12.424 31.30 15 51.74 28.00 99.00 37.11 30.17 21.95 30.48.7265 16.67.414 32.09 16 74.79 26.10 143.10 61.15 43.69 36.16 44.13.7276 16.71.393 33.80 17 86.45 24.90 165.40 73.43 50.47 43.38 50.98.7273 16.56.396 33.51 18 117.86 22.00 225.50 106.36 68.85 62.83 69.55.7276 15.95.404 32.83 19 25.40 30.60 48.60 9.41 14.80 5.63 14.96.7258 13.93.510 26.04 20 43.38 29.00 83.00 28.22 25.32 16.73 25.58.7258 16.50.422 31.47 21 51.38 28.30 98.30 36.59 29.95 21.63 30.25.7258 16.41.412 32.19 22 67.89 26.90 129.90 53.83 39.52 31.74 39.93.7258 16.66.394 33.64 23 85.77 25.10 164.10 72.65 50.11 42.95 50.61.7265 16.69.400 33.17 24 116.03 22.00 222.00 104.53 67.65 61.63 68.33.726? 16.36.395 33.60 25 27.96 33.00 53.5C 10.71 20.39 8. 2 20.59 c726? 15.74.439 30.24 26 40.04 32.10 76.60 23.26 29.15 17.23 29.44.7262 16.54.411 32.32 27 54.36 31.00 104.00 38.15 39.63 28.22 40.03.7254 16.64.399 33.26 28 77.25 29.80 147.80 61.67 56.32 45.54 56.90.7262 16.33.364 36.47 29 87.55 28.50 167.50 72.65 53.79 53.58 6-6.43.7258 16.91.386 34.37 30 122.30 26.00 234.00 (08.71 89.22 80.21 90.12.7258 15.57.394 33.68 31 21.53 33.20 41.20 4.18 16.67 3.41 16.84.7251 14.85.499 26.60 32 29.79 33.00 57.00 12.54 22.80 9.83 23.03.7251 15.62.437 30.3P 33 45.05 31.20 86.20 28.75 34.08 22.09 34.43.7251 16.63.409 32.44 34 58.49 30.90 111.90 42.34 44.84 32.91 45.30.7265 16.51.378 35.12 35 76.36 30.10 146.10 60.63 58.84 47.31 59.43.7280 16.09.3P6 34.42 36 92.51 29.00 177.00 77.35 72.55 61.40 73.28.7280 16.34.381 34.84

TABLE IX (continued) 37 121.36 26.20 232.2C 107.67 94.89 85.14 95.85.7288 15.63.389 34.08 38 30.58 37.50 58.5C 10.98 27.88 10.29 28.17.7254 16.23.410 32.35 39 43.49 36.20 83.20 24.57 39.64 22.79 40.04.7254 16.43.399 33.27 40 57.34 35.70 109.70 38.68 52.28 35.80 52.81.7254 16.38.385 34.42 41 76.47 34.80 146.30 58.28 69.64 53.78 70.35.7254 16.39.383 34.66 42 89.95 34.10 172.10 72.13 82.07 66.65 82.91.7254 16.73.377 35.23 43 118.85 32.40 227.40 101.92 108.48 94.13 109.58.7262 15.80.378 35.13 44 28.48 28.00 54.5C 13.85 12.59 6.25 12.72.7265 12.57.580 22.89 45 39.04 27.20 74.70 24.83 17.07 11.03 17.24.7262 14.90.467 28.40 46 50.96 2E.00 97.50 37.37 22.33 16.60?2.56.7262 16.51.423 31.36 47 73.17 24.00 140.00 60.63 32.02 26.86 32.35.7262 16.64.413 32.16 48 85.35 22.30 163.30 73.70 37.44 32.71 37.82.7262 17.14.420 31.61 49 106.10 2C.00 203.00 95.65 46.78 42.64 47.25.7262 16.94.410 32.34 50 29.01 30.50 55.5C 13.07 16.97 7.82 17.14.7258 14.41.478 27.76 51 40.66 29.30 77.80 25.35 23.78 15.06 24.02.7251 16.33.421 31.53 52 56.50 28.10 108.10 41.81 32.q9 24.75 33.33.7251 16.12.409 32.48 53 70.25 26.90 134.40 56.19 41.07 33.27 41.49.7251 16.40.400 33.21 O 54 83.83 25.40 160.40 70.56 48.90 41.65 49.40.7254 16.38.401 33.12 0 55 116.29 22.00 222.50 104.79 68.00 61.96 68.69.7254 16.51.390 34.00 56 27.34 27.80 52.3C 12.81 12.04 5.76 12.16.7311 12.44.616 21.53!7 46.52 26.20 89.00 32.82 20.43 14.63 20.64.7311 1S.01.457 29.02 58 63.92 25.00 122.30 50.85 28.07 22.62 28.36.7299 15.52.439 30.25 59 80.12 22.80 153.3C0 68.21 35.17 30.30 35.53.7296 15.71.452 29.36 60 103.64 2C.30 198.30 93.03 45.31 41.14 45.77.7284 16.02.443 29.94 61 67.16 27.00 128.50 53.05 39.21 31.37 39.61.7284 15.50.415 31.99 62 101.87 23.90 194.90 89.37 59.41 52.73 60.01.7280 15.75.411 32.31 ENGINE DATA RECUCTION... 0. HARRIh GT]N

TABLE X REDUCED DATA FOR ON-ENGINE CARBURETOR TESTS AT CtTA REUUCIXUN PkCGRAM FCR ENGINE TESTS CONSTANT THROTTLE ANGLE AND VARIABLE ENGINE SPEED **** PROGRAM RESULTS FOR THIS TEST**** THE TEST NUMBER IS 46 ENG1NE: FORD 289 V-8 THE TEST DATE IS 101667 CARBURETOR: CG AFB THE AMBIENT AIR DENSITY IS.0709 LM/FTS CLOSED THROaTLE: 10.0 THE SAE CORRECTICN FACTOR IS 1.00999 FUEL * STNDARD TREJL.AR THE ENGINE DISPLACEMENT IN CUBIC INCHES IS 288.52 INS *4SOHLIN 377 OF RUN RPM SCALE PMAN BHP FHP RATEF RATEA F/A 8SFC EFFVOL THFRMB ^SS^ 1 800.3 146.0 25.9 22.25 3.03 11.427 189.07.0604.5136 66.55 25.84 26.0o 2 1028.0 134.0 24.3 26.23 3.95 13.418 225.82.0594.5116 61.88 25.94.26.0 3 1199.9 128.0 22.8 29.24 4.98 14.947 249.95.0598.5111 58.68 25.96.26.0 4 1601.6 117.5 19.8 35.83 7,78 18.013 291.96.0617.5027 51.35?6.40 26.0 5 1863.7 S8.5 17.1 34.95 11.57 19.375 303.53.0638.5543 45.88 23.94.26.0 6 2504.6 68.5 14.3 32.67 17.88 20.122 315.84.0637.6160 35.5? 21.54 226.0 7 3001.6 51.0 12.6 29.15 24.06 22.573 327.09.0690.7745 30.70 17.13.26.0 8 1602.1 184.0 27.0 56.13 6.77 25.173 409.45.0615.4485 71.99 2q59 5 62.0 9 1606.5 164.0 25.5 50.23 7.01 23.060 387.54.0595.4591 67.87 28.90 36.0 10 1597.7 142.0 22.9 43.20 7.30 20.544 342.38.0600.4756 60.37 27.90 S1.0 11 1589.2 139.5 21.2 42.21 7.47 20.636 319.28.0646.4889 56.59 27.14 18.0 12 1603.3 114.0 19.4 34.80 7.69 17.340 283.48.0612.4983 49.81 26.63.25.5 13 1604.8 67,0 14.0 20.47 8.40 12.469 199.42.0625.6091 35.01 21.79 20.G co 14 1601.7 63.5 13.9 19.37 8.39 11.920 196.62.0606.6156 34.58 21.56 20.6 15 1599.5 40.0 11.0 12.18 8.80 9.767 150.10.0651.8017 26.44 16.55 18.1 16 1598.5 18.0 8.6 5.48 9.13 9.111 107.57.0847 1.6631 18.96 7.98 15.6 17 15S8.9 3.0 7.2.91 9.29 7.737 81.73.0947 8.4712 14.40 1.57 13.G 18 1594.1 2.0 6.0.61 9.71 7.264 57.73.1258 11.9655 10.20 1.11 iI.6 19 1594.5 1.2 5.2.36 10.08 6.355 41.91 1516 17.4428 7.40.76 10.0 RUN IMEP TORQF TORI BMEP IHP BHPC IHPC SG A/F ISFC THERMI 1 86.71 19.90 165.90 76.31 25.28 22.50 25.53.7265 16.55.452 29.36 2 80.59 20.20 154.2C 70.04 30.18 26.53 30.48.7265 16. 83.445 29.85 3 78.29 21.80 149.80 66.90 34.22 29.59 34.57.7262 16.72 437 30.38 4 74.74 25.50 143.00 61.41 43.61 36.27 44.04.7262 16.21.413 32.12 5 68.52 32.60 131.10 51.48 46.52 35.42 46.99.7262 15.67.416 31.86 6 55.40 37.50 106.00 35.80 50.55 33.17 51.05.7262 15.70.398?3.34 7 48.66 42.10 93.10 26.66 53.21 29.68 53.74.7262 14.49.424 31.28 8 107.77 22.20 206.20 96.17 62.90 56.76 63.53.7296 16.27.400 33.16 9 97.69 22.90 186.90 85.72 57.24 50.80 57.81.7284 16.81.403 32.94 10 86.76 24.00 166.00 74.22 50.50 43.70 51.00.7284 16.67 407 32.62 11 85.82 24.70 164.20 72.91 49.69 42.71 50.18.7280 15.47.415 31.95 12 72.75 25.20 139.20 59.58 42.49 35.22 42.92.7284 16.35.408 32.5? 13 49.39 27.50 94.50 35.02 28.87 20.76 29.16.7284 15.99.432 30.73 14 47.56 27.50 91.00 33.19 27.75 19.64 28.03.7280 16.49.430 30. 89 15 36.01 28.90 68.90 20.91 20.98 12.39 21.19.7276 15.37.465 28.51 16 25.09 30.00 48.00 9.41 14.61 5.62 14.76.7265 11.81.624 21.28 17 17.51 30.50 33.50 1.57 10.20 1.02 10.30 7269 10.56.759 17.4 18 17.77 32.00 34.00 1.05 10.32.71 10.42.7269 7.95.704 18.85 19 17.98 33.20 34.40.63 10.44.47 10.55.7269 6.59.608 21.81

EXPERIMENTAL VALUES OF INTAKE MANIFOLD VACUUM 0 (Engine Running) 2 I 4-: 6 Z 8 _ 2_ / / >^ /^ Ambient Pressure:-29.28" H6. 120 12 14 16 18 20 22 24 26 28 30 32 34 36 38 40 42 44 > 14 -J 0I16 z Ford 28r9 Cubic I nch V-8 Engine throttle angle and engine speed Fuel: Standard Reg. Gasoline LU 20- Carburetor: Ford C6AF-9510-B ~" 22 Ambient Pressure: 29.28"HG. z Ambient Temperature: 80 F 24 V 6os 1Q 12 14 16 18 20 22 24 26 28 30 32 34 36 38 40 4244 Csed Throttle at 5 THROTTLE ANGLE IN DEGREES Figure 35. Variations in intake manifold vacuum with throttle angle and engine speed

183 The boost venturi suction provides the potential for fuel flow within the main system, thus it is an important quantity within the simulation. In order to provide an experimental verification of the predicted metering signal values, the boost and main venturi suctions of typical carburetors were measured as a function of the total moist air mass flow rate. The results from one of these tests are presented in Figure 36. Note that the metering signal is slightly higher with no main system fuel flowing. Another experimentally determined parameter was the wide open throttle pressure loss across typical carburetors. This is the minimum intake manifold vacuum, and the values were determined as a function of the measured air flow rate. The data are shown plotted in Figure 37. Note that the pressure loss increases rapidly as the air flow increases, reaching a pressure loss of 1 inch of mercury at an air flow of about 700 lbm/hour. Brake specific fuel consumption curves are very important to the road load carburetor analysis and also to the engine data correlation technique. A series of these curves for a typical engine and a modified carburetor is shown in Figure 38. The carburetor modification consisted of a blocked enrichment system which prevented an increase in the fuelair ratio at low intake manifold vacuums. This is the reason the curves do not slope upward at the high load end. These values were obtained along constant engine speed curves. A comparison of the curve shapes for constant throttle angle and constant engine speed is given in Figure

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185 TOTAL PRESSURE LOSS THROUGH VENTURI 11.5 0 Ford C6AF-9510-B Carburetor -1.4 Main Venturi Diameter =.4 Inche c3o To=80~F P0=14.22PSIA Uil.3 _ Wide Open Throttle ~1.2 No Fuel Flowing z |H- 0 1.0- W9o 8 / H7 D.6 ~5-. - 4 0 LL z.3 U2 < U z 100 200 300 400 500 PER BARREL TOTAL 200 400 600 800 1000 MOIST AIR FLOW LBM/HOUR —^ Figure 57

186 ENGINE-CRRBURETOR EXPERIMENTAL DRTR ENGINE: 289 CUBIC INCH V-8 _" ~; ift lV~ \ \FUEL: STD. REG. GASOLINE @ 75~ F Z | \\ \ AMBIENT: PRESSURE = 29.18 INCHES HG. "S \ \ -- ----------------- TEMPERATURE = 75~ F REL. HUMIDITY = 34% z. 0 ENGINE BRAKE HORSEPOWER Figure 38. Brake Specific Fuel Consumption Curves For Various Engine Speeds Fiue3.B~eSpcfcFe,-supinCre o O ~ ~ ~ ~ ~~aiu EngneSped

187 ENGINE-CRRBURETOR EXPERIMENTRL DRTR 0_J 0 \ 0 \ t \~ TEMPERATURE = 750 F C- ^8. ______ -JD ____ ______ ------ ------ FUEL: STD. REG. GASOLINE @ 75~ F:. 1 0. AMBIENT: PRESSURE =0.00 209.18 INCHES HG.. ENGI TEMPERATURBRKE = 75~ FHORSEPOWER Figure 39. BSC Variations At Constant Throttle Angle and34% ENGINE BRAKE HORSEPOWER --------- Figure 39. BSFC Variations At Constant Throttle Angle and Constant Engine Speed

188 39. The intersection of the curve for a given engine speed,and the curve for a given throttle angle will be the brake specific fuel consumption and brake horsepower corresponding to that particular operating point. In the case shown, the operating point of 26~ and 1600 RPM would result in a BHP output of 35.0 and a BSFC value of 0.50. E. SPECIAL EXPERIMENTAL PROGRAMS 1. Suction Profiles Within the Boost Venturi An experimental program was conducted to determine the pressure (actually the suction) variation with position within the boost venturi for typical operating points. The goal was to determine both the radial and axial variations in venturi suction and thus check the validity of the one-dimensional assumption. Some of this data is shown in Figure 40, and the conclusions are as follows: 1. The one-dimension flow assumption is reasonable for the main and boost venturi, except in the region of the boost venturi throat. 2. In order to use a one-dimensional compressible flow analysis to predict suctions at the fuel discharge nozzle, the increase in suction due to any sudden expansions or contractions in area must be included. 3. The maximum suction occurs near the inner walls in the vicinity of the fuel discharge nozzle. These conclusions helped to clear up some of the difficulties in the compressible mixture flow subroutine as it was originally written. Initially the subroutine evaluated the one-dimensional compressible mixture flow relationships and analytically predicted boost venturi

189 LINES OF EQUAL SUCTION - - 0.78" -- 4 04 /113.5 13.1 i. 0.63" - \\ 0-.50".8- 1 2.3 0/. 0.25"- i j10-<I0. 0 _ /v 0.2612 )0,/ u11.0 2 9.2 9. 2 i I \ AIR FLOW RATE PER BARREL = 230 Ibm/hour Figure 40. Suction distribution in inches of water within a typical boost venturi

190 suctions that were significantly lower than the measured values. For example, 14.0 instead of 17.5 inches of water for the conditions in Figure 40. The results from the study of the suction variation within the boost venturi pointed out the fact that subroutine SIGNAL was predicting an average suction at each axial position, when in fact the suction acting on the fuel discharge nozzle was significantly higher than the average in boost venturi designs having sudden expansions or contractions, due to the sudden area change in that region. By including an additional pressure loss due to this sudden area change (where applicable), the predicted boost suction values agreed very well with the experimental data. 2. High Speed Movies of Fuel Discharge A standard Ford C6AF-9510-B 2-barrel carburetor was modified to permit visual observation of the fuel discharging into the air stream within the boost venturi. This was accomplished by making a vertical cut through the carburetor and exposing a cross section of the venturi (very similar to the cross section shown in Figure 4 on Page 29.) The section exposed by cutting was covered with a flat Lucite plate,thus giving an uninterrupted air flow path. High speed movies (3000 frames per second) were taken of the fuel discharge under many operating conditions, from the point at which the main fuel system begins to function, to conditions resulting in very high main fuel flow rates. A view of the experimental equipment associated with this

191 particular project is given in Figure 41. This particular view shows the camera mounted in the vertical position to observe the fuel discharge in a Rochester Quadrajet carburetor. The camera was mounted in the horizontal position to obtain the movies of the Ford carburetor. A single frame was taken from each of four movies and enlarged. (The enlarging process brought out some graininess of the film that is not noticeable in the movies.) The enlargements are presented in Figures 42 and 43, in the order of increasing fuel flow. The conditions corresponding to each photograph are: INTAKE ENGINE MANIFOLD FUEL FLOW PHOTOGRAPH FILM SPEED SPEED VACUUM PER BARREL frames/sec RPM inches Hg lbm/hour 42a 3000 1100 8.1 3.32 42b 3000 700 0.4 3.75 43a 3000 1500 7.8 4.90 43b 3000 3000 5.0 9.90 Note in photograph 42a that there are fuel droplets of various sizes leaving the boost venturi. Note also that the droplets are fairly large as compared to those in photograph 43b, where they form more of a mist, which indicates a greater degree of atomization. The throttle plate is apparent in photographs 42b and 43b, near the bottom of each picture. There is a distinct division of the atomized fuel stream at the throttlteplate in photograph 43b, which is shown even more clearly in the movies.

192 Figure 41 q Equipment utilized to obtain high speed movies of fuel discharge

193 PHOTOGRAPH A PHOTOGRAPH B Figure 42e High speed photographs of fuel discharge within the boost venturi Low fuel flow

194 PHOTOGRAPH A PHOTOGRAPH B Figure 43~ High speed photographs of fuel discharge within the boost venturi B High fuel flow

195 3. Transient and Pulsating Flow Study In the initial phases of this carburetor simulation project, an experimental study of the pressure variations in a carburetor under transient and pulsating conditions was conducted. This was done mainly to gain an understanding of the effects of rapid transients and to set bounds, if possible, on the steady flow region of operation. A Ford C4-AFB 2-barrel carburetor was completely instrumented with Statham strain gage pressure transducers. These transducers, which varied in range from ~ 1 psi to ~ 15 psi,were calibrated and installed in the boost venturi, the fuel channel below the main metering orifice, and below the throttle plate (in communication with the intake manifold vacuum). A wirewound potentiometer was connected to the throttle shaft, and was calibrated in terms of millivolts per degree of throttle angle. The carburetor was then installed on a Ford 289 cubic inch engine, and the potentiometer and strain gage pressure transducers were connected to the associated amplifying and recording equipment, which is shown in Figure 44. The transient portion of this test series consisted of sudden throttle openings and closings. This was accomplished by allowing conditions within the carburetor to stabilize at some engine speed and throttle angle and then rapidly opening or closing the throttle as far as possible. Just before the transient, the Visicorder chart was started and the pressure-time traces were recorded. Figures 45 and 46 show the pressure variations for the three pressure transducers, along with

Figure 44~ Equipment utilized in obtaining pressure - time traces under transient and pulsating conditions

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199 the throttle angle and crankshaft revolution indicators. Note the rapid increase in boost venturi suction in the case of the sudden throttle opening. This results from the large increase in the air flow rate and the corresponding increase in air velocity within the boost venturi. Also note that the pressure fluctuations decayed rather rapidly and within a few engine revolutions had stabilized at the periodic values associated with the new throttle angle. Another type of test that was performed using this equipment was the pulsating flow case in which the engine speed and throttle angle were fixed. This case is of more importance to the carburetor simulation since it indicates the pulsation amplitude for various pseudosteady operating points. Figures 47 and 48 show typical visicorder traces from this test series. The data were obtained for various specified engine speeds and throttle angles by allowing conditions to stabilize, running the visicorder, and then changing the throttle angle by ao0 and again letting the conditions stabilize. This resulted in mean and alternating pressures for each operating point. Note that the alternating (pulsating) component of the boost venturi suction is not large compared to the mean value except for large throttle angles. On the basis of these tests, an empirical pulsation factor was developed. This factor is related to the amplitude and frequency of the intake pulses, as well as the damping effect of the throttle plate. These wave parameters can be related to the physical variables of the

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A~~w A A:w 9ww 00 N~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~o~~~~~~~~~~~ ~ ~ ~ ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~r Figure 48. Waveforms For The Boost Venturi Suction A nd Main Metering Orifice Pressure Drop

202 carburetor and engine by the following logic: The frequency of the intake air pulses will be a function of the engine speed and the number of cylinders in communication with each carburetor barrel. The frequency will also be a function of the number of intake strokes per engine revolution per cylinder, which is 1/2 for a 4-stroke cycle engine, and 1 for a 2-stroke cycle engine. The amplitude of the intake air pulsations will be related to the mass of air drawn into each cylinder, which is dependent upon the swept volume of the cylinder and the density of the mixture in the intake manifold. The pulsations within the intake manifold are reduced in amplitude (damped) by the throttle plate. This damping effect may be related to the Mach number of the mixture at the throttle plate restriction. If the throttle plate Mach number is unity, the intake manifold pulsations will not be felt upstream from the throttle plate and the venturi flow will be steady. This corresponds to small throttle angles. As the throttle angle is increased, or the Mach number at the throttle restriction is reduced in any other manner, the damping effect will be decreased, with the maximum pulsation amplitude occurring at very low Mach numbers. If we now consider the boost venturi suction for both steady and pulsating air flow, it will be evident that for the same net air flow over a given time increment, the effective boost venturi suction will be greater for the pulsating situation than for the steady flow situation. This is because the velocity of the air within the venturi will fluctuate with time in the pulsating case. Since the metering signal will increase

203 as a function of the instantaneous air velocity squared (approximately), it is easily shown that the effective metering signal, averaged over a pulse cycle, will be greater than that for steady air flow. Let us denote the ratio of the effective metering signal for a pulse cycle, to the metering signal for steady air flow at the same average mass flow rate, as 1 + P. Or: 1 + = BVSUCW (pulsating) EQN 6.3 BVSUCW (steady flow) The physical meaning of the pulsation factor is illustrated by the two sketches in Figure 49. Note that the effective metering signal becomes greater than that for steady flow at the same air mass flow rate. This difference is a maximum at the wide open throttle point for each engine speed. At the air flow rate indicated by the vertical line in Figure 49, the maximum value of t would be given by the difference in metering signal between points P and S, divided by the metering signal at S. The empirical equation developed for the pulsation factor, Y, in terms of known variables within the simulation is: M = (constant) (1 - M)(Pman) Ncyc EQN 6.4 N Ncb where Ncyc is either 2 or 4 for a 2 or 4 stroke cycle. The constant must be evaluated for each carburetor geometry and engine, but typical values obtained in this project gave a correlation constant of about 25.

204 E. PM -TIME) M~AN / ^ ATERNATIN6S INSTANTANEOUS METERING SIGNAL U~~~~~1 ~~ # II_ T ~ WIDE OPEN THR TTMLE pulsating and steady flow conditions tL. TIME AVERAGED AIR MASS FLOW/ RATE Figure 49. Effective metering signal for pulsating and steady flow conditions

205 It should be emphasized here that this only considers the effective metering signal, and not the greater complexities of pulsating 2-phase flow in the fuel channel, which results from the periodic metering signal. The determination of the fuel flow situation under these conditions would require a knowledge of orifice discharge coefficient variations with fuel flow pulsation amplitude and frequency, which would obviously require an extensive testing and correlation project.

CHAPTER VII LUCITE FLOW MODEL TESTS A. REASONS FOR FUEL CHANNEL MODEL TESTS The bulk of the experimental work conducted during this project was directly related to carburetor fuel channel flow tests. These tests were necessary for three basic reasons: 1. To observe the overall operation of typical fuel channel configurations under many flow conditions, and from this to formulate a comprehensive computer model. 2. To accurately determine the effects of numerous important operating variables including fuel type, fuel temperature, and air bleed orifice diameters. 3. To obtain fundamental pressure and flow rate data for use in checking the carburetor simulation predictions. All fundamental fuel channel tests were conducted using a transparent flow model in conjunction with a test stand, rather than with an actual carburetor mounted on an engine. There are numerous arguments that can be presented in favor of this, but they will be more meaningful if a description of the fuel channel flow model is first given. B. LUCITE FUEL CHANNEL MODEL The fuel channel flow model, as illustrated in Figure 50, represents an actual, complete carburetor fuel channel in nearly every respect. The basic geometry corresponds precisely to that of one-half of the Ford Cx-AF 2-barrel carburetor series, where the x designates the model year. This series was selected on the basis that it represented a typical fuel channel configuration and because a large amount 206

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208 of information was readily available for this type of carburetor, including dimensions, tolerances, and performance specifications. The flow model contains the following systems, all in Lucite: 1. main fuel flow system 2. enrichment fuel flow system (with enrichment valve) 3. idle fuel flow system (with idle needle) 4. main air bleed flow system 5. idle air bleed flow system These systems, with the exception of the idle system, are shown inFigure 51, which is a cross-section of the actual lucite flow model. The circles at various points in the channel represent static pressure taps which are connected to a large manometer bank. Note that the Lucite flow model permits visual observation and photography of the fuel and air bleed flow pattern in the passages. It also provides complete channel pressure measurements by means of the six pressure taps at strategic points along the fuel channel. Thermocouples monitor the fuel temperature from bowl to discharge nozzle. The main metering and air bleed orifice sizes may be easily changed or blocked off completely. This is accomplished by means of main metering orifice adaptors and set screws in which precision air bleed orifices have been drilled. The enrichment valve, which is merely a vacuum closed valve in a bypass channel around the main metering orifice, may be opened to any desired setting by adjusting a micro-valve controlling the vacuum acting upon it. This vacuum corresponds to the engine intake manifold vacuum at the operating point being run on the flow model. The idle

209 OF BOWL FUEL LEVEL - INQr"' a -'; ),y// _ 6 Figure 51. Cross-Section of Lucite flow model (to scale) 1. Enrichment (Power) Valve 8. Idle Tube (Brass) 2. Enrichment Metering Orifice 9. Emulsion Tube (Lucite) 3. Enrichment Valve Vacuum Body 10. Main Metering Orifice 4. Lower Well Thermocouple 11. Fuel Discharge Tube 5. Air Bleed Well Body 12. Upper Air Bleed Body 6. Main Metering Orifice Adaptor 13. Anti-Swirl Baffle (In Bowl) 7. Pressure Tap (Typical)

2 Fo Mode& Test Sand

211 system contains an adjustable needle screw, as in the actual carburetor. C. FLOW MODEL TEST STAND A flow model test stand shown in Figure 52 is used in conjunction with the Lucite flow model. Complete fuel flow, air bleed flow, temperature, and pressure measurements can be made with this test stand over a very wide range of fuel flow rates and fuel temperatures. Nearly all operating variables can be accurately controlled and easily changed. This includes: 1. fuel type and temperature 2. fuel bowl head 3. boost venturi suction 4. orifice types and sizes 5. intake manifold vacuum Figure 53 shows the position of the Lucite flow model in relation to the test stand. The instrument at the bottom of the figure is the constant temperature bath and the glass burette on the left is one of the bubble flowmeters. The functions of both of these items are as follows: The Neslab constant temperature bath both controls and circulates the fuel in the bowl. The circulation is accomplished by means of build-in force and suction pumps. The force pump is used to deliver the fuel to the constant head fuel bowl, and the suction pump, which is of greater capacity than the force pump, continually removes fuel from the bowl by means of an adjustable stand pipe. This gives a constant fuel head and excellent temperature control, since the fuel in the chamber is being changed continuously. For test runs at fuel

L22 Figure 53, Relative Position of The Lucite Flow Model On The Test Stand

213 temperatures below 400 F, liquid nitrogen is used for supplementary cooling of the bath fluid. This is accomplished by means of a variable speed pump which continuously pumps bath fluid through a copper tube immersed in a liquid nitrogen dewar, and then back to the bath. The temperature at the tube outlet is monitored to prevent freezing of the bath fluid. The extremely low air bleed flow rates (less than 1.0 Ibm/hour) are measured by means of a bubble flowmeter. This flowmeter consists of a dispensing burette, open at both ends, with the provision for injecting a small soap or Photoflow solution bubble at the bottom of the burette. As the air is drawn into the air bleed system through the top of the burette, the bubble rises. If the time required for the bubble to displace 100 milliliters is obtained with a stopwatch, the flow rate can be easily calculated. This system has the following advantages: 1. It is extremely simple 2. It is a positive displacement meter (the most accurate type of air flow meter) 3. It has a very wide flow range and extends down to less than.001 Ibm air/hour By having both 100 and 500 milliliter burettes available, the flow rate range can be increased even more. One other important fact is that this system costs less than twenty five dollars. The schematic flow diagram in Figure 54shows that the fuel flows through the Lucite fuel channel model, through a variable speed pump, and to a 3-way valve. This valve will ordinarily be in the position which results in a recirculation of the test fluid through a bubble

AIR BLEED FLOW MEASURE IDLE SUCTION ENRICH. IDLE ~FLOWMETERS (l |~SIPHON TECHNIQUE IVACUUM LE SYMBOL KEY _____________|-_ W IF| -— > AIR t BLEED =MAIN EFL tOW 9T r I- *:::: ETFG EPARATOR MODT] UJ IDLEt | IDLE FLOW W HEATER R i FL. FILTER MA URE -~~~V~ ~INACUUM LINE |LW I RO gN II 3 WYVLCIRCULATE MAIN FLOW r W I BUBBL E PAN METER TEMPEATUREI I VACUUM I, SUPPLY FLOWMETERS (SIPHON TECHNIQUE) SCALE VACUUM SYMBOL KEY P R PI1 ^MA ~~~~~INFLOW (;J)4 ('CENTRIFUGAL -— IDLE FLOW PUMP VACUUM LINE VEN W1 T3 WAY VALVE —' I^ L T RAP METERING VALVE IDLE STORAGE CONSTANT VACUUM SUPPLY i VACUUM CIk,OGGLEVALVE TMPERATURE ^ I ) PUMP BALL VLVE COOLING UNIT LIQU.D N2 Figure 54. Schematic Flow Diagram Of Fuel Channel Model Test Stand

215 elimination chamber, a rotameter, and back to the constant temperature bath. A centrifugal pump, driven by a variable speed DC motor, was originally selected to generate the required boost venturi suctions. Note that venturi air flow is not actually needed in the fuel channel flow model since its only function is to produce a suction at the outlet of the fuel channel, and this can be accomplished by a pump. This results in a system in which the test fluid is easily recirculated through a constant temperature bath, and in which the fuel flow rate can be measured quite accurately with a scale and pan arrangement. One operational difficulty was that under certain conditions the air bleed flow rate was sufficient to unprime the centrifugal pump. Therefore, a variable speed, positive displacement pump and depulsing circuit were substituted for the centrifugal pump, and the operation of the flow stand proved to be quite stable. The rotameter, a Cox 3-tube unit which was modified for this particular flow stand, is used only to establish approximate system flow rates. The smaller tube (0.6 to 5.0 Ibm/hour) was isolated from the other two tubes, and is used to monitor the idle system fuel flow rate. When conditions have stabilized, the flow rates are accurately determined by turning a 3-way valve, thus diverting the flow into a scale and pan system instead of into the rotameter. This provides a fuel mass flow rate accuracy which is independent of fuel specific gravity, air bubble content, viscosity, or temperature of fuel in the

216 pan. When the measurement is obtained, the valve is turned to its original position and the fluid once more recirculates. Any operating point can be reproduced on this model by varying the speed of the boost suction pump, and by adjusting an idle flow valve at the inlet to the idle vacuum storage tank. These parameters fix the simulated boost venturi suction and intake manifold vacuum which, as was shown in Chapter 2, fix the carburetor-engine operating point. Therefore, by utilizing this fuel channel model and flow stand, fundamental carburetor flow studies can be conducted. D. ADVANTAGES OF USING THE FLOW MODEL AND TEST STAND Now that the general features of the flow model and test stand have been outlined, numerous advantages over actual carburetor fuel channel tests should be evident. The first advantage is that it permits comprehensive tests to be conducted on the fuel channel. It would be very difficult if not impossible to instrument an actual carburetor for on-engine tests in which system fuel flow rates, air bleed flow rates, temperatures, and pressure profiles were to be accurately measured. In addition, many operating variables on the flow model, such as air bleed diameters, can be easily changed, whereas on an actual carburetor this would be much more involved. The operating variables can be controlled more closely with the flow model than with the actual carburetor. Temperatures can be held to close tolerances by means of the fuel recirculation system and there is no vibration and sloshing of fuel in the bowl with the model.

217 One of the important advantages of the Lucite flow model is that the flow in the entire fuel system may be observed and photographed. The two-phase flow downstream from the air bleeds, as well as cavitation at orifices, and system back flow may be studied visually. Vapor lock phenomena and the effects of ice crystals and water drops in the fuel (due to moist air bleeding into cold fuel) can also be observed. These types of observations are invaluable in formulating a solution to a given problem. E. GENERAL TEST TECHNIQUES AND CONDITIONS Fuel channel flow tests were performed using the Lucite flow model and test stand described in the preceding sections. Thirty one data sets were obtained for a wide range of operating conditions. The fuel types utilized in these tests were: 1. Shell Woodriver mineral spirits. 2. Standard regular gasoline. 3. ASTM isooctane In order to ascertain the effect of fuel properties on the channel flow, the fuel temperature was varied from 250 F to 1350 F. In each data set the boost venturi suction was varied from zero to thirty inches of fluid in approximately one inch intervals. At each value of boost venturi suction the fuel flow rate, air bleed flow rate, channel pressure distribution, and fuel temperature changes were determined. A list of the Lucite flow model tests is given in Table 11. Note that in addition to various fuel types, fuel temperatures, and flow rates, tests were performed with the main metering or enrichment

218 TABLE XI LISTING OF FUEL CHANNEL FLOW TESTS MAIN ENRICH. LOWER UPPER TEST FLUID FLUID JET SYSTEM BLEED BLEED NUMBER TYPE TEMP. OF OPEN OPEN OPEN OPEN 524671 M.S. 700 YES 525671 M.S. 700 YES YES 526671 M.S. 700 YES YES 61671 M.S. 700 YES 67671 M.S. 700 YES 68671 M.S. 700 YES 612671 M.S. 400 YES 614671 M.S. 90~ YES 616671 M.S. 90~ YES YES 616672 M.S. 90~ YES 619671 M.S. 480 YES 621671 M.S. 1000 YES 622671 M.S. 1000 YES YES 622672 M.S. 1000 YES 623671 M.S. 48~ YES 711671 M.S. 800 YES YES YES 721671 M.S. 1200 YES 919671 M.S. 1350 YES 922671 M.S. 1350 YES YES 922672 M.S. 1350 YES YES 926671 M.S. 450 YES 102671 M.S. 400 YES YES 104671 M.S. 400 YES YES YES 1011671 M.S. 1350 YES YES YES 117671 GAS. 800 YES 117672 GAS. 800 YES YES YES 1110671 GAS. 320 YES 1113671 GAS. 320 YES YES YES 115671 1S0. 250 YES 1116671 1SO. 80~ YES YES YES 1118671 1S0. 80 YES

219 orifices blocked, and with some or all of the air bleeds closed. Other parameters that were varied in certain tests were: 1. Initial fuel spill point. 2. Enrichment valve vacuum. 3. Idle needle screw turns. The tests performed with the main metering or enrichment orifice blocked were conducted to obtain basic flow data for a single system. This data was utilized to check the predictions of subroutine FLOW. This assured that subroutine FLOW was correctly predicting the parameters for single-phase flow in one system before it was expanded to predict two-phase flow parameters in a network. For reasons of safety, most of the tests were conducted with mineral spirits as the test fluid. This solvent is also utilized by many automotive companies in flow testing production carburetors, also for reasons of safety. The pressure distribution in the fuel channel was obtained, as mentioned earlier, by six static pressure taps along the fuel channel. The important operating feature of this method is that the taps were connected to a six tube manometer bank in the order of length along the channel. This arrangement is shown in Figure 55. The connecting tubing and the manometer well and tubes contained the same fluid that was flowing in the model. This avoided the problems of moving twofluid iterfaces, and the filling of dial manometer pressure lines. By having the connecting tubing slope downward toward the manometer bank, the pressure distribution during two-phase flow was easily obtained. (The air bubbles remained in the fuel channel, rather than

Figure 55. Manometer Bank Utilized To Obtain The Static Pressure Distribbution With The Fuel Channel

221 entering the manometer tubing). Note that if there is no flow in the model, the fluid level in all six manometer tubes will be equal to the level in the fuel bowl. This was set at thirty inches on the manometer bank. The pressure loss from the fuel bowl to each pressure tap is indicated by the depression in the manometer reading below thirty inches. Therefore, the pressure distribution for any fuel flow rate was immediately evident. One test technique that was utilized for runs without air bleeds was to connect a long tube to the main outlet of the Lucite flow model. The fuel was then allowed to exit from the tube at a point about thirty inches lower than the model discharge level. This created a siphon with corresponding channel pressures that were exceedingly steady (as compared to creating the suction at the model outlet with a pump, which always resulted in some minor pulsations.) All single phase flow tests were conducted utilizing this siphon technique. F. RESULTS OF FUEL CHANNEL FLOW TESTS Typical data obtained in one of the Lucite flow model tests is presented in Table 12. This data was obtained during test number 117672, which was a flow test utilizing Standard regular gasoline at 80 F. Both main air bleeds, each of 0.037 inch diameter, were open, and the enrichment valve was closed. Note that the upper well temperature, which is the temperature of the fuel-air foam leaving the emulsion section, was about 750 F. The 50 decrease in fuel temperature

222 TABLE XII TYPICAL DATA SHEET FOR A LUCITE FUEL CHANNEL FLOW TEST USING GASOLINE CARBURETOR FUEL CHANNEL FLOW STUDY TEST| /1 7672 PURPOSE OF THIS TEST. 7 "-TLI P7pu?EIJ, APlA.. LEI T F-C:A^4E.g DATE 11/7/67'FLUID S71.pnefp.&,, -/'Y NOMINAL BOWL TEMP. &, or. MAIN METERING ORIFICE __-.o ENRICHMENT VALVE VACUUM 2.'' "HIG. BAROM. f..2.P. DRY BULB__ 7. O~F. WET BULB 6o.0 ~F. QEAKER WEIGHT G A GRAMS CHECK IF OPEN: MAIN JET L/F -5o1 ENRICHMENT ORIFICE I I IDLE NEEDLE I I UPPER AIR BLEED l;o I LOWER AIR BLEED ItO \.7 IDLE AIR BLEED{ I GENERAL COMMENTS:.'.'<Y T-/tPY _Wl'-''c.. /o F -.J'... so505 0,.?Z 30,l 30.50. 3J.J 3o.00 PUNCHp, /7/67 Lower Fuel Fuel Air Air Uppez TAP TAP TAP TAP TAP TAP Bowl Well Weight Time Vol. Time Well RUN 1 2 3 4 5 6 Temp. Temp. Grams sec. cc sec. Temp. 1 20.o0o;1,10 2o.5 20o,. ^,4; 16,15 7., | 7-9.5 10o,o 59.1 5 |.,O\ 10,10 7',o 2,.45 21.1;,.o.10o o.0.o4 17,15 80.0 Boo oo.00,0 bo 5,o \ lo50 75,5 3, 21.2 7tO,960, l,9021o 20. 80 |3, |0,0 60,d O1.o (,5,1 500,0 10.. o 7,.0 4 ZI.so j)Z. 2.z;0 3 o.,^ I 80.0 0.0.0 80.o, 00.o.',, 1 /.50 7.o 5 2,.t 3,7o 23.35 2, 359 2. 95 Zo,20o ) 7., 5 o100o 6(5 7 50-.O 12,."o 75.^ 6 ^'44& 1, I0 2.1.15.241' Do A. Ot IL 1e 765. \(0. 72, 5 5k.o.15oo 7-Sm 7 25,o5 25.6 251,_ 5;5,50 25.;. 23,05 80.3 7A,5 l0o,o 87.'o 5., /5, 7, 75^; 8 2,,00 Z 24 26., 2.4 1.o 21.,. - 7)-.3 7J, 5 I,0'o 96.5 5.,17, 7.oo 74.o 9 7t, 5 o.,.5, Jo 7,7,..o 80I., 7,.5 50o, 6S1,9 5(*.o,.:,, 76,0 310, 25o 0.70 205 27.oo i.2 7,5 500 eo, 500, 2. Q 76.. 12 - 13 14 15 - - 16 17 18 19 - 20 21 - 22 23 24 25 26 28,,

223 indicates that about 1.6% of the fuel by weight was vaporized in the emulsion section of the fuel channel. A complete data reduction program was written to process the model flow data. This program operated on the pressure tap, flow rate, and temperature data, and calculated all of the important parameters for each of the 31 data sets. The computer names for these variables and their meanings follow. (All are experimental values except VIDELA and WIDELA). BLEDPH Total air bleed mass flow rate RATEPH Total fuel mass flow rate RE Reynolds number of main metering orifice CDCHAN Discharge coefficient of entire main channel BVSUCW Boost venturi suction CDJET Discharge coefficient of main metering orifice PDROPW Static pressure differential of main metering orifice DELPBW Total pressure loss in bends DELPXW Total pressure loss in sudden area changes QDOTF Volume flow rate of fuel RATIOM Mass flow rate ratio (fuel to air) RATIOV Volume flow rate ratio (air to fuel) QDOTA Volume flow rate of bleed air AIRVEL Velocity of bleed air in 2nd main bleed VIDELA Ideal air velocity in 2nd main bleed WIDELA Ideal air mass flow rate in 2nd main bleed SUMERR Estimated total manometer reading error DELAW Static pressure differential across 2nd main air bleed The reduced data from two of the thirty-one tests (number 117672) are presented in Tables 13 and 14. There are numerous interesting values in these tables, and also in the reduced data for the twenty-nine additional tests. In order to present these values in a meaningful way, a special CALCOMP plotting routine was written for the flow stand data reduction program. This made possible the automatic plotting of any of seven groups of six different graphs, each available in four

TABLE XIII REDUCED DATA FOR A LUCITE FUEL CHANNEL FLOW TEST WITH AIR BLEEDS LUCITE FLOW MODEL TES't' [THIS DATA IS FOR TEST NUMBER 117672 I THIS TEST IS FOR LAB GAS AT A MEAN TEMP OF. *F I THE JET HAS A CIAMETER GF.0502 INCHES hAC A LENGTH OF.1830 INCHES TIE FLUID VISCLSITY IN CENTISTCKES IS.556 THE FLUIC SPECIFIC GRAVITY IS.721 THkt AIN JET IS CPEN THE LCWER MAIN AIR BLEED IS OPEN THE UPPER MAIN AIR dLEED IS OPEN THE INDEPENDENT PLOTTING VARIAPLE IS THE BCGST VENTURI SUCTION THE REYNOLDS NUMEER IS BASED Ch THE MAIN CRIFICE CIAMETER *** PROGRAM RESLLTS FUR THIS RUN *** CW OF p m ^^ MAIN T' BOST { Ps~ Acarr OOa? v' ASms,' miAR MM m i L "DY I5UCr.w.&. ljSIiL LO~T"SUTrrC RUN LE PH RATEPH RE CCC I-AN BVSUCW CDJET PDROPW DELPBW DELPXW EMULW PERCEN ACrs J M E JTW 1.1519 4.91 1541.6.5268 2.36.7023 1.33.07.00 1.03 44.1 2.202 6.41 2012..6165 2.93.7703 1.88.10.30 1.09 51.4 3.273 8.22 2581.5.6469 4.38.7746 3.06.12.04 1.4.9 4.30S 9.38 2850.3.6516 5.27.7715 3.76.21.04 1.58 61.4 5.357 10.89 3417.3.6963 6.63.8162 4.82.28.04 1.95 63.4 6.381 11.39 3574.1.6SC9 7.36.8086 5.?8.32.07 2.10 64.1 7.404 11.86 3723.7.6771 8.32.7924 6.08.43.07 2.28 64.8 8.426 12.19 3826.7.6795 8.73.7999 6.30.57.07 2.39 64.1 9 442 13.12 4117.7.6967 9.61.8166 7.00.43.07 2.69 65.0 10.460 13.43 4215.2.6874 10.35.8087 7.48.50.07 2.98 64.8 Ly.R La"/MR CNItws ~~e(i INCH ES IIACPIES IN~CJ# 5W 24~ 3C.4 7 20.21 4AO 89...6 1 0 4." 0 I4o RUN QUU1F RATIOM RATICV COCIA AIRVEL VICELA WIDELA SUMERR DELA tDAIR REAIRB 1.11 3C. 88 1, 95 2.18 40.5 96,.0.38 -.20 1.48.422 1044.8 2.14 31.75 19.40 2.76 51.4 108.5.43 -.22 1.89.474 1326.4 3.18 30.10 20.46 3.74 69.6 133.8.53 -.20 2,88.520 1794,6 4.20 2S.43 20.93 4.22 78.6 147.3.58 -.19 3.49.533 2027.1 5.24 3C.47 20.21 4.89 91.0 165.5.65 -.14 4.40.550 2346.8 6.25 29.91 20.59 5.21 96.9 174.7.69 -.13 4.91.555 2500.7 7.26 29.38 2C.97 5.53 102.8 186.1.73 -.12 5.57.552 2652.9 8.27 28.61 21.53 5.83 108.5 190.6.75 -.07 5.84.569 2798.9 9.29 29.66 20.77 6.05 112.6 199.8.78 -.16 6.42.564?905.5 o10.30 29.20 21.09 6.29 117.1 207.0.81 -.06 6.89.566 3020.6 WI'/,K FT r'/I/~ Fr/M LS&, / 1,C1 INO'S H'* " ~"

TABLE XIV REDUCED DATA FOR A LUCITE FUEL CHANNEL FLOW TEST WITHOUT AIR BLEEDS LUCITE FLOW MODEL TEST THIS DATA IS FOn TSFT NUnBER 117671 ITHS TEST IS FnR LAR GAS AT A MEAN TEMP OF 3.' OFI NO AIR BLEEDS T7dF JFV eT 1 )<A vIA&rTF, nF.Cr'V? IN.HFS ANr A LFNGTH OF.1R3r INCHES tkF ItLUTV VICrSIm' TV IT1^ C'fTISTnKFS IS.'S; THF Ftl'r' -fi rl" 9aAVITY S.*7?1 THr wA1,' jrr is r3Fri THr TrrsPf'r nr T PLrTTTIJr VA'^TA3LF IS THF MAIN JFT PRFICSSRF PRIIP ONLY?I tHF rYVNpl nJ N%'JMPF:c Its ASr) ON THF MAIN nrQFICF niAMFTFR ** PPr,PA^ r'jSlljl T< FOr T IS RIJN *** Josr R~PI I. CHAsMr B OS? -'E MAIN w, OF MESIUAL A55&1 FLNW K44F 5LAcn^ r AB? ago amuuX PsAAW. fTbh A? LOT AMcC MtJ P'Ik Mvsicr cTr- ~4 pCr rncc^HA RVSIJrW PFLPW r)E. oPw OEL PXW FIULL r)JET PFQCFN t *A''?.0 1l.^l'~.47r9 *4' 3.5.21.*2. 7.67'-2 41.P. 1 4'I.C' 1.R.4 f Q. 4f.7.7..^4.0 3.1.cP.r'' 7,rl' " 1, 7 L 1. I? * 9 PA l l 1.- 4.1^ ^ 4q.0 Of I Cc c. 4 4 7f, r. ro,.74^^?.^!.a1.1.c.".7c- 7 7(.3 1,: 7*' 7 12 ^:.. 7474?,.4A.3.1.^7.^4.7474 7 7 7. N * n. 7.?7... I 7?...2.7911 7c, 7 /, * 3<cr7 q * 7.4I 7. 8. i 7^ " 78 I 5? ~^ -. <'" 7. - r.".'?C* 47.' 4.27.'8 32.3F? R4. eQ 7 *.'4 1*. ^3 1A. * P^7 C,.4 r."' C. 8.7. "."7 A 4.?c,1 l., 12.14 rf'Q.7 *.1'. --.'or.. "'9 *4.724 22.'9q. 1"."4' o'"oQ.. q ^.L. " ^ A.1 3.."9.44.9?P/' q'.l 1 " 1".' 1'7., 4/.?7..q?o 7. C;4 7.-7 4' 51 P4,c5 R4-' 1' ^.s. 1'.- 4,.l..?39' q.4? R.l,.4..11..54. 8 5''. 1!4' 7 c,77'C1l. c. P4q q. 4 5.'*.13.5C.L633f 7.4 ir 1 ~ 1.7- ta".? P) cc'". 41 ] r.,7...1.1,.4 a-,? F7. a S?4. "')'~ 7., 4..7 c/!' 11.24.A,,. 4.1' *.8,6 9 u. 2 I 1 -'. "c. 7 5 Ci ^.5. 5f' I t ) 1 2.71.7,.7., 77.R 77 Pq.? 1" lr e' L f 5 "A," 7.P..45 134. 3?..7'.1.~.7 P74<c 7 P.! *r 1.' *'/. /- *./ ^r., 1,..44 1 c. l 8.9". l.~?. q 7 f "'4. l':',' 7 *l.?7'. &. 7 "'^ 1. ] 1. l.l. Q*.1.1, R74, ^.'3, 1. * ^). c o. &.4. t67/. 1 7.. 17. 1 27 I.;.O 1 7. 77 r 7,.? ~r,,*-y n'7r?14 A'.', 7?4 1. 4,4 I.P 18.. 14.90'. R, c 1. 5 15Cn ss!3.,,97^.c..^.15 1.V1.l1CH 9!.?J *r 6r. fOFS. wAlR IFIC. OES OF WATER

226 different scales. These computer plots were used to evaluate each test. Figure 56 illustrates the variation in total fuel mass flow rate with the static pressure differential across the main fuel system which, in an actual carburetor, would be the boost venturi suction. Note that the mass flow rate increases smoothly with boost suction, and that the actual flow rate is below the ideal value, which is based on ideal flow for the given pressure differential. The ratio of the actual mass flow rate to the ideal flow rate is the effective discharge coefficient for the entire main channel. The same data is illustrated in Figure 57 on log-log coordinates. This has the distinct advantage of representing the ideal flow curve as a straight line. It will also be recalled from Chapter 3 that constant discharge coefficient values will appear as straight lines on these coordinates. The method of plotting flow data on these log-log coordinates was utilized by Kreith and Eisenstadt37, who related the value of the slope to the orifice L/D ratio. There is a deviation from the general slope of the flow data at both the low and high head regions of the curve. Note that the slope of the mass flow rate data in Figure 57 begins to increase at pressure differentials less than 2.0 inches of water. Also, although it is not shown in this particular data set, the slope begins to decrease in the region of 60 inches of water. (It must do so or it would eventually cross the ideal line.) The air bleed flow rates were measured over a wide range of boost venturi suctions. The experimental values for the total main

227 FLUID FLOW RATE VS PRESSURE DROP MAIN ORIFICE NUMBER= F-50 RVERRGE TEMP = 80.0~F RUN NUMBER = 117671 TEST FLUID = GASOLINE __o. ____ (STD. RE&.) cc.00 2.50 5.00 7.50 10.00 12.50 15.00 17,50 20.00 22.50 25.00 BOOST VENTURI SUCTION IN INCHES OF WRTER Figure 56. Experimental Values of Gasoline Flow Rate As A Function Of the Metering Signal *^ — J^ - - --------------—..0I.,50.0 1.0 1.0 50 75 00 25 50,~~~~~~OS / ETR UTO N NHSO RE Fiue5.EprmntlVle fGslieFo aeA ~'i-//Fncio.... eern Sga

228 LOG-LOG PLOT OF SYSTEM FLON PRRRMETERS MRIN ORIFICE NUMBER= F-50 RVERRGE TEMP = 80.0'F`,- RUN NUMBER = 117671 TEST FLUID = GASOUNE ^:_ ___ __ _ ________ __ ______ _____(STD. _R__ --- - - _ - - --- --- -- -- — itit LO Jm rr -) OD -I L' — X' 1 2 2 3-..I The Metering Sig —nal'*............. -/ —'...... 1 ——.. --- ~___. L,_,-................ z/_. /". —................' - L/ /0 / 2 45 6 789 2 3 4 7 6,9 2 3 4 5 6 789 iXI{r I lXIO1 IXI~ BOOST VENTURI SUCTION IN INCHES OF WRTE8 Figure 57. Log Plot Of Total Gasoline Flow Rate Versus The Metering Signal

229 system air bleeds are shown in Figure 58. These data were obtained utilizing 0.037 inch diameter air bleed orifices for both main bleeds. (The bleed orifices were square-edged with an L/D ratio of 3.63.) Note that the bleed air mass flow rate is very small, being generally less than 0.5 pound per hour. Referring again to Table 13, it will be noted that the fuel mass flow rate is about 30 times that of the bleed air, but that the volume flow rate of the bleed air is about 20 times that of the fuel. It is this large volume flow rate of air within the channel that increases the velocity of the fuel-air foam, and increases the total pressure loss over that for single phase flow. Figure 59 illustrates the fuel mass flow rate data for run number 1110671, which was a test utilizing 32 F gasoline. Note that the measured fuel flow rates are very nearly equal to those obtained with 800 F gasoline (Figure 56). Actually the mass flow rates are slightly higher with the 320 F gasoline than the 80 F gasoline. The ideal mass flow rate curve is noticeably higher for the cold gasoline however. This is due to the increased density of the cold gasoline and to the fact that the ideal mass flow rate will increase as the square root of the fluid density for a given pressure differential (Chapter 3). The effect of fluid temperature on the fuel mass flow rate is a complex relationship involving the precise variations in the discharge coefficients with Reynolds number for each of the orifices being used, and the variation in density and viscosity with temperature for the particular fuel being used. (This was discussed in Chapter 3.) Thus,

230 RIR BLEED FLOW VS VENTURI SUCTION RIR BLEED DIRMETERS= -:7^, RVERRGE TEMP = 80.0F RUN NUMBER = 117672 TEST FLUID = GASOLINE 8 __________________________________________I STANDAIRP R6.) CD 83t- ___ _ _ -- -— I I, Q_ ~..... _ _. _______ 7.5 2 00 _...00 2.50 500 7.950 10.00 12.50 15,00 17.50 2.0 22.50 S5. BOOST VENTURI SUCTION IN INCHES OF WATER Figure 58. Measured Air Bleed Flow Rate As A Function Of The Metering Signal

231 FLUID FLON RRTE VS PRESSURE DROP MAIN ORIFICE NUMBER= F-50 RVERRGE TEMP = 32.0~F RUN NUMBER =1110671 TEST FLUID = STANDARD RE. ~..._.SOLINE ~ I 41^a~~~~~~~~~~~~~~. ~~~~~ —- ------.00 2.50 5.00 7.50 10.00 12.50 15.00 17.50 20.00 22.50 25.00 BOOST VENTURI SUCTION IN INCHES OF WRTER Figure 59. Mass Flow Rate Of Cold Gasoline As A Function Of The Metering Signal

232 for this particular fuel channel geometry and fuel type, the effect of increasing the fuel temperature was to decrease the fuel mass flow rate very slightly (less than 1%.) For mineral spirits the effect of temperature was quite different, as will be seen in the next series of graphs. The effect of numerous variables on the mass flow rate of mineral spirits is shown in Figure 60. First notice that the flow rate increases significantly as the temperature is increased from 480 F to 1200 F. This amounts to an 8.5% increase in mass flow rate for a 720 F increase in fuel temperature. This is for no air being bled into the fuel channel. Opening the main system air bleeds reduces the fuel mass flow rate at a given boost venturi suction by about 10%. Opening the enrichment valve, which in this case was a 0.052 inch diameter orifice in parallel with the main metering orifice, resulted in the mass flow rates shown by the upper curves in Figure 60. The fuel mass flow rates obtained in two other tests, using mineral spirits at 450 F and 135 F respectively, are shown in Figure 61. Note the effect of fuel temperature, which becomes more pronounced at very low flow rates. There is a greater flow rate change per degree temperature change at small pressure differentials than at large pressure differentials. This results from the greater slope of the orifice characteristic curve in the low head region. Thus, the region of increasing sensitivity to fuel temperature corresponds to the region in which the slope of the mass flow rate curve begins to increase, which

233 FLUID FLON RRTE VS PRESSURE DROP 0 0 MHIN ORIFICE NUMBER= F-50 RVERRGE TEMP = 48.0 Am 120.0 F RUN NUMBER = 619671 TEST FLUID = MINERAL SPIRITS ~_' __ 721671 OOI VNUI SUTOINICE FWTR F0f N o'00 2.50 5.00 7.50 10.00 12.50 15.00 17.50 20.00 22.50 25.00 BOOST VENTURI SUCTION IN INCHES OF WRTER Figure 60. The Effect Of Numerous Operating Variables On The Mass Flow Rate of Mineral Spirits

234 LOG-LOG PLOT OF SYSTEM FLON PRRRMETERS MRIN ORIFICE NUMBER= F-50 RVERAGE TEMP = 135.0~F 45^ RUN NUMBER = 919671 = (1'5F) TEST FLUID = MIN.SPIRITS 92CCG71 *4 (4-5*F) 431 — -- -- - - -- - -- ----- - - - - _ I I - -I-I-1- I I I - I I - c __ __-_ __-__ CC 1 L - BOOST VENTURI SUCTION IN INCHES OF WRTER _ Figure 61. The Effect Of Fluid Temperature On The Mass Flow Rate of Mineral Spirits

235 indicates a more rapid change in discharge coefficient. Figure 62 illustrates this concept quite well. Note that lines of constant discharge coefficient have been drawn on the log-log coordinates, and that the discharge coefficient is changing more rapidly in the low head, low flow rate region. The effect of various parameters on the air bleed mass flow rate is shown in Figures 63 and 64. These data were obtained using mineral spirits as the test fluid. Figure 63 illustrates the air bleed flow rate variations for both one and two air bleeds in the main system. Both curves increase smoothly with boost venturi suction, with the curve for two main air bleeds being slightly less than double that for one air bleed. If this data is compared to that in Figure 58, it will be evident that the air bleed mass flow rate curves are practically identical for gasoline and mineral spirits, although the two fluids have significantly different properties. Thus the air bleed flow rate is quite insensitive to fuel type. The effect of fluid temperature on the air bleed mass flow rate is evident in Figure 64, which is a plot of the air bleed flow data obtained in two tests at significantly different fluid temperatures. It may be noted that the air bleed mass flow rate is relatively insensitive to fluid temperature in addition to fuel type. This may explain one interesting fact that became evident during the Lucite flow model tests. It was found that the addition of air bleeds resulted in a fuel flow rate curve that was less sensitive to fuel temperature changes. By introducing

236 LOG-LOG PLOT OF SYSTEM FLOW PARRMETERS MRIN ORIFICE NUMBER= 5E-18 RVERRGE TEMP = 48.0~F RUN NUMBER = 623671 TEST FLUID = MIN.SPIRIT5 X- _ _,,___,.........___ 00 LO LL cr. Metering Signals.. rLj L n lc O " 9 7 936O9 MAIN SYSTEM PRFSSURF DROP IN INCHES OF WATER Figure 62. Illustrations Of The Rapid Change In The Main Channel Discharge Coefficient At Small

237 RIR BLEED FLON VS VENTURI SUCTION RIR BLEED OIRMETERS=.37 RVERRGE TEMP = 80.0 F RUN NUMBER = 711671 TEST FLUID = MINERAL SPIRTS5 o r.. -J Figure 63. Air Bleed Flow Rate Variations For One And Two Operating Bleeds

238 RIB BLEED FLON VS VENTURI SUCTION 135.0 F 0, os7 AVERAGE TEMP = 40.0 F RIH BLEED OIRMETERS= 0 0317 RVERRGE TEMP = 40.0 F RUN NUMBER = 104671 o4'F)e TEST FLUID = s14E-. WOORIVgR g ____ 2 _ 5 X7 iO 10 1671 ( 135F) * _____MINERAL SPIRITS f Kr _ I _ I-ii.00 2.50 5.00 7.50 10.00 12.50 15.00 17.50 20.00 22.50 25.00 BOOST VENTURI SUCTION IN INCHES OF WATER_ Figure 64. The Effect Of Fluid Temperature On The Air Bleed Mass Flow Rate

239 into the channel an air bleed flow which is relatively insensitive to fuel type or temperature, the overall sensitivity of the fuel flow rate to temperature change is decreased. For mineral spirits, the fuel mass flow rate increase was 1.2% per 100 F increase without air bleeds and 0.5% per 10 F with air bleeds. G. TWO-PHASE FLOW OBSERVATIONS As stated earlier, one of the advantages of the lucite model was that the two-phase flow within the fuel channel could be observed and photographed. This characteristic of the flow model was utilized to some extent in every flow test. It was discovered that occasionally, when using warm, highly volatile fuels, a vapor bubble would form below the main metering orifice, and would remain in that position until the fuel flow rate became sufficiently large to carry it away. While it remained in that position the metering characteristics of the channel were slightly altered. One of numerous other phenomena that were observed was the condensation of water from moist bleed air when the fuel temperature was less than about 400 F. These water droplets, being heavier than the fuel, would fall to the bottom of the air bleed well and collect there. Under certain conditions, this ball of water would be drawn into the idle tube, which would certainly result in a rough engine idle, if not a complete stall. High speed movies (300 frames per second) were taken of the two-phase flow in the emulsion section of the fuel channel. A few

240 i,1.11_ nilk - l~~~~~ Figure 65. High Speed Photographs Of Two-Phase Flow \Tithin The Lucite Model

241 consecutive frames from one of these movies were enlarged and are shown in figure 65. The view is that of the air bleed well and discharge tube, similar to the cross-sectional view shown in Figure 51. While the movies show significantly more detail than these enlarged frames, the bubble-type flow in the discharge tube is quite evident. The two-phase flow within the fuel channel was found to be in a few distinct regimes in nearly all cases. The flow in the emulsion section was in the bubble-flow regime, and the flow regime in the main discharge tube was either bubble or stratified, depending on the fuel flow rate. At low main system fuel flow rates the discharge tube flow was stratified, with the air flowing in the upper portion of the tube. As the fuel flow rate increased, the two-phase flow regime changed from stratified to bubble flow. The flow in the idle system was mainly slug flow, changing to bubble flow only at the highest idle fuel flow rates. The total pressure loss due to two-phase flow in the emulsion section of the fuel channel was determined experimentally, and is plotted in Figure 66as a function of the boost venturi suction. There are three important facts inherent in this data on the two-phase total pressure loss: 1. This pressure loss increased linearly with boost venturi suction 2. This pressure loss was not significantly affected by fuel type or temperature 3. This pressure loss was related to the volume of air bled in, but for typical air bleed orifice sizes the two-phase pressure loss was about 4.5 times that for fuel flow alone

242 r, —';~~-...t' jI~~~~~~~~~~~~~~~~~~~~~~~~~~I iL7- I -- 1 ff if fl;f I I If T f<j til10ti ~ii''I;-'- j,I....F.'.- J t If I It' <I I:.i i H V.... II~jI0Fe'}'4X0-l-ttf 0ifa A t'f't't~ II ~ K~Hil <-IS jji t< [4TF a t -SX~~~~~nt;$4-1 tppp ~~it lilfLti r fifitt~~ ttl< 41 l gIti fX XtIt I K 1 __ V i Uh1 t -tF I1 j v TLA Iti 2I r ftt<IfI 411 77 i!,i-!-!-~ ~-!!- I ~I-i-i:,-+t-!-i:, It,... i-r!!:,i...: _P,: Laid ttiF1 Lo ark:- A L —T1 Figure[ 6."~ Tota prssr los varatonsfo Ifw flo Iti the carburetor -~'i'i -J~-It ~:tttI -'' - I L.. - VI Ji IT I L;~iI it-.. ~ ~ ~ fi 1-'i'.i- 41 —' —:,2I' iltf -fl~ - Ki' —, -- 1:14~ ~ ~ ~~~I 1Fi L4 V 4lI i 1-r' " i ~.'i':~ "?~,~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~~~~~~~~~~rdr ~ i~ I~l Li V VIII j~ri ii~,jT, —,-, -4 - - t' 11. Itii i....~-...t'- f-K...I: lIi' i: Figure L 6. T o aI l 1eu l vi o Iwo-t~haso If l Vw withi n It-! I t~~~~~~~~~14 K4f'11 Figure 66. Total pressure loss variations for two-phase flow within the carburetor

243 H. COMPARISON WITH PREDICTIONS OF SUBROUTINE FLOW As mentioned in Section 7A, one of the reasons for conducting the fuel channel flow tests was to obtain fundamental flow data with which to check the operation of subroutine FLOW, which is the fuel channel analysis subroutine. A small main program was written to check the predictions of subroutine FLOW by supplying the geometric values, fuel properties, and other conditions corresponding to an actual fuel channel flow test. These values were operated on by the subroutine for each specified operating condition of the actual test, and corresponding lists of flow rates and pressure differentials were predicted (similar to the values in Table 6.) These values were plotted by the computer and could readily be compared to the experimental data. The plots in Figure 67 illustrate the comparison between the measured and predicted fuel and air bleed mass flow rates for a typical test. The first plot in this figure is for the main fuel mass flow rate as a function of the metering signal. Note that the predicted values were about 3 or 4% higher than the experimental values, and that the predicted curve follows the same trend as the actual data. The main air bleed mass flow rate values are shown in the second part of Figure 67. The experimental and predicted values in this case were for tests with 40~ F Shell mineral spirits as the channel fluid. It may be seen that the air bleed flow rate predictions were about 10% high for both 1 and 2 air bleeds open. On the basis of numerous comparisons such as those in Figure 67, the following general conclusions may be stated concerning the accuracy of the fuel channel flow predictions:

FLUID FLON RRTE VS PRESSURE DROP MRIN ORIFICE NUMBER= F-50 RVERRGE TEMP = 135.0 F RIR BLEED FLON VS VENTURT SUCTIr RUN NUMBER = 922671 TEST FLUID = MIN.SPIRITSS,, -- --- -- --- -- -- -- -- --- -- RA IR BLEED DIRMETERS= 007 RVERRGE TEMP = 40. 0 F RUN NUMBER = 102671 TEST FLUID = MINERAL SPIRFTS 8 _ _ _ _1$_ 8 -- ---- t _ IUPPER AIR BLEED IN (0.037.H: ) ~sl -- ----- SYS —-I I_ __ I ICE O_ ____, /a Figure 67. Comparison of The Flow Rate Predictions of'^[/_ _______________ D'~/ ^^ ---- i 8 -0o 2.50 5s00 7.50 10.00 12.50 15.00 17.50 2..s S.oo -— 0o 2. -- -.0o 7.50 IS.o- 12.s- I-.- D.so - 20.00 22.50 2s.-oo BOOST VENTURI SUCTION IN INCHES OF NTFR sk BOOST VENTURI SUCTION IN INCHES OF WRTER Figure 67. Comparison of The Flow Rate Predictions of Subroutine FLOW With Actual Fuel Channel Data

245 1. The fuel mass flow rate predictions were nearly always within 4% of the actual values with no air bleeds, and within 8% with air bleed flow. 2. In numerous cases where no air bleed flow existed, the fuel mass flow rates were predicted within 2% of the actual values. 3. The air bleed mass flow rate predictions were nearly always within 12% of the actual values, and in the majority of cases were within 8%. The greater accuracy of the predictions for single-phase flow situations is to be expected, due to the increased complexities encountered in describing the effects of two-phase flow within the channel.

CHAPTER VIII OPERATION OF THE COMPLETE SIMULATION A. GENERAL DESCRIPTION All of the foregoing analyses, in the form of their respective subroutines, were combined into one general carburetor simulation program. This was achieved by developing a main calling program that utilized each of the subroutines in a logical order of solution which was directly related to the actual metering process within the carburetor. The basic iterative scheme of the simulation is to determine the carburetor parameters corresponding to one fixed operating point, which is determined by a particular throttle angle and engine speed. However, the simulation program is able to evaluate carburetor performance over a wide range of operating conditions. In other words, if the simulation program can evaluate the performance of a carburetor for any one specified operating point, it is possible to perform the simulation repeatedly for various operating points, which correspond to certain physical situations. This is in fact what was incorporated into the simulation. Based on the ideas discussed above, the simulation was written to provide for seven types of carburetor analyses, each invoking the basic iterative scheme for one specified operating point many times. These analysis types actually represent various sequences of operating points which correspond to specific physical situations that are encountered in carburetor and engine work. The seven sequences of 246

247 operating points for which the carburetor can be analyzed are: 1. analysis at a specified operating point which is read as data (RPM and -) 2. analysis at constant engine speed and variable throttle angle 3. analysis at constant throttle angle and variable engine speed 4. analysis for the complete carburetor-engine operating map 5. analysis at road load operating conditions 6. analysis for the carburetor-engine-vehicle operating map 7. analysis with production variations in dimensions Each of the above analysis types utilizes the basic iterative scheme. This can be illustrated by briefly considering the second analysis technique above, the constant engine speed, variable throttle angle analysis. This consists of a series of repeated simulations, one for each operating point, with the operating point incremented each time. The engine speed remains constant at some specified value (which is read in as data), but the throttle angle is automatically incremented from completely closed to fully opened, in 2~ increments. In this case simulations will be performed for about 35 separate operating points, all corresponding to operation at the specified engine speed. Since all of the analysis techniques utilize repeated applications of the single operating point simulation, the basic iterative scheme of the main program will be discussed. (A complete listing of the main program is given in Appendix I.) However, the analysis cannot begin until the operating conditions have been completely specified by means of the input data. Thus, let us first consider the required input data before discussing the basic iterative scheme in detail.

248 B. REQUIRED INPUT DATA On the basis of the number of analyses presented in the preceding chapters, and the number of parameters to be evaluated, it should be evident that a substantial amount of input data is required for the simulation. The input parameters required by the complete simulation may be divided into the following categories: 1. orifice characteristic curve data 2. vehicle data 3. engine correlation data 4. carburetor geometric data 5. carburetor functional data 6. fuel data 7. ambient conditions data 8. data indicating the type of analysis desired, the printout level, and the particular computer plots to be drawn The actual data are read in the above order according to the formats listed in the main program. Table 15 shows a typical data set for a complete simulation run. These values should be compared to the formats given on the first and second pages of the main program. The first group of input data represents the characteristic curves for square-edged orifices with a wide range of L/D ratios, as well as for the actual main metering orifice being used. This data was listed previously at the conclusion of Chapter 3. Also included in this data group are the throttle plate discharge coefficient values. The second input data group consists of the parameters for the vehicle being used. Such items as the differential gear ratio, tire revolutions per mile, vehicle weight, and frontal area are included in this group.

249 TABLE XV REQUIRED INPUT DATA 60 216.0 1.0 cotgSm~r monWF~~wAu, & MYISr 1600 1600.0 1.0 cowsyr 0. 0 0. 0 0. 0 0. 0 FAWrOlr co~roL cAw FIA VS. DRY AIR FLOW 6.0 1.0 Flor cAl c COMPLETE OPERATInG MAP 6.0 1.0 4.0 ANALYsiS cAp 0.0 1.0 1 29.00 80.0 0.500 A14BjJr cMPrMrOS CAP STIANDARD REG. GASOLINE 1.0 80.0 0.400 FPuL c~D 0. 0730 0.0730 0.0000 0.001 0. 001 0.000 0.140 0.093 0.010 0.001 0.001 6.00 1. 00 FORD 2 BBL. C6AF-9510-B F-50 2.0 2.0 10.00 1.4370 0.375 ro DETERMINE CARBURETOR PERFORMANCE OVER A WIDE OPERATING RANGE REAS6M T WRi 1.250 1.000 0.780 0.070 0.0010 0.0100 0.0100 0.0100 0.0010 0.0010 0.0010 0.0010 0.0010 0.011i TOL&XAWCES 1.030 0.875 0.538 0.596 0.650 0.750 BW5OT YBOIW 3IA>MMs 0.0010 0.0010 0.0010 0.0010 0.0010 TOLBtANC6S 1.930 1.930 1.145 1.160 1.400 MAIW YEWW P1AMNtS 0.0000 0. 0000 0.0000 0. 0000 0.0000 90.000 75. 000 0.0000 15.000 90.000 0.0000 64.000 64.000 0.',00 0.0000 75. 000 0.C0000 0.0000 0.0000 0.0000 0. 0000 0.0000 90. 000 0.0000 26.000 EIJWr Ar5ES 2.0000 2.0000 2.0000 2.0000 2.0000 0.0000 0.0000 2.0000 0.0000 3.0000 2.0000 0.0000 0.C0000 0.0000 0.0000 0. 0000 2.0000 0.000O 1.0000 0.0000 3.0000 0. oooo 2. 0000 0. o0o0 2. 0000 SMW Tye 0.0312 0.1400 0.1250 0.1060 0. 0933 0.7060 0.7800 0.1060. 0000 0. 1060 0.1250 0.9375 0.2500 1.0000 0.3400 0.8120 0.1350 1.9300 0.1830 0.3120 0.1060 0.1250 0.3900 0.2060 0.1250 CMYAf U946H 0.0010 0.0010 0.0010 0.0010 0.0005 0. 0020 0. 00.30 0.0010 0'.0030 0. ('010 0.0010 0. 00,0 0 0. 0C 0. O020 OU 0 oo 0. 00o0 0.0010 0.0035 0.0005 0. 0O 20 0.0020 0.000 0.0020 0. 0020 0.0010 TOLAMcU5 0.044 0. 02 70 0 0 9 0.0350 0.0 260 0.1400 0 0140 0. 04200 0.0940 0 059-0 0.0310 0.14 0.I29 10. 150 0.2700 0.1600 0.2250 0.0610 0.0502 0. 1870 0.01 0. 15 0.1560 0. 1A 0.0280 FUEL CHANNEL 0.30 0.936 0.941 0943 0.945 0.4 0.946 0.60C | 0.734 0.8|l 0.870 0.890 |0.906 0.920 |T O I14.0 0.0 7.5 5 6 25 FIRS'r CA9IWWOM "MMT= OWX 1 0. C0 0L2.L50, O. O 0.C 00.O: 00 L 00.00 LASTrEN CAP 71.10 6.70 E65.50 R 6.5 151.40 3. 00 22.80 71.50 72.7 0 73.2I 50 73.30 72.90 72.10 5.OiO 12. 00.50 49 60 59.0 66.10 69.50 00000 o ri r 0. 00 CIO"0 Al O" QQ ('0.00 00.00 4.00" 1 lbriii 00 00I 00. OCu,00 00. 00 00.00 2. 00 27.60 2 I 2 2.0 80 00 L 16.40 10.05 31.00 1.20 1 2 31. 10 31.00 30.60 29.90. 000 I000 14 00 1.6" 26.10 29.00 30.50 AA O r i A 00 00 L 00 0i. 0o 00. 0" 00.00 00.00 21.60I 2.20 24 72 2 6.0 27.1:3 28.85 30.20 1:.40 14. O, 15 30 16. 1 11 0 18.40 19.86 19. 30 21 24. O 25.5 27.III 28.35 29.65 13.40 10.9 1016 10. 82 11. 48 13.4 16.32 2L0. 0 432.0 35.C. CIOL A 00. 0 0 14.0 000.0 400.0 9.30 1.0 Al 1.670 035 0001 0.001 0.050 1966 FORD 2 -8 4. 0105 T- 2.870 8.0 ENeME, 0~D 3.000 1. C 1 1.000 L 1 0 VEHICLE c,4l 1966 FORD FAIRLA-IE'5000 7 7.0 (I.010 0.00121 0.73 0.73 0.7 i' 0.41 0.74` 0. 74 0.743 LAST ORIF CAM 0.72 0. 26 0. 72 0. 7 2 734 0. 76 0.737 10. 58 L.0I 0. 0.620 0.O 0.685 0.703 0.712 0.751 0. ^^.75 0.757 0.759 L.760 0.761 0.730 0.734. 0. 743 0.746 0.747 0.749 7.230 0.000 0 7 0.647 0.6 0.711 0.724 0.729 0.772 0. 77 0.774 0.75A776 0.777 0.778 0.756 0.761 0. 7-4 0. 76- 0. 768 0 0.771 4 726 0.000 0.62 0. l. 710 0.7 74 0.741 0.750 0 q,7 A 790, 0.791 00 79. 0.8 3 0.793 0 - 7 7 6 0.7 7` (I.,71 01 A. 7 0',8 0.787 0.629 0.000 0.6b74 0.781 0.698 O RO. 0,- E.,L' 0CU(o C.L8.i (I.:;L I O,1u 0I.810 0.790 0. 7'-" ) 0. 79t 0.79 8 0.800 0. 8 1.804 1.426 0.000 0 ~~~~~~~~ 0.,ct 0',7 0 0.`4 0.788 0.790 0,713 0. 7 05 0700 0. 690 0. -2 0680 0.680 0. 67(7 0.67 LI ~0 0 6 7'c 0. 98 0.t86 0.676 0.616 0.000 0. 69 0. 0 0 7_L 0.6 0.668 0.700 0.6.Z5 0.625 0.624 0.623 0.622 0.621 0.620 0.620 0.638 0.635 0.633 0.631 0.629 0.627 0.626 0.100 0.000 0.663 0.665 0.654 0.648 0.644 0.641 0.9? 0702 0. 709 0. 716 0.722 0.728 0.7:4 614 0.69 0.6 00.66 0.6 0.84 WW 0;^ W~ ~0.70L2 0.73 0.761 0.783 21.0 1.o a~1o0 soo. o~ 11 00.0 oooORIFICE1 I I I I I ~WTA XC XNCD.TL XNCDSE DELXT 1TELX3L DELXSE coS~L.I ggggggg ggggiii g sgggtgggg ggI'S"gg ""gI2Wg 11gI"gU)4gd!gg 1esii!iiiiiI!iiiuii |i2>~ii? H4)5 *tf ~' <<jiS 1n NiMN ~m 3i )1233 n(3446 i,3.32 MU~ UU M 1~ ~m ~* w m1 "33*

250 The engine correlation data that is read in consists of two indicated horsepower curves and two friction mean effective pressure curves, as discussed in Chapter 5. These curves are read in as discrete points, as a function of the fuel-air ratio and engine speed respectively. Additional engine specifications that are required include bore, stroke, compression ratio, number of cylinders, and valve dimensions. The required carburetor geometric data is extensive, since this is the means by which a given carburetor design is specified for the simulation. This data includes: 1. the number of carburetor barrels, main metering orifices, and enrichment systems 2. the number of stations to be used in the main venturi and in the boost venturi 3. the number of elements in the complete fuel channel 4. the length, diameter, angle, and production tolerance of each fuel channel element 5. the diameter and production tolerance at each main and boost venturi station, as well as the throttle bore and shaft 6. the spill point, closed throttle angle, enrichment valve opening vacuum, idle needle included angle, and number of turns 7. all throttle bypass and choke restriction diameters and tolerances The fuel and ambient conditions data consists of the fuel type code (corresponding to those in subroutine FPROP), fuel temperature, ambient pressure, ambient temperature, and relative humidity. The required simulation control data consists of switches which select the type of analysis to be performed, the order of interpolation to be utilized in the general interpolation subroutine, STERL, the printout levels of the main program and subroutines, and the number and type

251 of CALCOMP plots to be drawn. The arrangement of the above data is such that the less frequently changed parameters are read in first, and the control data, which is changed quite often, are read in last. Thus, in many cases it is not necessary to reread all of the input data for consecutive simulation runs, but only the last one or two data groups. C. BASIC ITERATIVE SCHEME After the required data has been supplied to the main program, the determination of the values for the multitude of carburetor variables corresponding to a given operating point can begin. The basic iterative scheme for a carburetor simulation at one specified operating point may be best explained by referring toFigure 68, which is a diagram that illustrates the logical order in which the main program calls each of the subroutines, and the results of each call. It is by no means a flow chart for the main program or any of the individual subroutines. The diagram merely indicates the general procedure used in analyzing carburetor system performance and in evaluating the interactions of these systems. Note that the analysis begins with a specified operating point. This operating point may correspond to one in a series based on any of the seven analysis types listed in section 8A. Regardless of how the operating point is obtained, the basic analysis formally begins by calling subroutine THROTL for the specified throttle angle, throttle bore

READ ALL SPECIFY AN CALL THROTL CALL FPROP REQUIRED I OPERATING POINT _ / INPUT DATA (RPM AND 9) DETERMINE DETERMINE THROTTLE FLOW FUEL PROPERTIES AREA CALL AIRM CALL ALXMIX CALL ASSUME DETERMINE MIXTURE DETERMINE THERMODYNAMIC COMPONENT FLOW RATES -~ PROPERTIES OF THE MIXTURE - DETERMINE REASONABLE AND INTAKE MANIFOLD AT EACH STATION BASED ON A INITIAL GUESSES FOR ____VACUUM_____ ASSUMED F/A RATIO NUMEROUS PARAMETERS. ——. —---—.._____________________________________^ (41 —---------------- - CALL SIGNAL CALL SOLVE CALL FLOW DETERMINE BOOST - - SIGNAL CALLS ON SOLVE DETERMINE FUEL ANDVENTURI SUCTION TO DETERMINE MACH NUMBERS AIR BLEED FLOW RATES IN THE FUEL CHANNEL NETWORK TO PIINTA _ CALL CALCMP CALCULATE F/A RATIOS CALL STERL FROM FUEL RATES AND PLOT ONE OR MORE AIR RATES. COMPARE - - FLOW CALLS ON STERL OF ELEVEN GRAPHS THEM TO VALUES USED IN XMIX TO DETERMINE ORIFICE DISCHARGE COEFFICIENTS Figure 68. General Procedure Utilized in the Basic Iterative Scheme

253 diameter, and throttle shaft diameter. This subroutine evaluates the corresponding throttle flow area and returns it to the main program. Subroutine FPROP is then called for the specified fuel type and temperature. This subroutine calculates and returns to the main program all needed fuel properties, including density, viscosity, surface tension, vapor specific heats, molecular weight, and latent heat of vaporization. The next step in the procedure is to call subroutine ASSUME. This particular subroutine assigns reasonable initial guesses to numerous variables, including the main and total fuel-air ratios, and the fuel flow rates in each fuel channel branch. These initial guesses are based on a typical carburetor flow curve, and are used chiefly to reduce the number of iterations required within the simulation. The values of humidity, fuel properties, and the assumed fuel-air ratio are now utilized by calling subroutine XMIX. This subroutine evaluates all needed thermodynamic properties of the mixture at each station within the main and boost venturii. Included in this list of properties are the mixture molecular weight, specific heats, and specific heat ratio. Once the thermodynamic properties of the mixture are known at all strategic locations within the carburetor, a comprehensive compressible flow analysis (chapter 2) involving the interactions between the throttle plate pressure ratio and the engine air flow can be applied. This is accomplished by calling subroutine AIRMAS. Numerous parameters are calculated iteratively by this subroutine, the most important

254 of which are the mass flow rates of the mixture components, the intake manifold vacuum, and the throttle plate Mach number. The next operation in the analysis is to utilize the mixture flow rates supplied by AIRMAS, along with the specified venturii geometry, to obtain the boost venturi suction. Subroutine SIGNAL is called,and a general compressible flow analysis is applied to the venturii system. Subroutine SOLVE is called by SIGNAL numerous times to evaluate Mach numbers at various stations. When the multiple iterative parameters within signal have converged, the boost venturi suction is known, as are the pressures, temperatures, Mach numbers, and suctions at all other stations. At this point the intake manifold vacuum and boost venturi suction are known. Thus, the driving potentials for flow within the fuel channel network are known. Subroutine FLOW, the fuel channel analysis portion of the simulation, is then called. A comprehensive network flow analysis is performed iteratively, using the initial guesses for the system flow rates as a starting point. When convergence has been obtained, a large amount of information is known for each element in the fuel channel, including mass flow rate, total pressure loss,Reynolds number, velocity, and velocity head. In addition, the system flow rates are known, including the main, idle, and total (main + idle) flow rates. Many calls are made to STERL, the general purpose interpolation subroutine, during this network flow analysis. This is done to obtain discharge coefficient values for each orifice and iterative Reynolds number. The interpolation

255 is performed upon the characteristic curve data which was initially read in. Since the air flow rate and the main, idle, and total fuel flow rates have now been obtained, the next logical step is to calculate the main, idle, and total fuel-air ratios, and to compare them to the values that were initially assumed. A convenient error parameter is defined as the current fuel-air ratio minus the previous iterative fuel-air ratio. If any of the error parameters are greater than 0.0001, then new thermodynamic properties are calculated for the mixture and another iteration is performed. If all of the fuel-air ratio error parameters are very small, the iterations are terminated for that particular operating point, and the appropriate values are stored for later computer plotting. D. CARBURETOR ANALYSIS AT CONSTANT ENGINE SPEED OR CONSTANT THROTTLE ANGLE 1. Simulation Predictions The theoretical analysis of carburetor performance for constant engine speed-variable throttle angle conditions, or for constant throttle angle-variable engine speed conditions, is a useful extension of the basic iteration technique. In the first case, the throttle angle is automatically incremented from completely closed to fully opened, and in the second case the engine speed is incremented over the range from zero to 5000 RPM. The simulation predictions.for a typical constant engine speed analysis are listed in Table 16. Note that of the hundreds of carburetor

TABLE XVI SIMULATION PREDICTIONS FOR A CONSTANT ENGINE SPEED - VARIABLE THROTTLE ANGLE ANALYSIS UNIVERSITY OF MICHIGAN MECHANICAL ENGINEERING DOCTORAL THESIS DIGITAL SIMULATION OF CARBURETOR METERING CARBURETOP-ENGINE-VEHICLE OPERATING MAP OAVIO L. HARRINGTON THE.TYPE OnF ANALYSIS REQUESTED IS...e..COMPLETE OPERATING MAP THE TYPEbOF PLOT(ISI REQUESTED ARE......F/A VS. DRY AIR FLOW THIS SIMULATION PERFORMED ON..........12 MAR 1968 PURPOSE OF THIS SIMULATION RUN e.......TO DETERMINE CARBURETOR PERFORMANCE OVER A WIDE OPERATING RANGE ABS I E NT- C0NTO1N-S 6CARBURETOR FUEL ENGINE VEHICLE PRESSURE a 29.00 INCHES HG FODb 2 -BC. C6AF-95io-8 STANDARD REG. GASOLINE 1966 FORD 289 V-8 1966 FORD FAIRLANE TEMPERATURE a 80.0 DEGREES F MAIN JET - F-SO TEMPERATURE a 80.0 F DISPLACEMENT~?89.2 C.I. VEHICLE WFIGHTa343.0 HUMIDITY 5 50.0 PRCENT MAIN VENu1-1.145 IN. SPECIFIC GRAVITY..721 COPP. RATIO - 9.3 REAR AXLE RAT O. 3.00 DENSITY a.0713 LBM/FT3 CLOSED THROTTLEIO_.0 VISCOSITY a.556 CS VALVE FLOW ARFAa6.8? IN? TIRE REVS/MILF.775.0 UV, CARBURETPR-ENGINE OPERATION AT CONSTANT ENGINE SPFFD-VARIABLE THROTTLE OPENINC THROT INTAKE MOIST DRY BOOST MAIN THROT MAIN TOTAL TnTAL MAIN THROT AIR ENGINE THROT FLOW MAN. AIR AIR VFNTURI VENTURI MArCH F/A F/A FUFL FUEL TOTAL BLEE RPM ANCGLE AREA PRFSS FLOW FLOW SUCTION SUCTION NO. RATIO RATIO FLOW FLOW TEMP FLOW J 1600.0 10.0.0179 4.88 41.21 40.76.06.03 1.0000.0000.1560 6.3e9.000 80.0.000 4 1600.0 12.0.0286 5.31 60.81 60.14.14.07 1.0000.0000.1050 6.114.000 80.0 000 3 1600.0 14.0.0413 6.83 95.64 84.70.28.15!.0000.0000.078e 616?.000 80.0.000 1600.0 16.0.0559 8.77 115.74 114.47.53 *28 1.0000.0000.0519 5.914.000 80.0 000 2 1600.0 18.0.0724 10.86 149.61 147.97.89.47 1.0000.0120.0500 7.405 1.781 77.2 176 1600.0 20.0.0907 13.13 186.95 184.90 1.41.74 1.0000.0263.0536 9.916 4.R72 73.9?40 3 1600.0 22.0.1109 1517 22.46 2251.37 2.1? 1.11.9829.0367.0565 1P.776 8.775 71.4 300 3 1600.0 24.0.1329 17.91 265.86 262.94 2.91 1.52.8575.0446.0587 15.439 11.734 69.6 -356 I 100.0 26.0.1567 1 9.93 299.18 29590 3.70 1.94.7495.0502.0603 17.853 14.850 68.3 400 3 1600.0 28.0.1822 21*60 326.80 323.72 444 2.33.6586.0545.0617 19.930 17.603 67.3 450 2 1600.0 30.0.2094 22.96 349.36 345.53 5.10 2.67 *5817.0579.06?9 21.7?' 20.010 66.5 486 2 1600.0 35.0 *784R 25.26 388.70 384.44 6.37 3.33.4389.0698.069P 26.844?6.R44 63.7 453 3 1400.0 40.0.3700 210.8 406.30 7.15 3.73.3393.0705.0705 28.662?P.662 63.5 481 2 1600.0 45.0.4641 27.35 423.43 41A.79 7.62 3.98.2700.0710.0710 29.724?9.724 6. 497 2 1600.0 50.0.5662 27.80 430.92 426.19 7.91 4.13 *2205.0712.0712 30.348 30.348 63.4 506 2 1630.0 55.0.6749 28.07 435.5? 430.75 8.09 4.22 *1842.0714.0714 30.761 30.761 63.3 512 2 1600.0 60.0.7884 28.25 438.45 433.65 8.21 4.28.1572 *0715.*0715 31.018 31.018 63.3 516 2 1600.0 70.0 1.0135 28.44 441.61 436.77 8.34 4.35.1217.0717.0717 31.207 31.297 63.3 520 2 1600.0 80.0 1.0896 28.48 442.24 437.39 8.37 4.36.1129.0716.0716 31.2P7 31.297 63.3 520 2

257 and engine variables that were calculated, only the most important parameters were listed. (All of the others may be obtained if desired.) The results of this particular simulation run indicate that the mixture flow at the throttle plate is choked (Mach number of unity) up to a throttle angle of 20~. The air flow rate increases significantly in this range however, because the throttle flow area is increasing. Also note that the main system fuel begins to flow at a throttle angle of 18~, which corresponds to an air flow of about 75 pounds per hour in each carburetor barrel. The total temperature of the mixture at the throttle plate is equal to the ambient temperature until main system fuel begins to flow (the idle fuel flow does not affect the thermodynamic properties of the mixture at the throttle restriction,since it is discharged slightly downstream). Once the main fuel system begins to function, and fuel enters the air stream at the boost venturi, the total temperature of the stream is reduced due to fuel vaporization. It may also be observed from the predictions that the enrichment valve opened at a throttle angle of about 350, at which point the total fuel-air ratio increased abruptly. It is also obvious that this particular carburetor geometry (which had significantly different idle system dimensions than the production carburetor, in order to check the operation of the simulation) would result in a very lean,off-idle fuel-air ratio at this engine speed. The results of two constant throttle angle analyses are shown in Tables 17 and 18. The dimensions read in to the program in this case

TABLE XVII SIMULATION PREDICTIONS FOR A CONSTANT THROTTLE ANGLE ANALYSIS (CLOSED THROTTLE) AMBIENT CONDITIONS CARBURETOR FUEL ENGINE VEHICLE PRESSURE = 29.28 INCHES HG FORD 2 BARREL C6AFB STANDARD REG. GASOLINE 1964 FORD 289 V-8 1964 FORD FAIRLANE TEMPERATURE = 92.0 DEGREES F MAIN JET a F-50 TEMPERATURE = 80.0 F DISPLACEMENT=288.5 C.I. VEHICLE WEIfHT=3650.3 HUMIDITY = 40.0 PERCENT MAIN VENTURI=1.145 IN. SPECIFIC GRAVITY=.721 COMP. RATIO = 8.5 REAR AXLE RATIO= 3.25 DENSITY =.0704 LBM/FT3 CLOSED THROTTLE-10.0 VISCOSITY =.556 CS VALVE FLOW AREA=6.82 1N2 TIRE REVS/MILE =775.0 CARBUJkETOR-ENGINE OPERATION AT CONSTANT THROTTLE OPENING-VARIABLE ENG1JE SPEED THROT INTAKE MOIST DRY TOTAL THROT THROT MAIN TOTAL MI XT. THR3T THROT TROT ENGINE THROT FLOW MAN. AIR AIR MIXT. PLATE MACH F/A F/A CP/CV TOTAL TOTAL PLATE RPM ANGLE AREA PRESS FLOW FLOW FLOW FLOW NO. RATIO RATIO RATIO PRESS TEMP COEFF N U 500.0 10.0.0179 11.73 42.67 42.13 47.68 29.35 1.0000.0000.1188 1.406 29.277 92.0 700 5 600.0 10.0.0179 10.35 42.76 42.21 47.89 29.35 1.0000.0000.1216 1.406 29.277 92.0 700 4 700.0 10.0.0179 9.33 42.74 42.20 47.97 29.35 1.3333.0000.1239 1.406 29.277 92.0 700 4 800.0 10.0.0 179 8.56 42.73 42.18 48.03 29.35 1.0003.0000 1257 1.406 29.277 92.0 703 4 900.0 13.0.0179 7.95 42.72 42.17 48.09 29.35 1.0000.30000.1273 1.406 29.277 92.0 700 4 1000.0 10.0.3179 7.47 42.71 42.17 48.13 29.35 1.0000.0000.1286 1.406 29.277 92.0 703 4 1200.0 10.0.3179 6.77 42.69 42.14 48.19 29.35 1.0000.0000.1305 1.436 29.277 92.0 703 5 1400.0 10.0.0179 6.32 42.72 42.17 48.28 29.35 1.3000.0000.1319 1.436 29.277 92.0 703 4 1600.0 10.0.0179 5.97 42.71 42.16 48.31 29.35 1.03000 0000.1330 1.406 29.277 92.0 700 4 1800.0 10.0.0179 5.70 42.70 42.15 48.34 29.35 1.03030.0000.1338 1.406 29.277 92.3.703 4 2000.0 13.0.0179 5.48 42.69 42.15 48.36 29.35 1.0000.0000.1345 1.406 29.277 92.0 703 4 2200.0 130.0.0179 5.30 42.69 42.14 48.38 29.35 1.0000.0000.1351 1.406 29.277 92.0 703 4 2400.0 13.0.3179 5.15 42.68 42.14 48,43 29.35 1.0000.0000.1356 1.436 29.277 92.0 703 4 2600.0 10.0.0179 5.33 42.68 42.14 48.41 29.35 1.0000.0000.1361 1.406 29.277 92.0.70o 2800.0 10.0.0179 4.92 42.68 42.13 48.42 29.35 1.30000.0000.1364 1.406 29.277 92.0 700 4 3000.0 10.0.0179 4.82 42.67 42.13 48.44 29.35 1.0003.0000.1368 1.406 29.277 92.0 700 4 3200.0 10.0.0179 4.74 42.67 42.13 48.44 29.35 1.0000.0000.1371 1.406 29.277 92.0.70 4 3400.0 10.0 0.0179 4.66 42.58 42.04 48.36 29.35 1.0000.0000.1374 1.406 29.277 92.0 703 3 3600.0 10.0.0179 4.59 42.61 42.07 48.40 29.35 1.00000.0000.1376 1.406 29.277 92.0 700 3 3800.0 10 0.0179 4.54 42.63 42.09 48.43 29.35 1.000000.0000.1378 1.406 29.277 92.0.700 3 4000.0 10 0.0179 4.49 42.76 42.21 48.58 29.35 1.0000.0000.1380 1.406 29.277 92.0 700 2 4200.0 10.0.0179 4.44 42.70 42.16 48.53 29.35 1.0000.0000.1382 1.406 29.277 92.0 700 2 4400.0 10 0.0179 4.39 42.68 42.14 48.51 29.35 1.0000.0000.1383 1.406 29.277 92.0 700 3

TABLE XVIII SIMULATION PREDICTIONS FOR A CONSTANT THROTTLE ANGLE ANALYSIS (26~) CARBURETOR-ENGINE OPERATION AT CONSTANT THROTTLE OPENING-VARIABLE ENGINE SPEED THROT INTAKE MOIST DRY TOTAL THROT THROT MAIN TOTAL Ml XT. THROT THROT THROT ENGINE THROT FL3W MAN. AIR AIR MIXT. PLATE MACH F/A F/A CP/'V TOTAL TOTAL PLATE RPM ANGLE AREA PRESS FLOW FLOW FLOW FLOW NO. RATIO RATIO RATIO PRESS TEMP C3EFF 1 530.0 26.0.1568 28.07 136.74 134.99 141.58 135.24.2438.0299.0359 1.397 29.256 85.0.900 3 600.0 26.0.1568 27.62 156.22 154.23 165.70 158.80.2882.0584.0614 1.389?.247 78.4.90 9 700.0 26.0.1568 27.09 176.24 174.03 188.75 181.37.3336.0716.0719 1.385 29.237 75.3.903 1) 809.0 26.0.1568 26.51 196.02 193.52 209.73 201.51.3777.0709.3709 1.385 29.227 75.5.909 14 900.0 26.0.1568 25.89 214.30 211.56 228.89 223.31.4210.0690.0690 1.386 29.217 75.9.900 8 1000.0 26.0.1558 25.26 230.75 227.81 246.32 236.41.4625.0670.0670 1.386 29.207 76.4.903 8 1200.0 26.0.1568 23.94 258.94 255.64 275.05 264.31.5420.0630.0630 1.387 29.189 77.3.900 7 1490.0 26.0.1568 22.61 280.90 277.32 297.82 286.21.6169.3610.0610 1.388 29.174 77.8.903 8 1600.0 26.3.1568 21.34 296.97 293.19 314.86 302.62.6854.3613.3610 1.388 29.161 77.8.90) 8 1R800.O 0 26.0.1568 20.15 308.73 304.79 327.32 314.55.7487.0610.3610 1. 388 29.151 77.8.90) 7 2000.0 26.0.1558 19.04 316.88 312.84 335.95 322.96.8071.0610.3610 1.388 29.145 77.8.993 5 2200.0 26.0.1558 18.02 322.43 318.32 341.84 328.55.8609.0610.0610 1.388 29.140 77.8.903 5 2430.0 26.0.1558 17.09 325.87 321.72 345.48 331.95.9106.0607.0609 1.388 29.137 77.9.900 5 260.0 26.0.1568 16.25 327.91 323.73 347.57 333.58.9559.0593.0607 1.388 29.135 78.2.900 4 2809.0 26.0.1568 15.48 328.53 324.34 348.21 334.02.9983.0582.0607 1.389 29.135 78.4.900 4 3000.0 25.3.1568 14.80 328.86 324.67 348.56 333.92 1.0000.0572.3607 1.389 29.134 78.7.903 5 3200.0 26.0.15S8 14.20 329.03 324.84 348.78 333.84 1. 000.0563.3608 1.389 29.134 78.9.903 5 3400.0 26.0.1558 13.67 329.18 324.98 348.98 333.76 1.0000.0556.0609 1.389 29.134 79.1.900 5 3690.0 26.0.1558 13.19 329.20 325.01 349.36 333.73 1.) 333.0549.0611 1.390 29.134 79.2.900 4 3830,0 26.0.1568 12.77 329.34 325.15 349.26 333.64 1.0900.0544.0613 1.390 29.134 79.3.900 4 4000.0 26.0.1568 12.38 329.47 325.27 349.46 333.59 1.0000.0539.0615 1.390 79.133 79.4.903 4 4200.0 26.0.1568 12.03 329.57 325.37 349.64 333.54 1.0000.0534.0617 1.390 29.133 79.6.900 4 4400.0 26.0.1568 11.71 329.67 325.47 349.81 333.50 1.0000.0530.0619 1.390 29.133 79.6.900 4 4609.0 26.0.1558 11.41 329.75 325.55 349.97 333.46 1.0000.0526.0621 1.390 20. 133 79.7.90 4 4800.0 26.0.1558 11.14 329.83 325.63 350.11 333.43 1.0300.0523.0623 1.390 29.133 79.8.900 4 5000.0 26.0.1568 10.89 329.90 325.70 350.26 333.40 1.0000.0520.0625 1.391 29.133 79.9.900 4

260 were the actual nominal dimensions of the carburetor. Table 17 shows the simulation predictions for the case of completely closed throttle (0 = 10~). Note that the throttle plate flow is choked at all engine speeds, and that the main fuel system is not operating. The fuel-air ratio is very rich, and becomes richer as the engine speed is increased. This results from the increase in the intake manifold vacuum with engine speed, even though the air mass flow rate is constant. This was discussed in the analysis presented in Chapter 2. Table 18 shows the simulation predictions for a throttle angle of 260. It is immediately obvious that the flow conditions are significantly different from the previous case. The air flow rates are 3 to 8 times those at 100, and the throttle plate flow does not choke until an engine speed of 3000 RPM is reached. 2. Carburetor-Engine Operating Map A complete carburetor-engine operating map can be generated by performed the constant engine speed analysis for many RPM values, and the constant throttle angle analysis for many -- values. If this is done, all possible operating points can be shown on a single graph. This type of analysis was made available within the carburetor simulation program. When it is specified, a series of constant RPM and constant & analyses are performed, and the results plotted as shown in Figure 69. This is a very informative graph since it immediately gives the minimum possible air flow rate and intake manifold pressure.

deyI buITeGado aIqTOTPA - euIbu3 - Jo6ainqjeo'69 aJnbTj 3H S3H3NI NI 3]nSS3iJd OJiINUW 3>IU1NI 008'Z O0'0 Z Ol'OZ 00'9 1 00' 009 00'we 00'. 0 0 H/Sn# br^^ —- ^ _. ~'..;0 = - CD _ _ _ _ _ __/ _ _ 0 z _ co 0 OS'6=OJ11'dNOD.I" 9'88 =INiNflU]d IG 6 N 5UN4 NI I 1 3NN N-WOI 3ofJS TI~~~~~9~~~~~~ dUN GN~lUUdO 3NIGN3U013Un9UU T9Z~~~~~~

262 Using this type of computer plot it is possible to quickly determine the air flow rate and intake manifold pressure for any throttle angle and engine speed. For example it may be quickly noted that if the throttle angle is 210, and the engine speed is increased from 1600 to 3000 RPM, the measured air flow rate will remain constant at 205 pounds per hour. Another interesting feature of this operating map is the relation of the operating points to the road load conditions. (The method of obtaining the road load operating line will be discussed in the next section.) Combinations of engine speed and throttle angle which lie upon the road load operating line correspond to road load operating points. Operating points to the right of the road load line would result in vehicle acceleration or steady operation on an uphill grade. Conversely, operation at points on the left of the road load line would result in vehicle deceleration or steady operation on a downhill grade. The further away from the road load line, the greater the acceleration or deceleration conditions. Thus, for this particular carburetor, engine, and vehicle, a throttle angle of 210 and an engine speed of 1900 RPM will yield steady vehicle speeds of 45 miles per hour. A throttle angle of 21~ and an engine speed of 3500 RPM obviously corresponds to a heavy deceleration condition. 3. Accuracy of the Simulation Predictions The agreement between the simulation predictions and the experimental data was very good, as may be seen in Figure 69. The small points represent actual experimental data from Tables 9 and 10, and the lines represent the simulation predictions. The predicted air mass flow

263 rates and intake manifold pressures were within 8% of the experimental values in nearly all cases, and generally were within 3 or 4%. In numerous runs the experimental points corresponded precisely with the simulation predictions. The fuel flow rate and fuel-air ratio predictions were also quite good, being within 7 or 8% of the actual experimental data in nearly all cases, with the majority of the predictions being within 5% of the experimental values. Thus, actual data trends over a wide operating range, such as from 1600 RPM, closed throttle, to 1600 RPM, wide open throttle, were predicted quite accurately. The boost and primary venturii suctions were similarly predicted quite accurately. The predicted values were within about 8% of the measured values, with the predictions usually being slightly lower than the actual data. This is to be expected since the actual boost venturi suction is not uniform at the given section, but decreases with distance from the inner wall. The experimental values were given in figure 36 on page 184, and the predicted values for a typical venturii geometry will be presented later in this chapter. 4. Available Computer Plots With the large amount of information predicted in a complete carburetor-engine operating map analysis, many other computer plots may be obtained. There are eleven distinct computer plots available within the simulation, each available in four different scales. These plots are listed on the third page of the main program in Appendix I. Various combinations of two or more of these plots may also be specified.

264 One type of plot that may be obtained for a series of constant RPM analyses is presented in Figure 70. This is the variation in overall (total) fuel-air ratio with air flow, at various engine speeds. This is a very useful plot, since it corresponds to the standard flow box test of a carburetor. However, it has the distinct advantage of directly involving the engine variables, whereas a flow box curve does not. This type of plot immediately indicates how a proposed carburetor design will perform over a wide speed and load range. Note that the abrupt increase in fuelair ratio for each engine speed corresponds to the opening point of the enrichment valve. This plot also verifies a statement made in Chapter 2, that there are an infinite number of fuel-air ratios for a given air flow rate, depending on the engine speed and intake manifold vacuum. A computer plot of the predicted main system fuel flow rate, as a function of the metering signal, is given in Figure 71. (The data correspond to the same set of conditions as Figure 70). This type of plot may be obtained whenever the main fuel flow is to be examined in detail. Note that the main fuel flow does not begin until the boost venturi suction exceeds the spill point value, and also that the main fuel flow rate is not always the same at a given value of the metering signal. It was previously mentioned that each computer plot was available in four different scales. An excellent example of the practical use of this feature is Figure 72. This shows the carburetor-engine operating map for one of the other scales available. By comparing this plot with the one shown in Figure 69, it will be seen that the region of smaller

C G- JFB C RBU' OE 2a8 IN3 V-8 EN E ry.?- OFl DRY RIR FLOW RqTE IN LBM/HDUR x I \\ — F- 7\.Prdc-e F -52 MaIi VaJra A._. COMpuTERz *U #'774 uJ. -__ -._ ___ ___Figur___ 7__Fl _ Ratio Varatin u —. - -..... -..00 50so.oo00 1oo00.00 150.00oo 2o00.00oo 20.00 500.00 350.00. 4.00 50.00 500.00 550.00 600.00o 60.00 700.00 DRY RIR FLOW RFTE IN LBM/HOUR Figure 70. Predicted Fuel-Air Ratio Variations

266 COMPUTER PREDICTION OF FUEL FLON RRTE MRIN ORIFICE NUMBER=F-50 FUEL TEMPERATURE =80.0'F RUN NUMBER = /li58 FUEL =STANDARD 6AS. MAIII SYSTEM FUEL FOW PER BARREL Lc *A ]OTES PDHNT OF ENRICMMEI'-SI VALVE E O IR II 0_I I 1 I_1 1Q<1 1 1 -J 3 ~ t It'2.50 5.00 7.50 10.00 12.50 15.00 17.50 20.00 22.50 2.00 BOOST VENTURI SUCTION IN INCHES OF NRTER Figure 71. Predicted Main Fuel Flow Rate Variations

267 CRRBURETOR-ENGINE OPERRTING MAP PO= 29.18 HG TO= 92.0 F HUMIDITY= 25.07 DISPLRCEMENT=289.2 IN3 COMP. RAT IO=9. 30 EXND/ // io. 260__ __2. V_, / (V, c' / LL I, / \i___ ~; AN6 R21.EU IN INCHES —G _ LL 0 C. CCo-~~o.00 4,00 8,00 12.00 16,00 20.00 24,00 28.00 INTAKE MRNIFOLD PRESSURE IN INCHES HG _ 0 Figure 72. Carburetor - Engine - Vehicle Operating Map With Expanded Scale

268 throttle angles has been expanded. (The specified ambient conditions and fuel temperature were different in the two simulation runs, thus one is not merely an expansion of the other.) E. CARBURETOR ANALYSIS AT ROAD LOAD OPERATING CONDITIONS One very important feature of this simulation program is that a proposed carburetor design may be analyzed for a sequence of operating points that correspond to road load operation with a specified engine and vehicle. This is accomplished by varying the vehicle velocity in five mile per hour increments and calculating the required throttle angle and engine speed. Obtaining the throttle angle is a reasonably complex procedure, and was discussed in Chapter 6. Once this value has been obtained however, the values of the carburetor, engine, and vehicle parameters corresponding to that particular vehicle speed are calculated iteratively. This includes such important variables as the engine air flow rate, brake horsepower, brake specific fuel consumption, fuel-air ratio, and miles per gallon of fuel. The simulation predictions for a road load analysis of a typical carburetor-engine-vehicle combination are listed in Table 19. The input data was for a Ford C6AF-9510-B carburetor, utilizing Standard regular gasoline at 80 F. The ambient temperature and pressure were 800 F and 29.28 inches of mercury respectively. The engine and vehicle input data are listed in Tables 20 and 21. Note in the road load simulation predictions that the throttle angle increases very little at the lower vehicle speeds, but must be opened substantially at speeds greater than

269 65 miles per hour. Note also the variations in air flow rate and intake manifold pressure. It is these points that can be plotted on the operating map grids to obtain the road load operating point line, in the manner shown in Figures 69 and 72. The accuracy of the predictions made for the carburetor analysis under road load conditions was generally quite good. Actual road load data were not obtained in this study, therefore available proving ground data were utilized. The simulation runs were made for the carburetor, engine, and vehicle specifications corresponding to the proving ground tests. In this manner the simulation predictions could be compared to the actual data. The vehicle miles per gallon values are shown in Figure 73 for both the simulation run and the actual road load test. Although the experimental data were obtained only for vehicle speeds in the 30 to 70 miles per hour range, the simulation predictions agreed very well with these values. Not only did the actual and predicted miles per gallon peak at the same speed, but the predicted maximum value was within 4% of the actual value. The importance of the road load analysis portion of the overall carburetor simulation may be summarized as follows: 1. It permits the theoretical evaluation of carburetor performance for various engine-vehicle combinations 2. The influence of any one of hundreds of carburetor variables (or fuel, ambient, engine, or vehicle variables) on the road load fuel-air ratio and mileage can be predicted

TABLE XIX SIMULATION PREDICTIONS FOR CARBURETOR OPERATION AT ROAD LOAD CONDITIONS ROAD LOAD CARdURETOR-ENGINE-VEHICLE PERFORMANCE____ THF FOLLOWING VALUES ARECALCULATED FOR A TRANSMISSION GEAR RATIO OF 1.00C CAR ENGINE THROT MOIST --- MAN. F/A ENGINE ENGINE FUEL MPH RPM ANGLE AIRFLO BHP IHP PRESS. AC RATI C ISFC 8SFC RATE MPG MN 10. 387.5 11.75 59.30 1.73 3.51 15.91 39.51.1043 1.7484 3.5441 6.13 9.808 5!5.1 581.3 12.54 68.4? 2.83 5.60 12.69 36.91.1015 1.2266 2.4303 6.87 13.124 6 p_?"." 775.n 13.35 78.47 4.20 8.06 11.25 33.31 ___ C0968.9313 1.7866 7.51 16.015 4?5.n 968.7 14.38 c2.19 5.95 10.95 10.69 31.13.0930.7745 1.4256 8.48 17.24 5. 1162.5 15.59 109.75 8.16 14.34 10.68 3C.C3.0868.6563 1.1524 9.41 19.175 6 359. 1356.2 16.87 129.9.95 -n9 18.31 10.91 27.30.0792.5563.9308 1iC.19 20.660 5 41,. 155".1 18.38 155.88 14.40 22.98 11.43 21.96.0694.4655.7429 10.7C 22.490 6 495.* 1747.8 2".47 195.63 18.62 28. 50 12.63 18.38.C613.4169.6379 11.88 22.779 5. 1937.5 22.46 238.32 23.73 35.13 13.69 18.45.06C9.4085.6C47 14.35 2C.951 5 55." 2131.2 24.67 287.62 29.84 42.93 14.86 18.49.0607.4023.5788 17.27 19.149 5." 2325." 27.00 344.60 37.07 52.06 16.15 18.49.0607.3978.5587 20.71 17.423 5 65. 2518.7 29.61 409. 87 45.53 62.66 17.57 18.43.C61C.3946.5431 24.73 15.8C8 5 7". 2712.5 32.66 485.94 55.36 74.83 19.17 18.43.061C.3917.5294 29.31 14.362 5 75.0 2906.3 36.41 572.09 66.69 88.65 20.90 18.43.061C.3894.5176 34.52 13.067 5 8__.q" Al-1." 41.39 669.32 79.66 104.23 22.77 18.43.0610.3875.5070 40.39 11.912 5 89.n 3 2 93.7 46.9" 758.94 94.41 121.71 24.15.16.0636.3925.5060 47.77 10.100 4. 3487.5 54.80 851.86 111.10 141.16 25.43 20.46.0676.4034.5125 56.94 9.506 4 95.' 3681.2 85.42 952.8p 129.88 162.70 26.78 23.66.0717.4171.5225 67.86 8.418 14 THE MAXIMUM VEHICLE SPEEC HAS 9EEN ATTAINED.......THIS SPEED IS 95.0 MILES PER HOUR A RCAY) LOAD LINE WAS PLOTTEC WITH 18 POINTS

271 TABLE XX ENGINE INPUT DATA FOR ROAD LOAD ANALYSIS IHP AND FMEP INPLI CATA FOR THE 1966 FORD 289 V-8 ENGINE MEASURED AIR FLOW RATE = 200.C LBI/hCUR MEASURED AIR FLOW RATE = 432.0 LBM/HOUR PCINT F/A RATIO I-P1 POINT F/A RATIO IHP2 1..CCCO.00 1.0000.00 2.CG50.00 2.0050.00 3.C1OO.00 3.0100.00 4.C150.00 4.0150.00 5.0200.00 5.0200.00 6.0C250.00 6 0250.00 7.03C00 -.00 7.-.0300.00 8.C350 2.00 8.0350 5.CC 9.0400 5.00 9.0400 12.00 10.0450 14.00 10.C450 34.50 11.C5CO 21.60 11.0500 49.6C 12 C550 26.10 _ _12 _ _.0550_ 59.80 13 C6CO 29.0 13 0600 14.0650 30.50 14.0650 69.50 15.C7CO 31.00 15.0700 71.50 16.0750 31.20 16.0750 72.7C 17.C8co 31.20 17.0800 73.20 18.0850 31.10 18.0850 _73.50 19.0900 31.00 - 19.0900 73.30 20.C950 30.60 20.0950 72.90 21.1000 29.90 21.1000 72.10 22.1050 29.00 22.1050 71.10 23.1100 27.60 23.1100 68.70 24.1150 26.20 24.1150 65.50 25.1200 23.80 25.1200 60.50 26.1250 2C.80 26.1250 51.40 27.1300 16.40 27.1300 38.00 28.1350 1C.05 28.1350 22.80 29.1400 4.00 29.1400 10.00 30.1450 1.00 30.1450 2.50 31.1500.00 31.1500.00 32.1550.00 32.1550.00 33.1600.o0 33.1600.00 34.1650.00 34.1650.00 35.17CO.00 35.1700.00 FMEP AT WIDE CPEN ThROTTLE FMEP AT CLOSED THROTTLE PGINT ENGINE RPv FMEFP PCINT ENGINE RPM FMEP2 1.0 13.40 1.0 13.40 2 400.0 1C.95 2 400.0 14.09 3 800.0 10.16 3 800.0 15.30 4 12C0.0 1C.82 4 1200.0 16.18 5 16CO.0 11.48 5 1600.0 17.10 6 2000.0 13.45 6 2000.0 18.40 7 24CO.0 16.32 7 2400.0 19.86 8 2800.0 19.30 8 2800.0 21.60 9 3200.0 21.S5 5 3200.0 23.20 10 360C.0 24.00 10 3600.0 24.72 11 40CO.u 25.58 11 4000.0 26.06 12 4400.0 27.00 12 4400.0 27.18 13 4800.0 28.35 __ 13 4800.0 28.85 14 52CC.0 29.65 14 5200.0 30.20

TABLE XXI VEHICLE INPUT DATA FOR ROAD LOAD ANALYSIS VEFICLE INPUT DATA FOR THE 1966 FOKC FAIRLANE SCO VEHICLE FRONTAL AREA = 30.70 F12 VEHICLE CURB WEIGHT = 3435 LEt RCLLING RESISTANCE FACTCR =.01500 LEF/LBM WIND RESISTANCE FACTOR =.C0121 LBF/tPH FT2 TIRE REVOLUTICNS PER MILE = 775.0 REAR AXLE RATIO_= 3.000 ________LCW GEAR RATIO 1.COO SECOND GEAR RATIO = 1.OCO HIGh GEAR RATIO = 1.000 _~____________ ~INPUT CATA FCR CRIFICE CCEFFICIENTS CF_DISCHARGE POINT RE F-5C C.1CC 0.616 1.426 3.629 4.726 7.230 10.58 RE F-O L 1 C.0CC.CC.CcC.000.CC.000.OOC.0CO 0.000 2 500.577.663.690.737.674.623.570.525 100.361 3 1_CC.-656.665.720.766.715.680.647.620 2CO.467 4 1500.702.654.677.770.739.710.688.660 300.513 5 2000.734.648.668.774.759.727.711.685 400.550 6 2500.761.644.700.788.768.741.724.703 500.577 7 3C000.783.641.615.790.772.750.729.712 600.597 8 3500.804.638.677.790.776.756.730.720 700.614 9 4CO.820-.635.675.793.779.761.734.726 800.629 10 4500.832.633.670.796.781.764.739.729 900.643 11 50CC.840.631.678.798.783.766.743.732 1000.656 12 5500.848.629.6%8.800.785.768.746.734 1100.665 13 6CCC.854.627.6E6.802.786.770.747.736 1200.675 14 650CC.860.626.676.804.787.771.749.737 13CO.684 15 - 0.865 —.625. —- 713.5.788.772 751.738 1400.693 16 7500.869.624.705.806.789.773.753.739 1500.702 17 8CO0C.873.623.7CO.807.790.774.755.740 1600.709 18 8500.876.622.6CC.808.791.775.757.741 1700.716 19 90CO.879.621.682.809.792.776.759.742 1800.722 20 9500.881.62C.68C.810.793.777.760 7.743 1900.728 21 oT —-1 COo 883.62C.68C.810.793.778.761.743 2000.734

273 COMPUTER PREDICTION OF RORD LORD FUEL ECONOMY CARBURETOR: CGAF 2 BARREL ENGINE: P8. In3 VgJ VE ICLE 1E: FCQPN FAIRLANE - E1 De. g 0 <'- -- (rui/ 0 ______ ___ ___________ __-_.___ CL S ____- _ _ ___ ____ _ __ ___ Lu COMPI TER N) I3 0 * s \ __ ______ __ z81 ~ ~ ~ ~ ~ ~~VEIL MIE PEi HW 900 100. C3 / 0 F 73. Predicted And Exeimna Road Load Fuel w*iE Values 8 J ___ c^Iw- - --------------- - -- ------ ~j ---— __________ \O 00 00 00 00 000 6.0 7.0 6.0 9.0 100 z~ ~~~~~~~EICEMLSPRHU Fiue7. PeitdAdExeietlRa odFe JCY ~ ~ ~ ~ cnmyVle

274 F. CARBURETOR ANALYSIS WITH PRODUCTION VARIATIONS IN DIMENSIONS A very useful feature of the overall carburetor simulation is that the effects of production tolerances on carburetor performance may be evaluated theoretically. In effect, numerous "computer carburetors" may be constructed and tested, each having a random set of dimensions within the production limits. In this manner the fuel-air ratio spread to be expected among production carburetors, with specified sets of dimensions and tolerances, can be determined. The tolerances can then be perturbed, if desired, to determine the critical elements. The more critical tolerances could then be tightened, and the less critical tolerances increased, resulting in a lower fuel-air ratio spread among production carburetors, and a possible decrease in the average cost per unit. The dimensional variations among production carburetors are simulated by utilizing the arrays of dimensions and tolerances which are read in initially. Each dimension that is read in, such as the throttle bore diameter or the main metering orifice diameter, will have a corresponding tolerance read in as data also. This will be the - 3 W value for the dimension, or 3 standard deviations allowable on either side of the nominal dimension. Thus, if the blueprint specification for a given element diameter is 1.000 - 0.001, the nominal dimension is 1.000, the tolerance is 0.001, and the standard deviation is 0.00033. When the production dimension analysis is requested, the number of units to be "built", and the manner in which they are all to be

275 evaluated, is specified. The simulation then processes each nominal carburetor dimension in the input data, and assigns a random value to it, according to the specified tolerance. This is accomplished by calling on a random number generation subroutine, RANDND, which provides a random dimension within the tolerance band, on the basis of a Gaussian distribution of values. After this has been performed for each dimension, the carburetor is analyzed in any manner specified, and another carburetor is then "built". This continues until the desired number of units have been evaluated. A typical simulation output for this type of analysis is shown in Table 22. This run was performed to check the operation of the technique, and all of the nominal dimensions and tolerances were obtained from the blueprints for a Ford C6AF-9510-B carburetor. Twelve production carburetors were "built", and their performances were evaluated at one operating point, that of 1600 RPM and 26~ throttle angle. All of the nominal dimensions, as well as the dimensions of a typical production carburetor, are listed. The first carburetor was assigned the production dimensions listed in the table, and the middle carburetor (number 6) was assigned the nominal values. Note that all performance variations listed in the simulation printout are due to variations in dimensions from one production carburetor to the next. It can be seen that the total fuel-air ratio variation (at this operating point) is from 0. 0603 to 0.0628, or a spread of 0.0025. More units could, of course, be built in order to establish the standard deviation of the fuel-air ratio.

TABLE XXII SIMULATION PREDICTIONS FOR THE EFFECTS OF PRODUCTION TOLERANCES ON CARBURETOR PERFORMANCE UNIVERSITY OF MICHIGAN MECHANICAL ENGINEERING DOCTORAL THESIS DIGITAL SIMULATION OF CARRURETMR METERING CARBURETOR-ENGINE-VEHICLF OPERATING NAP OAVIO L. HARPIWrTON THE TYPE OF ANALYSIS REQUESTED IS......SPFCIFIE6 INPUT POINT THE TYPE OF PLOT'Sl REQUESTED ARE......NO PLOTS REOUFSTED THIS SIMULATION PERFORMEDO ON e..........1 MAR 194B PURPOSE OF THIS SIMULATION RUN........TI SIMULATE PRODUCTION VARIATIONS IN CARSURETOR DIMENSIONS AMBRIENT CONDITIONS CARURETOR FUFL FGINE VEHICLE PRESSURE = 29.00 INCHES HG FORD 2 RRL* CMF-9510-R STANDARD REG. GASOLINE 1966 FORD 28 V-4 1964 FORD rAIRLAWE TEMPFRATURE - 80.0 DEGREES F MAIN JET v F-50 TEMPERATURE a 80.0 F DISPLACEENTs'69.2 C..I. VEHICLE WFIGHtu343~.O HUMIDITY 50.0 PERCENT 4AIN VENTUPIal.145 IN* SPFCIFIC GRAVITY=.?!1 COMP. PATIO a 9.3 RFAR AXLE RArTn) 1.00 DENSITY.0713 LBM/FT3 CLOSED THROTTLF10.0 VISCOSITY a.556 CS VALVE FLOW MAREA6.P2 1N TIRF REVS/MIlF t 7T5.0 INPUT OATA FOR THE FORD 2 RBL. C6AF-9510=1 CARBURETR ***NOMINAL FOIMFNSIONS.*** MAIN METERING ORIFIC E rYPE - -O MAIN METERING ORIFICE DIAMETFR o.050? INCH MAIN METERING ORIFICF LENGTH a.1830 INCH MAIN METERING ORIFICE L/n RATIO a 3.6454 NUMBER OF MAIN METERING ORIFICFS * 2 COMPLETELY CLOSED THROTTLF ANGLE *10.000 DFGRFES THROTTLE BORE DIAMETER *'1.4370 INCHES THROTTLE SHAFT DIAMETER-.37l0 INCH INITIAL SPILL POINT OF MAIN SYSTEM w.140 INCH MAIN VENTURI THROAT DIAMETER a 1.1450 INCHES THROTTLE PLATE BYPASSS -- TRANSFER TUBE DIAMETER a.0730 INCH CHOKE BLEED RESTRICTION DIAMETER -.0000 INCH ENRICHMENT BLEED RESTRICTION DIAMETER *.0730 INCH GEOMETRIC RELATION BETWEEN 9BOOST AND MAIN VNYTI - XMV1 - 1.2500 INCHES XMV2 - 1.0000 INCHES XBV -.7800 INCHES XMB.oo0700 INCHES____

TABLE XXII (continued) MAIN VENTURI ELEMENT DIAMETER 1 ~ ~~ —^^ —---- 1 1.930 INCHES 2 1.930 INCHES 3 1.145 INCHES ___ 4 ____ 1.160 INCHES 5 1.400 INCHES BOOST VENTURI ELEMENT DIAMETER 1 1.030 INCHES 2.875 INCHES 3.538 INCHES 4.596 INCHES 5.650 INCHES 6.750 INCHES FUEL CHANNEL ORIFICF ELEMENT DIAMETER LENGTH L/D RATIO TYPE 16~ ~.050? INCH.183 INCH 3.645 1.0 24C.1870 INCH.312 INCH 1.668.0 _ 3 9.0810 INCH.106 INCH 1.309 3.0 4 0 —--.3 125 it H — 21 INCH 125 IC —-.400.0 5s.1560 INCH.390 INCH 2.500?0 6:.1350 INCH.206 INCH 1.526.0 7:.0280 INCH.125 INCH 4.464?,.0 8.1470 INCH.938 INCH 6.378.0 9.2910 INCH.250 INCH.859.0 10.1580 INCH 1.000 INCH 6.329.0 11.2700 INCH.340 INCH 1.259.0 12 7-~-.1600 INCH.812 INCH 5.075 0 13.2250 INCH.135 INCH.600 2.0 14.0610 INCH 1.930 INCH 31.639 0 15.0260 INCH.094 INCH 3.608 2.0 16.1400 INCH.706 INCH 5.043.0 17.0940 INCH.780 INCH 8.298.0 18.0420 INCH - 106 INCH 2.524 2.0 19.0940 INCH 2.000 INCH 21.277 0 20.0590 INCH.106 INCH 1.797 3 0 21.0310 INCH.125 INCH 4.032 _ 2.0 ----— 22.0446 INCH - 031 INCH --.700 2?0 23 __ _.0270 INCH _140 INCH 5.185 2.0 24 -.0390 INCH.125 INCH 3.205 2.0 25.0350 INCH.106 INCH 3.029 2.0

TABLE XXII (continued) DIMENSIONS OF A TYPICAL PRODUCTION CARBURETOR ____ MAIN METERING ORIFICE TYPE F-50 MAIN METERING ORIFICE DIAMETER -.0499 INCH MAIN METERING ORIFICE LENGTH s.1830 INCH MAIN METERING ORIFICE L/D RATIO 3.6651 ____ NUMBER OF MAIN METERING ORIFICES - 2 COMOLETFLY CLOSED THROTTLE ANGLE =10.056 DEGREES THROTTLE BORE DIAMETER a 1.4370 INCHES THROTTLE SHAFT DIAMETER=.3750 INCH INITIAL SPILL POINT OF MAIN SYSTEM a.140 INCH MAIN VENTURI THROAT DIAMETER - 1.1453 INCHES THROTTLE PLATE BYPASSES TRANSFER TUBE DIAMETER z.0725 INCH CHOKE BLEED RESTRICTION DIAMETER _.0000 INCH____ ENRICHMENT BLEF R ATRI CTMIfONW DAMFTERT-E.0735 INCH GEOMETRIC RELATION BETWEEN BOOST AND MAIN VENTURI XMV1 ~ 1.2501 JNCHES XMV2 -.9954 INCHES XBV -.7798 INCHES -- XMB a.0692 INCHES J 0:) MAIN VENTURI ___ ELEMENT - DIAMETER - 1 1.930 INCHES 2 1.930 INCHES 3 1.145 INCHES 4 _ 1.160 INCHES ___ ___ 5 1.400 INCHES BOOST VENTURI FLEMENT DIAMETER 1 _____ 1.030 INCHES 2.875 INCHES 3.538 INCHES 4.596 INCHES 5.650 INCHES 6 750 INCHES FUEL CHANNEL ORIFICE ELEMENT DIAMETER LENGTH L/D RATIO TYPE 1.0499 INCH.183 INCH 3.665 10 2 1680 INCH 312 INCH 1.660.0 _ 3._0817 INCH.106 INCH 1.296 30 - 4.3125 INCH.125 INCH.400.0 5.1558 INCH.390 INCH 2.504 2.0 6.1353 INCH.206 INCH 1.522.0 7.0276 INCH.125 INCH 4.524 2. 8.1469 INCH.938 INCH 6.383.0

TABLE XXII (continued) 9.2932 INCH.250 INCH 853.0 10.1576 INCH 1.000 INCH 6.347.0 11.2689 INCH.340 INCH1.265.0 12.1592 INCH.812 INCH 5.099.0 12.2230 INCH.135 INCH.601.O 1'.0601 INCH 1.930 INCH 32.091.0 I5 *.0258 INCH.094 INCH 3.642'.0 16.1401 INCH,.706 INCH 5 033.0 17.0954 INCH.780 INCH 8.179.0 18.04l1 INCH.106 INCH 2.530.0 1^s ~.0936 INCH?.000 INCH 21.376.0 20.0596 INCH.106 INCH 1.778 3.0 21.0313 INCH.125 INCH 3.980'?.0 2.0447 INCH.031 INCH.698.0 23.0271 INCH.140 INCH 5.159 7.0 24.0392 INCH.125 INCH 3.188.0 2-.0346 INCH.106 INCH 3.06?2.0 g\1 SIlMULATE 12 PRODLCTION CARBURETORS CARUPFETnR-ENGINE OPERATION FOR SPECIFIC nPFRATING POINTS (RPM AND THETA SUPPLIED AS INPUT DATA) THPOT INTAKE OIIST DPY 8BOST MAIN THROT MAIN TOTAL TTAL MAIN THROT AIR FNGINE THROT FLOW MAN. AIR AIR VENTURI VENTURI MA CH F/A F/A FUFL FUEL TOTAL BLEFD RPM AN(GLF AREA PRFSS FLOW FLOW SUCTION SUCTION NO. RPATIO RATIC FLOW FLOW TFMP FLOW J 1600.0?6.0.1566 1.91 298.87 295 59 3.69 1.94 7507.0505.0606 17, 912 14.938 58 413 3 1600.0 26.0.1568 19.91 299, 00?o5.72 3.67 1.95.7509.0517 0615 18.186 15.275 68. 0 96 3 1600.0?6.0.15 19.09 298P.80 295. 52 3.69 1,94 7521.0521.0623 1. 399 15.396 67,9 408 3 1600.0 76.0.1566 19.90 298.88 25, 60 3.70 1.94.7514.0519.0617 18. 238'5.355 67.9 409 3 1600.0 76.0.1567 19.91 299.03 2~5.75 3.70 1.95.7506.0511.0611 18. 083 5.119 68.1 404 3 1600.0 26 0.1566 19.91 298.95 295.68 3.68 1.94 7508.0509.0611 RIR 0 15.050 68, 1.405 3 1600.0 26.0.1569 19.92 299.29 296.01 3.69 1.95.7500.0516.0615 18.218 15.?77 68.0.40 3 1600.0 26 0.156C 19.88 298.69 295.42 3.65 1.94 7524.0524.0621 18 360 15.494 67.8 400 3 160o0.0 26. 0.1566 19.9Q 298.80 295 53 3.69 1.94 o7510.0507.0608 17. 67 14.983 68. 2 401 3 1600.0 26.0.1568 19.90 299.13 205.85 3.70 1.94.7514.0526.0628 18.575 15.567 67. 7 402 3 1600.0 26 0.1567 19.93 299.12 295. 84 3.70 1.95.7496.0501.0602 17 808 14.926 0 680.396 3 1600.0?6 0.1566 19.93 299o.05?9, 78 3.70 1.94.7499.0506.0603 17 841 14.959 68.2 41 3 a IN LYk I/R INCK NCES WC /In L% F LS IN6 H/ /mO H0/R / O

280 G. AUXILIARY SUBROUTINE PRINTOUTS It should perhaps be emphasized here that the individual subroutines were written to do significantly more than return a needed number to the main program. Each subroutine performs a comprehensive analysis of one component of the carburetor, and thus makes available a complete set of parameters for each operating point. An example of this is subroutine SIGNAL, which performs a complete analysis of the flow within the main and boost venturii for any specified geometry and air flow rate. Although the chief function of this subroutine is to supply the boost venturi suction to the main program, all of the other venturi parameters are also available. Thus, if this particular function of the carburetor is to be studied in detail, an auxiliary printout may be requested which will contain such variables as the Mach numbers, pressures, velocities, mass flow rates, and temperatures at each station within the main and boost venturii. One of these auxiliary printouts is shown in Table 23. for the entire air flow range of the venturii system. Note that the maximum possible air mass flow rates are given for both the primary and boost venturii (for the specified geometry and stagnation conditions). Note also that the boost venturi chokes at a total air flow rate per barrel of about 750 pounds per hour, after which the metering signal is constant. The total air flow rate can increase further because the primary venturi is not choked. When the air flow rate supplied to SIGNAL exceeds the capacity of the venturii system, the subroutine prints out this fact along with the

TABLE XXIII COMPUTER PREDICTION OF MAIN AND BOOST VENTURI PARAMETERS VALUES PREDICTED BY SUBROUTINES SIGNAL AND SOLVE MAIN 3UTLET TOTAL PRIMARY BOOST PRIMARY BOOST PRIMARY BOOST BOOST BOOST__ BOOST BOOST MAX. MAX. AI R PRESS. AIR' VENTURI VENTURI THROAT VENTURI VENTURI VENTURI OUTLET TOTAL TOTAL THROAT PRIMARY BOOST FRACT. ERROR FLOW FLOW FLOW MACH NO MACH NO SIGNAL SIGNAL PRESS. PRESS. TEMP. SUCTION FLOW FLOW J.6348 -.0000 50.00 15.87 9.13.0130.0198.051.113 28.996 29.000 80.00.109 708.0266.4 3,6348.0000 100.00 31.74 18.26.0259.0397.203.452 28.986 28.999 80.00.437 708.0 266.4 3.6348.0301 150.00 47.61 27.39.0389.0596.457 1.019 28.968 28.997 80.00.984 707.9266.4 3.6348.0001 200.00 63.48 36.52.0519.0796 814 1.81 28.942 28.995 80.00 1.753 707.9266.4 3.6349 -.0001 250.00 79.36 45.64.0650.0997 1.273 2.843 28.910 28.993 80.00 2.746 707.8266.3 4.6349.0000 300.00 95.23 54.77.0781.1199 1.836 4.108 28.870 28.990 80.00 3.967 707.7266.3-4.6349.0000 350.00 111.11 63.89.0912.1404 2.503 5.613 28.823 28.986 80.00 5.420 707.6266.3 4.6349 -.0000 400.00 126.99 73.01.1044.1610 3.276 7.366 28.768 28.982 80.00 7.111 707.5266.2 4.6350.0000 450.00 142.87 82.13.1177.1820 4.156 9.371 28.706 28.977 80.00 9.046 707.4266.2 4.6350.0300 500.00 158.75 91.25.1311 -.2032 5.144 11.639 28.636 28.971 80.00 11.233 707.3266.1 4.6350 -.0000 550.00 174.64 100.36.1446.2248 6.243 14.179 28.558 28.965 80.00 13.683 707.1266.1 4.6351.0000 600.00 190.53 109.47.1582.2467 7.453 17.003 28.473 28.958 80.00 16.404 706.9266.0-4.6351.0000 650.00 206.42 118.58.1719.2692 8.778 20.124 28.379 28.950 80.00 19.412 706.8265.9 4.6352.0000 700.00 222.32 127.68.1857.2921 10.220 2359 -28277 28.942 80.00 22.720 706.6265.9 4.6353.0000 750.00 238.23 136.77.1997.3157 11.781 27.328 28.167 28.933 80.00 26.347 706.3265.8 4.6353.0001 800.00 254.14 145.86.2139.3400 13.465 31.454 28.048 28.923 80.00 30.315 706.1265.7 4.6354.0000 850.00 270.06 154.94.2282.3650 15.276 35.966 27.920 28.913 80.00 34.649 705.9265.6 4.6355. —0- 9 O OI.OO ~285.9R — 164.02.24-27.3911 17.217 40.897 27.783 28.901 80.00 39.382 705.6 26.5-4.6356.0000 950.00 301.91 173.09.2575.4182 19.293 46.290 27.637 28.889 80.00 44.552 705.3265.4 4.6357.0000 1000.00 317.86 182.14.2725.4466 21.510 52.199 - 27.481 28.875 80.00 50.208 705.0265.3 4.6358 -.0000 1050.00 333.81 191.19.2877.4765 23.872 58.693 27.314 28.861 80.00 56.411 704.7265.1 4.6360.0000 1100.00 349.78 200.22.3133.5084 26.387 65.861 27.137 28.845 80.00 63.241 704.4265.0 4 j.6361.0000 1150.00 365.77 209.23.3191.5426 29.063 73.828 26.949 28.828 80.00 70.807 704.1264.8 4.6363.0000 1200.00 381.78 218o.2.3354.5798-31.907-82.769-26.749-28.810-80.00 79.259 703.7264.7 4.6365.0001 1250.00 397.82 227.18.3520.6211 34.932 92.950 26.537 28.789 80.00 88.818 703.4264.5 4.6368.0000 1300.00 413.89 236.11.3691.6681 38.150 -104.80 9267311 28.766 80.00 99.838 703.0 264.3 4.6371.0001 1350.00 430.02 244.98.3867.7241 41.577 119.171 26.071 28.740 80.00 112.939 702.6264.0 4.6375 -.0000 1400.00 446.25 253.75.4049.797145.239 138.047 25.81528.70980.00 129.456 702.2263.7 5.6382.0001 1450.00 462.70 262.30.4239.9323 49.189 172.458 25.540 28.667 80.00 153.742 701.7263.3 4.67490.0020 1500.00 486.72 263.28.4530.9998 55.427 188.962 25.105 28.660 6 80.00 157.889 701.1 263.3-3.6603.0020 1550.00 511.72 263.28.4851.9998 62.587 188.962 24.609 28.660 80.00 157.889 700.3 263.3 3.6709.0020 1600.00 536.72 263.28.5196.9998 -70.549 188.962 24.059 28.660 80.60 157.889 699.6263.3 3.6809.0020 1650.00 561.72 263.28.5571.9998 79.478 188.962 23.447 28.660 80.00 157.889 698.8263.3 3.6903.0020 1700.00 586.72 263.28.5985.9998 89.629 188.962 22.757 28.66080.00 157.889 697.9 263.3 3 06991.0020 1750.00 611.72 263.28.6455.9998 101.412 188.962 21.967 28.660 80.00 157.889 697.0 263.3 3.7075.0020 1800.00 636.72 263.28.7011.9998.115.581 188.962 21.039 28.660 80.00 157.889 696.1 263.3 3.7154.0020 1850.00 661.72 263.28.7724.9998 133.882 188.962 19.896_28.660 80.00 157.889 695.2263.3 3.7229 0020 1900.00 686.72 263.28.8895.998163.666 188.962 18.327 28.660 80.00 157.889 694.2 263.3 3.-THE AIR FLOW SUPPLIED TO SIGNAL EXCEEDS THE VENTURI FLOW CAPACITY ________ ____ ____ ___ __.7266.0020 1950.00 708.00 266.40.9998 1.0000 186.529 186.583 18.062 29.000 86.60157.889 708.0 266.4 0 THE AIR FLOW SUPPLIED TO SIGNAL EXCEEDS THE VENTURI FLOW CAPACITY.7266.0020 2000.00 708.00 266.40.9998 1.0000 186.529 186.583 18.062 29.000 80.00 157.889 708.0266.4 6

282 maximum values. H. COMPUTER TIMES REQUIRED The complete carburetor simulation program, consisting of the main program and 12 subroutines, was run on an IBM 7090 computer. Some subroutine debugging was performed using an IBM 360-65, however no complete simulation runs were performed on that machine. The computer plots were generated on a CALCOMP Model 763 digital incremental plotter. The times required for these operations varied considerably with the type of analysis requested within the simulation, and with the number and type of plots to be generated. A brief summary of these times is given in the following table. TABLE XXIV REQUIRED COMPUTER TIMES (APPROXIMATE) OPERATION TIME Compilation time on FASTRAN and MAD compilers 2.2 minutes Execution time for a typical constant RPM or constant e run 1.5 minutes Execution time for a carburetorengine operating map 9 minutes Execution time for a road load analysis 5 minutes Execution time for a production dimension analysis (12 units) 4 minutes Execution time for a complete carburetorengine-vehicle operating map 13 minutes Plotting time for all graphs except operating map 2.5 minutes Plotting time for operating map 4.5 minutes

CHAPTER IX APPLICATIONS OF THE COMPLETE CARBURETOR SIMULATION A. GENERAL APPLICATIONS The discussions given in the preceding chapter were concerned with the various analysis types that may be specified within the carburetor simulation. The topic to be considered in this chapter is that of possible applications of the complete simulation, utilizing one or more of the available analyses. Two of the obvious general applications have been mentioned previously; that of the evaluation of a proposed carburetor design by predicting the performance, and evaluating the effect of the production tolerances on the fuel-air ratio spread among carburetors. Other, perhaps less obvious, applications will now be considered, and suitable examples presented. B. SINGLE VARIABLE EFFECTS One of the most useful applications of the complete carburetor simulation is that of predicting single variable effects. This may be accomplished by performing the simulation a number of times, each time incrementing only the independent variable being investigated. The significance of this technique is that the independent variable under investigation may be any one of hundreds of carburetor, fuel, ambient, engine, or vehicle variables. Its effect on any of the dependent variables in the analysis could be predicted with just a few simulation runs. 283

284 The number of permutations and combinations that are possible is enormous. A few of these possible combinations are: 1. The effect of ambient pressure on the metering signal. 2. The effect of ambient temperature on the delivered fuel-air ratio. 3. The effect of fuel temperature on the delivered fuel-air ratio. 4. The effect of main venturi diameter on the road load miles per gallon. 5. The effect of throttle bore diameter on the road load throttle angle. 6. The effect of engine displacement on the delivered fuel-air ratio. 7. The effect of vehicle differential gear ratio on the road load fuel-air ratio values. The list could be extended considerably, however it should be obvious that there are many single variable effect applications. C. ADDITIONAL APPLICATIONS The simulation has numerous other useful applications in addition to the multitude of single variable effect situations. One group of applications is in comparing designs or parameters. A few examples of this utilization of the simulation are: 1. To evaluate various proposed carburetor designs by comparing their predicted fuel-air ratio curves. 2. To evaluate the mating of a particular engine with various proposed carburetors by comparing the resulting predictions for the road load BSFC values. 3. To evaluate various proposed venturi geometries by comparing the resulting predictions for the metering signal curve. Other applications are abundant, and are concerned with optimization of systems, and the sizing of components to comply with desired performance specifications.

285 D. EXAMPLES OF SINGLE VARIABLE EFFECTS Actual simulation runs were performed on numerous occasions in order to determine the influence of various independent variables. The results of two of these runs will be presented in this section as examples of the carburetor simulation applicability. The first example represents the results of a simulation run to determine the effects of a reduced ambient pressure, corresponding to an altitude of 6000 feet above sea level. A complete carburetor-enginevehicle operating map analysis was requested, and the simulation predictions are listed inTable 25, and plotted in Figure 74. The corresponding predictions for the sea level case were listed previously in Table 16, and plotted in Figure 69. The results of three constant engine speed analyses for the simulated altitude of 6000 feet are shown in Table 25. The 1600 RPM run at altitude may be compared to the 1600 RPM run at sea level (Table 16) with the resulting conclusions: 1. At altitude, the predicted air flow rate and intake manifold pressure are lower with the same throttle angle. 2. At altitude, the predicted boost and primary venturi suctions are larger for the same air mass flow rate. 3. At altitude, the predicted fuel-air ratio values are generally richer. One item that should be noted is that the fuel flow rate in the sea level run is the value for both barrels, whereas in the altitude run it is per barrel. Figure 74 shows the operating map for the altitude conditions. Note that it is significantly different from the sea level operating map. The minimum air mass flow rate and intake manifold

TABLE XXV SIMULATION PREDICTIONS FOR CARBURETOR PERFORMANCE AT ALTITUDE UNIVERSITY OF MICHIGAN — __-__~____________ _ ___ ~MECHANICAL ENGINEERING DOCTORAL THESIS DIGITAL SIMULATION OF CARBURETOR METERING ___________..CARBURETOR-ENGINE-VEHICLE-OPERATING 4AP DAVID L. HARRINGTON THE TYPE OF ANALYSIS REQUESTED IS......COMPLETE OPERATING MAP ___ THE TYPE OF PLOT(S) REQUESTEC ARE......COMPLETE OPERATING MAP.__THIS SIMULATION PERFORIMED ON.07 FEB 1968 PURPOSE OF THIS SIMULATION RUN........TO CHECK THE EFFECT OF ALTITUDE ON THE OPERATING MAP AMBIENT CONDITIONS CARBURETOR FUEL ENGINE... VEHICLE — PRESSURF- =24.00 INCHES HG - FORC 2 BBL.- C6AF-9510- STANDARC REG. GASOLINE 1966 FORC 28S V-8 16e6 FCRD FAIRLANE TFMPERATURE'- 70.0 DEGREES F MAIN JET = F-50 TEMPERATURE = 80.0 F DISPLACEMENT=289.2 C.I. VEHICLE WEIGHT-3435.C HUMIDITY = 40.01 PERCENT MAIN VENTURI=i.145 -— IN. -—'SPECIFIC GRAVITY=.721 COMP. RATIO - 9.3 REAR AXLE RATIO 3.00 DENSITY =.n6l01 LBM/FT3 CLOSED THROTTLE=10.0 VISCOSITY,.556 CS VALVE FLOW AREA'6.82 IN2 TIRE REVS/MILE -775.0 CARBURETOR-ENGINE OPERATION AT CONSTANT ENGINE SPEED-VARIABLE THROTTLE OPENING. 0o THROT INTAKE MOIST DRY BOOST MAIN THROT MAIN TOTAL TOTAL MAIN THRCT THROT __ENGINE.THROT__ _FLOW MAN. AIR AIR VENTURI VENTURI MACH F/A F/A FUEL FUEL TOTAL PLATE RPM ANGLE AREA PRESS FLOW FLOW SUCTION SUCTION NO. RATIO RATIO FLOW FLGW TEMP CCEFF J 8n00. 10.0.0179 5.48 34.93 34.66.05.03 1.0000.0000- —.1'2 08 2.C93.COC 7C.0.6e3 3...80. n.......12.0..0287.7.27 _ 51.49 51.1C.11.06 1.0000.0000.1163 2.S72.CC 7C.0.721 2 1"OO 1 4.0.0413 5.75 72.34 71.79.23.12 1.0000.0000 C940 3.374 COC 7C.0.757 3 8.O"n 16.0.0559 12.76 96.64 95.91.43.23.9931.0128 C824 3.S49.612 67.0.790 3 (NOM. 18.0.0724 15.65 120.22 119.31.67.36.8057.0270.0760 4.536 1.612 63.1.817 RO.q0 n0.0.0907 17.88 138.54 137.49.90.48 6617.0381.0711 4.ESC 2.621 61.1.838 800o. 22.o.1109 19.53 151.40 150.26 1.09.58.5504.0494.0623 4. 684 3.713 5e.4.854 80... 24.0.1329 20_.63 160.70 159.49 1.23.65 4694.0583.C636 5.C75 4.65C 56.4.859 3 prO n 26.0.1567 21.43 167.82 166.55 1.35.72.4042.0654 C675 5. 617 5.44E 54.7.865.....nn...... 28..0..1822 2 2.01 173.14 171.83 1.45.77 3517.0709.0715 6.140 6.092 53.4.871 3 R0." 30.n.2n95 22.44 177.12 175.78 1.52.81.3083.0746.C746 6. 553 6.553 52.5.876 AP.o 0 35.0.2848 23.12 183.03 181.64 1.63.86.2270.0766.0766 6.S58 6.S5E 52.1.esO 2 80n.0 40.0.3700 23.46 185.99 184.58 1.69.90.1742.0776.0776 7.165 7.165 51.8.SO 2 Rpo 0. 45.0.4641 23.64 187_.59 186.17 1.72.91.1381.0782 oC782 7.279 7o27S 51.7 S11 2 800.n 50.0.5662 23.74 188.50 187.08 1.74.92.1125.0785.0785 7.344 7.344 51.6.920 2 800.0........55_._0_.6749 23.80 _1_89.06.187.63.1.76._ 93.0939.0787.0787 7.383 7.383 51.6.S27 2 R8n. 60n,0.7884 23.84 189.40 187.97 1.76.94.0801.0788 C788 7.408 7.408 51.5.932 2 800n. 70.0 1.0134 23.89 189.77 188.34 1.77.94'.0619.079C.0790 7.435 7.435 51.5.940 2 nO0. 80.0 1.0894 23.90 189.85 188.41 1.78.94.0575.0790.0790 7.440 7.44C 51.5.943 1 THE COPERATING MAP GRID HAS BEEN DRAWN A LINE WAS PLOTTED WITH 19 POINTS

TABLE XXV (continued) ALTITUDE EFFECTS CARBURETOR-ENGINE OPERATION AT CONSTANT ENGINE SPEED-VARIABLE THROTTLE OPENING THROT INTAKE MOIST DRY BOOST MAIN THROT MAIN TCTAL TOTAL MAIN ThROT THROT FNGINE THROT FLOW MAN. AIR AIR VENTURI VENTURI MACH F/A F/A FUEL FUEL TOTAL PLATE RPM ANGLE AREA _PRESS FLOW FLOW SUCTION SUCTION NO. RATIO RATIO FLOW FLOW TEMP COEFF J 160...n 1_0.0.0_179.^ 3.63 34.92 34.65 _.05.03 1.0000.0000.1249 2.164.OOC 7C.0.683 3 160,.n 12.0.C287 4.50 51.60 51.21.11.06 1.0000.0000.1218 3.118.OOC 7C..721 2 160n.n 14.0.0413 5.59 72.41 71.87.23.12 1.0000.0000.1013 3.639.COC 70.0.757 2 1600.n 16.0.0559 7.^3 96.83 96.10.43.23 1.0000.0113.0885 4.253.545 67.3.790 3 1600.0 18.0.0724 8.74 124.54 123.60.72.38 1.0000.0272.C772 4.774 1.684 63.6.817 3 I6nn.r 20.0.0907 10.63 155.07 153.90 1.13.60 1.0000.0464.0669 5.145 3.571 59.1.838 4 16^n'.0 22.0.1109 12.67 188.41 186.99 1.69.89 1.0000.0610.0610 5.703 5.703 55.7.E54 3 160^.0 24.0.1329 14.66 221.50 219.83 2.35 1.25.8699.0610.0610 6.705 6.705 55.7.859 2 1600.n 26.0.1567 16.39 250.29 248.39 3.03 1.60.7577.0610.C610 7.576 7.56 557.865 2 160).1 28.0.1822 17.82 274.06 271.99 3.65 1.93.6639.0610.0610 8.296 8.296 55.7.871 2 16r. n. 30.0.2095 18.95 293.46 291.25 4.21 2.22.5869.0639.C63S 9.304 9.304 55.0.876 3 16^01. 35.n.2848 20.90 327.21 324.74 5.28 2.78.4410.0698.0698 11.338 11.338 53.7.890 3 160o.n 40.0 __.3700 22.0 _346.40 343.78 5.95 3.13.3423.0732.C732 12.58C 12.580 52.9.900 3 l6^n...45.n.4641 22.63 357.54 354.84 6.36 3.35.2730.0751.0751 13.329 13.329 52.4.911 2 16na. 50.0.5662 23. 01 364.19 361.44 6.61 3.48.2232.0763.0763 13.787 13.787 52.1.20 2 1601.0 55.0.6749 23.25 368.29 365.50 6.77 3.56.1867.070770 0770 14.C72 14.072 52.0.927 2 160l.oO __60.0 _.7884 23__.39 _37C.90_ 368.10 _ 6._88 3.62.1594 _.0775.C?75 14.255 14.255 51.9.932 2 160n0.n 7n0. 1.0134 23.56 373.74 370.91 6.99 3.68.1235.0779.079 14.455 14.455 51.8.40 2 16_^.0 8n...0. 1.894 23.59 374.33 371.51 7.02 3.69.1145.C780.0780 14.498 14.498 51.7.943 2 A LINE WAS PLOTTED WITH 19 POINTS A LINF WAS PLOTTED WITH 19 POINTS

TABLE XXV (continued) ALTITUDE EFFECTS CARBURETOR-ENGINE OPERATION AT CONSTANT ENGINE SPEED-VARIABLE THROTTLE OPENING THROT INTAKE MCIST DRY BOGST MAIN ThROT MAIN TCTAL TOTAL MAIN IHROT lHROT FNGINF THROT FLOW MAN. AIR AIR VENTURI VENTURI MACH F/A F/A FUEL FUEL TOTAL PLATE RPM ANGLE AREA PRESS FLOW FLOW SUCTION SUCTION NO. RATIO RATIO FLOW FLOW TEMP COEFF J?7^5."^ 1...0179 2.98 34.92 34.65.05.03 1.0000 0000.1265 2.192.OOC 7C.0.683 3?7r^. 12.0.0287 3.52 51.62 51.23.11.06 1.0000.0000.1241 3.178.CCO 7C..721 2?5s.' 14.0.r413 4.12 72.38 71.83.23.12 1.0000.0000.1045 3.753.COC 70.0.757 3 ^n^ 16.0.0,59 4.99 96.84 96.11.43.23 1.0000.C108.0920 4.422.52C 67.5.790 3 75"^.!8.".0724 6.0 6 124.65 123.71.72.38 1.9000.0256.C803 4.567 1.584 64.0.817 3 2, " —500^." 9-..09017 7.?9 155.34 154.17 1.14.60 1.0000.0428.0684 5.274 3.302 6C.C.838 3?2?.^ 2..n i11~9 P.6? 189.12 187.69 1.70. 1.000.0559.060S 5.711 5.245 56.9.854 3 70.n 24.0.1329 1.n2 225.35 223.65 2.44 1.29 1.0000.0579.C6C7 6.784 6.474 56.4.859 2 P7cno?6. r.1567 11.54 265. 2 263.02 3.40 1.80 1.0000.0603.0609 8.004 7.924 55.9.E65 2 75 0.0 28.0.1822 17.17 317.31 304.99 4.60 2.43.9656.0610.0610 9.302 9.302 55.7.871 2 275 n-. 30..2095 14.71 347.43 344.81 5.93 3.12.8627.0610.061C 10.517 10.517 55.7.876 2 5^"n." 35.n.2848 17.79 427.61 424.38 9.13 4.78.6582.0610.C61C 12.S44 12.944 55.7.8So 2 75^0.' 40.'.3700 19.74 480.06 476.43 11.63 6.r7.5187.0663.c663 15.7S9 15.79S 54.5.S00 3 7250.^ 45.'.4641 20. 8 513.70 509.82 13.43 6.99.4178.0701.0701 17.E7C 17.e7C 53.6.Sll 3 275^."^ 5^..56b2 21.77 535.10r 531.6 14.65 7.61.3436.0725.C725 19.251 19.251 53.0.920 3 2500.- 55...6749 22.?7 548.83 544.68 15.47 8.03.2884.0740.C74C 20.162 20.162 52.7.927 2 750n." 6 1.r0.7884 22.60 557.76 553.55 16.02 8.30.2469.0750.0750 2C.766 20.766 52.4.S32 2 25A7r - 7'-."^ - 1.7134 22.96 567.68 563.39 16.65 8.62.1918.0761.C761 21.447 21.447 52.2.;40 2?2c,' ~8.0 1.n894 23.'4 56 5.49 16.78 8.69.1780.0764.C764 21.593 21.593 52.1.943 2 A LINF WAS PLeTTFC WITH 19 POINTS A LINE WAS PLCTTFC WITH 19 POINTS A LINE WAS PLOTTED WITH 19 POINTS A LINE WAS PLOTTED WITH 19 POINTS

TABLE XXV (continued) ROAD LOAD CARBURETOR-ENGINE-VEHICLE PERFORMANCE 6000 FEET ALTITUDE TrH FOlLOWING VALUES ARE CALCULATEO FOR A TRANSMISSICN GEAR RATIO OF 1.000 CAR ENGINE THROT MI0ST - MAN.- F/A ENGINE ENGINE FUEL MPH RPM ANGLE AIRFLO RHP IHP PRESS. AO RATIO ISFC BSFC RATE YPG hN 10.0 387.5 12.81 5P.1I 1.73 3.47 15.02 38.57.1033 1.7147 3.4405 5.95 10.102 5 15.0 581.3 1.34 6.01 2.83 5.56 11.69 33.e1.0976 1.1298 2.2222 6.28 14.352 5 ~ 20.0 77r.0 14.21 74.78_ 4.20 8.01 1'0.37 30.19.0909.8417 1.6C3S 6.74 17.839 4 25.-0 968.7 15.49 - 9'.11 5.-95 10.8-7 1-0.09 -— 30-.01.0863.7107 1.2980 7.72 19.467 5 30.0 11h?.5 16.81 1l7.39 8.16 14.23 10.11 28.19.0812.6081 1.060C E.65 20.847 4 35.0 1356." 18.24 128.n2 1n.95 18.18 10.33 25.52.0749.5239.8704 9.53 22.094 5 40.0 15 "., 19.97 154.26 14.4n 22.80 10.89 19.78.067C.4505.7136 1C.27 23.415 45.0 174,.R 22.33 194.49 18.62 28.27 12.07 18.43.0610.4165.6322 11.77 22.986 4 50.0 1 97.5?4.55 235.49 23.73 34. 87 13.03 18.43.061C _.4C89.6008 14.2f 21.C85 4 55.0 2131.2 21. 7. 2P3.90 29.84 42.65 14.15 18.43.0610.4031.576C 17.19 19.241 4 60.0 2?75.'?o.92 34,.68 37."7 51.76 15.44 18.43.0610.3984.5564 20.62 17.455 4 65.0 25!8.7 33.4n 406.63 45.53 62.35 16.87 18.43.0610.3947.5405 24.61 15.882 3 70.0 2712.5'7.60 477.72 55.36 74.54 18.28 18.31.C619.3536.5255 29.34 14.349 3 75.0 2Y"6.3 42.28 547.57 66.69 88.44 19.41 18.70.0653.4013.5322 35.45 12.708 4 80.0 310^". 49.26 625.97 79.66 1:04.088 20.66 21.71.C691.4126.5391 42.94 11.203 4 85.0 329q. 7 64.46 714.19 94.41 121. 5E 22.03 24.63.0733.4273.5503 51.95 5.839 6 90.0 7487.5 85.( 764.55 111.10 141.09 22.25 25.C2.0739.4281.5437 6C.41 8.960 14 TH= MAXIMUM VFHICLE SPEEC HAS BEEN ATTAINED.......THIS SPEED IS 90.0 MILES PER HCUR THF HIGH GFAP ROaD LOAC LINE WAS PLCTTED

290 CRRBURETOR-ENGINE OPERRT TING MRP PO= 24.00 HG TO= 70.0 F HUMIOITY= 40.0% ~. DISPLRCEMENT=289.2 IN' COMP. RT I=9.30 0 O AL TUdE t00 ~ I Zc~~,~~ A |tud / /Vl 0 C/ U0 / i. - - -.-.......... AA Ao___ /_/_ I_. _ Fiur4.Caruro -Ee -Vl a INTKE MNIFLD PRESSURE IN INCHES Hi

291 pressure are less at the altitude condition, as is the air flow rate for each throttle angle. One important item to notice however, is that the road load operating line is affected very little, except that the top speed of the vehicle is decreased (the intersection of the road load line with the wide open throttle line.) The second example represents the results of a simulation run to determine the effects of a reduced ambient temperature, in this case 0 F. Again a complete carburetor-engine-vehicle operating map analysis was utilized. The fuel temperature specified for this simulat0 ion run was 30 F, which represented a reasonable float bowl temperature under these ambient conditions. The simulation predictions for the cold inlet air case are listed in Table 26, and are plotted in Figure 75. If these results are compared to the corresponding results for normal ambient conditions (Figure 69 and Table 16), the following conclusions may be drawn: 1. The air mass flow rate is greater at the same throttle angle for the cold inlet air case. 2. The boost and primary venturi suctions are less at the same air mass flow rate for the cold inlet air case. 3. The fuel-air ratios for the cold inlet air case are leaner than for normal inlet air temperatures at some air flow rates, and richer at other air flow rates. 4. The minimum air flow rate is greater, and the minimum intake manifold pressure is less for the cold inlet air case.

TABLE XXVI SIMULATION PREDICTIONS FOR CARBURETOR PERFORMANCE WITH REDUCED AMBIENT TEMPERATURE UNIVERSITY CF MICHIGAN MECHANICAL ENGINEERING COCTORAL THESIS ___ CIGT TALSIMULATICN CF CARBURETOR METERING ________ ________ CIRBURETUR-LNGINE-VEHICLE OPERATING MAP ______ ______ CAVID L. HARRIKGTCht Tt-E TYPE OF ANALYSIS RECUESTEC IS..... COMPLETE OPERATING MAP TFtE TYPE OF PLUT(S) REQUESTED ARE.... —COMPLETE OPERATING MAP ThIS SIMULATICN PERFORMEU ON. 1 FEB 1968 ______________ PURPOSE OF THIS SIMLLATION RUN...... TO CHECK TFE EFFECT AMBIENT TEMPERATURE ON THE OPERATING MAP AMbIENT CLNDITIONS CAR8U)NEM4I FUEL ENGINE VEHICLE --— AM-I-NT-C-NDITION —--- ---------— ETC —----- ------— IF —----------------— E-GI —----------- EIL PRESSURE = 29.28 INCHESG - ----- G ^ — 95-10 —- ^K^A ^^ —EC 96 -FO0 2 89' V-29 1966 FORD FAIRLANE TEMPERATURE.0 DEGREES F MAIN JLT_ = F-50 TEMPERATURE = 30.0 F DISPLACEMENT=28S.i C.I. VEHICLE WEIGHT=3435.0 HUMIDITY = 40.0 PERCENT- --- MNF NTU]TI.145 N.SPECTFVC ~GRAVITY=~752-COMPJRATTO 3 -- -REAR AXLE RATIC 3.00 DENSITY =.0845 L3M/FT3 CLOSED ThPCTTLE=10.0 VISCCSITY =.753 CS VALVE FLOW AREA=6.82 IN2 TIRE REVS/MILE =775.0 CARbURETOR-ENGINE OPERATIEN AT CCNSTANT ENGINE SPEED-VARIABLE THROTTLE OPENING NO THROT INTAKE MOIST -OHY BCLST MAIN TWRiT- MATW-TOTAL F101AL - MAIN THROT THRCT ENGINE THROT FLOW MAN. AIR AIR VENTURI VENTURI MACH F/A F/A___ FUEL FUEL TOTAL PLATE RFM ANGLE AREA PRESS FLCW- FLOW SUCTICN-SUCTION NO. RATIc RATIO iLUW --'FLUW TEMP COEFF J 80C.O 1u.0 017; 6.26 45.Sl 45.91.06.03 1.0000 000.1321 3.031 000.0 683 3 800.0 12.0.02f6 8.34 67.49 67.49.14.07 1.0000.0000.1109 3.742.000.0.721 3 80C.0 14.0.0413 11.2719.28.15 1.0000.011l.0909 4.281.474 -2.4.757 3 80C.0 16. U0559 14.83 125.49 125.49.52.27 1.0000.0289.0759 4.764 1.813 -6.8.790 3 80C.0 16.0.0724 - 18.38 157.47T57-47-.83 -.44.9 — 0&03 —O657-5776 3.61 -11.8.817 3 800.0 20.0.0907 21.25 183.51 183.51 1.15.60 6929.0610.0610 5.597 5.597 -14.4.838 3 80C.0 22.0.1109 -23. 37 203.28 203.28 1.42.74.5759.0613.0613 6.229 6.229 -14.4.854 2 80C.0 24.0.1329 24.80 217.27 217.27 1.63.86.4912.0656 0656 7.131 7.131 -15.5.859 3 80C.0 26. 0 1567-25.87 227.i5-227.75 1.80.94 -.4221-)-.0689.0689-J.845 7.845 -16.2 865 3 8CC.0 28. 1822 26.64 235.41 235.41 ___1.94 1.01.3662.0712.0712 8.386 8.386 -16.8.871 2 800.0 30.0.2094 27.21 241.08241.08 2.04 1.07.3203.30.0730 8.799 8.799 -17.2 876 2 80C.U 35 0.284t 28.09 249.83 249.83 2.20 1.15.2361.0757.0757 S.453 9.453 -17.8 890 2 800.0 40.0.3,99- 2E.53 254.24 254.24 2.29 1.20.1813.0770.0770 9.791 9.791 -18.2.900-2 80C.0 45.0.464C 2 28. 77 256.62 256.62 2.34 1.22.1439.0778.0778 S.977 9.977 -18.3.911 2 800.0 50.0 5 66C —2c.91 258.0 C 2158 00 2.37 1.24.1172.0782.U782 10.085 10.085 -18.4 920 2 80C.0 55.0.6747 28.99 258.E3 258.83 2.38 1.25.0978.0784.0784 1C.150 10.150 -18.5 927 2 800.0 60.0.7b82 29.0 5 2 599 35 2.40 1.25.0834.0786 0786 10.191 10.191 -18.5 932 2 800.0 70.0 1.0131 29.10 259.91 259.91 2.41 1.26.0645.0788.0788 10.235 1C.235 -18.6.940 2 80C.0 80.0 1.0889 29.11 260.C2 260.02 2.41 1.26.0599.0788.0788 1C.244 10.244 -18.6.943 1 ThE CPERATING MAP GRID I-AS BEEN DRAWN ______________________________________________ A LINE WAS PLOTTED WITH 19 FLINTS

TABLE XXVI (continued) A LINE hAS PLOTTED 6ITH 1S FCINTS -CARBEURTGR-ENIE -PER-RAT-I-C — AT — CCNSTANT ENGINE SPEEC-VRAgCUETHROTTLE — OPEN ING IHRCT INTAKE PCIST DRY BGCST MAIN TFROT MAIN TOTAL TCTAL MAIN THRCT THPCT ENGINE THRUT FL-UW IAN. AIR AIR VENTURI VENTURI MACH F/A F/A FUEL FUEL TOTAL PLATE, RPF ANGLE AREA PRESS FLCI FLCW SLCTIGK SUCTION NC. RATIO RATIO FLOW FLCW TEMP COEFF J o 160C.0 10.0.017S 4.24 45.S5 45.S5.06.03 1.0COO.0OO0.1389 3.191.000.0.683 3 160C.0 12.0-.-0286 5.06 - 67.52 - -7.52.-.14 7.07 OOO —-~000-.-205 - 4.C65.000.0.721 3 160C.0 14.0.0413 6.37 94.39 94.39.29.15 1.0000.C091.1018 4. E05.431 -2.2.757 3 -60C*0 16.0.U559 E.09 125,81 125.81.52.27 1.000 0248.O850 5.349 1.56Z -5.8.790 3 160C.0 16.0.0724 1C.13 161.66 161.66.88.46 1.0000.0443.0681 5.506 3.581 -10.4.817 3 160C.0 20.0.0907 12.39 202 E.63 -2 02 63 - -. — 1.0000 -.0539 -.0615 6.226 5.45E -12.7.838 3 1600C.0 22.0.1109 14.85 248.13 248.13 2.12 1.11 1.0000.0572.0607 1.530 7.101 -13.5.854 2 160C.0 24.0.1329 — -1-I7.25 292.89 2.92.89 -.98 —1~.56~.9C18.06-10.0610 - 8.932 8.927 -14.4.859 2 160C.0 26.C.1567 19.42 333.C1 333.01 3.88 2.03.7861.0610.0610 10.157 10.157 -14.4.865 2 160C.0 2E6..1822 21.22 366.46 366.46 4.2 2-.47.6892.0610.0610 11.177 11.177 -14.4.871 2 16CC.0 3C.0.2094 22.69 393.77 393.77 5.48 2.86.6076.0610.0610 12.010 12.010 -14.4.876 2 16CC.0 35.0.284 - 25.17- -44I7.7. 441 79 - - 3.6-2 -.-4569 -.-0668. —— 0668 14.748 14.748 -15.7 -.890 3 160C.0 40.0.3699 26.58 469.52 469.52 7.91 4.11.3552.0710.0710 16.680 16.680 -16.7.900 3 16CC.0 45.0.464C - 4 7.39 485.75- 485.75 —.50 —4. —-.237-.-0735 -. —-.0735 17.7863 17.863 -17.3.911 3 160C.0 50.0.566G 27.88 495.52 495.52 8.67 4.60.2320.0750.0750 18.593 18.593 -17.7.920 2 160C. 55.0.6747 28.19 501.55 501.55 9.10 4.72.1942.0760.0760 19.C50 19.050 -17.9.927 2 160C.0 60.0.7882 26.38 505.4C 505.40 9.26 4.80.165E.0766.0766 19.345 19.345 -18.0.932 2 160C.0 70.0 1.0131 28.5-9 509.59 - -509.59 — 9. -4-288 --. -285 —.0772-.0772 —19.669-19.669 -18.2.940 2 16CC.0 bu.O0 1.0889 28.63 510.46 510.46 9.46 4.90.1192.0773.0773 19.737 19.737 -18.2.943 2 A LINE WAS PLOTTED T —ITR 9 — 9~ 19 ATS. —--------- ---.- ----- --—. A LINE WAS PLCTIED WITH 19 FCINTS

TABLE XXVI (continued) CARBLdETLk-ENGINE UPERATICh AT CLNSTANT ENGINE SPEED-VARIAbLE THROTTLE OPENING ITIHKL-T INTAKE - CIS T D2RY -BCCST- MAIN- -TROT MAIN TOTAL TCTAL PA IN THROT ENGINE THROT FLUW MAN. AIR AIR VENTURI VENTURI MACH F/A F/A FUEL FUEL TOTAL PLATE RPt ANGLa AKEA - PRESS FL.C. FLL- SLCTICN SUCTION NO. -RATIG RATIO FLOW FLCW TEMP COEFF J 250C.G 10.U.u179 3.54 45.E4 45.84.06.03 1.0COO.0000.1416 3.246.000.0.683 250C.0 12.0.0286 3.94 67.53 67.53.14.07 1.0000.0000.1246 4.207.000.0.721 3 2500.0 14.0.0413 94.67 94-.29- 94.29.28.15.700.00 O8. -1071 5.C5.0.414 -2.1.757 3 250C.0 16.0.0559 5.70 125.5 _ 125.95.52.27 1.OC0000.0237.0907 5.709 1.491 -5.6.790 3 250C.0 18.0.o 724 7.00 162.02 162.02.88.46- 1.0000. 0415.0728 5.S01 3.365 -9.8.817 3 250C.0 2U.G.J907 8.46 203.27 203.27 1.41.74 1.0000.0493.0652 6.631 5.006 -11.6.838 3'25G-C- 22.0.0lCS 1C.04 248.99 248.99 2.13 1.12 1.0000.0510.0633 7.880 6.352 -12.0.-54 2 25CC00.0 24.0.1329 11.7C 296.72 296.72 3.05 1.60 1.0COO.0530.C619 9.180 7.864 -12.5.859 2 2500.0 26.0.1567 13.50 -348.81- 348.8 — 4-.-25-.. 2.22-~..O0-00Q —.0553 —.0610 10.634 9.653 -13.0.865 2 250C.0 28.0.1622 15.42 404.39 404.39 5.77 3.01.9984.0581.0607 12.267 11.744 -13.7.871 3 250C.0 30.0.2094 17.30 458.92 45-8.-92 -- 7.48 3.89 —.8941..0610.0610 — 13.S97 13.997 -14.4.876 3 2500.0 35.0.2848 21.14 57C.31 570.31 11.74 6.08.6833.0610.0610 17.395 17.395 -14.4.890 2 -50G.u 40.0.3699 23.65 643.66 643.66 15.15 7.81.5360.0621.0621 19.992 19.992 -14.7.900 2 25CC.0 45.0.464C 25.20 o91.C9 691.09 17.63 9.05.4327.0668.0668 23.097 23.097 -15.8.911 3 2500C.0 50.0.5660 26.18- 72 —54-72-.54- 19.33 -9.90. — —.3563.C699 9. 0699 25.202 25.202 -16.5.920 3 250C.0 55.0.6747 26.82 741.16 741.16 20.48 10.47 _.2993.0718. 0718 26.605 26.605 -16.9.927 3 250C.0 6J.0.7882 27.23 753.99 753.99 21.26 10.85.2563.0731.0731 27.542 27.542 -17.2.932 3 250C.0 70.0 1.0131 27.69 768.27 768.27 22.15 11.29.1992.0745.0745 28.602 28.602 -17.5.940 3 25G7.0 o80.0 1.08689 27.79 771.31 771.31 22.34 11.38.1850.0748.0748 28.E30 28.830 -17.6.943 2 A LINtE WAS PLCT1ED WITH 19 FLINTS A LINE WAS PLCTIED WI TH 19 FC INTS -- A LINE WAS PLOTTED hITH 18 FLINTS A LINE WAS PLCTlEO h-ITH 16 FCINTS -T

295 CFRBURETOR-ENGINE OPERT TING MRP PO= 29.28 HG TO= O.OF HUMIDITY= 40.0%. DISPLRCEMENT= 289.2 IN3 COMP.RRTIO=9.30 ~ GlCO INET AIR o THR.....,I /.zl 0-L.JLc' __ACD / / / /\ c-r 0) o!/ /[ ^ 0..___ ___ __ C; a: C, Figure 75. Carburetor - Vehicle Operating Map For Reduced Ambient Temperature

CHAPTER X RECOMMENDATIONS Although the simulation as written provides a reasonable description of carburetor performance over a wide operating range, there are nevertheless many areas in which further investigations are needed. Some of these areas will be discussed briefly. The fuel channel model should be extended to include fuel vaporization and temperature changes within the channel network. The current model utilizes a constant fuel temperature throughout the channel, and does not include the flow of fuel vapor. The ASTM distillation curve for each possible fuel type should be made available in the analysis. The residence time of the fuel-air mixture within the fuel channel and the changing volume flow rate of the bubbles should both be considered. The volume flow rate of the gas phase will be affected by the following factors: 1. Fuel vaporization along the channel. 2. Pressure and temperature changes along the channel. 3. Changing gas phase composition. 4. Condensation of bleed air moisture. Another important area of further study is that of pulsating flow. Basic analyses should be performed on the air pulses within the carburetor, and upon the resulting fluid pulsations within the fuel channel. The pulses should be described in terms of the engine and carburetor variables, and the damping effect of the throttle plate analyzed. The effect of fluid pulsation frequency and waveform on the discharge 296

297 coefficient of orifices should also be investigated. There are numerous additional areas which could and should be studied in the future. This includes the effects of back or reverse flow within the fuel channel, the improved description and prediction of fuel drop size distributions, and the extension of the simulation to air valve carburetors.

APPENDIX A ADDITIONAL SIMULATION PREDICTIONS

299 LOG-LOG PLOT OF CRRBURETOR FLON PPRRMETERS M I N ORIFICE NUMBER= F-50 FUEL TEMPERRTURE 80.0 ~F me RUN NUMBER = 1.18 FUEL = STANDARD GASOLINE O' — — _ a: LD,.~~~~~~~~~~~~~~~~~~~~~~~~1~~' r' ----- -— ""' — -^ ----? -Z ^ _ _ ___. ___7_ _ _ __ _ _ Figure 7 6. Simulation Predictions Of Main Fuel Flow Rates'' —---- ----....BO cu....... I F 7 T..... Figure 76. Simulation Predictions Of Main Fuel Flow Rates

TABLE XXVII SIMULATION PREDICTIONS FOR THE EFFECTS OF PRODUCTION TOLERANCES ON CARBURETOR PERFORMANCE (FORD C 4AFB- 91 CARBURETOR UNIVERSITY OF MICHIGAN MECHANICAL ENGINEERING DOCTORAL THESIS DIGITAL SIMULATION OF CARRURETOR METERING CARBURETOR-ENGINF-VEHICLE OPERATING MAP DAVID L. HARRINGTON THE TYPE OF ANALYSIS REOUFSTED IS......SPECIFIED INPUT POINT THE TYPF OF PLnTIS! REOUESTED ARE......NO PLOTS REQUFSTED THIS SIMULATION PERFORMED ON *..*.... 05 MAR 196f PURPO$E OF THIS SIMULATION RUIN *......TO StMULATF PRODUCTION VARIATIONS IN CARBURETOR DIMENSIONS AP lENI CONOIT INS CARBURETOR FUEL ENGINE VEHICLE PRFSSURF * 2?CO INCHES HG FORD 2 BARREL C4AFB-91 STANDARD REG. GASOLINE 1966 FORD 289 V-8 1966 FORD FAIRLANE TEMPERATURE * 80.0 DEGREES F MAIN JET = F-50 TFMPERATURE - 80.0 F DISPLACFMENT=289.2 C.I. VEHICLE WEIGHTm3A35S0 HUMIDITY 50.0 PERCEiNT -MAIN VfENtURI'.145 IN. SPFCrFiC'-GRAViTY=.721 COMP. RATIO = 9.3 - REAR AXLE RATIO 3.00 DENSITY.t0713 LRM/FT3 CLOSED THROTTLE- q.Q VISCOSITY.556 CS VALVE FLOW ARFA=6.82 IN2 TIRE REVS/MILE I775.0 INPUT DATA FOR THE FORD 2 iARREL C4AFU-9- CARURETOR. ***NOMI NAL DIMFNSIONS*** _ MAIN NMTERING ORIFICE TYPE F-50 o MAIN METERING ORIFICE DIAMETER -.0502 INCH o MAIN METERING ORIFICt L'NGTH-,-.1830 INCH i MAIN METERING ORIFICE L/D RATIO - 3.6454 NUMNER OF MAIN NETERING nRIFICES -- -2. -- COMPLETELY CLOSED THROTTLE ANGLE - 5.000 DEGREES THROTTLE PORE DIAMETER - 1.4370 INCHES THROTTLE SHAFT DIAMETER- *3750 INCH INITIAL -SPiLL POINf OF MAIN SYSTEf -.200 INCH - - - --- AIN VENTURI THROAT DIAMETER - 1,1450 INCHES THROTTLE PLATE BYPASSES TRANSFER TUBEi DtAMETER "'0730 INCH CHOKE BLEED RESTRICTION DIAMETER -.0000 INCH ENRIHMENT-i BLFED RESTRICTION DIAMETER -.0730 INCH GEONETRIC RELATION BETIEEN BOOST AND HAIN VENTURI XMIVI 1.2500 INCHES XWV2 a 1.0000 INCHES XwV -.b-780 " INCHES MB -.0700 INCHES

TABLE XXVII (continued) OITK'SIVNS OF A TYPICAL PROnfCTInN CARRURETnR ______ ____'4AIN mcETrFRINr ORIFICE TYPE F-50 4AIN METERIINC npIFifF DIAMETER..0V) INCH MAIN MFTFRICG nqIFICF LENGTH a.IP'40 INCH 14AIN "FTFRTINr ORIFICr L/n RATIl 10 3.6572 _ NiIMRFR PF MAIN METFRING OR IFICES 2 CnPitCTFLY CLPSF") THPnTTl F ANGI.E = 5.02 DEGRFES THRnTTLF rl'Qc nIAMETFR z 1.4375 INCHFS TNHRTTLF SH4AFT DTAMFTFR=.3745 INCH INITIAL SPILL PniNT PF MAIN SYSTEM a.200 INCH 4AIN VFNTtRI THRIAT VIAMETER 1.1450 INCHES __ THPOTTLF —PIATF RYPASSFS TRANSFEP TURF niAF-TFR a.0730 INCH CHOSF RLFEn RFSTRICTTnN rIAMETER -.')')t INCH _____ ENPICrMFNT RL FFK RF.TRICTiCN ITAMETFR =.-0732 INCH GFnMcTRTC PFLATION PFTWCEN RnOST AND <AIN VENTURI XIV1 1.240AP INCHES X*~V? 1.^0O? INCHES_ _ ___ ___ _ =q *~7&6' TNH HFS - - -- - -- --- - - - - --- ___ — - - =~ #.9C INCHES 0 M<AIN VENTURI _ _ ____________ ____ ________ -_____ - l FLFMFNT PIAMETER -- -- __._ 1 1.030 INCHES 2 l.P?3> INCHES 3 1.14^ INCHES 4 1.160 INCHES _ _______________ _______ 5 INCHS. INCHFS "IST VENTUjRI FLEMFNT PIAMETFR 1 1.^30 INCHES ____________________________ 2.^875 INCHES 2.513R INCHES 4.5916 INCHES 5 1640 INCHES 6.750 INCHES FUEl CHANNEL -- ---- ORIFICE FLEMFNT nIAMFTER LENGTH L/D RATIO TYPE 1 0500 INCH.183 INCH 3.657 1.0? 1875 INCH.312 INCH 1.664.0 2___*___~5081Q INCH.106 INCH 1.311 3.0 4.3133 INCH.125 INCH.399 0 F.1561 INCH.390 INCH 2.498 2.0 6 1349 INCH.206 INCH 1.527.0 7.0282 INCH.125 INCH 4.438 2. 0 8 e1471 INCH.938 INCH 6.372.0

TABLE XXVII (continued) MAYN VFNT1JRI EtFMFNT DIAMETER 1 1.930 INCHES 2 1.930 INCHES 3 1.145 INCHES ~~4 -_ 1.160 INCHES 5 1. 40 INCHES ROCST VFNT1UPI FLF4EENT IA4FTER 1 1.0 0 INCHES? R75 INCHF S 3.*3R INCHES 4 *~OA. INCHES *650 INCHFS.75" INCHES FIEl. CHANNEL - - -.- ORIFICE FLFMFNT OIAMETER LENGTH L/D RATIO TYPF 1.0512 INCH.183 INCH 3.645 1.0 0 2 1870 INCH.312 INCH 1.668.0 3.0810 INCH *ln6 INCH 1.309 3.0 _____ __ 4.3125 INCH 125 INCH.400.0 5 15'(40 INCH *390 INCH 2.500 20.1350 INCH.206 INCH 1.526 0 7~ ~ ~.C2 R INCH I1)5 INCH 4.464 2.0 0.147C INCH.3Q INCH 6.378.0 _Q ______.2910 INCH?* INCH.859.0 T-,~.1580 INCH 1"n INCH 6.329.0 i1.2700 INCH *4' INCH 1.259.0 12.1600 INCH.AI? INCH 5.075.0 1I.2250 INCH.135 INCH.600 2.0 14.0610 INCH 1.930 INCH 31.639 *0 1I ______________0260 INCH.094 INCH 3.608 2.0 it.1400 INCH.706 INCH.5043.0 17 *0940 INCH.78O INCH 8.298.0 IP.0420 INCH.106 INCH 2.524 2.0 1<9 ~ ~.0940 INCH 2.000 INCH 21.277.0 20 0590 INCH.106 INCH 1.797 3.0 _ _ Y_ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _,. 12 I C ^310_INC4.0? r'2 ----.0446 INCH.031 INCH.700 2.0 23.0270 INCH.140 INCH 5.1 5 2.0 24.0390 INCW.125 INCH 3.205 2.0 25.0350 INCH.106 INCH 3.029 20_, 0

TABLE XXVII (continued) ~ ^.Q6A INCH.75n INCH _.861 __.0 10.15R3 INCH l.00 INCH 6.316-.0 11.:77?. INCH 340 INCH 1.25n.0 17.16^r INCH.Al? INCH 5.074.0 1'.2243 INCH.135 INCH.602 2.0 14.0I609 INCH 1.930 INCH 31.687.0,l 002h0 INCH.094 INCH _ 3.614 2.0 1 I.139 INCH.706 INCH 5.068.0 17^ CH 9478 INCH. INCH 297.0 19.'41 INCH. 16 INCH 2.534 2.0 095qK INCH 2.000 INCH 21.006.0?'.s9.1l INCH.10A INCH 1.7q4 3.0 71."21le INCH.1?5 INCH 4.032 _2.0 f-.044A INCH.31 INCH.705 2.0- ------- - ---??.n277 INCH.,40 INCH 5.121 2.0.0.r9 INCH.125 INCH?.214?.0 7*.3S1 tINC.NC 6 INCH 3.016 2.C C&2TUPFTQ-NGINJF OPERATIONN FR _SPECIFIC nPERATING POINTS (RPM AND THETA SUPPLIED AS INPUT DATA) THRnT INTAKE O IST DRY TROOST M14 AIN HR N TOTAL TOTAL MAIN THROT AIR ENGINE THPnT FL' W 4A' AIR 4IR VENTURI VENTURI MACH F/A /A FUEL FUEL TOTAL BLEED RPW 4I(NC.LF ARFA FSS FLO FLOW SUCTION SUCTION NO. RATIO RATIO FLOW FLOW TEP FLOW J Ih'.0 30.'.2153 2;3.-C-35~4.82 350.94 5.26 2.76-.5626.0629.0629 72.091 22.091 65.3.16 2 16^".0 3f.0.2152 23. R 354.82 350.9Q 5.27 2.77.5633.0637.0637 22.352 22.352 65.1 *416 2 1600.f,C..2151 23.28 354.78 35^.90 5.27 2.7R.5636.0640.0640 22.447 22.447 65.1.412 2 16^".0 3r.0. 15^ 23.?7 354.66 35?.77 5.24 2.75.5638.0637.0637 22.333 22.333 651.420 2 f160o. 30.0.2152 2. 29 354.74 350.86 5.25 2.76.5631.0632.0632 22.172 22.172 65.2.415 2 16n'.0 t3.2151 23.28 354.84 35?.9'5 5.24 2.77.5635.0641.0641 22.487 22.487 65.0.423 2 160i0. 30.0..?3.27 354.82 350.94 2.27 2.77.5639.0644.0644 22.615 22.615 65.0.408 2 1600.0 3r.^.2152 23.27 3S4.82 350.03 5.26 2.76.5639.0644.0644 22.590 22.590 650.15 2 1600.0 30,..2152 23.29 354.82 350.94 5.78 2.76.5629.0633.0633 22.216 22.216 65.2.419 2 1600.0 30.0.2151 23.27 354.79 350.90 5.27 2.76.5639.0643.0643 22.573 22.573 65.0.411 2 1600.0 30.0.2152 23.2? 354.89 351.00 5.24 2.75.5630.0637.0637 22.370 22.370 65.1.409 2 1600. 30t.C.21SC 23.28 354.70 350S.1 S.26 2.76 5636.36 066.0636 22.294 22.294 65.2.414 2

APPENDIX B THROTTLE FLOW AREA The throttle plate-shaft combination will be analyzed geometrically to obtain the throttle flow area as a function of throttle angle, plate and shaft diameters, and throttle closing angle. This flow area corresponds to the throat area of the converging nozzle which is used as the throttle plate model. The symbols used in this analysis are: D = throttle bore diameter d = throttle shaft diameter - = throttle angle 4O = throttle angle in completely closed position A = area Figure77illustrates the variables involved in the throttle flow analysis. Note that the minimum possible throttle angle is:o and that the throttle shaft constitutes a variable restriction which depends on the throttle angle. (It contributes very little at small throttle angles and is the entire restriction at wide open throttle.) Note that the throttle bore area is irD2/4 and that the throttle restriction area is: r D2 / cos0s 4 \cos. o If the throttle shaft were negligibly small, the flow area would be; 304

305 V) (b~ 0 0 o o 0 Q Q U),...-.. -'. —..-. —.k ul — c,) X'+-> I cO o r/ O J 11 11 I. o CCo 0 (0~~ 0u~ C b II II~~~~~~~~~~~

306 flow = TD_ iD2 ros = 1Do r - cos o 4 4 coss 4 cosoj However, the shaft is usually so large that its effects may not be neglected. Note that the maximum flow area is shown in the sketch: FLLOw I LO \ AAr..Ut An.A fA Thus, in the general case of an angle -, the flow area will be given by determining what portion of the ellipse is not adding to the restriction, but is only blocking a region already blocked by the shaft. [~ Thus: Flow = Throttle - Shaft - Cross hatched area Bore area region of ellipse Area Note also that the shaft area is not a simple rectangle but is rounded at the ends. or if A* is the region shown in the above sketch,then: Net Flow Area = Throttle - Total area + A* - A bore area of ellipse shaft The determination of A*, the portion of the ellipse which is blocked by the throttle shaft, involves the evaluation of an elliptic integral.

307 ~ = D cos e r -$X O —-- dA = 2 x dy y =d/2 Y =d/2 A* =2 dA = 2 2 x dy y=o y=o But the equation of the throttle 4 x 2 421 EQN plate ellipse above is: D2 D2 cos2'0 cos2 or: X =|D2 _y2 cos2^o 4 cos2 4 y l thus: A* = 4[ y2 cos2O 1] cos2O dy y-o For convenience, let: R =D thus: 2 D2 y cos2, 1 2 2 2 2 4 cos cosO o B = R costherefore: y_=d 4 A 1/2 A*= cos J, B2 cos20 dy Y=o

308 Integrating: -_-1 d/2 A* = - 2 [y coseB2 - y2 cos2 F+B2 sin y cosO) cos4)' cos4G L \ B:J 0 Or: A*= 2 d I cosG cos [i cosO- cos2 - d2 cos2Q 2 2-4 4 cos2- sin /d cos cD cos 0. EQN B2 A restriction resulting from the integration is that; d cos-O/b cos-9l1 or that; cos#> d cos-0o D This corresponds to the physical situation shown in the sketch to the left. Note that the throttle plate is not reducing the flow area for this (or larger) values of the throttle angle Q. Thus simplifying: A* = d D2 cos2 d2 cos24+ D2 cos- si D cos.E 2VCos z 2 cos in D cos EQN B3

309 In a similar manner, the cross sectional area of the shaft is found to be: A d 2 2 2 shaft D d 2 -1 d EQN B4 A simple check may be made here: when d = D shaftshould equal Tr D 4 Check: shaft + sin (1) = D2 2 2 Thus: Aflow = TrD2 1 - cos0 ] + A* - A EQN B5 Ashaft EQN B5 4 Cos Now substituting the relationships for A* and A shaft, the final equation for the throttle flow area is:'Tr Cos2- d 2 2 cos Ao Aflow = TTD l - cos 1+ d D cos2- d' cos2. 4 L cos _J 2 cos4 + D cos sin -1 cos d -d2 + D2 sin 2 D cos 2 2 EQN B6 This obviously requires a computer subroutine to evaluate AFLOW for any 0, D, d, and 6O.

310 In the subroutine THROTL the following symbols have been defined: THETA = 0 in degrees RTHETA = i in radians THETAO = * in degrees RTHETO = GO in radians 2 DT = D in inches ASTAR = A* in inches 2 DS = d in inches ASHAFT = Ashaft in inches For a typical carburetor used in this study,the variables have the following values: D = 1.438 inch d = 0.375 inch' = 0.700 Actually the closing angle 0- is 5.0~ but, as discussed in Chapter II, to have the above equation yield the throttle plate leakage area when 0 = 5.0~ (completely closed), a smaller value of 46 is used. This is far superior to neglecting the leakage area, especially for small throttle openings.

APPENDIX C IDLE NEEDLE FLOW AREA A large proportional of the pressure loss in the idle flow channel is across the idle needle screw. This screw has a tapered section which projects through a drilled hole on the downstream side of the throttle plate. Since this idle needle flow area is very influential in determining the idle fuel flow, it must be known in terms of the needle geometry. The symbols used in this analysis are: di = Idle discharge port diameter in inches d n Idle needle diameter blocking the port in inches Nth = Number of threads per inch on idle screw o< Included angle of idle needle in degrees TURNS = Number of turns of needle screw from fully closed position The geometric arrangement of the idle needle and port is illustrated in Figure 78. Note that one turn of the idle screw from the fully closed position will move it 1/Nth inches. This opens up the annular flow area between diameters dn and di. It is this annular flow area that we wish to calculate. Note that from the right triangle formed by the portion of the idle needle projecting into the port we obtain: TAN ( O</2) = A RADIUS 1/Nth EQN C1 Where A RADIUS is 1/2 of the difference between di and dn. Thus the change in diameter or (di - dn) per turn is given by: 311

IDLE FLOW AREA Dr~~~A SECTION AA JIES Figure 78. Idle Needle Flow Area Variables

313 A DIAMETER= (d. - d) = 2 TAN (c</2) [TURNS] EQN C2 Nth Thus: dn d - 2 (TURNS) TAN(/2 EQN C3 or: Annular Idle = 2 - r r2 (TURNS Flow area d - TAN /2) EQN C4 For the typical values of: - = 25~ Nth = 32 threads/inch i = 0.060 inch TURNS - 2 2 AIDLE = 0.002827 - 0.7854 0.060 - (4.0)(0 2217)0 L 32.0 J or 2 AIDLE = 0.002006 in

APPENDIX D THERMODYNAMIC PROPERTIES* OF AN AIR, WATER VAPOR, AND FUEL VAPOR MIXTURE * Molecular weight, specific heats, and specific heat ratio of a multi-component mixture of ideal gases. Sub s cripts: 1 = fuel vapor 2 = air 3 = water vapor VARIABLES: n = number of moles m mass of component W = molecular weight y = mole fraction FAMAIN = main system fuel-air ratio by weight FATOTL total fuel-air ratio by weight (main + idle) (D = water vapor-air mass fraction, = relative humidity T temperature OF = Pressure - psia The number of moles of component i is given by m. n. I l- EQN D1 1 Wi and the mole fraction is then: n. y = l EQN D2 314 314

315 The molecular weight of the multi-component mixture is given by: total yii = Y1W1+2W + y3W3 EQN D3 By using equation (2), Wtotal may be expressed as: nl W1 + n2 W2 + n3 W3 Wtotal = nt EQN D4 total But: ml + m2 + m3 ntotal = W1 W2 W3 m3 m3 m + 1 + - Therefore m2 m2 mI + m3 1 m m2 + m3 = m2 2W+ mw 3 3 total = "1 + m2 + m3 2 LW1 W2 W3J W1 W2 W3 EQN D5 But the mass fractions have the following meanings: mi m3 = fuel-air ratio 3 m2 m2 Where W( is related to the partial pressure of the water and the relative humdity by the following relationship:71 0.622 P3 4 Ptotal P3 is the vapor pressure of the water at the temperature of the mixture and is correlated very well by the equation: P3 = 1.302 ( T ) - 0.765 (.) + 0. 413 ( T ) psia 3 100 *E100 100 EQN D6

316 over a temperature range from 20~F to 120~F. Thus the expression for the molecular weight of the mixture becomes: 1 + F/A + C.O _ Wtotal = F/A _1 + ) Wfuel Wair WH 0 EQN D7 Since fuel may be introduced at two points in the air flow path, the thermodynamic properties of the mixture must be calculated using the local fuel-air ratio. Noting that the total mixture ratio is given by: FATOTL = FAMAIN + FAIDLE, the fuel-air ratio to be used is as follows: a) before boost venturi; F/A O b) between boost venturi and idle discharge; F/A = FAMAIN (including throttle plate) c) between idle port and engine cylinder; F/A = FATOTL Therefore, for an analysis of flow at the throttle platethe molecular weight to be used is: 1 + FAMAIN + OMEGA WMOLEC = FAMAIN + 1.0 + OMEGA FUELM 28.95 18.016 EQN D8 and for an analysis of flow from the carburetor to the engine cylinder the molecular weight is: 1 + FATOTL + OMEGA WMOLEC = FATOTL + 1.0 + OMEGA FUELM 28.95 18.016 EQN D9 where the computer variables names have been introduced.

317 SPECIFIC HEATS: C (mix) = m m3 mtoa ( - (C) + p (Cp) 3 mtotal ( p)l + mtotal p2 mtotal EQN D10 But: m -m + m + m total - fuel vapor air water vapor or: mtotal = ml + m2 + m3 p (mix) = ml (Cp)l + m2 (Cp)2 + m (Cp)3 mi + m2 + m3 EQN Dll But mtotal is not convenient for carburetor work therefore divide by m2 instead of mtotal: thus: r (C)1 + (Cp) + 3 (C )3 C? (mix) = 2 m2 P M+ 1 + mI12 m2 But m 3 m I m2 m2 Therefore: C (mix) (C ) + w (C ) + (F/A)(C ) P p air P H 20 p fuel 1 + (A + F/A EQN D12 Similarly: (mix) = r ) + o (C ) + (F/A)(C )f C (mix) = v air v H20 v fuel v.... 1 + h) + F/A EQN D13

318 Or in computer nomenclature: C (mix) CVAIR + OMEGA*CVH20 + FATOTL*CVFUEL v 1.0 + OMEGA + FATOTL the specific heat ratio is given by: (C (C (C) (F/A)(C ) K = P mix = Pair p H2 + p fuel mix (Cv)mix (C) a+ W (C) + (F/A) (C)f v air v H20 v fuel EQN D14 Program values used to evaluate the mixture values are: 0 (C ) a.240 (C).445 btu/lbm R P air p water vapor (C) air = 171 (Cv)water vapor =.335 TYPICAL FUELS Normal Iso Ethyl Methyl ~___ __ <~Octane Octane Alcohol Gasoline Alcohol (C ) fuelvapor.400.400.460.400.410 (C ) fuel vapor.381.381.407.381.370 v I i......

APPENDIX E EXPLANATION OF SUBROUTINES 1. THROTL Subroutine THROTL operates on the geometric data for the throttle plate and shaft and returns a throttle flow area. For a specified throttle bore diameter, throttle shaft diameter, completely closed throttle angle, and throttle plate opening, this subroutine evaluates the equations resulting from the elliptic integral (Appendix B) and returns a throttle flow area. This area is per barrel and is in square inches. 2. ASSUME This subroutine provides reasonable initial guesses for the main, idle, enrichment, and total fuel rates and also for the main, idle, and total fuel-air ratios. Any iteration in the main program which requires an initial guess for a fuel rate or fuel-air ratio may call on ASSUME with an air flow rate and intake manifold vacuum. On the basis of typical carburetor curves of fuel-air ratio versus air flow rate, reasonable values are assigned to the initial guesses. This greatly reduces the number of iterations required, since the values are in the correct range initially. 3. FLOW This subroutine determines all important parameters associated with flow in the fuel channels. With the fuel properties, complete channel geometry, air bleed sizes, metering signal, and intake manifold 319

320 vacuum specified, subroutine FLOW iteratively evaluates the Reynolds number dependent flow network which constitutes the fuel channel. Total pressure losses due to orifices, bends, sudden expansions and contractions, two-phase flow, and viscous friction are evaluated. Fuel and air flow rates in each of the twenty five elements in the five branches of the flow network are adjusted according to the pressure loss error in each element until convergence is obtained. When this occurs, the system parameters are known for each element. These include flow rate, velocity, total and static pressures, and Reynolds numbers. Thus, the overall fuel system parameters such as main, idle, and enrichment fuel flow rates, and air bleed flow rates are known. 4. AIRMAS This subroutine operates on engine-throttle plate input data and returns mixture flow rates and intake manifold pressure to the main program. Thus the main function of AIRMAS is to theoretically determine the dry air, water vapor, and fuel vapor flow rates in pounds per hour, and the intake manifold pressure in inches of mercury. The ambient conditions, engine specifications, and needed carburetor geometry are first supplied to the subroutine. Then, for any engine speed and throttle flow area, AIRMAS simultaneously evaluates the exhauster (engine) and nozzle (throttle plate) flow equations and, by repeated iteration, obtains the mixture and component flow rates and intake manifold pressure which satisfy the equations. The moist air flow rate,or the sum of the dry air and water vapor flow rates, is of particular interest

321 since this is the quantity measured in an engine air flow test. The iteration method is basically as follows. For any assumed intake manifold pressure two moist air flow rates are calculated. These flow rates result from the exhauster and nozzle flow equations respectively. Equation 2.19 yields a moist air flow rate which satisfies the exhauster flow conditions and equation 2.10 gives a flow rate which satisfies the compressible mixture flow through the converging nozzle (throttle plate). This is shown in Figure 5. Continuity, of course, requires that the moist air flow rate to the engine be the sum of the moist air flows through and around the nozzle. Accounting is made of the fact that air, water vapor, and fuel vapor are flowing and that multiple bypasses exist around the throttle plate. The iteration then proceeds until the error parameter is within a specified value. 5. SIGNAL This subroutine evaluates all aspects of the compressible mixture flow through the primary and secondary venturii. Its chief function is to calculate the theoretical metering signal (the boost venturi vacuum at the fuel discharge nozzle in inches of water) based on the geometry and flow conditions which have been supplied. After the total mixture flow rate has been obtained by AIRMAS, subroutine SIGNAL iteratively determines what fraction of the moist air flowsthrough the main venturi, and what fraction flows throug ththe boost venturi. Then, with the flow rates known, the Mach numbers, pressures, and temperatures

322 are calculated at each station of the venturii. Interacting phenomena such as increased mixture flow rate in the boost venturi due to fuel vaporization, and changing mixture properties with distance are included. The analysis is performed for any fuel type, temperature, and flow rate as specified by the main program. 6. SOLVE Subroutine SOLVE evaluates the Mach number for any compressible flow situation. That is, if the flow conditions at any station are supplied, the Mach number will be returned by SOLVE. Thus,if the flow area, local stagnation conditions, mixture molecular weight, mixture specific heat ratio, and mass flow rate are specified, a Mach number can be iteratively obtained. The Newton-Rhapson iterations are required because the compressible flow relationships are not explicit in the Mach number. This is discussed in detail in Chapter II. Subroutine SOLVE incorporates certain other features including checks to determine if the specified conditions result in a valid flow situation, and accurate initial guesses for the Mach number based on linearizing the flow equations. This reduces the number of iterations required for a given error level. 7. XMIX The function of XMIX is to provide the thermodynamic properties of a mixture of air, water vapor, and fuel vapor. These properties are determined for the relative proportions of each component in the mixture.

323 These proportions are related to the fuel-air ratio and relative humidity of the mixturewhich are specified in the subroutine list. Thus, for a given fuel type, air temperature, fuel-air ratio, and relative humidity at a given carburetor station, subroutine XMIX will calculate the mixture nmlecular weight, specific heats, and specific heat ratio, and return them to the main program. 8. STERL This subroutine is essentially a generalized Mth degree interpolation program which is utilized many times in the overall simulation. When supplied with a set of data (for anything) and an X argument, STERL will return a corresponding Y value to the calling program. Basically this subroutine operates on the N data points supplied to it and generates a difference table. It utilizes Sterling's techniquewhich is the sum of the Gauss forword difference and the Gauss backward difference,to obtain an Mth degree interpolation value, with M less than or equal to N-1 (For complete information see Appendix F). Thus, for discharge coefficient data, engine IHP data, etc., accurate interpolated values can be obtained for specified values of the abcissa. 9. FPROP Subroutine FPROP contains property correlations for numerous fluids and supplies the property values to the main program whenever it is called. The fluid properties correlated as a function of temperature include specific gravity, viscosity, and surface tension. The temperature

324 range in most cases is 200 F to 110~ F although some data extends to slightly higher temperatures. Values are also supplied for liquid specific heat, constant pressure and constant volume specific heats of the vapor, molecular weight, lower heating value, and latent heat of vaporization. All of this is available for nine fluids of interest in carburetor work. These include iso-octane, four brands of gasoline, ethyl alcohol, mineral spirits, air, and water. Thus, any property value of any of these fluids can be supplied to the main program by FPROP. 10. CALCOMP PLOTTING There are three separate CALCOMP plotting subroutines or external functions. They provide the detailed instructions and formatting required to produce eleven different plots automatically. The plotting portion of the simulation is specific to the University of Michigan system, that is, the plotting instructions have meaning only in that particular system and in any other computer system they would have to be modified. The three plotting subroutines are written in the MAD language. The eleven plots available will not be given here since they are listed early in the main computer program in Appendix I. Most of the common plots encountered in carburetor work are available in the plotting routines if desired. The naming scheme within these routines is illustrated by considering the first two entries which are CALMAP and CALMVH. The CAL in all cases indicates a CALCOMP plot and the last

325 three letters indicate the type of plot. In the first case it is a complete operating map (carburetor-engine-vehicle) and in the second it is a plot of fuel mass flow rate versus head. The main purpose of these routines is to provide for automatic computer plotting of the simulation predictionswhich presents the results in a familiar form and reduces the man-hours required to evaluate a computer run.

APPENDIX F MULTI-PURPOSE INTERPOLATION SUBROUTINE A general purpose subroutine was written to accurately perform all needed data interpolations within the simulation. These interpolations are performed on actual data many times per operating point iteration, and are required for the following reasons: 1. to obtain an orifice Cd value for a specific Re argument 2. to obtain a throttle plate Cd value for a specific Oargument 3. to obtain an engine IHP value for a specific F/A argument 4. to obtain an engine FMEP value for a specified RPM argument The interpolation scheme utilized in subroutine STERL is basically a generalized form of Sterling's method, which uses a combination of the Gauss forword difference technique (GFF) and the Gauss backward difference technique (GBF). These techniques begin by first generating a difference table from the X and Y data arrays supplied to the subroutine. This table is generated by determining the difference between consecutive values in the next lower order, starting with the Y values. Figure 79 shows the difference table corresponding to nine data points which represent the variation in Cd with Reynolds number for a square-edged orifice with an L/D ratio of 3. 629. Note that the number of data points is N, and that the divided difference columns are designated by SM-' where M is the divided difference order. This order corresponds to the degree of interpolation desired, which is the degree of a polynominal that is passed through the data points in the vicinity of the X argument. 326

xcI) - [X(D] _ I REYNO NUMBER Cj_ 0 00 0. 000 0. 6754 07 1 500.0 0. 74 -- 6.33 - - I- --- I0.041 --- 0.6 IG —- 2 1000.0 0.715 - -0.017 ---- 0-O3 5 C I o —- O --- 0.013 --- 0.583 -- 3 1500.0 0.7359 -O.4 -0.020 — 0. 56 60,020 ---— 0007.0021 053 —-- 4 2_000.o 0.759 -- -0.01 1 - 01001 --— 03 —- -05.6 -o — 00o9 --- 0.006 --- -0.002 --- o00 -- 5 25000 0.78 -- -0o.5 --- ~-0o f | -a.L - ------ o.oo - 0.005 O —-~-0.005 G 300.0 0.772 -— 0-00 -0.006 - - 0.004 --- -0001 7 3500.0 0.776 -0001 8 4000.0 0 779 Figure 79. Sample Difference Table Using Actual Square-Edged Orifice Data

328 The interpolated value can be related to the values in the difference table by the GFF and GBF. First let us define the following symbols which appear in these functions: N = number of data points M = desired interpolation degree (M -- N-l) XARG = X argument for which an interpolation is desired DX = increment of X data points Xstart = the X data point used to start the interpolation. (in most cases the closest one to XARG). SMf(Xstart) Mth order divided difference of f (XSTART) A convenient interpolation parameter can be defined in terms of the above variables. This is: = XARG - XSTART C< = - D EQN F1 DX The Gauss forword and backward functions can be expressed in terms of the above variables and the divided differences in the table69. GFF: f(XARG) = f(XSTART) + "c l1 f(XSTART + DX/2) + o(o<- 1);2 f(XSTART) O2 ( -1 + o(<-1)l(o(+l) 3 f (XSTART +) DX/2) 3! +. EQN F2 GBF: f(XARG) = f(XSTART) +o(1lf(XSTART - DX/2) + <(o<+1) 2 f (XSTART) -__ — + o((o(+l)(o(-l) 3f(XSTART - DX/2) 2* EQN F3

329 Sterling's interpolation technique utilizes the sum of the GFF and GBF to obtain the desired interpolated value, f(XARG): STERL = GFF + GBF 2 EQN F4 Combining equations F2 and F3, the resulting relationship for Sterling's interpolation method is: f(XARG) = f(XSTART) + f [6If(XSTART + DX/2) + Slf(XSTART - DX/2)j+ o 2 f (XSTART) 21- - + o<((+l) (ol) [ 3f(XSTART + DX/2) + S3f(XSTART-DX/2) + g2! 2.3! EQN F5 A simple example of this interpolation technique can be given for the data shown in Figure 79. If the X argument is 2200.0, what is the interpolated value, f(XARG)? Let the desired interpolation degree M be equal to 2 (for simplicity). Thus: XARG = 2200.0 XSTART = 2000.0 M = 2 < = 0.40 f(XARG) = 0.759 + 0'40 (0.009 + 0.020) + (040) (-0.011) 2 2 f(XARG) = 0.759 + 0.0058 - 0.00088 = 0.76398 or: f(XARG) = 0.7640

APPENDIX G GENERAL CONVERGENCE TECHNIQUE A general convergence technique which was utilized extensively in this simulation will be discussed. The simulation contains a very large number of trial and error (iterative) solutions which have very complex error terms. A rapid and stable method of obtaining the required solutions was obviously needed. The following technique adequately met this need. First consider the familiar Newton-Rhapson iteration technique which is commonly used to obtain the roots of a polynomial, f(x). Figure 80 illustrates the derivation of the simple relationship for obtaining the next guess, Xi+1, after one arbitrary initial guess, Xi. f(X) IS A KNOWN f() DIFFERENTIABLE FUNCTION -/ / f(Xi CORRECT', (ERROR) x I Xi+l XI Figure 80. Illustration of the Newtonian iteration technique 330

331 df(x) = f(xi ) or i+ =i - f(xi ) dx Xi - Xi+l df(xi) dx EQN G1 But what if the function to be minimized is a complex relationship which cannot be expressed analytically and which therefore cannot be differentiated? Such is the case in figure 81 where a generalized error, E(Z), is shown as a function of the parameter Z. 0: _ I 7 i E /E W / I o / IZI z2 /\ NEW GUESS GUESS \ I-I I CORRECT Z Figure 81. Illustration Of Generalized Convergence Technique This error function can be related to many variables and may be so complex that it can only be generated by trying values of Z. For example, Z may be a fuel flow rate, and the iterative error parameter, E(Z), may be the difference between pressure losses predicted by different subroutines. In any case, the problem is to continuously change Z and reduce E(Z) to a small value. This method begins with a completely

332 arbitrary guess for Z and, no matter how complex the calculation, a resulting value for the error, E1. Next,another arbitrary guess is made for Z (usually a small distance from Z1) and a different error valueE2, results. Now the next iterative value for Z can be obtained by similar triangles: z - z z22 - zr (- 2 Z2 _ = __2 r 21 E2 E2 (Z2- Z1) or E2 E2 -E1 E2 - E EQN G2 Equation G2 gives the next iterative value,Zi,as a function of the values and errors of the two previous guesses. This worked extremely well in all cases and gave fairly rapid convergence for a wide range of functions.

APPENDIX H ANALYTICAL PREDICTION OF FUEL VAPORIZATION WITHIN THE CARBURETOR Consider the steady state vaporization of a single spherical droplet in an infinite gaseous environment. The droplet temperature does not vary within the drop or with time. This corresponds to the period in time following t*. (illustrated in Figure 9.) The variables to be used in this analysis and their respective units are given in the following list: Poo = ambient pressure in psia Tf = fuel droplet temperature in OR Psurf = fuel vapor pressure at Tf in psia Pvos = fuel vapor pressure at oT in psia m = droplet mass in lbm m = droplet vaporization rate in lbm/sec t = time in seconds df = droplet diameter in microns d = sauter mean diameter in microns Wf = fuel molecular weight in lbm per lb mol Dv = mass diffusivity of fuel vapor in air - Ft per hour R = Universal gas constant in Ft lbf per lb mol OR A = area in ft2 2 g, = mass conversion factor - ft Ibm per lbf sec f = fuel density in Ibm per cubic ft. Vrel = relative velocity between droplet and air in feet per sec. 333

334 U air = absolute viscosity of air in lfb sec per Ft2 First considering zero relative velocity between the drop and the surrounding medium, the diffusional mass transfer process can be described by the Stephan diffusion equation for spherical geometry:17 dm df PDv Wf d ( - )] dt dlog RTdr oge -P)I RTf dr PEQN H now integrating on the drop radius from r=r to r=oo we obtain: dm 2rdfDv Wf ( - P EQN H2 dt =S..P EQN H2 R Tf where Pbm is the log mean partial pressure, The ratio of Poo/Pb is usually close to unity15 unless the partial pressure of the fuel vapor is a significant portion of the total pressure P,. Letting this ratio be unity, and noting that the mass of the droplet, m, may be written as; Tlof df /6 and that dm is negative (mass is leaving the droplet) we obtain: -d (d3) = (6)(2)T Dv Wf d (P - P) dt Trff R Tf v or -(3 df) d(df) - 12 D Wf (P - ) dt /R Tf or integrating from t = o to t = t and from the initial diameter ds to df: f t -3 dfJ( =12 Dv (P -P ) dt vds ~ Kes v.R

335 or in the correct units: 2 2 8 D W d = ds (l2192)(304800) R (P -P microns2 vf / x / R ^rf EQN H3 equation H3 gives the droplet diameter as a function of time for zero relative velocity. The vaporization rate in the correct units can be obtained by rearranging equation H2 and noting that the droplet surface area A is 1Td. = (12192.0) 2 Dv Wf p - P Ibm A, -- - s 2^ —R Tf df sec ft2 EQN H4 (The conversion between microns and feet has been used in the above two equations; 304,800 microns per foot.) Now for mass transfer in the presence of a relative velocity between the drop and the surroundings, the quiescent equations will be modified by a mass transfer Nusselt number, (Nu)m. This dimensionless number is a function of the Reynolds and Schmidt numbers which are defined as: Re = Droplet Reynolds number= (Vrel) (df) (/Oair)'air S = Schmidt number= Pair ((air) (Dv) 20 Ranz and Marshall20 offered the following mass transfer correlation: 1/2 1/3 (Nu)m =2.0+0.6 (R) (S() Since the mass transfer consists of a quiescent contribution and a convective contribution, the Nusselt correlation modifies equation H4 in the following manner:

336 I =(12192.0) DvWf 1/2 1/3 i]bm -= (12192.0)' (P-p + 0. 6(R) (S) ] m A Tf df vooL c sec ft2 EQN H5 which reduces to equation H4 for zero relative velocity (Zero Reynolds Number.) At this point the spray characteristics must be introduced. If the total vaporization rate of the spray is desired, then df and A must be parameters which describe the entire spray. This was accomplished in Chapter 2 where the Sauter mean diameter was discussed. Thus, for a spray mass flow rate of m(spray)lbm/sec, the total spray surface area is: Aspray = (6)(304 800) sprai 2 pay () (d s pray ft /second EQN H6 (~f) (d)' and the number of drops formed per second is given by: drops _ (6)(304,800) mspray second -,o 3 EQN H7 /of ds The fraction of the spray vaporized in a time At is an important parameter and can be obtained by considering equation H5 and the expression for the droplet mass. In a short time increment t, the droplet of initial size ds will lose a small amount of masslmloss. The fraction lost will be; FRACT = m /m FRAGT = mloss/m initial but the initial droplet mass is: 3 minitial = /~f Trds 6-Ibm EQN H8 (6)(304,800)3

337 and the droplet surface area is: Adrop = ds 2 (304,800)2 ft EQN H9 the mass lost can be obtained by substituting the droplet area into equation H5 and noting that the droplet diameter df will be equal to d. S mloss = (Adrop) (12192.0) DvWf (Ps - P ) (Nu) At lbm R Tf ds thus in a small time interval At: FRACT= mloss rd 2(6)(304,800)3 D ( initial (324,800) d- (121920)DvWf (Ps-Pv)(Nu) A t (304,800) /-f ds (iU4bUs UR Tfd, f s or simplifying: RCT (6)(304,800)(12192) vWf (PP2 1[2.0+06(Re) (S ] t ffR Tf ds EQN H10 This is valid only for the first 20 to 25% of the mass vaporized since it was assumed that the droplet diameter did not change greatly from ds. Larger percentage vaporizations could be handled by taking small time steps and recalculating df and Re for each step. It is now advantageous to express the fraction vaporized as a function of the downstream distance in the carburetor, A z. In order to eliminate At, an expression for the time required for the droplet to travel a distance A z inches must be obtained, and this entails an analysis of the droplet motion after it enters the air stream.

338 2 The force acting on the drop will be F = C A [/air Vr] drag p rel a _ _ EQN H11 Where Cdrag is the drag coefficient and Ap is the projected area of the drop. This force will result in a z motion with time described by: F = m d2z g~- c d~ -~t2~ ~EQN H12 If we restrict our analysis to the initial acceleration of the droplet (not in the portion where the relative velocity is nearly zero), then over the short time interval of interest here: Z = o Fave t2 or t =\ 2mZ cm Fave where Fave is the average force acting on the droplet in the interval from 3 2 t = 0 to t = t. but: m = ftds and A 1Td 6 4 thus: At = 2 /,fTrd (4)g (2) AZ 6 gc Cdrag11d2 /%air V2 rag ^ / a ir rel or simplifying and introducing the correct units: At " 2/0f ds AZZ (1304,800)9 /air Cd rel. EQN H13 In the Reynolds number range less than 1.0,the drag coefficient is given by Stokes Law: Cdrag = 24 = (24) (304,800) fair gc EQN H14 ee (/air Vrel ds

339 Thus, in the Stokes Law range, the time to go a distance A Z is given by substituting equation H14 into equation H13: At = d - 1 /f A seconds EQN H15 304,800 (108) air Vrel g It is quite doubtful that the droplet Reynolds number would be less than 1.0 for the region of interest which is the brief time period after the fuel enters the air stream. This is the time of maximum relative velocity and droplet diameter and hence1Reynolds number. Thus Cdrag was obtained 29 by an equation approximating the drag coefficient curve for spheres29 Thus the mass fraction vaporized in the distance AZ inches (restricted to AZ values which do not give over approximately 25% vaporized) is: _ _[DvWf (Ps-P ) ]/of d,Z l FRACT = (12192) 304 800!.. —f T f n dg _ /:pair Cdrag Vrel 1/2 1/3 [2. 0+0.6 (Re) (Sc) EQN H16

APPENDIX I LISTING OF MAIN PROGRAM MAIN PROGRAM: RANDOM DIMENSIONS SPECIFIED INPUT POINT ANALYSIS CONSTANT ENGINE SPEED ANALYSIS ROAD LOAD ANALYSIS CONSTANT THROTTLE ANGLE ANALYSIS CARBURETOR - ENGINE OPERATING MAP CARBURETOR - ENGINE - VEHICLE OPERATING MAP

341 $._._.._..COMP... I........ P E FASTRAN, EX EC UTE, PUNCH OBJE CT DIGITAL SIMULATION F AN AIR-BLEDOOST VENTURI CARBURETOR C _ C C DIMENSION ONAM(I)}, SCRACH( 45),PMAN(30),WETA(30) DIMENSION FMEP ( 35) FMEP2 ( 35),XMPG( 21 ),SPEED( 21) DI MENSION DCHAN ( 25) XLCHAN(25),CTYPE (25),DMV( I ),OBV( 6) O___ I MF NSION _ DCHNOM (25-) DM M DVNOM( 1 DNM( 6) DIMENS ION CDI( 21 ),CD2( 21), C 3(211,CD4( 21) DIMENSION C05( 21),CD6(21),C7( 21),CfDB21),C D9(21) DIMFNSION ANAME(4), FNAME(4),PNAME(4) ENAME(4) DIMENSION ANGLC( 25) DCHTOL (?5),OMVTL (1OC-),DBVTOL( 6),XLD(25) DIMENSION VNAME(4),CNAME(4),WHYt12) DI MENSION_ ACHAN( 25), AMVt10),ABV( 6) DIHP1(35),DIHP2(35) DIMENSION TRANS( 5) CTHROT( 15) tHPP(2 1) DIMFNSION CD(21), E(21), X I HPP 21),BOO ST W 21 ),T TLFA(21) DIMENSION FLOWTP ( 2 1),FLOWMP(21, DRYAP ( 21),BSFCP(21 C COMMON ORDER,PRINTF,REJET CDJET,D-ELXJ,DELXJL,DELXSE,XNC -J, __1__ _ XNCDJL,_NCDSEt TURNS SPILL 1_ RPMDI SPL C R tOBLEED TRANS 2 DCH OKE, PR IN TA XMACHT TO TF,t ACHAN,XL CT YPE, A NGL C CD 1, CD2, 3 CD3,CD4,CO,CD6,CD7,CD8,CD9,SCRACH C C C _ ___ _____READ INPUT TAP E _2____1 2, XNCDJ, XNCDJL, XNCD SE_, DEL XJ, DFL XJL.,DELXSE NCDJ=XNCDJ NCDJIL=XNCDJL NCDS E=XNCDSE READ INPUT TAPE 7,209 ONAM(1), (CD (I ), I =,NCDJ ) READ INPUT TAPE 7, 209, ONAM( 2 ),(CD2 (I ) I=1 NCJL )._-.__ ____ _ READ INPUT TAPE 7 _209i1ONAM. 3),(C.D3.I ),1,NCSE ). READ INPUT TAPE 7,209,ONAM(4 ),(C4(I),I=1 NCOSE ) READ INPUT TAPE 7,209,ONAM( 5),(CD5 I ),I =1NCDSE ) READ INPUT TAPE 7,209,ONAM(6),(CD6(I ),I=1 NCDSE ) READ INPUT TAPE 7,209,ONAM(7),(CD7(1),I=1NCDSE ) READ INPUT TAPE 7,209,ONAM( 8), (C (I ),I=1,NCOSE ) -___ READ INPUT TAPE 7.209_QNAM(9.)_,CD9(I )=1..... NCDSE ) READ INPUT TAPE 7,203,VNAME( ),VNAME ( 2,VNAME 3),VNAME 4), 1 WEI GHT, ARE A, TI RENROLLDRAG READ INPUT TAPE 7,204,RATIO,TRANS(1 ),TRANS(2),TRANS(3) READ INPUT TAPE 7,201,ENAME(1),ENAME ( 2),ENAtME ( 3,ENAME( 1 4), 1 BORE,STROKE,CYL _ ____ R E AD__I N P U T T APE 7, 2Q5_CRDlAN VJALyE S. VED VS T EM BO RT_ L STOL CR TO-L READ INPUT TAPE 7,210,AIRFL1,AIRFL2,XNIHP,XMINRDELXR,XNFMEP, 1 XMINS DELXS NFMEP=XNFMEP NIHP=XNI HP READ INPUT TAPE 7,205,(FMEPI(I ),I=1,NFMEP)

342 DIG.ITAL _.SIMLATIO..N OF AN AIR-BLED,BROOST VENTURI CARBURETOR READ INPUT TAPE 7,205,(FMEP2(I),I =1,tNFMFP) READ INPUT TAPE 7,205,(DIHP1(I)1I=1,NIHP ) READ INPUT TAPE 7,205,(DIHP2(I),I=1,NIHP ) READ INPUT TAPE 7,207,XNTHET, XMINTDELXTNMVNBVNCHAN NTHETA=XNTHET READ INPUT TAPE 7,205, (C'THR!T( I),= 1.,NTHETA) READ INPUT TAPE 7,205,( DCHNOM(I),I=1,NCHAN READ INPUT TAPE 7,205,(DCHTOL(I),I=1,NCH.AN! READ INPUT TAPE 7,205, XLCHAN( I),I=1,NCHAN ) READ INPUT TAPE 7,205iCTYPE(I),I=1,NCHAN ) RF EAD I N PUT TAPE 7,205 ANGL C () I = 1, NCHAN READ INPUT TAPE 7,205,(DMVNOM I ),I=1NMV ) READ. INPUT TAPE 7205, (DMVTOL I),I=1,NMV! READ INPUT TAPE 7,205, ( OBVNOM( I ), I =1,NRV ) READ INPUT TAPE 7,205,(DBVTOL(I),i=1,NBV ] READ INPUT TAPE 7,210iXM1NOMXM2NOM, XBVNnM, XMBNOM,XMTOLt, ___1 ___XMI2TOL- XBVTOL XMBTOL 20 READ INPUT TAPE'7,213,(WHY(I),I=1,l11) READ INPUT TAPE 7,208,CNAME(1),CNAME(2),CNAME(3),CNAME(4), 1 ORNAM,BBLS,JETS,THONOM,DTNCM,DSNOM READ INPUT TAPE 7,205,SPILL1,SPILL2,THOTOL,DTTOL,DSTOL,OPENE 1 TURNS ______ _READ INPUT TAPE 711,_DBLNOM_,DTRNOMOCNM..DBTOL, DTRTOLtDCTOI READ INPUT TAPE 7,201,FNAME( 1),FNAME(2),FNAME(3)-,FNAME(4), 1i FT YPE,TFUEL, FRACT READ INPUT TAPE 7,200,POHG,TOF,HUMID READ INPUT TAPE 7,214,RANVAR,XNUNIT,NUNITS READ INPUT TAPE 7,201,ANAME I1),ANAME 2),ANAME(3),ANAME(4), __1 _ATYPE, A PRYINT1,ORDER READ INPUT TAPE 7,202,PNAME(1'),PNAME(2),PNAME(3),PNAME(4), 1I PTYPE,SCALE READ INPUT TAPE 7,204,PPRINTA,PRINTF,PRINTS,DEBUGA C C C 200 FORMAT (3F10.4) 201 FORMAT {4A6,6X,3F10.4) 202 FORMAT (4A6,6X,2F10.4.) 20 3 FORMAT ( 4A66X 5F.__.4_ _ __ _.4________ 204 FORMAT (4F10.4) 205 FORMAT (7F10.4) 20-6 FORMAT 715) 207 F..ORM AT (3F10.4,315 208 FORMAT (5A6,5F10.4) -_209__ ____ ___ MA 1A6 F 4 I _/ _F 10..___ _ _ ______ 210 FORMAT (8F10.4) 211 FORMAT (6F10.4) 212 FORMAT 915) 213 FORMAT (11 A6) 214 FORMAT (2F10.4,t5 ) 215 ___ FORMAT (_5F10.4)__ __ ____ _______ _________ C C C C

343 _DIGITAL SIM._SULAT ION OF AN AIR-BLE,BOOST VFNTURI CARBURETOR C C C ATYPE INDICATES THE CONDITIONS UNDER WHICH THE CARBURETOR C IS TO BE ANALYZED C C ATYPE=1.-.*.... ANALYSIS OF ONE OPERATING POINT (RPM AND THETA) C A TYPE=2.0....CONSTANT ENGINE SPEED-VARIABLE THROTTLE ANGLE C ATYPE=3.C.....CONSTANT THROTTLE ANGLE-VARIABLE ENGINE SPEED C ATYPE=4.O....CARBURETOR-ENGINE OPERATING MAP C ATYPE=5.0..,,.CARBURETOR ANALYSIS UNDER ROAD LOAD CONDITIONS C __ ATYPE=6.0..*.. CARBURETOR-ENGINE-VEHICLE OPERATING MAP C C C PTYPE INDICATES THE TYPE OR TYPES OF CALCOMP PLOTS DESIRED C C PTYPE=O,......NO PLOTS __ PTYPE=1 Q.....MAIN JET DISCHARGE COEFFICIENT VS. REYNOLDS NO. PTYPE=2.*.....MAIN SYSTEM FUEL FLOW VS. BOOST VENTURI SUCTION'~ PTYPE=3.0.....MA IN SYSTEM FUEL FLOW VS. BOOST SUCTION (LOG-LOG) PTYPE=4.0....MAIN JET DISCHARGE COEFFICIENT VS. BOOST SUCTION C...PTYPE=5.O.....MAIN JET DISCHARGE COEFFICIENT VS.TOTAL FUEL FLOW PTYPE=6.0.....TOTAL F/A RATIO VS. AIR FLOW RATE _..PTYPE=7.O.......VEHICLE MILES PER GALLON VS. MILES PER HOUR;' ~ PTYPE=8.O....ENGINE BSFC VS. ENGINE BHP S.PTYPE'=9.O.....ENGINE IHP VS. AIR FLOW RATE ] PTYPE=10.O....ENGINE IHP VS. TOTAL F/A RATIO Z: PTYPE=l11......COMPLETE CARBURETOR-ENGINE-VEHICLE OPERATING MAP; PTYPE=12.0.....CURVES 11.0 AND 2.C ____ PTYPE=13.0.....CURVFS 11.0 AND 6.C PTYPE=14.0.....CURVES 11.0 AND) 7.0 CTYPE INDICATES THE TYPE OF PASSAGE WHICH COMPOSES THE I-TH FUEL CHANNEL ELEMENT. THIS WILL BE USED TO INDICATE WHETHER DISCHARGE CF___FFIC IENTS MUST _E.CALCJULATED FOR THAT ELEMENT CTYPE(I)= 0.0..o..NOT AN ORIFICE CTYPE(I)=1.0.....A STANDARD CARBURETOR MAIN METERING ORIFICE C TYPE(I )=2.0....A SQUARE-EDGED ORIFICE CTYPE( I)= 3.0.....A VAR I ABLE AREA OR I F ICE SUCH AS AN ENRICHMENT -__ ____ _ __ __VALVE OR IDLE NEEDLE. PRINT1 INDICATES WHICH INPUT DATA SHOULD BE PRINTED OUT PRINTI=0.0....NO INPUT DATA PRINTED; _.__._._PRINTi= 1.. __.OQNLYTHE INITIAL HEADING PR INTED; PRINT1=2.,....HEADING PLUS CARBURETOR INPUT DATA PRINTED PRINT1=3,0....HEADING PLUS CARBURETOR AND ENGINE DATA PRINTED; PRINTI=4.0 *....HEADING,CARBURETCR,ENGINFEVEHICLE DATA PRINTED ] PRINT1=5.0... ALL INPUT DATA PRINTED __.._ _ __ WRITE OUTPUT TAPE 6. 2. __ _. ___._ _ _2_ _ __ 22 FORMAT (1H1l WRITE OUTPUT TAPE 6,1 1 FORMAT (I1H,49X,24H UNIVERSITY OF MICHIGAN /tH,41X, 1 40H MECHANICAL ENGINEERING DOCTORAL THESIS /tH,41X,

344 DIGI.. TAL SIMULATION OF AN AIR-BLEOBOOST VENTURI CARBURETOR 2 4T3h DIGITAL SIMULATION OF CARPURETOR METERING, 1H,42X, 3 41H CARBURETOR-ENGINE-VEHICLE OPERATING MAP,23Xt 4?1H DAVIf) L. HARRINGT.ON /,1H ) WRITE OUTPUT TAPE 6,6,ANAME( 1),ANAME(2),ANAME(3),ANAME(4) ~ 6 _._____FORTMAT (__H,__QX,_4QHX THE TYPE OF ANALYSIS REQUESTED IS.....*. 1 44A6 WRITE tOUTPUT TAPE 6,7,PNAME( I),PNAME(2),PNAME(3),PNAME (4) 7 FORMAT ( 1H 10X,40H THE TYPE OF PLOT(S) REQUESTED ARE...... 1 4A6 ) CALL TODAY (DAT E, DATE2) WRITE OUTPUT TAPE 6,5,DATEIODATE2,WHY(1),WHY(2),WHY(3), I TWHY(4),WHY(5),WHIY(6),WHY(7),WHY( 8 ),WHY (9), WHY(10),WHY( 1) 5 FORMAT ( 1H,10X,40H THIS SIMULATION PERFORMED ON.*.....*.. 12A6t/,tlXt 4CH PURPOSE OF THIS SIMULATION RUN..t.....,11A6 ) WRITE OUTPUT TAPE 6:,47 WRITE OUTPUT TAPE 6 2 2 _ 0 FORM AT. 1H- 130 H AMBIENT CONDITIONS CARBUR E 1R FUEL ENGINE 2 VEHICLE ) WRITE OUTPUT TAPE 6,3 3 FORM AT ( 1H,130H -. 1 ------ -~ ~ ~- ---— ~ —----- ~2, - - - - - -...=. —..................... ) C C PO IS IN PSIA TO IS IN DEGREES RANKINE C DISPLACEMENT IS IN CUBIC INCHES C PO=POHG*0.4912 __ _TOPR=TOF + 459.6 PCH= 100.0 HUMID AMOFNS=14. 696*144.0 cPOHG/( 29.92*5'3.34 *TCR) DISPL=O. 785398* BORF*. BORE*STROKE*CYL AVALVE=,.7854*CYL*((VALVED-0.150)*(VALVED-0.150)-VSTEM*VSTE I /RBLS Pi ___ DUTHO= T HO NOM CALL FPRnP (FTYPE,TFUEL TFUEL,SGFUELt VI SKM,CORR,CLIO,CPFUEL, 1 CVFUFL WMOLECtHVAPORSIGMAHEATV ) DO 171 I=1INCHAN,l 171 XL ( I )=XLCHAN(I)/DCHNOM(I) RNC=O. C IF(PRINTi-O.O) 25,25,24 24 CONTINUE WRITE OUTPUT TAPE 6,4,POHG,CNAME(1),CNAME(2),CNAME<3), 1 CNAME(4),FNAME(1 ),FNAME(2),FNAME(3),FNAME(4),ENAME(1), 2 _ ENAME(2 ) _ENAME(3_)ENAMF(4)_ VNAME(1),VNAME(?),VNAME(3),. 3 TOF,.ORNAMTFUEL,D ISPL,WEIGHT,PCH, DMVNOM(3),SGFUEL, 4 CR, RATIOCD, AMDENS,DUMTH,VISKM,AVALVE,TIREN 4 FORMAT (1H,11H PRESSURE =,F6.2,16H INCHES HG,4A6,4A< 1 2X,4A6r,3X,3A6/,lH,14H TEMPERATURE =,F5.1,24H DEGREES F MA] 2JET =,A6,7X, 14H TEMPERATURE =,FS5.I, 21H F DI SPLACEMENT=,F ~3_.2_4H C._I. _ VEHICLE _WEIGHT=,.F6.6_,_/_,_!H_,_I1_H_ t HUMIDT_.YT__,F5..,_!.. 4 30H PERCENT MAIN VENTURI=,F5.3,23H IN. SPECIFIC GRA\ 5Y=,FS5.3,17H COMP. RATIO =,F4.1,9X, 17H REAR AXLE RATIO=,F5.2/< 6 1H,10H DENSITY =,F7.4,32H LBM/FT3 CLOSED THROTTLE=,F4.' 7 15H VISCOSITY =,F6.3,25H CS VALVE FLOW AREA=tF4.2,23H

345....IG...IT........AL SI MULATION OF AN A R-BLEO, BOOST VENTURI CARBURETOR 82 TIRE REVS/MILE =,F5.1/ ) IF (PRINT1-2.0) 185,170,170 C PRINT THE CARBURETOR INPUT DATA 170 WRITE OUTPUT TAPE 6,172,CNAMF(1),CNAME(2),CNAME(3),CNAME(4) W. ITE OUT. PUT TAPE,1 73,ORNAM,DCHNOM ( 1),XLCH AN 1),XLD (1) t, 1 JETS, THONOMDTNOMDSNOMSPILL1DMVNOM (3 ) WRITE OUTPUT TAPF 6,174t,DTRNCMtCNOM, BLNOM,XM1NOMXM2NOM, 1 XBVNOMtXMBNOM WRITE OUTPUT TAPE 6t175 WRITE OUTPUT TAPE 6,176 DnO 2 36 -I=1.NMV,1 236 WRITE OUTPUT TAPE 6, 1.77,t, MVNOM( I) WRITE OUTPUT TAPE 6,179 WRITE OUTPUT TAPE 6,176 DO 237 I=1,NBV,1 237 WRITE OUTPUT TAPE 6,177,I,DBVNOM(I ) WRITE OUtTPUT TAPE 6,181 WRTTF OUTPUT TAPE 6,182 DO 238 I=lNCHAN,1 238 WRITE OUTPUT TAPE 6,183, I,DCHNCM(I),XLCHAN(I),XLD(I),C'TYPE(I) 172 FORMAT( HO, 5X,20H INPUT DATA FOR THE,4A6,11HCARBURFTOR. /, 1 1H, 9X,27H **NOMINAL DIMENSIONS*** // ) 173 FORMAT (1H,1lX,28H MAIN METERING ORIFICE TYPE =,A6 /, 1 11X,33H MAIN METERING ORIFICE DIAMETER =,F7.4,6H INCH /, 2 11X,31H MAIN METERING ORIFICE LENGTH = tF7.4,6H INCH /, 3 11X,34H MAIN METERING ORIFICE L/C RATIO =,F7.4, /J 4 11X,35H NUMBER OF MAIN METERING ORIFICES =,F3.0, /, 5 1I1X,35H COMPLETFLY CLOSED THROTTLE ANGLE =,F6.3,9H DEGREES /,..6_ 1X, 5H THROTTLF BORE DIAMETER =,F7.4, 8H INCHES /t 7 11X,25H THROTTLE SHAFT DIAMETER=,F7.4,6H INCH /, 8 11Xt37H INITIAL SPILL POINT OF MAIN SYSTEM =,F5.3,6H INCH /, 9 11X, 31H MAIN VENTURI THROAT DIAMETER =,F7.4,8H INCHES // ) 174 FORMAT ( 5X,25H THROTTLE PLATE BYPASSES //, 1 11X,25H TRANSFER TUBE DIAMETER =,F6.4,6H INCH /,......_ X3.....5H CHOCKF BLEED RESTRICTION DIAMETER =, F6.4,6H INCH /, 3 11X,40H ENRICHMENT BLEED RESTRICTION DIAMETER =,F6.4,6H INCH // 4 5X,51H GEOMETRIC RELATION BETWEEN BOOST AND MAIN VENTURI //t 5 llX, 7H XMV1 =,F7.4,8H INCHES /, 6 11X, 7H XMV2 =,F7.4,8H INCHES /9 7 11X, 7H XRV =,F7.4,8H INCHES /I -_ 8 llX 7H XMB__ = F7,4, 8H INCHES // ) 175 FORMAT (1H4,9X,15H MAIN VENTURI /,14X, 9H ELEMENT,1OX,IOH 0 IIAMETER 176 FORMAT ( 11X,14H ------- --,6X, 14H --------- ) 177 FORMAT 11X, I 8,1 X, F9.3,8H INCHES ) 179 FORMAT (IHC,9X,15H BOOST VENTURI/,14X, 9H ELEMENT,10X,1OH D II._ AMETER 181 FORMAT ( 1HO, 12X, 3HFUEL CHANNEL,79X9H ORIFICE /, 14X, 1 9H ELEMENT,13X,10H DIAMETER,13X,1OH LENGTH,13X, 2 11H L/D RATIO,10X,10H TYPE ) 182 FORMAT (11X,14H - t,X,14H ~.....,9X, 1 14H -------,9X, 14H ---- ---,9X,3H -------- ) 1&3-.._ _ FQRM AT ll__X_.9_.t 1.2XtF9. 4, 5H...NC_., 9X,.F9. 3, 5H I NCH, 1 IX, F 1O. 3. 1 13X,F9.1 ) 185 CONTINUE IF fPR INT1-3.0) 192, 186, 186

346................................DIGTAL SIMULATION OF AN AIR-BLEDBOOST VENTURI CARRURETOR C PRINT THE FNGINE INPUT DATA (IHP VS. F/A AND FMEP VS. RPM) 186 WRITE OUTPUT TAPE 6,87, ENAME(1),ENAME(A2,ENAME(3 tENAMF(4) WRITE OUTPUT TAPE 6,188,AIRFL1,AIRFL2 WRITE OUTPUT TAPE 6,189 WRI rE OUTPUT.TAPE 6,230 WRITE OUJTPUT TAPE 6,231 DUMFR=XMI NR-DELXR+0.0000001 00 190 I=1,NIHP,1 DUMFP=DJUMFR+DFLXR 190 WRITE OUTPUT TAPE 6,191, I,DUMFR,DIHP1(I ),I,DtMFRpDIHP2( ) WRITE OUTPUT TAPE 6,232 WRITE OUTPUT TAPE 6,233 WRITF OUTPUT TAPE 6,231 DUMR PM=X MI NS-DEL XS+O. 0000001 DO 235 I=1,NFMEP,1 DUMR PM=DJUt MRP M +E L X S 235._.WR I TE OUTPU.T T AP E 6,2 34, I, DUMRPM,F ME P1 (I ) I, DUMRPM, FMEP2( I ) 187 FORMAT (1H4,25X,33H IHP AND FMEP INPUT DATA FOR THE,4A6, 1 7H ENGINE // ) 188 FORMAT (1H,10X,25H MEASURED AIR FLOW RATE =,F6.1,IOH LBM/H 1R,20X,25H MEASURED AIR FLOW RATE =,F6.l,10H LBM/HOUR ) 189 FOPMAT ( 11X,41H —------------------------------------- 230 FORMAT (11X,6H POINT,8X,11H F/A RATIO,7X,9H IHP1 1 20X,6H POINT,8X,11H F/A RATIO,7X,9H IHP2 ) 231 FORMAT (11X,6H -. —,8X,11H —--------,7X,9H — 1 2nX, H ---—, 8X,11H —-- -—,7X9 H —----- 191 F(ORMAT (10X,15,1i.X,F8.4,1 X,F6.2,22Xt 5,1XtF8.4,10X,F6.2 ) 232 _____ PMAT {_H _/,lHO 6X,28H FMEP AT WIDE OPEN THROTTLE,33X, 1 25H FMFP AT CLOSED THROTTLE /) 233 FORMAT ( 11X,6H POINT,8X,12H ENGINE RPM,5X,8H FMEP1, 1 22X,6H POINT,7X,12H ENGINE RPM,6X,8H FMEP2 234 FORMAT (1lX, I5,t10X,F8.1,0XF6.2,22X, 5,tlOXF8*1,1t XtF6.2 192 CONTINUE'F (PR INT1-4.) 169,163, 163 C PRINT THE VEHICLE INPUT DATA 163 WRITE OUTPUT TAPE 6,167,VNAME(1),VNAME(2),VNAME(3),VNAME(4) WRITE OUTPUT TAPE 6,168,AREA,WEIGHTROLLtRAGTIRENRATIOD, 1 TRANS(1),TRANS(2),TRANS{3) 167 FORMAT (1 H4j _5X _,28H VEHICLE INPUT DATA FOR THE,4A6, /// ) 168 FORMAT 1H,10X,23H VEHICLE FRONTAL AREA =,F6.2t5H FT2 /, 1 11X,22H VEHICLE CURB WEIGHT =,F6.0,5H LRM /, 2 11X128H ROLLING RESISTANCE FACTOR =,F6.5,9H L8F/LBM /, 3 11X,25H WIND RESISTANCE FACTOR =,F6.5,13H LBF/MPH FT2 /t 4 11X,28H TIRE REVOLUTIONS PER MILE =,F6.1, /, 5__5_.1__ lX. t _8H__REAR AXLE RATIO =,F6.3 /, 6 11X, 17H LOW GEAR RATIO -,F6.3 /, 7 11X,20H SECOND GEAR RATIO =,F6.3 /, 8 11X,18H HIGH GEAR RATIO =,F6.3 / ) 169 CONT I NUE C ____ __ _IF_ (L P R I NT 1- 5.. 1__._.9 3 4 193 C PRINT THE ORIFICE COEFFICIENT INPUT DATA 193 WRITE OUTPUT TAPE 6,194 WRITE OUTPUT TAPE 6,196,ONAM( 1 ),(ONAM(I),I=3,9),ONAM(2) WRITE OUTPUT TAPE 6,197

347 O IGITAL SIMULATION OF AN AIR-BLEDBOOST VENTt IR CARBURFTOR DU1=-DFELXJ + 0.000001 DOJUM2=-DELXJL + 0.000001 DO 198 I=1,NCDJ,1 OU=J 1.=DUMO 1 + DEL. XJ __ UM2=DLJM2 + DELXJL 198 WRITE.OUTPUjT TAPE -6,199,, OUMI,CD1 (I),CD3(I ),CD4( I), 1 CD5(I ),CD6(I),CD7( I),CD8(I),CD9(I:,DUM2,CD2(I) 199 FOR. MAT (19,F9.O, 8F93,8X,F8.0,F1 0. 3 ) 194 FORMAT (1H2,34X,50H INPUT DATA FOR ORIFICE COEFFICIENTS OF DI 1SCHARGE // ) 196 FO~MAT 5X,13H POINT RE 4X,A6 3X,A6,3X, A6,3X A6,3 X, A6, 3X, 1 A6,3X, A6,3X, A6, 1X, 4H RE,5X,A6 ) 197 FORMAT (117H -—. —- ------ - 2 — ) 25 CONTINUE AMAX=995.0 SET=2.0 PTHETA=0.0 IF (PTYPE-11.0) 14, 158,1'58 158 IF (SCALE-2.0) 13,12,13 12 AMAX=740.00 DX= +3CC. O0/7.50 DY= +750.00/7.50 GO TO 14 13 IF (SCALE-3.0) 66,65,65 65 AMAX=370.00 DX=+30.00/7. 500 OY=3 75.0Cg/ 7. 500 GO TO 14 66 CONTINUE AMAX=995.0 DX= +30.00/6.375 DY=1000.00/8.500 4__ ___ CONTINUE SET=2.0 C C SET CONTROLS THE PLOTTING SUBROUTINES C C SET=O0O.....SET GRID,PLOT POINTS,END PLOT SET= 1.0... ___ PLOT POINTS,. END PLOT SET=2.0.....SET GRID,PLOT POINTS SET=3,..... PLOT POINTS NOW BUILD CARBURETORS WITH PRODUCTION VARI ATONS IN DIMENSIONS 8 CARBNO=0.0 GENERATE PRODUCTION DIMENSIONS FOR AIR AND FUEL PASSAGES 243 CARBNO=CARBNO+1.0' 00 9 J=1,NCHAN,1 d, SIGMA IS THE STANDARD DEVIATION OF THE POPULATION OF DIMENSIONS; RANDND IS A LIBRARY SUBROUTINE WHICH PRODUCES RANDOM NUMBERS ~; WITH A GIVEN NOMINAL (MEAN) VALUE AND STANDARD DEVIATION

348 D. IG ITAL SIMULATION OF AN AIR-BLED,BOOST VENTURI CARBURETOR C SI C-M A=DCHTOL (J )/3. DCHAN ( J)=RAND NDX CHNOM (J,S IGMA RNO) 9 XLD( J)=XLCHAN(J )/DCHAN( J)..... 00 10....... J_- l=N...MN V... SIGMA=DMVTOL (J )/3.0 10 DMV( J )=R AN, NDI DMVN.M Jm( J, SIGMA, Rn O DO 11 J=lNBVl1 SIGMA=ODBVTOL(J )/3, 11 DBV (J)=RANDN( DBVN nOM (J,S IGMA,RNO) S IGMA =XM T OL/3. 0................................................. _... XMV1 =R ANDND( XM 1NOM, SIGrMARNO) S IGMA=XM 2TL/3.0 XMV2 =R A N N 0(XM 2NOM,SIGMA,RNO) SIGMA=XRVTOL/3. XSV =R ANDNMD( XBVNOM, S IGMA,RNO) SICGPMA=XM BTL /3.0 X MP =RANDND(XM8NOnM, SIGMA RNO) SIGMA=THOTOL/3.0 THETAO=R ANDND( THONOtSIGMA, RNO) SIGMA= OTTOL/3.0 DT =R ANOND(DTNOM,S IGMA,RNO) _SIGMA= DSTOL/3.O DS =RANDND(DSNOM,S TGMA,RNO) SIGMA=ORTOL. /3.0 DBL EED=R ANDND( DBLNOM S IGMA, RNO ) SIGMA=DTRTOL/3.0 DTRANS=RAN ND( TRNOM,M S IGMA,RNO) SIGMA=DCTOL /3.0 DCHOKE=RANOND(DCNOM, SIGMARNO) IF (CARBNO-1.0) 19I225, 19. 225 IF (PRINT1-2.0) 19,226,226 226 WRITE OUTPUT TAPE 6,224 224 FORMAT (1H1,5X,48H DIMENSIONS OF A TYPICAL PRODUCTION CARBL T O /........... WRITE OUTPUT TAPE 6,173,ORNAM DCHAN 1 ) XLCHANI ) XLD( 1) JE1 I1 THETA),DT, DS,'SPILL1iOMV(3) WRITE OUTPUT TAPE 6,174,DTRANSIDCHOKE,DBLEED,XMV1,XMV2,XBVi 1 XXMB WRITE OUTPUT TAPE 6,175 ___ ___ ____WRITE OUTPUT TAPE 6,176 DO 178 I=1, NMV,1 178 WRITE OUTPUT TAPF 6,177,tDMV(I) WRITE OUTPUT TAPE 6,179 WRITE OUTPUT TAPE 6,176 DO 180 I=1,NBVl, 18 0 W_ RWITE OU TPUT TAPF 61.77,IDBVI ) WRITE OUTPUT TAPE 6,181 WRITE OUTPUT TAPE 6,182 O0 184 I=1,NCHAN,1 184 WRITE OUTPUT TAPE 6,183, I,DCHAN(I),XLCHAN(I ),XLDI),CTYPE(! C C_____ NOW ALL THE DIMENSONS HAVE BEEN _GIVEN PRODUCTION VALUES 19 CONT I NUE DO 223 J=1,NBV,1 223 RV( J)=0.785398*DBV(J)*DBV(J)

349 DIGITAL. SIMULATION OF AN AIR-BLED,ROOST VENTURI CARBURETOR CAI..L THR.OTL (9O. OC,TH.ETAO,DT,DS,AWO'T AMV( 1)=.785398*OMV( I )*DMV( 1 AMV( 2)=O.7 85398*fDMV(2) *DtMV{2) -AfBV(2) AMV( 3)=.785398*DM V(3) *DMV(3) -ABV(6) AtV. 4)=. ) AMV.7 85398*n MV(4)*DMV(4) -ABV(6) AMV( 5)=0.785398*OMV(5 )*DMV 5 AMV(6)=AWOT AMV( 7)=0. 785398*DMAN*OMAN*CYL/RRLS AMV(8) =AVALVE DO 15 J=1,NCHAN, 1 15 ACHAN(J ) =0.785398*DCHAN(J )*OCHAN (J) C C THE FOLLOWING VALUE OF THFTAO ACCCUNTS FOR THE LEAKAGE AREA C WHEN THE THROTTLE IS COMPLETELY CLOSED DUMTHO=THETAO THETAO=THETAO - 3.8CO -0.1000*THETAO I IF (THETAFO) 150,15 1. 1 51 150 THETAO=0.q1151 CONTINUE IF (ATYPF-1.O) 221,245,221 245 CON'T INtEF IF (CARBNO-l.O) 227,30,227 C C C C CALCULATE SPECIFIED OPERATING POINTS C 30 WRITE OUTPUT TAPE 6,45.45 __ ____FORMAT ( IH4,16lX,98H CARBURETCOR-ENG INE OPERATION FOR SPECIFIC 10PERATING POINTS (RPM AND THETA SUPPLIED AS INPUT DATA) //) WRITE OUTPUT TAPE 6,3.64 WRITF OUTPUT TAPE 6,165 WRITE OUTPUT TAPE 6, 166 WRITE OUTPUT TAPE 6,146 77 _ READ INPUT TAPE 7,23,RPM THETAPRINTnSTOP 23 FORMAT (4F10.4) 227 IF (STOP) 263,263,262 262 IF (XNUNIT-CARBNO) 271,271,263 271 SET= 1.0 263 CONTINUE......,.1..__- _ __L,0.. K= 0 VACMAN= 120 GO TO 268 270 IF (RANVAR) 2124141,242 242 IF (XNUNIT-CARBNO) 241,241,243 241 CON_...C ___ TINUE ___ IF (STOP) 244,244,20 244 CAR NO=1.0 GO TO 77 C 221 IF (ATYPE-2.0) 31,79,31 31.__ I __LFATYP F-4~. L_8Q 879, 88 88 IF (ATYPE-:6. ) 7a, 79,70 79 CONT INUE C C

350.DIGITA.L.SIMULATI ON OF AN AI R-BLED, BOOST VENTURI CARBURETOR C C CALCULATE C[ONSTANT RPM LINES C IF (PRINT1-1.0) 32,32,222 222.CONT.I NUE WRITE OUTPUT TAPE 6,22 WRITE OUTPUT TAPE 6,2 WRITE OUTPUT TAPE 6,3 WRITE OUTPUT TAPE 6,4,POHG,CNAME(1),CNAME(2),CNAME(3), 1 CNAME(4 ),FNAME( 1),FNAME( 2),FNAME(3),FNAME(4),ENAMF(i.)I 2_ _E.AME(2 ), EN AM E(3),ENAME( 4), VNAME ( 1 ) VNME(2) VNAME ( 3 ), 3 TOF,OPNAM,TFUEL,DISPLtWEIGHT,PCH,DMVNOM(3),SGFUEL, 4 CP,RATIO AMDENS,DUMTHO, VI SKM,AVALVE,TIREN 32 READ INPUT TAPE 7,?3,RPM,R PMLIM,PRINTO IF (PRIN'TO)149,149,148 148 WRITE OUTPUT TAPE 6,47 WRITE OUTPUT TAPE 6,144 144 FORMAT (1H4, 16X,82H CARBURETCR-ENGINE OPERATION AT CONSTANT!NGINE SPEED-VARIABLE THROTTLE OPENING //) WRITE OUTPUT TAPE 64164 WRITE OUTPUT TAPE 6,165 WRITE OUTPUT TAPE 6,166 WRITE OUTPUT TAPE 6,146 164 FORMAT ( 132H THROT INTAKE MOIST 1DRY BOOST MAIN THROT MAIN'TOTAL TOTAL MAIN 2THROT AIR ) 165 FORMAT (132H ENGINE THROT FLOW MAN. AIR 1AIR VENTURI VENTURI MACH F/A F/A FUEL FUEL 2TOTAL BLEED _ 166 FORMAT (132H RPM ANGLE AREA PRESS FLOW 1LOW SUCTION SUCTION NO. RATIO RATIO FLOW FLOW 2 TEMP FLOW J ) 146 FORMAT (132H 1 —-- ------— ). _.... 2 -....__ ---...-_.__. 1..................... 149 CONTINUE 1=C K=O PLOT N=C. 0 PLOT I=0.0 DUMA=, _...... SWITCH=0.00 VACMAN=21.00 + RPM/800.0 268 CONTINUE GUEJ F SS = V ACMAN XGUESS=O.65 _ C8=.400 * 1.25*1545.4*585.C*(CR-1.0/(.28.95*CR*0.4912) C9=( CR-O.5 )/CR DRYA2=DISPL*RPM*(POHG*C9 —VACMAN)/(C8*1. 0620) CALL ASSUME (DRYA2,VACMAN,OPENE,FAMAINtFATOTL,FARICH, I FLOCWM, FLOWT,FLOWE! RATEMF=2.0*FLOWM C_._NOW I____NITIAL_GUESES S HAVE_BEEN MA DE..FOR EACH NEEDED PARAMETER.OLDFA 1=F ATOTL OLPFA2=FAMA IN OLDAIR=DRYA2 IF (ATYPE-1.0) 260,18,260

351 DIGITAL SIMULATION OF AN AIR-tBLED,BOOST VNTURI CARBURETOR 260 THFTAn=UMTHO 246 DUJMA=DUMA + 2.0 IF (OUMA-DUMTHO-...10 ) 246,246,247 247 CONTINUE 16_.. -__..... _9_, 248?49 248 THETA=DUMA GO TO 29 249 IF (THETA-29.9) 27,27,28 27 THFTA=THETA+2.000 GO TO 29 28 _ IF (THELTA-,59 9) 257, 257,258 257 THETA=THETA+5.000 GO TO 29 258 THETA=THETA + 10.*0 29 CONTINUE IF (THETA - 84.00) 18,7,17 18 I=I+1 CAIL THROTL (THETA,THETAO,D T,DS,AFLOW) AMV(6)=AFLOW OPEN=T HETA-THETAO CALL STERL(CTHROT,XMINT,OELXT, ORDER, XNTHET,SCRACH,OPEN,CDT, 1 0.0 ) J=0 250 CONTINUE IF (J-15) 253,254,254 254 WRITE OUTPUT TAPE 6,255 255 FORMAT (46H NO FUFL-AIR CONVERGENCE WITHIN MAIN PROGRAMGO TO 261 253' J=J+1 CALL AIRMAS (POHG,TOF,HUMID,THETA,CDT,AFLnOW,FTYPE,TFUEL,.i FRACT,GUESS,,FAMAIN,FATOTL,VACMAN,DRYAIR,WETAIR,VENFLO GUESS=VACMAN CALL SIGNAL (POHG,TOF,HUMID,VENFLO,FTYPE,TFUEL,RATEMF, 1 AMV,AB V,XMV1,XMV2,XBVXMB,BBLS,FRACT, XGUESS,PPINTS, __2X__ XFV.BVFL _PV VF LO_,__V.M.ACHPVMACHt._B V SUCW,PVSUCw RATEMF=BBLS*FLOWM XGUESS=XFV CALL FLOW (POHG,TOF,HUMID,BVSUCW,VACMAN,OPENE,F'TYPE, 1 TFUELNCHAN, FLOWM. FLOWT, FLOWE, FLOWJ, FLOWISUMAIR FAMA IN=BBLS*FLOWM/DRYAIR FATOTL=BBL S*FLOWT/DRYAIR DELFAI=-FATOTL-OLD FA.DEL FA2=FAMAIN-OL DFA2 DELA IR=DRYAI R-OL OAIR OLOFA 1=F ATOTL OLOFA2=FAMAIN ___ _ OLDA IR=DRY AIR ___ __ IF (ABSF (DELFA)-0.00020) 251,251,250 251..IF (ABSF(OELFA2)-0.00020) 252,252,250 252 IF (ABSF(DELAIR)-0.250 ) 261,261,250 261.CONTINUE -. PRE S S= POHG-VACMAN _. ___PMAN(i)= PRESS__________ __ _ _ WETA( I )=WETAIR CD..... CO I )=CDJET. RE( I =REJET.BOOSTW(I )= BVSUCW

352 -. _.............. _DIGI TAL SI MULAT ION OF AN AIR-BLED BOOST VENTURI CARBUR ETOR FLCWTP ( I )=FLOWT FLOWMP ( I )=FLOWM TOTLFA(I )=FATOTL ORYAP (I )=DRYAIP DU.MFT=BBLS*FLnWT OUMFM= RRLS*FLOWM SUt AIP=BBLS*SUMA IR'IF (PRINTO) 239,239,259 259 WRITE OUTPUT TAPE 6,256,RPM, THETA, AFLOW,PRE SS,WETAI R, ORYAIR I BVSt.CW, PVSUCWXMACHTFAMAIN,FATOTL,DJM JFT,DtJMFMTOTF, SUMAIR..25.6 FOFM AT ( F81. 1,9,F9 9.2, F9. F9 2, F9. 28. 2 4, F9.4, F8.4,F8. 3, 1 F 8.3,F8.1,F7.3,I4 1 239 CONTINUE IF (ATYPE-1.0) 264,78,264 264 IF (SWITCH-O.O) 61,61,26 61 CONTINUE C IF (WFTAIR- AMAX) 26,26,50 50 K=I PLOT 1= I SWITCH=10 26 CONTINUF __G.T TO 16 17 C ONT INUE C PLOT A CONSTANT RPM LINE IF (PTYPE-O.O) 40,40,91 91 CON TINUE IF (ATYPE-2.00) 78,84,78 8 4 I F (RPML -RPM) 85 t85, 78 85 SET=1.O 78 CONT INUE TYPFL=-1.O PLOTN= I IF (PTYPE-1.O) 301,300,301 300Q __ DXCR=10. 00/7.50 OYCR=-. 500/7.50 CALL CALCVR ( RE,CDPLOTNtO,.O,XCR,0. 50,OYCR,1,.O,SET,1.O, 1 1.0,I.O, TYPEL, 68.0,TFUEL,0.O ) SET=3.0C GO TO 40 30 1 IF (PTYPF-2.0) 303,302,303 30 2 DXMH=25. 00/7.50 OYMH=40. 00/7.50 CALL CALMVH (BOOSTW,FLOWMP,PLOTN,O.0,OXMH,C.,DYMH,.0,SET, 1 1.0,1.0,1.0,+1.00, 68.00,TFUEL,l.O ) SET=3.0 _GO TO 40 303 IF (PTYPE-3.0) 3C5,304,305 304 XEXP=-1.0 DXLL=3.00/7.50 YEXP=-1. 0 DYLL=3.00/7 50 __ ____ 3DO 315 J=li_ ____ __ _ IF (BOOSTW(J)-0. 00) 317,316,316 317 BOOSTW{ I)=0. 100 316 IF (FLOWMP(J)-.0.100) 318,315,315 318 FLWMP ( J )=0. 100

353..I..........GITAL SIMULATION OF AN AIR-BLED, BOOST VENTURI CARBURETOR 315 CONTINUE CALL CALLOG R(B(ROSTW, FLOWMP,PLOTN,XFXPDXIL, YEXP,DYLL,I.O, I SET, 1.O,.0,l.OTYPEL, 68.0T,TFUEL,l.0 ) SET=3.O GO TO 40 305 IF (PTYPE-4.*) 3 7,306,307 306 nXCH-25. /7.50 OYCH=.500 7.50 CALL CALCVH (BOOSTW, CD,PLOTN,0.0,DXCH,0.50,DYCHl.OSET, 1 1.0,1.O,1.0,+1.00, 68.00,TFUEL,1.O ).............. SET = 3.0 GO TO 40 307 IF (PTYPE-5.0) 3:9,308,309 30 8 D XCM=25. 00/7.50 DYC M=M0. 5 00/7. 50 CALL CALCVM (FLOWTP, CO,PLOTN,0.O,DXC M,0.50,DYCM,.,OSET, 1 1*0,1.0,1.0,TYPEL, 68.00,TFUEL,0.0....... _.................................._......... -'D I TYPE L, 6 8.0 0,TFU EL,O.O \ SET=3O. GO TO 40 309 TF (PTYPE-6.0) 311,310,311 310 DXF A= 700.0/8.9?5 OYFA=0. 1 00/6.375......................................... ALL CALFVA ( YAP,TOTLFA,PLCTN,.0, DXFA,0.300,DYFA, 1.0,SFT, 1 1.0,2.0,2.0,+1.0, 1.0,TFUEL,1.0 ) SFT=3.)0 GO TO 40 311 IF (PTYPE-11.0) 4C,86,86 86 COtN-T INUE I.. F (ATYPF-l.O) 265,266,265 266 K=I PLnT 1= I GO TO.267 265 IF (SFT - 2.50) 43,43,46 46 XSTART=1.00O + (PMAN(1) - O0.00)/OX Y START= 1.0 + (WETA ( 1 ) - 0.0o)/DY CA L PENUP (XSTART,YSTART) 43 CONTINUE PMAN 1+1)=PMAN(I) WETA(I+1)=WETA(I IF (K-C) 55, 55,56 55 _ ___ K= I PLOTI=I 56 IF (WETA(K) - AMAX -3.0C0) 80,80,81 81 PMAN(K)=PMAN(K)-(WFTA(K)-AMAX)(( PMAN(K)-PMAN(K-1)) / 1 (WETA( K )-WETA(K- 1 ) ) ) WETA(K)=AMAX 80 C.ONT INJUE 69 IF (SCALE-3.0) 67,68,68 68 MH=(K+1)/2 + 3 GO TO 76 67 MH=( 1+1)/2 76 CONT INJUE. -- - -_ —.__ F. R.PM-19~.Q J. 63._ 64,,64 63 MH=MH-1 64 CONTINUE 72 IF ( P.MAN(MH)-23.00) 73,73,71 71 MH=MH- 1

354............. ____IGITAL..._SI.M ULATION OF AN..: AT R-BLED BOOST VENTURI CARBURETOR GO TO 72 73 CONTINUE ML=MH - 1 C. ~A.......... NGLR=ATAN ( ()X*( WETA ( MH ) -WET A( ML ) ) / (DY*( PMAN( MH) -PMAN( ML) ) ANGL D=ANGL R 180.00/3.1415926 YVAL=1.060 + WETA(MH)/DY XVAL=1. 0 + PMAN(MH)/DX CALL PSYMB ( XVAL,YVALt-0.100,9H RPMtANGLDO9 ) CALL PFNMBR (XVALYVAL,-0.100,RPM,ANGLDt,6H(F5.0)) 267_ __ CALtL CALMAP (PMAN,WETA,PLOTI,0O.0,ODX, 00,o DY,POHG,SET,PCH, 1 1.00,1.00, CR,DISPL, TOF,SCALE ) SET= 3. IF (ATYPE-1.O) 272,270,272 272 WRITE OUTPUT TAPE 6,152t PLOTI 152 FORMAT (39H A LINE WAS PLOTTED WITH,F4.0, 1 ___8H POINTS ) CALL PENUP (2.000, 1.125) 40 CONTINUE IF (ATYPE-1.O) 269,270,269 269 IF (PTHETA) 108,108,75 108 IF (RPMLIM-RPM) 70,70, 32 70 CONTINUE IF (ATYPE-5.00) 89, 21.89 89 IF (ATYPE-6.00) 136,90,136 21 SET=n.0 90 CONTINUE C C C CALCULATE CARBURETOR-ENGINE-VEHICLE PARAMETERS ALONG A C ROAD LOAD CURVE C WRITE OUTPUT TAPE 6,141 14_1 Fs.OPMAT (_lH1i,.40_X X,51H R OAD LOAD CAR BURETOR-ENGINE-VEHICLE PE1 1RMANCE / / NGEAR=1 CALL THROTL (90.00,THETAODT,DS,AWOT ) 133 RATI OT=TRANS (NGEAR) WRITE OUTPUT TAPE 6,139,RATIOT _139 _FORMAT (1H _O71 H THE FOLLOWING VALUES ARE CALCULATED FOR A 1ANSMISSION GEAR RATIO OF,F5'.3//.. L=O WRITE OUTPUT TAPE 6,145 WRITE OUTPUT TAPE 6,142 WRITE OUTPUT TAPE 6,143 145 ___ _ FRM AT. ( 32H.._ CAR.ENGINE THROT MOIST 1 MAN. BLEED F/A ENGINE ENGINE FUEL 2 ) 142 FORMAT (132H MPH RPM ANGLE AIRFLO BHP 1 IHP PRESS. AIR RATIO ISFC BSFC RATE 2 MPG NN _.L43.___ F RMAT.. __ M 32H __.-.-.-... ~ -2 r m —-- 2 ) 104 VMPH=5.00 DEBUtG=O.0

355 D......IGITAL SIMULATION OF AN AIR-BLED,BqOOST VENTURI CARBURETOR PRI NTO=0.0 EP 2=0. 2 rTHSTEP=2. RPM= TIRFN*P ATInD*RAT IOT*10.0/60.O VACMAN=14. 1. GJF SS=VACMAN XGUF SS=. 65 C8=0.400, 1. 25*1 545. 4*5 85. * ( CR-1. ) / ( 28 95*CR*0.4912) C9=( CR-0.5)/CR DRYA?=D SPL*RPM*( POHG*C9-VACMAN) /( C81. 0620) _CALl, ASSUJMFE ( DRY A2, VACMAN,OPENE,FAMAI N, FATOTL F AR ICH, 1 FLOWM,FLOWTFLOWF ) RATEMF= 2.O*FLOWM C NOW INITIAL GUESSES HAVE BEEN MADE FOR EACH NEEDED PARAMETER C 134 L=L+1 105 VMPH=VMPH + 5.000 ROADHP= (VMPH1 375. C) * (ROLL*WE IGHT+DRAG*A RE A*VMPH*VMPH) DRIVEN=O.8600- (VMPH/1210.00)-( VMPH*VMPH/333300.00) RHP= PnADHP/DRI VEN RPM= T IRE N*RAT I OD*RAT IOT*VMPH/60. OO CALL STFRL (FMEP1,XMINS,DELXS,ORDERXNFMEPSCRACHRPM,FMIN, 1. ___ DE BUG ) CALL STFRL (FMEP2,X MINS,DELXS,ORDERXNFMP,SCRACH,RPM,FMAX, 1 DERUG ) CHANGE=0.0 NN=0 C MAKE AN INITIAL GUESS FOR THE THROTTLE PLATE OPENING T_HFTA=DUMT HO +5.700+46. 50*VMPH*VMPH /100-00.00 120 CONTINUE NN=NN+1 IF (NN-33) 121,121,122 122 WRITE OUTPUT TAPE 6,123 123 FORMAT (1HO,3'2H NO THROTTLE ANGLE CONVERGENCE ) ___ ___GO TO 113 121 IF (NN-14) 159,219,159 219 IF ( AWOT*0.99-AFLOW ) 113,113,159 159 IF (NN-21) 153,154,.153 154 WRITE OUTPUT TAPE 6,155 155 FORMAT (61H 20 ROAD LOAD ITERATIONS HAVE BEEN ATTEMPTED..o.T _ _1RY 2 M _1 _ __MOR _ _ WRITE OUTPUT TAPE 6,138 138 FORMAT (80H THIS IS A ROAD LOAD DEBUGGING PRINTOUT TO CHEC 1K THROTTLE ANGLE CONVERGENCE ) EPS2=1. 000 CHANGE=0, 0 THETA:160,0 ______ _ -THETA60__ __ ------- - THST EP=34.00 153 CONTINUE CALL THROTL (THETA,THETAO,DT,DS,AFLOW } AMV(6) =AFL OW OPEN=THE TA-THETAO -_ ~_-___ CALL _STIERCTHROTiXMINTDELXT,GRDERXNTHET, SCRACH,OPENCDT, 1 0.0 ) CALL AIRMAS I(POHG,TOF,HUMID,THETA,CDT,AFLOW,FTYPE,TFUEL, 1 FRACT,GUESS,FAMAIN,FATOTL,VACMAN,DRYAIR, WETAIR,VENFLO ) GUESS=VACMAN

356 I.-,GITAL SIMULATION OF AN AIR- BLED, BOOST VFNTURI CARBURETOF CAll SIGNAL (POHGTOF,HUM.D,VENFLO,FTYPETFUELtRATEMF, 1 t tMV,ABV, XMVl,XMV?,XBVXMB, BBLSFRACT, XGUFSS,PRINTS, 2 XFV BVFLO, PVFLO, VMACH, PVMACH, BVSUCW, PVSUCW ) RATEMF-=RBLS*FLOWM XGUFSS=XFV CALL FLOW (POHG,TOFHUM It,VSUCWVACMANOPENEFTYPE, 1 TFUJELNCHAN, FLnWM, FLOWTFL FLWE, FLOWJ, FLnWISUMAIR FAMA IN=BBLS*FLlWM/DRYAIR FATOTL = BL S FLOWT/DRY AR CALL STERL (DIHP1,XMTNRD ELXR,ORDR, XNIHP,SCRACHFATOTL, 1 _.._... ___..XI.X HP 1, DEBUG ) CALL STERL ) DIHP2t XMINR, DELXR,ORDER,XN HPSCRACH,FATOTL, 1 XIHP2nDEBUG ) IF (XIHP1 ) 109,127,127 10 9 XI HP 1=0r8O. 0 127 IF (XIHP?) 128,t129,129 128. I H P 2,_C...1_.I. 129 CONTINUF XIMEP1=5 252.0 150.8* XIHP1/( RPM* DISPLt XIMEP2=5252.010 5.8*X IHP2/( RPM*OD ISPL) SLOPF= (X IHP2-X IHP ) / A IRFL 2-AI RFL 1 ) AO=AIRFL2 - XIHP2/SLOPE PM = POHG - VACMAN FMEP=FMN Fi N+ (FfMAX-FM I N) *(POHG- PM /(POHG-3 000) TORQF= FMEP*) ISPL 1 50.8 FHP=TORQF*RPM/52 52.0 X IHP=BHP+FHP AIRFLO=AO + XIHP/SLOPE FUEL. FA L R T.TL * *A I R FL o X I SFC=FtFJEL R/XI HP RSFC=FUELRP/BHP TF (CHANGE ) 112 111, 112 111 ERP1=DRYAIR-AIRFLO IF (ARSF(ERR1)-EPS2 ) 113t113125 125'_THOL = T'H ET_ A THFTA=THETA-THSTFP*ABSF ( ERR 1 )/ERR1 CHANGF= 1.00 GO TO 110 112 ERR2=DRYA IR-A IRFLO IF (ABSF(ERR2)-EPS2 ) 113,113,114 11 4 SAVE1=THETA IF (ARSF(EERR2-ER1)-.005 ) 229,229, 195 229 THFTA=THETA - ERR2*0.10 GO TO 228 195 CONTINUE THFTA=THETA+ERR2* (THFTA-THOL )/ ( ERR1-ERR ) 228 _ IF (THETA-DUMTHn 115116, 16 115 THETA=DUMTHO GO TO 117 116 IF (THETA-90.00) 117,117,118 118 THFTA=85.00 117 CONTINUE..___ _.__ THOL - --—. —-- - - -_ __._ - - --- ERR1 =ERR2 110 CONTINUE IF (EPS2-1.000) 120, 124,120 124 WRITE OUTPUT TAPE 6,106,NN, VMPH, RPM,THOLD,THETA,AIRFLOORY

357 DI.. GITAL SIMULATION OF AN AIR-BLEDBOOST VENTURI CARBURETOR 1,WETAI R, ERR1, FATOTL,X'IHPBHP 106 FORMAT (I 5,7F10.,2F10.4,2F10.3) GO TO 120 113 WETA (L)=WETAIR PMAN tL)=POHG-VACMAN XMPG (L ) = VMPH*SGFUEL*231.0*62.400/( 1728.0 *BSFC*RHP) SPEEf)( L =VMPH CO(L)=CDJET RE(L)=RFJET BOOS TW (L )-= PV SUCW FLOWTP L )=FLOIWT FLWMP ( L ) = FLOWM TOTL FA L )=FATOTL DRYAP (L)=DRYAIR 8SFCP(L )= SFC BHPP(L )= BHP.._ XIPP( L )=X I HP SUMAI= R =8L S*SlMA IR 130 WRITE OUTPUT TAPE 6, 131,VMPH,RPM,THETA,WETAIRRHPXIHP, 1 PMAN(L) StJMAIR, FATOTL, X ISFC,BSFC, FUELR,XMPG(L) NN 131 FORMAT (2F 9.1,6F 9.2,3F10.4,F10.2 F9.3,16 ) IF AFLOW-0.99*AWOT) 160,162,162 162 WRITE OUJTPUT TAPE 6,161,VMPH 161 FORMAT (1HO, 5X,65H THE MAXIMUM VEHICLE SPEED HAS BEEN ATTAIN 1ED.......THIS SPEED IS,F5.1,16H MILES PER HOUR //) GO TO 137 160 IF (RPM-3900o.) 119,119,137 119 IF (WFTAIR-AMAX + C3.0O 134,134,137 137 __ CNT I NUE IF (PTYP F-.O0) 92, 92,93 93 CONTINUE C ALL PTYPE CHECKS WILL GO HERE PLOT I=L TYPE L=-l.0 PLOTN=L _.......... IF (PTYPE- 1.0) 351,350,351 350 DXCR=10.00/7.50 OYCR=O. 5 00/7.50 CALL CALCVR ( RF,CD,PLOTN,0.0,DXCR,0.50,DYCR,1.0,SET, l.0, ~1 1.0, 1.0,TYPE L 68.0, TFUEL,0.0 SET= 3.0 _ GO TO 375 351 IF (PTYPE-2.0) 35'3,352,353 352 DXMH=25.00/7.50 OYMH=40.00/7.50 CALL CALMVH (BOOSTW,FLOWMPPLOTNO.O,DXMH,.O,OYMH, 1.0,SET, _-1____A(0,1.L.Ql..0+1.COiA 68.QO, TFUF L,10 SET=3.0 GO TO 375 353 IF (PTYPE-3.0) 355,354,355 354 XEXP=-1.O DXLL=3.00/7.50 YE XP=-.0..... DYLL=3.00/7. 50 DO 376 J=1,L,1 IF (BOOSTW(J)-O.100) 378,377,377 378 BOOSTW( J )=O. 100

358 - t IGI....ITAL _S I.JUL.ATN OF AAN AI R-BLF D,B f3ST VENTUI URCARRETOR 377 F... (FLOWMP(.J)-.100) 379,376,376 379 FLOWMP J )=0.100 376 CONTINUE CALL CALLOG (BOOSTWFLOWMP,PLOTN XEXP,DXLL,YEXP,DYLL,1.0, 1_ _ __..SETr1_.0,1*0,1._TTYPEL, 68.00,TFUEL 1.0 ) SET= 3.0 GO TO 375 355 IF (PTYPE-4.0) 357,356,357 356 DXCH-?5.00/7.50 DYCH=O.500/7.50 _ C-ALL CALC.V. CALH (. 0B SW tW.. COD, PL TN,. OD XCH t,. 5 0, DYCH 1.0, SET, 1 1.0,1.0,I.0, TYPEL, 68.00,TFUEL,1.0 ) SET=3. 0 GO TO 375 357 IF (PTYPE-5.0) 359,358,359 358 DXCM=25.00/7.50 OYCM=O.500/7.50 CAlL CALCVM (FLOWTP, CD,PLOTNt,o. 0,XCMt0.50,DYCMO, 10,SET, 1 1.0,1.0,1.O, TYPEL, 68.00,TFUELO.O SET=3.0 GO TO 375 359 IF (PTYPE-6.0) 361,360,361 360 DXFA=700.00/8 925 YE A=0. 100/6.375 CALL CALFVA (DRYAP,TOTLFAPLOTN,0.0,DXFA,0.0300,DYFA, 1.t0,S 1 l.O,2.2.02 +0,t+l.OCl.,TFUEL,1.0 ) SET=3.0 GO TO 375 361 ____ F _(PTYPE-7..0). 363 362,363 362 OXMS=100.00/6.375 DYMS=28. 00/8.925 CALL CALMVS (SPEED,XMPG,PLOTNtO,.DXMSO.0,DYMS,1.0,SET, I. 1 2.0, 2.0,-1.0,1. OTFUEL,1.0 ) SET=3.0 GO TO 375 363 IF (PTYP -8.0) 365,364,365 364 DXBB= 10.00/l1O.lO DYBB=2.00/10.00 DO 373 J=1,L,1 IF (BSFCP(J)-2.500) 373,373,372 372 BSFCP( J )= 2.500 373 CONTINUE CALL CALBVB (BHPP, fSFCP,PLOTN,0.0,DXBB0.4, DYBB,1.0,SET,.( 1 2. 0,2., +1.00, 1., TFUEL,1.0 ) SET=3.0 GO TO 375 365 ___ __ yp9.7..PE9. _.,. _. _....... 366 DXIA=700.00/8.925 DYIA=1CO.00/6.375 CALL CAL IVA (DRYAP,XIHPP PLOTNO.0,DX A,0.0,DYIAl,.0,SET, 1 1.0,t 2.0,2. 0,+1.00,1.0,TFUEL, )1.0 SET=3.0 __ _GQT Q_ 37G5 ____ 367 IF (PTYPE-10.0) 369,368, 369 368 DXIF=0.1400/8.925 DYIF=1CO.00/6. 375 CALL CALIVF (TOTLFA,XIHPP,PLOTN,0.0,OXIF,0.0,DYIF,1.0,SET,

359 DIGITAL SIMULATION OF AN AIR-BLED,BOSC1T VENTURI CARBURFTOR 1 1.C2.02.,2., TYPE, 1.O,TFUEL, 1. SET=3 *0 GO TO 375 369 IF (PTYPE-11.O) 375,370,370 370 E _ _IF (RATIOT-1_.OiO 1) 140,1 40, 92 140 CONTINUE WRITE OUTPUT TAPE 6,132 132 FORMAT (44H THE HIGH GEAR ROAD LOAD LINE WAS PLOTTED ) CALL CALMAP (PMAN,WETA,PLO TI,.OnOX, O0.0,DYtPOHG,SFT,-1.O-, 1 1. OC,1..00, CR,DISPL, TOFSCALE ) __ SET=3.0 375 CONTINUE 92 CONTINUE IF (RATIOT-1.0001) 136,1 36,135 135 NGEAR=NGEAR+1 GO TO 133 136 _ CONTINUE C IF (ATYPE-3.0) 240,96,240 240 IF (ATYPE-4.0) 95,99,95 95 IF (ATYPE-6.0) 62,99,62 96 SET=2.C 99 __ CONTINUE C c C C CALCULATE CONSTANT THROTTLE LINES C IF (PP INT1-0.0) 39,t39, 87 87 WRITE OUTPUT TAPE 6,22 WRITE OUTPUT TAPE 6,2 WRITE OUTPUT TAPE 6,3 WRITE OUTPUT TAPE 6,4,POHG,CNAME(1),CNAME(2),CNAME(3), 1 CNAME(4), FNAME(),FNAAME(2 ), FNAME 3),FNAME(4),ENAME(1), ____?__ ENAME 2_ENAE3,ENAME 4),NAME 1 _VNAME ( 2 ), VNAMEVNAE2 ()3 ), 3 TnF, ORNAM,TFUEL, ISPL,WF IGHT,PCH, MVNOM (3, SGFUEL, 4 CRRATIODOAMOENStOUMTHO,VISKM,AVALVE,TIREN 39 READ INPUT TAPE 7,23,THETATHETALtPRINTO IF (PRINTO)157,157,156 156 WRITE OUTPUT TAPE 6,47 WRITE OUTPUT TAPE 6J147 147 FORMAT (1H4,16X,82H CARBURETOR-ENGINE OPERATION AT CONSTANT T I.HROTTLE OPENING-VARIABLE ENGINE SPEED // WRITE OUTPUT TAPE 6,164 WRITE OUTPUT TAPE 6,165 WRITE OUTPUT TAPE 6,166 _______WRITE OUTPUT TAPE 6,146_ 157 CONTINUE 47 FORMAT UH //} SW ITCH=0.0. K=Q PLOT N=O.0 __. DE BUGO.0 _ ______ ____ ___ __ PTHETA=1.0 PLOT I=0. 0 RPM= 000.0 IF (THETA-25.0) 54,14, 51

360 DIGI TAL. S IMULAT ION.OF AN AI R- 3LD,FO OO ST VENTURI CARBURETOF 51 IF (THETA-64.0) 52,52,53 52 P PM= 50. Ce GO TO 54 53 RPM-=l100.0 54 _ C. CONTINUE PMAN(1) POHG WETA(1)=0n.O00 VACMAN=0 * 10 GUES S=VACM AN XGUFSS=0.65 C 8=0.4*1 25* 1545. 4*58 5. C* ( CRR-1. 0 ) / ( 28.9 5*CR *O 49 12 ) C9=(CR-n.5)/CR ORYA2=DI SPL*RPM *(POHG*C9-VAC MAN)/( C8*1.0620) CALL ASSUME (DRYA2 VACMAN,OPNE, F A MA IN, FATOTL,FAR ICH, I FLOWM,FLOWT,FLOWE ) RATEMF=2.O*FLOWM C NOW INITIAL GUESSES HAVE BEEN MADE FOR EACH NEEDED PARAMETER OLDFAl=FATOTL nLDFA2=FAMAIN OLDAIR=DRYA2 0D 33 I=2,28,1 IF (RPM-199. ) 34,34,35 34 __ I F (THETA-15.0.) 48,48, 49 48 RPMN=RPM + 25.00 GO TO 38 49 PM-=RPM + 50.00 GO TO 38 35 IF (RPM-999.0) 36,36,37 36 RPM=RPM+ 100. GO TO 38 37 RPN=RPM+250.0 38 CONTINUE CALL THR THROLTHETA,THETAO, TDS,AFLOW ) AMV(6)=AFLOW _ OPEN=THETA-THETAn CALL STERL(CTHROT,XMINT,OELXT,ORDER,XNTHET, SCRACH,OPEN,CODT 1. 0.0 J=0 320 CONTINUE IF (J-15) 323,324,324 324__ WRITE OUTPUT TAPE 6,325 325 FORMAT (46H NO FUEL-AIR CONVERGENCE WITHIN MAIN PROGRAM GO TO 331 323 J=J+1 CALL AIRMAS (POHGTOF,HUMID,THETA,CDT,AFLOW,FT'YPE,TFUEL, 1 FRACT,GUESS, FAMAIN,FATOTL,VACMAN,DR YA.IRWETAI R VENFLO ) __ UES S= VACM AN CALL SIGNAL (POHGTOFHUMIDVENFLOFTYPETFUELRATEMF, _1.AMV,ABV,XMVl XMV2, XBV XMB BBLS,FR ACT, XGUESS, PRINTS, 2 XFV,BVFLO, PVFLO, BVMACH,PVMACH,BVSUCW, PVSUCW ) R ATE MF=B BLS*FLOWM XGUESS=X FV __ ___ ___CAL L _FOW ( POHGTO F1 HUM I _D,.VSUCW,_VAC MAN,OPE N 5E, FTYPE, 1 TFUEL,NCHAN, FLOWM, FLOWT, FLOWE, FLOWJ, FLOWI,SUMAIR ) FAMA IN=BBLS*FLOWM/DRYAIR FATOTL=BBLS*FLOWT/DRYAIR DEL FAI=FATOTL-'OL DFA1

361 DIGITAL SIMULATION OF AN AIR-BLED,BOOST VENTURI CARBURETOR DELFA2=FAMAIN-OL FA2 DEL. IR=D YAIR-OL DAIR OLPF A].=F AT OTL OLDFA2=FAMAIN OLDAIR=DRYAIR IF (ABSF (DELFAI )-O.00060) 321,321,320 321 IF (ABSF(DFLFA2)-C.00060) 322,322,320 322 IF (ABSF(DFLAIR)-C.750 ) 331,331,320 331 CONTINUF PRFSS=POHG-VACMAN PMAN(I)= PRESS WETA( I)=WETAIR CD (I )= CDJ ET RF( I )=REJET BOOSTW( I )=VSUCW FLOWTP( I )=FLO..WT FLOWMP I )=FLOWM TOTL FA( I)=FATOTL DRYAP (I )=DRYAIP DUMFT=BBLS*FLOWT OUMFM=BRLS*FLOWM SUSA IRP=BBLS*SJSMAIR -DLJMPR=PR INTO......IF.('RPM"-4c-"0"0) 1f3, 103, 102 103 PR INTR.=0.0 102 IF (RPM-5010.O) 100, 100,101 101 PRINT[O=0.0 100 CONTINUE IF (PRINTO ) 347,347,348 348 WRITE OUTPUT TAPE 6,256,RPMTHETA,AFLOW,PRESS,WETAIRODRYAIR, 1 BVSUCW,PVSUCW,XMACHT,FAMAIN,FATOTL,DUMFT,DUJMFM,TOTF, SUMAIR,J 347 CONTINUE PRI NTI=DUMPR IF (SWITCH-O.0) 60,60,33 60 CONTINUE IF (WETAIR- AMAX) 133,33,57 57 K=I PLTT I= I SWITCH=1.00 33 CONTINUE C PLOT A CONSTANT THROTTLE ANGLE LINF C IF (PTYPE-0.0) 75,75,94 94 CONTINUE C ALL PTYPF CHFCKS WILL GO HERE 44._ I THETAL-THETA 42424...... 42 SEI=1.0 41 CONT INIJE XSTART= 1.0 + (PMAN(]) - O0.00)/OX YSTART= 1.0 + (WETA(1) - O.00)/DY CALL PENUP (XSTART, YSTART)._.._.__ IF (K-O) _58__59_- — _.-.- -. 58 K=I PLOT I=I 59 IF (WETA(K) - AMAX -3.000) 82,82,83 83 PMAN(K)= PMAN(K)-(WETA(K)-AMAX)*( ( PMAN (K)-PMAN( K-1 ) /

362 D GIT.AL SIMULATI.'ON OF AN AIR-BLED,BOnST VENTURI CARBURETOF 1 (WFTA( K)-WETA(K-1) ) WETAK )=AMAX 82 CONT INUE CAlt. CALMAP (PMANWFTA,PLOTI,OO.O,,DX,OO0.ODY,POHGSFET PCH 1___ ___ 1.O,__ 1. 00t,_ CfR TDISPL, TOF,SCALE SET=3.0 ALIMI T=09OO*AMAX IF (WETA(K) - ALIMIT) 74,74,75 74 XVAL=PMAN(K)/DX - 0.480 + 1.000 YVAL=WETA(K)/D)Y - 0.040 + 1.000 CAlL PFNMBR (XVAL,YVAL,-O.lOC,THETA,.nrOO,6H(F4.1)) 75 CONTINUE IF (THETAL-THETA) 626 2,39 62 CONTINUE GO TO 20 END

APPENDIX J LISTING OF SUBROUTINES SUBROUTINES: THROTL ASSUME FLOW AIRMAS SIGNAL SOLVE XMIX STERL FPROP PLOTTING ROUTINE 1 PLOTTING ROUTINE 2 PLOTTING ROUTINE 3

364.......$........... COM.P I.F FASTRAN,PUNCH OBJECT PAGE 1 S UBRO._ UTIN E T. HRCOTL ( THETATTA, O, T, OS, AFLOW C C THIS SUBROUTINE CALCULATES THE FLOW AREA AT THE THROTTLE C RESTRICTION FOR ANY VALUE OF THFTATHETO,THROTTLE BORE DIAMETER C AND THROTTLE SHAFT DIAMETER. C IF (THETA-THETAn) 20,t?01,201 201 IF (90.0-THETA) 212,202,202 212 THETA= 180.0 - THETA 202 CONTINUF RTHETA=3. 1415 926* THETA/180.0 R THETO=3. 141 52 6*THETAO/180.0 OlM 1 =C OS ( RTHETA) OUM2=DUM*DUM 1 DUM3=COS (RTHETO) OUM4= nUM3*DUM3 DUM5= DS*DUM3/( DT*DUM ) D J...M6= DUMI /DUM3.. DUM7= S/DT IF (DT-DS) 200,203,203 203 DUM8= D,M7*DUM3 ANG1= ARCSIN (DUM7.) DUM9=OT*OT-DS*DS. ASHAFT=0.,5*SQRT_( tUM.9).*DS + 0.5**DT*T*ANG1:F (DUMI-DUM8) 204,205,205 204 CONT INUE ASTAR=0.785398*OT*DT*DUM6 AFLOW=O.785398*DT*DT - ASHAFT GO TO 209....... ANG=ARCSIN (D UM5) ASTAR=DS*SQRT ( T*DT*DUM-2-DS*S*DUM4)*0.50/UM1 +ANG*DT*DT*OUMI* I 0. 50/DUM3 AFL OW=. 785398*DT*)DT* (1.-DUM6)+ASTAR-ASHAFT GO TO 2C9 200 CONTINUE _ _..21_ Q_W0RIT E OURI TPUT TAPE 6 206 _ _ 206 FORMAT (47H THETA NOT WITHIN LIMITS OR DS GREATER THAN DT ) THFTA=THETAQ GO TO 202 209 CONT INUE 208 RETURN _ ~__ END_...........................................................................................

365..,.COMP IL FFASTRANPUNCH OBJECT SUBROUT INE ASSUM F (ORYA2,VACMANOPENE F AMAIN,FA TTL,FAR ICH, "1 -FLOWMFLOWTFLOWE ) C C THESE ARE APPROXIMATE TYPICAL VALUES FOR THE FUFL-AIR PATIOS C DELIVER.ED BY THE MAIN AND IDLE SYSTEMS. THIS IS USED ONLY TO C GENERATE INITIAL GUESSES FOR THE FUEL FLOW RATES IN EACH SYSTEM C _ FAR ICH=O.0000 IF (DRYA2-50.00) 51,51,5? 51 FAIDLE=O.1100 FAMA IN=O.0000 GO TO 60 52 IF (ORYA2- 75.0) 53, 53, 54 53 FAIDLF=. 1100-0.11nOB{*ORYA2-50.O00 /125.0 FAMA IN=0.0000 GO TO 60 54 IF (DRYA2-175.0) 55,55,56 55 FA ILE=O. 1100-0. 100 (ORYA2-50.00)/125.0 FAMAIN=0.0 61 *( DRYA2-75.0OC) / 100. 00 GO TO 60 56 FAIDLE=0.0000 FAMA IN=.0610 60'IF (VACMAN-OPENE) 57, 57,58 57 FAI) LE=FAI DLE*VACMAN/( 12. 0-VACMAN) CUM8 =FAMA IN FAMAIN=FAMAIN*( 20.OO+OPENE-VACMAN) /20.OO FAR I CH= FAM A I N-D M GO TO 61 58 IF. (VACMAN-12.00) 61,59,59 59 FAIDLE=FAIDLE + 0.0420*(VACMAN-12.00)/(44.00-VACMAN) _62 FAMA IN=FAMA IN*37.0/( VACMAN+25. 00) 61 FATOTL=FAMAIN + FAIDLE C THESE ARE THE SYSTEM FLOW RATES PER BA.RREL C FLOWM=0. 5*FAMAIN*DRYA2 FLOWT=0. 5*FATOTL*DPYA2 __ _ FLOW E=. 5*FAR ICH*DRYA 2 C C END OF FUEL-AIR RATIO APPROXIMATION FOR INITIALIZATION PURPOSES C PRETURN END

366.$. COM..... PIL E F ASTRAN,PUNCH OBJECT PAGE 1 SUBROUTINE FLOW (PPHG,TOF, HUMID, BVSUCWVACMAN,OPENE,FTYPF, 1 TFUEL,NCHAN,XFLOWM, XFLOWT,XFLOWE,XFLOWJ,XFLOWI,SUMAIR ) C THIS SUBROUTINE CALLS ON FPROP AND STFRL OIMPNSION CDl(21),CD2(21),CD3(21),CD4(21),CDS(21),CD6(21) DIMENSION CD7(21),CD8(21),C09(21),ACHA<(25),XLD(25),CTYPE(2DIMENSInN 0(25),DUMR(25'),DELPTW(25),DUMLO(10),S( 45),VEL(251 DIMENS.ION ANGLC( 5), SKIP( 25),ODN( 25) CBL F ED(5) DIMENS ION RE(25) tVHEADW(25) COMMON ORDER,PR INTF,REJET,CDJET,nELXJ,DELXJL, DELXSE, XNCDJ, 1 XNCOJL, XNCOSETURNS,SPILL1,RPM,OISPL,CR,DBLEEO,DTRANS, 2 DCHOrKE,PRINTAXMACHTTOTFACHANXLOCTYPEANG LCTCD1,CD2~ 3 C.3,C04,CD5,CD6,C07,CD8,CCD9,S SAVE3=XLD( 3) SAVE4=XLD( 20) SAVE5=ACHAN( 3) SAVE6=ACHAN( 20) SAVE 11=0.000 SAVEI 2=0.000...............CAL. _._R P.. F.._...... ( FTYPE, TFUEL, T FUEL, SGFUE.., VI SKM CORR,C LI Q, CPFUEL 1 CVFUEL,WFUEL,HVAPOR,GAMMA,HEATV ) GAMMA=C. 000 1 DENS F=SG FU EL *62.34 TOP=TdF + 459.6 AMnENS= POHG*0. 49 12*144. 0/(53.34*TOR )._VI SKE= V SKM/92 903... V ISAG=V I SKE*)F NSF VISAE=VISAG/32. 174 AVISKM=12.0774 + 4.6452*TOF/100.0 AVISKE=AVISKM/92903.0 DPEJ ET=0.0 SETUP=1*0 VACW=13. 594*VACMAN VACM=VACMAN IF (VACM) 46,46,47 46 VACM=+0.010 VACW=13. 594*VACM 4 CONT.. INUE................ DX=DELXSE XN=XNCDSE ARI CH=ACHAN( 3) D(20)=SQRT(ACHAN ( 20)/0.7854) AIDLE=ACHAN( 20)-0o,7854*( ( D( 20)-0. 4430*0. 0312*TURNS) *2)................. I _ _F _AI OL.E-0 _,0a 0_ lQ o ).48_,49.,_49.... 48 AIDLE=0.= 00001 SETUP=0l. 0 49 IF (AIDLE-ACHAN( 20)) 89,89,88 88 AI DL E=ACHAN( 20) 89 CONTINUE

367 ITFRI=0 ITERE=0 ITFR J=0 EOUM= 1.0 OUMMYP=PRI NTF DUMLD( 3)=0.100 UMLD (4) =0.616 DUML O(5)= 1.420 CUML 6)= 3.630 DUML D( 7) = 4.730 DUMLD(8)= 7.230 DUMLD (9)= 10.56 DUMLD(10)=10.56 CBI EED(1)=0.600 CB_ EED(2 )=0.600 CBL E ED (3 )=0.600 CBLFF0(4)=0.600 CB.EED( 5 )=C.600 FLOWT=XFLOWT FLWM=XF LOWM FLOWE=XFLOWE FLOWJ=FtLOWT-FLOWE FLOW I=FLOWT-FLOWM 00 9 I=1,NCHAN,1 SKIP(I)=0.0 IF (ACHAN( I)-0.0000002) 112, 111,111 112 ACHAN(I )=0.0000002 _SKIP ( )=1.0 111 CONTINUE DELPTW(I )=0.0 VEL( I )=0.0 VHFADW I )=0.0 DN(I )=DENSF 9____D ( I) =S QRT ( AC, HA N ( I }/ 0.7 8 5 3 9 8) ON ( 2 1 )=AMOFNS ON(22)=AMDENS ON(23)=AMOENS DN( 24)=AMDENS DN( 25 )=ADENS C NOW CALCULATE THF ENR ICHMENT VALVE OPENING IF (VACM-OPENE) 6,5,5 5 ARICH=.0000001 FLOWE=0.0 00 74 I=3,7,1 74__ SKIP(I )-1.0__ FLOWJ=FLOWT EDUM=.0 GO TO 8 6 IF (FLOWE) 00,100,1,101 100 FLOWE=1.00 _ _______ FLOWT=FLOWT+ 1.0 FL OWM=F LOWT FLOW 1=0.0 101 IF (VACM-OPENE/3.000 ) 43,43,7 7 AR CH=AR ICH*(OPENE-VACM ) *(OPENE-VACM ) /0.4444*OPENE*OPENE

368 PAGE 3 AIDLF= 0000001 SETIJP=0-. BVSMIN=SPILLI *SGFUEL+GAMMA/D (13) IF RVSUCW-BVSMIN) 81,81,8 43 AIDLE=0. 0000001 SETU P=0.0 PVSM IN=SP ILL 1*SGFUFL+GAMM A/D (13) IF ( BVSUCW-BVSMIN) 81,81 8 8 CON T INUE D( 3)=SORT ( ARICH/0.785398) 2........... )=S RT(AIDLE/0.785398) XLD( 3)=XLD( 3)*SQRT(.ACHAN( 3)/0.7854)/D( 3) XLD( 20 )=XLD( 20 )*SQRT ACHAN( 20) /o.7854 /D( 20) ACHAN( 3)=ARICH ACHAN(20 )=AIDLE IF (SETUP) 91,91,90 90 FLOW M=0. 0_ 00 72 1=10,13,1 72 SKIP(I)=1.0 SKIP(21)=1.0 SKIP(22) =1.0 SKIP(23)=1.0 FLOW I=FLOWT XMDUM=. C CBLEED I t)= 0.000001 Cf3LEED( 2 )=0.000001 CBLEED( 3 )=0.000001 91 IF ( A ILE -0.000002 ) 127,127,128 _127 _ ___FLOW I=0.0 DO 71 1=14,20,1 71 SKIP(I )=1.0 SKIP(24)=1.0 SKIP(25 )=1. CBLEED( 4 )=0.000001 C,CBL E E 5 O= 0.OQ.0o _. IF (XMDUM) 81,81,82 81 AIRM1=O 0 AI RM2=.0 A IR I 1=0.0 AIR 12=0.0 FLOWM=0.0 FLOW T= O.0 FLOWE=0. 0 FLOW J=0. 0 RE( 1)=0.0 COJ-=O.0 _Etp._P TJA )'=0 0 SETUP=0.0 VHFADW( I )=0.O ITERF= GO TO 149 82 CONT INUE -____ ____ FOWMELOFW T ___ _ _ ____ ____ _ __..__. XIDUM=0.0 128 C8=360 0.0* SQRT(14.696*2.0* 32. 174/ ( 406.62*144 0~ )) AIRM 1= C8 *ACH AN (2 1) *CBLEED( 1) *SQRT( AMOENS: *BVSUCW0.68) AIRM2=C8*ACHAN (23)*CBLEED(3 ) SQRT( AMDENS*8VSUCW*0.90)

369 4 AIPII=C8*ACHAN(24)*CBLEED(4)*SQRT(AMDENS*VACW*0.060 ) AIR 12=C8*ACHAN ( 25)*CBLEED(5)*SQRT( AMDENS*VACW*. 250 ) IF (SAVEI2) 179,1179,178 178 AIR I1=SAVEI1 AIR I 2=SAVE 2 179 StMAI R=A IRM1+A I1M2 C C NOW LOGICAL GUESSES HAVE BEEN MADE FOR THE FUEL AND AIR BLEED C FLOW RATES IN EACH SYSTEM C FLOWJ=FL OWT-FLOWE FLOW I=FL WT-FLOW M C DDUMR(f IS THE FUEL FLOW RATE THRU FUEL CHANNEL ELEMENT I C FtLOWJ IS THE FUEL FLOW RATE THRU THE MAIN METERING ORIFICE C F L OWE IS THE FUEL FLOW RATE THRU THE MAIN ENRICHMENT VALVE ORIFICE C F-LOWI IS THE FUEL FLOW RATE THRU THE MAIN IDLE CHANNEL C _ FLOWM IS THE FUEL FLOW RATE THRU THE MAIN MAIN DELIVERY CHANNEL C FLOWT IS THE TOTAL FUEL FLOW RATE PER CARBURETOR BARREL C IRM1 IS THE AIR.LEED FLOW RATE THRU THE FIRST MAIN AIR BLEED C AIRM2 IS THE AIR BLEED FLOW RATF THRU THE SECOND MAIN AIR BLEED C AIRI1 IS THE AIR BLEED FLOW RATE THRU THE FIRST IDLE AIR BLEED C AII2 IS THE AIR BLEED FLOW RATE THRU THE SECOND IDLE AIR BLEED C.___ __.... XI SW=O.C DUMDP=. 0 C1=128.0*1728.0*4C6.62/(3. 14159*3600.0*2116.62 ) C2=8.*1 44.0*406.62/( 3. 14159*3 141 59*3600.0*3600.0*14.696) C3=406.62/( 2116.6*2.0*32. 174) C4=406.6 2 144.0/( 3 600.0*O3600.0*14.69 6*2.0*32.174) 118 CONTINUF XJSW=O.0 ITFRJ=O 120 OUMR ( 1 )=FLOWJ DU(JR (2)=FLOWJ _ESW=0 O................... ITERE=O. UMR (8 )=FLOWT DUMR (9)=FLOWT OUMR (10) =FLOWM DUMR (11 )=FLOWM+A IRM1 ___ _ UM RR(12)=FLOWM+A IRM1+A IRM2 DUMR( 13)=FLOWM+AIRMl+AIRM2 DO 11 K=14,16,1 11 DUMRfK)=FLOWI UMR I 17 )=FLOW I+A IRI 1 D1MR ( 18 )=FLOW I-+A I I 1 _DUMR(19)=FLOWI+AIRI 1+AR12 DUMR(20)=FLOWI+A IRI1+AIR I2 DUMR(21)=AIRM1 DUMR (22) =A IRM1 DUMR(23)=AIRM2 OUMR(24) =AIR I1 ___ ___DUMR (25) =AIRI 2 SUMAI R=A IRM1+A IRM2 AI DENS= ( POHG-VACMAN*0.50O 0)*0.4912*144.0/( 53.34*( TFUEL+459.6 ) ) IF (SKIP(13)) 103,103,104 103 DN(11)=(AIRM1+FLOWM)/(AIRMl/AMOENS+FLOWM/DENSF)

370 PAGE 5 ON( 12)= (SUMAIR+FLOWM )/( SUMAIR/AMDENS+FLOWM/DENSF) DN( 13)=DN(12) 104 IF (SKIP(20)) 105,1C5,1C6 105 DN(1I 1.7 )=( AIR I I+F OW / ( AIR I 1/A I OENS+FLOWI/OENSF) CN(18)=DN(17) DN(19)=(AIR I1+AIRI2+FLOWI)/ (AIRI1+AIRI2)/AIDENS+FLOWI/OFNS ON(20)=DN( 19) 106 CONTINUE 55 DO 10 K=3,6,1 10 DUMR K ) FLOWE*2. OUMR (7)=FLOWE DO 5 1 I= 1,NCHAN, 1 IF (SKIP(I)) 76,76,51 76 CONTINUE VEL( I)=144.0*DUMR( I)(ON(I)*3600.0*ACHAN(I) RE( I )=VEL( I )*D( I )/( 12.0*VISKE) VHEADW( I) =406.62*DN( I )*VFL( I )*VEL (1) /2116.6*2.0*32. 174) IF (1-20) 107,107,108 108 RE( I)=VEL( I)*D( I)/( 12.0*AVISKE) 107 CONTINUE IF (RF(I)) 99, 102,102 99 WRITE OUTPUT TAPE 6,180, I,DUMR(I),VEL(I),RE(I) 180 FORMAT (33H NFGATIVE REYNOLDS NUMBER IN FLOW,I10,3Fl0.3 OUMR(I )=0.001 VEL(I) =0.001 RE( I )= 10.00 102 IF (CTYPE( I )-1.C) 12,13,14 C THIS CHANNEL ELEMENT IS A SIMPLE PASSAGE C CALCULATE THE SUDDEN EXPANSION OR CONTRACTION LOSS C 12 IF (I-i4) 25,26,25 26 CC=0.62 + 0.38*(ACHAN(14)/ACHAN(9))**3 F1= (.0O/CC - 1.,0)*(VEtL(14)/VEL( 13) ))**2 _ __GO TO 21 25 IF (I-8) 171,170,17l 170 FI=( ( 1.0-ACHAN(7)/ACHAN(8l ) *(FLOWE/FLOWT) )**2 GO TO 21 171 IF ( ACHAN(I)-ACHAN( I-1 ) 19, 20,18 18 Fl= (1.0-ACHAN(I-1)/ACHAN( I) **2 GO TO 21 19 CC=O..62 + 0.38*(ACHAN(I)/ACHAN(I-1))**3 FI= ( (1.0/CC- 1.0)*(ACHAN(I-1)/ACHAN( I )))**2 GO TO 21 20 F1=0.O C NOW CALCULATE THE BEND LOSS 21 ANG=ANGLC(I)*3.14159/180.0 F2=0.900-O.900*COS ( ANG) FACTOR=F1 + F2 DPEN TRP=C3*DN( I )*VEL (I- 1 )*VEL (I-1) FACTOR IF (I-?) 168,167,168...1.... __ 67 D._____ PEJET= DPENTR _ _ 168 CONTINUE IF (RF(I) - 2100.0 ) 15,15,16 15 FOARCY=64.0/RE( I) DPW=FDARCY*XLD( I )*VHEADW( I )

371 GO., TO 1 7 16 FOARCY=0.3164/ RE( I )**.250) PPWV=FDARCY*XLD( I )*VHEADW( I) 17 nELPTW(I )=DPENTP + DPW GO TO 50.. C THIS CHANNEL ELEMENT IS A MAIN METERING ORIFICE 13 OERUG=O. O IF (RE(I )-10000.O) 6, 85,85 85 RE( I )=10000.0 GO TO 23 86 CONTINUE IF (RE(I) - 2000.0) 22,22,23 22 CALL STFRL(C02,0.0,DELXJL, ORD,XNCDJL,S,RE(I),CDJ,DEBUG GO TO 24 23 CLL STERL (CD I,0.,OELXJ,CPDER, XNCDJ,S,RE( ),COJ,DEBUG) 24 CONTINUE CJC UM =._ J.-C*C DJ ADUM=1.0 IF (CDJ-0*005) 119,119,155 119 DELPTW(I)=0.0 GO TO 50 155 DELPTW(I)=C4*UMR(T)*UMRDUMR(I)*ADUM*CUM/(DENSF*ACHAN(I)* _!___I ___ _.ACHAN( I)*C J*CDJ ) GO TO 50 C C THIS CHANNEL ELEMENT IS A SQUARE EDGED ORIFICE C 14 IF (RE(I)-11000.0) 84,84,83 83 R E DUM=100........ GO TO 92 84 REOUM=RE(I) 92 0D 27 J=3,10,1 IF (XLDO I)-DUMLD(J ) 28, 28,27 27 CONT I NU E 28 OE__ _nE8_UG=0.0. IF (J-4) 29,30,31 29 CALL STERL (CD3,0.0,DX,ORDER,XN,S,REDIUMCDSE,DEBUG) GO TO 41 30 CALL STERL (CD3,0.0 O X,ORDERXN S,REDUM,CDSE1,OEBUG) CALL STERL (CD4,0.0,DX, ORDER, XN,S,REDUMCOSE2 DEBUG) GO TO 40. 31 IF (J-6 ) 32t33,34 32 CALL STERL (CD4,0.OOX,ORDER,XN,S,REDUtM,CDSE1,DEBUG) CALL STERL ( C5,0.0,OX,ORDER,XN,S,REDUM,CDSE2 DEBUG) GO TO 40 33 CALL STERL (CD5,0. O0DX, ORDERXN,S,REDUM,CDSE1,DEBUG) _ CALL S TERL ( CO6,0.ODO__._XO-.RDER, XN, SREOUM, CDSE2,DEBUG) GO TO 40 34 IF (J-8 ) 35,36,37 35 CALL STERL (CD6,0.0,DXORDERXN,S,REDUM,CDSE1,DEBUG) CALL STERL (CD7,0. O,DX,ORDER,XN,S,REDUM,COSE2,DEBUG) GO TO 40 36 ____CALL _STERL_ (CD7 0__,__0DX, ORDERXN,S, REDUM, CDSE1,DE BUG) CALL STERL (CD8,0.0, DX', ORDER, XN, S,REDUM,CDSE2,DEBUG) GO TO 40 37 IF (J-10) 38,39,39 38 CALL STERL (CD8,0.0,DX, ORDER,XN,S,REDUM,CDSE1,DEBUG)

372 PAGE_ 7_ CALL STERL (C09,0.0,DX, ORDER,XN,SREDUM,COSE2,DEBUG) GO TO 40 39 CALL STFRL (C09,O.0,DX,VRDER,XN,SREUM,COSDSE,DEBUG) GO TO 41 40 CONT INUF X=DUMLD( J )-DUMLD (J-1) Y=CDSE2-CDSE 1 CDSF=CDSE1+(XLD( I)-DUMLD<J-1))*Y/X 41 CDUM= 1.0-CDS E*CO SE IF (1-20) 110,110,109 109 L=1-?0 CBLEEnL )=CDSE GO TO 50 110 CONTINUF IF (ACHAN(I-1)-ACHAN(I)) 44,45,45 44 CC=O..6:2 + 0.38*(ACHAN( I )/ACHAN( I-1))**3 FACTOR=( (1.0/CC-1.0)*ACHAN( I-1)/ACHAN ) ) ) **2 DELPTWI )=C3*DN( I)*VEL(1-1)*VEL ( I- 1*FACTOR GO TO 50 45 CONTINUE ADUM=1.0-( ACHAN( I ) /ACHAN ( -) )*2 DEfLPTW ( I )=C4*DUMR( I)*DUM1R( I) *ADtUM*CDUM/(ON( I )*ACHAN(I)* 1 ACHAN(I)*CODSE*CSE ) C C NOW THE PRESSURE DROP ACROSS THIS PARTICULAR ORIFICE IS KNOWN C 50 CONT INUE C IF ( VACM -.,_OPENE).58.,_61,61 58 IF (1-7) 61,80,61 80 DU MV2= 144.0*DUMP (2) /(ENSF*3600.0*ACHAN( 2 ) ) OUMVH2=406.662*DFNSF*DUMV2*ODUMV2/(2116.6*2.O0*32.174) SUMOPJ=DELPTW(1) + DFLPTW<2) +OUMVH2 IF (ESW) 52,52,53 52 SUMDPE=DELPTW (_3) + DEL PT W (4)+D E L PTW ( 5 )+DE L PTW ( 6).+ D E L P T W ( 7 ) + VHEADW(7) ERRE 1=SUMOPE-SUMDPJ ITERE=1 EPSE=0.015 IF (ABSF(ERREl)-0,100 ) 42,42,54 54 CON T INTU E OLOFE=FLOWE FLOWE=FLOWE-O. 100*ARSF( ERRE 1)/ERRE 1 IF (FLOWE) 181,182,182 181 FLOWE=0.0005 182 FLOWJ=FLOWT - FLOWE D_UMR (1 )=FLOWJ - DUMR (2 )=FLOWJ ESW= 1.0 GO TO 515 53 ITERE=ITERE+1 IF ( ITERE-O10) 116,115,116.__.._115.__ EPSE:16__O _ ~_1__6. 116 IF (ITERE-16) 122,122,60 122.. CONTINUE SUMDPE=DELPTW( 3)+DELPTW( 4 ) +DELPTW(5)+DELPTW(6)+DELPTW(7)+ 1.VHEADW(7)

373 FR F E 2= SUMDPE-SUM MOP J IF (ABSF(FRRE2)-EPSF ) 42,42,56 56 SAVE=FLOWE FLOWE=FLOWF+ERRF2*(F. OWF-nLDFE)/( ERRE1-ERRE2)..F.......F...... i F _OWE)..59,. 57, 57 59 FLOWF= 0.0005 57 OLOFF=SAVE ERPE1=FPRE2 FLOWJ=FLCWT - FLOWE DOIJR( )=FLOWJ...DUMP(2.. _. -R 2)=_FLOWJ GO TO 55 \2 CONT INUF S0 FLOWJ=FLOWT FLOWE DUNMR (1.= FLOWJ DUMP ( 2 )=FLOWJ 1. _ C ONT I NU E'IF (1-13) 75,62, 75.)2 IF (XJSW) 63,63,64 53 SUMDPM=DELPTW( 1)+DELPTW 2)+S PILL 1SGFUEL+VHEADW( 13)+ i O. 1*GAMM A/D( 13 00) 65 L=8, 13,1,5 SU M Dst PjPM.=SUMPM+DLPTW ( L ) ERR.J 1=SU MOPM-BVSUCW ITER J=1 EPSJ=0.0 150 IF (ABSF(ERRJl)-0.1000) 164,164,66,6 CONTINUE COLF FJ=FL CWJ_ FLOWJ=FL OWJ-0. 250*ABSF (ERRJ 1)/ERRJ1 IF (FLOWJ) 175,176,176.75 FLOWJ=0.100 76 CONTINUE FLOW E=FLOW E*FLOWJ/OLDFJ _ XJSW=1~ 0 _.._. ______ _ =__. L 0. _ T L0 W _'-J _._......_. 0._-..... _..F...."-'............_....... _............................................... FLOWT=FLOWJ+FLOWE FLOWM=FLOWT-FLOW I IF (FLOWM) 87,87,120 4 ITFRJ=ITERJ+1 IF (ITERJ-10) 117,121,117 21 FPSJ=0.160 17 IF (ITERJ-16) 124,124,125 25 WRITE OUTPUT TAPE 6,126 26 FORMAT (34H NO MAIN CONVERGENCE WITHIN FLOW ) GO TO 73 24 CONTINUE SUD 10 OP M=D EL PTW( I )+DELPTW( 2 ) +SPI LLI SGFUFL+VHEADW( 13) 1 O. lGAMMA/D(13 ) DO 67 L=8,13,1l:7 SUMDPM=SU.DPM+DELPTW(L) ERR J 2=SUMD PM-BVSUCW IF (ABSF(ERRJ2)-EPSJ ) 164,164,68 8 _ SAVE=FLOWJ __ __ FLOWJ=FLOWJ+ERRJ2* ( FLOWJ-OLDFJ)/(RR-ERRJ-ERRJ2) IF (FL.OWJ) 69,70,t70 9 FLOW J=+O0. 100 0 OLDFJ=SAVE

374 PAGE 9 _.. FLOWE=Ft OWE* FLOWJ /OLOFJ ERPJ 1=ERJ 2 FLOWT=FLOWJ+FLOWE FLOWM=FLOWT-FLOW I IF ( FLOWM) 87, 87,120 87 FLOWM=0. AI PM 1=C0. AIRM2=0. 0 FLOW I=FLtOWT GO TO 120 164._ L DAMl- AIRM1 OLDAM2=A IRM2 DELPM=EL PT W( 1 +DELPT W( 2 )+OEL PTW( 8) +ELP TW(9 )+OELPTW( 10)+ 1 VHEADW(10) DFLPTW( 23 )=DEL PTW ( 1 ) +OFLPTW 2 )+OELPT 8 )TW () +ETW(9) +DELPTW(10 ) + 1 rOUDELPTW( 11)+VHEADW( 12) IRM2=C,8*ACHAN( 2 3)*CBLEED( 3)*SQRT( AMDENS*DELPTW(23) ) IF (SKIP(21) ) 113,113,114 113 UtJM21= 1. /(ACHAN (21 )*ACHAN( 21 )*CBLEED( 1 )*CLEED( 1 ) ) DUM22=1.C /(ACHAN (22)*ACHAN (22 ) *CBLEED( 2 )*C8LEE( 2 )) AIRM1l=C8*SORT( AMDENS*DELPM ) /SQRT( OUM21+DUM22 ) f ELPTW(21)=DELPMB/( 1.0+ACHAN 21)*ACHAN( 21)*CBLEED( 1)* 1 C'BLFFO ( 1)/ (ACHAN(22)*ACHAN 22)*CBLEED(2)*CBLEFO(2) ) FLP TW (22 )=DELPM:B-DELPTW( 21) 114 IF (A SF(AIRM1-OLDAM1)-0.005) 165,165,118 165 IF ( ASF(AIRM2-OLDAM2)-0.005) 73,73,118 73 FLOW T=FL OWJ+FLOWE FLOWM=FLOWT-FLOW I 75 CONTINUE IF (AIDLE-0.000002) 130,129,129 129 IF (I-25) 130,131,130 131 CONTINUE IF (XISW) 132,132,133 132 SUD P I=DELPTW( 1 ) +DL PTW ( 2 ) +DEL PTW( 8 ) +OELPTW( 9 +VHEADW( 20 ) 00 134 L=14,20,1 134 SUMDPI=SUMDP I+DELPTW(L) ERR I 1= SUMDP I-VACW XISW=1.0 ITFR I=1 E_ PS I = 0. 1 50 IF (ABSF(ERRI1 )-0.750) 162,162,135 135 CONTINUE OLDF = FLOWI FLOWI=FLOW I-. 500*AB SF( ERR I 1 )/RR I IF (FLOWI) 143,144,144 143_____ FLOWI-0,_QOQ5__ A IP11=0.0 AIR I 2=0.0 144 CONTINUE IF (SKIP(13)) 148,148,147 147 FLOWM=0.0 ----— ___PAI RMl=O _. 0Q _ _ _._ _ _ _ _ A I R M 2=0 FLOWT=FLOW I FLOWJ=FL OWT-FLOWF GO TO 118

375 148 RATIOP= (DELPTWt 1)+ELPTW(2)+DELPTW(8)+DFLPTW(9) )/BVSUCW IF (RATIOP-0.950) 96,96,95 95 RATIOP=0.950 96 CONlTINUE _IF _(RATI)P* (OL.F.I-FLOW I) +FLOWM) 1 56, 1 56, 1 57 156 FLOWM=0. 100*FLOWM GO TO 158 157 FLcWM=FLOWM+RATIOP* (OLOF I-FLOW I) 158 CONTINUE FLOWT=FLOW I+FLOWM FLOWJ=FL.OWT-FLOW E _ GO Tn 118 133 ITFRI=ITERI+l IF ( ITERI-10) 17 2,123,172 123 EPSI=1.0=I 0 172 IF f ITERI-16) 136,1'36,137 13_7... WRITF __. OUTPUT TAP E 6, 138 138 FORMAT (39H NO IDLE CONVERGENCE WITHIN FLOW ) GO TO 149 136 CONTINUE SUMOPI =DELPTW( 1 )+DELPTW( 2)+OELPTW( R) +OELPTw(9 )+VHEADW(20) 00 139 L=14,20,1 139 SUMD P I=SUMDPI+E LPTW(L ) ERPI 2=SUMOPI-VACW IF (ABSF(ERRI2)-EPSI ) 162,62,162,140 140 SAVE=FLOWI FLOWI=FLOWI+ERRT2*(FLOWI-OLDFI)/(ERR I 1-ERR12) IF (FLOWI-15.0o) 146,'146,145 145 FLOWI=15.00 146 CONTINUE I F (FLOWI 141,142, 142 141 FLOWI=O.0005 A IPI 1=0.0 AIR 12=0.0 142 OLF I=SAVE _ ERR 11=ERRI2 IF (SKIP(13)) 154,154,153 153 FLnWM=O. 0 AIRM1=0.0 A IRM2=0.0 FL OW T.= FL.OW I FLOWJ=FL OWT- FLOW E GO TO 118 154 RATIOP=(DELPTW(1)+DELPTW(2)+DELPTW(8)+OELPTW(9))/BVSUCW IF (RATI OP-0.990) 98,98,97 97 RATIOP=0 990 98 CONT INU E IF I RAT I OP*OLDFI-FLOWiI-)*+FLOWM) 15 9,159,160 159 FLOWM=0.100*FLOWM GO TO 161 160 FLOWM=FLOWM+RATIOP*(OLDFI-FLOW ) 161 CONTINUE _____-__FLL.T__T — FWI+FLOW M__ FLOWJ=FLOWT-FLOW E GO TO 118 130 CONTINUE 51 CONTINUE

376 PAGE _....... 162 OLDA I=A IR I OLOAI2=AIR I2 IF (SKIP(2C)) 169,169,149 169 CONT INUE ELPTW( 4 )=DELPTW ( )+DELPTW( 2 ) +OEI. PTW( 8 +DELPTW(9)+DELPTW (1' 1 +DELPTW( 15)+VHEADW( 16) DELPTW( 25) =ELPTW( )+DEL PTW(2)-+DELPTW(8 +OFLPTW(9)+OELPTW( 1 1. +DELPTW( 15 )+DEtPTW( 16)+DELPTW( 17)+DELPTW(1 8 )+VHFAOW( 19 AIRI l=C8*ACHAN( 24)*CBLEE( 4)*SQRT(AIDENS*DFt PTW(24) ) AIPI 2=C8*ACHAN(25) *CBLEED(5 )*SQRT( A I ENS*DE PTW ( 25) ) _IF (ABSF(AIRIl-OLDAIl)-O.008) 163,163,1 66 163 IF (ARSF(AIRI2-OLDAI2 )-O.008) 149,149,166 166 X ISW=.0 ITFR I=C GO TO 118 149 SlIJMAI R=AIRMI+AIRM2 IF (SETUP) 94, 94, 93 93 BVSMIN= SPILLl*SGFUEL*1.08 + GAMMA/O(13) + (DELPTW(1) + 1 DELPTW( 2)+DELPTW(8)+OELPTW(9)) SAVFI1=AIR 1I SAVE I2=AIR I2 SETUP=. 0 IF ( BVSUCW-BVSMIN ) 94,94,89 94 XF OWT=FLOWT XFLOWM=FLOWM XFt OWE=FLOWE XFLOWJ=FLOWJ ____XFLOWI=FLOWI REJET=RE (1) CD.JET=C DJ OPJET=DELPTW(1) + VHEADW() + OPEJET IF (SKIP(20) ) 77,77,78 77 ITFR=ITERI GO TO 79 78 ITER=ITERJ 79 CONTINUE IF (DUMMYP) 150,150,151 151 WRITE OUTPUT TAPE 6,152,BVSUCWVACM,FLOWM,FLOWT,FLOWJ, 1 FLOWE, FLOW! ICDJET,DPJET, ITER, ITERE, ITERJ, ITER I, 2 A_ _AI RMi~ AIR M2 A IR1 A IRI2 152 FORMAT ( 1HO//, 9F8.3,4 15,4F8.3// ) 150 CONTINUE XLtD 3)=SAVE3 XLD( 20)=SAVE4 ACHAN( 3)=SAVE5 _.. ___ _ ACHAN (20)= SAVE6_____ RETURN..END............

377 $...COM.PILE FASTRAN., PUNCH OBJ ECT SUBROUTINE AIRMAS ( POHG TOFHUMID,THFTA,CD T A FLOW, FTYPE, T FUEL, 1 FRACT,GUESS,XMAINR,XTOTLR, VACM,DRYAIR,WETAIR,VENFLO ) C C GASFLO IS THE TOTAL. MIXTURE FLCW RATE IN THE INTAKE MANIFOLD C THF UNITS OF GASFLO ARE...... LBM/HOtUR C C D_ R D YAIR IS THE DRY AIR FLOW RATE IN THE CARB.URETOR AND MANIFOLD C WETAIR IS THE WET AIR FLOW RATE IN THE CARBURETOR AND MANIFOLD C AND IS THE SUM OF THE DRY AIR AND WATER VAPOR FLOW RATES C C HUMID IS THE RELATIVE HUMIDITY DIMENSION CD 1(21 ),CD2( 21)C3( 21,),CD4(21),C05(21 ),CD6(21) DIMENSION CD7(21),CD8(21),~CDq(21),ACHAN(25),XLD(25),CTYPE(25) DIMENSION ANGLC(25),S(45) COMMON ORDERPRINTFREJET,CDJET,OELXJ,DELXJLtDELXSEXNCDJ, 1 XNCOJL, XNCDSE,TURNS,SPILL1,RPM,DISPL,CRDBLEEDODTRANS, 2 __DCHOKEPRINTA,XMACHT,TOTF, ACHANXLDCTYPEANGLCCD!, CD2, 3 CD3,CD4,CD5,CD6,CD7,CD8,CD9 S C CHECK FOR A NEGATIVE THROTTLE,FLCW AREA IF (AFLOW) 20,21,21 20 WETA2=0.00 PR= 1.00 GO QTO13 21 CONTINUE VACM AN=VACM FATOTL=XTOTLR FAMAIN=XMAINR GUFSS IS AN EXTERNALLY SUPPLIED INITIAL VALUE IF (GUESS-0.0010) 78,78,79 79 VACMAN=GUESS EPS=0.,100 GO TO 26 78 CONTINUE VACMAN=12.Q0 EPS=O.200 26 CONTINUE NOW AN INITIAL INTAKE MANIFOLD VACUUM HAS BEEN ASSUMED N=C EXHEAT=1.0 PO=POHG*t0.4912 PT=PO PTHG=POHG

378 PAGE 2... TOP=TnF + 459.6 TOTR=TOR TOTF =TOF D(O.MHU=HM I D D..UMMYP= DEBUGG,. DJMPA=PR I NTA CDBL= O. 40 CDTR=O.B40 VCL=DOSPL/( CR- 1.0) ABL EE O=C. 785398*OfL ELEED*DBLF _ATRAN S'=C. 7 53 98*DTRANS*P'TRANS ACHOKE= 0. 7 5398* DCHFK E*DCHOKE SWITCH=C. TF=TOF/100.0 PMAXW-=1. 302*T*TF *TFTF-0.765*TF*TFF+0.413*TF OMFGA=O.6 22*HUM ID*PMA XW/PO C GET THE PROPERTIES OF THE MOIST AIR F A=.0000 CALL XMIX (TOF, POHG,HUMID,FTYPE, TFUEL, FA,WMOTST,CPWET,CVWET 1 GKWET ) CALL XMIX (TOTF,PTHG, OJMHU,FTYPETFUEL,FATOTL,WiOLFM,CPMIX, 1 CVMIXGKMIX ) DLUMF A= FA MA IN*FRACT CALL XMIX (TnTF,PTHG,DUMHU FTYPE TFUEL,D UMF A,WMOLET,CPMAIN, 1 CVMAINGK ) C GET THE FUEL PROPERTIES CAlL FPROP (FTYPETFUELTFUELSGFUFL,VISKM,CORR,CLIQ CPFt)EL 1 CV FUJE L,WFUEL,HVAPOR, SIGMA,HEATV ) FAIDLE=FATOTL-FAMA IN TOTR=TOR + FRACT*FAMAIN*HVAPOR/CPWET TOTF=TnTR-459.6 TMAN= TOR +FATOTL*HVAPOR/CPWET + EXHEAT*60.O TMANF=TMAN-459.6 IF (FATOTL-O.0400) 44,44,45 44.TCLR=650. + 70..0. *FAT TL /.400 GO TO 50 45 IF (FATOTL-O.800) 47,46,46 46 TCLR=1350.0-70 0.0*( FATOTL-O.0800 )/.0700 IF (TCLR-650*O) 48,50,50 48 TCLR=650.0.. GO TO 50 47 TCt.R=1350.0 50 CONTINUE TCYLR=TMAN+TCLR/.00 C5=TCYLR/ T AN C6=TCLR/TMAN.C7=C 5/C... C 8=0.400*C5*1545.4*TMAN*(CR-l.0 )/(WMOLEM*CR*0.4912) C9= (CR-C7)/CR C 10= (GKWET-1). 0)/GKWET C 11=(GKWET+l.) /(2.0*GKWET) C 12=3600.0*SQRT(GKWET*'WMO IST*32. 174/1545.4)*ABLEED*PO* I SQRT(2._0/1GKWET-1.0))/SQRT(TOTR) C13=3600.0 *SQRT( GKWET*WMOIST* 32. 174/1 545.4)*ACHOKE*PO* I SQRT(?. 2C/ GKWET-1.0) )/SQRT(TOTR) PRBMAX=1.0/((2.0/(GKWET+I.0) )**(GKWET/(GKWET-1I.O ) ) C

379 10 CONTINUE N=N+1 IF ( N - 21) 71,72,71 72 EPS=O.80 SWITCH=0.0 VACMAN=8.0 OUMHU=HUMI 0 WRITE OUTPUT TAPE 6,14 14 FORMAT (1H,65H 20 ITERATIONS HAVE BFEN PERFORMED WITHIN AIRM!AS.... TRY 8 MORF ) IF (PPRINTA) 71,71,56 56 DUMMYP=l. 71 CONTINUE GASM2=DISPL*RPM*(POHG*C9-VACMAN)/C8 C DUMMY 1=GASM2/10CC.O C _ PT=STAGNATION PRESSURE AT THROTTLE PLATE IN PSIA C PTHG=STAGNATION PRESSURE AT THROTTLE PLATE IN INCHES HG C CORRELATED PO LOSS IN VENTURI IS 1.0 INCH HG FOR' 912.0 LB/HOUR PT=PO - 1.200*0.4912 OUMMY1*OUMMYl PTHG=PT/0.4912 OUMHU=PT*OMEGA/{(.622*PMAXW) C VLIMIT=( PC-PT )/0. 4912 IF (VACMAN-VLIMIT ) 61,61, 62 61 VACMAN=VLIMIT + 0.0001 GO TO 71 62 CONTINUE PR=PT/(_PO-VACMAN*0. 49 12) PRMAX=1.0/ ((2.0/(GK+1.0) )**( GK /(GK-1., ) )) IF (PR-PRMAX) 12, 11,11 11 PR=PRMAX 12 CONT INUF C 1=2.0*3600.O*SORT(GK*WMOLET*32. 174/1545.4)*AFLOW*PT* 1 S__QRT (2.Q/_( GK-1.0) /S ) /SQRT TOTR C2=(GK-1.O)/GK C3=(GK+1.0)/ 2. 0*GK ) C HECK=PR**C2 IF (CHECK-1.00) 63,64,64 63 WRITE OUTPUT TAPE 6,65 65 FORMAT (_lH0 _40H_ THE PRSSURE RAT IO IS LESS THAN 1.000 ) WRITE OUTPUT TAPE 6,66,PR,PO,PT,VACMANVLIMIT,PRMAX,N 66 FORMAT (6F15.6 I15 ) PR= 1.0040 64 CONTINUF GASMT=C1*SQRT(PR**C2 - 1.0)*CDT/(PR**C3) ___PRBL=PO/(PO - VACMAN*,.4912) IF (PRBL-PRBMAX) 67,68,68 68 PRBL=PRBMAX 67 CONTINUE A IRMB=CDBLC 12*SQRT (PRBL**C -1. 0C ) / ( PRBL**C 11 ) AIRMC=CDBL*C13* SQRT(PRBL**C 10-1.00)/(PRBL**Cl. ) G ASMTR=CDTR*C1( ATRAN S/AFLOW_) *SQRTPR**C2-1. 0 )/(PR**C3 ) GASMi=ASSMT+A IRMB+GASMTR+A IRMC CHOKED FLOW FOR GK=1.4 WILL RE 1914.40*2.0*AFLOW*PT/SQRTITOTR)+ 13.0 IF (SWITCH-O. O ) 33,34, 33 3-4 WETA2=GASM2*( 1.0+OMEGA)/( 1.0 + OMEGA + FATOTL)

380 PAGF 4 WETA1 =GASM1*(1 ". +.A1MEGA ) 1.0 + OMEGA + FAMAIN) E =WETA1-WETA2 IF (APSF (E -EPS ) 13,13,39 39 CONTINUE VOL D=VACMAN VACMAN=VACMAN - O.0500*ABSF(F1)/F SWITCH= 1.0 GO TO 36 33 WETA2-=GASM2*( 1l.C+OMEGA)/(l. + OMEGA + FATOTL) WETA1=GASM1*( 1.0+OMEGA)/(1.0 + OMEGA + FAMAIN) E 2=WETAI-WFTA2 IF (ARSF(E2)-EPS) 13, 13,35 35 SAVE=VACM AN IF (El) 40,13,41 40 STFP=1.100C GO TO 42 41 STFP=0.900 42 CONTINUE VACMAN=VACMAN+E2*( VACMAN-VOLO )*ST EP/( E 1-E2) VOLD= SAVE E1.=E2 36 CONTINUE __ __IF (DULMMYP) 7,,5.. 15 WRITE OUTPUT TAPE 6,16,N,RPM,THETA,VOLD, WETA2,WETA,El, 1 VACMAN INAMAINtFATOTL,PTHG,TMANF 16 FORMAT (14,2F10. 1,FIO.2,2F10.1,?F1.O.2,2Fl0. 4,F10.2,Fl0.1 17 CONTINUE IF (N - 29) 31,30,30 30c WRITF OUTPUT TAPE 6,32 32 FORMAT (IHO,46H NO MANIFOLD VACUUM CONVERGENCE WITHIN AIRMAS ) GO TO 13 31 CONTINUE IF (VACMAN-VLIMIT) 27,?7,28 27 VACMAN=VLIMIT + 0.0001 GO TO 10 28 IF (VACMA N —POHG*C9) 10;29,29 29 VACMAN=POHG*C9 - 0.010 GO TO 10 13 WETAIR=WETA2 GASFL O=GASM2 VENFLO=WETAI R-AI RMB DRYAIR=WETAIR/(1.0 + OMFGA) XMACHT=SQRT(2.0/(GK-1.0 ))*SQRT(PR**((GK-1.0)/GK)-1.000) PMAN=POHG-VACMAN VACM=VACMAN XMAI NR= FAMAIN XTOTLR=F ATOTL. IF (DUMPA )76, 76,75 75 WRITE OUTPUT TAPE 6,77,RPM, THETA,AFLOW,PMAN,WETAIR,DRYAIR, 1 GASFLO,GASMT,XMACHT,FAMAIN,FATOTL,GK,PTHG,TOTF,CT,N 77 FORMAT (F8.1,F9.1,F9.4,F 9.2,3F9.2,F8.2,F9.4,F9.4,F8.4,F8. 3 1 F8.3,F8.1,F7.3,I4 ) __76 CONTINUE____ RETURN END

381 $. C...._COMPILE FAST RAN, PtUNCH OBJFCT...SUBROUTINF SIGNAL (POHG, TOF,HUMI O, VENFL, FTYPETFUEL,RATEMF, 1. Af AMV ABV,XMV1, XMV2t XBV XMB BBLS,FRACT XG7)JFSS, PRINTS, 2 XF VVFLO, PVFLO,P VMACH,PVMACH, BVSUCW,PVSUCW ) DUMMYP=PRINTS CIMENSION AMV(10),ABV(10) DUMFt.LO=VFN FLO/BRLS CALL FPR.OP { FTYP ETFUFJEL, TFUE LSGFUEL,VISKM,CF3RR,CL IQ, CPFUE.., 1 CVFUFLWFUtELHVAPOR,GAMMA,HEATV ) FRACTR=FRACT*. 400 FPS=0, 01 2 TOR=PTOF+459. 6 TntO R= TO R TO BR=TOR TOf F=TOF TOFF=TCF PO= P OHG*. 4912 POMHG=POHG PR0RH G= P HG PORHG=POHG POM= P.f POR= PO C GET THE PROPERTIES OF THE MOIST AIR IN THE PRIMARY VENTURI CALL XMIX (TOF,POHG,HUMID,FTYPE,TFJEL,0.0,WMOISTCPWFT, 1 CECVWET,GKWET ) C1=SQRT(GKWET32. 174*WMOIST/ 1545.4*TOR) ) C2=2.0 t 2. 174*144.0*. 4912 C3=O.50*(GKWET + 1.0) C4=O.50*(GKWET +. 1.0)/(GKWET-1.O) C5=C3**C4 C6=3600. 0*PO*C1/C5 FMAXB=C6*ARV (3) FMAXM=C6*AMyV. 3 FMAX T= FMAXM+FMAX IF (FMAXT-DOUMFLO) 28,29,29 28 WRITE OUTPUT TAPE 6,30 30 FORMAT (1H,67H THE AIR FLOW SUPPLIED TO SIGNAL EXCEEDS THE V 1ENTURI FLOW CAPACITY ) =_... _ _.__._..~_._.........._.. GO TO 51 29 CONTINUE J=0 SW ITCH=O.0 IF (XGUESS) 11,11,10..._ XF=XGUESS ___ ____ ___ _ __ GO TO 12 11 XF=O.800*AMV (3)/(AMV( 3)+ABV(3)) 12 CONTINUE J=J+1 IF (J-12) 53,54,53

382 P AG E... 2 54 EPS=O.C0028 GO TO 15 53 -IF (J-15) 55,56,55 56 SWITCH=0.0 EPS=O.CQ,10 XF=O.650 FMAX3=C6*A8V( 3) FMAXM=C6AMV( 3) FMAXT=FM AXM+FMAXR GO TO 15.........._.5....._CONTINUE........ IF (J-25) 15, 13, 13 13 WRITE OUTPUT TAPE 6, 14 14 FORMAT (1HO,33H NO XF CONVERGENCE WITHIN SIGNAL /) GO TO 23 15 RATE M=XF*DUMFLO RATER=PUMFLO-RATEM IF (FMAXB-RATEB) 26,36,36 36 CONTINUE C GET THE'TOTAL PRESSURE LOSS IN THE BOOST VENTURI CALL SOLVE (POHG,TOF, PHGiG, TOF, HUMID,ARV ( 3), RATEBWMO IST, 1 GKWET, FMAXB3 RHOB3,PBHG3, TBF3 RMACH3,SUCWR3 ) IF (FMAXB.3-RAT EB) 37,38,38 37 DtJOR B'=FMAXB3 GO TO 39 38 CU.MRB=RATEB 39 CONTINUE VEL R3=ODU.MR B* 144.0/ ( RHOB3*ABV (3) *3600. 0) POPBH G=.PO.HG-RHOB3*VELB3*VEL B3( ( 1.0-ABV( 3 V) RV(4) ** 2 ) /C2 C GET THE BOOST VFNTURI SUCTION AT THE FUFL DISCHARGE NOZZLE CALt SOLVE ( POHGTOF, POBHG, TOF, HUM ID, AB V( 3),RATFB,WMO IST, 1 GKWET FFMAXB4,RHOB4.,PBHG4, TBF4,BMACH4,SUCWB4 ) C TRY ARV(3) HERE IF BOOST SUCTIONS APE TOO LOW FMAXB=FMAXR4 I F FMAXB-RATE.B) 26.,27,27 26 RA'T EB=FMAXB RATEM=DUMFLQ-RATEB XF=R ATEM/DUMFLO GO TO 36 27 CONTINUE,-.._. -^...,,___ ^ -.,_. -..._ _.~......~........... _........... c C FLVAPB IS THE FUEL VAPOR MASS FLOIW RATE AT THE BOOST VENTURI EX C FLLIQB IS THF LIQUID FUEL MASS FLOW RATE AT THF BOOST VENTURI EX C BFA IS THE F/A RATIO OF THE VAPOR MIXTURE LEAVING THE BOOST VENT C FLVAPB=0. 5*RATEMF*FRACTR FLLI QB=O.5*R AT EM F*(1.O-FRACTB) BFA=FLVAPB/RATEB FLMI XR=RATEB+FLVAPR C GET THE PROPERTIES OF THE MIXTURE LEAVING THE BOOST VENTURI TOBR= TOR +BFA*HVAPOR/CPWET T OR F= TO BR-4 59.6 _ CALL XMIX (TOBF,POBHGHUMIDFTYPE,.TF.UEL,-RBFA,WMIXBCPM[iX, 1 CVMIX,GKMIX ) C FIND THE MAIN VENTURI MACH NUMBER AT STATION 4 DUtMMYM=RATEM/ 10C 0.0

383 3 POMHG= POHG-1.200*DUMMYM*DUMMYM C GET THE PRIMARY VENTURI THROAT SUCTION CALL SOLVE (POHG TOF POMHG,TCMF.,HUMID,AMV( 3 ),RATFMWMOIST, 1 GKWET,FMAXM3,RHOM3,MG3 TM PMAG3 TMF3,PMACH3,SUCWM3 ) FMAXM= FM AXM3 CALL SOLVE (POHG,TO F,POMHG, T CMF, HUMID,AM V (4, RATEM,WMO IST, 1 GKWETFMAXM4,RHOM4,PMHG4TMF4,PMACH4,SUCWM4 ) PM4W=13. 594*PMHG4 C FIND THE MACH NUMBER AT THE BOOST VENTURI OUTLET CALL SOLVE (POHGTOFPOBHG,TnBFHUMI,ABV(5),FLMIXBWMIXB, 1_ K __GKFMAIXBFM AX RB5, R HOB 5 PBHG5, T BF 5,BMACH5, SUCW95 PB5W= 13. 594*PBHGC 5 FMAXT=FMAXM+FMAXB IF (FMAXT-OUMFLO) 44,43,43 44 WRITE OUTPUT TAPE 6,30 51 RATEF=FMAXB _ ____ RATEM= FMAX M XF=RATEM/ ( RATEM+RATER ) DUMMYP= 1.0 GO TO 22 43 CONTINUE 41 IF (FMAXM-RATEM) 24,42, 42 24 RATEM=FMAXM XF=R ATFM/DUMFLO RATE R= DUMFLO-R AT EM GO TO 36 42 IF (SWITCH) 16,16,17 16 E1=PB5W-PM4W _ _ _____IFASF(ABSF(E1)-EPS.23,23,33 33 CON TINUF XFl. XF SWITCH=1.0 XF=XF -.010*ABSF(E1 )/El GO TO 32 17 E 2=PB SW-PM4W IF (ABSF(F2)- EPS ) 23,23,18 18 SAVE=XF IF (BMACH4-0.999) 45,45,46 46 IF (E2) 45,23,47 47 RATEB=FMAXB ___ ____RATE M=DUMFLO-RATEB XF=RATEM/OUMFLO GO TO 22 45 IF (PMACH3-O.999) 48,48,49 49 IF (E2) 50,23,48 50 RATEM=FMAXM -__- __ RAT EB=DUMFLO-RATEM XF=RATEM/DUMFLO GO TO 22 48 CONTINUE XF=XF-E2*( XF1-XF )/( E1-E2) XF1= SAVE _._.._____ ELiE. _____.__ —__._..-_._ _...... _ 32 CONTINUE IF ( X F-o0 500 ) 1.9 12,20 19 XF=0.0500 GO TO 12

384 PAGE 4 20 IF (XF-0.9500) 12,12,21 21 XF=0.95n0 GO TO 12 C C NOW fTH-.F. FRACTION OF THE AIR FLOW PASSING THROUGH EACH VENTURI C ANDt THE ROOST VENTURI SUCTION ARF KNOWN C 22 CONTINUE CALL SOLVE (POHGTOF,POBHG,'TIF,HUMIDABV(3),RATEBtWMOIST, 1 GKWETFMAXB34,fHOP4,PBHG4, TBF4BMACH4,SUCWB4 ) -__CALL SOLVE (POHG TO F POMHGTCMFHUMIOtAMV(3),RATEM WMO IST, 1 GKWET,FMAXM3,RHOM3 PMHG3,TF3, PMACH3, SUtCWM3 CALL SOLVE (POHGTFHGTF G,TOMF,HUMID,AMV(4),RATEM,WMOIST, 1 GKWET,FMAXM4,RHOM4 PMHG4,TMF4,PMACH4tSUCWM4 ) CALL SOLVE (POHGTOF POR HG,TO RBFHUM IDABV(5),FLMIXB,WMIXB, 1 GKM I X, FMAXB5, RHOPR5, PBHG5,TBF5,BMACH5, SUCW35 ) E2=1 3._594* (P HG5-PMHG4) IF (F2-0.0100) 23,23,57 57 E2=0.0020 23 PVFLO=RATEM RVFLO=RATEB PVMACH=PMACH3 BVMACH=BMACH4 PVSUCW= SUC WM3 PVSUCW=SUCWB4 XFV= XF IF (DUMM.YP) 40,4e0,34 3 __4__ ___ __WRITE OUTPUT TAPE _6 35 XFV, E, VENF LO, PVFL 0, BVFL 0, PVMACH, 1 BVMACH PVSUCW, BVSUCW PMHG4, P1BHG TOBFf, SUCWB3,F tMAX M 2 FMAXBJ 35 FOPMAT(F8.4,F 10. 4,F9.F 92,F 9.2 2,F9.4,F9.4,F8.3,F93F93,F93, 1 FP.3,F8. 2,F8.3,F8.1,F7.1, 14 ) 40 RETURN END

385 $_ CCOM,PILF FASTRANPUNCH OBJECT SUPROUT INF SOLVE (POHG,TCF, PCLHG,TOLF,HUM[, A,FLO,WMOLEC, GK, 1 OFLOMAX,RHOL,PLHG,TLF,XMACH,XSUC ) C BB1F( X)=1.0*/X BB2F(X) = { ABSF(X))** 2 BB3F( X)=X*A14 B B4F( X)=BB2F X)*A14 BB5F(X)=1., + A15*BB2F(X) BB6F X )=A8*BBSF(X ) BB7F(X)=l.O+GK*BB2F( X) RF8F(X)=A2/BB7F(X) BB9F(X =(1.O-BB2F X))/(GK*BB2F(X)) 3 l F( X )X=BB2F( X) /A8 B 1 F(X )=ELUG( BR2F(X)) B12F(X)=BB2F(X)/A7 - 1.0/A4 613F( X) =B82F( X/A7 - 1.0 B14F(X )=A8/R2F(X) - 1.0/A4 B1......(X)=- A3* 32X..).. B._ -,1. B17F(X )=A7 * ELOG (BB6F(X)) 818F(X )SQRT (BB6F(X ) B19F(X)=SQRT (B85F(X) )/A8**A9) B2CF( X)=1,/( GK*BB2F( X)) 821F( X) = A1.7*BB2F(X) / BB5F(X) B 22F( X )=BBS5F( X)_**A9 B23F( X)=BB5F(X)**A16, C C THE FOLLOWING FUNCTIONS ARE USED WITH NEWTONS METHOD TOPF(X)=C3*B22F(X) - X B OTF ( X)=A17*C3*X* f23F.( X)...__ YTOPF(X) = BB9F(X)+A7*ELOG(821F(X)) - HH YBOTF(X) = -2.,0*BB1F(X)*(B20F(X)-A7/BB5F(X)) QTOPF (X)=X*B19F(X )-Q QBOTF(X)=(BB5F(X)+A15*tBR2F(X ) * ( A8**(-A9) )/SQRT (BRR5F( X)) C _.____ AL 1_=-.I. ___ _____ _______.. _ _ _ __ -. —----------------------- A2 =GK+1.0 A3 =1.O/Al A4 =A2/A1 A5:=GK/A1 A6 =SQRT (GK) ____. A7 =A2/12.7~GK ____._...__ _ ______ ___ _____._ __ __ A8 =2.0/A2 A9 =A2/(2,0*A1 A 10Q=A 2**2 A 11-2.0* A3 A12=SQRT (2.0A 2)

386 PAGE.2..__ A 13=2.0*A 5 A 14=GK/2. A 15.=A 1/2,0 A 16= 3.0-GK)*.5/A1 A17=A?7/2.0 18=1.0/A6 C Q=l.O HH= 1 0 AGA IN=0.0 POPOQHG*O.49 2 POL'= POL HG*0. 4912 TOP= TOF+459.6 TOn R=TOLF+459.6 RHOL = 144. O*POL.*WMOLEC/ ( 1545.4*TOLR ) C1=SORT (GK*32. 174*WMOLEC/( 1545.4*TI. R ) C2= 3600. f*A*POLT*C1 C3=FLn/C 2 FLCM AX=C2/ 22F( 1.00) C4=L.O + ( 22F(1.0)-1.0)*FLO/FLnMAX IF (FLIMAX-FLn) 7,9,9 7 XMACH=1. GO TO 19 9 CONTINUE FPSLON=0.000050 C THIS IS AN INITIAL GUFSS FOR THE MACH NUMBER O)UM ACH= C4* C2 I TFR=G. ___.....H GE.= T P F.DU MA CH ) /B OTF (DUM ACH ) SAVE =nDUMACH nUMACH=rDUMACH- CHANGE I TF'R= ITER + 1 IF (AGAIN) 23,23,24 24 WRITE f UTPUT TAPE 6,25,ITER,SAVE,CHANGE, UMACH 25 ___ FORMAT ( 3n0X 18,3F12.6 23 CONTINUE 40 IF ( ITER-18) 13, 13, 11 11 WRITE OUTPUT TAPE 6,12 12 FORMAT (1HO,41H NO MACH NUMBER CnNVERGENCE WITHIN SOLVE ) IF (AGAIN) 21,21,14 21 _ _ AGAI N= 1. O GO TO 9 13 CONTINUE IF (DUMACH-1.000) 16, 16,15 15 DtU ACH= 1.0000 GO TO 10 16 IF ( DOUMACH) 17 17,18 17 DUMACH=O.00001 GO TO 10 18 CONTINUE IF (ABSF(CHANGE) - EPSLON) 14, 14,10 14 XMACH=DUMACH.....1 ___..____9 PLHG=PLHG/_ BB5F (_XMACH) **A5) XSUC=1 3. 594*.( POHG-PL HG ) TLP=TOLR/R85F( XMACH) TLF=TLR-459.6 RHOL =RHOLZ / BBF ( XMACH ) *CA3 )

387 3 20 RETURN END

388......................CO'MPILF FASTRAN, PUNCH OBJ CT PAGE 1 SUH ROUTINE XMIX (TOF, POHG,HUtMID0, FTYPE,TFtUELt, FA,WMOL, 1 CPMIX,CVMI X, KMIX ) C C THIS SUBROUTINE CALCULATES THE THFRMODYNAMIC PROPFRTIES OF AN C IDEAL GAS MIXTURE CONSISTING nF AIR,WATFR VAPOR, AND FUEL VAPnO C THIS IS DONE FOR ANY SPECIFIED FUE,FUFL-AIR RATIOPRESSURE, C _ __T EMPERATUPRE, AND HUMIDITY C C PO=POHG*0. 4912 TOR=TOF + 459.6 TF=TOF/100.0 PM MAXW=].. 3 2*TF*TF*TF - O.765*TF*TF + 0.413 TF OMEGA=0. 622*HUM O*PMAXW/PO C C GET AIR PROPERTIES C FLU ID=8. tCALL FPRP_(FLUIP _,TO FTOF,tDENSMVI SKMCORRCLIQ CPAIRCVAIR, 1 WAIRHVAPORSI GMAHEATV ) C C GET WATER VAPCR PROPERTIES FLU D=2.0 C_____ ALL FPROP (FLUIDTOF TOFOENSMVI SKMCORRtCL IQ CPH20,CVH20, i fWH20,HVAPORS IGMAHEATV ) C C GET FUFL PROPERTIES C CALL FPROP (FTYPETFUEL,TFUELDENSMVISKMCORR,CLI Q,CPFUEL, ____I_ CVFUELWFUEL,HVAPOR, SIGMAA HEATV ) C4=1.0 +FA +OMEGA C5=FA/WFUEL + 1.0/WAIR + OMEGA/WH20 WMOL-=C4 /C5 CPMI X= CPA IR+OMEGA*CPH20+FA*CPFUEL)/C4 C VM I X= C VA I R+OME GA*CVH 2+FA*CVFUEL ) /C4 GKMIX=CPM X/CVMI X RETUlRN END

389 $..............COMPILE MAD, PUNCH. O JECT 17 MAY 1967 VERSI-ON) PROGRAM LISTING......... EXTERNAL FUNCTION (Y,XXMINDELTA XFMF N,SCRACHXARG,YEST,.]1 DE BUG ) INTEGER I, J,M,N, ISTART, -MA X M,ME, MO INTEGER, R,NPOINT,NX,IKKOKKE,NDP,CCUN'T, NUM DIMAENSION X{?250 ENTRY TO STERL. M=FM DUml=FN DUM1=DUM1 - 1.0 N=DUM1....__ST. CHECK FOR OfBVIOUS ERRORS WHENEVFR N.L, 1 PRINT RESULTS N N=1 M=l END OF CONDITTONAL WHENEVER M.G.N PRINT COMMENT $0 M EXCEEDS N $ PRINT COMMENT $0 M WILL RE SET EQUAL TO N $ PRINT RESULTS MN M=N END OF CONDITIONAL WHENEVFR M.L.I PRINT COMMENT $0 M WAS LESS THAN I SO M WAS SET EQUAL TO I $ PRINT RESULTS M M=l END OF CONDITIONAL THROUGH SETUPIFOR I=Ot,,-I.G.N __ _DU.NM 2= I SETUP X(I)=XXMIN + DUM2*DELTAX WHENEVER XARG.L. X(0) PRINT COMMENT $0 THE X ARGUMENT IS SMALLER THAN THE MINIMUM $ YEST=Y{1)-(X(1)-XARG)*(Y(1)-Y(O))/(X(1)-X(O)) PRINT COMMENT $ AN EXTRAPOLATION HAS BEEN MADE $ XMIN=XXMIN XMAX=X(N) XVALUE= XARG YVALUE=YFST PRINT RESULTS XMIN,XMAXXVALUE,YVALUE TRANSFER TO DONE END OF CONDITIONAL _ WHENEVER XARG.G. X(N) PRINT COMMENT $0 THE X ARGUMENT IS LARGER THAN THE MAXIMUM $ YEST=Y(N)-(XARG-X(N))*(Y.(N)-Y(N-1l))/(X(N)-X(N-1)) PRINT COMMENT $ AN EXTRAPOLATION HAS BEEN MADE $ XMIN=XXMIN XVALUE= X ARG YVALUE=YEST PRINT RESULTS XMIN, XMAX,XVALUEYVALUE TRANSFER TO DONE END OF CONDITIONAL

390. WHENEVER. DEBU Rt G.E. 1.00 PRINT FORMAT NVALN VECTOR VALUES NVAL=$lHO S4C, 23H THIS DATA SET HAS N = 14 PRINT FORMAT ATITLE VFCTOR VALUES ATITLE= $1HO,S39,32H X ( I) THROUGH LIST,FOR IOQ,,lI.G.N LIST PR INT FORMAT NEATt I,X(I)(Y I ) VFCTOR VALUES NEAT=$1H,S30I, O,F15.,3,F15.3 *$ END OF CONDIT IONAL BEGIN THE INTFRPOLATION BY SETTING UP THF DIFFERENCE TABI FIND THE Y(I VALUE WHICH IS CLOSEST TO XARG AND USE THIS AS THE CENTRAL DIFFERENCE STARTING POINT UNLESS M EXCEE MMAX FOR THIS STARTING POINT WHENEVER XARG.G.X( C AND.(XARG-X( O ) LE ( X( )-X(O))/2*.O ISTART=1 TPANSFER Tn TESTM END OF CONDITIONAL WHENEVER XARG.L X( N).AND. ARG-XN-1)).GE ( ( XN)-X(N- 1) / [STAPT=N-1 TRAANSFER TO TESTM END nF CONDITIONAL THROUGH SCANFOR I=OL1,I.G.N WHENEVER.ABS. ( XARG- X I) ),L,. OC 01*( X(N)- XN-1 )) ISTART= I YFST=Y( I) TRANSFER TO DONE END OF CONDn ITIONAL -._. WHENEVER XARG.L. X(I), TRANSFER TO WHERE SCAN CONTINUE WHERE WHENEVER (X(I)+X( I-1)-2O*XARG).G.( CO) I START= I-1 nR WHENEVER.ABS.(X( I)+X(I-1)-2.O*XARG).L. (O.005 *(X(I)-X( 1 )).AND..GE.(N/2) ISTART=I-.. OTHERWISE ISTART=I END OF CONDITIONAL NOW THE OPTIMUM STARTING POINTY(ISTART),IS KNOWN NOW CHECK TO SEE IF THE CI FFER ENC TABLE - STARTI NG AT Y(ISTART), EXTENDS OUT TO THE DESIRED M VALUE TESTM WHENEVER ISTART.LE.(N/2) MAXM= ISTART*2 OTHEPW __I SE MAXM= (N-I START) *2 END OF CONDITIONAL THUSFOR THIS XARG,WE NOW KNOW THE MAXIMUM POSSIBLE VALUJ E OF M WHICH MAY BE SPECIFIED. __ __CHECK TO3 SEE..IF A LARGER M H A S BE EN. SP E C I F I EO_ WHENEVER M.G.MAXM.AND. I STAR T LE.(N/ 2 IST APT=( M+1) }/2 TRANSFER TO MOVEUP END OF CONDITIONAL

391 WHENEVER M..G,MAXM ISTART=N - ((M+1)/2) END OF CONDOITIONAL MOVEUP CONTINUE THE FOLLOWING TWO FUNCTIONS MAKE CONVENIENT USE OF....I NTEGER DIVISION R=(M+1) /2 NPOINT= (2*R)+1 NPOINT IS THE NUMBER OF DATA PPINTS REQUIRED FOR AN M-TH DEGREE EVALUATION USING STIRLING'S FORMULA THIS MERFLY ASSURES THAT THE SCRACH ARRAY IS INITIALLY ZERO THROUGH ZERO,FOR I=O,, I.GoN ZERO SCRACH( I)=O.O THROUGH SHIFTtFOR I=0,lI.G.(NPOINT-1) SHIFT SCRACH( I)=Y(ISTART-R+I) N...... OW_ST__ TO SEE IF M IS AN ODD OR EVEN DIFFERENCE BECAUSE THE ITERATION TECHNIQUE DEPENDS ON THIS'ODEVEFN=(-I).P.M WHENEVER ODEVEN.G. 0 M E= M NDI.)M=O0 OTHERWI SE ME=M-1 MO=M NDUM= 1 END nF CONDIT IONAL NX=2*N-1 NX IS THE MAXIMUM SUBSCRIPT FOR THE SCRACH ARRAY COUNT IS AN INDEX WHICH COUNTS THE NUMBER OF CENTRAL DIFFFR.ENCES THAT ARE SAVED IN THE SCRACH ARRAY K=0 KO= 0 KE= 0 COUNT = 0 _T_. THR OUGH_ BET A, FOR J=NPO IN.T- -. FJ. N DU M K=K+1 EVEND= (-1).P.K EVENOD IS A VARIABLE WHICH INDICATES WHETHER THECURRENT DIFFERENCE COLUMN IS ODD (FIRST COLUMN) OR FVEN (SECOND __ COLUMN) _THIS IS NEEDED BECAUSE WE RETAIN TWO VALUES FOR THE ODD CASE AND ONE VALUE FOR THE EVEN CASE. THROUGH ODDFOR I=C11,I.E.J ODD SCRACH(I)=SCRACH(I+1) - SCRACH( I) WHENEVER EVENOD.L. 0 KO= KO+ 1 _ ~__ 5.___SCR AC H(NX- 3 *KO+ 3 _) = SC RACH ( R-KO+1) SCR ACH( NX-3*KO+2 )= SCRACH ( R-KO ) COUNT= COUNT +2 OTHERWISE KE=KE+1 SCRACH(NX-3* KE+1 )=SCRACH (R-KE)

392 ___ CO Ul1-=COUNT +1 END OF CONDITIONAL BETA CONTINUE SWITCH TAKES THE DIFFERENCE VALUES FROM THE UPPER PART 0 THF SCRACH ARRAY AND PLACES THEM IN THE LOWERMOST PORTIO THROUGH SWITCH,FOR I=O, 1I.E.COUNT SW I T C H SCR AfAH( I) =SCRACH (2*N-COUN T +I) SCRACH( COUNT )=Y( ISTART) THE SCRACH ARRAY IS NOW IN ITS FINAL ORDFRED FORM, WITH SCRACH(O) CONTAINING THE HIGHEST FORWORD DIFFERENCE NOW COMPUTE ALPHA AND EVALUATE THE INTERPOLATING POLYNOMIAL FOR THIS VALUE OF XARG. ALPHA=(XARG-X( ISTART))/(X(ISTART+1)-X(ISTART)) E=SCRACH( 2*(M-ME) ) THROUGH ETFRM,FOR I=ME,-2 t,I.L 2 ETERM E=E*( (ALPHA +( -2)/2.0)*(ALPHA-( I-2)/20) )/{I* I-l1)) 1 +SCRACH( 3*( ( MF- I2 / 2) + 2 ( M-ME ) NOW ALL OF THE EVEN TERMS HAVE REEN EVALUATEDINCLUDING OD (SCRACH(M-MO)+SCRACH(M-MMO+1))/2.0 THROUGH OTERMFOPR I=MO,-2, I *L.3 OTERM OD=OD^)((ALPHA+( I-])/2.O)*(ALPHA-(I-1)/?20)) /(I*(I-l ) 1 + (SCRACH(3*( (MO-I+2)/2?)+(M-MO) )+SCRACH(3*( (MO-I+2 /2 2 +IM-MO+1) )/2.0 00=ALPHA* O NOW ALL OF THE ODD TERMS HAVE BEEN EVALUATED YES'TE+OD DONE CONTINUE WHFNEVER DEBUG.E. 1.00 PRINT COMMENT $ STERLING HAS COMPLETED AN INTERPOLATION PRINT RESULTS MNtXARGtYEST END OF CONDITIONAL FUNCTION RETURN END OF FU NCTION

393 $.$~-.-....CO.P IL_ FASTRAN,. PUNCH OtBJECT 1 _..SU.R OU-TINE FPROP (FLUI D, T E MP, TMAN, E N SM,VISK M,CORR,C LI Q, I CPFUEL,CVFU EL,WMOLEC,HVAPOR,SIGMA, HEATV ) C C SIGMA IS THE SURFACE TENSION OF THE FLUID IN CONTACT C WITH AIR IN DY'NES/CM C C _ EST FIT CURVES FOR SPECIFIC GRAVITY AND VISCOSITY C C ISO-OCTANE...... FLUID)=0,0 C STANDARD REGULAR,.FLU0= 1.0 C WATER...... FLUID=2.0 C ETHYL ALCfOHOL.....FLUID=3.0 C _SHELL PREMIUM. F.... FLUID=4.0 C CLARK 100,)..... FLUID=5.0 C MARATHON REG..... FLUID=6.C C MINFRAL SPIRITS....FLUID=7.0 C AI R............FLUID=880 C SWITCH=0_..0 20 IF (FLUID - 0.0) 21,30,21 30 SWITCH=i.0 DENSM=0. 72 19-O. 00043826*.TMP VISKM=-0.4378 + 313.3462/(TEMP +200.0) CORR=SQRT ((0.721 9-0.00043826*TMAN)/DENSM) CLIQ = 0.4800 CPFUEL= 0.4000 CVFUEL= 0.3810 WMCLEC= 114.00 HVAPOR= -141.0 SIGMA= 22.2000- 0.050* TEMP HE AT V= 1_9 C80. __, GO TO 10 21 IF (FLUID - 1.0) 22,31,22 31 SWITCH=1.0 DENSM=24720.0/(TEMP +6270.0)-3.172 VISKM= 135.79/(TEMP +132.5)-0.0830 COPR=SQRT ((24720,O/(TMAN+6270.0)-3,17)/DENSM) CLIQ = 0.5810 CPFUEL= 0.4000 CVFUEL= 0.3810 WMOLEC= 126.00 HVAPOR= -142.0 ________ S I GM A= 24. 1000 O.,__0 B E. -_, I_' ___.._T__.__-................_._....... HEATV=19000.0 GO TO 10 22 IF (FLUID - 2.0) 23,32,23 32 SWITCH=1.0 OENSM=I.000-0.000133*TEMP

394 PAGE 2 VISKM=-O.1570+1O2.0/(TEMP +20,0) CORP=SQRT ((1.00-0.000133*TMAN)/DENSM) IF (TEMP-32.0) 14,14, 15 14 VISKM=1.00000.0 15 _ CONTINJUE CLIQ = 1,.O00 CPFtJEL= 0.4600 CVFUEL= 0.3600 WMPLEC= 18.016 HVAPOR= -1125.C'0+-1.5625*TEMP _ SIGMA= 72.7 HEAT V= 00000.0 GO TO 10 23 IF (FLUID - 3.0) 24,33,24 33 SWITCH=1.0 DENSM=0.830-0. OC0340*TEMP V ISKM=-0 0890+'346.0/( TEMP +190.0) COPR.=SQRT ((0.830-0.000340*TM/AN)/DENSM) CLIQO 0.4800 CPFUEL= 0.4600 CVFUEL= 0.4070 WMOLFC= 46.000 HVAPOR= -361.0 SIGMA= 2.6. 86- 0. 04 * TEMP HEATV=11550.O GO TO 10 24 IF (FLUID - 4.0) 25,34,25 34 SWITCH= 1.0. DENSM=0.7893-O.000472*TEMP VISKM=C. 7710-0. C02440*TFMP CORR=SQRT ((0.7893-0.000472*TMAN) DENSM) CLIQ = C.4800 CPFUFL= 0,4000 CVFUEL= 0.3810...........WM 1L EC= 126.00............... HVAPOR= -142.0t SIGMA= 2-7.20- 0.052. - TEMP HEATV=19000.0 Gn TO 10 25 IF (FLUID - 5.0) 26,35,26 35 SWITCH=1.0 DENSM=0. 7480- (0. 00040) *TEMP VISKM=0.6740-(0.001933) *TEMP CORR=SORT ((0.7480-(0.000400)*TMAN)/DENSM) CLIO = 0.4800 CPFUEL= 0.4000 __ CVFUEL 0. 3810 WMOLEC= 126.00 HVAPOR= -142.0 SIGMA= 25.30 - 0.052 * TEMP HEATV= 19000.0 GO TO 10.._._........._ 26 _.___ I_F__ (FLUID_-_6.0 ) 27_,36,27 _-.....__,__ _........................... 36 SWITCH=1.0 DENSM=2328.56812/( TEMP *1.8+32.-2074.76544)+2.03898 VISKM=118.12441/(TEMP *1.8+32.+77.16928)-.07321 CORR=1,.0

395 33 CLIt = 0.51 50 CPFUEL= 0.4000 CVFUEL= 0. 3810 WMOLEC= 126.00 HVAP.R= -1420.... SIGMA= 24.80- 0.049 * TEMP HEATV= 19000.0 GO TO 10 27 IF (FlUID - 7.0) 28,37,28 37 SWITCH= 1. _ DENSM=C0.6409 + 41.88/(TEMP +215.0) VISKM= -0.1250 + 201.0/( TEMP +65.30) CORR=SQRT ((0.6409+41.88/(TMAN+215.0))/DENSM) CLIQ=1.0 CPFUEL=0.5 CVFUEL=0.4 _WM'OL EC= 00.0 HVAPOR= -10.O0 SIGMA= 38.60-'0 07 *E TMP HEATV=19000. 0 GO TO 10 28 IF (FLUID - 8.0) 10,38,10 38_ __ SWITCH=1.0 DENSM=0.6360/(TEMP +459.6) VISKM= 12*.0774+4. 6452*TEMP /100.0 CORR=1.0 CLIQ = 0. 000 CPFUEL= 0.2410 _ _ CVFUEL= 0.1710 WMnL EC= 28.950 HVAPOPR= — 000.0 SIGMA= 0.00C0 HEATV=00000.0 10 IF (SWITCH) 11,11,12 11 __ WRITE OUTPUT TAPE 6............... 13 FORMAT (1H4,68H THE VALUE OF FLUID IS NOT BETWEEN 0.0 AND 8.0 1 TTHE VALUE IS,F10.3 ) FLUI D=1.0 GO TO 20 12 CONTINUE ____ RETURN END

396 COMP IL E MIAD _n (1967 VERSION) PROGRAM LISTING...... EXTFRNAt. FUNCTTON (XXYYPOINTS, XM IN,GXYM INGY, VAR1,SAMEX, 1 FSYMBn,X, YO,FTYPE,FRUN,TEMP,MAIN ) INTEGEP SYM BOL, NPOINT,J T,TYPE,RUN INTEGER K ENTRY TO CALMAP. S.AMAX=SAME X SAMAX=0.....SFT GRID,END PLOT SAMAX=1. n...END PLOT ONLY SAMAX=2.0...SFT GRID ONLY SAMAX=3.0...NFITHER XORIG=xn YOR =YOr DX=GX DY=GY _CHANGE TO INTEGER. FORM NPO INT=POIT NTS RUN:FRIUN SYM ROL= FSYMR TYPE=FTYPE P, TRFC. PLTSIZ. (1i000) WHENEVER SAMAX. E.1.0.OR.SAMAX. F. 3.,tTRANSFER TO NEXT4 BEGIN A PLOT DRAW THE X AND Y AXES WHENEVER MAIN.G, 1.50 PAXIS. XO RGYORG,YMAPT,+28t7. 50, 9n.O,YMIN Y,0.500) PENUP. (0.670,6.400) PFNDN. (0.670, 7.500) PENON. (0.5670,6.400}) PAXIS. (XORG, YORG, tXMAPT,-38,7. 5 0, 0., XM IN,DX,. 500) PENUtP. (2. 500,,.570) PENDN. (7.500,0. 570 PENDON. (2.500,0.570) PLTOFS. (XMIN,DX,YMIN,DY XORG,YORG ) PGRID. (XORGYORGO.50,.50, 15,15 ) PSYMB._I (70,9 50, C20, HEADM n.On.Ot ) PENUP ( 1. 700, 9.45 ) PENON. (7.300,9.450) PENDN. (1.700,9.4C50) PSYMB. ( 1..90 o9.00,..14, TFSTM,0.00,48 ) PSYMB.( 2.1,8.70,0o14tMAPINF,0o.00,8 ) PNUMBR. (2.60,9.00,0.14,VARl,0.00,$f5.2*$) PNUMBR. ( 3. 70 8. 70, O. 14, FRUN,0.00, $F5. 1 $ ) P INUMBR. (6.97,9.0, 0.14, FSYMB,000,$F 5. * PNUMBR. (6.55, 8.70,t0.14,FTYPE,0.0, $F4.2*$ ) PNUMR. (4.45,9.00,O.14,TEMP,0.0,,F5S.1$ ) END OF CONDITIONAL

397 WHFENEVER MAIN.. 1. 59 PAXIS.XORG, YORG, YMAPT,+28 38, 50,90.0,1 YM TN,,DY.42 59) PENlON. (.7 X N0,8 N.0) PENDN. ( C. 70,6.65' )^ PAXIS.( XORG,YOPG,XMAPT,-38,6.375,., XMINX rX 4250 ) PENSP.( 2.2 _450,.61,0) PFNN. (. 0, I. A 1O ) WHENEVEy.'PRI 2 IN rT, 25NPt OI OM335 PSYM. (2.20,1,50..2"0,HAD'?M,03.^0,33 ) _ PFNUP.G ( 1. 0, J0,: 1I 45P ) PENTIN. (6U..801 45 PEN DN( 1, 20' 1.,45 PSYTRB. (1.4VAL., I1 4TE STM, A 0 MA48 ) PSYMR. ( 1.6t 9 7n r, 14 tMIA P I NApF t 0.0 L H8 P VNA S MTRFT.. I$ 1, 4 1,VAR1 0.,.$FH5.?) PNLUMBR.I3.2,_19,T70o.14,FRUN,Oi,00 $F5. 1. Ok).MP:N.BR.. (6,4710n,:.,....,. ),...... PN. MRR..5,. 7n,0.14,FTYPE,,',.F4 2*$ ) P..U.M....:,1. 0, 14 TEMP,0,00$F5I 1' ) END OF CONOIT[iNAL PRINT FORMAT SPACE VFCT..,R VALUES SPACE =$. HO *C. PO TWHENV ER NPfI 3:3 5H ATPO NT K=0 PRINT COMMENT $ THE OPERATING MAP GRID HAS BEEN DRAWN THROUGH CHECK, FOR J=0,1 J. E.NPOI NT WHENEVER XX(J).L. 1.0.OR, XX(JI.G. 35.0,K=K+1, C ON T I NUE J NPOI NT= NPOI NT-K VECTOR VALUES XMAPT=$ INTAKE MANIFOLD PRESSURE IN INCHES HG $ VECTOR VALUE S YMAPT=$ L,OIST AIR FL.TW IN LBM/HOt..tR $ VECTnR VALUES HFEADN=$ CARBURETOR-ENGINE OPERATING MAP $ VEC FfTOR VALUES TESTM=$ PO= HG TO= F HtUMID ITY= V F CT=R VALUES MAPINF='.DISPL_ACEMENT= COMPRATIO= $ XS= XORG + (XX( ) - 00 O,)/D X YS= YORG+(YY(1)-,O )/DY PENUP. (XSYS) PLOT THE DATA POINTS NPOINT= -NPOINT SYMB ROL = +1 T=O WHENEVER FSYMB.L. 0.0, T=+l PLINE. (XX[( 0) tYY (0 ), NPOI NT 1, T, SYMBOL 1 )! NPOINT= -NPOINT PLINE,.(XX(O) YY(O),NPOINT, 1,TSYMBOLt1) WHENEVER SAMAX.G. 1.50,TRANSFER TO EXTR4 PL. TEND. CONTINUE FUNCTION RETURN __ ENTRY TO CALMVH. XOR G= X O YORG=YO SAM AX= S AM EX DX=GX

398 OY= GY NJ PO INT=PO INTS RUN =FR!.N SYcM 3BOL = FS YM R TYPE=FTYPF PLTRFC. WHENEVER S MAX.E.. I.On..TRSAM AX.F,3.0, TRANSF FR TO NEXT BEGIN A PLOT DRAW THF X ANn Y AXIS...[N=O. INDEPENDFNT PLOTTING VARIABLE IS MAIN JET LOSS MAIN=1. I NDEPENDENT PLOTTING VARIABLE I S BOOST SUCTION MAIN=?,: INDFPENDENT PLOTTING VARIABLE IS ENRICH. LnSS WHENEVER MAIN,.. Q. PAX I S. XRG,YORG, XTITLD,-43,7.50,t On., XMIN, DX r.75 ) VECTPOR VALUE1S XTIUTLD=$ MA-IN JET PPRSS!JRE DROP IN INCHES OF WAT.R END OF CONDITIONAL WHENEVER MAIN.E. 1.0 PAX S( XORG, t YOR G, XTITLF — 42,7.50,'0.0,r XM IN,Dt X t 0.75 ) VFCTOR VALUES XTITLE=$ BOOST VFNTURI SUCTION IN INCHES OF WATER $ FN!D OF CONDITIONAt.. WHFNEVIR MAIN.F. 2.0 PAXIS.(XnRG,YnRG, XTITLF, -5,7.5nO.O, XMTNDX,0.75 ) VFCTOR VALUES XTITLF=4 ENRICHMENT OR..IFICE PRESSURE DROP IN INCHES 1 TER $ END OF CONDITIONAL PAX IS. (XRG,YORG,YTITL,+32,7,50,9.n, YMIN Y, r, 75 ).VCT.:OR VALUES YTITL =$ FUFL FLOW RATE IN LRM/HnrUR $ PIT TOFS. (XMI N, DX,YM IN,:DY, XOPR.G,YORG ) PGR ID. ( XnRG,YORP G,01.75,O. 75i, 10, 1..) PSY'MB. ( 1.7,9.5C,0n.2 O,HFADN,0,.3 8 ) VECTOR VAtLUES HEAf)N =$COMPUtTER PREDICTION OF FUEL FLOW RATE $ PSYM.B. ( 1.8,9.'00,. 1.4, TEST2,0.3,49)...CTOR VALUES TEST2=$ MAIN ORIFICE NUMJFP= FUEL TEMPERATU PSYMB. (2..,8.7.0,n.14,INFOR 0.0,014) VECTOR VALUES INFOR =$ RUN NUMBEFR = $ PSYMB, (5.4,8.7,. 14,Lt TQUID,0.n,14) VECTOR VALUES LIQUID=$ FUEL = $ PNU MB. (P [ 3.6,8.7,O,0. 14, RUN,.0,$.1 7$ - PNrJ Mfi R. ( 7.4,_ 9., _.0 0 14, 4TE M.P 0.0 $ F 5. 1* _ PLOT THE DATA POINTS NEXT PL. I NF. X X ( 1 ), YY( 1 ), NPOI TNT, 1, TYPE, SYMBnL, 1) WHENEVER SAMAX,G. 1.5,TRANSFER TO EXTRY PLTEND. EXTRY CONTINUE FUN CTIfON RETURN ENTRY TO CALLOG. XORG=Xn YORG=YO SAMAX=SAMEX ) X=GX DY=GY__ __ NPO INT=POINTS — RUN=F- R UN SYMROL= FSYMB TYPE=FTYPE WHENEVER SAMAX.E.1.0.OR.SAMAX.E.30 TRANSFER TO NEXT3

399 __DRAW THE X AND Y AXIS WHENEVER MAIN.E.'.O PLGAXS. ( XORG,YOPG, XTITtL -M43,7.50, OO.C,XMINDX VECTOR VALUES XT.ITLM=$ MAIN JET PRESSURE DROP IN INCHES OF WATER $ END. OF CONDI[ TI )N At. WHFNEVFR MAIN.F. 1.0 __ LGGAXS. (XORTG, YnR(?',,XTITLN,-4?2,7.50,-.O,XMIN,DX ) VFCTOR VALUES XTITLN=.t ROOST VENTURI SUCTION IN INCHES OF WATER I END OF CONDITIONAL WHENEVER MAIN.E. 2.0 PLGAXS. (XORGC,YORG,XTITLO,-S3,7.,^OO'.OXM'IN,DX VECTOR VALUES XTITLO=$ ENRICHMENT ORIFICE PRESSURE DROP IN INCHES OF WA I TER $ END OF CONDITIONAL PLGAXS. (XORG, YORGYTITL3,4+33,7.50,90., YMIN,DY ) VE:CTOR VALUES YTITL3=$ FUEL MASS FLOW RATE IN LRM/HOUR. $ PLTFIFS. (XMTINDX,YMIN,DY,XORG,YORG) Xn= 1. o/DX YP I =1./DY PL!GGRD. (XORGYOPGtXD,7.50,+7.5, 0. ) PLGGRD. (XORRG YOR G,tYD, 7.50,- 7.5, 90. O)) PSYMB. (1.5,9.5n,C.?0,HEAD3,0.0,49) VECTOR VALJUES HEAD3=$PREDICTION OF MAIN FUEL Fl OW PARAMETERS S PSYMR. ( 1.8,9.. 0n,0.14, TEST6,"..0o49) V_ ECTOR VALUFS TEST6.=$ MAIN ORIFICF NUtMRER= FUEl TEMPERATURE = $ P S Y M. { 2.0, 8-'"7':- i. 1:4-p I F.0 R-3,. 0, 1/+ ) 4... VECTOR VALUES INFt)PR3=$ RUN NUMBER = $ PSYMB. (5.4,8.70,n. 4,.LI,ID,.Ot 4), VECT]OR VALUES LIQLUID=$ FUEL = $ PN..MR (3.6,8. 700t, 0.14, R UN n 0$1 7*$ ) PNUMBRR. (7., 9.C00. 14tTEMP, O.o$F5.1$ PLOT THE DATA POINTS PLTLOG. (3) PI, INF. (XX( 1),YY ( 1),NPOINT, 1,TYPE SYMBOIL.I) 1 P TR EC. WHENEVER SAMAX.G. 1.5,TRANSFER TO EXTR3 PLTEND. TRANSFER TO EXTP6 CONTINUE CON T INUE FUNCTION RETURN ENTRY TO CALAVHo XORG=XO YORG= YO SAMAX=SAMFX DX=:GX DY= GY NPO INT=POINTS RUN =FPRUN SYMB OL=FSYM - TYPE=FTYPE PLTREC. WHENEVER SAMAX.E.1.0.OR.SAMAX.F.3.0,TRANSFER TO NEXTA PAXIS.( XORGYORGXAIRT,-42t,7.50,O0.0,XMIN,DXO.75 ) PAXIS. ( XORG t YORG YAIRT, +3 t 3,7.5,90. OYMI N, DY,O. 75 ) VECTOR VALUES XAIR T=$ BfROOST VENTURI SUCTION IN I-NCHES F WATER $ VECTOR VALUES YAIRT=$ AIR BLEED FLOW RATE IN LBM/HOUR $ PLTOFS. (XMINDXYMINDYXORGYOR. G ) PGRID. (XORGYORG,0.750.75,10tIn ) PSYMBR(1.5,9.50,0.?,0AHAD,0.,0 49 )

400 VF CTfR VALUES AHFAD=$ CrfMPI. TFER PREfOCTION.F AIR BLEED FLOW RATE P SYMB. ]..8,9.9 It 1.4, ATFET T, o,4t 9 VECT1!R VALUES ATEST=$ AIR BLF F DIAMETERS= FUEL TFMPERAT..lR PSYMB. ( 2. t 8. 70,.0 14 ANFORMt,.0 n 14 4 VECTO VR VALUES ANFORM=$ RUN NUMBFR = $ PSYMB. (5.4t,8.7'.,, *14,FLOAI,..,14) VECTOR.. VALUEFS FLOA IR=$ Fl.IFL = PNUMBRR. (, 6 B. 7Tn, o. 14, RUN ~.n. $I 7*f ) PNIUMBR (7.4,9r09 C,0. 14,TEMP,.' $FS5. 1t PLOT THE DATA POINTS NEXTA CPL INE.( XX ( I ), YY ( 1 ), NPOINT, 1, TYPF SYMBOL l 1) WHENEVER SAMAX.G. 1.5,TRANSF R TO AFXTR __ PLT ENDF AEXTR CONT INUt E FUNCTION RETURN END OF FUNCTION

401 COMPII F MAO [AY 1967 VFRSION) PROGRAM t ISTING......... FXTFP'NAl''FUNCTIO.N (XX,YY,POINTS,XMINGX,YMIN,GY, VAR]1,SAMEX,. FSYM-,XO,YO, FTYPE,FRJUNTFMP,MAIN INTEGER SYMROL, NPO I NT J,T,TYPE RN.. ENTRY TO CALCVP, x RG Xn XflRG= XC) YORG= YO SAMAX=SAMFX OX=GX DY= GY N PNT = POINTS RUN =F P. t,N M _ SYBOL= F S YM. TYPEI=FIYPE Pt TREC. WHFNEVER SAMAX.F.1,I..ORSAMAXF. F.'3,0,TRANSFER TO NXTPLT rEGIN A PLOT DRAW THE X AND Y AXIS WHENE VER MAIN F, 0. 0 PAXIS.( XOPRGYVRGY ITLA, + 3 7,7t%9fl.3, YMINDvY'.7 )f VECTOR VALI.UES YTITLA=$ MAIN JET COEFFICIENT OF DISCHARGE $ P SYMB:..3,9.50,.r20,HEfADNA,00.C,I44 ) VFCTOR VALUES HFEADNA=$ MAIN METERING OPIFICE CHARACTERISTIC CURVF $ END OF CONDITIONAL WHENEVER MAIN.F. 1.0 PAX IS. XORGYOR.G,YTITLRB + 3 9 t7 9., YMIN DY, 75) VECTOR VALUES YTITLB=$ MAIN CHANNEL COEFFICIENT OF DISCHARGE $ PSYM. ( 1.3 9, 5,0. 20, HE ADNtR O,. 35 VECTOR VALUES HEADNB=$ MAIN CHANNFL CHARACTERISTIC CURVE $ ENf OF CONDITIONAL WHENEVER. MAIN F.. 2.0 PAX I S. ( XOR, YORG, YTTI.C C,+45'7,90, YMN IDY,. 7) VFCTOR VALUES YTITLC=$ ENRICHMENT ORIFICE COEFFICIENT OF DISCHARGE $ PSYMB1.3t9,..50 0....20,HEADNCO0.0,n41 ) VEFCTOR VALUES HEADNC=$ ENRICHMFNT ORIFICE CHARACTERISTIC CURVE $ END OF CONDITIONAL PAXIS.(XORGYORGXTITLR -34,7. 50,".0,XMIN.DX,.75 ) VECTOR VALUES XTITLR=$ REYNOLDS NUMBER OVER ONE THOUSAND$ PITOF S. (XMI N, DX,YMIN,DYXORG, YO RG) PGRI. (XORG,YORG,.75,.75,10,10) PSYMB.( 1.8,9.00,O.14,TFST 1,.0,49 VECTOR VALUES TEST1=$ MAIN ORIFICE NUMBER= FUEL TEMPERATURE = $ PSYMB._(2.0,8,.7n.14, INFORM,0.0,14 ) VECTOR VALUES INFORM=$ RUN NUMBER- $ PSYMB. (5.4,8,70, 0.14tL IQU ID,c'"14) VECTOR VALUES LIQUID=$ FUEL ='$ PNUMR. (3.6, 8. 700, 0. 14,RUN tO.O,$I7T ) PNUMBR. (7. 4,9. 00C,. 14, TEMP,O.O, $F5. 1*5 ) PLOT THE DATA POINTS _ f PI. INF. (XX(1),YY(I1),NPOINT,1,TYPE, SYM.OL, ).WHENEVER SAMAX.G. 1.5,TRANSFER TO EXTRA PLTEND. CNNT INUE FUNCTION RETURN

402 ENTRY TO CALCVM. XORG=XO SAMAX=SAAMFX DX=GX DY=GY NPOINT=PO. INTS R IU N F R i J N SYMBnL=FSYMR TYPE=FTYPF PITRFC. WHENEVER SAMAX E. I OR. SAMAX.F, 3.,TRANSFER TO NEXT2 ___DRAW THE X AND Y AXIS WHENEVER MAIN *F. 0.0 PAXISo (XnRG,YORG,YTITLJ,+32,7. 50,9n., Q YMINDY, n75! VECTOR VALUES YTITLJ=$ MAIN JET DISCHARGE COEFFICIENT $ PSYMB.( 1.3, 9 5.C,O.20, HE ADJ, 00. 45 ) VFCTRP. VALUES HEADJ=$ MAIN JET DISCHARGE COEFFICIFNT VS FtL.W RATE END OF CONDITIONAL WHENEVER MAIN.. E 1. PAX I S ( XORGYORG, YT I TLK, +41 7.50, 9., YM IN, Y,0.75 ) VECTOR VALUFS YTITLK=.$ MAIN FLOW CHANNEL DISCHARGE COEFFICIENT $ PSYMR.(1.3,9.50,0.20,HEADK,O0.O,45 ) VECTOR VALUES HEADK=$ CHANNEL DISCHARGE COEFFICIENT VS FLOW RATE END OF CONDITIONAL WHENEVER MAIN.F. 2*0 PA XI S, ( XORG, YOPG, YTITLL,+4?,7,50-C', 9.. O, YMIN DY,. 75 ) VECTOR VALUES YTITLL=$ ENRICHMENT ORIFICE DISCHARGE COEFFICIENT $ PSYMB,.( 1.3,.50,.0.?OTHEADL,OO.n,45 ) VECTOR VALUJES HEAD)L=$ ENRICHMENT ORIFICE COEFFICIENT VS FLOW RA. TE __ NOF CONDITIONAL PAXIs,( XORG,YOPGXTITL?2,-33,7.5O,.O,XMINOXO.75 ) VECTFOR VALUES XTITL2=$ FUEL FLOW RATE IN LBM/HOUR $ PL TOFS. (XMIN,DX,YM IN, Y,XORG,YORG PGRID. (XORGVYORG,.i 75. 75, 10,1 1 PSYMB.( 1.8,g9.r00.,0, 14,TEST5,n.O49 VCTOR VALUES TEST5=$ MAIN ORIFICE NUMBER= FUEL TEMPERATU PSYMB.(2.0,8.70n,014, INFOR2,0.0,14 VECTOR VALUES INFOR2=$ RUN NUMBER = $ PSYMB. (5.4,8.7,0.14 LIQUID,0.0, 14) VECTOR VALUES LIQUID=$ FUEL = $ PNUMBR. (3.6,8.,7C0, 0. 14,RUN, 0.0, $17$ ) ~__.PNUMBR. (7.4,9.000,0.14,TEMP,0.0,$F5.15s _ PLOT THE DATA POINTS NEXT? PLINE. (XX(I),YY(1),NPOINT, 1,TYPE,SYMBOFL,1) WHENEVER SAMAX.G. 1.5,TRANSFER TO EXTR2 PLTEND. EXTR2 CONTINUF UNCTION RETURN ENTRY TnO CALCVH. XOR G= XO YORG=YO SAMAX=SAMEX ) DX= GX _______DY= GY ____ NPO INT=POINrSTS RUN=FRUJN SYM ROL= FSYMB TYPE=FTYPF PLTREC.

403 WHENEVFR SAMAX. F...O.R. SAMAX. E..0, TRANSFER T(O NFXT1 DRAW THE X AND Y AXIS WHEtNEVER MAIN.E. 0. - PAXIS. (XORG,YOPGtXTITLG, -47,7., O.,O XMIN DX,.75 ) PAX IS. ( XF. PR3,, YORG,YTITLG,+32,7. 0,90. O,YMI NT, Y,f0.75 PSYMP. 1.1,9.,* 01O.20,HEADG,: t.., r49 VECTOR VALUES XTITI.G=$ MAIN ORIFICE PRESSURE DROPn IN INCHES OF WATER $ VECTOR VALUES YTITLG=.. - MAIN JET DISCHARGE COEFFICIFNT $ VECTOR VALUES HEAOG=$ MAIN JET DISCHARGE COEFFICIENT VS PRESSURE LOSS $ END OF CONDITIONAL WHENEVER MAIN.E. 1.0 PAXIS ( XORG,YOR G,XTITLH,-42,7.*5t,00 XM IN, X,. 75 ) PAXIS. (XORG,YORG, YTITL G,+3,7.5 +2,90.P,YMIN,DY,.75 ) PSYMBR. 1..1, 9. 50, t.20,1EADH, 00.0,49 ) VECTOR VALUIES XTITLH=$ BOOST VFNTURI SUCTION IN INCHES OF WATER $ VEfCTOR VAl.UFS YTITLH=$ MAIN FLOW CHANNEL DISCHARGE COEFFICIFNT $ VFCTOR VALUFS HFADH=$ CHANNEL DISCHARGE COEFFICIENT VS nBOST SUCTION $ END OF CrlONDIT IONAL WHENEVFR MAIN.F. 2.0 PAXIS. R,,IXO1YnRG, XTITL. I,-53,7.50n*..,XMI.7 PAX IS.(XORGi,YORGYTITLI,+42,7.5 C0,90.,YMINOY,0.7 7 PSYMR.(. 1 9..50, 0. 20?,HE AD, I 00.0, 49 ) VFCTOR VALUFS XTITLI=$ ENRICHMENT ORIFICE PRFSSURE DRCOP IN INCHES OF WA 1 TER $ VECTOR VAL.ES YTITLI=$ ENRICHMENT ORIFICE DISCHARGE COEFFICIENT $ VFCT-OR VALUFS HFADi=$ FNRICHMENT ORIFICE COEFFICIENT VS PRESSURE LOSS $ END OF CONDITIONAL PLTOFS. XMIN,DX,YMIN,DY,XORG,YORG) PGRID.(XOf yoYRGt,0::.75.7, t, ) P SYMB. ( 1.8, 9..0,.,. 1.4,TfST4,F.t t 4q ) VECTOR VALUES TEST4=$ MAIN ORIFICE NUMBER= FUEL TEMPERATURF = $ PSYMR.( 2.0, 1 8. 70, C. 14, INfnPI1 t0. 0, 4) VFCTOR VALUES INFORI=$ RUN NUMBER = $ PSYMB. (5.4,8.70,0.14,LIQUID,0.0,14} VECTOR VALUES. IQ1 IO=$ FUEL = $ PNUMBR. ( 3.6, 8. 7',0..14 RUN, t.O, $I7*$ PNtUMR. (7.4,99.C:00,O.*.14,TEMP,0.0,$F5.1*$ ) PLOT THE DATA POINTS PL.NE. ( XX(1),YY( 1,NPOINT, 1,TYPE, SYMBOL, ) WHENEVER SAMAX.G. 1.5 TRANSFER TO EXTR1 PL TEND. CONTINUE F UNCTION RETURN END OF FUNCTION

404 4 ~ f~l~ COMPILE MA{. (1.7 MAY 1967 VERSINN) P ROGRAM LISTING.. EX TP....N AL Fp... uNCT ITO f)N (XX, YY,PO I NT S, XM IN, G X, YM IN,tGY,.V AR, IS A ME X 1.F SY tXO, YOFTYP F RUNt TFMPMAIN ) INTEGERP SYMBOL, NPOINT,TYPE, UN ENTRY TO CALIVA. XORG= X-O Y OR G = Y.. SAMAX=SAMEX ) X = G; X r)Y= GY NPO. INT= PO INITS RUsN=FRI.N TYPE=FTYPf PLTREC. WHFNEVFR SAMAX.E. 1.0.OR, SAMAX.E. 3., TRANSFER TO NFXTIA BFGIN A PLOT DRAW THE X AND Y AXIS XT= 8. 92 5/14. 00 PAXIS. (XORG,YORG,YTITL5,+2?, 6.375,gr,0, 0,nYYT ) PL. TOFS. {(0DX,0 O DY,XORG,YORGJ VECTOR VALUES YTITL5=$ INDICATED HORSEPOWER PAXIS. (XORGnRG,XTIT. 5,-33,8.925 tO.C,.O,DX,XT ) ___ VECTOR VAtUIES XTITL5=$ DRY AIR FLOW RATE IN LBM/HOUR $ PGRID. (XORGYyRG,XT,YT,1.4,10) PSYMB. (3.0,9,1252.20tHCHEA05jn O43 ) VFCTtR VALUES HEAD5=$ SIMULATION OF CARBURETOR-FNGINE OPERATION NEXTIA PLINE. (XX(1),YY(1),NPoI NT,1,TYPESYMBOL, 1 WHENEVER SAMAX.G. 1.5,'TRANSFER TO EXTRIA PLTEND. EXTRIA CONTINUE FUNCTION RETURN ENTRY TO CALIVF. XCRG= XO YORG=YO SAMAX=SAMEX DX=GX DY=GY NPOINT=POINTS RUN =F RUN SYMBOL=FSYMB TYPE=FTYPE __ PLTREC. WHENEVER SAMAX.E. 1.0.OR. SAMA.X.F, 3.0TRANSFER TO NEXTFI BEGIN A PLOT DRAW THE X AND Y AXIS XT=8. 92 5/14. 00 YT=6. 375/10.00 PAXIS. (XORG,YORGYTTL3 +22, 6.3 75, 90.,0.D. y DY Y T T PLTOFS. (O.,OtDX,O.O,DYtXORGYORG) VECTOR VALtU ES YTITL3=$ INDICATED HORSEPOWER $ PAXIS. (XORG, YORG, XTITL3,-27,8.925,,.OO,0f,DX, XT ) VECTOR VALUES XTITL3=$ OVERALL FUEL-AIR RATIO $

405 PGRI ——. (.XORG, YORG,XT YT, 14,1 0 ) PSYMf[,. (3.,9.12,HEA3 43 ) VCF ~,TOR VA tJFS HEArD3=$ SIMULATION OF CARBURETOR-ENGINE OPERATION $ FI P INE. (XX( 1),YY( I),NPOINT,1,TYPF,SYMBOLl, ) WHENF~VFR SAMAX.G. 1.50tTRANSFER TfO EXTRFI PI. TFND. F I C N T NUEJ FUNCTION RETURN ENTRY TO CALBVP. XnRi G= xOn YOR G= yO SAM AX= S AM EX DX=GX NP T NT= POIN N'TS RUN =FRU N SYMBOL. = FSY Y.MB TYP E=FTYPE PL TR............. PUT.S1. (C 75!') WHENEVFR SAMAX.E'1.0.OR, SAMAXF., E, 3,,TPRANSFER TO NEXTBB BEGIN A PLOT DRAW THE X AND Y AXIS PAXIS. (XPRGYORG,YTITLl,+47,1 0.,9 0,0, 30. 10,1.00 _ L LTnFS. (.O t l O,I ().30,0,0, O, XfRG vYORG) VECTOR, VAI,.UES YTITLL=$ BRAKE SPECIFIC FUElt CONSUMPTION IN LRM/BHP HR $ PAXIS, (AX ORG, x YRGXTITt..,-27.10,000 O t,001.1r ) VECTOR VALUJFS XTITLI=$ ENGINE BRAKE HORSEPOWFR $ PGRID. (XORG, YORG, I.0, 1.00, I:10) PSYMB. (3.30,1?.90..2HHEAD1,0'.043 ) VECTOR VALUES HFAD1_=$ SIMULATION OF CARBURETOR-ENGINE O PERATION - PSYMB. (4.30v 12,4~0n.240tHEAD 2, 2". )3 VECTOR VALUES HEAP?=$ POAD LOAD:SFC VALUES $ BR PLINE. (XX(1),YY( ),NPOINT, 1, TYPE., SYMBOLI 1 WHENEVFR SAMAX.G. 1.50,TRANSFFR TO EXTRBP PLT END. B_ _CON TI NU E FUNCTION RETURN ENTRY Tn CALFVA. XORG=XO YORP G=YO( SAMAX=SAMF X D__ X=GX DY=GY NPOINT=PPOTINTS P U N T = Pf] I N T S RtJN=F RUN SYMBOL=FSYMB TYPE=FTYPE PLTREC. WHENEVER SAMAX.F. 1.0.OR. SAMAX.F. 3,o,TRANSFER TO NEXTFA BEGIN A PLOT DRAW THE X AND Y AXIS XT=8. 2 5/14.00 YT=6. 375/10.00 ____ PAX IS. (XfRGtYCR G,Y T I T L4,t + 24, 65.375_!90._ f ~.a,__ );3:__ _, Y PL T OF S. (O. O, nX,. O300,D Y,XORG,YO RG) VFCTOR VALUES YTITL4=$ OVERALL FUEL-AIR RATIO $ PAXIS. (XORG, YORGXTITL4,-33,8.925,0.O,0.0,OXXT ) VECTOR VALUES XTITL4=$ DRY AIR FLOW RATE IN LBM/HOUR $ PGRID. ( XORG, YORG,XTtYT,14,10 )

406 PSYMB. (3.,9.125, 0.200,HEAD4, * 43) _ VECTOR VALUES HFAD4=$ PREDICTED FUEL-AIR RATIO VS. DRY AIR FLOW NEXTFA PLINE. (XX( ),YY( 1 ),NPOINT, 1,TYPE, SYMnBOL,1 WHENEVER SAMAX.G. 1.50,TRANSFER TO EXTRFA PLTEND. EXTR FA CONTI NUE FUNCTION RETURN ENTRY TO CALMVS. XORG=XO YORG=YO SAMAX= S AMEX DX=GX DY=GY NPO NT=POI NTS RUN=FRUN SYM ROL= FSYM R TYPE=FTYPE PL TREC. ____ WHENEVER SAMAX.E. 1.0.OR. SAMAX.. 3.0 TRANSFER Tn NEXTMS BEGIN A PLOT DRAW THE X AND Y AXIS XT=6.375/1.00 YT=8.925/14*.00 PAXIS. (XORG, YORG,YTITL6,+27,8.925,o90. o,oODYtYT ) _ PLTOFS. ( 0.. OX,O. O, DYXORG,YORG ) VFCTOR VALUES YTITL6=$ VEHICLE MILES PER GALLON $ PAXIS. (YORG,YORG,XTITL6,?25, 6375,0.0, 0. DX,XT ) VECTOR VALUES XTITL6= VEHICLE MILFS PER HOUR $ PGRID. (XORGYORGtXTYT,10,14) PSYMB. (2.05r11.75,0.5 0,HEAD6,0.Ot39 } VECTOR VALUES HEAD6=$ PREDICTED ROAD LOAD FUEL ECONOMY $ NEXTMS PL NF. (XX( I ) YY(i ), NP OINTf 1,TYPE SYMBOL t. WHENEVER SAMAX.G. 1.50, TRANSFER TO EXTRMS PL'TEND. EXTRMS CONTINUE FUNCTION RETURN END OF FUNCTION

APPENDIX K ADDITIONAL FLOW MODEL CURVES AND DATA UTILIZED WITHIN THE SIMULATION

TABLE XXVIII REDUCED DATA FOR A LUCITE FLOW MODEL LUCITE FLOW MODEL TS TEST USING HOT MINERAL SPIRITS THIS DATA IS FCR TEST NUMBER 1011671 THIS 1FST IS FCP MINFRAL SPIrITS AT A ECAN TMPFRATUPRE OF 135,0 T14 JtT'4!S A CIAMrLTLK CF.*J2 iNCHIES AN[: t LENGTh CF.1830 TNC-FS T-E FLulJ viSi.LsTY N1 CFi\TISlCKES iS.I:76 T-E fLuIL SPECIFIL;'AVIHiY IS.761 TFE I 3iJii I I CPO\ ThE LLw0 — v' l A 4A^ it- L E;CU IS UPCN Ti-I LPOE-, vAI\N AlrK *3LLfF IS CFEN T -E l\JEP. 1 PLuTTItG VAkIjtLt IS T1HE 3CCST VENTURI SUCTICh TI: kIcY'4LCS NUMBcK IS EtSEC CN THE 4AIN CFIFILC CIAMETER *** FQJGQAM kECULTS Ft) IT1S RLN ** RU4 DL E'-c fAT t PH RE L CFCAN evSUCW CDJET PDROPjW 0CLPRW OELPXIL FPULW PFFCFU 1.211.t8 125E.).5b3 3.23.7362 2.12.13 -.03 1.24 53. 2.'27 5.46 159.3.6 63 4.40.7794 3.03.17.3 1.56 57.7 5 348 1C.36 1951.1.6663 6.21.7776 4.56.25 -.3 1.32 9 4.3u li.49 2162.8.6656 7.63.7903 5.43.28 -.02 2.44 62.5 5.429 13.2? 249C.9.6960) 9.28.8106 6.84.40 -.o2 2.70 S5.6 - 6.4b4 14.14 2662.0.6959 10.60.8141 7.75.53 -.01 3.15 6.4 7.4t!8 14.75 277.9.6943 11.60.8076 8.57.47.00 A.42 66.6 9.528 16.37 3G25.3.7160 12.94.8246 9.75.57.31 3.62 63.3 9.567 17.13 3220.9.7198 14.51.8277 10.97.57.02 4.10 68.9 13.592 18.07 3401.8.7194 16.20.8267 12.27.68.03 4.4 60.4 11.I3J 18.1? 3412.1.7251 16.05.8346 12.11.67.)2 4.48 69.3 12.612 18.d7 3552.7.7262 17.34.8395 12.98.7?.23 4.37 68.6 RUN QCOTF hATIICM RATICV CCCT AIRVEL VIDELA WIDELA SUMERR OELAW COAIR REAIRB - - - - - ---- - - - - - - -~ 1.14 31.61 20.81 2.93 54.5 114.1.44 -.14 2.21.477 1426.1 2.18 30.42 21.62 3.85 71.7 134.2.52 -.16 3.06.54 1876.7 3.22 2'^.80 22.07 4.82 89.6 161.2.63 -.18 4.41.556 2345.9 4.24 29.76 22.08 5.34 99.4 177.8.69 -.15 5.36.559 2602.2 5.28 3C.34 21.32 5.94 113.5 197.1.77 -.09 6.50.561 2894.0 6.30 3C.49 21.57 6.42 119.4 210.4.82.00 7.52.568 3127.9 7.31 3C.21 21.76 6.76 125.8 220.2.85.04 8.23.571 3294.3 8.34 3C.45 21.59 7.31 135.9 233.2.91.11 9,23.583 35^9.3 9.36 30.19 21.78 7.85 146.0 246.8.96.19 10.34.591 3823.0 10.3E 3C.50 21.56 8.20 152.6 261.1 1.01.25 11.57.584 3996.6 11.38 30.79 21.35 8.15 151.6 259.7 1.01.23 11.45 584 3970.0 12,40 30.83 21.33 8.48 157.7 269.9 1.05.21 12.37.584 4128.8

TABLE XXIX REDUCED DATA FOR A LUCITE FLOW MODEL TEST USING COLD MINERAL SPIRITS LUCITE FLOW MODEL TEST THIS DATA IS FCR TEST hUMBER 1110671 THIS TEST IS FOR LAB GAS AT A MEAN TkMP UF 32." F NO AIR BIBED5 ThE j(T HAS A:IAPL-TtR CF.'7'2 INCHES ANt A LENGTh OF.1E3C INCHES ThE FLUI) VISCSITY IN CENTISTCKES IS.742 ThU -LLUIC SPFL IlIC GRAVITI IS.751 THC PAIN J-T IS CPEN THE IN0EPE.%MJtAT PLUTTING VARIAeLE IS THE PAIN JET PRESSURE ORCP ThE kEYNULOS NU10FR IS ASfC CLN THE IMAIN CRIFICE GIAMETER *** PUWUGAM RESULJTS FU- TtilS RIN *** RUN HVSUC kTEPYH HE CCCEAN BVSUCW CELPW DELPBW UELPXW EMULh CDJFT PtCF 1 1.1 3.44 77t.4.4433.74.66.01 03.04.6815 6 2 2.14 5.57 125E.).716) 1.58 1.47.05.06.09.7407 73.4 3 3.C3 6.86 1548.6 74C8 2.23 2.10.14.10.11.7638 16.6 4 3.8 t 7.4 1793.3 7581 2.86 2.70.24.10.14.17794 7.9 5 5.13 9.40) 2121.d.7 00 3.78 3.68.27.09.18.7919 83.2 b. 1C.38 2343.7.7934 4.46 4.37.34.07.18.014 44.9 7 6.93 11.13 2513.0.7948 5.11 5.00.35.10.24.8030 5.7 I 7. c 11.97 27C2.9.8CC07.82 5.73.41.10.25.8074 6.8 9 9.25 13.17 2 73.9.8142 6.82 6.74.46.10.29.8186 88.1 IC 1C.62 14.25 3216.3.t218 7.83 7.74.54.13.32.8264 88.6 11 12.64 15.65 3532.3.273 9.31 9.23.63.13.38.8309 89.7 12 13.91 16.50 3724.2 E314 1C.25 1C.17.69.15.39.8347 97.2 13 13.t7 16.50 3724.2.8326 1C.22 10.15.69.16.39.8353 93 14 1.C5 17.26 3895.7.8361 11.C9 11.05.76.18.39.8375 99 15 16.73 18.35 4141.9.t1431 12.33 12.27.82.10.43.8452 91.2 16 1t.21 19.17 4327.6.444 13.42 13.33.85.19.44.8472 91.3 17 19.td 2C.20 456C.".6559 14.50 14.37.86.23.43.8598 91.3 18 21.44 21.19 4783.2.86C1 15.60 15.59.94.21.49.8658 91.2 19 21.53 21.13 477C.4 656C 15.86 15.62.97.14.52.8627 91.0 2C?3.15 21.94 4953.6.572 17.C6 16.81.99.35.39.8636 91.3 21 24.55 22.76 5138.3.8635 18.C9 17.83 1.02.31.54.8697 91.5 22 25.99 23.28 5255.? 68584 19.15 18.77 1.81.53.42.8671 91.2 23 27.94 24.30 548fc.3.8642 2C.59 20.19 1.13.27.77.6727 91.5

410 LOG-LOG PLOT OF SYSTEM FLON PRRRMETERS MRIN ORIFICE NUMBER= F-50 RVERRGE TEMP = 32.0~F RUN NUMBER =1110671 TEST FLUID = STANPDARD Rt. __ SOUNE LO~ —- - - -- - - - - - -- D CD _ _J cN - r — LO CD y\ / I.l_ 2 3 4 5 6 789 2 3 4 5 6 789 2 3 5 6 789 MAIN JET PRESSURE DROP IN INCHES OF WRTEB Ui- _ __- - _-^ ^ — - - -- Figure 82. Fuel Mass Flow Rate As A Function Of The Main Metering Orifice Pressure Differential In The Lucite Flow Model

411 MR I CHRNNEL CHHRRCTERISTIC CURVE MRIN ORIFICE NUMBER= F-50 fVEIRGE TEMP = 100.0 F RUN NUMBEH - 621671 TES:T FLUID MIN.SPIRITS LA. _ _- _ -------- UI o I ~LLLJ / _ __ Cr I-I i cr REYNOLDS NUMBER OVER ONE ThOUSRND Figure 83. Main Fuel Channel Discharge Coefficient Curve

412 FLUID FLOW RATE VS PRESSURE DROP MRIN ORIFICE NUMBER= F-50 RVERRGE TFMF = 135.0 F o RLIN NUMBER = 919671 TEST FLUiJ = MIN.SPIRITS 0 C: NO Al BLEED 0 1; -J U-^~~~~~~~~~~~ - Lo L — --- -..... —--- C0 2.50i 5. 7.50 10.00 1 i 1.00 1.50 2i.00i 2 S 25.i00 UO0T1 VENTU9I SUCTION IN INCHES OF HATER Figure 84. Mass Flow Rate Of Hot Test Fluid Within The Lucite Flow Model

413 TABLE XXX SPECIFICATIONS AND EXPERIMENTAL VALUES FOR A TYPICAL TEST CARBURETOR Carburetor Model: C6AF-95 10-B Carburetor Type: Ford 2-barrel, fixed jet, air bled, 1 boost venturi Main venturi throat diameter = 1. 1450 inches Throttle bore diameter = 1.4370 inches Boost venturi throat diameter = 0.538 inches Boost venturi outer diameter = 0.750 inches Throttle plate shaft diameter = 0.375 inches Main venturi area = 1. 0257 in2 (per venturi) Throttle bore area = 1.6211 in2 (per bore) Maximum throttle flow area = 1.0910 in2 (per bore) Boost venturi throat area = 0.2273 in.2 (per venturi) Net main venturi throat flow area = 0.5787 in2 (area external to boost venturi) Net main venturi area = 2 = 2.586 Ratio of: Boost venturi throat area Total venturi throat flow area = 0.8442 in2 (per barrel) Throttle angle (fully opened) = 85.0~ Throttle angle (fully closed) = 10.0~ Throttle angle (normal idle) = 12.50 EXPERIMENTAL AIR FLOW VALUES Throttle plate leakage (throttle closed) = 13.90 lbm air/hr (per barrel) Maximum transfer tube flow = 4.40 Ibm air/hr (per tube)

414 TABLE XXX (continued) Maximum enrichment valve air bleed flow = 4.35 lbm air/hr. Total air flow with closed throttle = 2(13.90) + 2(4.40) + 4.35 = 41.0 lbm/hr. (both barrels) Idle air flow (typical value) = 64.0 Ibm air/hr. (both barrels).

TABLE XXXI VISCOSITY CONVERSIONS UTILIZED IN THE SIMULATION ENGLISH SYSTEM METRIC SYSTEM PROGRAM PROGRAM NAME NAME UNITS NAME NAME UNITS ABSOLUTE None VISAE lbfsec = slug Poise VISAM dyne sec gm VISCOSITY ft ft sec or (centipoise) cm cm sec Centipoise KINEMATIC None VISKE ft2 Stoke VISKM cm2 VISCOSITY sec or (centistoke) sec centistoke ABSOLUTE CONVERSIONS 1 bf sec = 4.79 (10)4 centipoise 1 centipoise = 1/4.79(10)4 bf sec ft2 ft2 VISAE = 4.79 (10) VISAMVAM = 1/4.79(10)4 VISAE KINEMATIC 1 ft 2 2 KINEMATIC |1 ft = 92903.0 centistokes 1 centistoke = 1/92903.0 ft2 CONVERSIONS sec sec VISKE = 92903.0 VISKM VISKM = 1/92903.0 VISKE An additional useful quantity within the simulation is VISAG, which is defined as: VISAG = 32.174 ~ VISAE ibm ft sec

416 TABLE XXXII CONSTANTS UTILIZED IN THE SIMULATION Standard atmosphere = 14.6959 lbf/in2 = 2116.62 lbf/ft2 = 29.92"Hg. Standard atmosphere = 406.857 in. H20 at 39~ F Standard atmosphere = 407.787 in. H20 at 60~ F Standard atmosphere = 557.086 in. gasoline of 0.732 SG Density of water (sat. at 32~ F) = 62.4142 Ibm/ft3 Density of water (sat. at 60~ F) = 62.286 lbm/ft3 Density of water (1 gm/cm3) = 62.428335 Ibm/ft3 Air density at 60~ F and 14.696 psia = 0.07636 Ibm/ft3 Air density at 70~ F and 14.696 psia = 0.07492 Ibm/ft3 1 Ibm = 453.59237 grams 1 in3 = 16.387162 cm3 1 inch = 2.540005 cm 1 cm =.393700 inch (definition) Density of Mercury = 13.5951 gm/cm3 at 32.00 F Density of Mercury = 13.5458 gm/cm3 at 68.0~ F R (universal gas constant) = 1545.4 ft lbf lb mol OR R (air constant) = 53.34 ft lb Ibm OR.

APPENDIX L EXPLANATION OF SYMBOLS USED IN THE SIMULATION The meanings of the primary variables in the simulation are listed here for reference purposes. The variables used for indexing, switching, substituting, and temporarily saving values are listed but the meanings are not given. The symbols have been arranged in alphabetical order, in the following categories: 1. non-subscripted variables in the simulation 2. subscripted variables in the simulation 3. non-subscripted variables related to the plotting and interpolation routines 4. subscripted variables related to the plotting and interpolation routines 5. symbols associated with constants and dummy variables, and with indexing and switching 6. variables related only to initiating plots and constructing axes i. NON-SUBSCRIPTED VARIABLES IN THE SIMULATION SYMBOL MEANING ABLEED Flow area of enrichment valve vacuum bleed orifice ACHOKE Flow area of choke restriction orifice ADUM Approach velocity factor for fuel channel orifices AFLOW Throttle flow area AIDENS Density of bleed air in idle system AIDLE Flow area at idle needle screw 417

418 SYMBOL MEANING AIRFL1 Air mass flow rate for first engine IHP data set AIRFL2 Air mass flow rate for second engine IHP data set AIRFLO Air mass flow rate which will give the required IHP for the current iterative fuel-air ratio AIRI1 Mass flow rate of first idle air bleed AIRI2 Mass flow rate of second idle air bleed AIRM1 Mass flow rate of first main air bleed AIRM2 Mass flow rate of second main air bleed AIRMB Air flow rate through enrichment valve bleed orifice AIRMC Air flow rate through choke orifice AMDENS Ambient air density AO Air flow rate intercept on IHP plot AREA Vehicle frontal area ARICH Enrichment valve flow area ASHAFT Transverse cross-sectional area of throttle shaft ASTAR Throttle flow area parameter ATRANS Flow area of throttle bypass orifice ATYPE Control variable specifying the type of analysis to be performed AVALVE Total intake valve flow area AVISKE Kinematic viscosity of bleed air in English units AVISKM Kinematic viscosity of bleed air in centistokes AWOT Maximum throttle flow area per barrel BBLS Number of carburetor barrels

419 SYMBOL MEANING. BFA Fuel-air ratio of mixture leaving boost venturi BHP Engine brake horsepower BMACH3 Mach number at boost venturi station 3 BMACH4 Mach number at boost venturi station 4 BMACH5 Mach number at boost venturi station 5 BORE Engine cylinder bore diameter BORTOL Tolerance of the engine bore diameter BSFC Engine brake specific fuel consumption BVFLO Air mass flow rate in one boost venturi BVMACH Boost venturi throat Mach number BVS MIN Minimum boost suction to initiate main system fuel flow BVSUCW Boost venturi suction CARBNO Current carburetor being built for the production dimension analysis CC Vena contracta coefficient CDBL Discharge coefficient of the enrichment vacuum bleed orifice CDJ Iterative main metering orifice discharge coefficient CDJET Predicted main metering orifice discharge coefficient CDSE Discharge coefficient of square-edged fuel channel orifice CDSE1 Iterpolated Cd for next lowest known L/D ratio CDSE2 Interpolated Cd for next highest known L/D ratio CDT Throttle plate discharge coefficient CDTR Discharge coefficient of throttle bypass orifice

420 SYMBOL MEANING CDUM Total pressure loss factor for fuel channel orifices CLIQ Liquid fuel specific heat CORR Correction factor for fuel head variations with density CPAIR Constant pressure specific heat of dry air CPH20 Constant pressure specific heat of water vapor CPMAIN Constant pressure specific heat of the mixture at the throttle plate CPMIX Constant pressure specific heat of the mixture in general CPWET Constant pressure specific heat of moist air CPFUEL Constant pressure specific heat of fuel vapor CR Engine compression ratio CRTOL Engine compression ratio tolerance CVAIR Constant volume specific heat of dry air CVFUEL Constant volume specific heat of fuel vapor CVH20 Constant volume specific heat of water vapor CVMAIN Constant volume specific heat of the mixture at the throttle plate CVMIX Constant volume specific heat of the mixture in general CVWET Constant volume specific heat of moist air CYL Number of cylinders in engine DBLEED Production diameter of enrichment valve vacuum bleed DBLNOM Nominal diameter of enrichment valve vacuum bleed DBTOL Tolerance on the enrichment valve vacuum bleed diameter DCHOKE Production diameter of choke bleed restriction

421 SYMBOL MEANINGS DCNOM Nominal diameter of choke bleed restriction DCTOL Tolerance on the choke bleed restriction diameter DELAIR Change in engine air mass flow rate for the current iteration DELFA1 Change in total fuel-air ratio for the current iteration DELFA2 Change in main fuel-air ratio since the last iteration DELXJ Reynolds number increment used in main metering orifice data DELXJL Reynolds number increment used in low head data for the main metering jet DELXR Fuel-air ratio increment used in engine IHP data DELXS RPM increment used in engine FMEP data DELXSE Reynolds number increment used in square-edged orifice data DELPMB Static pressure differential across first main system air bleed DELXT Throttle angle increment used in throttle Cd data DENSF Fuel density in pounds per cubic foot DENSM Fuel density in grams per cubic centimeter DISPL Engine displacement in cubic inches DMAN Effective average diameter of intake manifold runner DPEJET Exit pressure loss for the main metering orifice DPENTR Entrance pressure loss for a fuel channel element DPJET Predicted static pressure differential of main metering orifice DPW Element total pressure loss due to fluid friction DRAG Vehicle air resistance coefficient DRIVEN Total vehicle drive train efficiency DRYA2 Initial guess for the engine dry air flow rate

422 SYMBOL MEANINGS DRYAIR Total dry air mass flow rate to engine DS Production diameter of throttle shaft DSNOM Nominal diameter of throttle shaft DSTOL Tolerance on the throttle shaft diameter DT Production diameter of throttle bore DTRANS Production diameter of throttle bypass orifice DTNOM Nominal diameter of throttle bore DTRNOM Nominal diameter of throttle bypass orifice DTRTOL Tolerance on the throttle bypass orifice diameter DTTOL Tolerance on the throttle bore diameter DUMACH Iterative venturi Mach number El General error of the previous iteration E2 General error of the current iteration EPS General maximum allowable convergence error EPS2 Maximum allowable air mass flow rate error EPSE Maximum allowable enrichment pressure drop error EPSI maximum allowable idle system pressure drop error EPSJ Maximum allowable main jet pressure drop error EPSLON Maximum allowable Mach number error ERR1 Air mass flow rate error on the previous iteration (see Figure 5) ERR2 Air mass flow rate error on the current iteration (see Figure 5) ERRE1 Pressure error on previous enrichment flow iteration

423 SYMBOL MEANINGS ERRE2 Pressure error on current enrichment flow iteration ERRI1 Pressure error on previous idle system flow iteration ERRI2 Pressure error on current idle system flow iteration ERRJ1 Pressure error on previous main jet flow iteration ERRJ2 Pressure error on current main jet flow iteration EXHEAT Intake manifold heat parameter Fl Sudden expansion or contraction pressure loss factor F2 Bend pressure loss factor FA General fuel-air ratio FACTOR Sum of Fl and F2 FAIDLE That portion of the total fuel-air ratio due to idle fuel flow FAMAIN Main system fuel-air ratio FARICH Initial guess for the total fuel-air ratio with the enrichment system functioning FATOTL Total (overall) fuel-air ratio FDARCY Darcy friction factor FHP Friction horsepower of engine FLLIQB Liquid fuel mass flow rate leaving each boost venturi FLMIXB Mass flow rate of air, water vapor, and fuel vapor leaving each boost venturi FLOWE Fuel mass flow rate in enrichment system FLOWI Fuel mass flow rate in idle system FLOWI Fuel mass flow rate through main metering orifice FLOWM Fuel mass flow rate in main system

424 SYMBOL MEANINGS FLOWT Total fuel mass flow rate per barrel FLUID Fluid type code FLVAPB Mass flow rate of fuel vapor leaving boost venturi FMAX Maximum engine FMEP at a given RPM FMAXB Maximum possible moist air mass flow rate through one boost venturi FMAXB3 Maximum possible moist air mass flow rate at the boost venturi throat FMAXB4 Maximum possible moist air mass flow rate at boost venturi station 4 FMAXB5 Maximum possible moist air mass flow rate at boost venturi station 5 FMAXM Maximum possible moist air mass flow rate through one main venturi FMAXM3 Maximum possible moist air mass flow rate at main venturi station 5 FMAXM4 Maximum possible moist air mass flow rate at the main venturi throat FMAXT Maximum possible moist air flow rate through one carburetor barrel FMEP Friction mean effective pressure of engine FMIN Minimum FMEP at the specified engine speed FRACT Initial guess for the fraction of the main fuel flow vaporized between the boost venturi and the throttle plate FRACTB Initial guess for the fraction of the main fuel vaporized within the boost venturi FTYPE Variable denoting the fuel type code FUELR Total fuel mass flow rate for all barrels

425 SYMBOL MEANINGS GAMMA Fuel surface tension GASFLO Total mixture mass flow rate to the engine GASM1 Iterative air flow rate from nozzle equations GASM2 Iterative air flow rate from exhauster equation GASMTR Air mass flow rate through throttle bypass orifice GASMT Mixture mass flow rate at throttle plate GK General Specific heat ratio GKMIX Specific heat ratio of mixture at throttle plate GKWET Specific heat ratio of moist air GUESS Initial guess for the intake manifold vacuum HEATV Lower heating value of fuel HUMID Fractional relative humidity HVAPOR Latent heat of vaporization of the fuel JETS Number of main metering orifices NBV Number of boost venturi stations in the analysis NCDJL Number of points in the low head main metering orifice Cd data NCDJ Number of points in the main metering orifice Cd data NCDSE Number of points in the square-edged orifice Cd data NCHAN Number of elements in the fuel channel NFMEP Number of points in the engine FMEP data NGEAR Number of transmission gear ratios in the road load analysis NIHP Number of points in the engine IHP data NMV Number of main venturi stations in the analysis

426 SYMBOL MEANINGS NTHETA Number of points in the throttle plate Cd data NUNITS Number of carburetors to be built for the production dimension analysis OLDFE Enrichment fuel flow rate for the previous iteration OLDF1 Idle system fuel flow rate for the previous iteration OLDFJ Main jet fuel flow rate for the previous iteration OMEGA Water vapor to air mass ratio OPENE Vacuum at which the enrichment valve begins to open ORDER The iterpolation degree utilized by STERL PB5W Boost venturi outlet pressure in inches of water PBHG3 Boost venturi throat pressure in inches of mercury PBHG4 Pressure at boost venturi station 4 in inches of mercury PBHG5 Boost venturi outlet pressure in inches of mercury PCH Per cent relative humidity PM4W Pressure at main venturi station 4 in inches of water PMACH3 Mach number at main venturi throat PMACH4 Mach number at main venturi station 4 PMAN Intake manifold pressure in inches of mercury PMAXW Vapor pressure of water for 100% humidity PMHG3 Main venturi throat pressure in inches of water PMHG4 Pressure at main venturi station in inches of mercury PO Ambient pressure in PSIA POB Stagnation pressure at boost venturi inlet POBHG Stagnation pressure at boost venturi outlet in inches of mercury

427 SYMBOL MEANINGS POHG Ambient pressure in inches of mercury POL Local stagnation pressure in general POM Stagnation pressure at main venturi inlet POMHG Stagnation pressure at main venturi station 4 in inches of mercury PR Pressure ratio across throttle plate PRBL Pressure ratio across throttle bypass orifice PRBMAX Maximum possible pressure ratio for throttle bypass orifice PRESS Intake manifold pressure in inches of mercury PRINT1 Variable which controls data printout within main program PRINTA Variable which controls auxiliary printout by subroutine AIRMAS PRINTF Variable which controls auxiliary printout by subroutine FLOW PRINTO Variable which controls auxiliary printout of road load values PRINTS Variable which controls auxiliary printout by subroutine SIGNAL PRMAX Pressure ratio for choked throttle FLOW PT Stagnation pressure of mixture at throttle plate in PSIA PTHG Stagnation pressure of mixture at throttle plate in inches of mercury PTYPE Variable which controls the type of CALCOMP plot obtained PVFLO Air mass flow rate in one primary venturi PVMACH Primary venturi throat Mach number PVSUCVW Primary venturi suction RANVAR Variable which indicates whether a production dimension analysis is to be performed RATEB Moist air mass flow rate in each boost venturi

428 SYMBOL MEANINGS RATEM Moist air mass flow rate in each main venturi RATEMF Total main system fuel flow rate for all barrels RATIOD Vehicle differential gear ratio RATIOP Fraction of the boost venturi suction lost in elements 1 to 9 RATIOT Current vehicle transmission gear ratio REJET Reynolds number of the main metering orifice fuel FLOW RHOB3 Air density at boost venturi throat RHOB4 Mixture density at boost venturi station 4 RHOB5 Mixture density at boost venturi outlet RHOM3 Air density at main venturi throat RHOM4 Air density at main venturi station 4 RHOLZ Local mixture density in general ROADHP Required rear wheel horsepower at a given vehicle speed ROLL Rolling resistance factor for vehicle RPM Engine speed in revolutions per minute RPMLIM Maximum engine speed for which an operating map is desired RTHETA Throttle angle in radians RTHETO Completely closed throttle angle in radians SGFUEL Fuel specific gravity SIGMA Standard deviation of carburetor dimensions, also fuel surface tension SLOPE Current slope of the IHP versus air mass flow rate curve SPILL 1 Initial spill point of carburetor SPILL2 Secondary spill point of carburetor

429 SYMBOLL MEANING S STOL Tolerance for the engine stroke STROKE Engine stroke SUCWB3 Suction at boost venturi throat in inches of water SUCWB4 Suction at boost venturi station 4 in inches of water SUCWB5 Suction at boost venturi outlet in inches of water SUCWM3 Suction at main venturi throat in inches of water SUCWM4 Suction at main venturi station 4 in inches of water SUMAIR Total air bleed mass flow rate-for the main system SUMDPE Sum of the pressure differentials in the enrichment system SUMDPI Sum of the pressure differentials in the idle system SUMDPJ Sum of the pressure differentials for elements 1 and 2 SUMDPM Sum of the pressure differentials for the main system TBF3 Static temperature at boost venturi throat in ~F TBF4 Static temperature at boost venturi station 4 in F TBF5 Static temperature at boost venturi outlet in ~F TCLR Absolute temperature of the gases in the cylinder clearance volume when exhaust valve closes TCYLR Absolute temperature of the mixture in the cylinder when the intake valve closes TEMP Fuel temperature in degrees Fahrenheit TFUEL Fuel temperature in degrees Fahrenheit THETAL Maximum throttle angle for which an operating map is desired THETAO Production value for the completely closed throttle angle THETA General throttle angle

430 SYMBOL MEANINGS THONOM Nominal value for the completely closed throttle angle THOTOL Angular tolerance for the completely closed throttle angle THSTEP The throttle angle increment used in the road load analysis TIREN Tire revolutions per mile TLR Local static temperature in degrees Rankine TMAN Absolute temperature of mixture leaving the intake manifold runner in OF TMANF Temperature of mixture leaving the intake manifold runner in ~F TMF3 Static temperature at the main venturi throat in OF TMF4 Static temperature at main venturi station 4 in 0F TOBF Stagnation temperature at boost venturi inlet in ~F TOBR Stagnation temperature at boost venturi inlet in OR TOF Ambient temperature in degrees Fahrenheit TOMF Stagnation temperature at main venturi inlet in OF TOMR Stagnation temperature at main venturi inlet in OR TORQF Friction torque of the engine TOR Ambient temperature in degrees Rankine TOTF Total temperature of the mixture at the throttle plate (OF) TOTR Total temperature of the mixture at the throttle plate (OR) TURNS Number of turns of the idle needle screw from the completely closed position VACM Intake manifold vacuum in inches of mercury VACMAN Iterative intake manifold vacuum in inches of mercury VALVED Intake valve seat diameter

431 SYMBOL MEANINGS VCL Total clearance volume of engine VELB3 Velocity of moist air at boost venturi throat VENFLO Total moist air mass flow rate per venturi stack VISAE Absolute viscosity of fuel in English units VISAM Absolute viscosity of fuel in centipoise VISKE Kinematic viscosity of fuel in English units VISKM Kinematic viscosity of fuel in centistokes VLIMIT Lower bound for intake manifold vacuum VMPH Vehicle velocity in miles per hour VOLD Intake manifold vacuum for the previous iteration VSTEM Valve stem diameter WAIR Molecular weight of dry air WEIGHT Vehicle curb weight WETA1 Moist air flow portion of GASM1 WETA2 Moist air flow portion of GASM2 WETAIR Total moist air mass flow rate to engine WFUEL Molecular weight of fuel being used WH20 Molecular weight of water vapor WMIXB Molecular weight of mixture leaving boost venturi WMOIST Molecular weight of moist air in general WMOL Molecular weight of a mixture in general WMOLEC Molecular weight of fuel in general WMOLEM Molecular weight of mixture in engine cylinder

432 SYMBOL MEANINGS WMOLET Molecular weight of mixture at throttle plate XBVNOM Nominal venturi dimension (see Figure 2) XBV Production venturi dimension (see Figure 2) XBVTOL Tolerance of venturi dimension (see Figure 2) XF Fraction of the total venturi air flow that does not flow through the boost venturi XF1 Value of XF for the previous iteration XFV Value of XF for the previous air flow value XGUESS Initial guess for XF XFLOWE Predicted enrichment system fuel mass flow rate XFLOWI Predicted idle system fuel mass flow rate XFLOWJ Predicted main metering orifice fuel mass flow rate XFLOWM Predicted main system fuel mass flow rate XFLOWT Predicted total fuel mass flow rate per barrel XIHP1 Indicated horsepower from high air flow data set XIHP2 Indicated horsepower from low air flow data set XIHP Indicated horsepower corresponding to the current iterative air flow and fuel-air ratio XIMEP1 Indicated mean effective pressure corresponding to XIHP1 XIMEP2 Indicated mean effective pressure corresponding to XIHP2 XISFC Engine indicated specific fuel consumption XMACHT Mach number of the mixture flow at the throttle plate XMAINR Fuel-air ratio based on main fuel flow and venturi air flow XM1NOM Nominal venturi dimension (see Figure 2)

433 SYMBOL MEANINGS XM1TOL Tolerance of venturi dimension (see Figure 2) XM2NOM Nominal venturi dimension (see Figure 2) XM2TOL Tolerance of venturi dimension (see Figure 2) XMB Production venturi dimension (see Figure 2) XMBNOM Nominal venturi dimension (see Figure 2) XMBTOL Tolerance of venturi dimension (see Figure 2) XMINR Fuel-air ratio of first point in the engine IHP data XMINS Engine speed at first point in the engine FMEP data XMINT Throttle angle at first point in the throttle Cd data XMV1 Production venturi dimension (see Figure 2) XMV2 Production venturi dimension (see Figure 2) XNKGDJ Same as NCDJ except floating point XNCDJL Same as NCDJL except floating point XNCDSE Same as NCDSE except floating point XNFMEP Same as NFMEP except floating point XNIHP Same as NIHP except floating point XNTHET Same as NTHETA except floating point XNUNIT Same as NUNITS except floating point XTOTLR Total fuel-air ratio of mixture leaving intake manifold

434 2. SUBSCRIPTED VARIABLES IN THE SIMULATION SYMBOL MEANING ABV Boost venturi flow area ACHAN Fuel channel element flow areas AMV Main venturi flow areas ANAME Description of analysis ANGLC Angles between the current fuel channel element and the preceding one BHPP Engine brake horsepower values for plotting BOOSTW Boost venturi suction values for plotting BSFCP Brake specific fuel consumption values for plotting CBLEED Air bleed orifice discharge coefficients CD Main metering orifice Cd values for plotting CD1 Cd data for main metering orifice being used CD2 Cd data (low head) for main metering orifice CD3 Cd data for square-edged orifice with L/D = 0.100 CD4 Cd data for square-edged orifice with L/D = 0.616 CD5 Cd data for square-edged orifice with L/D = 1.426 CD6 Cd data for square-edged orifice with L/D = 3. 629 CD7 Cd data for square-edged orifice with L/D = 4.726 CD8 Cd data for square-edged orifice with L/D = 7.230 CD9 Cd data for square-edged orifice with L/D = 10.58 CNAME Carburetor description CTHROT Throttle plate discharge coefficient values

435 SYMBOL MEANING CTYPE Type codes for fuel channel elements D Fuel channel element diameters DBV Boost venturi production diameters DBVNOM Boost venturi nominal diameters DBVTOL Tolerances for boost venturi diameters DCHAN Production diameters for fuel channel elements DCHNOM Nominal diameters for fuel channel elements DCHTOL Tolerances for fuel channel element diameters DELPTW Total pressure loss of fuel channel elements DIHP1 Indicated horsepower values at the lower air flow DIHP2 Indicated horsepower values at the higher air flow DMV Production diameters of the main venturi DMVNOM Nominal diameters of the main venturi DMVTOL Tolerances for the main venturi diameters DN Density of the fluid within the fuel channel elements DRYAP Dry air mass flow rate values for plotting ENAME Engine description FLOWMP Main system fuel flow rates for plotting FLOWTP Total fuel flow rates for plotting FMEP1 Friction mean effective pressure values at full throttle FMEP2 Friction mean effective pressure values at closed throttle FNAME Fuel description ONAM Orifice descriptions

436 SYMBOL MEANING PMAN Intake manifold pressure PNAME Plot description RE Fuel channel element Reynolds numbers SCRACH Work area for subroutine STERL SKIP Array used to indicate whether flow exists in a fuel channel element SPEED Vehicle speed TOTLFA Total fuel-air ratio values for plotting TRANS Transmission gear ratios VEL Velocity of the fluid within the fuel channel elements VHEADW Velocity head of the fluid within thie fuel channel elements VNAME Vehicle description WETA Total moist air mass flow rate for plotting WHY Description of the simulation run XIHPP Engine indicated horsepower values for plotting XLCHAN Fuel channel element length XLD L/D ratio of fuel channel elements XMPG Vehicle miles per gallon 3. NON-SUBSCRIPTED VARIABLES RELATED TO THE PLOTTING AND INTERPOLATION ROUTINES SYMBOL MEANING ALPHA General interpolation parameter DELTAX X spacing of data supplied to interpolation routine FM Degree of interpolation to be used

437 SYMBOL MEANING FN Number of data points supplied to interpolation routine FRUN Run number for the simulation plots FSYMB Plotting symbol to be used FTYPE Type of line plot desired GX Grid line spacing for X axis G.Y Grid line spacing for Y axis MAIIK Variable which determines the plot scale POINTS Number of points to be plotted SAI4EX Variable which controls the number of curves pl::ted on one grid TEMP Temperature to be printed on plot VAR1 A number to be printed on plot XARG The X argument for which an interpolated Y value is desired XMIN The X value at the plot origin XO X Coordinate of the plot origin XXMIN Minimum value of the X data supplied to the interpolation routine YEST Interpolated Y value YMIN The Y value at the plot origin YO Y coordinate of the plot origin

438 4. SUBSCRIPTED VARIABLES RELATED TO THE PLOTTING AND INTERPOLATION ROUTINES SYMBOL MEANING XX General array of values associated with the X axis of a plot Y General array of data supplied to interpolation routine YY General array of values associated with the Y axis of a plot 5. SYMBOLS ASSOCIATED WITH CONSTANTS AND DUMMY VARIABLES, AND WITH INDEXING AND SWITCHING Al to A18 DUMLD J RNO AGAIN DUMMY1 K SAVE ANG DUMMYM L SAVE 1 ANG1 DUMMYP M SAVE5 Cl to C13 DUMPA MH SAVE6 CHANGE DUMPR ML SAVEI1 DATE 1 DUMR N SAVEI2 DATE2 DUMRB NN SETUP DEBUG DUMRPM OLDAI1 STEP DEBUGA DUMTHO OLDAI2 STOP DUM1 to DUM22 DUMV2 OLDAIR SWITCH DUMA DUMVH2 OLDAM 1 TF DUMDP EDUM OLDAM2 THOLD DUMFA ESW OLDFA1 X DUMFLO HH OLDFA2 XIDUM DUMFM I OPEN XISW DUMFR ITER ORNAM XJSW DUMFT ITERE PM XMDUM DUMGAM ITERI Q XN DUMHU ITERJ REDUM Y 6. VARIABLES RELATED ONLY TO INITIATING PLOTS AND CONSTRUCTING AXES ALIMIT DXFA DYCM PLOTN AMAX DXIA DYCR SCALE ANGLD DXIF DYFA SET ANGLR DXLL DYIA XEXP DX DXMH DYIF XSTART DXBB DXMS DYLL XVAL DXCH DY DYMH YEXP DXCM DYBB DYMS YSTART DXCR DYCH PLOTI YVAL

BIBLIOGRAPHY COMPRESSIBLE MIXTURE FLOW 1. Dodson, J. E., Booth, C. T., and Metsger, A. B., "An Investigation of the Air Metering Characteristics of Various Combinations of Carburetor Elements", M. S. thesis, M.I.T., 1940. 2. Fries, B. A., Davis, F. J., and Hull, D. E., "Engine Air Flow by the Total Count Method", SAE Preprint 85, 1959. 3. Gerhart, R. V., et al, "Thermodynamic Properties of Air", Mechanical Engineering, April, 1942, pp. 270-272. 4. Hwa, W. Z., "A Study of Double Venturis for Aircraft Carburetors", M.I.T. thesis, Oct., 1941. 5. Mirsky, W., and Bolt, J. A., "A Preliminary Literature Survey of the Fuel Metering and Induction Processes for Spark-Ignited Engines", University of Michigan Research Institute paper, project 2813, 1958. 6. Newhall, H. K., and Starkman, E. S., "Thermodynamic Properties of Octane and Air for Engine Performance Calculations", SAE paper 633G, 1963. 7. Oppenheim, A. K., and Chilton, E. G., "Pulsating Flow Measurement - A Literature Survey", ASME paper 53-A-157, 1953. 8. Prien, W. F., "A Study of the Effect of Air Pulsations on the Operation of A Carburetor", M.I.T. thesis, May 1954. 9. Rogowski, A. R., "Elements of Internal Combustion Engines", McGraw-Hill, New York, 1953. 10. Shapiro, A. H., "The Dynamics and Thermodynamics of Compressible Fluid Flow", The Ronald Press Co., New'York, 1953, Chap. 4, 6, 7 and 8. ATOMIZATION AND VAPORIZATION 11. Bahr, D. W. "Evaporation and Spreading of Isooctane Sprays in High-Velocity Air Streams", NACA Report RM E53I14, 1953. 439

440 12. Benson, G. M., et al, "The Determination of Cross-Sectional DropSize Distributions of Liquid Sprays by a Fluorescent Technique", University of Wisconsin research report, June, 1958. 13. Consiglio, J. A., "The Effect of Operating Variables on Sprays Produced by a Pressure-Type Nozzle", Ph.D. thesis, University of Michigan, 1961. 14. Fuchs, N. A., "Evaporation and Droplet Growth in Gaseous Media", Pergamon Press, New York, 1949. 15. Graves, C. G., and Bahr, D. W., "Atomization and Evaporation of Liquid Fuels, "NACA report 1300, 1957, Chapter I. 16. Ingebo, R. D., "Vaporization Rates and Drag Coefficients for Isooctane Sprays in Turbulent Air Streams", NACA report TN3265, 1954. 17. Jakob, M., "Heat Transfer", Vol. I, John Wiley and Sons, Inc., 1949. 18. Marshall, W. R., "Atomization and Spray Drying", Chem. Eng. Prog. Monograph Series, No. 2, Vol. 50, 1954. 19. Nukiyama, S., and Tanasawa, Y., "Experiments on the Atomization of Liquids in an Air Stream, Reports 1, 2, and 4, Defense Res. Board, Ottawa, March, 1950 (Translated from Trans. Jap. Soc. Mech. Eng., Vol. 4, No. 14, Feb. 1938. pp. 86-93). 20. Ranz, W. E., and Marshall, W. R. Jr., "Evaporation from Drops", Chem. Enq. Prog., Vol. 48, No. 3, March, 1952, pp. 141-146; No. 4, April, 1952, pp. 173-180. 21. Rice, E. J., "The Effect of Selected Fluid Parameters on Spatial Drop Size Distribution", Ph.D. thesis, University of Wisconsin, 1966. FUEL AND AIR BLEED FLOW 22. Baker, O., "Simultaneous Flow of Oil and Gas," The Oil and Gas Journal, July 26, 1954, pp. 183-186. 23. Daily, J. W., and Harleman, D. R. F., "Fluid Dynamics", AddisonWesley Pub. Co., Inc., Reading, Mass., 1966, Chapt. 13 and 14. 24. Huey, C. T., and Bryant, R. A. A., "A Theory for Froth Flow in Horizontal Pipes", ASME paper 65-WA/FE-5, 1965.

441 25. Ishikawa, M. and Ito, M., "The Effect of Temperature on Carburation and its Compensation", Journal Soc. Mech. Engr., Vol. 31, No. 140, Dec. 1928. 26. Kay, J. M., "Fluid Mechanics and Heat Transfer", Cambridge University Press, London, 1963, Chap. 6, 15, and 18. 27. Langhaar, H. L., "Steady Flow in the Transition Length of a Straight Tube", Journal of Applied Mechanics, Trans. ASME, Vol. 64, 1942, p pp. A-55-58. 28. Lockhart, R. W. and Martinelli, R. C., "Proposed Correlation of Data for Isothermal Two-Phase Two-Component Flow in Pipes", Chem. Eng. Prog., Vol. 45, 1949, pp. 39-48. 29. Streeter, V. L., "Fluid Mechanics", McGraw-Hill, Inc., New York, 1958, Chapters 4, 6 and 10. 30. Ting, C. H., "Analysis of Air Bleeds and Several Typical Idling Systems for Carburetors", M.I.T. thesis, 1946. 31. Weir, A., "Two and Three-Dimensional Flow of Air Through SquareEdged Sonic Orifices", Ph.D. thesis, University of Michigan, 1954. ORIFICE FLOW 32. Bond, W. N., "The Effect of Viscosity on Orifice Flows", Proc. Royal Soc., Nov. 1921, pp. 225-230. 33. Earles, S. W. E., and Zarek, J. M., "Use of Sharp-Edged Orifices for Metering Pulsating Flow", Proc. Inst. Mech. Engr., 1963, Vol. 177, No. 37, p. 997. 34. Greenland, L. S., "Fluid Flow Through Restrictions", Aircraft Engr., June, 1943. 35. Hall, G. W., "Analytical Determination of the Discharge Characteristics of Cylindrical-Tube Orifices", Jour. Mech. Eng. Science, Vol. 5, No. 1, 1963, pp. 91-97. 36. Kastner, L. J., and McVeigh, J. C., "A Reassessment of Metering Orifices for Low Reynolds Numbers", Proc. Instn. Mech. Engrs., Vol. 180, Part 1, No. 13, 1965, pp. 331-355. 37. Kreith, Frank, and Eisenstadt, Raymond, "Pressure Drop and Flow Characteristics of Short Capillary Tubes at Low Reynolds Numbers", ASME paper 56-SA-15, June, 1956.

442 38. Lichtarowicz, A., Duggins, R. K., and Markland, E., "Discharge Coefficients for Incompressible Non-Cavitating Flow Through Long Orifices", Jour. Mech. Eng. Science, Vol. 7, No. 2, 1965, pp. 210-219. 39. Mirsky, W. and Bolt, J. A., "Flow Characteristics of the Carter Type 120 Carburetor Metering Jet", Project 2813 final report, U. of Mich. Research Institute, Aug. 1960. 40. Nakayama, Y., "Action of the Fluid in the Air Micrometer", Japanese Soc. of Mech. Eng., Vol. 4, No. 15, 1961, pp. 507-515. 41. Spikes, R. H. and Pennington, G. A., "Discharge Coefficient of Small Submerged Orifices," Inst. Mech. Engrs., pp. 9-13. 42. Starrett, P. S., Nottage, H. B. and Halfpenny, P. F., "Survey of Information Concerning the Effects of Nonstandard Approach Conditions upon Orifice and Venturi Meters", ASME paper 65-WA/FM-5, 1965. 43. Zucrow, M. J., "Discharge Characteristics of Submerged Jets", Purdue Research Bulletin No. 31, June 1928. CARBURETOR DESIGN AND TESTING 44. Bolt, Jay A. and Boerma, M., "The Influence of Inlet Air Conditions on Carburetor Metering", SAE paper 660119, 1966. 45. Carnell, N. W., "The Flow Box - An Instrument to Measure Fuel Metering Devices for Internal Combustion Engines", General Motors Eng. Jour., March 1960, pp. 30-36. 46. Freeman, J. H. and Stahman, R. C., "Vehicle Performance and Exhaust Emission, Carburetion Versus Timed Fuel Injection", SAE paper 650863, 1965. 47. Goetsch, E., et al, "Actual Pressure Differentials in the Main Metering System of a Fore 2-V Carburetor", Ford Motor Co. Internal Report, April, 1965. 48. Muller, H. L., Kay, R. E., and Wagner, T. O., "Determining the Amount and Composition of Evaporative Losses from Automotive Fuel Systems", SAE paper No. 660407, 1966.

443 49. Robinson, J. E., and Wagner, R. W., "Part Throttle Vapor Lock Test Development", SAE paper 956A, 1965. 50. Shaffer, E. S., "Nozzle and Venturi Design Criteria for 4MC Carburetor", Rochester Products Internal Report, March, 1964. 51. Smith, S. B., "Effect of Change in Fuel Specifications on Carburetion", Bendix Corporation Internal Report 4190, Dec., 1944. 52. Stoltman, Donald, "The Design Evolution of the Quadrajet Carburetor", SAE paper 660127, 1966. 53. Sytz, W. E., and Harkins, J., "The Effect of Increasing Gasoline Viscosity on Engine Performance", California Research Corp. Report, April, 1961. 54. Tice, P. S., "Theory Governing Carburetor with Intake Throttle," Automotive Industries, November, 1923, pp. 1099-1101. 55. Yu, T. C., "Fuel Distribution Studies - A New Look at an Old Problem", SAE Trans., P. 610, 1963. 56. Wahrenbrock, R. J., "The Effect of Fuel Density on Carburetion", Ethyl Corp., Research Memo ERM-H13, April, 1953. ENGINE AND VEHICLE TESTS 57. Bolt, J. A. and Holkeboer, D. H., "Lean Fuel-Air Mixtures for HighCompression Spark-Ignited Engines," SAE Trans., Vol. 70, 1962, pp. 195-202. 58. Bigley, H. A., Jr., Domke, C. J., and Niles, H. T., "CRC Looks at Cars, Fuels, and Vapor Lock", SAE paper 650860, 1965. 59. Cleveland, A. E., and Bishop, I. N., "Fuel Economy", SAE Journal, Aug. 1960, pp. 27-33. 60. Fuchs, E. J., "Laboratory Engine Method for Measurement of Detergency Effectiveness of Gasoline Additives on Carburetor Throttle Body Deposits," SAE paper 379D, 1961. 61. "Fuel Economy Tests at Steady Speed", Ford Motor Company Internal Reports, 1965-67. 62. Kerley, R. V. and Thurston, K. W., "The Indicated Performance of Otto-Cycle Engines", Ethyl Corp. Research paper 61-17, Nov. 1961.

444 AUTOMOTIVE SIMULATION TECHNIQUES 63. Huber, P.,and Brown, J. R., "Computation of Instantaneous Air Flow and Volumetric Efficiency", SAE paper 812 B, 1964. 64. McAulay, K. J.,Borman, G. L., et al, "Development and Evaluation of the Simulation of the Compression-Ignition Engine", SAE paper 650451, May, 1965. FUEL PROPERTIES 65. Hurd, B. L., Jr., "Fuels for High Compression Engines"., SAE preprint 260B, 1960. 66. Maxwell, J. B., "Data Book on Hydrocarbons", Van Nostrand Co., Inc., 1950. 67. Rossini, F. D., et al, "Selected Values of Physical and Thermodynamic Properties of Hydrocarbons and Related Compounds", Carnegie Press, Pittsburgh, 1953. 68. Van Duyne, R. J., "Measurement of Dynamic Surface Tension Changes in Froth-Forming Aqueous Solutions", Ph.D. thesis, University of Michigan, 1961. GENERAL REFERENCES 69. Carnahan, B., Luther, H. A., and Wilkes, J. O., "Applied Numerical Methods", Volumes I and II, John Wiley and Sons, Inc., New York, 1964. 70. Taylor, C. F., and Taylor, E. S., "The Internal Combustion Engine", Int'l Textbook Co., 2nd Edition, 1962. 71. VanWylen, G. J., and Sonntag, R. E., "Fundamentals of Classical Thermodynamics," John Wiley and Sons, Inc., New York, 1966.