THE UNIVERSITY OF MICHIGAN COLLEGE OF ENGINEERING Department of Mechanical Engineering Technical Report THE TURBO-SUPERCHARGED SPARK IGNITION ENGINE WITH VARIABLE COMPRESSION RATIO E. T. Vincent Kamalakar Rao ORA Project 05847 under contract with: U. S. ARMY TANK-AUTOMOTIVE CENTER PROPULSION SYSTEMS LABORATORY CONTRACT NO. DA-20-018-AMC-0729-T WARREN, MICHIGAN administered through: OFTFICE OF RESEARCH ADMINISTRATION ANN ARBOR April 1966

TABLE OF CONTENTS Page LIST OF FIGURES v LIST OF TABLES vii ABSTRACT ix I. OBJECT 1 I. o INTRODUCTION 2 III. METHOD OF CALCULATION 5 Method 1 5 Method 2 7 IV. PROCEDURE 9 Method 1 9 Ao Standard Engine 10:1 Compression Ratio 12 B. Turbocharged Engine with VCR Pistons and 15:1 Boost Ratio, Without Aftercooling 16 Vo RESULTS 20 Method 2 34 Effect of Fuel-Air Ratio 42 Equivalent L-141 Engine Performance 42 Turbocharger With Aftercooling 53 Comparison With Standard Engine 54 Method 2b 58 7io DISCUSSION 66 VIT. RECOMMENDATIONS 68 VIIo REFERENCES 69 iii

LIST OF FIGURES Figure Page I. Specific volume vs. pressure. 6 2. Manifold pressure vs. rpm curves. 10 3. Naturally aspirated cycle for 10:1 ratio. 13 4. Supercharged cycle for boost ratio of 1,5:1. 16 5o Specific performance of turbocharged system without aftercooler. 23 6. Specific performance of turbocharged system with aftercooler. 25 7. Specific performance of directly driven charger without aftercooler. 27 8. Specific performance of directly driven charger with aftercooler. 29 9. Compression ratio and maximum pressure without aftercooling. 31 10o Manifold pressure vs. speed data. 52 11. Specific performance at full power operation, for F/A = 0.0782. 33 12, Reciprocal of knock-limited manifold pressure vs. compression ratio, for 83-octane fuel. 36 135 Knock-limited temperature vs. density relationship without aftercooling. 37 14. Knock-limited temperature vs. density relationship with aftercooling. 41 15o Compression vs. boost ratio obtained with and without aftercooling, 43 v

LIST OF FIGURES (Concluded) Figure Page 16o Frictional losses and correction factors for 80.6 cu in, engine. 48 17. Gross BHP for 80,6 cu in, engine. 50 18. SFC curves for 80 6 cu ino engine at different F/A. 51 19o SFC curves for 80,6 cu ino engine at different F/A. 52 20. Net performance, (a) BHP, (b) SFC. 55 21. Fuel flow vs. net BHP for turbocharged engine without aftercooler, 57 22. End gas temperature vso density relationship, 58 23, Knock-limited end-gas temperature vs. density for 83-octane fuel. 59 vi

LIST OF TABLES Table Page I. Assumptions Employed 11 II, Specific Performance of Turbocharged Engine Without Aftercooler, for Constant End-Gas Density 20 III. Specific Performance of Turbocharged Engine with Aftercooler, for Constant End-Gas Density 20 IV, Specific Performance of Directly Driven Supercharger Without Aftercooler, for Constant End-Gas Density 21 V. Specific Performance of Directly Driven Supercharger with Aftercooler, for Constant End-Gas Density 21 VI. Specific Performance and Manifold Pressure 22 VII. Throttled Operation of Engine 34 VIII. Knock-Limited Density-Temperature for 83-Octane Fuel 35 IX. Knock-Limited Density Versus Boost Ratio, Without Aftercooler 39 X, Knock-Limited Compression Ratio, Without Aftercooler 39 XI, Knock-Limited Density Versus Boost Ratio, with Aftercooler 40 XIIo Knock-Limited Compression Ratio, with Aftercooler 40 XIII Constant End-Gas Density for Part Load Performance 42 XIVo Estimated Engine Performance 46 XV. Comparison of Standard and Turbocharged Engines on Pavement in Fourth Gear and on Soft Ground 58 XVIo Knock-Limited Curve for 83-Octane Fuel 61 XVII. Knock-Limited End-Gas Density for Various Boost Ratios 62 XVIII, Compression Ratio for End-Gas Temperature-Density Condition with No Aftercooler 65 vii

LIST OF TABLES (Concluded) TabLe Page XIXo Compression Ratio and Boost Ratio for End-Gas KnockLimited Condition with No Aftercooler 65 viii

ABSTRACT This report discusses the use of a turbocharger, rather than a throttle, to vary the power output of a spark-ignition engine using a variable-compression-ratio piston. Performance data are established for use in comparing the L-141 engine having 141 cu in. displacement (used in the M-151 vehicle) with a supercharged version having 80.6 cu in. and developing the same maximum net power, 61 BHP at 3600 rpm. Systems with and without aftercooling are considered. Three methods of limiting knock are used. The results show fairly close agreement; hence they can be considered accurate enough for this preliminary examination The results indicate that fuel consumption at vehicle speeds of 355 mph or less can be reduced, at the expense of a small increase at higher speeds. As with all other turbocharged engines, there will be a lag between throttle operation and the speed-up of the turbine. The problem of matching the turbocharger and the engine has not been investigated ix

I. OBJECT The object of the study reported here was to predict the performance characteristics of a turbocharged spark-ignition engine fitted with a piston having an automatically variable compression ratio. The power output is varied by changes in the degree of supercharge rather than by a throttle, so that pumping losses and engine size are reduced and economy is increased. The results obtained are applied to the L-141 engine, used in the M-151 vehicle, for comparative purposes. The problem was proposed to the writers by Mr. Floyd Lux of the Power Plant Laboratory at the Army Tank Automotive Command. 1

II. INTRODUCTION Most spark-ignition engines are controlled by a throttle valve which regulates the mass of mixture to suit the load on the engine. The procedure with which the present investigation is concerned is to vary the air mass flow over as wide a range as possible by using a variable-speed turbocharger to change the inlet manifold pressure, resorting to throttle operation only when the required manifold pressure falls below atmospheric pressure. The output of the spark-ignition engine is limited primarily by the detonation characteristics of the fuel; any degree of supercharging of a normally designed engine demands that the usable compression ratio be reduced to limit detonation. It follows that any engine fitted with supercharging must lose some fuel economy as increased supercharge is applied, but gains in power output; these conditions are well known. As a result of the reduced compression ratio light-load fuel performance is also adversely affected. Hence supercharging of normal engines is resorted to only when power output is the most important consideration, as with racing engines and aircraft. The development of the Continental Aviation and Engineering Corporation's variable-compression-ratio (VCR) piston has created the possibility of modifying the operation of an engine according to the load of the vehicle. For a heavy load, the needed large power output would be provided by operating the engine with supercharging and low compression ratio; for light load, fuel economy would be increased by operating at a compression ratio higher than normal Fuel consumption would then depend on the operating schedule. If the engine had long periods of idling and low-power operation, and only short periods of full-power operation, it would use less fuel than a standard oneo The range of ratios might be roughly as follows: Compression Ratio Standard engine Supercharged engine Idle 7-5:1 15:1 Light load 7.5:1 15 to 10:1 Light to medium load 7.5:1 10 to 7.0 Medium to heavy load 7.5:1 7.0 to 4.0 With such a wide operating range, the engine should be adjusted to be at its optimum point for all loadso This is usually the condition in which the 2

engine is at the point of detonation at all times. For strictly comparative purposes, this proposed power plant for the M-151 vehicle should have a maximum output comparable with that of the standard engine, 61 BHP net at 3600 rpm. This output could be secured by using as high a supercharge ratio and compression ratio as possible without detonation; from these two ratios the mean effective pressure (MEP) for each cycle can be determined, and then the engine displacement can be calculated. The displacement will of course be much less than that of the present engine; therefore losses, etc., will also be less. Thus the increases in specific fuel consumption (SFC) resulting from the reduced compression ratio at heavy loads, when supercharging occurs, will be offset to some extent. As the load is reduced, a condition will eventually be reached at which no supercharging is necessary. The engine will then behave as a naturally aspirated one, but will use a high compression ratio as a result of the VCR pistonO With further reduction in load, a throttle will have to be provided to reduce manifold pressure still further, and thus air flow. Pumping will then cause some power loss, but much less thanina conventional engine throttled over the whole power range. This reduction in losses due to pumping will also result in some improvement in light-load operation, by reducing the fuel flow requirements. At the same time the piston will adjust the compression ratio at a considerably higherratio.than in the standard engine, and cycle efficiency will be higher. The sum of these gains and losses could result in improved engine operating conditions under the most common Army operating conditions, the loss at heavy load being more than offset by the gain at light load. If the scheme fulfills expectations, it will have the following advantages and disadvantages: lo The engine will be smaller and lightero 2o The range of operation for a given fuel supply will be greater. 3. Little maximum vehicle performance will be lost. 4. Acceleration will be slightly reduced, because of the longer time required to speed up the charger. 5 The manifolding of inlet and exhaust pipes will be some what complicated. 60 The reduced size and bulk will reduce basic engine costs. 7. The application of the turbocharger will increase the basic cost slightlyo 80 A carburetor to handle the combined manifold conditions will need to be developed. 9o The material and structure of the exhaust valves might need some improvement. 10. The structure of the engine might need some strengthening if high peak 3

pressures are encountered. The calculations to be carried out will determine whether this change is necessary. 11. Since the maximum output will remain unchanged, the present cooling system will probably be adequate for such changes in heat rejection as will occur 12. The use of a variable compression ratio, with its accompanying lubrication problems, etc., will cause some complications. 4

III. METHOD OF CALCULATION The most important part of this problem is to determine a method of predinting the characteristics of an engine which will approach the conditions of detonation at all times. Such a prediction will make it possible to compare the turbocharged engine with the standard one; and, if the turbocharged engine shows enough promise to warrant further research, the prediction will provide a basis for that research. The problem of detonation is quite complicated, and most methods of studying it are not generally applicable to all sizes and shapes of engines. The most favored one is that based on the fuel octane requirements of an engine; the engine is adjusted to the desired fuel, usually on the basis of the results of bench and road tests. In the case to be examined it seems that the engine's performance must be predicted on the assumption that the standard 83-octane military fuel, MIL-G-3056A, will be used. Therefore relative compression ratios must be determined for a series of manifold pressure ratios at each of which it is possible to approach detonation with equal closeness at all times, by automatic adjustment of the variable-compressionratio (VCR) piston. In an actual engine test this is readily done by advancing the spark, adjusting the F/A ratio, etc., as appropriate for any given load and speed, since the VCR piston will respond to a near-detonating condition by adjusting the ratio downward until detonation is suppressed. Without such. engine tests the conditions must be determined by calculation; it is here that more information is needed. It is proposed to follow two broad methods, as follows: 1. Take as the limiting condition the state of the end-gas portion of charge just before detonation (Ref. 1)o 2o Take as the limiting condition the ratio of air density to compression temperature (Ref 2). METHOD 1 The first method involves the assumption that the combustion of a few molecules of gas occurs slowly enough that, during normal burning,pressure is uniform throughout the combustion chamber. As a result, the molecules combining at any instant, being an extremely small fraction of the total in the cylinder, burn at almost constant pressure. As they expand, they compress the unburned mixture ahead of the flame front, increasing its pressure and temperature until it reaches the detonation pointo Then all the rest of 5

the mass undergoes instantaneous combustion, or else the flame front passes through it completely before detonating conditions are reached, giving normal engine combustion. If detonating conditions are reached before combustion is complete, the amount of charge that detonates burns at constant volume, since under detonating conditions the rate of combustion is many times faster than normal flame propagation and pressure equilibrium throughout the cylinder is not established. The result is an instantaneous increase in the pressure in the pocket of charge, which therefore detonates, producing a shock wave which travels across the chamber and is responsible for knock. This process can be represented by a specific volume-pressure relationship as shown in Fig. 1, P P 2' f 2 PD - W X _ ~0B m 0 Specific Volume Fig. 1. Specific volume vs. pressure. where 0 represents the specific volume of the charge at the beginning of compression, and 0-1 represents the compression process reaching the compression pressure Pc at 1, the TDC of the engine. The first few molecules that combine, releasing heat, do so at approximately constant pressure, the specific volume of the element changing along the line 1-1'. In the gradual combustion process, as heat is released and pressure is increased, the unburned gas is compressed ahead of the flame front. As a result, the unburned mixture continues to undergo the compression process along the line 1-2, reaching the maximum firing pressure Pf at 2; at this point, if combustion is nor6

mal, the last elements of the charge burn along the line 2-2Ko But if detonation occurs when the pressure has reached PD at 3; the whole remaining portion will ignite so rapidly that its volume will. remain constant volume along the line 3-3', reaching a higher pressure P3to Detonation will therefore occur at some point such as 35, depending upon the state of the unburned mixtures It has been established (Refo 1) that this process does not violate the usually accepted principles of thermodynamics, cycle efficiencies, mean pressures, etco; combustion is considered to occur at TDC with the piston stationary, but even this limitation is not a necessary condition. The problem under consideration can be solved by assuming that a small amount of charge, say 5% reaches the state of detonation during the standard ideal cycle of the engine. Hottel's Charts can be used, within the range of their applicability, to determine the effects of various mixture ratios, chemical equilibrium, etco If this last 5% is brought to the same state, or subjected to the necessary combination of factors, for each of the various cycles to be investigated, it should be possible to compare the cycles and thus determine the detonation point for eacho The calculations herein are based. on two assumptions: (a) that detonation always occurs at the same density, and (b) that there is a relationship between the density of end gas and the temperature at which detonation will occur (see Refo 2); calculations based on this assumption.are considered below at Method 2bo On the basis of these assumptions, cycles having various supercharging ratios were studied to determine, for each one? the compression ratio at which the last 5% of the mixture would detonateo From the results the IMEP, ISFC, etco, were then obtainedo METHOD 2 In Calculations by the second method the work of Refo 2 was applied di rectly, by constructing diagrams showing the reciprocal of the knocklimited manifold air pressure versus compression ratio for 83-octane fuel, as well as a plot of knock-limited compression density versus calculated compression temperature. In this application, Siegel considers that the pressure and temperature at the end of the compression stroke, rather..than at the end of combustion, will define the detonation limits and determine the limiting performance of the engineo Since the actual portion of the charge that detonates is the last portion to burn, there is considerable doubt about whether this theory applies to all engineso Siegel, however, reports results obtained from his test unit which more than suggest that it doeso We have therefore applied his theory in calculating engine performance, as an alternative procedure to show the combined effects of compression temperature and density of the charge on the limiting compression ratioo 7

Three slightly different approaches, then, have been employed to determine the possible operating compression ratio as the degree of supercharging changes'They are based, respectively, on the following criteria: 1. The last 5% of the end gas has a constant density at the point of detonation~ 2o The end-gas density and temperature have a certain relationship. 3 The compression gas density and temperature have a certain relationship It is hoped that by this means the actual engine conditions have been bracketed closely enough to give a reliable picture of the process being investigatedO 8

IV. PROCEDURE METHOD 1 The end-gas method of calculation was applied to the L-141 engine in the following manner. First, the ideal standard engine cycle of the L-141 engine was examined on Hottel's rich mixture charts for compression ratios of 7.5:1 (standard) and 10:1. The latter ratio was predicted as a possible upper limiting condition for the highly supercharged engine, since that engine's displacement will be considerably less than that of the standard L-141. A redesigned head would be needed to obtain the maximum possible ratio. It is of considerable importance that the unsupercharged ratio be as high as possible; otherwise intolerable conditions will arise when the engine is supercharged at the reduced ratios resulting from use of the VCR piston. When these ideal cycles were known, the pressure, temperature, density, etc., of the last 5% of the end gas in the cylinder were determined and used as the factors limiting the compression ratio for a -turbocharged engine. In the second step, the compression ratio that produces the same end-gas conditions as in the first step was determined for supercharge ratios of 1.5, 2o0, 2.5 and 3.0:1, to be supplied by the turbocharged with and without aftercooling. The engine with aftercooler was taken to have an effectiveness E of 70%. The necessary solutions for the compression ratio were obtained by trial and error; information from the combustion charts was used in order to include chemical equilibrium, etco, in the solution. Where the method of compression gas density-temperature relationship was used, it was found more convenient to employ the method described in Ref. 2, In all cases the cycle was analyzed for the output per pound of air supplied to the engine. The IMEP, thermal efficiency, IHP/lb of air/sec, specific fuel consumption in lb/IHP/hr, etc., were obtained. In tests of an actual engine these results would have to be adjusted for the effects of volumetric efficiency, frictional losses, pressure losses between atmosphere and engine manifold, etc. Since the pressure drop between the atmosphere and the manifold, and the temperature change caused by fuel addition, hot-spot heating, etc., are fairly stnadardized, the values referring to the inlet air were modified to give the analysis a closer approach to reality. The losses were estimated as follows: 9

Air cleaner and carburetor pressure drop at = 2.0 psi full speed (3600 rpm) Air cleaner and carburetor pressure drop at = 0.75 psi 800 rpm Temperature drop due to fuel addition = -40~F Temperature increase due to hot spot = +80~F Calculations using the above values result in a manifold pressure and temperature of 12.7 psi and 580~ abs for an ambient condition of 14.7 psi and 80~F at full speed when naturally aspirated, and 19.95 and 580~ abs at low speed. At intermediate speeds the manifold pressure for the naturally aspirated engine was taken as proportional to the speed change; it is represented by the conditions in Fig. 2. P 13.95 Boost Ratio 1.0:1 - -[-I - -~-t12.7 psi I I I I 800 3600 Fig. 2. Manifold pressure vs. rpm curves. 10

Other important assumptions about the engine conditions investigated are given in Table I. TABLE I ASSUMPTIONS EMPLOYED Maximum Power A/F Ratio = 0.0782 Ambient Pressure and Temperature, 14.7 psia and 540~ abs Supercharger ratio 1:1 1.5:1 2.0:5:2.51 30:1 Fraction of exhaust gas (f) in new charge 0.035 0.032 0.03 0.029 0.028 Temperature of exhaust (~F at TDC) 1600 1650 1700 1750 1800 Inlet manifold pressure at full load and speed (psi) 12.7 20.1 27.4 34.8 42.2 Exhaust manifold pressure when turbocharged (psi) 14.7 17.1 25.3 29.6 35.9 For an engine operating with any form of charger, the temperature of the air supply to the carburetor was calculated by the following equation: 1 k-l T T [1 + - (Rk 1)] (1) T a qc k where TT = temperature of air leaving charger (~abs) Ta = ambient air (~abs) nc = compressor efficiency R = compressor ratio k 1.4 This delivery temperature TT was then corrected for fuel addition and hotspot heating, as already mentioned, and the inlet manifold conditions Pm, Tm obtained. The next step in the operation of the engine is to mix the new charge with the f lb of exhaust gas remaining in the cylinder. During this step the exhaust gas is first compressed to the pressure of the air inlet manifold, changing its temperature slightly. Then the inlet charge is mixed with this gas under constant enthalpy conditions. The cylinder then contains f lb of exhaust gas, consisting of f lb of burnt air and (F/A) f lb of burnt fuel, plus (1 - f) lb of fresh air and (1 - f)F/A lb of unburnt fuel, giving an overall weight of (1 + F/A) lb per cycle at P1 and T1. 11

The final cylinder charge conditions Pi and T1 were calculated by use of the energy equation, and from the results state 1 of the cycle was located on the charts. From this point the whole cycle was determined. The procedure of calculation can be illustrated by analysis of two exampleso In the first analysis, the density at which the end gas detonates in a standard engine with a compression ratio of 10:1 will be determined. In the second, the compression ratio at which the same end-gas density is achieved in a turbocharged engine with a boost ratio of 1.5:1 will be found. A. Standard Engine 10:1 Compression Ratio Assumptions Ambient air 14.7 psia and 80~F Exhaust dilutant f = 0.035 Exhaust temperature Te ~ = 2060~ abs Manifold pressure Pm = 1.5 x 147 - 2.0 =20.1 psia Manifold temperature Tm = 540 - 40 + 80 = 580~ abs Assume that Pm and Pe' the pressure at the end of the exhaust stroke in the naturally aspirated engine, are equalo Then Enthalpy of mixture = Enthalpy of + Enthalpy of new charge exhaust gases (1 + F/A) Cp Ti = (1 + F/A)(1 - f)CpmTm + (1 + F/A)f Cp T -e e Cp T1 = (1 - f)CpmTm + f Ce Te Using gas tables for the values of the specific heats at the various temperatures gives (1 - 0 035) x 0.242 x 580 + 0.035 x 0.295 x 2060 Tyj = 0.247 = 628 R Thus the starting point of the cycle is P1 = 12o7 and T1 = 628~R. The cycle is shown in Figo 5. The chart for F/A = 0.782 gives the following values for points 1-5: 12

35, PD {\ V 7 Pm Fig. 3. Naturally aspirated cycle for 10:1 ratio. Point 1 P1 = 12.7, T1 = 628, V1 = 18.5, E1 = 23, S1 = 0.1125 where V1 = volume in cu ft of (1 + 0.0782) lb of mixture E1 = Internal energy of mixture (Btu) S1 = Entropy of mixture Point 2 S2 = 0.1125, V2 = V1/CR = 18.5/10 = 1.85 P2 = 280, T2 = 1315~, E2 = 178 Energy of Combustion Ec = 1507 (1 - f) + 300 f = 1465 Btu Point 3 E3 = E2 + Ec = 1643 Btu V3 = v2 = 1.85 P3 = 1180, ss = 0.525, T3 = 5110~ abs 13

Point 4 V4 = 18o5, S4 = 0.525 P4 = 66,0, E4 = 925, T4 = 2920 net work = (E3 4) E4) - (E2 - El) = 718 - 155 = 563 Btu cycle efficiency = net work/heat added = 563/1465 = 38.4% IMEP = work done/change of volume = 563 x 778/(18o5 - 1.85) x 144 psi = 182a6 psi Horsepower = work x 778/550 (1 - f)/lb of air charge/sec = 563 x 778/550 x 0o965 = 826 hp/lb air/sec Fuel flow = 0,782 x 360 = 282 lb/hr SFC = 282/826 = 0.341 lb/IHP/hr The, above values represent ideal performance for a given manifold pressure and temperature. A well developed actual engine operating under these conditions would develop an IMEP of about 165 gross mean pressure, indicating a relative cycle efficiency of about 0.90 and a BMEP of 1355 psi at 81.5% mechanical efficiencyo This compares with 109 psi for the L-141, indicating a maximum volumetric efficiency of about 80%; however, when heat losses are also included a value of 70% seems closer to the mark. Conversion can be made in this manner for actual output BHP, etc, when desired. In this analysis it is proposed to employ the ideal cycle analysis since relative results will make it possible to evaluate the basic principle being examined It is now necessary to establish the state of the 5% of end gas which is to be considered at the detonating pointo In Ref. 1, it is established that the pressure rise due to combustion at any instant, P - P2, is proportional *to the amount of charge burnt. It follows that PD, the detonating point of the 5% (see Figo i), is given by 14

PD = P2 + 0.95 (P3 - P2) = 280 + 0o95 (1180 - 280) = 1135 psia The 5% of unburnt charge then, has been compressed from pressure P1 to PD, isentropically in the ideal case. This operation cannot be read off the mixture chart, because the range of the chart is too small. Hence the desired value was found by obtaining from the gas tables the average values of k for the process, and using them in the following equations: k h P1V1 = PD VD (2) TD = T1 (PD/P) (k-l)/k (3) The results obtained when k - o1324 satisfied the temperature range from T. = 630 to TD = 1895; solving then showed that VD is VD = 0.623 cu ft When the density at detonation is considered constant, then, p = P/RT = constant Therefore, PD/TD = constant and _ 11355 x 144 PD/TD 1895 86 Thus the density at detonation must be held as close as possible to 86.2 at all times for all the other cycles having varying degrees of supercharge. 15

B. Turbocharged Engine with VCR Pistons and 1.5:1 Boost Ratio, without Aftercooling Assumptions Ambient Air 14.7 psia and 80~F Exhaust dilutant f = 0.032 Exhaust temperature Te = 16500~F = 2110 R Manifold pressure = 1.5 x 14.7 - 2.0 = 20.1 psia Temperature after compressor = Tr = Ta (1 + 1 [R (k-l/k) - 1]) Tc Ta = Ambient air = 540~ abs qc = Compressor efficiency = 0.70 P = Pressure ratio = 1.5:1 TT = 540 (1 + 1/0.70 (1.5.286 - 1)) = 635~R Manifold temperature T = TT - 4 + 80 = 675~R With supercharging at 20.1 psia and exhaust manifold at 17.1 psia (see Table I), the indicator diagram is as shown in Fig. 4, where it is seen that 2 P. Fig. 4. Supercharged cycle for boost ratio of 1.5:1. 16

the exhaust dilutant is compressed from Pe to Pm, increasing its temperature and pressure by the addition of work. The mixture temperature is then given by Cp T1 = (1 - f)Cm Tm + f [CPeTe - Cv(Te7 T ) (4) k-l/k Te7 = Tee x (Pm/Pe) (k = 13.5 for T6 = 2110) = 2110 x 1.043 = 220~R From the gas tables, pm = 0.242, CPe = 0.512, Cp =0.25 and CV = 0.245. Substituting in Eq. (2) gives Temperature of charge T1 = 716~R Point 1 P1 = 20.1, T1 = 716~, V1 = 1.5, E - 39.0, S1 = 0.11 Point 2 Since the compression ratio that will produce PD/TD = 86.2 is unknown, the only known fact about point 2 is that the heat of combustion released at this point is given by E = 1507(1 - f) + 300f = 1468 Btu A trial-and-error solution is resorted to, a compression ratio is assumed, and the calculations are completed to obtain PD /TD. The compression is then charged until PD/TD = 86.2, as nearly as possible. When a ratio of 7.1:1 was employed, the following data were obtained: 17

V2 - - 19 cu ft, P2 = 270 psi 7.1 T2 = 1300~R, E2 174, S2 = 0.11 Point 3 V3 = V2 = 1.9, E3 = 174 + 1468 = 1642, P3 = 1160 psi, T3 = 5120~R Point 4 V4 = 13.5, S4 = 83, P4 = 100 psia, T4 = 3220~R, E4 = 1013 PD = P2 + 0.95 (P3 - P2) = 0.95 P3 - 0.05 P2 1114 psi 0.24 TD - T1 (PD/P1) = 1880 PD/TD = 85.5, close to the desired 86.2. (E - E) -(E ) (Pm - Pe)(V1 - V2) x 144 Work done = (E3 - E4) - (E2 - El) + 778 = (1642 - 1013) - (174 - 39) + 3.01 x 11.6 x 144 778 500.4 Btu Thermal efficiency- 00 5.3 1468 IMEP 23 0.4 x 78 = 235 psi (15.5 - 1.9) x 144 hp 500.0 x 778 731 hp/lb air/sec 550 x 0.968 Fuel flow 282 lb/hr SFC =282 0,386 lb/IHP/hr 731 It is true that the value of PD/TD is not exactly the desired value, but it was impossible to read the charts accurately enough to obtain exact equality. 18

The actual difference in ratio between 85.5 and 86~2 is small and will of course be meaned out by plotting the results obtained in the subsequent diagrams. By proceeding in the above manner for the various supercharging ratios a series of results was obtained for the constant density relationship. In the case in which aftercooling was employed, it was assumed that a heat exchanger with an effectiveness of 0.7 was employed. That heat exchanger is defined by TT - Ta Exchanger effectiveness E = TT - T0 where T = temperature after exchanger and before carburetor a TO = ambient air temperature Ta = TT - 0.7 (TT - TO) = 0.3 TT + To With the fuel addition and hot spot effects, T changes as already defined and the manifold temperature becomes T = T - 40 + 80 = T + 40 a 19

V. RESULTS The data obtained when the value of PD/TD was held approximately constant are shown in Tables II-V for the various cases indicated by the table headings. TABLE II SPECIFIC PERFORMANCE OF TURBOCHARGED ENGINE WITHOUT AFTERCOOLER, FOR CONSTANT END-GAS DENSITY (A/F = 0.0782; To = 540~R; Po = 14.7) Boost Ratio 1:1 1.5:1 2.0:1 2.5:1 3.0:1 Work (Btu/cycle) 563.0 500.4 452 440 417 Thermal efficiency (%) 38.4 35.3 30.8 29.9 28.3 IMEP (psi) 182.6 235 267 500 355 IHP/lb air/sec 826 731 660 641 607 SFC lb/IHP/hr 0.341 0.386 0.414 O.44 0.465 Compression ratio 10:1 7.1:1 6.0:1 5.5:1 4.8:1 P/TD 86.2 85.5 85.9 86.3 86.6 Pm 12.7 20.1 27.4 34.8 42.2 Tm 628 675 748 812 877 TABLE III SPECIFIC PERFORMANCE OF TURBOCHARGED ENGINE WITH AFTERCOOLER, FOR CONSTANT END-GAS DENSITY (A/F = 0.0782; Po = 14.7; TO = 5400R; e = 0.70) Boost Ratio 1.0:1 1.5:1 2.0:1 2.5:1 5.0:1 Work (Btu/cycle) 563.0 467 4.4 367 274 Thermal efficiency (W) 58.4 51.8 28.1 24.9 18.6 IMEP (psi) 182.6 251 307 352 347 IHP/lb air/sec 826 683 603 535 399 SFC lb/IHP/hr 0.341 O.413 0.467 0.528 0.707 Compression ratio 10:1 6.1:1 4.3 3.6 3.0 PD/TD 86.2 86.2 86.0 87.0 87.0 pm 12.7 20.1 27.4 34.8 42.2 Tm 628 608 630 649 666 20

TABLE IV SPECIFIC PERFORMANCE OF DIRECTLY DRIVEN SUPERCHARGER WITHOUT AFTERCOOLER, FOR CONSTANT END-GAS DENSITY (F/A = 0.0782; PO = 14.7; To = 540~R; c, = 0.70; e = 0.70) Boost Ratio 1.0:1 1.5:1 2.0:5:2.51 50:1 Work (Btu/cycle) 563 483.0 426.7 416 375 Thermal efficiency ( 3) 38.4 32.9 29.0 28.3 25.5 IMEP (psi) 182.6 225 252 284 302 IHP/lb air/sec 826 705 622 607 546 SFC lb/IHP/hr 0.341 O.40 0.453 0.465 0. 516 Compression ratio 10;1 7.1:1 6.0:1 5.5:1 4.8:1 PD/TD 86.2 85.9 85.9 86.6 Pm 12.7 20.1 27.4 54.8 42.2 Tm 628 675 748 812 877 TABLE V SPECIFIC PERFORMANCE OF DIRECTLY DRIVEN SUPERCHARGER WITH AFTERCOOLER, FOR CONSTANT END-GAS DENSITY (F/A = 0.0782; Po = 14.7; To = 540~R; ic = 0.70; c = 0.70) Boost Ratio 1.0:1 1.5:1 2.0:1 2.5:1 5.0:1 Work (Btu/cycle) 563 448 385 328 225 Thermal efficiency (%) 38.4 30.5 26.1 22.3 15.3 IMEP (psi) 182.6 241 286 315 285 IHP/lb air/sec 826 655 561 477 328 SFC lb/IHP/hr 0.341 0.431 0.502 0.591 0.851 Compression ratio 10:1 6.1: 1 4.:1 6:1 3.0 PD/TD 86.2 86.2 86.0 87.0 87.0 Pm 12.7 20.1 27.4 34.8 42.2 Tm 628 608 630 649 666 When a direct-drive charger was used, the necessary adjustments for the power required for its operation, plus a 2% loss for the gear set, were made. The isentropic efficiency of the compressor was taken at 70%, a value capable of being achieved by a compression type of blower, but too high for one of the Rootes type. In addition, the engine mean effective pressure was adjusted to allow for the fact that the exhaust manifold pressure will be approximately atmospheric when such a compressor is used. 21

The above results are plotted in Figs.5 to 8, and Fig. 9 shows a comparison of compression ratio, maximum pressure, and detonation temperature for the turbocharged engine with and without aftercooling. All of the results presented give the maximum performance data at full speed and load for each boost ratio with F/A = 0.0782. As the engine speed decreases the boost ratio will decrease, because of the reduction in mass flow of gas through the charger. Let us assume that the manifold pressure will decrease along a straight line until the engine is idling at 600 rpm. The manifold pressure will *then be 13.95 psia, and this value will remain constant at the speed no matter what the speed control of the charger is in use. That is, at 800 rpm the charger will give no boost, but the pressure drop, due to flow through the air cleaner, the charger, the carburetor, etc., will be 0.75 psi (at 3600 rpm it is 2.0 psi), then the diagram shown in Fig. 10 can be constructed to represent the approximate manifold pressure relationship versus rpm for the engine. If a constant F/A ratio of 0.0782 is employed as the full throttle mixture ratio at each point, the cycle analysis gives the maximum power outputs that can be obtained over the range of manifold pressures shown in Fig. 10; the results are given in Table VI and Fig. 11, from which one can determine the performance that will be obtained by using a VCR piston at any manifold pressure and speed for a F/A ratio of 0.0782 and constant end-gas density. TABLE VI SPECIFIC PERFORMANCE AND MANIFOLD PRESSURE F/A = 0.0782; TO = 504e'R; PO = 14.7 Manifold pressure, psia 42.1 34.75 33.1 27.4 23.1 20.1 18.1 16.0 12.7 Work (Btu/cycle) 417 440 442 452 484 500.4 521 532 563 Thermal efficiency ({) 28.3 29.9 30.0 30.8 32.9 35.3 35.5 36.2 38.4 IMEP (psi) 355 306 307 267 247 235 217 206 182.6 IHP/lb air/sec 607 641 643 660 708 731 761 777 826 SFC/lb/IHP/hr 0.465 0.44 0.439 0.414 0.399 0.386 0.371 0.363 0.341 Compression ratio 4.8:1 5.5:1 5.5:1 6.0:1 6.6:1 7.1:1 7.9:1 8.4:1 10.0:1 In addition the throttled operation of the unsupercharged engine was determined and added to Fig. 11 for manifold pressures of 10.0 and 7.5 psia at a F/A ratio of 0.0605; and the compression ratio was determined for the same constant end-gas density. At pressures below 7.5 psia the compression ratio increased to such high values that a practical engine would not be possible; hence the condition giving a maximum ratio of 19:1 was the highest calculated. This ratio is probably higher than could be conveniently designed into the engine. The data for throttled operation are given in Table VII. From the results of Tables VI and VII, as plotted in Fig. 11, it is possible to obtain peak power for all possible manifold pressures up to 42.1 psi. 22

ronstent End Gas Density — Knock-Limnted DenaitY 600 x I~~~~ 800J ^^ ^-X>_ IHP/3b Air/Sec _________ 700 600 o.65 500 | 0.60 400 rP 300 01_ -\ ~~~0.50 40 Effiency 0 0 o. 45 30 0 ~~~~~~~~~~~0.40 SFc Ibsi? 2~0 1 20 0.~55 10 350 10 8 0 ~~~~~~~~~~ ~~~~~~~~~6 E= ComapressiO En~i ~m 250 ~r4 O' Knock-Limited 1 1 Density-Temperature 2 200 (a) 150 1.0 1.5 101.0. Chsrger Ratio 25

Constant End-Gas Denstiy Constant Ap^; ~ Knock-Limited End-Gas Density ------- 2000 a f X X 1600 -1- Pa 0-~ - 1200 0 P0 1100 m mnax 100 - -1000 g9o0 PD/TD 9~~0, O OO, 80 70 ~, 500 A 4~^~~~~~~~0 OI0 ^~ ~~~~~0 400 (b) 1.0 1.5 2.0 2.5 3.0 Fig. 5. (Concluded) 24

800u Constant End Gas Density - pf 800 f I 0 E EKnock-Limited Temperature-Density - p ------- 700 -' 500 H 300 I I PX 0.7- M 0.5 Indicated SFC bs.....!0.0.- |P X 400 0.7 n o 6 P1 20. 0 3 o0 0 0 8. 6.Seii.o 2 100 A (a)5 o a o I I (a ) 4.0 o 100 2.0 1.0 1.5 2.0 2.5 5.0 Boost Ratio Fig. 6. Specific performance of turbocharged system with aftercooler. 25

X 2000 0 1-gU~ ^s^Constant End Gas Density E o1800C Knock Limited Temperature Density - - - - 18oo 1600 - X X 1400 _ _ X200 X ---- x -- -X - PC 1100 \ o mmax Pf 1000 10oo 1 o 90 - PD/TD 900 90~;D 0 0 0 p 80 70 600 0. < 4oo 400 | - _ _ | (b) 200 1.0 1.5 2.0 2.5 3.0 Fig. 6. (Concluded) 26

Constant End Gas Density 800 ~ ~700I ^ — aHP/lb air/sec 600 -- 500 40.0 ff icien cy % 5 h 0.40 -. ^_. "- 50.0 o~~0~~~~.^^55^~ 0300 0.50 0 0 20.0 o.45 0 Indicated SFC lbs/IHP/hr 0.40 0 10.0 250 - IMEP, = ^ssi oR<;-. 0.35 400 10.0 550 8.0 00 x 250 - C~mpresso ~~~~~~~~~~~~x ~~~4.0 200 (a) 2.0 1.0 1.5 2.0 2.5 5.0 Boost Ratio Fig. 7. Specific performance of directly driven charger without aftercooler. 27

2200 Constant End Gas Density ao 2000 T D co X 0 1600 l~OO 1600 1500 P m max ^ - 1200 90 l_______ _ _ _ ~8o -— 0-0 - - JE 70 - 6100 - o n 5000 90~~0 800 70 Output BTU' s/lb Air: 400 5oo (b) 1.0 1.5 2.0 2.5 5.0 Boost Ratio Fig. 7. (Concluded) 28

800 i Constant End Gas Density 700 600 - Attq I 400 x 300 - 40.0 0/ 10.0 I 0.8 -o 0.7 ~ >2 0O.5& 10.0 00S - oo 0.8 H 8.0, Indicated MEP pji 0.3 8. 300oo o )4 ~,4 6.0 \ 1 L 0292 -- 4.0 - — 100 0. I I (a) 1.0 1.5 2.0 2.5 3.0 Boost Ratio Fig. 8, Specific performance of directly driven charger with aftercooler. 29

oo2000 Constant End Gas Density 1800 4 x X =' TD E-4 o 1600 - 1o00 1200 3^*Ss. ^^-^^ - 00~~~~~~~~~~~1100 Pp4 2~~~~6~~~~~~~~~~~~._1000 1 00' 4oo -- 500 "-4^ (b) 2,0' 0 Fig. 8 (Concluded 00 300 (b) 200

2200 - Constant End Gas Density Knock Limited Compression Temperature-Density ------- 0 4 2000 r -X —-- 0 4JI x XI o4 co 1800 - ^ Temperature ~ABS. at Detonation P |qG X No Aftercooling 0^^"^^', | With Aftercooling - 1600 1600 ^^^3s^ /^ X No Aftercooling 1 1100 9 ^^^^^ O 0 With Aftercooling 10.0 100 8-~I. - -- X, —---- V co Maximum Pressureion Rati X No Aftercooling ~~o ^^~ G ~0 With Aftercooling 6.0 -- r-'x0 H 8.0 100 Enmine Conpression Ratio X No Aftercooling H4 50 0 4o ~ X X 0.H 2.0 1.0 1.5 2.0 2.5 3.0 Supercharger Ratio Pm/Po Fig. 9. Compression ratio and maximum pressure without aftercooling. 51

50.0 Manifold Pressure versus Speed 0o 0. EfX0~ 200 -.0.9 Q 0 -2 10.0 13~9.... Boost Ratio 1.0:1 800 1200 1600 2000 2400 2800 3200 3600 3800 RPM Fig. 10. Manifold pressure vs. speed data. 32

20.0 F/A = 0.0782 Constant Density Parameter 18.0 _ 16.0 3 ~~ 00 s\X~ ~~~~~~~~~~ ~ - ~14.0 I \^.%p,~~ 200~ <12.0 0 400 10.0 m or\500 0 0 00~~- 6.0 4.0.4 200 100 ~~~~~~~~~~~~~0 g9x'oo 800 u 700. 600 0.5 o. 0.5 L - -~03- ^ — \ t-l l40 ~~~~~0 10 ~ 20 30 Manifold Pressure psia....Secific prformce at full power operation, for F/A = 00782. 55

TABLE VII THROTTLED OPERATION OF ENGINE F/A = 0.0605; TO = 540~A; PO = 14.7 psia Manifold pressure (psia) 10.0 7.5 Work (Btu/cycle) 565 630 Thermal efficiency (0) 50.3 51.1 IMEP (psi) 140.1 116 IHP/lb air/sec 829 927 SFC lb/IHP/hr 0.341 0.304 Compression ratio 14.0 19.0 METHOD 2 In Method 1 the effects of both pressure and temperature upon detonation are taken to have roughly equal influence. It is generally believed, however, that temperature has more influence than pressure does. After intensive test work on a cooperative fuel-research engine, recorded in Ref. 2, Siegel suggested that a plot of compression temperature and compression density could give coordinating data over a wide range of conditions. When this approach is viewed in its broad aspects, these pressures and temperatures seem to have no direct bearing upon the state of the gas at detonation, since between the end of engine compression and the detonation point the end-gas density and temperature undergo a change roughly of the order of 4 to 10:1. However, the compression state was shown to have some significance in the engine tested in Ref. 2; as a result, the principle will be employed in a second approach to the problem under review. The results presented in Ref. 2 cannot be applied directly to the problem in hand, since they apply to a very different system. They do include, however, a range of knock-limited manifold air pressure values that can be employed for fuel of any given octane value. If, then, any one actual test point representing the state of the charge inside the cylinder undergoing the cyclical process is available for the L-141 engine, the magnitudes of this pressure at all other points can be estimated. To employ this method it will be assumed again that the naturally aspirated engine at a compression ratio of 10:1 represents the limiting condition for detonation of the MILG3056-A, 83-octane fuel to be used in engine tests. The description of the standard engine performance of the 10:1 version, given on page 12, records that, at the end of the compression stroke, P2 = 280, V2 = 1.85, and T2 = 1515~ and that the mass of the charge is 1.0782 lb. It follows that the compression density is 1.0782/1.85 = 0.582 lb/cu ft and the temperature is 1515~ R. Thus 34

the coordinates of one point of the desired knock-limiting curve are known; also the reciprocal of the knock-limited manifold pressure is 1/12.7 = 0.0788. This value permits the construction of Fig. 12 for 83-octane fuel, which is similar to Fig. 7 of Ref. 2. Now the performance has already been examined for additional manifold pressures of 20.1, 27.4, 34.8, and 42.2 psi or reciprocal values of 0.0495, 0.0365, 0.02875, and 0.0237. Obtaining the corresponding compression ratios from Fig. 12, we get 6.65, 5.15, 4.25, and 3.7, whereas the constant end-gas density relationship gave 7.1, 6.0, 5.5, and 4.8; thus this appears to be a reasonable check of the method despite the varying temperature in the system being considered. However, the same manifold pressures were used for the system using an aftercooler; here the temperature of compression will again change considerably, but Fig. 12 does not take this into account. It therefore becomes necessary to calculate the equivalent of Fig. 13 of Ref. 2 from the one known point, namely a knock-limited compression density of 0.582 at a compression ratio of 10:1. Plotting a curve in Fig. 13 through this value with the corresponding values determined from the relationship gives W K - L Manifold Pressure = (CR - 1) Disp = Const (CR - 1) where W = lb of air/hr Disp = displacement in cu ft/hr Then, since Pm = 12.7 psi at 10:1 ratio, the constant becomes 114.3 and Pc = 0.582, if the chart values for displacement are used, whereas if the relations Pc = PI (CR)1.332, Tc = T1 x CR0O332 and P1V1 = wRT1 (where R = 53.34, w = wt of air [lb]) are employed for Pc its value becomes 0.542. This latter method of calculation will be employed, since this is the method of Ref. 2; and the data of Table VIII are calculated. TABLE VIII KNOCK-LIMITED DENSITY-TEMPERATURE FOR 83-OCTANE FUEL Compression Ratio K-L Manifold Pressure T1 Tc PC Pc 16 7.62 620 1560 305 0.528 14 8.79 624 1500 295 0.551 12 10.39 628 1435 285 0.536 10 12.7 632 1360 273 0.524 8 16.32 636 1269 260 0.554 6 22.85 640 1160 248 0.578 4 38.1 644 1020 241 0.638 2 114.3 648 814 288 0.955 35

0.0588 0.05539 0.10 - 0.0490 p 09 0.0 441 0.08 _ 0.0392 Ik~~~~ ~~0.0387 Operating Point of 0.07 / unsupershcared engine.00~43 0 0.07 0.0343 o a / a o.o6 I.0294 0.065 1 -/0.0245 1 0o o 1 I 0.04 0.0196 o. o~t- I I 0.05 I - 0.0147..... /, I I I 0.02: I 0.0098 iii I I / iI j I I 0.01 - oI 0.0049I 1 2 4 5 67 8 9 10 11 12 1 14 15 16 17 1 2 4 7 8 11121Compre sion Rati11617 Compression Ratio Fig. 12. Reciprocal of knock-limited manifold pressure vs. compression ratio, for 83-octane fuel. 56

1.0 0.9 Lines of Pe -T / ~-9l \ ~ Line of pC - T relationship for different com- O Com pression ratios/ F Fig. 13. Kfor compression ratio pression ratios F ~ 0.8 D Oc, /2~i~ 0/7 0.6 * u,~ PC Boost Ratio 1.0 A 0.530 o 0 b' C 0.4 800 go900 1000 1100 1200 1300 1400 1500 1600 Compression Temperature T ~R Fig. 13. Knock-limited temperature vs. density relationship without aftercooling. 37

Plotting the pc - Tc relationship gives curve AB of Fig. 13. It now remains to obtain density-temperature data for each of the various boost ratios, in order to obtain a common intersection from which the desired compression ratio satisfying Pc - Tc can be obtained. Now the knock-limited density pc for the boosted conditions is given by 144Pc K - L pc 144PRTc where Pc = compression pressure (psi) Tc = compression temperature R = gas constant = 53.99 Pc = P1 (V/v2) 332 Tc = T. (V1/V2) 33 V1 = wRTI/P1 From these relations the data of Table IX were calculated. Plotting this information on Fig. 13 gives the curves CD, EF, etc. Reading the point of intersection of the boost ratio lines with the Pc - Tc line for 83-octane fuel then gives the data in Table X. The compression ratio is obtained from Eq. 1 of Ref. 2: (CR - i) = K L Pc x displacement (5) weight of air where displacement = VI (1 - -) Substituting in Eq. (5), we get CR (CR - ) - _K vl-K - LP x Vi(CR 1) W CR CR - (K -L c)V W

TABLE IX KNOCK-LIMITED DENSITY VERSUS BOOST RATIO,WITHOUT AFTERCOOLER Boost Compression V1 152 (CR)0.552 T, T 2.67 P/T Ratio Ratio Vc P 1.5 10.0:1 21.5 432 2.148 716 1556 0.751 8.0 15.99 321 1.995 716 1429 0.600 6.0 11.87 238.5 1.812 716 1297 0.491 4.0 6.55 127.7 1.585 716 1155 0.300 2.0 2.52 50.7 1.258 716 900 0.1505 2.0 10.0 21.5 589 2.148 784 1685 0.954 8.0 15.99 438 1.995 784 1565 0.747 6.0 11.87 325 1.812 784 1421 0.610 4.0 6.35 173.5 1.585 784 1243 0.375 2.0 2.52 69.1 1.258 784 986 0.187 2.5 8.0 15-99 556 1.995 845 1687 0.88 6.0 11.86 413 1.812 845 1531 0.72 4.0 6.35 221 1.585 845 1340 0.44 2.0 2.52 87.7 1.258 845 1064 0.22 3.0 8.0 15.99 675 1.995 904 1804 1.00 6.0 11.86 501 1.812 904 1638 0.816 5.0 8.52 360 1.705 904 1541 0.624 4.0 6.35 268 1.585 904 1434 0.499 2.0 2.52 106.5 1.258 904 1138. 0.250 TABLE X KNOCK-LIMITED COMPRESSION RATIO, WITHOUT AFTERCOOLER Boost ratio 1.0 1.5 2.0 2.5 5.0 K-L density Pc 0.542 0.54 0.5375 0.535 0.55 lb air/cycle 0.965 0.968 0.970 0.971 0.972 Total cylinder volume 17-75 12.8 10.3 8.73 7.71 V1 cu ft/cycle Compression ratio 10.0 7.14 5.7 4.81 4.2 V1, the total volume of the cylinder, and W, the air charge are known for each inlet condition. Thus the compression ratio can be calculated. 39

This process is now repeated for an engine with an aftercooler having an effectiveness of 0.7. The results are shown in Tables XI and XII and in Fig. 14. TABLE XI KNOCK-LIMITED DENSITY VERSUS BOOST RATIO, WITH AFTERCOOLER Total Boost Compression V133 c (CR) T T P Charge Ratio Ratio V2 = 2.67 TC Volume c (cuft) 1.5 10.0 21.5 432 2.148 655 1407 0.82 12.0 8.0 15.99 321 1.995 655 1307 0.656 6.0 11.87 239 1.812 655 1187 0.538 4.0 6.35 128 1.585 655 1038 0.329 2.0 2.52 50.7 1.258 655 824 0.1645 2.0 9.0 18.65 510.5 2.074 672 1392 0.98 9.4 8.0 15.99 438 1.995 672 1340 0.873 6.0 11.87 325 1.812 672 1218 0.713 4.0 6.35 174 1.585 672 1065 0.436 2.0 2.52 69.1 1.258 672 845 0.218 2.5 7.0 13.35 463 1.909 693 1323 0.935 7.8 6.0 11.87 412 1.812 693 1255 0.877 5.0 8.52 297 1.706 693 1183 0.670 4.0 6.35 221 1.585 693 1098 0.537 3.0 4.32 151 1.439 693 996 0.405 3.0 6.0 11.87 501 1.812 708 1284 1.043 6.4 5.0 8.52 360 1.706 708 1208 0.795 4.0 6.35 268 1.585 708 1122 0.638 3.0 4.32 182 1.439 708 1019 0.477 2.0 2.52 107 1.258 708 890 0.321 TABLE XII KNOCK-LIMITED COMPRESSION RATIO,WITH AFTERCOOLER Boost Ratio 1.0 1.5 2.0 2.5 3.0 K-l density Pc 0.542 0.561 0.580 0.589 0.598 lbs air cycle 0.965 0.968 0.97 0.971 0.972 Total cylinder volume, 17.75 11.70 8.81 7.16 6.04 V1 cu ft/cycle Compression ratio 10.0 6.78 5.27 4.34 3.72 40

w O / / 1/ P and T.: Relation 10.08 0 O -)0 qLI 0.9 p -T Como Rel io n e T 4:41 0.7 0.6 0.5 0 2 0.I 0.1 800 go900 1000 1100 1200 1300 1400 1500 1600 Compression Temperature Tc R Fig. 14. Knock-limited temperature vs. density relationship with aftercooling. 41

The points of intersection of the Pc - Tc curves of 83-octane fuel with the K - LPc at different boost are obtained from Fig. 14, and the accompanying compression ratios are recorded in Table XII. The results obtained by the different methods plotted in Fig. 15 reveal that the greatest difference between systems with and without aftercooling occurs when the end-gas density relationship is employed. The knock-limited condition gives a much smaller spread between the two curves. These effects will be discussed later. Effect of Fuel-Air Ratio To provide a better understanding of the overall picture of engine performance, a series of calculations were made for those F/A ratios for which combustion and compression charts were available, and for the manifold pressures given in Fig. 10. The F/A ratios used were F/A = 0.0782 at 3.0:1 boost ratio; 0.0665 at 2.5:1; and 0.0605 at 2.0, 1.5, and 1.0:1 boost ratios. These values represent fairly well the typical operating conditions for an engine at full power and economy performance. The results obtained are listed in Table XIII for constant end-gas density. TABLE XIII CONSTANT END-GAS DENSITY FOR PART LOAD PERFORMANCE Manifold pressure, psia 42.1 34.75 32.71 27.4 22.9 20.1 18.0 15.98 12.7 F/A Ratio 0.0782 0.o665 0.0665 0.0605 0.0605 0.0605 0.0605 0.0605 0.0605 T 904 823 809 766 726 697 674 649 626 P1 42.2 34.75 32.71 27.4 22.9 20.1 18.0 15.98 12.7 Work, Btu/cycle 417 448 416 447 475 475 480 484 527 Thermal Efficiency (%) 28.3 36.0 33.5 595 41.9 42.0 42.6 43.0 46.8 IMEP (psi) 355 325 292 260 249 228 221 198 175 IHP/lb air/sec 607 651 605 652 691 695 703 708 773 SFC/lb/IHP/hr' 0.465 0.368 0.375 0.310 0.293 0.29 0.287 0.286 0.261 Compression ratio 4.8 5.25 5.4 6.4 6.9 7.4 7.7 8.4 10.4 Pmax 1250 1220 1200 1195 1170 1160 1150 1155 1170 With the material now available it is possible to approach data on the performance of an actual engine. Equivalent L-141 Engine Performance So far this report has been concerned with the performance of an ideal engine consuming air at the rate of 1 lb/sec. It is now proposed to convert 42

11.0 Pt = Constant density of end gas = Knock-limited compression temperature-density e = Knock-limited end gas density-temperature 10.0 e 9.0 8.0 7.0 Fig. 15. Compression vs. boost ratio obtained with Aftercooling o 6.0 -X P- 4 a) Pe 0 0 5.0 4.0 Aftercooled 5.0 2,0 1.01 1.0 1.5 2.0 2.5 5.0 Boost Ratio Pm/Po Fig. 15. Compression vs. boost ratio obtained with and without aftercooling. 43

the data so that the resulting net output is that of the L-141 engine, 61.0 BHP. This can be done by including suitable volumetric efficiency and efficiency ratios in order to obtain a close approximation to the output likely to be developed if an engine equivalent to the L-141 is operated in the proposed manner. The official Engine Performance Curves for the L-141, issued by the Ford Nbtor Co. and dated May 13, 1958, give the following data: rpm = 3600 gross BHP = 70.5 Friction hp - 17.0 IHP = 87.0 Mech. Effy. = 80.5% SFC = 0.495 lb/gross hp/hr Compression ratio = 7-5:1 An ideal cycle analysis with the above compression ratio results in the following data, if the same air cleaner and carburetor resistance as for the other ideal cycles, 2.0 psi, is assumed. pi = 12.7 psia, T1 = 630~R, V1 = 18.7 cu ft, E1 = 22 Ratio = 7.5.. V2 = 2.49 cu ft, P2 = 185, T2 = 1200~R, E2 = 149 P3 = 840 psi, T3 = 4932~R, V3 = 2.49, E3 = 1563.5 P4 = 66, T4 = 3066, V4 = 18.7, E4 = 940 Work of negative loop = -5.98 Btu Work of cycle = (1563.5 - 940) - (149 - 22) - 5.98 = 490.52 Btu/0.965 lb of air Heat added = 1415.5 Btu Cycle efficiency = 49012 x 100 = 4.7% 1415.5 IMEP = 490.52 x 778 - 164 0 psi 16.2 x 144 hp/lb of =ir/sec 490.52 x 778 hp/lb of air/sec = = 719 hp 550 x 0.965 44

Fuel flow = 3600 x 0o0782 = 282 lb/hr SFC = 282/719 = 0.392 lb/IHP/hr When these values are compared with actual engine performance, it is seen that there is a cycle ratio of 0.392/0.495 = 0.792 or 79o2%; this factor includes the effects of volumetric efficiency, heat loss, etc. This value is somewhat lower than that usually expected when the ratio is calculated by the above methods; the difference could be due to poor volumetric efficiency, abnormal heat flow to the jacket due to combustion-surface-to-volume ratio, etc. However, if the value is used in converting the ideal values obtained so far into values for an actual engine system, it is believed that the result will be comparable to the performance of the present L-141 engine, though performance might still be improved, The aim will now be to predict the size of an engine without aftercooler, which develops 87 IHP at 3600 rpm when supplied with a turbocharger having a boost ratio which appears to be roughly optimum for calculated overall performance, True, the engine will be smaller if aftercooling is employed, but the compression ratio is then so low that the SFC is very large, being 0.892 lb'/IHP/hr in place of 0.589 lb/IHP/hr for the straight turbocharged unit, It is believed that the relative value of the proposed control system can be judged from this one set of data without aftercooling, If useful improvements seem apparent, any one or more of the other solutions could then be carried through to a final performance map, For the engine defined above, Table XIV can be generated from the data in Tables VI and XIIIo This conversion is based on the assumption that a 10:1 compression can be achieved in the engine by adjustments of the shape of the conmbustion chamber, the valve location, the ignition and valve timing, etc.o, and by the great reduction in the size of the cylindero The relative engine size is determined on the basis of two assumptions: that a boost ratio of 2,5:1 is about the highest that can be used without too great a sacrifice in fuel economy, and that the efficiency ratio remains constant at 79.2% over the range of operation. The ideal cycle at full load, then, is (see Table II) Boost ratio = 2,5:1 Thermal efficiency = 29.9% IMEP = 300 psi 45

TABLE XIV ESTIMATED ENGINE PERFORMANCE (Displacement = 80.6 cu in.) Ratio rpm Pm Tm, F/A IMEP, SFC, I F BHP, SFC, Boost Comp. psi OR psi lb/IHP/hr Gross lb/BHP/hr 4.8 3600 42.2 877 0.0782 265 0.587 97.2 10.5 86.7 0.685 5.3 2700 33.1 781 0.0782 243 0.554 66.8 6.2 60.6 0.610 6.6 1750 23.5 686 0.0782 196 0.504 34.9 3.1 31.8 0.553 3.0 10.0 800 13.9 580 0.0782 150 0.435 12.2 1.1 11.1 0.478 5.2 2700 32.7 810 0.0665 250 o.464 68.8 6.2 62.6 0.509 6.9 1750 23.2 685 0.0605 198 0.370 35.3 3.2 32.1 0.408 5.5 3600 34.8 81- 0.0782 238 0.555 87.3 10.1 77.2 0.627 6.o 2700 28.1 706 0.0782 214 0.520 58.9 6.3 52.6 0.583 6.6 1750 21.5 194 0.0782 194 0.505 34.6 3.1 31.5 0.555 2.5 10.0 800 13.9 580 0.0782 150 0.435 12.2 1.1 11.1 0.478 5.3 3600 34.8 810 0.0665 250 0.464 91.6 10.1 81.5 0.521 6.4 2700 27.8 692 0.0665 216 0.435 59.4 6.4 53.0 o.486 6.9 1750 21.0 685 0.0605 194 0.375 34.6 3.2 31.4 0.413 6.0 3600 27.4 708 0.0782 212 0.522 77.7 10.2 67.5 0.600 6.6 2700 23.1 686 0.0782 195 0.504 53.7 6.45 47.2 0.574 7.9 1750 18.5 623 0.0782 172 0.469 30.7 3.2 27.5 0.523 2.0 10.0 800 15.9 580 0.0782 150 0.435 12.2 1.1 11.1 0.478 6.4 3600 27.4 730 0.0605 206 0.393 75.5 10.3 65.2 0.454 6.9 2700 22.9 685 0.0605 198 0.307 54.5 6.5 48.0 0.419 7.7 1750 18.4 626 0.0605 176 0.363 31.3 3.2 28.1 0.406 7.1 3600 20.1 675 0.0782 185 0.487 67.8 10.5 57.3 0.575 7.9 2700 18.1 623 0.0782 171 0.470 47.1 6.6 40.5 0.546 8.4 1750 16.0 599 0.0782 163 0.458 29.0 3.3 25.7 0.516 1.5 10.0 800 13.9 580 0.0782 150 0.435 12.2 1.1 11.1 0.478 7.4 3600 20.1 652 0.0605 180 0.366 66.0 10.6 55.4 0.435 7.7 2700 18.0 626 o.o605 175 0.362 48.3 6.4 42.9 0.407 8.4 1750 16.0 599 0.o605 157 0.355 28.0 3.3 24.7 0.403 10.0 3600 12.7 580 0.0782 144 0.432 52.8 10.9 41.9 0.545 10.0 2700 13.1 580 0.0782 146 0.433 40.3 6.7 33.6 0.519 10.0 1750 13.5 580 0.0782 148 0.434 26.4 3.4 23.0 0.497 1.0 10.0 800 13.9 580 0.0782 150 0.435 12.2 1.1 11.1 0.478 10.4 3600 12.7 580 o.o605 138 0.33 50.6 11.0 39.6 0.422 10.4 2700 13.1 580 0.0605 140 0.335 38.5 6.7 31.8 0.406 10.4 1750 13.5 580 0.0605 142 0.336 25.3 3.4 21.9 o.388 14.0 3600 10.0 580 o.o605 111 0.332 40.6 11.5 29.1 0.463 Th rott d 14.0 2700 10.0 580 0.0605 111 0.332 30.5 7.0 23.5 0.431 14.o 1750 10.0 580 0.0605 111 0.332 19.8 3.5 16.3 0.404 14.0 800 10.0 580 0.0605 111 0.332 9.0 1.2 7.8 0.383 19.0 3600 7.5 580 0.0665 91.8 0.328 33.6 12.3 21.3 0.517 19.0 2700 7.5 580 0.0665 91.8 0.328 25.2 7.5 17.7 0.466 Throttl 19.0 1750 7.5 580 o.665 91.8 0.328 16.4 3.7 12.7 0.422 19.0 800 7.5 580 0.0665 91.8 0.328 7.5 1.25 6.2 0.97 46

IHP/lb of air/sec = 641 SFC = 0.44 lb/IHP/hr Compression ratio = 505:1 Actual engine performance expected would then be 79.2% of the above, Thermal efficiency = 23.7% IMEP = 237.5 psi IHP/lb air/sec = 508.0 SFC = 0.555 lb/IHP/hr Compression ratio = 5o5:1.0 IHP 8 Mean pressure x displacement x rpm IHP = 87o0 = — 792000 Dispt 87,0 x 792000 Displacement = - 237.5 x 3600 = 80 6 cu ino Air flow = -8 = 0.1712 lb/sec 508.0 =616 0 lb/hr Total cylinder volume (4 cylinders) = Displacement + clearance volume 80,6 = 80.6 + =806 + 17.9 5.5-1 98,5 cu in. Check on cylinder volume 616 1 + 0 ) Total charge/hr 0 ( 971 = 684 lb/hr 47

Total cylinder volume/hr = 98.5 x 180 x 60 1728 = 6160 cu ft/hr Weight of charge/hr = RT _34.7 x 144 x 6160 53.34 x 845 = 683 lb/hr It is seen that the proposed displacement will handle a total mass flow within 1 lb/hr of that estimated. It is now possible to obtain the IHP, air flow, fuel flow, etc., from the ideal cycle, IMEP, for each of the manifold conditions shown in Fig. 10. These data are given in Table XIV. The frictional horsepower employed was estimated from Fig. 16, where the FMEP of the standard engine is plotted on an rpm base. It is assumed that the same FMEP will be lost in a similar engine at the same speed regardless of any change of displacement, i.e., that the FHP is proportional to displacement. Then with the VCR pistons there is also an accompanying change of ratio and thus cycle pressures, plus of course the effect of supercharging raising the pressures throughout the cycle. These effects have been covered by the correction factor shown in Fig. 16, plotted on a ratio basis. 30 20 x -,o - F H Correction FactOr x-ti ^_ ^^ - ^^resBiOn Rat,io Cor e 1 2 4 6 8 10 12 14 16 18 19 Compression Ratio 800 1200 1600 2000 2400 2800 3200 3600 RPM Fig. 16. Frictional losses and correction factors for 80.6 cu in. engine. 48

As an example, let us calculate the FHP of the 80,6 cu in, engine at 2700 rpm and 33.1 psi manifold pressure. Here Standard engine FMEP = 21.1 psi at 7o5:1 ratio Compression ratio of supercharged engine = 5o3:1 Correction factor (Fig. 16),= 1.06 FMEP required = 1.06 x 21.1 = 22,4 psi FHP = FMEP x Disp x rpm 792000 6.12 hp FHP (Fig. 16) of 141.5 cc engine = 10.2 hp By this procedure the estimated gross BHP, SFC, and lb/BHP/hr for the proposed 80 6 cu in, engine have been calculated, They are shown in Table XIV, and plotted in Figs. 17 to 19. Figure 17 shows BHP and compression ratio versus boost ratio for various rpm. The BHP curves represent an averaging of the points in Table XIV; i.e., the various F/A ratios are includedO The result is that the BHP curves shown represent a typical performance of an engine fitted with a carburetor which delivers an F/A ratio of 0,0782 at full load and speed, and leans out to 0.0665 at about 2700 and to 0,0605 at 1750; then the mixture is enriched to 0,0782 at 800 rpm, The compression ratio curves in Fig. 17 indicate this ratio by solid lines for F/A of 00782 and by broken lines for the leaner mixture. When the boost ratio of 1,0:1 is reached, output must be reduced by throttling. This condition is represented in Fig, 17 by the broken line labeled "throttled" with its scale on the left-hand side; compression ratio is seen to increase rapidly up to 19:1o In view of the wide range of compression ratios involved, from 4.8 to 19,0, it is believed that the practical problem of the design of the VCR piston will limit the range that can be used to perhaps 4.8 to 15.0:1.0 approximately; this factor will be neglected in this report. In Figs. 18 and 19, the solid line shows the values for a constant F/A ratio of 0.0782 (rich mixture) from 3600 to 800 rpm, and the broken one shows how the SFC will change if the carburetor gives an F/A varying from 0,0782 at 3600 rpm to 0.0665 at 2700 to 0.0605 at 1750 and back to the rich mixture of 0.0782 at idle at 800 rpm. Since the engine is fitted with a VCR piston, the compression ratio also varies as the F/A ratio; thus the broken lines in these diagrams give the combined effect of these two variables, 49

- 19.0 - 18.0 12.0 17.0 16. O -15.0 11.0 - 4.0 o ~ 9-1.0 -800 12.0PM 9 r 12.0 \ *J__________- ___-_____ -___ _10.0 -11.0 o \ 80 10.0 70 \ \ x 8.0 W \' 60 CD 9.0 0s 0' Xm~ X~~~ 14m 4oo IX 50. /..... 14~0 ~0 0 I I I I I.0 Boost Ratio.0 0.5 1.0 1.5 2.0 2.5 3.0 Boost Ratio Fig. 17. Gross BHP for 80.6 cu in. engine. 50

0.7 0.6 / ~ 0.. ~'' / / ~^^^* ~ W d*/ Boost Ratio 3.0:1 ~05 / 0j F/A 0.0665 0.4? -- F/A 0.0605 0.6 ~ *.^^' / Boost Ratio 2.5:1 ~ 0.5 b 06,02~ ^ ^- - / Boost Ratio 2.0:1 o~ [ X F/A o0.0665 0.46 F/A 0.0605 5~/ Boost Ratio 2.0:1 RPM Fig. 18. SFC curves for 80.6 cu in. engine at different F/A. 51

0.6 > 7// 0.5;' //Boost Ratio 1.5:1 0.5 0.4 - X /.__ F/A 0.0665 F/A 0.0605 0.6 0.6 0.5 H |. v/ Boost Ratio 1.0:1 o - 0.4 - _ _.__.. F/A 0.0605 0.4 F/A 0.0o605 0.55 0.3 Boost Ratio 0.51:1 0.5 -'~^^ F\Pj^ Boost Ratio 0.68:1 0.40 0 l I I I I I I I 800 1200 1600 2000 2400 2800 3200 3600 RPM Fig. 19. SFC curves for 50.6 cu in. engine at different F/A. 52

When the engine has to be throttled below the boost ratio of 1,01, F/A has been assumed to be constant at 0,0605 for a boost ratio of 0,68:1, and at 0.0665 for a ratio of 0.51:1. Hence only one line is given for these two conditions, Turbocharger With Aftercooling For the system with aftercooling, as Fig. 15 shows, the permissible compression ratio is less than in the system considered above regardless of the method used. Also, Figs. 5b and 6b show how the maximum cylinder pressure changes with the boost ratio, From the data in Fig. 5b it is seen that the maximum cylinder pressure increases from 1180 to 1250 psi as the boost ratio changes from lO0 to.0:,1. By the VCR principle this seems to be a fairly good characteristic for satisfactory operation of the variable-ratio piston. The piston motion would be under control at all times, so that an increase in load would make it tend to shift to a lower ratio at which it would be stable. The broken line on the same diagram represents Pmax for the knocklimited end-gas density assumption. Here again conditions are stable9 provided that the range of possible ratios designed into the piston extends from 40 to 10.0:1, and from about 4.0 to 15,0:1, if at all possible, for throttled operation, Examination of Fig. 6b shows that, when an aftercooler is used, maximum pressure decreases as load increases when the constant end-gas density method is used, and remains roughly constant when knock-limited temperature-density is the deciding factor, Reduction in pressure would produce a definitely unstable condition, since the VCR piston produces an essentially constant pressure, Hence the movable head would be forced down to a lower ratio by a reduced pressure rather than by an increased one. Under the effects of inertia9 the ratio would increase to the point of detonation, which would fcrce the piston down to the ratio desired for elimination of knock. But under these conditions the pressure is less than that for which the piston must be set for the naturally aspirated engine with a compression ratio of 10,o1. l The compression ratio will therefore immediately increase and induce detonation again, so that there will be a continual hunting between the ratios of 101.o0 and 5o0 1o In addition, as already pointed out, the operating ratio with aftercooling is about 3,0:1 in any case, so that fuel economy is very poor, The maximum pressure with aftercooling, determined by the knock-limited temperature-density condition and shown as a broken line in Fig, 6b, would be a satisfactory stable operating condition, It follows that the correct conditions determining detonation are essential if an aftercooler is usedo 53

For the above reasons the aftercooling condition has not been examined in complete detail. Comparison With Standard Engine The performance curves available for the standard engine are based upon net output, which includes the power used by the fan, the generator, and exhaust system. To compare the present calculations with the available data, the losses resulting from these items are obtained from the official engine performance curves of the Ford Motor Company, dated May 13, 1958; they are as follows: rpm 3600 3200 2800 2400 2000 1600 1200 800 Horsepower loss due to accessories 9.2 8.0 6.5 4.7 3.0 2.5 2.1 2.0 When the estimated gross hp preformance is corrected accordingly, the results are as shown plotted in Fig. 20 to which have been added, as broken lines, the 100%, 75%, 50%, and 25% load curves of the standard engine, taken from Ref. 3. By using these curves, the data were converted into a fuel flow versus net hp diagram, given in Fig. 21, on which have been shown, again as broken lines, similar curves from Ref. 3, for 3600, 2200, and 1000 rpm for the standard engine. It is at once apparent that performance for a given speed and horsepower has been improved at all low speeds, with some small sacrifice at full load and speed. This is to be expected, since the turbocharging for power variation with fuel of a given octane value has reduced the compression ratio at heavy loads and increased it at light loads. Another major improvement is that the substitution of a 80.6 cu in, engine having the same output as the 141,5 cu in, standard one reduces the frictional losses, which have a greater influence upon the SFC at light loads than at heavy ones. This overall reduction in fuel flow can be seen from Table XV, which gives figures for standard and turbocharged engines installed in M-151 vehicles with the same transmission and operated on pavement in fourth gear and also on soft ground with twice the resistance of a paved surface. It is plain that for a vehicle operating during the 48-hr battlefield day of Ref 35, when the engine idles during 10% of its operating time moves at 30 mph or less during 80% of that time, and moves at speeds above 30 mph during only 11% of the time, fuel flow will be materially reduced. 54

T-C Engine Standard Engine - 70 0 )o~' ~ i;' — 5 Ltoad 60o (a) BHP 1~~~ ~~~50.55 40 / 0 5~ XOOO Boost 20' 3 ~Boos 2t% Load (a) BHP Fig. 20. Net performance. (a) BHP. (b) SFC. T5

0./ \07 " 0. 7 l l ~ l50% SFC Load \ \0\* /\V/ __~0.6 \__O~ O 100% SFC Load o.F. 2 0 0.6 ( Co c ud d 0.6 -- -X 0*^ N^^s. ^^'^v ^ ^^^ ^^~ -^^-X1 - 0.5 0.5 _X__ _ _ __,5 SFC Load 0.5 X X X 0.4 0.4 - 1.0 C i 2^ a o /o w9 N0'0.9 N.0 CD 0 0. 0 - / 0.8 0.6",""~'. /,O /100% 0.6 0\ 00 1<o.'5 —~Z0... 0.5 x - x X 800 1200 1600 2000 2400 2800 3200 5600 RPM (b) SFC Fig. 20. (Concluded) 56

/3600 R 55 Turbocharged Standard ------- 50 - 4500 RPM 45 53600 RPM STD. 40 5000 RPM STD. 35 /1,jh3~0:j~ //y~/ 600 RPM STD., 25 20 / 2200 RPM STD. 15 V yy//y 21800 RPM STD. o -40oo RPM STD. 10 /, 0 1000 RPM STD. 1000 RPM - 800 RPM 0 10 20 50 40 50 60 70 80 Net BHP Fig. 21. Fuel flow vs. net BHP for turbocharged engine without aftercooler. 57

TABLE XV COMPARISON OF STANDARD AND TURBOCHARGED ENGINES ON PAVEMENT IN FOURTH GEAR AND ON SOFT GROUND Speed Net hp Fuel Flow, lb/hr Vehicle, Engine, Pavement 2 x Pavement mph rpm Pavement 2 x Pavement Std. T.C. Std. T.C. 20 1210 3.2 6.4 5.8 2.8 6.5 3.9 30 1820 8.3 15.9 8.7 4.5 10.3 7.3 40 2420 16.2 32.4 12.0 8.4 16.4 15.2 50 3030 30.0 59.6 17.1 11.7 38.0 37.0 60 3630 48.0 95.6 27.4 32.0 Idle 800 0 0 4.0 2.0 4.0 2.0 METHOD 2b It remains to determine whether the method based on the density-temperature relationship of the end gas will give results significantly different from those obtained by the method based on the relationship between compression density and compression temperature. This question will be examined, first, with respect to the system with no aftercooling, since in the cycle of this system the large range of inlet temperatures can be expected to give the maximum variation in compression temperatures. The method can be represented by the diagrams in Figs 22 and 23. The P3 _- - Pf P P P 2(a) P(b) P2 P2 --- Ppsi P =P P1 — M Pm 1 1 Volume Vf Specific Volume Fig. 22. End gas temperature vs. density relationship. 58

2.2 2. _ *00 1.8 0 X ~ Boost Ratio vi'' 0 - -21600 F~ 1.04o 1400 1.2 160 170 18 - 10 20 210 220 2 00 0.61 800 ~0.6~ - 6 00. o.8 -- 400 Ii I I 00 o0 ~ ~ ~ 30.4, I200 2.0 3.0 4.0 15.0 16.0 710 8.0 9.0 10.0 0.0 0.2 11.11 I II I 0.0 400 1500 1600 1700 1800 1900 2000 2100 2200 2300 Fig. 23. Knock-limited end-gas temperature vs. density for 83-octane fuel. 59

former represents the P - V curve of compression and combustion plotted on a normal displacement basis, and the latter is a specific volume plot on which end-gas conditions can be shown to advantage. In these diagrams P1 is the pressure at point 1, which is also equal to the manifold pressure, P2 is the compression pressure due to the engine compression ratio; P3 is the maximum firing pressure due to combustion; and Pf(= P3), Vf, are the pressure and the specific volume respectively, of the end gas at temperature Tf which has been compressed by the combustion process along the line 2-3' of Figa 22b and in which no combustion has taken place. The problem of the density-temperature conditions of the end gas at state Pf Tf can be solved by using the perfect gas laws as in Refo 2. Average values for the ratio of the specific heats k are determined from the data extracted from the combustion charts for the various cycles solved by the chart method. By this means, if k = 1.55, the following equations are obtained: P2 P(R)k (6) Pf - Ps PRf)k (7) where Rf = Final ratio of compression of the last element to burn R = Compression ratio of engine = V1/V Heat of combustion = H = wCr(T3 - T2) T3 = - + T2 (8) wCv Equation (7) can be written as Pf = p(R)k x T3/T2 Substitute for T3 from Eq. (8): H + T2 Pf = P = p(R)k wCv T2 Now the variation of the value of H/wCv, as determined by the combustion charts for all of the cycles with F/A = 00o780, is from 3770 to 3790. Using a constant value of 35780 results in an error of only ~0.4%, which is negligible in relation to the other assumptions made. With this value for H we get Pf P3 = p1(R)k 3780 + 60

But T2 = T1(R)k-l Substituting in the above gives Pf P3 = P1(R) T1(R) + 780 Substituting from Eq. (7) for Pf gives Pl(Rf)k = P- (R) Tl(R) k- + 3780} T1 L (10) (Rf)1'55 = - Tl(R)0O55 + 3780o By Eqs. (6), (9), and (10), the data of Table XVI can be used in calculating the cycle of the basic standard engine having 10:1 ratio and using 83-octane fuel. As in Method 2, the density-temperature curve along which the engine must operate, shown in Fig. 23 and Table XVI, can be determined from Fig. 12. TABLE XVI KNOCK-LIMITED CURVE FOR 83-OCTANE FUEL Knock-Limited Compression Ratio Manifold T1 T2 T Rf Tf Pf of Pressure 16 7.62 620 1637 5417 38.7 2230 1046 1.274 14 8.79 624 1571 5351 34.7 2160 1053 1.302 12 10.39 628 1500 5280 30.5 2080 1049 1.345 10 12.70 632 1417 5197 26.3 1985 1045 1.406 8 16.32 636 1319 5099 22.9 1903 1046 1.467 6 22.85 640 1198 4978 17.2 1732 1065 1.64 4 58.1 644 1047 4827 12.4 1556 1144 1.96 2 114.3 648 826 4606 7.15 1290 1626 3.365 61

To locate the actual operating points with the varying boost ratios and initial temperatures, a series of compression ratio calculations similar to the example below was made for each boost ratio, and the results are recorded in Table XVII. Plotting these points on Fig. 23 gives the common point of operation satisfying the two conditions; from this point the compression ratio can be calculated. TABLE XVII KNOCK-LIMITED END-GAS DENSITY FOR VARIOUS BOOST RATIOS Ratio Boost Comp. T1 T2 T3 P2f 1.0 10.0 632 1417 5197 284 1045 26.3 1985 1.406 10.0 716 1604 5384 450 1512 24.5 2190 1.854 8.0 716 1484 5264 333.5 1185 20.4 2062 1.534 1.5 6.0 716 1340 5120 222.5 862 16.08 1895 1.215 4.0 716 1144 4924 129.5 558 11.7 1695 0.878 2.0 716 912 4692 51.22 263.5 6.73 1397 0.504 8.o 784 1625 5405 454.5 1511 19.5 2220 1.817 6.0 784 1468 5248 307.0 1098 15.5 2045 1.434 2.0 5.0 784 1377 5157 241.0 903 13.3 1940 1.245 4.0 784 1274 5054 177.8 705 11.1 1820 1.035 2.0 784 999 4779 69.8 334 6.38 1505 0.592 6.0 845 1580 5360 389 1320 14.8 2170 1.625 5.0 845 1485 5265 305 1082 12.76 2058 1.405 2.5 4.0 845 1374 5154 225 844 10.6 1931 1.167 3.0 845 1240 5020 170.5 691 9.18 1833 1.006 2.0 845 1077 4857 88.6 399 6.10 1590 0.672 6.0 904 1690 5470 472 1529 14.3 2296 1.777 5.0 904 1585 5360 371 1257 12.4 2195 1.53 3.0 4.0 904 1467 5247 273.5 978 10.25 2042 1.279 3.0 904 1326 5106 207.0 798 8.8 1935 1.102 2.0 904 1150 4930 107.5 461 5.86 1680 0.752 Example 1 Calculate the temperature and density for the basic engine cycle having a compression ratio of 8.0:1 and an inlet temperature of 656~R. 62

Figure 12 gives K - L manifold air pressure as 16o32 psi. Therefore T2 = T1(R) k1 = 636 x 8~ 35 = 636 x 2o07 = 1319~R T3 = T2 + 3780 = 1319 + 3780 = 5099~R From Eq. (10), Rf1.35 = R [TL(R)0.35 + 3780)] 5099 x 8,0 6405 = 64.05 636 Rf = 22.9 Tf = Ti(Rf)035 = 636 x 2.99 1905 Pf = P((Rf)1o35 = 16.32 x 64.05 1046 End-gas density = 144 x f 53599 x Tf = 2.67 x -— 6 1903 = 1,467 Example 2 Calculate the end-gas density and pressure for the case in which the boost ratio is 1,5:1, the inlet temperature is 716~ and the compression ratio is 8.0:1, P1 = 14,7 x 1.5 - 2~0 = 20.1 psi T2 = T1(R)0 ~35 = 716 x 80~35 = 716 x 2,07 = 1484 R 65~~~~~~~~...

T3 = T2 + 3780 5264~R P2 = P?(8)1~35 = 20.1 x 16.6 33355 psi P3 = Pf = P2 x T3/T2 = 3335 x 5264 1484 = 1185 psi Pf = PI(Rf)1l35 Rf = (Pf/Pl) 1/1.35 (1185/20,1) 1/1.55 = (58.9) 1/1.35 20.4 0.35 Tf = T3.(Rf) = 716 x 2.88 2062~R End-gas density = 2.67 x Pf/Tf = 1.534 T2 = T(R) k-1 = 636 x 80~35 = 636 x 2.07 = 1319~R T3 T2 + 3780 319 + 3780 5099~R By Eq. (10), (Rf)1035 = *R [Th(R)0-35 + 3780] 5099 x 8.0 0 5 656' - o 636 Rf = 22.9 The boost-ratio curves intersect with the 85-octane one at the values given in Table XVIII, where the desired values of pf and Tf are obtained, Then, the value of pf can be obtained by 64

TABLE XVIII COMPRESSION RATIO FOR END-GAS TEMPERATURE-DENSITY CONDITION WITH NO AFTERCOOLER Boost Compression Ratio Tf Pf Ratio 1.0 1.4o6 1985 lo45 10.0 1.5 1.4 1987 1043 7.05 2.0 1.385 2010 1043 5.92 2.5 1.37 2040 1046 4.85 3.0 1.345 2082 1049 4.3 P = pf Tf (11) 2.67 By plotting Pf versus R for each boost and compression ratio, as shown in Fig. 23, the desired compression ratio for the knock-limited density of the cycle is obtained; it is shown in the diagram, and the important data are recorded in Table XIX. TABLE XIX COMPRESSION RATIO AND BOOST RATIO FOR END-GAS KNOCK-LIMITED CONDITION WITH NO AFTERCOOLER Boost Compression Ratio m max e Ratio 1.0 12.7 630 1045 1.406 10.0 1.5 20.1 716 1043 1.4 7.05 2.0 27.4 784 1043 1.385 5.93 2.5 34.7 845 1046 1.37 4.85 3.0 42.2 904 1049 1.345 4.25 This compression ratio is plotted as a broken line in Fig. 5a. It is seen to be almost identical with the results produced by the constant density method. 65

VI. DISCUSSION In this discussion the results derived when using a mechanically driven blower will be neglected, because of the reduction in power and economy resulting from the power absorbed by the blower, A comparison of the data in Tables II and IV shows that at a boost ratio of 2,5:1. with and without aftercooling, the ratios of the outputs are 641 hp/lb air/sec at Pm = 34,7 psi and Tm = 812~R without cooler, and 535 hp/lb air/sec at 3407 psi and 693~R with cooler, Specific volume without cooler = RTm/Pm = 8.67 cu ft/lb Specific volume with cooler = 53.34 x 693/144 x 347 = 7.4 cu ft/lb It follows that the 80.6 cu in. engine without aftercooling would have to be reduced to approximately 69.0 cu in. to develop the desired net BHP of 61o0, or 17.25 cu in, per cylinder in a four-cylinder engine. This displacement would require a cylinder diameter of approximately 2-3/4 in, if a square engine was employed. The size is becoming very small, but the fuel consumption is increasing rapidly because of the reduction in compression ratio, there being a 20% increase in the fuel required in the ideal engine cycles which would mean a brake specific fuel consumption approaching 0.8 lb/BHP/hr at full load. The turbocharged engine without cooler was taken as the reference point. Figure 21 presents a comparison of the standard engine and the proposed turbocharged one, It is seen that the major economics are made at low vehicle speeds and low power, a condition which is appropriate to the type of operation involved. At the same time the loss in economy at high power and speed is rather small; however, the gains more than offset the losses. From Fig, 20a it will be observed that in the range from 800 to about 2400 rpm the standard engine will develop a few more hp at full throttle than will the supercharged one, This is the result of the charge pressure falling with engine speed because of reduction of gas flow. As a result the time of acceleration of a fully loaded vehicle will be somewhat longer with a turbocharger, It is possible that the use of variable geometry in the charger, which will be needed anyway, can offset this deficiency to a major extent, The compression ratios calculated for the different engines studied are diagrammed in Fig, 15, It is seen that the general trends are similar but that the individual curves show differences amounting to about 0,5 to 0~75 of a ratio, depending on the methods, In view of the widely different as66

sumptions made, this is considered to be good agreement between results^ however, a difference of say 0.5 in the ratio brings about a major change in the thermodynamic performance. Most of the work was devoted to the system without aftercooling because of the higher ratio it requires which gives better performance at high boost and because it procuces pressures suitable for the use of a VOR piston. 67

VII. RECOMMENDATIONS The work that produced the above results took longer than was expected. As a result, some short cuts have been employed for the sake of a coherent description. This work is presented for use by the staff of the Power Plant Laboratory in deciding whether any of the schemes discussed would be useful to the Army. If so, one or more of the analyses herein could be extended to give predictions of the performance of all the components of the system — engine, turbo, and controls. It would then be possible to determine the range over which the turbo could be operated successfully, and to make performance maps of power output, fuel consumption, and other properties as needed for a complete and detailed description of the performance of the system. 68

VIII. REFERENCES 1. W, E, Lay, C. W. Good, and E. T. Vincent, The Internal Combustion Engine, Edwards Brothers, Inc., Ann Arbor, 1939o 2. B, R. Siegel, "Use of Temperature-Density for Measuring Antiknock Quality," Society of Automotive Engineers Transactions, Vol. 66, 1958, pp. 421-441, 3. E, To Vincent, The Flexible Engine, Report No. 05847-3-F9 The University of Michigan, Ann Arbor, May, 1964. 69

UNIVE0352OF7 HIGA2 3 901403527 2908