THE UNIVERSITY OF MICHIGAN INDUSTRY PROGRAM OF THE COLLEGE OF ENGINEERING HEAT TRANSFER FROM ACOUSTICALLY RESONATING GAS FLAMES IN A CYLINDRICAL BURNER William No Zartman A dissertation submitted in partial fulfillment of the requirements for the degree of Doctor of Philosophy in The University of Michigan 1960 July, 1960 IP-445

Doctoral Committee: Professor Stuart Wo Churchill, Chairman Professor John Ao Clark Associate Professor Don E. Rogers Professor Lawrence H. Van Vlack Professor Edwin H. Young

ACKNOWLEDGEMENTS I wish to express my appreciation to: The doctoral committee for their advice and assistance during this investigation. Dr. S. W. Churchill, the chairman of the doctoral committee, for his interest} suggestions, and encouragement, The Department of Chemical and Metallurgical Engineering and Esso Research and Engineering Company for their financial support of this research. Dow Chemical Company for providing a fellowship. The Industry Program of the College of Engineering for its help in reproduction of this report. ii

TABLE OF CONTENTS Page ACKNOWLEDGEMENTS * a 4 o a a. * a O O h a. * O a. * a a a O a O O a a a a e. o a s a a o 0 * 0 0 * 8 0 0 080 o @ 8 0 0 ii LIST OF FIGURES a o o O. o o a.,o a O O OO a O a a r a O O O ao 4 oO a 0 o a a a O O o a O O o 0 * a 0 t a 0 0 0 a vi NOMENCL.ATUTRE- 8 8. a a. a a a o a a * * a * 4 @ @ * 8 * 0 * 0 0 * 0 @ * 0 0 * * 0 8 * 0 0 0 4 8 * 0 8 0 0 0 X ABSTORACTI0O * * l*aa 0 00*0a 00 80 a 00 a @00 0000 00 4 0o a 808 0 a 0Is 0 * a X0 V 80 0 0 0 a x I]NITRODU CTIONO... * 0 @ o 0 8.80 0 0 * * * a O * 0 0 a a * o **$ * * o ff O a a e * * a * a a ~ a Q* @ * a a o. 1 LITERATURE SURVEY.oOOOOOOOo.O.o.... ooo.a.o... O.e. o...o 4OO...oo. 4 Heat Transfer from Flames 0008888 0 0 ** Is 0 0 0 0 a8 8 4 Radiationr from Flames... * 4 o..................0.... 4..... 4 Convective Heat Transfer... * * * 5 Heat Transfer from Chemically Reacting Systems...0000080 @0080* 6 Heat Transfer from Particular Burners,.........0*888e0 *O 0.0o 8 7 Effect of Oscillations on Heat Transfer Rates...080.. $a I 000 00 0 000 9 Heat Transfer from Oscillating Flames 8*.0 08 O*... 0o8*o... 12 Combustion Instabilities l o880 80 o o o4 o00o o @0 o 0 o 00a e 0 80e 08 88 0 13 Acoustically Resonant Frequencies.. 80^00080000000 @800 008800 15 Conditions for Flame-Generated Oscillations..0 0880000v. f 14 Flame-Generated Longitudinal Oscillations 0 0008 0008880000 15 Sensitive Time Lag Criterion *.,0000800 O Oaooo o oe 08o0 o80088 16 Generation of Transverse Oscillations0*800800088008 17 Screeching Combustion..,, Q0 l 00 00 8 0 @0 00 800a 8' 0 400 8 'aa040 8 0 08 0 0 a@04 18 Mechanisms to Explain Screeching Combustion, 008*,..80. 19 Methods for Damping Oscillations.80000000 0 0 00 80 00 21 Effects of Oscillations on Combustion.00800 8 080. 0 * 0 80.8080. 21 Theories of Flame Stabilization80*.. 0800080 eo0 80* 0 a. 23 Turbulent Flame Speeds 0 8 a 00 @ 00. o O 0 0 80 8 oX4 00 08 8 0 o@ 25 APPARATUS..000**046 ** 00*.008*0000008O 0O*O 4~ 27 General Features of Comiplete System...O O..00 0 80 0 80 27 General Features of Combustion C3hamber 00 0..,... OO O8080 32 Embedded Thermocouples for Heat Transfer Measurement.,,,....,0,,. 33 X-Rays to Locate Thermocouples Precisely0 000000 36 Windows and Pressure Taps,,O8O. * @88O 0 800o a0 a 0@ 808 aa* 00 88 a l 37 Flameholders 808000O @00 0 0000 * 0800008 0 0 OQooo 0e 80e0 * 0800 0 4 o ~ o o 8 358 Sodium Injection Through Flameholder.,*......800*080 *... 0008 39 Cooling Water and Spray Quench.8 0 88800O000OO O0 O808*400 39 Mixing Chambert o0 O O 0 0 0 0 8 0 * @ 8 8 8 0 0 @, 8 40 iii

TABLE OF CONTENTS (CONT'D) Page Sonic Orifice...................4...... 4..,,4.4.4...44, 41 Sodium - Line - Reversal System.............................. 42 Extension Leads and Miscellaneous Thermocouples...*........... 44 Measurement of Sound in Cham ber................................ 46 Propane System..*. *-* *... *. ****.4.-. * * * ^* * 47 Air Supply and Test Cell*.....#..............*. 47 EXPERIMENTAL THEORY AND ACCURACY,..........*......*..........*.. 49 Evaluation and Accuracy of Local Heat Fluxes..**..............0 49 Accuracy of SLR Method,................4. 4 4 4.4............., 51 Bulk Mean Gas Temperature., 4,*4....,........., 54 Justification of Microphone Position................... 55 Combustion Efficiency from Pressure Measurement.................. 55 Prediction of Resonant Frequencies..........4* 4 4 *.......,.. 57 Theory of Acoustical Damping..................... 4........ 59 Accuracy of Flow Measurements......*.............. 59 EXPERIMENTAL PROCEDURE......................60 Steady-State Measurements....................... ** 60 Cold Flow Measurements............................ 62 Control of the Flame-Generated Oscillations.................... 62 Corrosion of the Burner4 *........................444.... 63 EXPERIMENTAL RESULTS* < * 44 44 4 4..4 4 64 4.4 4 44444 444 4 4 64 Range of Process Variables.,,. o........... *.,, 4. 4. * 64 Form for Data Presentation....,.....,........,.44.........,,,.,, 64 Effects of Transverse Oscillations on Heat Transfer Profiles..,. 66 Temperature Profiles and Transverse Oscillations4.....*.......... 93 Short Burning Lengths and Transverse Oscillations............... 93 Flow Rates and Transverse Oscillations......................... 94 Moderately Intense Screeching Combustion....,............*. 94 Fuel-to-Air Ratio and Heat Transfer Profiles............... 95 Effects of Longitudinal Oscillations..*............... 95 Comparison of the Two Acoustic Modes....................,...... 96 Hysterists with Organ-Pipe Oscillations............ 96 Fuel-to-Air Ratio, Flow Rates, and Organ-Pipe Oscillations...... 97 Transverse Oscillations with Ring-type Flameholder............. 97 Effect of Higher Wall Temperatures on Screech...........4.. 97 Local Heat Transfer Coefficients...,........,.,. *.......... 97 iv

TABLE OF CONTENTS (CONI'D) Page Correlation of Heat Transfer Coefficients..............o..... o o 118 Behavior of Burner with Increasing Fuel-to-Air Ratio.....o..0o. 119 Stable Burners o o o o.............o...... 120 Effect of Inlet Flow Conditions,..,,, o120 Heat Balances...........o ao.. a.. a o a o a 0oa U o a a 04 121 Pureness of Flame-Generated Notes.......o..O e.o...*.*.. o.. 121 Comparison of Combustion Efficien1ies......00a.0090a.Q,..00,.. 122 Additional Combustion After 7-1/2 Inches, o, e,.,.................. 122 DISCUSSIQON, o f o a oo e oo ao o oao a 0 oo 0 oe 0o a ao o a a v o o o o e o a a 0 a o A4 aao o a123 Flame Temperatures.......... o....*...........o o...O.......4 123 Temperature Profiles.. o. o 4 Oa a* e Oa O a l o a a a.. a.... 124 Physical Versus Combustion Effects of the Oscillations,......e ooo 125 Corroboration by Other Investigations...O.O....O #*o.............. 126 A Reference Sound Pressure Lel.e..O..O..OOoe o a................ 126 Effect of Frequency., a 0 Ca aO a 4 O..... a o o o oe. 4 * o. 4.o4 aa4. e.. a a a 4 a. o 127 Agreement with the Literature.........o..................... 128 Difference in Cor rela1tions o o a 129 Explanation of Burner Failures O 129 Determination of Resonance for Longitudinal, Oscillation,..o 404.. 130 Designation of the Acoustical Mode f or SreechL, a oa....... 130 Failure of Pressure-Drop fMthhol at HEgh. Sound PressuresO... 131 Importance of Inlet T.hrbulenceo. O 4 ooo o 4 o o 4 4 133 Explanation for Slight Difference in Heat Balances.............oo 133 C0NCLUSI0Ns a a a a O 0 a O a a O a a O O a O a a e Q a 0 o 0 a 0 o o 0 a a o o o 0 o a a a a O a ~ a O O 0 0 a 0 4 0 ~ a a 134 APPENDIX A - (3RIGITNAL AMND PROCESSED DATAo,,GOoo,,,o,,,o oo, 0oo o o 135 List of Flameholders o o o o o...........Q.O.O.O...a...o........o.o 14 List off' 141 APPEND1'X B - SAMPLE CALCUfLATIONO,,O00,, 0 a00 0 a0oo o 0 40 0 ao aaO aOa 142 APPENDIX C - DERIVATIOrS.............o..c.... 156 APPENDIX D - CONTUCTIVITY OF TUBE WALL AND LAMP CALIBRATION..O.OO.. 163 ~v166

LIST OF FIGURES Figure Page 1 Schematic Flow Diagram of the Apparatus, o oo oo o o o. 0 28 2 Photograph Showing the Manometer Panel on the Left, the Metering Panel on the Right, and the Vertical Mixing and Combustion Chambers in the Center, partially hidden..a, o..... 29 3 Photograph of the Combustion Chambera a........,.a,.a.... 530 4 Photograph of the Metering Panel............... e..-. 31 5 Detail of Combustion Chamber3..,,.............. o.........34 6 Detail of Thermocouple Section,,.......... 35 7 Schematic Diagram of Sodium-Line-Reversal System......a..... 43 8 Profile of Heat Flux - Damped versus Undamped Screech at Re 47 000 67 9 Profile of Heat Flux - Damped versus Undamped Screech at Re = 40, 500 Oa00a..a.,.a........a..0aa00a.....a....4aa.0... 68 10 Profile of Heat Flux - Comparison of Flameholders under Stable Conditions 0...... &o o..........o o.... o. o o. 69 i.1 Temperature Profile - Damped versus Undamped Screech at Re 40 500~ a a *o ooaa a a * aaaaaaaaaaaaaaa*a 70 12 Profile of Heat Flux - Damped versus Undamped Screech for Lb 13,1/2-inches o.............. o a a a a a o ao a. 71 13 Profile of Heat Flux - Effect of Burning Length During Screeching0..O..... a a a a o a 0 a a a a 0 aa a * a a a a ao a 4 72 14 Profile of Heat Flux - Effect of Flow Rate During Screeching, 73 15 Profile of Heat Flux - Effect of Flow Rate and Slight Change in Sound Level0.a., a a a a a a ao a a a a a a a a a a a a a a a 74 16 Profile of Heat Flux - Screeching versus Stable Combustion at Re = 47,700...00aooaa. a oaooo. a a..O.. o......o..aoo 75 vi

LIST OF FIGURES (CONTtD) Figure Page 17 Temperature Profile - Screeching versus Stable Combustion at Re = 47,700.~.......................................... ~ 76 18 Profile of Heat Flux - Screeching versus Stable Combustion at Re = 40,500...........*......... *........ 77 19 Temperature Profile - Screeching versus Stable Combustion at Re = 40,500...............................-. 78 20 Profile of Heat Flux - Effect of Varying Fuel-to-Air Ratio with a Flameholder that is Prone to Screech.................... 79 21 Temperature Profile - Effect of Varying Fuel-to-Air Ratio with a Flameholder that is Prone to Screech......*.....**.......,... 80 22 Profile of Heat Flux - Effect of Varying Fuel-to-Air Ratio with a Flameholder that is Prone to Screech with Lb = 13-1/2 Inches..........e*e..ee...e...............e.e w.w............ 81 23 Profile of Heat Flux - Longitudinal - Oscillating versus Stable Combustion at Re = 35,000............................... 82 24 Profile of Heat Flux - Damped versus Undamped Longitudinal Oscillations at Re = 40,500.........e.......................... 83 25 Profile of Heat Flux - Damped versus Undamped Longitudinal Oscillations at Re = 46,000...........w..... w.c e....... 84 26 Temperature Profile - Damped versus Undamped Longitudinal Oscillations at Re = 46,000ooo..*....................... w 85 27 Profile of Heat Flux - Screeching versus Longitudinal - Oscillating Combustion at Re = 47,000..........*............... 86 28 Profile of Heat Flux - Screeching versus Longitudinal - Oscillating Combustion at Re = 40,500......................... 87 29 Hysterisis Behavior of the Longitudinal Oscillation with Fuelto-Air Ratio..*......... ew.......................... e.. 88 30 Profile of Heat Flux - Effect of Flow Rate during Longitudinal - Oscillating Combustion....... wee. e...... e......*......... 89 vii

LIST OF FIGURES (CONTtD) Figure Page 31 Profile of Heat Flux - Effect of Varying Fuel-to-Air Ratio During Longitudinal - Oscillating Combustion..4........ 90 32 Profile of Heat Flux - Comparison of S-1 and S-4R Flameholders During Screeching Combustion....................... 91 33 Profile of Heat Flux - Effect of an Approximately 200~F Rise in Wall Temperature During Screeching Combustion........ 92 34 Coefficients Taken without Combustion, h'/h', versus Distance from Flameholder.................. o..... 99 35 Local Coefficient for Convective Heat Transfer, 13-1/2 Inches from Flameholder, versus Sound Level in decibels............ 100 36 Local Coefficient for Convective Heat Transfer, 13-1/2 Inches from Flameholder, versus Sound Pressure Amplitude.....0..4.. 101 37 Local Coefficient for Convective Heat Transfer, 9-1/2 Inches from Flameholder, versus Sound Pressure Amplitude4.4..,,, *.. 102 38 Local Coefficient for Convective Heat Transfer, 7-1/2 Inches from Flameholder, versus Sound Pressure Amplitude............ 103 39 Local Coefficient for Convective Heat Transfer Based on E = 80 per cent, 13-1/2. Inches from Flameholder, versus Sound Pressure Amplitude....................... 104 40 Behavior of Screeching Combustion with Fuel-to-Air Ratio..,.. 105 41 Profile of Heat Flux Comparison of S-1 and S-4R Flameholders During Stable Combustion...,...,.................. 106 42 Temperature Profile - Comparison of S-1 and S-4R Flameholders During Stable Combustion1..,,.,,.......... 107 43 Profile of Heat Flux - Effect of Varying Fuel-to-Air Ratio During Stable Combustion....................... 108 44 Temperature Profile - Effect of Varying Fuel-to-Air Ratio During Stable Combustion..... o...................... 109 viii

LIST OF FIGURES (CONT'D) Figure Page 45 Profile of Heat Flux -- Effect of Burning Length During Stable Combustion.... *... *.........................*. 110 46 Profile of Heat Flux -- Effect of Varying Inlet Turbulence Intensity by Moving Sonic Plate..................*...... ll 47 Profile of Heat Flux -- Effect of Atmospheric Humidity....... 112 48 Profile of Heat Flux -- Effect of the Injection of Sodium Salt... * *@.9...*..................,............ 113 49 Summary of Heat Balances,.......... 114 50 Typical Frequency Traverse During Screeching Combustion...... 115 51 Comparison of Combustion Efficiencies Obtained by the SLR and Pressure-Drop Measurements..................1......... 116 52 Difference in Combustion Efficiency at the 7-1/2 and 13-1/2 Inch Distances from the Flameholder..........*.... 117 53 Temperature Gradients in the Tube Wall at the Five Measuring Stations...........** **.*...**........ 146 54 Complex Mapping Technique for Analysis of Error Caused by a Thermocouple Hole on the Heat Flux..................... 160 55 Thermal Conductivity of Tube Wallt Croloy, as a Function of Temperature...'.... I...I.*.....It*....*......... 164 56 Calibration Curve of Tungsten Ribbon Lamp with Vycor Window in Line of Sight..a.................................... 165 ix

NOMENCLATURE a s.peed of sound, ft/sec A area, ft2; A for inside surface area; AT for total area C a constant Cp specific heat at constant pressure, Btu/lb~F; Cps for heat capacity of species S; Cp for mean heat capacity of a mixture D diameter, ft. E combustion efficiency, i.e., the fraction of available heat released by chemical reaction Er, EL intensity of emmission of radiant energy at the wave lengths of the sodium D-lines and in the direction of sight, (energy)/(area) (time); EF for the flame; EL for the lamp f sonic frequency, cps; or friction factor FD drag of flameholder and tube walls, lb force per lb mass gc conversion factor, ft(lb mass)/ft(lb force) sec2 G mass velocity, lbs/hrft2 h local coefficient for convective heat transfer, Btu/hrft2~F; hv for a position x along the tube; ha is the predicted coefficient for fully developed turbulent flow; h for the coefficient without combustion Jm cylindrical Bessel function k thermal conductivity of fluid, Btu/hrft2~F per ft; ks for evaluation at the surface temperature L length, feet; commonly the distance from flameholder; Lb for the burning length, exclusive of any spray quench; Le for acoustically resonating length, feet m a wave number for transverse modes of oscillation M molecular weight,lb mole; M for the mean value of a mixture n, nx wave numbers; n for radial modes of oscillation; nx for longitudinal modes of oscillation

NOMENCLATURE (CONT' D) Nu Nusselt number, hD/k; Nu for evaluation at the surface temperature P absolute pressure, psia; or the root-mean-square pressure amplitude of a sonic oscillation; Po for the sound pressure amplitude at 130 db, 0.0092 psi Pr Prandtl number, Cp~i/k; Prs for evaluation at the surface temperature ci rate of heat transfer per unit area, Btu/hrft2; qR for the radiant heat flux Q rate of heat transfer, Btu/hr; Qi for the integration of the profile of local fluxes; Qw for the heat absorbed by the tube's cooling water; Qt for the total heat loss from the flame per unit mass of fluid, Btu/hrlb Qr(To) heat released due to chemical reaction at reference temperature To, Btu/lb QR(T ) heat released by complete combustion at reference temperature To, Btu/lb r radius, inches; ri and r. for the radii of thermocouple tips, i and j; rs for the inside tube radius R inside radius of tube, feet Re Reynolds number, DG/Ci; Res for evaluation at the surface temperature t time, hour T temperature, OF or OR; TSLR for the temperature measured by the SLR method; Tb for the bulk mean fluid temperature; Ts for the surface temperature u fluid velocity, ft/sec; or coordinate in complex mapping problem v coordinate in complex mapping problem V volumetric rate of flow, ft3/hr W mass rate of flow, lb/hr xi

NOMENCLATURE (CONT'D) x distance along tube, feet; or coordinate in complex mapping problem y mol fraction; or coordinate in complex mapping problem z plane in complex mapping problem Greek Symbols CaF absorptivity of flame cmn values that satisfy a condition in the solution of the wave equation C emissivity; cg for the flame; Es for the tube surface p. viscosity of fluid, lb/hrft E 3E3.1416 p density, lb mass/ft3 9 angular coordinate, radians actual fuel-to-air ratio in inlet mixture divided by the stoichiometric fuel-to-air ratio Subscripts av average D drag due to flameholder and tube walls f.h. flameholder g gas i inlet conditions o outside or outer surface r partial derivative with respect to r xii

NOMENCLATURE (CONT' D) s surface w water 1,2 any two positions, usually 1 for upstream of flameholder and 2 for conditions near the exit Abbreviat ions cps cycles per second db decibels div divergence or dot product f.h., fh flameholder gpm gallons per minute grad i + j + k level distance from exhaust end of tube, excluding spray quench Yn natural logarithm mil 0.001 inch SCFM standard cubic feet per minute (at 60~F and 1 atm) SLR sodium line reversal SPL sound pressure level xiii

ABSTRACT Heat transfer from premixed propane-air flames to the cooled walls of a five-inch diameter, ramjet-type burner was studied with and without flame-generated, acoustically resonating oscillations. The oscillations generated were transverse oscillations, i.e., screeching combustion, of approximately 4000 cps and longitudinal oscillations, i.e., organ pipe, of approximately 350 cps. Bluff-body flameholders with greater than 90 per cent blockage of the free-stream area were used to stabilize the flame from 8 to 18-1/2 inches from the end of the tube. The inlet flow velocity upstream of the flameholder varied from 13 to 18 feet per second. Local heat-flux densities and local inside wall temperatures were measured with and without combustion at five stations downstream from the flameholder. Flame temperatures were measured by a sodium-linereversal technique at two of these stations. Flame temperatures were also determined from pressure-drop measurements and a thermocouple traverse of the flame in a lean propane-air mixture. Flame temperatures varied from 1600oF to 2800oF as the propane-to-air ratio was varied in the range of combustible lean mixtures. Local coefficients for convective heat transfer were evaluated using the measured values of heat flux, wall temperature, and flame temperature. The coefficients for heat transfer from the flame could be evaluated only at two stations. However, coefficients for heat transfer without combustion were evaluated at all five stations. In order to calculate flame temperatures at points other than where the flame temperatures were measured, coefficients for heat transfer from the flame were assumed to be proportional to the coefficients measured without combus tion. xiv

The sound level and frequency of the oscillations were measured and recorded with a high intensity microphone in the combustion tube upstream of the flameholder. Control of the oscillations were obtained by the use of various flameholders, and by a spray-quench muzzle on the end of the burner. Flameholders that stabilized the flame close to the tube wall were prone to screech, The spray-quench muzzle damped out the longitudinal oscillation. Profiles of the local heat-flux density and of the flame temperature along the combustion tube are presented. The heat flux density was increased significantly by the oscillations; however, the temperature profiles were not changed significantly. The sonic oscillations had a greater effect on the heat transfer phenomena than on the combustion efficiency. The local coefficients for heat transfer 13-1/2 inches downstream of the flameholder can be represented by the expression h P h -- ~~ e44 p + 1.08 The quantity h is the measured, local coefficient for convective heat transfer from the flame at the sound pressure amplitude, P; h* is the coefficient determined from cold flow measurements and corrected for the change in physical properties due to the combustion; and Po is the sound pressure amplitude of the stable burner. The sound level ranged from 130 db to 160 db, which corresponds to a range in pressure amplitude, P, from 0.0092 to 0.29 psi. The effect of frequency or mode of oscillation on the heat transfer was insignificant.

INTRODUCTION The fields of heat transfer from vibrating fluids and from flames have recently received increased attention. The recent emphasis on more powerful jet engines has lead to problems of flame-generated oscillations and the prediction of heat transfer rates. The field of combustion is a very complex one, and a fundamental understanding of the many variables and phenomena involved is lacking. Some of the variables in ramjet-type combustion studies include: fuel, oxidant, flow rates, mixture ratios, geometry of flameholder, combustion chamber design, inlet temperature, inlet turbulence, and pressure level. Combustion instabilities are a whole field of investigation in themselves. The causes, mechanisms, and nature of flame-generated oscillations have been investigated. For ramjet-type burners properly designed to isolate the fuel and oxidant supplies from any instabilities in the combustion chamber, the flame-generated oscillations, including those associated with screeching combustion, have been shown to be acoustically resonating waves with the mechanism of generation connected to periodic formation of vortices at the flameholder. The effect of oscillations on phenomena such as the recombination of dissociated combustion species and the gas-side boundary layer, which can be influential in determining heat transfer rates, is unknown. Work on heat transfer from flame-generated oscillations is (7) sparse and incomplete. In an early study by Berman and Cheney,(7) only overall rates of heat transfer from a small rocket chamber were measured with shock-type and sinusoidal combustion instabilities. In a more recent investigation by Sundstrom(78), local heat fluxes along the burner -1 -

-2 -were measured with longitudinal oscillations, but heat transfer coefficients were not evaluated. In a work related to this field, Tailby(80) studied the effect on heat transfer rates of sonic vibrations imposed on a diffusion flame. The majority of work on the effect of vibrations on heat transfer has been done for natural convective heat transfer. Recently Harrje(22) and Jackson, Harrison, and Boteler(28) studied heat transfer from pipe flow with sonic vibrations applied. Since no heat transfer studies have been conducted on screeching combustion and since the fields of heat transfer from vibrating fluids and heat transfer from high temperature flames are in the frontier stage of investigation, it is felt that a heat transfer study of screeching combustion can make a contribution to all three of these subjects. Screeching combustion is particularly interesting because of reports that burner walls have rapidly eroded when an unexpected screeching or transverse oscillation was generated. The objectives of the present study are (1) to design a burner in which an intense transverse oscillation as well as a longitudinal oscillation can not only be generated but also damped; (2) to make quantitative measurements of heat transfer rates at several points along the combustion chamber; (3) to measure flame temperatures at one or two points along the chamber and hence to evaluate local heat transfer coefficients. Preliminary studies in two uninstrumented burners were necessary before a burner to accomplish the first objective could be designed.

In the present investigation of propane-air flames, the measurements include flame temperatures, pressure drops, local heat fluxes at five locations, and the sound pressure level and sound frequency. Various flameholders and sound attenuators are used to control the oscillations, both longitudinal and transverse waves being studied. Experimental data are presented for local rates of heat transfer downstream from the flameholder and for local heat transfer coefficients.

LITERATURE SURVEY The work in the fields of combustion instability, heat transfer from chemically reacting systems, and heat transfer from vibrating fluids has on the whole been done in the last decade and at an increasing rate. Heat transfer data for individual ramjets, special burners, and for nozzles is fairly abundant; however, basic studies on heat transfer from flames are limited. The work on the effect of vibrations on heat transfer has dealt mainly with natural convection and with specialized cases. Only recently has any basic study dealt with forced convection. Some exploratory investigations have been made on the interactions of vibrations and combustion, and some rather definitive studies have been made on flame-generated oscillations, but very little work has been done on the subject of heat transfer from vibrating flames. The literature on all combinations of the three subjects, heat transfer, sonic oscillations, and combustion, is reviewed. The order of presentation follows the general arrangement of heat transfer combined with the other two, then vibrations and combustion, and finally a short treatment of one problem in the field of combustion -- turbulent flame speeds and stabilization. This latter treatment gives a good indication of the state of knowledge in the whole field of combustion. The problems connected with combustion processes are complex and as yet largely unresolved. Heat Transfer from Flames A review of the literature dealing with the problem of heat transfer from chemically reacting systems is presented first. The -4 -

-5 -possible mechanisms of heat transfer include forced and natural convection, conduction, radiation, catalytic surface reactions, transference of excess energy by collision of high energy gas molecules with the solid wall, and exothermic displacement of chemical equilibria. In the case of flame temperatures below 3000~F, Mach numbers significantly below one, and cold burner walls, the only important mechanisms are convection and radiation. Radiation from Flames The radiant contribution for non-luminous flames can be estimated by the methods presented by Hottel in McAdams(48), if the flame temperature and composition are known. Prediction of the radiation involves prediction of the flame temperature and composition. Only the heterogeneous molecules make a significant contribution to the radiation from non-luminous flames. Luminous flames, which are characterized by their yellow color and are commonly associated with the diffusion flame, have a greater emmissivity than the non-luminous ones, mainly because of the presence of carbon particles. Here the accurate prediction of the radiation is more difficult because of the added problem of estimating the size and concentration of the carbon particles. Convective Heat Transfer The convective contribution to the heat transfer can be affected significantly by a number of variables. Under some conditions, the coefficient for convective heat transfer from the flame to the wall may be estimated from one of the common correlations developed for fluids flowing in a pipe. Summerfield(77) reviews a number of theories of convective

heat transfer in turbulent flow with regard to high temperature combustion chambers. Zellnik(91) studied the problem of high temperature difference between a hot gas and cold wall. He discovered that the well-known Dittus-Boelter relation Nu = 0.023Re'Prl/3 (1) correlated the data well if the fluid properties were evaluated at the bulk temperature. A factor (Tb/Ts)'33 must be applied to the right side of the equation when the fluid properties are evaluated at the surface temperature. For gas film convective heat transfer coefficients in rocket motor combustion chambers and nozzles, Greenfield(18) recommends the expression hg - (0.029 G08 Cplz0 2)/D0"2 (2) Bartz(4) presents an equation for rapid estimation of rocket nozzle convective heat transfer coefficients. He points out that variations in velocity and temperature boundary layer thickness are secondary while mass flow rate per unit area is the dominant factor in determining heat transfer rates in the nozzle. Heat Transfer from Chemically Reacting Systems Hirschfelder(25) has analyzed heat transfer from chemically reacting gases. He presents an equation for calculating the thermal conductivity based on the classical treatment of Eucken for gaseous mixtures; however, local chemical equilibrium must exist.

Kilham(35) studied heat transfer from carbon monoxide-air and hydrogen-air flames to a rotating refractory tube. He assumed that at equilibrium the rate of heat transfer from flame gases to the tube by forced convection and radiation was equal to the heat loss by radiation to the surroundings. Experimental heat transfer coefficients for the carbon monoxide-air flame agreed closely with values predicted from McAdamS' correlation(48) for pure convection. The lack of agreement with the hydrogen-air flame was attributed to recombination of radicals at the surface of the tube. Schotte(70) shows analytically and experimentally that heat transfer coefficients for flow with gas-phase, instantaneous chemical reactions can be predicted by using calculated effective thermal conductivities and effective specific heats in conventional heat transfer correlations. Methods are described for obtaining these effective physical properties. Studying heat transfer in a tube for the dissociating system N204 = 2N02, Brokaw(9) found the experimental data in accord with the usual Nusselt-Prandtl-Reynolds number correlation for this type of convective heat transfer. The thermal conductivities and kinematic viscosities were computed using rigorous expressions from the kinetic theory of gases. The thermal conductivity includes a large contribution arising from the diffusional transport of chemical enthalpy. Heat Transfer from Particular Burners Ziebland(92) performed heat transfer experiments in small rockettype combustion chambers and found the experimental heat transfer coefficients exceeded the computed values by two-fold. He attributed the

-8 -difference between experimental and computed values mainly to the unestablished flow pattern near the inlet of the combustor. He also noted that the calculated emissivities may have been low due to the extrapolation of low pressure emissivity data to high pressure. Shorin and Pravoverov(74) in measuring local heat transfer rates from laminar diffusion flames found that radiant heat transfer predominated. In a 6-inch diameter gas turbine combustion chamber, Winter(89) estimated that 50 to 80 per cent of the heat transfer was by radiation. Hammaker and Hampel(20) studied heat transfer from a diffusion flame burning inside small diameter tubes. The fuel was injected through a jet at the entrance to the tube with air being sucked in from the surroundings. The heat transfer rates were fairly constant from a point six inches from the inlet to over forty inches. Neither inside flame temperatures nor internal heat transfer coefficients were estimated. In equipment similar in design to that of Hammaker and Hampel, Tailby and Ashton(79) studied heat transfer from a diffusion flame, varying the fuel-to-air ratio, gas burner characteristics, excess air entrained into the system, and horizontal tube length. Both convective and total radiant heat transfer were measured. Radiation was the dominant of the two in the heat transfer from the lower portion of the tube, while convection dominated in the upper sections. Luminous radiation from the flame constituted the major portion of the total radiation. The results were not compared with any of the usual empirical heat transfer expressions. Earlier Tailby and Saleh(81) did a similar study in a vertical diffusion burner.

-9 -In their heat transfer study of hot combusted gases flowing through a water-cooled tube, Timofeev and Uspenskii(82) measured gas temperatures, radiant heat transfer, and local total heat transfer at several positions along the length of the tube. The radiant contribution agreed with an analytical prediction. The coefficients for convective heat transfer were scattered about an empirical curve from the literature. The total heat transfer coefficient correlated well with the Reynolds number, indicating the dominance of convection over other effects. Effect of Oscillations on Heat Transfer Rates Several contributions have been made on the effect of vibrations, sonic or mechanical, on heat transfer rates. A few of the more noteworthy investigations in the areas of natural convection as well as forced convection are discussed below. Holman and Mott-Smith(26) give experimental evidence that the heat transfer coefficient for free convective heat transfer from a horizontal cylinder may be increased by more than 100 per cent in the presence of strong constant pressure sound fields. No appreciable effect occurred until the sound pressure level exceeded about 134 db. The heat transfer coefficient is independent of frequency except near this critical sound level where the frequency effect was slight. In a qualitative analysis, the authors attempted to explain the test results as an effect of the interaction of the phenomenon of acoustical streaming with the free convection boundary layers. In an experimental study similar to that of Holman and MottSmith, Fand and Kaye(16) found that a critical sound pressure level

exists between 136 and 140 db, depending on the frequency, above which the heat transfer increases rapidly with increasing intensity. Kubanski(39) studied the influence of standing sound waves on heat transfer by natural convection from a heated horizontal tube. The natural convective heat transfer coefficients were increased by two-fold or more as a result of the vibrations. An optical study of the flow field revealed the presence of acoustical streaming. Jackson and others(28) imposed sound waves on air flowing through a horizontal tube and studied the effect upon natural and forced convective heat transfer. At a sound pressure level above 118 db, the free convective forces influenced the heat transfer coefficient only slightly. Above 118 db free convection was apparently negligible and the effect of sound appeared to be an increase of 30 to 40 per cent in the heat transfer coefficient at 140 db. In a discussion of Jackson's paper, Kreith(38) points out that in this case the wave motion may be a resonance phenomenon controlled primarily by the over-all geometry of the system and may therefore affect the mechanics of the boundary-layer waves only indirectly by virtue of its effect on the flow far away from the boundary. One would, therefore, look for an explanation rather in terms of macroscopic flow phenomena, whereas in some other cases the vibration may affect the microscopic motion of the boundary layer directly. It was also pointed out that the 118 db figure is probably only a relative value. Harrje(22) imposed axial-type sinusoidal pressure and velocity fluctuations on a steady flow of hot gas under conditions of fully established turbulent pipe flow. The fluctuations produced a maximum increase

in the steady-state heat flux of less than 10 per cent. However, the heat-flux increase was found to be almost linearly dependent on the amplitude of the unsteady component of velocity. Havemann(23) studied heat transfer from rapidly compressed and oscillating gases in a cylinder. He found that the increase in heat transfer over a gas at rest was dependent on the amplitude of the pressure fluctuations and, to a lesser extent, on the frequency of oscillation. Vibrating wires of differing diameters were studied by Lemlich(43) for the effect on natural convection rates. The heat transfer coefficient was increased by four-fold for low temperature differences. West and Taylor(86) improved heat transfer 70 per cent in a double pipe heat exchanger by applying 100 pulses per minute to the water. Martinelli and Boelter(51) increased coefficients for heat transfer five-fold by vibrating a cylinder in natural convection under water. On the basis of acoustic streaming, i.e., flow created by the acoustic disturbance, Kubanski(40) explains the increased heat transfer in these experiments by Martinelli and Boelter and Lemlich. Havemann and Rao(24) found that if the frequency is low enough the effect of pulsations becomes negligible as might be expected. This minimum frequency appears to be about 20 to 30 cps for fluids that are not highly viscous. Morrell(55) proposed a method for calculating heat transfer rates in resonating gaseous pipe flow. His method treats the oscillations as shock waves and uses the relations that apply to shock waves in deriving his correlation, which therefore has limited applicability.

-12 -Heat Transfer from Oscillating Flames Berman and Cheney(7) conducted a study of combustion instability in a three-inch rocket chamber. They observed no abnormal heat transfer rates from flame-generated sinusoidal-type oscillations with amplitudes up to 100 psi peak to peak. However, shock-type instability, with amplitudes up to 500 psi, was accompanied by heat transfer rates up to 2.5 times the normal values. Tischler and Male(83) state that the combustiondriven oscillation known as screeching can cause abnormally high heat transfer rates. They mention an air-cooled engine which had as much as 1/4 inch of solid stainless steel eroded from the chamber in runs of a second duration. Tailby and Berkovitch(80) applied sonic vibrations to the gas stream of a diffusion flame burning at the inlet of a water-cooled tube and measured the total heat transfer as well as the radiation to the tube. The main effects of the sound were to increase the heat transfer by factors of 2 to 3 in the lower parts of the tube and to shift the position of maximum heat transfer upstream. Also the vibrations in general reduced flame temperature, shortened the flame, and reduced its luminosity at high sound levels. In a water-cooled, 1-inch diameter tube, Sundstrom(78) measured local heat transfer rates from propane-air flames with and without selfsustaining longitudinal oscillations. He concluded that flame-generated longitudinal oscillations flattened the peak in the heat transfer curve for damped combustion, and shifted the peak of the damped curve toward the flameholder.

Combustion Instabilities A combustion instability is any repetitive perturbation around steady conditions of the flow pattern, flame temperatures, and/or flame speed. A combustion instability is often revealed by sonic measurements because the instability is usually a cyclic or periodic variation, having a frequency within the spectrum of sound. Except for instabilities associated with rough burning of a rich fuel mixture or with uneven fuel injection, combustion instability has been found to be an acoustically resonant phenomenon. Acoustically Resonant Frequencies The resonant frequencies of the various possible modes of oscillation within a combustion chamber may usually be predicted through the standard wave equation.(54) This classical wave equation is strictly valid only for small perturbations of the fluid; however, numerous investigators(8121'33,62,83) have found that the classical equation predicts the frequencies well, considering that within a combustion chamber there are large temperature and velocity fluctuations across the radius and length and with time. Maslen and Moore(54), after analyzing flamegenerated transverse waves in a combustion chamber, concluded that such waves have frequencies independent of amplitude and do not steepen with time, i.e., do not form detonation waves. The standard wave equation was solved originally by Rayleigh. (66) Morse(56) presents the solution for a cylinder with both ends closed. The slight modification to arrive at the solution for a cylinder with one end open and one closed is readily made. The frequencies of the

-14 -various acoustical modes for this cylinder are then given by the expression fmnnx = 1/2 () 2 + (3) Le R Any choice of the wave numbers, m,n,nx, as positive integers or zero corresponds to a possible natural mode of acoustical oscillation within the cylinder. The three wave numbers can be viewed as representing three sets of waves. When n = m = 0, the longitudinal waves or organ pipe solutions are given by the wave equation. Here the motion is parallel to the axis of the cylinder. The waves, for which motion is entirely radial and for which nx = m = 0, are those which focus the sound along the cylinder axis and are called radial waves. The transverse waves for which nx = n = 0 are those which travel close to the curved walls of the tube and have little motion near the cylindrical axis. Of course any combination of these three pure waves is a possible mode of acoustic, resonant oscillation within the cylinder also. The primary longitudinal or organ-pipe oscillation is of a lower frequency than the fundamental transverse or radial oscillation in the normal burner, the length of which is greater than its diameter. The primary longitudinal mode has a pressure antinode and velocity node at the closed end and a pressure node and a velocity antinode at the open end of the cylinder. Conditions for Flame-Generated Oscillations An intermittent source of energy is required to drive the oscillation and overcome the ever-present damping forces in the systenm In the

-15 -case of a self-sustaining flame-driven oscillation, Rayleigh's hypothesis(66) states that an oscillating component of the rate of heat release must be in phase with the oscillating component of the pressure. This hypothesis has been justified analytically using thermodynamic principles by Putnam. (62) By employing one additional assumption, Putnam is able to explain the amplification in his burner of certain natural frequencies. This assumption dictates that the point of heat release must be near the point of maximum pressure amplitude in the combustion tube. Flame-Generated Longitudinal Oscillations Putnam(65) has written a comprehensive review of organ-pipe oscillations in combustion systems. He groups the burners in which oscillations occur into diffusion burners, flash tubes, gauze-tone burners, rocket-shaped burners, burners utilizing secondary air, and ramjet-type burners. The acoustical behavior of each system is described and possible driving mechanisms for producing the observed oscillations are indicated. In one study(64) a bank of hypodermic tubes was employed to lead the gases from the mixing chamber to the combustion chamber. The combustion chamber was considered a driver which forced slugs of gas in the hypodermic needle ports to oscillate. Burning of the incremental pulses of combustible mixture periodically issuing from the ports furnished energy to drive the oscillation when the pulses burned in phase with the oscillating component of the pressure in the chamber. Putnam and Dennis(62) found that longitudinal oscillations are most likely to occur when the flameholder is near a pressure antinode.

-16 -Bailey(2) studied some organ-pipe oscillations in a tube with a gauze-type flameholder. He proposed a driving mechanism depending on a flame speed which is a function of position as well as mixture strength. The resultant instability is found to be in accordance with Rayleigh's criterion. Dunlap(15) studied resonance of a propane-air flame in a 1 x 1 x 12-inch combustion chamber, acoustically open at both ends. Agreement was obtained between experimentally observed frequencies and those predicted by assuming a longitudinal resonance of hot and cold gases. The flame was not prone to resonate at extremely rich or lean mixtures. Dunlap noted, as Putnam later verified, that the oscillation of any particular mode occurred when the flameholder was in the region of a pressure antinode for the mode. He postulated the following driving mechanism, which satisfies Rayleigh's hypothesis. Standing sound waves in the combustion chamber produce a variation in pressure and temperature at the flame front with time. The dependence of flame speed on temperature and pressure results in a cyclic variation of burning rate. Sensitive Time Lag Criterion Crocco, Grey, and Harrje(l3) have postulated a theory based on a sensitive time lag for ignition of a gobule of unburned gas to explain flame-generated oscillations. They have observed that there is an upper limit to the chamber length above which a mode of longitudinal pressure oscillation cannot occur in a combustion chamber. They state that this upper chamber limit cannot be explained by any other mechanism advanced to date (December, 1958).

-17 -Working with a plungerjet rocket engine, Shieber(73) discovered this upper chamber limit and found stable operation above that length. The most noteworthy thing in Shieber's work, however, is the fact that the onset of instability was sooner and the amplitude greater when the larger of two replaceable exhaust nozzles was installed in the engine. In fact, he states that the smaller of the two throats practically inhibits pressure oscillations. Generation of Transverse Oscillations The question of which mode of resonant oscillation to expect in a given burner does not have as yet an explicit answer. The propensity of a burner to amplify transverse waves appears to be strengthened by several factors. A bluff-body-type flameholder of high blockage, a short combustion chamber of reasonable diameter, high wall temperatures, high inlet temperature of fuel, Mach number close to but below one, and fuel-to-air ratio near stiochiometric are all believed to make a burner more prone to screech.(3,45,67,85) The tendencies of fourteen different fuels and three fuel blends to produce high frequency oscillatory combustion were measured by Tischler and Pass(58) in a 200-pound thrust, water-cooled, liquid-oxygenfuel rocket engine. In this apparatus, the fuels in order of increasing screeching tendency were 1) hydrazine (it did not screech:.at all), 2) branched-chain paraffins, aromatics, and amines, 3) straight-chain paraffins. This trend of screeching tendency correlated with increasing fuel evaporation rate. An explanation was given by a combustion model that indicated combustionfor which flame propagation through a gaseous

mixture is rate controlling,is more sensitive to pressure changes than is combustion, for which fuel-droplet burning is rate controlling. The bulk of the experimental evidence points to the fact that the acoustical modes of first order are the preferred modes of oscillation in rocket engines. (83) Maslen and Moore (54) point out on the basis of viscous energy dissipation in the boundary layer that the low-order modes are., indeed, mIgore easily driven than the higher-order modes. Also they found that for large length-to-diameter ratios longitudinal waves are most likely to occur. They determi.ned analytically and experimentally that while strong longitudinal waves in the chamber will inevitably develop shock fronts, the strong, transverse-wave pressure distribution is symmetr ical. Screeching Combustion Blackshear, Rayle, and Tower(8), and Harp, Velie, and Bryant(21) developed a microphone probe to investigate the phenomena of screech and to ascertain if it. was truly a transverse or radial solution to the wave equation. With the probe microphones, the frequency, the relative amplitude, and relative phasing of the oscillations were measured at various positions within a screeching combustor. Thlrough this detailed probing they verified that the phenomenon of screech is truly an acoustically resonating oscillation and was the first transverse mode in their 6-inch diameter afterburner. Tischler and Male (3) present some enlightening photographs of transverse waves in cylindrical combustion chambers. A streak photograph reveals a continuous trace of helical form for the transverse wave as

-19 -it travels along the axis of the burner. This helical form indicates that the transverse wave is rotating or spinning, i.e., the pressure head travels around the periphery of the chamber. The transverse wave can evidently be either in the standing (or sloshing) form or in the spinning form. The wave equation does not answer this question and the theoretical frequencies for either form are identical. Mechanisms to Explain Screeching Combustion Kaskan and Noreen(33) investigated transverse oscillations in a two-dimensional burner by searching for periodic flame-area variation during oscillation. Their screech limits for propane-air prescribed that a minimum inlet velocity of 35 feet per second was necessary to induce screeching combustion. Changing screens upstream from the flameholder and thus changing the inlet turbulence level had no effect on the screech limits. High speed motion pictures revealed that the transverse oscillation was accompanied by the periodic formation of vortices, which distorted the flame front. The frequency with which these vortices were formed was equal to the frequency of oscillation, which was about 4000 cps. The vortices were also shown to have a definite phase relationship with the oscillatory parameters such as velocity and pressure. The vortices appeared to form as a result of the oscillatory part of the velocity, thus possibly providing the feedback between gas oscillation and driving force, which appears necessary in self-maintaining vibrations. Furthermore, Kaskan and Noreen mentioned as a driving mechanism the periodic variation in flame area caused by the periodic vortex formations at the

-20 -flameholder lip. The authors' pictures of the flame with a longitudinal oscillation also revealed the formation of vortices with the periodicity of the oscillation. Here the vortices also distort the flame, but in a more longitudinal fashion. Kaskan and Noreen's pictures show that both oscillations can also exist at the same time independently of one another. Kaskan and Noreen's theory that variations in flame area drive the transverse mode is open to debate. Smith and Springer(75) argue that the pressure and temperature rise accompanying the acoustic wave increases the reaction rate in phase, or nearly so, with the pressure, and the necessary temperature rise is more conceivable than an equivalent increase of flame area. Rogers and Marble(67) made a study similar to that of Kaskan and Noreen in a two-dimensional, rectangular burner, using air and vaporized gasoline. Their high speed motion pictures also showed that the high frequency oscillation is accompanied by vortices shed periodically from the flameholder lip with. the same frequency as the oscillations. However, they h.a.ve postulated a different driving mechanism for these oscillations, which they have stated very concisely. A. mode of transverse oscillation is excited as the result of periodic transport of combustible material associated with the vortices into the hot wake of the flameholder. The vortices, in turn, are generated at the flameholder lips by the fluctuating transverse velocity. When the ignition time delay lies in the proper range, the phase relationship between oscillations in transverse velocity and combustion intensity is such that the oscillation is amplified.(67)

-21 -Recently Barker(3) in similar equipment verified this mechanism of screech generation. The analysis of heat-driven oscillations by Merk(52) is not too applicable because it is for a special burner with long multiple ports which introduce the gas to the combustion chamber and serve as stabilizers. He analyzes the fluctuating heat transfer from these long metal burner ports. Met hods for Damping Oscillations Putnam and Dennis(63) studied the suppression of flame-driven, organ-pipe oscillations with acoustical dampers. The effectiveness of the quarter-wave tube was found to be critically dependent on length, but relatively insensitive to location as long as the tube is placed in the region of the pressure antinode. It did not have to be placed near the particular antinode where energy was fed into the oscillation. Other means of suppression included holes drilled in the side of the tube and placed within 10 per cent of a wave length from a pressure antinode. Helmholtz resonators were also effective. Some of their work dealt with reflectors near the exit of the combustion tube. The most successful damping of screeching combustion was obtained with a perforated liner inside the combustion chamber. (8,21,37) This was the only method found in the NACA studies that completely eliminated screech under all operating conditions. Effects of Oscillations on Combustion Some of the effects of transverse and longitudinal oscillations on the combustion phenomenon are available in the literature. The changes

-22 -brought about by a transverse or longitudinal oscillation are given mostly in a qualitative manner, however. Screeching combustion results in increased flame propagation, increased mixing, increased combustion efficiency, and higher operating temperature of combustor parts and shell.(8,33,54,84) Another study by NACA, this one by Mickelsen(53), analyzes the effect transverse waves have on fuel-oxidant mixing in a cylindrical burner. In the burner that he has analyzed, the fuel is injected into the oxidant stream at a short distance upstream from the flameholder. Several investigations have been made by applying a sound field to the flame. Tailbyts work was mentioned earlier under heat transfer studies since he also measured heat transfer from his flames. In Kippenram's experiment(36), high frequencies, 26 kc to 58 kc, were imposed on the combustion zone of pre-mixed propane-air flames and were found to have little effect on the normal flame velocity. The combustion zone configuration, however, was changed. The usual cone for laminar flames became a flattened bowl shape and for turbulent flames became a suspended violently agitated zone. Both possessed remarkable stability. The negative effect on flame velocity would seem to confirm Markstein's(50) opinion that the oscillation phenomena which occur in tubes should be ascribed primarily to variations of flame surface area rather than of burning velocity. Loshaek, Fein, and Olsen(47) applied a sound wave with a frequency of 12,700 cps to a laminar propane-air flame. The sound altered the flashback limit so that the flame became more stable and altered the

-23 -blowoff limit so that the flame became less stable. The burning velocity and flow velocity profiles were unchanged. In Hahnemann's experiment(l9), intense sound vibrations of 5000 cps were imposed upon a stationary propane-air flame issuing from a nozzle. In addition to a slight increase of the flame velocity, a fundamental change both in the shape of the burning zone and in the flow pattern could be observed. This was explained as a transition at the nozzle from jet flow to potential flow. Havemann(23) studied the effect of oscillations on flames burning inside tubes. He found that the apparent flame velocity increased with amplitude and frequency of oscillation. Schmidt, Steinicke, and Neubert(69) also noted an increase of flame velocity with amplitude for a combustion wave propagating in a tube. Theories of Flame Stabilization Theories or experiments attempting to explain the stabilization of a flame on a bluff body, the turbulent flame speeds, or the propagation of flames are plentiful, but their conclusions or explanations are varied and conflicting. It is worthwhile reviewing some of this literature to understand the current state of knowledge in the field of combustion. Longwell's(46) view is that stabilization occurs in a zone with a high mixing intensity and approximately homogeneous composition. The stability range depends on the residence time in that zone. Under certain conditions combustion appears to proceed homogeneously as a secondorder chemical reaction. This hypothesis of Longwell serves to explain

z24 - many gross features associated with flame stabilization behind bluff o bjects in high velocity air streams. Wright and Becker(90) studied the ignition of combustible material by means of two streams flowing parallel to each other. They found that a propagating flame is established only when the residence time of combustible material in the mixirg zone is long enough to lead to ignition of a mass adequate to serve as a secondary ignition source. This result was applied to the explanation of bluff-body flame stabilization and blowoff. The existing 'theories of flame stabilization seem to differ only i.n their degree of si.mrplification of one of the two fundamental aspects, ije., the chemical kinetic viewpoint or the fluid mechanical one (including heat transfer). The theories are based explicitly either upon energy balance (Williams, Hottel, and Scurlock(88) and Khitrin and Goldenberg(-4)) or on mass balance (Longwell, Frost, and Weiss(46)) or on mass balance (Longwell, Frost, and Weiss](46)) or on purely kinetic considerations (Zukoski and Marble (93)), Cheng and Kovitz (ll) however, tackle the problem wi'thout an initial assumption of the preponderance of chemical. kinetics or fluid mechanics. Their work begins with Adamson's work(49) and the extension of his work by the authors in the Sixth. SymposiumO (10) An.other recent contribution was made by Karlov-tz(-l) when he presented a theory which permits the dl.rect calculation of the combustion wave area from the turbulent parameter and the laminar burning velocity'. Th.e work on flame stabilization by Zukoski and Mairble(93) makes an interesting point. The authors state that the most important

-25 -consideration is the time spent by the fresh gas in the shear layer rather than the residence time in the wake. Turbulent Flame Speeds Many variables interact complexly in flame spreading and no accurate, simple description seems likely. Neither the concept of a wrinkled laminar flame nor of an extended reaction zone, nor of homogeneous combustion fits the data generally; although any one concept may be acceptable over a restricted range. Petrein and Longwell(60) point out that burning is probably discontinuous in micro-time, making inapplicable theories assuming continuous burning. Several theoretical works have suggested that the speed of combustion is influenced not only by the turbulence of the upstream flow, but also by the turbulence which occurs during combustion. These theories are those of Landau(42), Markstein(50), Scurlock(71), and Karlovitz.(32) Prudnikov(61) measured turbulence in flames by an optical diffusion method and found the turbulence to be increased by combustion. He also states that Westenberg(87), who came to the opposite conclusion, took measurements at a distance where turbulent intensity practically equals tube turbulence. Friedman(l7) feels that for low levels of turbulence the wrinkled flame model, first proposed by Damkohler(14), is valid and for very high intensities of turbulence the distributed reaction zone model is more. appropriate. Through the effect of turbulence on radiation intensity, John and Summerfield(29) concluded that turbulent mixing breaks up what would be a continuous laminar flame sheet and that this break-up modifies chemical reaction and transport processes in the flame zone.

Shetinkov(72) used the model of micro-volume burning to calculate the turbulent flame velocity. In this model, which is contrasted with the surface mecphansm model, the turbulent stream is regarded as consisting of individual turbulent moles or gobules which constantly appear and disappear.

APPARATUS The attainment of accurate and meaningful heat transfer measurements is the primary objective of this design of a burner in which screeching combustion could be generated. A vertical, cylindrical design was chosen because the symmetry of a cylinderts walls is important to enable measurements at one point on the wall to yield representative heat transfer rates for that level. Also a vertical cylinder eliminates any density effects other than those along the tube axis. One important property of the combustion chamber that could not be foretold from the literature is its propensity to screech with a propane-air flame. It was known that the burner diameter could be made too small to permit screeching combustion; however, since the air and fuel supply rates were limited, an upper limit was placed on the diameter. Therefore, preliminary experiments were conducted in two uninstrumented burners, one a four-inch pipe, and the other a five-inch pipe, both water cooled. Since higher screech intensities by 10 db were obtained in the 5-inch pipe, this size was picked for the investigation. General Features of Complete System A schematic diagram of the equipment is presented in Figure 1. The four streams, air, propane, cooling water for the combustion chamber, and cooling water for the flameholder, are shown entering the vertical assembly of mixing and combustion chambers. The details of each stream and each piece of equipment are given later. Three pictures of the equipment are presented in Figures 2, 3 and 4. An overall view is presented in Figure 2. In back of and above -27 -

ELECTRIC HEATER BLOW- OUT DISC 6 MIL PROPANE AIR NaHCO$ BRASS SHEET ROTAMEER ROTAMETER DUSTER EXIT F.H. WATER ROTAMETER PRESSURE REGULATOR PRESSURE REGULATOR EXIT EXIT TUBE COOLING TUBE COOLING lWATER WATER FLAME HOLDER O COOLING WATER TRAP AIR 0 FILTER 1 a; - — 1 @ @ an S} v TANK COMPRESSED LIQUID AIR,95 PSIG ROTAMETER PROPANE ROTAMETER WATER FOR SPRAY OUENCH GASES TO EXHAUST COMBUSTION - TUBE COOLING WATER Figure 1. Schematic Flow Diagram of the Apparatus.

i1iili:I B ~i~:~........:.................. iiiiiiiiii':i:!::.... ~ '~!::~iii~':::i~~~~~~~~~~~i::,l::i:::: ~~~~~~~~~~~~~~~~~~~~~~~::: ~~~Tiei.............. -. iiiiiii1iii F'igure 2. Photograph Showing the Manometer Panel on the Left, the Metering Panel on the Right', and the Vertical Mixing and Combustion Chambers in the Center, partially hidden.

-30-.~..~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~...... Fiue3 htgrp fteCmbsinCabr

-31-~~~~~~~~~~~~~~~~~~~~~~0...:j-: i::~~~~~~~~~~~~Bi Figure 4. Photograph of the Metering Panel.~~ii

-32 -the manometer panel, the vertical mixing chamber is visible. The combustion chamber is hidden from view. In Figure 3, a view taken from in back of the manometer panel, the combustion chamber is shown with the pressure taps and one row of ports of windows visible. The last picture, Figure 4, shows the front of the metering panel. General Features of Combustion Chamber The instrumented chamber is constructed from a six-inch tube of hot rolled, low alloy stainless steel with a nominally 1/2 inch thick wall. The alloy is Croloy, which is a 9 per cent chromium, 1 per cent molybdenum steel. Its complete composition and a plot of its thermal conductivity versus temperature are given in Appendix D. The inside surface of the tube was given a very smooth and even finish by a honing operation and the outside was cleaned up on a lathe. The final dimensions are an inside diameter of 4.920 + 0.003 inches, an outside diameter of 5.937 + 0.005 inches, and a length of 27 inches. The local rates of heat transfer are measured at five thermally isolated stations, where the temperature gradients through the wall are measured by three thermocouples. These thermocouple sections are located at five positions along one side of the tube, at distances of 4, 10, 13, 15 and 17 inches from the exhaust end of the tube. Pairs of ports, 5/8 inch in diameter, are at three of these levels, the 4, 10, and 15-inch levels. Pressure taps are located at the 2-inch level and 25-inch level as well as at the 4, 10, 13, and 15-inch levels. The microphone mount is at the 22-inch level. The term level is being used to indicate the height or distance above the bottom or exhaust end of the burner. The

gas flows down and out the bottom of the tube. A schematic diagram of the mixing and combustion chambers is given in Figure 5. Some miscellaneous items built into the chamber are a spark plug mount at the 2-inch level and four, 1/2-inch holes at the 16-inch level. Plugs, which completely fill the holes and make a smooth inside surface, were in these holes throughout all the recorded runs. Their purpose is to make it possible to place quarter-wave tubes at this position or some other acoustical dampers there. Embedded Thermocouples for Heat Transfer Measurement The thermocouple sections are one-inch square units that are thermally insulated from the rest of the tube and contain three thermocouples at three depths in the tube wall. Four slots, 30 mils wide, were milled deeply into the tube wall to form the four sides for each thermocouple section. These slots, which literally box off a one-inch square, reach within 20 mils of the inside surface. They are filled with strips of mica bonded with silicon resin. The tube was baked at 400OF for one hour to cure the resin. A diagram of a thermocouple section is shown in Figure 6. The thermocouple assemblies are contained in holes, 42 mils in diameter, drilled from three edges of the boxed section to three different depths within the tube wall. The bottom of each hole is in the center of the square area, and thus the bottoms of all three holes are on the same radial line extending from the center of the tube. The thermocouple assemblies were prepared from specially insulated and shielded thermocouple wire. This special wire consisted of

METERED AIR METERED PROPANE 1/4" BALLS 5-INCH CAP SUPPORTING RING FOR FLAME-HOLDER MIXING CHAMBER i 5-INCH PIPE WATER FOR s R - FLAME- HOLDER THERMOCOUPLE TEMCULGLAND N PRESSURE '~ ~g~ 4 GAGE COOLING WATER THERMOCOUPLE MICROPHONE SECTION It. PORT WINDOWS L _ COMBUSTION ' TUBE COOLING WATER S NMUZZLE WATER WATER SPRAY Figure 5. Detail of Combustion Chamber.

-35 -STAINLESS STEEL SHEATH T.C. WIRES a) PERSPECTIVE VIEW OF A TYPICAL THERMOCOUPLE SECTION LONGITUDINAL SLOT CHORDAL SLOT // \ -- WATER JACKET 16 GAUGE,STAINLESS STEEL WINDOW - -- WINDOW PRESSURE TAP b) SECTION A-A WITH WINDOWS AND PRESSURE TAP SHOWN ALONG WITH THERMOCOUPLE SECTION Figure 6. Detail of Thermocouple Section.

36-gauge chromel-alumel thermocouple wires packed with magnesium oxide within a stainless steel sheath, the outside diameter of which is 40 mils. Thermocouples were formed from this special thermocouple wire by cutting it into 6-inch lengths and carefully removing the sheath for a short distance at each end to expose the 36-gauge wires. A twisted tip was carefully silver-soldered and cut off cleanly just in front of the sheath's end. The thermocouple tip was held firmly by the packing and could not move from side to side. The tips were examined under a microscope and were rejected if they were more than 10 to 15 mils long. The thermocouple assemblies were then placed in each hole with the tips soldered to the bottom with a small chip of silver solder. The sheaths were soldered to the tube at the top of each hole so that the assembly was held firmly in place. X-Rays to Locate Thermocouples Precisely Since the angle and depth of each thermocouple hole was checked after drilling, the location of each thermocouple tip was known fairly accurately, probably to + 10 mils. However, two uncertainties existed. The drill may have wandered, leaving the holes not perfectly straight. Also the thermocouple tip might not be soldered to the very bottom of the hole. Therefore, at the close of all the experiments, these two questions were checked by cutting out the thermocouple sections and taking x-ray pictures of them. The metal on the side, free of a thermocouple, was removed so that only a 1/32 inch of metal separated the plane of the thermocouple tips from the x-ray paper. The x-rays reveal that the holes are perfectly straight and that in every case the tip is at the very

-37 -bottom of each hole. The thermocouple locations were also measured from the x-ray negatives and are now known to the nearest 1/64 inch or + 0.007 inches. The bottom-most thermocouple is, on the average, 19 mils from the inside surface, the middle one is 210 mils above the first, and the top thermocouple is 219 mils above the second, or 60 mils from the outside surface. Windows and Pressure Taps Two ports, 5/8 inch in diameter, are located diametrically opposite each other at each of the three levels, 4, 10, 15 inch. The windows, which sealed each port in conjunction with a teflon gasket, are 1/8-inch thick vycor discs, 1 inch in diameter. They were originally designed to sit almost flush with the inside surface of the burner; however, difficulty was encountered in keeping the windows perfectly free and clean of the sodium bicarbonate dust. This problem was solved when the gasket assembly was modified to hold the windows about 3/4 inch from the inside chamber wall. The pressure taps are 1/16-inch holes placed at six positions, 2, 4, 10, 13, 15, and 25-inch levels, along the remaining free quarter of the burner, i.e., directly opposite the thermocouple sections. The inside edge of each hole is rounded off smoothly. The pressure taps are connected with 3/16-inch copper tubing through a manifold of valves to either of three manometers for a wide range of measurements. All three manometers are made by Meriam. The smallest is an inclined draft gauge indicating 0-0.5 inches of water, the intermediate

-38 -one is an inclined well-type manometer, indicating 0-10 inches of water, and the largest is a vertical U-tube manometer, indicating as much as 30 inches of water, differential pressure. Flameholders The flameholders employed in this study are all of the bluffbody type and are water cooled by means of a 3/16-inch copper tube coiled into three or four loops and silver soldered to the backside of the flameholder. The flameholder is a flat metal disc held firmly and precisely in the center of the stream by a 5/8-inch steel tube soldered to the center of the upstream side of the flameholder. This tube contains the leads to the copper-cooling coil and passes through two centering plates or spokes. One centering support is located between the flanges that join the combustion tube with the mixing chamber, i.e., at the 27-inch level. The other, a three-pronged centering wheel, is about 18 inches higher and fits snugly in the mixing chamber walls. Several flameholders were used in the course of the experiment, but they all have a high blockage, being 90 per cent or more of the tube cross-section. Except for some slight differences in diameter within each group, the flameholders may be categorized in three groups according to variations of the basic geometry. These groups are 1) the plain 1/8-inch thick disc type, 2) the type with a 10-mesh screen placed in the annulus between the edge of the metal disc of the flameholder and the tube wall, and 3) the type with an effectively much thicker disc. The latter type includes one flameholder, the S-2, which was made thicker than the others by soldering a 1-1/4 inch wide ring of 1/16-inch thick

-39 -copper sheet to the back of the flameholder. The diameter of the copper ring is Within 1/32 inch of the diameter of the flameholder disc. The 10-mesh screen used for the annulus of the flameholder has 0.047-inchdiameter, stainless steel wire. The flameholders are tabulated in Appendix A. Sodium Injection Through Flameholder In conjunction with the sodium-line-reversal system of measuring the flame temperature, a sodium salt is injected into the flame. The sodium salt, sodium bicarbonate powder, is introduced into the flame through a small hole in the center of the face of the flameholder. A small fraction of the air stream is used to entrain some of the sodium bicarbonate powder as this air blows across a vess"el of the power. The air with entrained sodium bicarbonate travels down a 1/8-inch copper tube that is contained within the 5/8-inch supporting and centering tube, and enters the burner through a 1/32-inch diameter hole in the center of the flameholder. The rate of sodium salt injection is easily controlled by a valve in the small 1/4-inch air line through the duster. Cooling Water and Spray Quench The water jacket, surrounding the whole 27-inch length of the combustion chamber, was formed with a 16-gauge sheet of stainless steel. Two one-inch pipes diametrically opposed lead the water into the l/4-4nch annulus formed by the water jacket and provide more even cooling than one inlet pipe would. The vertical arrangement of the chamber has also provided a more even cooling by the water, since there is no tendency

-40 -for gas present in the water to accumulate anywhere and since the effect of density changes occurring in the water are symmetrical about the tube axis. The spray quench, that could be placed over the exhaust end of the burner, is more correctly called a muzzle than a nozzle since its diameter is essentially the same as that of the main tube. This muzzle consists of an extra-heavy 5-inch pipe, 2-3/4 inches long, which has two circular rows of twelve 1/8-inch holes through its wall which allow the water from its own water jacket to quench the flame. A 10-mesh stainless steel screen of 0.047 diameter wire may also be placed in the muzzle below the water jets. A flange welded to the end of the burner serves to join the muzzle to the burner. Mixing Chamber The mixing chamber, which is also 27 inches long, was constructed from extra-heavy 5-inch pipe that -was honed on the inside to give an even and smooth surface of 4.860 inches in diameter. A bourdon pressure gauge, 0-30 psi, and an iron-constantan, 24-gauge, thermocouple are located 4 inches above the flange-junction of the mixing and combustion chambers. A 4-inch diameter blowout or safety disc is located 21 inches above the flange junction. This blowout disc is a sheet of 0.006-inch brass shim stock, held between two 4-inch flanges. Its purpose is to relieve the pressure caused by a flashback; however, a better pressure release is provided by the failure of the 18-gauge copper wire that supported the flameholder and its centering rod.

-41 -The propane and air streams converge at a 1-inch cross and flow through a 6-inch length of 1-1/2 inch pipe packed with 1/4-inch ceramic balls. To the upper fitting of the cross is attached a 150 psi safety disc. A short length of connecting assembly, consisting of a 5-inch cap and a 1-1/2 inch flange, brings the gases into the top of the mixing chamber. The flow is broken up further by the steel piece, resting on the top of the 5-inch pipe of the mixing chamber, that supports the flameholder and the sonic piston. The 5-inch cap is fitted with four 1-inch couplings, so that the quarter-wave tubes can be attached here. Sonic Orifice Provision for three possible locations of a sonic plate or orifice has been made in order to isolate the air and propane streams from the oscillations generated in the burner. One location is the 1-1/2 inch flange just above the mixing chamber; another is between the 5-inch flange, connecting the combustion and mixing chambers; and the third sonic plate, being in the form of a piston, may be placed anywhere in the mixing chamber or in the combustion chamber above the flameholder. The sonic plates have an even distribution of 70 to 75, 1/16 -inch diameter holes through which the flow of gas is maintained at sonic velocity. The 1/8-inch plate used between the 5-inch flanges has 75 of these holes besides the 5/8-inch center hole for the flameholder supporting rod. The sonic piston has 70 of these holes, is 1/2-inch thick, is supported by three 3/8-inch rods, and is sealed with the chamber walls by means of an O-ring.

_42 - Sodium - Line - Reversal System The sodium - line - reversal system, denoted hereafter as SLR, which is employed to measure flame temperatures, involves a tungsten ribbon lamp, whose brightness temperature is calibrated as a function of electrical direct current, two lenses of equal size and focal length, a high quality spectrometer, a controlled and steady source of d.c. current, and a high quality d.c. ammeter. A schematic diagram of the SLR system is given in Figure 7. The lamp is a 6 volt, 18 amp., tungsten-ribbon lamp, type T10, made by General Electric. The lenses have a 4-5/8 focal length, a 3 -inch diameter, and are coated. The spectrometer is the Bausch and Lomb wave-length, laboratory spectrometer. The ammeter is a GE DP-11 with a dual range of 0-10 and 0-20 amp. The ammeter was purchased new for this project and had an accuracy of 1/2 of one per cent of full scale. The brightness temperature of the lamp was calibrated by General Electric's Nela Park division with a vycor disc between the lamp and their pyrometer at five temperatures from 15000F to 35000F with respect to direct current. The accuracy of calibration is claimed to be + 8~K and any aging of the lamp is claimed to be less than 1 per cent through the first forty hours of burning at full-rated current. The lamp used in the experiment is estimated to have been burned a total of about thirty hours at 70 per cent of rated current. The mounting of the lamp, lenses, and spectroscope was done very carefully to achieve perfect alignment and focusing. The focal length of the lenses was checked before mounting and found to be 4-5/8 + 1/64 inches. The lenses are mounted by means of lens holders and

BURNING GASES COLORED WITH NoHCO3 POWDER CALIBRATED TUNGSTEN RIBBON LAMP SPECTROMETER LENS LENS I= VYCOR WINDOW ~D.C. GENERATOR,1MOTOR I II 1 AMUETER 0-10-2O Amp. z EXHAUST GASES Figure 7. Schematic Diagram of Sodium- Line - Reversal System.

-44 -precisely placed slots on the basic framework surrounding the burner. The distance between lenses is 18-1/2 + 1/32 inches, with the burner in the middle. The lamp and spectroscope are mounted so that the filament and spectroscopic slit are each 9-1/2 + 1/32 inches from their respective lens. Since measurements are to be taken at the 10-inch level as well as the 4-inch one, the four items in the optical line are mounted by means of tongues and slots at each level, so that they can be quickly lifted from one level to the other and slipped into position. In the case of the lens mounts, it was found prudent to attach leveling bulbs on the lens holders, so that it can be noted at a glance whether or not the lens holder has been completely and snugly slipped into its slot. A direct current supply system was assembled that can be controlled to within 0~05 amp. from 6 amp. to 16 amp. and which gives a steady current. A 12-volt Autolite d.c. generator is driven at about 2100 r.p.m. by a 1/2 hp. electric motor. Two, 1-ohm 100-watt, and one 1-ohm 500-watt rheostats plus a 2-ohm 100-watt resistor are employed to control the current. An optical pyrometer by Leeds and Northrup of the disappearing filament type is an important part of the SLR equipment, serving to test the light scatter from the lens and window. Extension Leads and Miscellaneous Thermocouples The thermocouple assemblies embedded in the tube are connected by 16-gauge twisted thermocouple extension wire of chromel and alumel. Before the extension wires were silver soldered to the delicate 36-gauge wires, the weight of the extension leads was supported by means of tape.

The junctions are covered with Duco cement for support and thermal insulation as well as with fiberglass. The extension wires lead to a 24-couple switch box. A Leeds and Northrup portable, precision potentiometer, model #8662, is used to measure the e.m.f. between an ice bath and any of the thermocouples embedded in the tube or in the various streams. The potentiometer's standard cell was checked at the beginning and end of the experiments with a standard cell that had recently been calibrated by the National Bureau of Standards. No change was found in the potential of this project's standard cell. The potentiometer rests on two inches of foam rubber to insulate it from mechanical vibrations within the room and building. All the iron-constantan thermocouples were checked in boiling water while the thermocouples embedded in the tube were checked at two temperatures. The burner was filled with fiberglass to prevent any heat transfer through the tube walls, so that all three thermocouples in each section would read the same. With cooling water circulating at a high rate, there was little temperature rise from inlet to outlet, about 0.10F, and this was corrected by a linear interpolation. Thus readings were made at cooling water temperature, about 520F, and at room temperature, about 750F. Two of the embedded thermocouples were in error, but the remaining 13 all read the same. Of these two, one failed to function later in the project and the other never read correctly. One is in the 10-inch level section and the other in the 17-inch level. Temperatures of all the various liquid and gas streams are measured with iron-constantan, 24-gauge thermocouples. Specifically,

they are located in the inlet and outlet water streams of the water jacket, the inlet and outlet streams to the flameholder's cooling coil, and in the propane and air stream just downstream from each rotameter. In the water streams the thermocouples are placed in wells, protruding at least three inches into the stream. Oil is placed in the well with the thermocouple. The well in the exit water jacket stream has six brass 14-mesh screens soldered along its length, and it protrudes seven inches into the stream. The pipes between the jacket and the thermocouple wells are insulated with fiberglass. The thermocouples in the gas streams are bare and are sealed with Conax thermocouple glands at their entrance into a stream. Measurement of Sound in Chamber The rigid, high intensity Massa microphone, model 141-B, which is located flush with the inside chamber wall at the 22-inch level is a crystal type microphone, completely enclosed in a stainless steel cover with a metallic diaphragm. It is suitable for use with the General Radio sound level meter, Type 1551-A, extending the range of the meter to 190 db. The General Radio sound analyzer, Type 760-B, is employed to measure the frequencies of an oscillation and to give the relative amplitude of different notes, if more than one is present. An Ampex 601 tape recorder was used to record the sound for a few conditions. The microphone, sound level meter, and Ampex 601 tape recorder have flat frequency responses from 25 cps to (at least) 10,000 cps + 2db. The range of the sound analyzer is 25 cps to 7500 cps + 2 db, with a frequency accuracy of 1-1/2 per cent and a band width of 2 per cent.

-47 -Propane System The propane was purchased from a commercial distributor and was analyzed twice on the mass spectrometer during this project and at least once on a previous project. The combined analyses indicate a composition of 98 per cent propane and 2 per cent propylene with a maximum variation of 1 per cent. The propane is stored outdoors in a four hundred pound tank, which is equipped with three 0.750 kw. immersion heaters, each with a 100 square inch area. These heaters provide the heat of vaporization when gaseous propane is withdrawn and are regulated with individual 110 volt variacs. A flash vessel approximately 9 inches in diameter and 15 inches tall is located in the propane line between the tank and metering panel to prevent any liquid propane from being entrained in the line from the storage tank. A Moore nullmatic pressure regulator, model 42H, 0-100 psi, is upstream from the rotameter in the 1/4-inch pipe line to keep the propane at a constant pressure for accurate and steady metering. The rotameter which was calibrated by Fischer and Porter, the manufacturers, has a capacity of 10.6 SCFM of propane metered at 70OF and 50 psia. Air Supply and Test Cell The air is supplied by a 40 hp. compressor at 95 psig at a maximum rate of about 130 SCFM. The compressed air goes through a bed, approximately a 15-inch cubical, which is filled mostly with glass wool plus some 1/4-inch ceramic balls. This bed removes the oil drops entrained in the air from the compressor. The piping for the air line is 1-inch pipe. The air pressure is regulated upstream from the air rotameter by another Moore

-48 -nullmatic pressure regulator, type 42H, 0-100 psi. The air rotameter, which was calibrated by the manufacturersFischer and Porter, has a capacity of 152 SCFM of air metered at 50 psia and 700F. A 1.5 kw electric heater is located in the air line downstream of the rotameter. The apparatus section would not be complete without mentioning the cell or room in which the project was carried out. The room is an engine test cell in the University's Automotive Laboratory and is equipped with a high-capacity vacuum exhaust and ventilating system. Also the one-foot, poured concrete walls and double, explosion-proof doors enabled this extremely noisy project to be carried out with a minimum of disturbance to the others in the building.

EXPERIMENTAL THEORY AND ACCURACY Several theories are involved in converting the measured data into meaningful and useful quantities. The thermocouple readings must be converted into heat transfer rates; the pressure drop measurements must be converted into combustion efficiencies; the SLR (sodium-linereversal) measurements must be converted to average gas temperatures; and the mode of oscillation must be interpreted from the frequency measurements. The special theories or equations needed to process the data are presented in this section and the accuracies of the measurements are discussed. Derivations are presented in Appendix C, if they are special and not readily accessible in the literature. Evaluation and Accuracy of Local Heat Fluxes The appropriate heat transfer equation is readily deduced from the general equation for conduction through an isotropic solid, p Cp t = div(k grad T) (4) In the case of the isolated thermocouple sections, several terms are zero, thus T _ aT T, (5) at 9a ax These simplifications are valid, because the data are taken under steadystate conditions, and because the insulated longitudinal and chordal slots prevent the flow of heat in those directions. The thermal conductivity of the tube may be assumed to have a constant, average value. This assumption is validated by Churchill(l2) for a similar case but where the thermal

-50 -conductivity of the test object is even more dependent on temperature than is Croloy. He showed that the heat transfer rate calculated with the assumption of a constant average thermal conductivity differed negligibly from the result obtained by a more involved and rigorous procedure. Therefore, the radial flux at the inside surface of the tube is given by Q/As = kav Ti - Tj (6) rs in rj/ri where iyj. In three of the five thermocouple sections, three temperatures are measured, giving two independent temperature gradients, and thus a check is made. An overall check of the heat transferred through the tube walls is made, using the heat absorbed by the cooling water from the tube to check the integration of the locally measured heat transfer rates. AT Q WCp Tw f= (Q/AS) As (7) 0o where ATw is the net increase in water temperature due to heat transfer through the internal wall alone. The presence of the thermocouples distorts the heat flux throughthe cylinder wall. By a conformal mapping technique an estimation of the error introduced is made, assuming the extreme case that the thermocouple holes are perfect insulators and that they lie perpendicular to the temperature gradients, i.e., parallel to the tube wall. This analysis, which is presented in Appendix C, indicates a maximum error of 3 per cent due to the distortion of the heat flux by the thermocouples.

-51 -The other simplified case to analyze is that of the thermocouple holes being vertical to the tube wall but still perfect insulators. Beck and Hurwicz(6) have analyzed this case and present their results in dimensionless distances and heat fluxes, so that the error is easily evaluated and is 4 per cent. The actual error in the heat flux caused by the presence of the thermocouples is thus no greater than 4 per cent. The only remaining sources of error in the heat transfer measurements are the uncertainty of 7 mils in thermocouple location and an uncertainty of 3 microvolts in the e.m.f. measurement. The location uncertainty represents a possible error of 2.8 per cent, and the e.m.f. inaccuracy represents an error of 1/30F in the temperature gradient or less than a 1/2 per cent error for heat fluxes over 10,000 Btu/hr.ft. Accuracy of SLR Method The principle of the sodium-line-reversal, SLR, method of flame temperature measurement is based on Kirchhoff's radiation law. At the matching condition, the following relation is fulfilled. EL = EF + (1 - CF) EL (8) A detailed explanation of the SLR method is given by Reference (41). The specifications of all the items in the SLR system are given in the Apparatus Section, and the calibration curve for the lamp is placed in Appendix D. The calibration of the lamp's brightness temperature versus its current is claimed to be accurate to + 15~F by General Electric. The ammeter, having an accuracy of 1/2 of 1 per cent of full scale, is the source of a possible 50F error in the range of use in this study.

-52 -Light scattering or absorption by the lens or window between the flame and spectroscope is of no consequence because the intensity of the lamp and flame would be reduced equally and the comparison is not altered. Since the lamp's calibration included the effect of the lampside window, the only uncertainty is the effect of the lamp-side lens. This error was evaluated with an optical pyrometer of the disappearing filament type and was found to cause a lowering of the apparent lamp temperature of no more than 200F. Any error due to inexact focusing of the lamp and the flame images on the spectrometer slit is held to a minimum. After the lamp, lenses, and spectrometer were mounted at the proper distances + 1/32 inch, a check was made of the filament's image at the spectrometer slit and found to be in focus and exactly the same size as the filament. The accuracy of the SLR measurement is reduced by one peculiarity of a flame, particularly in a large combustion chamber. Although all of the burner conditions were steady, including heat transfer rates, sound level, flow rates, and wall temperatures, there was a constant flickering of the flame temperature about a constant average value. However, an increase in lamp temperature of 30F to 500F would always produce steady dark D-lines, and a similar decrease in lamp temperature would always produce steady light D-lines. A safe estimate of this source of error is + 500F. The intense flame-generated oscillations did not cause any visible flickering of the D-lines, because their effects were averaged out in a shorter time than is visually perceptible. Another possible source of error arises from the presence of radial temrperature gradients in the flame. The radiation from the hot

central core of burned gases will be dominant in determining the SLR matching temperature, but the boundary layer of cooler gas will have some influence depending upon its thickness, temperature, and sodium vapor concentration. In Reference (41) the equations are derived and an example problem carried out for a similar evaluation of the effect of temperature gradients. Three assumptions are made: 1) the temperature distribution corresponds to that of fully developed turbulent flow at the Reynolds number of the hot gases, 2) the sodium vapor concentration is even throughout the flame, and 3) the flame can be considered as two regions, a central core and a boundary layer, for this analysis. The first assumption is discussed later and evidence of its validity 13-1/2 inches from the flameholder is given then. The analysis, which is based on the emissivities of the two regions being proportional to their thickness, indicates the SLR reading is less than the central core temperature by 30~F to 50 F, depending on the temperature level. The higher temperature levels have the higher deviations. Because this analysis only places a limit on the effect of the boundary layer and does not prescribe a precise correction factor, no correction was made to the SLR readings and they are taken to represent the core temperature. When all of these possible errors in the SLR measurement are combined, the limits for the uncertainty in the SLR core temperature are found to be -50~F to +900F. Although these limits are wide, when it is considered how large the corrections and uncertainties are for thermocouple measurements of flame temperatures ranging up to 33000F, and how non-ideal are conditions in the flame, then the relatively high accuracy of the SLR method may be appreciated.

-54 -Bulk Mean Gas Temperature The bulk mean temperature of the gases is desired for the evaluation of combustion efficiencies and for the calculation of heat transfer coefficients. The feasibility of assuming that the velocity and temperature distributions could be represented by fully developed turbulent flow at the 4-inch level, or 13-1/2 inches from the flameholder, was investigated. Thermocouple and pitot-static tube traverses of the flame at the 4-inch level were taken at a low fuel-to-air ratio. The conduction and radiation corrections for the 16-gauge bare chromelalumel thermocouple were made using the methods and charts of Scadron and Warshawsky.(68) The velocity and temperature distributions were flat, not falling off until within 1/4 inch of the wall, and so did not contradict the distributions for a fully developed turbulent flow. The bulk mean temperature obtained for such a flow by a graphical integration is given by the relation Tb - 0.82 (TSLR - TS) + Ts (9) Uncertainties in the interaction of the combustion and the flameholder on the flow pattern and temperature distribution are admittedly large; however, verification of the mean bulk temperature determined in this manner from the SLIR flame temperature is given by the combustion efficiencies found independently through pressure-drop measurements. The combustion. efficiencies determined by these two methods agree within 6 per cent for all of the stable combustion runs and the average of the two methods agrees within 2 per cent.

-55 -Justification of Microphone Position In the chamber volume between the flameholder and sonic plate, the sound is believed to be uniformly distributed and of a random nature rather than of a resonating nature. Theory supports this belief. None of the frequencies generated in the combustion chamber correspond to possible primary or first harmonic resonant modes in this space where the microphone is located. The location of the microphone within this volume would have been critical if resonance existed; however, minor changes of an inch in the flameholder position around the 17-1/2 inch level as well as a major shift to the 13-1/2 inch level produced no irregularities in the measured sound intensities. Further verification of the lack of resonance is indicated by the fact that upstream changes, such as moving the sonic plate, had little if any effect on the intensity or frequency of the generated sound. The accuracy of the sonic measuring equipment is presented in the Apparatus Section. A simple check was made with the Massa microphone by comparing its reading with the reading of the General Radio microphone which came with the sound level meter. The two microphones were placed next to each other for this test. Application of the correction factor determined by the relative impedances of the two microphones brought the two readings to within 2 db of each other for sound levels of 100 to 130 db. Combustion Efficiency from Pressure Measurement The combustion efficiency is determined independently by the SLR measurements and by pressure-drop measurements. The evaluation of

the bulk mean temperature from SLR measurements is discussed earlier in this section. The combustion efficiency is readily found, once the temperature of the gases is known, by use of Equation (14) below. An outline of the method and theory used to evaluate combustion efficiency from pressure-drop measurements is presented below. For a thin discontinuity in flow, the general mass, momentum, and energy relations can be reduced to the following approximate onedimensional equations. Mass: Pi U1 A1 = P2 u2 A2 (10) Momentum: (P1 + u) A = (P2 +. ) A2 + FD (11) gc gc Energy: Cp (T - To) + + Qr - Qt 2 Cp2 (T2 - To) + 2 (12) If no steep gradients exist at stations 1 or 2, the equations can be applied to a deflagration with negligible error. The use of the ideal gas law and several simplifying assumptions leads to the following equations from which the flame temperature and then the combustion efficiency are calculated. T2 _ P2 M2 A2 gc A2P1 Pu1 (13);.-I -P2 PD + (13) T1 P1 M1 Al Plul gAl c E (T) x 100 CP2(T2 - T1) + Qt x 100 (14) gT1) Q..(T1)'

-57 -The derivation of these equations is presented in Appendix C. Subscripts 1 and 2 refer to conditions at the inlet and at the outlet, respectively, i.e., the 25-inch and 2-inch levels. The reference temperature is that of the inlet, i.e., To = T1. QR(T1) is the possible chemical heat release at T1 for total combustion of the limiting reactant. All the inlet conditions are known as well as A2. Integration of the local heat fluxes plus the heat absorbed by the flameholder yields Qt, the total heat lost by the flame. The drag of the flameholder and walls, PD, is estimated from cold flow data and from the calculated temperature profiles of the flame. The drag of the flameholder is assumed equal to its cold flow drag at the same inlet Reynolds number. The drag of the walls, which is a minor part of the total drag, is evaluated using the calculated temperature profile of the flame, an estimated exit composition, the ideal gas law, and the friction factor for smooth pipe and for the local Reynolds number. The estimated composition is revised if the calculated combustion efficiency disagrees with that assumed in the estimation of the composition. The calculations would then be repeated. Since the average molecular weight, M2, and the mean heat capacity from T1 to T2, Cp2, are first estimated on the basis of approximate values for T2 and E, revisions of these estimates may also be necessary before the final T2 and E are calculated. Prediction of Resonant Frequencies The wave equation in cylindrical coordinates is 2 1 PQ - 2 a [Prr + Pr + 2 +a Pxx = Ptt (15)

-58 -The appropriate boundary conditions are 1. P is finite at all times 2. P is cyclic in Q 3. P-= 0 at = TC/2 4. dP/dt = O at t = O 5. P is finite at all positions 6. dP/dr = O at r = R 7. dP/dx. - at x = O (flameholder) 8. P = O at x - Le (open end) The solution is readily obtained by the method of separation of variables and differs only slightly from the case presented by Morse(56) of a cylinder closed at both ends, instead of just at the one end, x - O, in this study. P -= ' cos mQ cos ix + 1/2) mx Jm r) e 2i (16) ) e (16R) where n, nx, m- 1, 2, 3,. o are the woare nxnbaers. Values of Cmnny which. satisfy the requirement that dJmJdr -0 at r - R are given by Morse. The frequency, f, is given by the relation f (nx + 1/2)2 2 fm, nnx + (3) mnn 2 Le R The significance of the various wave numbers is given in the Literature Survey.

-59. Theor of Acoustical Damping The theory of the quarter-wave tube as a damping influence on longitudinal waves is simple. When the tube is placed at a pressure antinode, a pressure condensation will travel along the tube and be reflected as a condensation from the end of the quarter-wave tube and return to the main tube out of phase with the oscillation there. Thus damping is accomplished. The theory of the spray muzzle as a damping influence on longitudinal oscillations is also readily explained. The spray quench when placed at a velocity antinode hinders the particle movement of the wave due to the large inertia of the water particles. Accuracy of Flow Measurements The propane, air, and water rotameters were calibrated by the manufacturer accurately to within 1 per cent of full scale reading. The propane and air rotameters were spot checked with a wet test meter and readings that agreed within 1 or 2 per cent were obtained. The water rotameters were checked with a bucket and a set of scales.

EXPERIMENTAL PROCEDURE A typical run starts after the behavior of the combustion process has been investigated and the desired conditions for the run decided upon. The flameholder is positioned at the desired burning length and carefully centered in the combustion tube before ignition of the flame. After the air flow is set at a moderately high rate anrd the water streams to the chamber jacket and the flameholder are flowing, then the propane is turned on and slowly increased in rate as the spark plug is continuously being fired. Ignition of the propane and air is thus accomplished at as lean a mixture as possible. If the spray-quench muzzle is attached to the end of the burner, the water spray is turned on immediately after ignition. The flovw rates are now adjusted to the conditions for the run. Steady state, which is usually reached within five minutes, is checked by taking several readings of key thermocouples over several minutes' time. Steady-State Measurements After steady state is reached, the following data are read: pressure drop from the 25-inch level to the 2-inch level, flow rates of air, propane, flameholder-water, burner-water, thermocouple readings of the air, propane, and the combined gas streams, as well as of the inlet and outlet water streams to both the burner and flameholder, and the sound pressure level and frequencies. If any of the readings at the beginning and end disagree, the run is repeated. A complete set of readings of the thirteen operable embedded thermocouples is taken about midway through a run with over half of them being read twice to check the equilibrium. -60 -

Next the sodium-line-reversal measurements are made. The sodium bicarbonate duster is turned on immediately after all of the embedded thermocouples have been read, but the lamp is turned on about five minutes early to allow it to warm up. If any steam is condensing on the lenses, air jets are played on both sides of each lens while the SLR measurements are made. Two sodium-line-reversal measurements at one level in the burner are taken a few minutes apart to be certain that the lamp is at equilibrium at the flame temperature. Readings are taken at the 4-inch level for all runs and at both the 4-inch and 10-inch levels when the burning length is 17-1/2 inches or more. The sodium bicarbonate is dusted into the flame only during the SLR measurements, unless otherwise noted for a particular run. The sound level is measured with the Massa microphone in the burner, and the frequency spectrum is scanned during every run with the sound analyzer. For a few runs the sound level outside of the burner is also measured. The Massa microphone is connected to the tape recorder for a few recordings of transverse and organ-pipe oscillations in the burner. The heaters in the propane tank are adjusted at the beginning of a run to maintain the propane pressure at a fairly constant level. When the outdoor temperature is above 40~F, the heaters are adequate to maintain the propane pressure even at high propane rates, but when the outdoor temperature drops much below 300F, adequate propane rates are not possible.

-62 -Cold Flow Measurements For each series of runs cold flow measurements, i.e., measurements without combustion, are taken of pressure drops and of the heat transfer coefficients. The cold flow drag of the flameholder and tube walls is measured for air flowing at the same inlet Reynolds number as that of the run. Heat transfer rates and coefficients are evaluated at the average Reynolds number of the murned gases using air heated to about 1700F and two thermocouples at the 4-inch level to measure air temperatures. Integration of the local heat transfer rates along with an energy balance determines the air temperature at the other stations. Since it is not feasible to insulate the burner' s water jacket, some heat is transferred to the water stream from the room. A correction for this is evaluated by measuring the temperature rise of the water when there is no gas flow in the burner. Control of the Flame-Generated Oscillations The various flame-generated oscillations are studied and controlled by the use of different flameholders and by the use of different conditions at the end of the burner. T'e flameholders with a free annulus are suitable for studying flame-generated longitudinal oscillations. The attenuation of this longitudinal oscillation can be varied considerably. The spray-quench muzzle with a screen placed below the spray damps out the organ-pipe completely, while without this screen a fairly intense longitudinal oscillation is possible, and without the muzzle the attenuation at the end of the burner is a minimums Thrie blockage of the flameholder also offers control over

-63 -the sound intensity because an increase in blockage increases the intensity of the longitudinal oscillations due to improved reflection of the oscillation at the flameholder. The flameholders with the screen in the annulus are suitable for the study of a transverse mode of oscillation. The screen stabilizes the flame closer to the tube walls and thus brings a greater release of energy into the region where the pressure amplitude of the transverse wave is greatest and where the energy is most beneficially applied to drive this oscillation. The transverse mode is kept free from a separate organ-pipe oscillation by using the spray muzzle with its screen to damp the latter mode. The transverse oscillation may be damped out by making the annulus of the flameholder long and thus causing the unburned gases to jet through the annulus and sweep the area near the tube wall free from any active combustion. Corrosion of the Burner The burner walls and windows were regularly inspected and cleaned if necessary. No corrosion nor tarnishing of the inside tube wall occurred throughout the experiments. At the end of the project, the outer wall of the main tube, i.e., the cooling-water side, was found to be clean and about 95 per cent rust free.

EXPERIMENTAL RESULTS The results of the heat transfer studies on propane-air flames are presented in graphical form. The main emphasis has been to study the effect of the dependent variable, sound level, on the local rates of heat transfer and on the local convective coefficients. The effect of process variables such as fuel-to-air ratio and Reynolds number are not of primary interest. In fact, the main interest in the process variables and in the geometry of the burner rests on their effect upon the flamegenerated oscillations. Range of Process Variables The range of Reynolds numbers to be studied, 35,000 to 47,000, is limited because a large burner was required as determined by preliminary experiments to generate screeching combustion, ioe,, transverse osaillations. The safe minimum. flow rates to prevent flashbacks are appricximately 25 per cent less than the maximum capacity of the air supply ysvt-emr. 'e study is limited to lean fuel-air mixtures not only because of lir..itaticns on the propane supply but also because this is the region of most practical interest and because the burning tends to become rough in rich fuel-air mixtures, particularly in a large burner. The burning lengths are also dictated by sonic considerations. Form for Data Presentation The effects of flame-generated oscillations and other variables such as burning length, Reynolds number, and fuel-to-air ratio on the profile of local rates of heat transfer along the tube are presented in

-65 -graphical comparisons. Temperature profiles are presented in a similar manner for a few runs. Coefficients for convective heat transfer are also presented along with a correlation for the coefficients as a function of sound level. At the end of this section, some heat transfer profiles for a quiet burner plus some miscellaneous curves are included. For the profiles of both local heat flug and gas temperatures, the data are plotted as 1-inch wide lines rather than as points since the heat fluxes represent average values over the 1-inch long thermocouple sections. The calculation of the heat flux has been discussed, and the details of the calculations are in Appendix B. The flame temperature is measured at the 4-inch level for all runs and in addition at the 10-inch level for the.runs with a 17-1/2-inch burning length. Therefore, to evaluate the gas temperatures closer to the flameholder and thus to obtain a temperature profile of the flame along the entire burner, the following procedure is employed. The heat transfer coefficient at the 4-inch level, h4, determined by the measurement of the flame temperature is used to evaluate a multiplier, h4/h 4, by which the cold flow coefficients at the other four stations, h x, are multiplied. h4, hx = (- -) h x (17) h4 x The resulting coefficients, hx, are then used in conjunction with the local heat fluxes and radiation corrections to calculate the flame temperatures closer to the flameholder.

-66 -A tabulation of the flameholders, denoted f.ho in the figures, is given in Appendix Ao The complete listing of the data for all the runs is also in Appendix A. Effects of Transverse Oscillations on Heat Transfer Profiles The effect of a strong transverse oscillation on the local rates of heat transfer is depicted in Figures 8 and 9 at two different Reynolds numbers. The lower curve in each figure is the profile for the case where the screech has been damped by the long annulus flameholder, S-2. The sound level of 130 to 133 db is that of stable combustion or of a "quiet" burner, ieo,, a burner in which no one frequency predominates nor is resonant. The sound level recorded for cold flow is around 124 db. T-Phis comparison is not entirely of screeching versus non-screeching combusai.on because the flameholders are different. However, the effect of bre flameholders can be evaluated under non-oscillating or stable conclitions, which 'is the case in Figure 10. Here the S-1 flameholder is seen to produce a 20 per cent higher peak and a 8 per cent greater amount of tota. heat transfer. A similar comparison with similar results can be made with Runs 14 and 50. Intense screeching combustion, 151 to 154 db, thus causes a ret increase in the peak of the heat transfer profile of 30 per cent and a net increase in total heat transferred to the tube of about 50 per cent instead of gross increases of 50 and 60 per cent, respectively.

60,000 50,000 '1" 0~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ 30,000 Iz 420000 - 20,0 40 0 ol DISTANCE F~ROM FLAMEHOLDER,-INCHES Figure 8. Profile of Heat Flux —Damped Versus U~ndamped Screech at Re ~ 47,000. x - Izd.. U SYMBOL F.H. Db fcps Q i Btu/hr 21 x-x~~r S -I 154 4150 80,300 43 D-E El -2 133 - - 48,600 0 2 ~ ~~4 6 8 10 12 14 1.6 DISTANCE FROM FLAMEHOLDER,-INCHES Figure 8. Profile of Heat Flux —Damped Versus Undamped Screech at Re w 47,000.

506 00 Re 4o,5oo = 0.895 406 000 fi0: CI = 20,000 14000 RUN SYMBOL F.H. Db fcps QI BTU/HR 16 X X S-I 151 4150 72,700 45 '- S-2 130 - 45,900 0 2 4 6 8 I 0 12 14 16 DISTANCE FROM FLAMEHOLDER - INCHES Figure 9. Profile of Heat Flux —Damped Versus Undamped Screech at Re 1 40,500.

RUN SYMBOL F.H. Qi BTU/HR 50,000 18 X-K S-I 41,500 Re = 46,500 44 - S-2 38,400 Db = 132 60 -0 F-5 33,500 *| =0O.68ll 61 0 F-6L 38,200 LL W 40,000 C-:3 0,000 uI - w o M 20,000 -J~~~~_Jj LL I — IO, 000 ' O~0 2 4 6 8 10 12 14 16 DISTANCE FROM FLAMEHOLDER-INCHES Figure 10. Profile of Heat Flux —Comparison of Flameholders Under Stable Conditions.

3,000 Re 40, 500 0.895 2,500 0 2 2000 w w 2 1, 500 w w 12000~~~~~~~~~~~~~~~~~~~ -J RUN SYMBOL F.H. Db fcps 16 *-X S-I 151 4150 45 D-0 S-2 130 - 0 2 4 6 8 10 12 14 16 DISTANCE FROM FLAMEHOLDER -INCHES Figure 11. Temperature Profile —Damped Versus Undamped Screech at Re x 40,500.

60,000 ~, Re = 47,000 0.83 50,000 Icc D- 30,000 z or. 20,000 w I 10,000 RUN SYMBOL F.H. Db f cps Qi BTU/HR 29 X-K S-I 1 156 4100 65,500 37 E-0E S-2 132 - 35,600 _ _ _ _ _ _ I I I I 0 2 4 6 8 10 12 DISTANCE FROM FLAMEHOLDER - INCHES Figure 12. Profile of Heat Flux —Damped Versus Undamped Screech for Lb = 13-1/2 Inches.

o,ooo00 Re = 47,000 F.H. = s-I =0.94 50,000 END OF TUBE U. a %. 30,000 U) 2 4 6 8 10 12 14 RUN SYMBOL Db fcpS Lb Qi BTU/HR Figure 23 Flux —Effect of Burning Length 82,600 30 I- 157 4150 $'~' 67, 500 0 2 4 6 8 10 12 14 16 DISTANCE FROM FLAMEHOLDER-INCHES Figure 13. Profile of Heat Flux —Effect of Burning Length During Screeching.

60,000 =0.86o { o. Db= 154 f = 4150 cps F.H. S- I 50,000 12 X 40,500 76,40500000 30,000 47,500 80,300 cr 16 a 20,000 X ooo 0 2 4 6 8 I0 12 14 16 DISTANCE FROM FLAMEHOLDER - INCHES Figure 14. Profile of Heat Flux —Effect of Flow Rate During Screeching.

50,000 __Il 0 = 0.67 f = 3850 cps F.H. =s-I IL 40,000 cr X I --- " 30,000 Iz w a c 20,000 -J. X~~~~~ Iw: I 0,000 RUN SYMBOL Re Db Qi BTU/HR 25 X X 47, 00 149 44,200 35 D, 40,000 147 38,000 0 I I I. 0 2 4 6 8 10 12 DISTANCE FROM FLAMEHOLDER-INCHES Figure 15. Profile of Heat Flux —Effect of Flow Rate and Slight Change in Sound Level.

50,000 Re = 47, 700 F.H.- S-I — 406000, U-4 WL. I~i 30,000 C') z UJ -.o 20,000 X..J U. I — W. I 0,000 RUN SYMBOL Db fcps ~ Qi BTU/HR 17 X-K 148 3850.65 51,200 18 E - 132 -.67 41,500 _ _ _ _I i I I I! _ 0 2 4 6 8 10 12 14 16 DISTANCE FROM FLAMEHOLDER-INCHES Figure 16. Profile of Heat Flux —Screeching Versus Stable Combustion at Re = 47,700.

3,0000 I Re = 47,700 F.H. = s-I 2,500 L. 2,0002 4 6 8 10 12 14 16 Re = 47,700. 18 I-. 132 - -.6 Re 47,700..

50,000 Re = 40, 500 F.H. s-I IL 40,000 3000 a, o 30,000 uJ~ ~ ~~ ~ ~~~~~~~~~~~~~~~~~~~~~~~~~~~~I 0 20,000 n rl RUN SYMBOL Db fcps Qi BTU/HR -j 13 )X-K 0.84 148 4150 60,900 1 5 0-0 0.79 133 - 48,800 X 10,000 0 2 4 6 8 1O 12 14 16 DISTANCE FROM FLAMEHOLDER - INCHES Figure 18. Profile of Heat Flux —Screeching Versus Stable Combustion at Re = 40,500.

3,000 Re = 40,500 F.H.= S-1 2,500 U. 02000 0. 1,500 I w Id U11000 RUN SYMBOL Db fcps 13 *-K l 0.840 148 4150 15 O-O 0.794 133 - 500 0 2 4 6 8 10 12 14 16 DISTANCE FROM FLAMEHOLDER-INCHES Figure 19. Temperature Profile —Screeching Versus Stable.Combustion at Re = 110,500.

60,000 Re = 47,500 DISTANCE~ ~ FRM LMEOF.H.s= - I 50,000 N.: 40,000 -- >w 30,000 z I 19 IID --- —~ 0.7 %.## 133 ~ - 46,700 I0,000 20 O 8 1 4 150 4125 7 1, 400 21 O- 0.861 154 4150 80, 300 23 A — 0.951 155 41 75 82,600 O~0 ~2 4 6 8 10 12 14 16 DISTANCE FROM FLAMEHOLDER - INCHES Figure 20. Profile of Heat Flux —Effect of Varying Fuel-to-Air Ratio with a Flameholder that is Prone to Screech.

3,000 _ __ Re= 47,500 F. H. S - I 2,500 LL * 2,000 a.4. 1,500 w I-oo _j 1,000 RUN SYMBOL Db fcps 17 *-)( 0.648 148 3850 19 E-09 0.735 133 - 20 o-o 0.814 150 4125 21 -O 0.861 154 4150 23 A — 0.951 155 4175 0 2 4 6 8 10 12 14 16 DISTANCE FROM FLAMEHOLDER -INCHES Figure 21. Temperature Profile —Effect of Varying Fuel-to-Air Ratio with a Flameholder that is Prone to Screech.

60,000 Re-= 40,000 F.H.= s-I 50,000 = 40,000 >: 306000 z I DISTANCE FROM FLAMEHOL D b f cps i BTU/H R 32 13 --- —— E 0.892 152 4150 64,100 Figure33 22. Profile0769 143o 4050 40,800 34 a Flameholer0.749 132that is Prone to 38,600 35 Ais AN& 0.668 148 - 3850 38,000 3,6 g 3 0.675 129 - 29,900 DISTANCE FROM FLAMEHOLDER- INCHES Figure 22. Profile of Heat Flux —Effect of Varying Fuel-to-Air Ratio with a Flameholder that is Prone to Screech with Lb = 13-1/2 Inches.

Re= 35,000 ll|RUN SYMBOL Db fcps Qi BTU/HR 54000 | F.H. = F- - 3 X X 152- 350 59,600 =.63 4 132 - 3,100 S40,000 Z~~~~~~~ 30,000 I- z = 0,000 ~ ~ J aJ 0 2 4 6 8 00 12 14 16 DISTANCE FROM FLAMEHOLDER-INCHES Figure 23. Profile of Heat Flux —Longitudinal-Osclillating Versus Stable Combustion at Re = 35,000.

Re = 40,500 F.H.= F-S = 0.77 50,000 40,000 7 30 000 Figure 24. Profile of Heat Flux —Damped Versus Undamped Longitudinal Oscillations at20,000 RUN SYMBOL Db fcps Q i BTU/HR 54 X- 155 345 72,500 57 ElO-G 130 - 42,000 o 2 4 6 10 12 14 16 DISTANCE FROM FLAMEHOLDER- INCHES Figure 24. Profile of Heat.Flux —Damped Versus Undamped Longitudinal Oscillations at Re = 40,500.

Re =46,000o = 0.58 FH= F-5 60,000 vO OC \RUN SYMBOL Db f Qi BTU/HR 58 X- K 160 350 73,600 59 O3- 131 - 25,100 50,000O I- 40,000 m 30,000... o 2 4 6 8 20 12 14,0 DISTANCE FROM FLAMEHOLDER - I NCHES Figure 25. Profile of Heat Flux —Damped Versus Undamped Longitudinal Oscillations at Re = 4,000. Oscillations at Re = 46.,000.

2500 2000 UL 0 w CI: - 1500 Q.I L I Re=46,000 0=0.58 F.H.= -5 I0 0 2 4 6 8 10 12 14 16 DISTANCE FROM FLAMEHOLDER- INCHES Figure 26. Temperature Profile —Damped Versus Undamped Longitudinal Oscillations at Re M 46,000.

60,000 Re 47,000 30,000;-: 410 o00 az I...r RUN SYMBOL F.H. Db f cps Qi BTU/HR 21 X X-K S-I 154 4150 0.861 80,300 55 - F-5 156L 345 0.783 84,100 _ I I I 0 2 4 6 8 10 12 14 16 DISTANCE FROM FLAMEHOLDER-INCHES Figure 27. Profile of Heat Flux —Screeching Versus Longitudinal —Oscillating Combustion at Re = 47,000.

60,000~ Re = 40,500 _ *_ 1 RUN SYMBOL F.H. Db fops * Qi 12 X- S-I 154 4150 0.854 76,500 54 - E a F-5 155 345 0.777 72,500 40,000 44000 z a X 2 4 6 8 ~I0 1TNC2 14 16 DISTANCE FROM FLAMEHOLDER-INCHES Figure 28. Profile of Heat Flux —Screeching Versus Longitudinal —Oscillating Combustion at Re = 40,500.

1701 I Re =46,000 I ~~~~~~~~~~~Lb=I17 -1 INCHES. m 160 FH.=F-5 -s - ~~~~~~~~~~~~MUZZLE (WITHOUT W ~~~~~~~~~~~~~~SCREEN) ON END OF W ~~~~~/BURNER W~~~~~~~~~ cc 150 (O) z o 140 U)I 130- - - I -_ __ 0.5 0.6 0.7 0.8 0.9 1.0 (I Figure 29. Hysterisis Behavior of the Longitudinal Oscillation with Fuel-to-Air Ratio.

=0o. 78 F.H.= F-5 f: 345cps 50,000 HU. C 40,000 X 0T 30,000 z w a LL. ~~~~~, I4 w I 04000 RUN SYMBOL Re Db Qi BTU/HR 54 X X 40,400 155 72,500 55 046,000 156I 84,100 2 000 0 2 4 6 8 10 12 14 16 DISTANCE FROM FLAMEHOLDER-INCHES Figure 30. Profile of Heat Flux —Effect of Flow Rate During Longitudinal — Oscillating Combustion.

Re = 46,000 F.H.= F-5 60,000 / 50,000 U. m 40,000 I cr w 30,000 '8 ~/ l l ~~56 Eb-5 El 0.690 157 1 335 75,00 5 0,000 O 2 4 6 8 10 12 14 16 DISTANCE FROM FLAMEHOLDER - INCHES Figure 31. Profile of Heat Flux —Effect of Varying Fuel-to-Air Ratio During Longitudinal —Oscillating Combustion.

:60,000 LF I I I I. 50,000........ i_ N / g RUN SYMBOL 'H. Db f, cp i 0 21 4 415 80 X 20,000 - ~tITANE FRO FAMEHLER - INCHES 10Figure. Profile of Heat Flux —Comparison of S- and S-4R F 54 4200 78lameholders During Screeching Combustion.

50,000 ------------- F H. = S -40,-000 --- —---.. ] co |0// 1 74 457 OF 157 4190 78,00 10,000 0 2 4 6 8 10 12 14 16 DISTANCE FROM FLAMEHOLDER - INCHES Figure 33. Profile of Heat Fluxc —Effect of an Apprfoximately 200OF Rise in Wall Temperature During Screeching Combustion. _ _ _ _~~~~ ~ ~ ~ ~ ~~~~ ~ ~ ~ ~ ~~~~ ~ ~ ~ ~ ~~~~ ~~~~~~~~~~~~~~~ ~.._ _ _ _ _.._ _ _ _ _.._ _ _ _ _.. _ _ _ _.. _ _ _ _ _.. _ _ _ _. _ _ _ _.[._ _ (/023 1 2 41 Z ~ ~ ~ ~ ~ ~ ~ DSAC FRMFAEODRICE LU ~ ~ ~ ~~Fgr ',.rfl0fHetFu-Efc o nApoiael 00 iei Wall Temperature Luring Screeching Combustion

-93 -Temperature Profiles and Transverse Oscillations The relative importance of changes in flame temperature compared to changes in heat transfer coefficient is indicated by the temperature profiles in Figure 11 for the runs of Figure 9, The two temperature profiles are similar~ Short Burning Lengths and Transverse Oscillations Comparison of damped versus undamped transverse oscillations for a shorter burning length of 13-1/2 inches is similar to that for the 17-1/2-inch burning length0 In Figure 12, the peak is raised over 60 per cent and the total heat transfer by over 80 per cent when the sound level is increased from 132 db to 156 db, A comparison of the two burning lengths during screeching combustion is shown in Figure 13 where it is seen that burning length has little effect on the profile. The flamegenerated oscillation is slightly more intense for the shorter burning length. Two runs, numbers 8 and 9, were conducted at a burning length of 8 inches although no profile of heat transfer rates could be determined. An increase in the propensity of the burner to screech was noted for this short burning length because not only was the screech more intense, but it was generated without the screen in the annulus of the flameholder to stabilize the flame closer to the wall. It is noted that the increase in total heat transferred to the tube due to an increase in sound level from 133 db to 159 db is about three-fold, judging from the heat absorbed by the tube's cooling water.

-94 -Flow Rates and Transverse Oscillations The effect of flow rate during screeching on the local rates of heat transfer is shown in Figure 14. The higher flow rate tends to shift the peak downstream and to increase the rates downstream from the peak. A similar comparison of flow rates during screeching is made for the 13-1/2-inch burning length in Figure 15. However, in this case the sound levels are not identical, so that the higher flow of Run 25 together with its higher sound level is causing the general increase in its heat transfer profile. Moderately Idtense Screeching Combustion The effect of a moderately intense transverse oscillation compared to a stable combustion with the same flameholder is shown in Figure 16 and is seen to be less than for the more intense screech. The temperature profiles in Figure 17 are similar except for a higher peak for the damped case. Another comparison of the effect of moderately intense screeching combustion at a lower flow rate is made in Figure 18. The peak is increased by 27 per cent and the total heat transfer by 25 per cent for Run 13 with the 148 db transverse oscillation compared with the stable Run 15. It should be noted that the flameholders are the same in this comparison, but the fuel-to-air ratio is lower by 6 per cent in the stable run. Temperature profiles are also presented for these two runs in Figure 19 and are seen to be very similar,

-95 -Fuel-to-Air Ratio and Heat Transfer Profiles The general pattern in heat transfer profiles is portrayed by the five runs in Figure 20. Heat transfer rates are seen to increase with 9, i.e., fuel-to-air ratio as a fraction of stoichiometric, and with sound level. The corresponding set of temperature profiles follows in Figure 21. A similar pattern is obtained at the 13-1/2-inch burning length as seen in Figure 22. Effects of Longitudinal Oscillations The longitudinal oscillations have an effect on the heat transfer similar to that of the higher pitched transverse oscillations at the same sound level. Comparisons of the heat transfer profiles for damped and undamped longitudinal oscillations are presented in Figures 23, 24, and 25 at three different Reynolds numbers. The sound levels of the oscillation vary in each case, primarily because the degree of damping is varied. It is noted that the damping of the longitudinal oscillation is done with a spray-quench muzzle on the end of the burner and thus does not change the flow conditions in the burner. In Figure 24, the peak for the case of an intense longitudinal oscillation is increased by over 75 per cent and the integrated heat transfer by almost 75 per cent. The increases due to the organ-pipe oscillation are similar in Figure 23. In the case of Run 58 with its counterpart, number 59, with damped oscillation, the increases for the longitudinal oscillation of 160 db are essentially three fold. No muzzle was on the

burner in Run 58 and one of the higher blockage flameholders was used. In all three comparisons the peak is moved closer to the flameholder by the oscillation. The temperature profile for Runs 58 and 59 is given in Figure 26. The temperature profiles are not as similar as in earlier cases; however, the maximum or peak temperatures are of the same order of magnitude. The biggest difference is their position. Comparison of the Two Acoustic Modes The transverse and longitudinal modes of acoustic oscillation appear to produce similar effects, A comparison of their profiles of local heat fluxes is made in Figures 27 and 28, In Figure 27 where the Reynolds number is 47,000, the longitudinal mode causes a 5 per cent greater heat transfer to the tube than the transverse mode, This increase is probably accounted for by the greater intensity of the longitudinal oscillation, In Figure 28 at a Reynolds number of 40,500, the intensities are approximately equal. Here the transverse mode causes a slightly greater rate of heat transfer as expected because the propane-air mixture is closer to stoichiometric, i.e., 0 is closer to 1,0. Hysterisis with Organ-Pipe Oscillations A pronounced hysterisis effect exists in the case of longitudinal oscillations. When the fuel-to-air ratio has been increased high enough to bring the intense organ-pipe oscillation one the fuel-to-air ratio can be decreased by as much as 10 to 20 per cent without any change in sound

-97 -level. This phenomenon is shown in Figure 29 for the case of the F-5 flameholder and the muzzle without its screen on the end of the burner. The solid line represents the sound level as 6 is increased from a low value in a stable burner. The dotted line shows the sound pattern as is decreased after the intense longitudinal oscillation has set in. Fuel-to-Air Ratio, Flow Rates, and Organ-Pipe Oscillations The next two figures, numbers 30 and 31, depict the effect of varying flow rates and fuel-to-air ratio with intense longitudinal oscillations being generated. Increases in the profile occur with increases in either flow rates or fuel-to-air ratio as was true with the transverse oscillations. Transverse Oscillations with Ring-type Flameholder Some additional studies were made of the transverse oscillation with a different type of flameholder. In Figure 32, a comparison is given of the heat transfer profile with a ring-type flameholder to that with the previous screen-in-annulus flameholder, The difference is slight with a definite rate of heat exchange at the flameholder in the case of partial stabilization of the flame by an eighth-inch, asbestos ring cemented to the tube wall at the flameholder level. Effect of Higher Wall Temperatures on Screech The effect of higher wall temperatures on screeching combustion was tested to a limited extent, by slowing the flow rate of the tube's cooling-water enough so that it boiled through all but the first 4 inches of the burner length. Wall temperatures were thus raised by about 2000F.

-98 -The effect on the heat transfer profile is not large as shown in Figure 33; however, the sound level did increase by a significant amount, from 153 db to 157 db. Local Heat Transfer Coefficients The heat transfer coefficients to be presented are for convective heat transfer, with the radiation corrections to the local measured fluxes being estimated by the methods in McAdams.(48) Flame temperatures were measured at three distances from the flameholder by the SLR method. Local coefficients are calculated at these three points using the bulk gas temperatures determined by Equation (9) from the SLR measurements. The details of the calculations are included in Appendix B in conjunction with the sample calculations. The effects of varying flow rates, varying gas temperatures and properties, and different flameholders on the coefficient, h, is removed by dividing it by h, and h'/h',. The quantity, h., is the coefficient predicted for fully developed turbulent flow by the empirical correlation recommended by Zellnik for heat transfer from high temperature gas streams to a cooled tube. hD Nus = 0.023 Res0U8 Prsl/3 Tb/TsO.33 (18) ks The ratio, h /h', is the local coefficient measured without combustion divided by the predicted coefficient without combustion. This ratio of local coefficients for cold flow is plotted against tube length in Figure 34 for the various flameholders.

SYMBOL F. H. Re -14,000 < ~0 F-I, F-2, F-3 8INLET AIR T =1700 F X F-5, F-4, F-6L 4 i I 1 I 1 O -— 0-S- I N 3 -' 2 S-2 0 2 4 6 8 10 12 14 16 18 DISTANCE FROM FLAMEHOLDER-INCHES Figure 34. Coefficients Taken Without Combustion, h'/h', Versus Distance from Flameholder.

-100 -2.4 SYMBOL F.H. O F" SERIES S-I 2.2 O S-2 X S-3R, S-4R * RUNS 61,62 -: 2. C0 RUNS 24,52 0 2.0 0 Iz: U) u 1.8 z I- 11.6 1.4 I.4 (-)~ 0 e 1.2 1.0_ 0.8 ___3 __ 120 130 140 150 160 170 SOUND PRESSURE LEVEL,DECIBELS Figure 35. Local Coefficient for Convective Heat Transfer, 13-1/2 Inches from Flameholder, Versus Sound Level in db.

2.4 - * 2.2 0 0 0L 2~0 w 1 A 1.8= -yA h/h ]D l l. h|h'RSRE:co 044 + 1.08 z 1.6 rrA B SYMBOL F.H. TYPE OF OSCILLATION < 1.4 0 RF" SERIES ORGAN- PIPE _8A~~ A~ S-I SCREECH 1.2. E S-2 NONE X S-3R, S-4R SCREECH 8 1.0~ —tt- + — + -~ 1RUNS 61,62 I RUNS 24,52 0.8Ii I I 3 5 7 9 11 13 I5 17 19 21 23 25 27 29 31 33 RATIO OF SOUND PRESSURE AMPLITUDE, P/Po Figure '36. Local Coefficient for Convective Heat Transfer, 13-1/2 Inches from Flameholder, Versus Sound Pressure Amplitude.

24 LL~~~~~~~~~~I 1 A~~~j 2.0 0 1 i.6 I_ 1 1 L I I SYMBOL FR TYPE OF OSCILLATION z~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ 0 *FOSERIES ORGAN-PIPEI 1.4 S- SCREECH h/ha(h/h) 0.050 +1.0 NONE _.c8 1.2 i 1 4 l { | l | - | | X S-3R'S-4R SCREECH _~ z | | @ [ 1 | | | z RUNS61,;62 1.0 g~ I O RUNS 24,52 - 'C 0.8 I 3 5 7 9 11 13 15 17 19 21 23 25 27 29 31 33 35 RATIO OF SOUND PRESSURE AMPLITUDES, P/Po Figure 37. Local Coefficient f~or Convective Heat Transfer 9-1/2 Inches from Flameholder, Versus Sound Pressure Amplitude.

3.2 3.0 2.8 c 0 -2 NONE 2.6 U.: 2.4:Eh/hoo(I/h~ 0.069 - + 0.93 0 RUNS 24,52 - U. 2.2 L> 2.0 z -f' 1.61 O X SYMBOL FH. TYPE OF OSCILLATION ' "F''ERIES ORGAN - PIPE = 1.4 ~ —& S I SCREECH 13 S-2 NONE 1.2 ~' I X S-3RS-4R SCREECH ~ RUNS 61,62 1.0 0 RUNS 24,52 0.8 I $ 5 7 9 II 13 15 17 19 21 23 25 27 29 31 33 35 RATIO, OF SOUND PRESSURE AMPLITUDES, P/Po Figure 38. Local Coefficient for Convective Heat Transfer, 7-1/2 Inches from Flameholder, Versus Sound Pressure Amplitude.

2.3 0 } 0 o I 2.1 C') Id~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ z 1.9 -INM A A 1.7 o~ a 0 1.5 SYMBOL F H. TYPE OF OSCILLATION OD. X,, i. '3 (3 0 F SERIES ORGAN PIPE ' 1.3 S-I SCREECH,p.- /x X 0 S-2 NONE Oa h/h o(1/t(D) =0.041 +I103 ~~~~~~~~~B~~~~:.~~ 1. 1.03 _ 'r~ ~ ~ XPO~~h SX-3RS-4R SCREECH 0 ~ RUNS 61,62 0, o. RUNS 24,5 0.7 I 3 5 7 9 II 13 15 17 19 21 23 25 27 29 31 33 35 RATIO OF SOUND PRESSURE AMPLITUDES, P/Po Figure 39. Local Coefficient for Convective Heat Transfer Based on E = 80 Per Cent, 13-1/2 Inches from Flameholder, Versus Sound Pressure Amplitude.

170 Re =47,000 no~~~~~~~~~~~~ I I I I Lb =17 INCHES 160 FH= S -I Id > MUZZLE ON END OF BURNER JI 4150 CPS Id: 150 Cn 3850 CPS Iz nr- I o 140 130 0.5 0.6 0.7 0.8 0.9 1.0 1.1 1.2 Figure 40. Behavior of Screeching Combustion with Fuel-to-Air Ratio.

50,000 L 40,000 co 30,000 Z 0=0.80 Re 40,500 X 201000 UJ c 1U.. Db:132 w I I0,000 ~L_____RUN SYMBOL F.H. Qi Btu/hr 15 X NI --- S - 48,800 67 S- 4R 51,200 0 2 4 6 8 10 12 14 16 DISTANCE FROM FLAMEHOLDER -;-INCHES Figure 41. Profile of Heat Flux —Comparison of S-i and S-4R Flameholders During Stable Combustion.

3000 2500 2000 LL < 1500 w w HFigureI42. Temperature Profile —Comparison o 1 000 RUN SYMBOL FH 15 x-K S-I 67 O-E S-4R 500 =O0.80 Re 40,500 Db:=132 0 2 4 6 8 10 12 14 16 DISTANCE FROM FLAMEHOLDER - INCHES Figure 42. Temperature Profile —Comparison of S-1 and S-4R Flameholders During Stable Combustion.

Re =40,000 RUN SYMBOL Qi BTU/he 50,0 00 F H. S - 2 46 -G0.670 361200 50 Q-O 0.766 41$00 Db =131 45 X-K_ 0.895 45,900 U. W I t I 1 47 0-0 1.027 49,800 D 40,000 I-;, 30,000 z 10,000~~~~~~~~~~~~~~~~~~~~ U.. x,-20,000 w 0 2 4 6 8 1O 12 14 16 DISTANCE FROM FLAMEHOLDER - INCHES Figure 45. Profile of Heat Flux —Effect of Varying Fuel-to-Air Ratio During Stable Combustion.

3000 2500 2000 I0~ W 1500 2 3 iooo ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ w _j 1000 IU. RUN SYMBOL 46 1 — 0.670 500 50 0.766 50 (9-~; O. 766 45 X- 0.895 47 1.027 Re =40,000 FH. = S-2 Db =131 0 0 2 4 6 8 10 12 14 16 18 DISTANCE FROM FLAMEHOLDER - INCHES Figure 44. Temperature Profile —Effect of Varying Fuel-to-Air Ratio During Stable Combustion.

50,OOC 4-:O.895 Re 40,500 F.-H.: S-2 Db:Iz 30 I-40,000 30,000 z w x RUN SYMBOL LbH U. ~~~ ~~~40 X-X 131/20 45 0-D 17 1/2 0 0 2 ~~4 6 8I10 1 2 14 1 6 DISTANCE FROM FLAMEHOLDER-INCHES Figure 45. Prof ile of Heat Flux —Effect of Burning Length During Stable Combustion.

Re = 36, 500 50ooo Lb= 17 3/4"_ Db= 131 RUN SYMBOL SONIC PLATE LOCATION Qi BTU/HR F.H.= F-2 4 =0.77 6 X _X UPSTREAM OF MIXING CHAMBER 36,500 N I I 1 7 OF-G~3 10" ABOVE FLAMEHOLDER 39,300 U. 40,000 I m D Ia 30,000 zH w 2Q000 x w 10,000 0 2. 4 6 8 10 12 14 16 DISTANCE FROM FLAMEHOLDER-INCHES Figure 46. Profile of Heat Flux —Effect of Varying Inlet Tulrbulence Intensity by Moving Sonic Plate.

60,000 Re 40,400 Db = 155 F.H. =F-5 50,000f _ 345 cps P 0.77 LL cr 40,000 cr >- 30,000 4 I / I I I l RUN SYMBOL HUMIDITY Qi BTU/HR c| / l l ~] | ~54 ]- 70%REL.H. 72,500 1 20,000 54 __ __ 70%_REL.H. 72,500 0 2 4 6 8 10 12 14 16 DISTANCE FROM FLAMEHOLDER -INCHES Figure 47. Profile of Heat Flux —Effect of Atmospheric Humidity.

60,000 A 50,000 I I // i i i `t~~~ RI i I-t. 40,000 Ira I U. 20,000 w RUN SYMBOL SODIUM INJECTION. Qi13 ~0 o H H~~ ai-J 21 A ---- NO 80,300 22 X YES 79,900.0,000 0f0.861 Re:47,500 Db:154 f4150cPS. FH.=s-i 00 2 4 6 8 10 12 14 16 DISTANCE FROM FLAMEHOLDER - INCHES Figure 48. Profile of Heat Flux —Effect of the Injection~of Sodiun Salt.

-114 -80,000 D~~~~~~~ ' 70,000 CY "~L ~ I )3% ERROR Id w 60o,ooo000 CO z 0 0 U __________ H~EAT BALANCES EQUAL -1 50,000 w Id m3 0 I0 w 40,000 an O: 0 u, 0 4 tw 30,000 20,000 0 10,000_____ 1I0,000 20,000 30,000 40,000 50,000 60,000 70,000 80,000 INTEGRATION OF LOCAL FLUXES, Qi BTU/HR. Figure 49. Summary of Heat Balances.

JJII I I l I I I IimiiIIII I I I a9 100% =:Q95 R@:44,000 331 Lb:17-" 809Mo Db =152 0a FH.:s-I IQ. 60% LJ C,) C,) H wH a.. 2400/0 QL. w 0 3400 3600/ 3800 4000 4200 4400 4600 4800 5a FREOUENCY j CYCLIES/SECOND. Figure 50. Typical Frequency Traverse During Screeching Combustion. a. I'Li.% a,. 3400 3600 3800 4000 4200 4400 4600 4800 5000 FREQUENCY, CYCLES/SECOND. Figure 50. Typical Freq~uency Traverse During Screeching Combustion.

-116 -100 I. OSCILLATING a.+ COMBUSTION I, w 80 - -- w~80 z 2 70 2 to 0 SYMBOL Lb m+ 13 0 _70 70 80 90 100 COMBUSTION EFFICIENCY FROM SLR MEASUREMENTS E -% Figure 51. Comparison of Combustion Efficiencies Obtained by the SLR and Pressure-Drop Measurements.

-117 -100 m 90 NO CHANGE IN Z COMBUSTION 7it'~~~~ |EFFICIENCY 80 z z |seADDITIONAL COMBUSTION U. w 70 z 50 6 50 60 70 80 90 100 110 COMBUSTION EFFICIENY 13FROM.EHi E %/ Figure 52. Difference in Combustion Efficiency at the 7-1/2 and 13-1/2 Inch Distances from Flameholder.

-118 -The local coefficients, 13-1/2-inches from the flameholder, for convective heat transfer from the flame divided by the above terms are presented in Figure 35 as a function of sound pressure level in decibels. This normalized coefficient doubles for an increase in sound level from stable conditions of 130 to 133 db to an intense oscillation of 155 to 157 db. The effect of the transverse and the longitudinal oscillation on the coefficient are seen to be very similar. The transverse oscillation is associated with the "S" series of flameholders, while the longitudinal oscillation is associated with the "F" series. Correlation of Heat Transfer Coefficients The extreme curvature in the correlation can be removed by changing the scale for the sound pressure level. Since the decibel scale is a logarithm of the ratio of pressure amplitudes a logical scale is the linear one of the ratio of pressure amplitudes. The local coefficients at 7-1/2, 9-1/2, and 13-1/2 inches from the flameholder are plotted in Figures 36, 37, and 38 versus the sound pressure amplitude divided by the amplitude corresponding to 130 db, A straight line correlation appears valid, particularly for the stations farthest from the flameholder. The correlation at 7-1/2 inches from the flameholder, where the combustion is more active and the effects of combustion more pronounced, is not clear. In addition to the coefficients calculated from measurements of the flame temperature, heat transfer coefficients for the 13-1/2-inch distance were also calculated assuming the combustion efficiency at this

point was 80 per cent for all of the runs. The assumption of combustion efficiency determines flame temperatures at that point, These coefficients normalized as before are presented in Figure 39 and are in surprising agreement with those based on the measured flame temperature. The correlations for these coefficients at three distances from the flameholder are 13-1/2-inches: h 0.044 P/Po + 1.08 (19) ho h'/h' 9-1/2-inches: hh/ = 0.050 P/Po + 1.02 (20) 7-1/2-inches: h h/h = 0069 P/P + 093 (21) E = 80 %, 13-1/2-inches: h = 0.041 P/Po + 1.03 (22) ha h'/h't, The accuracy limits are + 10 per cent for all the correlations except at the 7-1/2-inch distance, where they are + 20 per cent. The correlation at the 7-1/2-inch distance is justified by the existence of clear correlations at the other points, Behavior of Burner with Increasing Fuel-to-Air Ratio The pattern of the flame-generated transverse oscillations as a function of fuel-to-air ratio is represented in Figure 40 where sound pressure level is plotted against fuel-to-air ratio, As the fuelto-air ratio is increased from a very low value, a 3850 cps note rapidly increases in amplitude beginning at a 0 of about o0.6 and reaches a plateau of about 148 db. At a 0 of about 0.68 the oscillation suddenly ceases; then beginning at a 0 of about 0.77 a 4150 cps note rapidly increases in amplitude to a higher plateau of about 155 db.

-120 -Stable Burners Some additional profiles of local rates of heat transfer are presented to show the effects of f~iameholders, flow rates, and fuel-toair ratio in a, sta;ble burner. Also runs taken to check possible sources of error are presented. In Figures 41 and 42, the ring-type flameholder in compared Wi;h- t'E- iscreen-in-annulus type wit.;h regard to thle hea't transfer and temperature profiles. The effect of increasing the fuel-to-air ratio with th.e oscillations damped is shown in Figures 43 and 44. It is noted that the temperature profiles increase in a general fashion like the heat transfer profiles. The effect of burning length is compared in Figure 45 for stable combustion. In a previous figure, number 10, the effect of four flameholders on the heat transfer profile is shown. The curve for Run 61 shows a step increase 5 inches from the flameholder because a 1/32-inch asbestos sheet lined the inside of the tube from 5 inches above to 5 inches below the flameholder for this run. The purpose of this liner was to increase, the inside surface temperature to intensify screech as was done earlier by a decrease in the cooling of the tube. However, its acoustical impedance was low and so actually proved to be an effective damper of screech. Effect of Inlet Flow Conditions The effect of changing the inlet flow turbulence is shown in Figure 46, where in Run 7 the sonic plate is 10 inches above the flameholder and in Run 6 it is upstream of the entire mixing chamber. Negligible

-121 -effects are also shown by a similar comparison, using Runs 2 and 4. The humidity of the air did not vary much due to its compression to 105 psia, which lowered its humidity to 0O003 lbs/lb, or below the lowest atmospheric humidity encountered. The effect of running on a rainy day compared to a day of low humidity is shown in Figure 47, Since in most runs the sodium salt was injected only during the SLR measurements, there is the question of what change occurred in the heat transfer profile. In Figure 48, a comparison of Runs 21 and 22 shows a negligible effect. Other similar comparisons may be made with Runs 26 and 28 or 48 and 49. SHeat Balances The difference between the total heat transfer through the tube as determined from the tube's cooling water and that determined from the integration of the local heat flux is shown for each run in Figure 49, The heat transfer determined by the cooling water is consistently high, averaging about 4 per cent above the integrated value, Pureness of Flame-Generated Notes When the frequency spectrum is scanned during a resonating oscillation, a typical bell-shaped curve is obtained, such as presented in Figure 50, The band 'width of a pure note measured by the sound analyzer is 2 per cent of the measulred frequency. The band width of the flamegenerated transverse oscillations averaged 3,7 per cent and that of the organ pipe 3.3 per cent. Only in Runs 24 and 52 did more than one note register greater than 10 per cent on the sound analyzer. In these riuns a relatively weak organ pipe note was present along with the strong transverse note,

-122 -Comparison of Cotnbustion Efficiencies The combustion efficiencies determined by the two independent methods, that of pressure-drop and SLR measurement of flame temperature, are compared in Figure 51. The averages of the two methods for a 17-1/2 -inch burning length and a stable burner are within 2 per cent of each other. The pressure-drop combustion efficiencies, when the burning length is 13-1/2-inches, are consistently higher than those determined from flame temperature measurements. When the sound level increases due to a resonating note, the pressure-drop combustion efficiencies become meaningless, being over 100 per cent except for the three runs with low resonating intensities, the points for which are circled in the figure. Additional Combustion After 7-1/2-Inches The combustion efficiencies for the 17-1/2-inch burning length are evaluated at both 7-1/2-inches and 13-1/2-inches from the flameholder based on the SLR measurements at these points. The plot of one against the other in Figure 52 reveals that additional combustion occurred in every run between the 7-1/2-inch distance and the 13-1/2-inch distance. On the average this increase was 5 per cent.

DISCUSSION A significant result of this study is the correlation of forced convective heat transfer with sound pressure level. Also of importance is the finding that a transverse oscillation is just as influential on the heat transfer process as a longitudinal oscillation of the same intensity. The reported failures of burners in the literature due to screeching combustion are, therefore, probably connected with rising wall temperatures and subsegquent increases in the intensity of the oscillation. The evidence that the acoustic oscillations cause greater hydrodynamic changes than changes in the combustion phenomena is presented as well as explanations for the various results and identification of the modes of oscillation. The measurement of the local heat fluxes is the primary objective of this study, with the measurement of flame temperature being a secondary objective. Whereas the measurements of heat flux have been covered previously and their accuracy shown to be high, the accuracy of the measurement of flame temperature needs further discussion. Flame Temperatures In this combustion study, the average gas temperatures determined from sodium-line-reversal measurements are substantiated by the temperatures determined from pressure-drop measurements in the case of stable combustion. Accurate determinination of heat transfer coefficients does not require temperature measurements accurate to the nearest degree -123 -

-124 -or even ten degrees because the temperature differences are large, approximately 2000~F, The accuracy of the coefficient is not altered by more than 5 per cent even if the flame temperatures are in error by 1000F. The limits of the SLR inaccuracy are estimated in the section, Experimental Theory and Accuracy, to be - 500F to + 900F. Since the bulk mean temperature is given by the relation Tb = 0o.82 (TSLR - Ts) + Ts, (9) the inaccuracy limits on the average temperature are only 82 per cent as large or approximately - 40'F to + 750F, which corresponds to a 3.7 per cent error in a 20000F difference. If the distribution factor of 0.82 is in error, it is probably a consistent error and would result in a consistent error in the coefficients and thus not disturb the correlation. However, this factor is not only corroborated by the pressure-drop measurements, but also by the thermocouple and pitot-static tube traverses as discussed in the section, Experimental Theory and Accuracy. Good evidence of how uncritical the gas temperature is in determining the correlation of heat transfer coeffients is given by those coefficients at the 13-1/2-inch distance which were determined from the assumption of a combustion efficiency of 80 per cent at that point. Temperature Profiles It is recalled that the temperature profiles depended on the scaling of the cold flow coefficients for heat transfer in such a way

-125 -that at the 4-inch level they are equal to the measured value during combustion. This method of evaluating the coefficients does not assume that the combustion process or the oscillation does not have any effect on the coefficients, but rather assumes that the effect of the combustion and oscillations is the same along the entire tube. This assumption is reasonable since the combustion chamber is only slightly more than three diameters long, This method of employing cold flow data is reasonable since there is evidence in the literature that convective heat transfer from high temperature combustion products can be approximated from empirical data for non-burning gases.(35)(82) However, possible errors in the cold flow data plus the possibly large change in flow pattern caused by combustion mean that the temperature profiles have some degree of uncertainty. Physical Versus Combustion Effects of the Oscillations Several indications exist that the sonic oscillations affect the hydrodynamic conditions such as turbulence intensity and boundary layer thickness to a greater extent than the combustion phenomena, such as efficiency and flame speed. The correlation of the heat transfer coefficients with sound level is strong evidence that changes in the hydrodynamic phenomena are primary effects of the oscillations. The studies of several investigators(3)(33)(67) have indicated that a change in the flow pattern is associated with the flame-generated oscillations, particularly the periodic formation of vortices at the flameholder lip.

-126 -The similarity of the temperature profiles and the rather constant values of combustion efficiency for a damped versus an intense oscillation are two good indications of the relative insensitivity on the part of the combustion process to the oscillations. However, visual observations indicate an increase in flame speed, since a marked shortening of the flame is observed when oscillations, transverse or longitudinal, set in. Kippenham(36) and Markstein(50) concluded in their studies on the effect of oscillations on flames that apparent changes in flame velocity should be ascribed to changes in the flame area caused by the oscillations. Corroboration by Other Investigations Corroborations of the proposed correlation for the heat transfer coefficients as a function of sound pressure level are given by the works of Jackson(28) and HarrJe.(22) They both found that the heat transfer coefficient increases with the sound pressure level independent of frequency. Harrje in his study of fully developed turbulent pipe flow found that the heat flux increase was linearly proportional to the amplitude of the oscillation. Jackson found a critical sound level of 118 db below which the imposed sonic oscillations had little effect. A Reference Sound Pressure Level It appears that the critical sound pressure level is a relative value. This is the main reason for choosing the sound level in the stable burner as the reference level and thus setting the ratio of pressure amplitudes equal to one there. In future studies this reference level may be different but will probably be the sound level for the flow, free of an applied or generated sonic field.

-127 -Effect of Frequency One interesting result is the fact that thq frequency or mode of oscillation has very little effect as long as the intensity is constant. At 13-1/2-inches from the flameholder very little difference exists in the coefficients for transverse or longitudinal oscillations; however, at 7-1/2-inches from the flameholder, the two modes of oscillation produce different coefficients with the longitudinal mode producing larger coefficients than the transverse oscillations. The following explanation is offered. The longitudinal oscillation has a pressure antinode at the flameholder. The periodic increase in pressure at the flameholder periodically slows the flow of the unburned gases past the flameholder. During a period of slow flow, the flame in the region of most active combustion propagates closer to the tube wall causing higher rates of heat transfer and a pronounced peak in the heat transfer profile. The transverse oscillation also causes periodic fluctuations in the flow, but since they are at a much higher rate the flame has less time to propagate to the wall. Sundstrom(78) found a flattening of the peak in the heat transfer profile with the longitudinal oscillation, and he states that the movement of gas particles back and forth is causing this flattening. However, in his case the longitudinal oscillation was resonating between the exhaust end and a plenum chamber, which acted as an open end several feet upstream from his low blockage flameholder. The pressure antinode was well upstream from his flameholder, so that instead of large pressure fluctuations downstream from the flameholder there was considerable gas particle movement.

-128 -Agreement with the Literature The general similarity in the effects of the two different frequencies is substantiated by the literature. Jackson, Harrison, and (28) Boteler in their study of convective heat transfer with sonic fields imposed were not able to draw any conclusions as to the effect of frequency, although they varied the frequency from 125 cps to 2400 cps. In his heat transfer study, Havemann(23) found the frequency effects minor compared to the sound level. However, Tailby, in a study imposing sonic fields on a diffusion flame, found the 600 cps note to be more effective in promoting mixing and heat transfer than the 1700 cps note. Harrje(22) found the frequency was not the important variable but rather the amplitude of the unsteady velocity component. In the present study, not only are the frequencies different but the entire mode of acoustical oscillation, so that the direction of particle movement is completely changed. The transverse oscillation causes particle movement around the tube's circumference and the longitudinal oscillation in the direction of the tube's axis. It also is worth noting that particle displacement in a sound field is reciprocally related to frequency for a given sound pressure, so that the lower frequency note might be expected to cause the greatest changes. Further comparison of this study with Sundstrom's study(78) of longitudinal oscillations in a one-inch diameter burner reveals one other major difference, The organ-pipe oscillations in his study did not cause as great an increase in the total heat transfer to the tube as they did in

-129 -this study. The explanation rests mainly on the fact that the heat transferred to the tube in his study averaged approximately 25 per cent of the total heat released by the combustion process compared to about 10 per cent in this study. Thus the temperature of the gas fell twice as rapidly in the small tube with its greater surface area per unit volume than in the large tube. Difference in Correlations The variation in the correlation for the three distances from the flameholder may be caused by the influence of the combustion process. The positions closer to the flameholder are in general closer to the region of most active combustion. The turbulence intensity and the temperature and velocity profiles may be influenced by the combustion. By the 13-1/2-inch distance the flame had in general terminated except for the stable runs of very low fuel-to-air ratio. Therefore, the correlation at this position is probably the most free of combustion influences..Explanation of Burner Failures The increase in intensity of screech with higher wall temperatures is a significant finding. It leads to an explanation for the burner failures reported in the literature.(83) If the cooling of the combustion chamber were inadequate and an unexpected screeching combustion set in, the wall temperature would increase due to the increased heat transfer associated with the oscillation. Furthermore, the higher wall temperature would cause an increase in the screech intensity, and thus the amplitude of the oscillation and the wall temperature could reach very large values.

-130 -Determination of Resonance for Longitudinal Oscillation Much evidence has been acquired to support the statement that the longitudinal oscillation is a primary mode, resonating between the flameholder as a closed end and the exhaust end. The frequency determined by the wave equation for a primary mode of longitudinal oscillation in a cylinder with one end open and one closed agrees with the measured frequency, ice., the 350 cps note. The frequency calculated for the case of resonance occurring between the exhaust end and the sonic plate did not agree with the measured one. The method of Jost(30) was used in this calculation to account for the column of gas being hot gas between the end of the burner and flameholder and cold gas from there to the sonic plate. As unquestionable proof that the flameholder is acting as a closed end, the sonic plate was placed at several positions from 2 inches to 3 feet above the flameholder with no effect on the frequency. Designation of the Acoustical Mode for Screech The high pitched note can be identified on the basis of its frequency as a primary transverse oscillation because of previous investigations(8)(21) that have shown screeching to be an acoustically resonant phenomenon and because the second mode of transverse oscillation and the first mode of radial oscillation have frequencies approximately 6300 cps and 7800 cpscrespectively. The primary mode of transverse oscillation has a predicted frequency of 3800 cps at a mean gas temperature of 3000 R, compared to the measured frequency of 3850 to 4250 cps4

-131 -The primary mode is also the most probable one as pointed out by Tischler(83) and Maslen.(54) Thus a 4000 + 300 cps note has the wave numbers m = 1 and n = O with the nx wave numbers not clearly determined by frequency measurement since their effect on the frequencies is about two hundred cycles per second. However, the fact that the frequency of the screeching combustion does not change significantly when the burning length is varied from 8 inches to 17-1/2-inches gives good evidence that there is no counterpart resonance in the longitudinal direction; thus nx = 01 and the screech is a pure primary transverse mode of oscillation. The change in frequency from 3850 cps to about 4150 cps with an increase in fuel-to-air ratio from a f = 0.65 to 0.9 can be accounted for by the increase in gas temperature and the accompanying increase in sonic velocity. The possibility exists, however, that the mode of oscillation shifts as the fuel-to-air ratio is increased from a pure transverse mode with wave numbers, m = 1, n = 0, nx = 0, to a transverse mode resonating in the longitudinal direction alsolwith wave numbers, m = 1, n = 0, nx = 1. This change in mode would also explain the change in frequency and is suggested by the behavior of the transverse oscillation with increasing fuel-to-air ratio as shown in Figure 40. A definite answer to this question of the exact mode of oscillation can only be obtained by detailed probing of the flame with a microphone. Failure of Pressure-Drop Method at High Sound Pressures The pressure-drop determinations of the combustion efficiency are a good corroboration for the combustion efficiency determined by the

-132 -SLR measurements in a stable burner. However, at high sound levels the pressure-drop method appears to have little value. This failure at high sound levels is probably caused by the failure of two of the assumptions employed in this method to remain true during unstable combustion, but it may possibly be due to sonic waves in the manometer leads causing erroneous readings. The two key assumptions made in reducing the pressure measurements to combustion efficiencies are 1) that the pressure drop across the flameholder is unaffected by the combustion process or sonic oscillations, and 2) that the flow is one-dimensional with no gradients at the points of pressure measurement. Either of these conditions can be disturbed by a flame-generated oscillation because, as pointed out by Rogers, (67) Kaskan,(33) and Barker, there are definite changes in the flow pattern associated with the oscillation, particularly at the flameholder, Evidence that oscilla' tions do cause increases in the pressure drop is given by Bayley,(5) who studied pulsating flow and found the pressure loss coefficient to increase proportionately to the amplitude of the oscillation. The assumptions are evidently reasonable in a quiet burner. (78) Sundstrom, in fact, obtained good values with both quiet and oscillating flames, The pressure drop across the flameholder, however, is a higher proportion of the total pressure drop in the present study, but the drag due to the wall is larger in Sundstromts small diameter tube. It might be recalled that the drag of the flameholder and wall as determined in cold flow are subtracted from the measured pressure drop to arrive at the pressure drop due to momentum changes.

-133 -Importance of Inlet Turbulence The fact that the turbulence level upstream from the flameholder has little effect on the phenomena downstream from the flameholder is not surprising because the blockages of the flameholders are 90 per cent or more of the free stream area. Thus contraction of the stream in passing through the annulus between flameholder and tube wall is dominant in setting the flow pattern and conditions downstream from the flameholder, Changes in the contraction process caused by a long-annulus flameholder or by a screen in the annulus naturally can have a strong irnfluence downstream. The long-annulus flameholder is believed to cause the unburned gas to jet through the annulus, sweeping the area near the tube wall free of combustion and thus preventing screech, Also the formation of vortices may be deceased due to the more streamlined annuluso The screen-in-annulus flameholder increases the stabilization of the flame near the wall and thus helps the generation of screeching combustion, Explanation for Slight Difference in Heat Balances The consistently 4 per cent higher heat absorption by the tube's cooling water compared to the integrated local fluxes may be explained by the fact that the room is warmer when the flame is burning, particularly near the burner; thus the correction, obtained from the cooling water temperature rise without combustion, is expectantly lowo

CONCLUSIONS 1) Local coefficients for convective heat transfer can be correlated as a function of sound pressure level. The correlation approximately three tube diameters downstream from the flameholder is h /h' = 0.044 P + 1.08 (19) P0 2) Transverse oscillations in a ramjet-type burner are just as influential in promoting heat transfer to the wall as lQngitudinal oscillations. 3) The hydrodynamic changes brought about by the sonic oscillations are the primary effects, while changes in the combustion phenomena are secondary. 4) The burning length has little effect on the heat transfer rates unless a chnange occurs in the intensity of the flame-generated oscillations. The shorter burning lengths promote screeching combustion. 5) The tendency of the flame to generate transverse oscillations in a ramjet-type burner can be promoted by increased flame stabilization near the tube wall, 6) Longitudinal oscillations can be damped by a spray-quench muzzle at the end of the burner. 7) Maximum rates of heat transfer in a stable burner are observed near stoichiometric inlet mixtures. -134 -

APPENDIX A ORIGINAL ANID PROCESSED DATA -135 -

APPENDIX A ORIGINAL AND PROCESSED DATA Run No. 1 a'b 2a'b 3b 4b 55 6a'b 7b 8b 9b 10 11 12 13 14e 15 16 17 18 19 G lb/hrft2 3730 3710 3650 3670 3580 3780 37go 5010 5000 4130 4140 4200 4220 4150 4170 4180 4940 4940 4830 Re 36,000 35,900 35,200 35,500 34,700 36,500 36,600 48,500 48,400 40,000 40,000 40,500 40,700 40,100 40,300 40, 500 47,800 47,700 47,60 0 ~~~0.772 0.635 0.632 0.628 0.606 0.763 0.776 0.920 0.863 0.810 o.86g 0.854 0.840 0.785 0.7g4 0.895 0.648 0.674 0.735 Flameholder F-1 F-1 F-1 F-1 F-1 F-2 F-2 F-3 F-3 F-3 F-3 S-1 S-1 S-1 S-! S-1 S-1 S-1 S-1 Lb, in. 17-3/4!7-3/4 17-3/4 17-3/4 17-3/4 17-3/4 17-3/4 8 8 18-1/2 18-1/2 17-1/2 17-1/2 17-1/2 17-1/2 17-1/2 17-1/2 17-1/2 17-1/ SPL, db 131 130 152-1/2 132 151-1/2 130 133 159 133 147-1/2 152 154-1/2 148 132 133 151 148 132 133 f, cps - - 350 - 345 - - 4250 - 4150 340 415~ 4150 - - 4150 3850 -- TSiA~F, 4 in. 1. 2840 2510 2210 2485 2110 2910 2960 - - 2725 2750 2920 3010 2895 2930 3030 2460 2575 2805 TSLR~F, 10 in. 1. 2825 2420 2260 2360 2130 2820 2880 - - 2800 2880 3070 3120 2910 2925 3155 2440 2525 2780 Tb ~F, 4 in. 1. 2355 2090 1840 2060 1755 2415 2460 - - 2265 2295 2430 2500 2405 2430 2525 2050 2145 2330 lTb~F, 10 in. 1. 2355 2020 1900 1970 1785 2345 2390 - - 2340 2410 2570 2610 2430 2445 2640 2045 2105 2325 ESLR,%, 4 in. 1. 78 82 79 81 78 80 80 - - 74 74 79 79 79 79 78 78 78 79 ESLR,%, 10 in. 1. 73 75 76 77 73 74 74 - - 72 72 78 78 75 75 76 74 73 75 E~ep ~, 2 in. 1. 75 82 - 78 - 84 79 -. -. -... 85 81 - - 75 80 h, 4 in. 1. Btu/hrft2 ~F 9.4 9.2 12.9 9.7 13.1 9.3 9.6 - -12.9 15.0 14.3 12.4 9.2 9.6 14.5 13.8. 1. h, 10 in. 1. Btu/hrft2 ~F 13.3 11.6 22.9 11.2 22.9 9.0 9.1 17.6 19.9 19.8 1. 47 1. 88 l. 55 1. h/(hoo~~~~~~~~~~~~~~~~~~~~~~~~~~~1. 1h. /h. 03)101.51. 4 1n.. 1.25 1.26 1.87 1.34 1.96 1.13 1.16 - - 1.50 1.75 1.74 1.49 1.12 1.16 1.75 1.53 1.11 1.09 h/ (ho h'/h' 03) 10 in. 1. 1.48 1.33 2.76 1.30 2.84 0.88 0.88 - - 1.63 1.84 1.78 1.62 1.34 1.37 1.67 1.57 1.27 12 Ti ~F 72 75 77 76 81 76 82 78 78 75 77 78 4 6 8 9 8 9 Qwatr Bu/hr 45,0OO35, 00 3, 00 3, 50 58 9O 39 30039,9OO49, 300 15, 800 61,100 81, 000 78,100 63, 400 50,100 51, 600 74, 500 52, 900 43,100 48, 30 Qi Btu/hr 42,10033,600 59,600 33,100 55,100 36,500 39,300 40,500 13,100 59,800 78,300 76,500 60,900 47,200 4,0 2705,0 1504, Qfh Btu/hr 5,600 8,900 9,200 9,100 8,100 5,200 5,600 13,100 5,100 7~800 8,500 9,400 6,500 4,700 4,900 9,100 6,000 4,400 5,100 Local Heat Fluxesg q, 17 in. 1. Btu/hrft2 4,100 2,600 14,400 2,500 13,000 3,100 3~000 - - 10,700 24,800 9,100 6,900 3oo 47,8,1,0,4 q, 15 in. 1. Btu/hrt2 12000 8800 3,200,400 2J7007,800 9}800 - - 27,100 49,200 43,200 21,300 15,100 16,500 30,700 17,200 12,500 14,10 q, 13 in. 1. Btu/hrft2 21,200 14,500 48,400 13,700 47,300 13,700 15,9OO - - 42,500 58,400 60,800 35,000 25,600 26,300 49,100 30,800 23,000 24,900 q,10 in. 1. Btu/hrft~ 32,300 24,200 40,200 22,700 37,500 23,500 24,100 - - 40,700 46,800 50,100 47,1OO 36,300 37,100 49,500 37,400 32,300 35,80 q, 4 in. 1. Btu/hrft2 24,600 20,800 24,000 21,400 23,000 25,100 26,200 58,300 16.400 30,600 35,300 36,200 33,200 24,700 26,000 38,300 28,500 23,400 25,90 Surface Temp. T ~F, 17 in. 1. 99 91 157 90 150 94 93 - - 138 210 126 113 97 104 123 101 93 0 Ts ~F, 15 in. 1. 134 116 239 113 237 113 4 1 32 29 18 15 16 8 19 6 14 Ts ~F, 13 in. 1. 171 139 299 133 294 132 143 - - 272 348 365 236 190 193 8 1 11 g Ts~F, 10 in. 1. 215 179 251 170 235 177 179 - - 247 271 29 8 4 6 7 5 1 3 Ts ~F, 4 in. 1. 163 148 161 152 156 165 172 293 128 185 6 1 19 17 19 1 19 16 12

-137 -Run No. 20 21 22d 23 24 25 26 27 28d 29 30 31 32 33 34 35 36 37 38 G lb/hrft2 4810 4820 4810 4810 4210 4860 4860 4860 4860 4890 4840 4170 4190 4170 4130 4130 4130 4830 4830 Re 47,500 47,500 47,500 47,500 40,700 47,100 47,000 47,000 47,000 47,300 46,900 40,400 40.600 40,300 40,000 40,000 40,000 46,900 46,800 I0 0.814 0.861 0.861 0.951 0.955 0.666 0.676 0.745 0.679 0.829 0.932 0.805 0.892 0.769 0.749 o.668 0,675 0.834 0.746 Flameholder S-1 S.1 S-1 S-1 S-1 S-1 S-1 S-1 S-1 S- 1 S-S-1 S-1 -1 S-1 S- S-1 S-1 S-2 S-2 Lb, in. 17-1/2 17-1/2 17-1/2 17-1/2 17-1/2 13-1/2 13-1/2 13-1/2 13-1/2 13-1/2 13-1/2 13-1/2 13-1/2 13-1/2 13-1/2 13-1/2 13-1/2 13-1/2 13-1/2 SPL, db 150-1/2 154 153 155 152 149 131 144 131 156 157 153 152-1/2 143 132 147 129 132 131 f, cps 4125 4150 4150 4175 70 4175 3850 - 4050 - 4100 4150 4075 4150 4050 - 3850 - - - 305 340 TSLR~F, 4 in. 1. 2815 2905 2920 3100 3150 2570 2710 2710 2730 2870 3135 2890 3120 2795 2850 2545 2590 3135 2850 TSLR~F, 10 in. 1. 2900 3030 3050 3160 3190 - - Tb~F, 4. in. 1. 2350 2425 2440 2585 2620 2140 2255 2255 2275 2405 2620 2415 2605 2320 2370 2120 2155 2605 2375 Tb~F, 10 in. 1. 2425 2535 2550 2650 2665 - ESLR%, 4 in.1. 76 76 76 74 74 78 80 75 81 75 74 78 78 75 79 77 76 77 76 ESLR%, 10 in. 1. 74 74 74 71 71 - - - - Ep%, 2 in. 1. - - - - - - 83 96 81 - - - - 93 88 - 83 87 82 h, 4 in. 1. Btu/hrft2'F 15.1 16.8 17.3 16.5 12.6 15.6 11.6 12.9 12.6 21.3 19.9 19.5 18.8 11.6 11.5 13.1 9.7 12.4 13.7 h, 10 in. 1. Stu/hrft2~F 20.1 21.4 20.8 20.8 16.1 - - h/(. h'/h.), 4 in. i. 1.63 1.81 1.86 1.74 1.49 1.47 1.07 1.19 1.17 1.98 1.82 2.04 1.93 1.21 1.20 1.41 1.02 0.94 1.07 h/(h, h'/h1), 10 in. 1. 1.61 1.70 1.65 1.64 1.42 Ti F 81 81 84 79 86 79 79 80 80 76 77 80 80 80 81 83 80 80 81 Qvater Btu/hr 75,700 83,100 83,500 84,700 69,400 46,400 36,600 45,600 38,500 68,700 69,900 62,700 65,900 42,300 39,600 38,500 31,100 37,300 34,900 Qi Btu/hr 71,400 80,300 79,900 82,600 68,300 44,200 35,100 44,200 37,200 65,500 67,500 60,600 64,100 40,800 38,600 38,000 29,900 35,600 32,800 Qfh Btu/hr 8,800 9,100 8,700 9,300 7,800 6.200 4,200 5,900 4,400 9,000 9,200 8,400 8,600 6,100 4,400 5,300 3,900 5,400 4,80o Local Heat Fluxesg q, 17 in. 1. Btu/hrft2 7,600 8,400 8,600 8,300 7,300 - - - - - - - - - - - - - - q, 15 in, 1. stu/hrft2 31,300 38,800 37,500 39,100 37,600 - - - - - - - q, 13 in. 1. Btu/hrft2 49,700 56,700 55,200 56,000 50,500 6,300 3,800 7,200 4,900 11,000 12,300 11,300 12,500 7,500 5,700 5,400 3,100 4,200 4,600 q, 10 in. 1 Btu/hrft2 47,500 52,600 51,700 54,000 44,100 32,000 23,100 33,200 24,100 44,800 50,300 42,000 47,300 34,800 29,200 26,400 20,300 18,300 13,600 q, 4 in. 1. Btu/hrft2 36,300 41,200 42,500 43,800 35,700 33,400 27,600 30,200 29,800 49,700 51,900 46,500 49,200 28,600 29,000 28,500 22,500 34,700 33,600 Surface Temp. Ts~F, 17 in. 1. 123 127 129 126 120 Ts~F, 15 in. 1. 230 267 262 271 263 TsF, 13 in. 1. 310 345 338 342 313 105 93 109 98 127 135 130 138 110 102 100 90 96 97 Ts~F, 10 in. 1. 277 295 291 308 264 207 168 215 175 207 293 256 283 224 199 186 159 152 129 Ts F, 4 in. 1. 209 234 239 245 208 199 166 188 177 264 272 251 262 182 181 179 155 202 199

-138 -Run No. 39 40 41 42 43 44 45 46 47 48 49d 50 51 52 53Ce 54e 55e 56e G lb/hrft2 4820 4200 4170 4160 4810 4790 4160 4110 4180 4890 4950 4180 4240 4130 4170 4180 4760 476o Re 46,600 40,600 40,400 40,300 46,600 46,500 40,400 39,800 40,500 46,900 47,.goo 40,500 41,100 40,100 40,400 40,400 46,000 46,000 0.680 0.895 0.769 0.665 0.842 0.677 0.895 0.670 1.027 0.901 0.897 0.766 0.905 0.899 0.760 0.777 0.783 0.69o Flameholder S-2 S-2 S-2 S-2 S-2 S-2 S-2 S-2 S-2 S-2 S-2 S-2 F-4 F-5 F-5 F-5 F-5 F-5 Lb, in. 13-1/2 13-1/2 13-1/2 13-1/2 17-1/2 17-1/2 17-1/2 17-1/2 17-1/2 17-1/2 17-1/2 17-1/2 17-1/2 17-1/2 17-1/2 17-1/2 17-1/2 17-1/2 SPL, db 131 130 129 129 133 132 130 130 133 133 133 132 132 139 155 155 156-1/2 157-1/2 f, cps. 80~4175 345 345 345 335 20% 350 TSLR~F, 4 in. 1. 2630 3135 2910 2570 2970 2585 3110 2560 3295 3125 3100 2845 3270 3105 2525.2575 2605 2345 TSLR~F, 10 in. 1..... 2960 2490 3150 2460 3275 3135 3115 2820 3320 3140 2645 2710 2750 2450 Tb~F, 4 in. 1. 2190 2605 2420 2140 2465 2145 2580 2125 2735 2600 2575 2365 2715 2580 2105 2145 2175 1960 Tb~F, 10 in. 1. 2470 2075 2625 2050 2725 2615 2595 2350 2765 2620 2225 2275 2320 2070 ESLR%, 4 in. 1. 75 74 76 75 74 77 75 77 75 75 74 75 80 76 75 75 76 76 ESLR%, 10 in. 1..... 71 71 73 71 69 72 70 71 77 73 72 73 74 73 Ep%, 2 in. 1. 80 83 84 80 75 73 79 72 79 80 78 76 86 91.... h, 4 in. 1. Btu/hrft2~F 14.o 11.8 11.5 11.9 10.1 9.5 8.9 8.9 8.6 11.2 11.8 8.3 8.5 10.6 16.6 16.6 19.5 18.9 h, 10 in. 1. Btu/hrft2~ F. 14.2 12.5 12.5 12.5 11.9 14.6 15.1 12.5 13.2 13.7 26.8 25.9 30.0 35.0 h/(h. h'/h'), 4 in. 1. 1.12 1.00 1.00 1.07 0.89 0.86 0.86 0.92 0.82 0.93 1.01 0.82 0.91 1.19 1.96 1.95 20.6 20.5 h/(h. h'/hl), 10 in. 1. - - - - 0.99 0.90 0.95 1.02 0.89 0.95 1.01 0.98 1.14 1.22 2.54 2.44 2.55 3.06 Ti~F 81 79 79 80 79 79 80 86 86 85 85 76 70 83 77 77 80 80 'Q..ter Btu/hr 30,700 40,300 31,900 27,400 51,000 38,900 47,200 37,700 51,800 56,400 57,500 46,100 52,400 58,900 73,900 74,100 88,000 78,300 Gi Btu/hr 29,400 39,700 30,700 25,500 48,600 38,400 45,900 36,200 49,800 53,400 54,600 41,800 50,600 55,400 71,500 72,500 84,100 75,000 Qfh Btu/hr 4,300 5,000 4,600 3,700 5,200 4,300 5,200 4,000 4,700 5,200 5,200 4,300 8,500 8,600 9,700 10,000 9,800 8,900 Local Heat Fluxesg q, 17 in. 1. Btu/hrft2 4,000 3,600 5,200 3,900 5,000 5,300 6,100 2,600 5,600 6,300 5,200 6,500 6,700 5,500 q, 15 in. 1. Btu/hrft2 14,900 11,000 16,200 10,900 19,600 15,700 14,000 12,300 17,500 16,700 33,800 32,000 36,600 26,700 q, 13 in. 1. Btu/hrft2 3,900 4,900 3,300 3,000 24,200 17,900 27,400 17,500 31,100 27,100 28,200 21,500 28,300 25,600 54,300 53,500 58,700 50,600 q, 10 in. 1. Btu/hrft2 13,600 25,900 16,400 13,500 36,200 26,500 34,500 26,200 35,500 39,400 40,400 30,700 39,100 37,800 54,600 54,400 62,700 62,900 q, 4 in. 1. Btu/hrft2 31,000 33,300 29,600 26,500 27,500 22,000 26,400 20,600 27,700 31,800 32,900 22,400 27,300 30,400 34,600 35,500 41,400 35,700 Surface Temp. TS'F, 17 in. 1. - l o t 101 98 110 102 111 103 118 91 113 118 111 121 124 105 Ts~F, 15 in. 1. 149 129 160 127 174 153 144 138 160 156 145 136 157 210 Ts~F, 13 in. 1. 93 98 89 87 191 160 207 157 224 207 210 175 208 197 338 334 360 319 Ts~F, 10 in. 1. 127 188 144 131 232 185 223 182 223 257 243 205 242 24o 314 313 349 351 T,sF, 4 in. 1. 189 199 183 171 175 153 171 147 176 205 197 155 175 187 ' 203 207 224 207

-139 -Run No. 57 58b 59 60 61 62 63 64 65 66 67 68 69 70 71 72 73f 74f G lb/hrft2 4210 4710 4760 4760 4760 4720 4250 4340 4350 4220 4220 4250 4910 49140 910 4570 4570 4570 Re 40,600 45,500 46,000 545,900 45,900 45,500 41,000 41,800 41,800 40,700 40,600 40,900 47,300 47,400 47,300 44,000 44,000 44,100 0.768 0.570 0.583. 0.685 0.677 0.673 0.926 0.919 0.826 0.757 0.815 0.900 0.749 0.811 0.896 0.896 0.910 0.905 Flameholder F-5 F-5 F-5 F-5 F-6L S-3L S-3R S-3R S-3R S-4R S-4R S-4R S-4R S-R -S-14R S-1 S-1 S-1 Lb, in. 17-1/2 17-1/2 17-1/2 17-1/2 17-1/2 17-1/2 17-1/2 17-1/2 17-1/2 17-3/4 17-3/4 17-3/4 17-3/4 17-3/4 17-3/4 17-1/2 17-1/2 17-1/2 SPL, db 130 160 131 132 131 132 148 147 133 147-1/2 131 151-1/2 149 132 154-1/2 153 156 157 f, cps - 350 - - - - 4100 4100 - 4030 - 4200 4030 - 4200 4175 4190 4190 TSLR 1F, 4 in. 1. 2870 1930 2345 2610 2625 2640 3085 3075 3020 2820 2945 2870 2710 2970 2915 3005 3045 3060 TSLR~F, 10 in. 1. 2830 2000 2100 2480 2560 2600 3155 3135 3050 2880 3000 2980 2750 2990 2985 3055 3150 3140 Tb~F,4 in. 1. 2385 1620 1945 2165 2180 2190 2565 2560 2505 2345 2445 2390 2255 2465 2430 2505 2550 2580 Tb~F,10 in.- 1. 2360 1690 1745 2060 2135 2170 2635 2620 2545 2405 2500 2495 2300 2490 2495 2555 2650 2655 ESR%, 4 in. 1. 79 77 78 76 79 80 75 75 79 81 78 74 78 79 73 76 77 79 ESLR%, 10 in. 1. 73 72 67 69 73 74 72 72 75 78 75 71 75 75 70 73 74 75 EAp%, 2 in. 1. 77 - 80 76 81 78 - - 79 - 81 - - 83 h, 4 in. 1. Btu/hrft2 F 10.1 20.8 8.7 9.5 10.2 10.3 12.9 12.5 9.4 11.6 9.7 15.3 14.1 10.1 17.5 15.3 16.7 16.9 h, 10 in 1. Btu/hrft ~F 12.0 36.4 7.8 9.6 13.4 15.3 17.3 17.6 15.3 16.7 13.4 19.6 18.4 14.3 21.1 19.9 20.7 22.0 h/(h la'/h), 14 in. 1. 1.13 2.39 0.95 0.99 1.06 1.01 1.34 1.27 0.95 1.23 1.01 1.62 1.34 0.93 1.65 1.74 1.92 1.98 h/(h. h'/h.'), 10 in. 1. 1.08 3.36 0.69 0.80 1.12 1.23 1.45 1.46 1.27 1.44 1.13 1.67 1.42 1.07 1.61 1.67 1.77 1.92 Ti ~F 75 85 70 72 72 70 71 68 68 69 70 69 68 67 67 68 67 67 Qvater Btu/hr 44,000 78,900 26,700 35,100 39,300 41,900 69,300 70,500 54,100 57,400 52,800 77,600 64,900 56,700 80,200 80,600 - - Qi Btu/hr 42,000 73,600 25,100 33,500 38,200 40,200 67,700 68,002 50,900 55,600 51,200 74,800 61,900 54,500 78,400 78,200 78,800 78,000 Qfh Btu/hr 6,300 9,000 6,000 6,400 5,200, 4,100 5,900 5,900 5,400 8,600 7,500 9,000 8,900 7,700 9,300 8,000 8,500 8,400 Local Heat Fluxesg q, 17 in. 1. Btu/hrft2 4,300 10,600 3,000 3,400 2,800 2,000 6,900 6,100 4,500 14,000 18,800 17,200 15,900 19,000 18,200 11,500 7,900 8,300 Q, 15 in. 1. Btu/hrft2 12,800 45,500 7,600 8,700 6,800 6,500 31,600 32,700 15,400 20,300 20,900 28,600 25,100 21,300 33,000 40,700 33,600 33,300 q, 13 in. 1. Btu/hrft2 19,600 61,600 10,400 13,000 12,400 14,900 44,300 45,100 31,400 30,200 26,300 49,800 38,200 26,800 53,700 53,000 51,500 54,100 q, 10 in. 1. Btu/hrft2 29,800 52,300 14,500 21,200 29,100 33,100 46,200 46,500 39,800 40,200 35,200 48,600 41,500 36,800 51,100 50,300 52,000 53,600 q, 4 in. 1. Btu/hrft2 26,500 31,300 18,100 22,400 23,900 24,400 35,500 34,400 26,600 29,200 26,600 37,800 32,700 27,900 43,000 39,900 42,600 42,000 Surface Temp. Ts~F, 17 in. 1. -100 142 93 94 91 85 118 111 99 147 172 163 150 165 157 123 265 269 TsF, 15 in. 1. 136 312 110 115 105 104 227 233 146 169 170 207 190 172 228 262 393 399 T, F, 13 in. 1. 168 374 125 137 134 146 288 291 222 215 196 308 246 193 321 312 458 475 Ts0F, 10 in. 1. 210 302 130 158 193 212 271 274 243 241 218 254 238 231 - 287 273 384 457 Ts~F, 4 in. 1. 171 191 133 139 151 149 203 199 156 177 159 207 189 157 228 215 301 390 Footnotes and Flameholders are listed on the following two pages.

Footnotes aIn this run the sonic plate is upstream of the mixing chamber. In the other runs the sonic plate is located between the flanges joining the mixing and combustion chambers. bIn this run a spray-quench muzzle is not attached to the end of the burner. In the other runs the muzzle is attached. CThis run was taken on a particularly humid day, i.e., it was raining. dFor this run all of the data were taken during injection of the sodium bicarbonate. In the other runs, sodium bicarbonate is injected only during the SLR measurements. eIn this run the screen that is normally in the muzzle is not in place. fin this run the tube's cooling water was decreased to approximately 1/2 gpm and boiled in the jacket. gThe local heat fluxes, q, are listed for the five levels above the exhaust end of the burner, i.e., the subscript 4 in, 1. refers to 4 inches from the end of the burner exclusive of any spray quench,

-141 -List of Flameholders All are bluff-body flameholders. Designation Fh, Blockage of Thickness, Screen-in-annulus Tube Cross-Section, inches (10 mesh, 47 mil per centa diameter wire) F-1 90.8 1/8 No F-2 90.8 5/8 No F-3 92.7 1/8 No F-4 95.0 1/8 No F-5 94.6 5/16 No F-6Lb 95,3 5/16 No S-1 96 5 1/8 Yes S-2 96.5 1-3/8 Yes S-3Lb 98.3 1/8 Yes S-3Rc 98.3 1/8 Yes S-4Rd 97.1 1/4 Yes Footnotes: aBlockage includes that of the screen in. the annul us bThis flameholder is used with a 1/32-inch thick asbestos liner cemented to the tube wall from the 12-1/2-inch level to the 22-1/2-inch level, cThis flameholder is used with. a 1/32-inch thick asbestos liner cemented to the tube wall from the 17-1/4-inch level to the 22-1/2-inch level. dThis flameholder is used with a 1/8-inch thick asbestos ring 1/2-inch wide cemented to the tube wall from the 17-1/2-inch level to tI"he 18-inch level.

APPENDIX B SAMPLE CALCULATION

APPENDIX B SAMPLE CALCULATION Run Number 48 Data Air rate = 131 SCFM Propane rate = 4.97 SCFM Inlet mixture temperature = 85OF Tube-water rate = 11.4 gpm Flameholder rate = 24 cc per sec Temperature rise of tube water = 10.2~F Inlet water temperature = 66.8~F Temperature rise of tube water without combustion = 0.3~F Temperature rise of flameholder water = 27.1~F Sodium-line-reversal temperature at 4-inch level (i.e., 13-1/2-inches from flameholder) = 3125~F Sodium-line-reversal temperature at 10-inch level (i.e., 7-1/2 inches from flameholder) = 3135~F Pressure drop (25-inch. level to 2-inch level) = 16.30 inches IE20 Pressure drop withLout combustion = 15.52 inches 1I20 Sound pressure level = 133 decibels No predominant frequencies Burning length = 17-1/2-inches (excluding muzzle) Muzzle on end (with a screen in muzzle) Sonic plate 10 inches abcve flameholder -143 -

-144 -Flameholder: number S-2 (screen-in-annulus) blockage = 96.5 per cent (including screen) annulus length = 1-3/8 inches Temperatures at the measuring station, 4-1/2 inches below flameholder with the thermocouple locations: TOF Radius, inches 203.2 2.480 167.5 2.690 133.1 2.909 Heat Flux and Heat Balances The calculation of the local heat flux is shown only at the section 4-1/2 inches below the flameholder, because all five local fluxes are calculated in the same manner. kay (Ti-T j) Q/As = rs n rj/r (6) Using the inner and outer thermocouples, 153 (203,2 - 133,1) 227 Btu/hrft Q/A = 38 n2o. 9 = 27,100 Btu/hrft 2 480 $ 2.909 2.480 Using the inner and middle ones, 154 (203.2 - 167.5) - 27,200 Btu/hrft =/As - - 2 e6902 2,480 in 2.4-6 The second value merely serves as a check on the first, The heat flux

-145 -at the other four stations are found in a similar manner and are L, inches Q/As, Btu/hrft2 T ~F (from flameholder) 1/2 5,300 103 2-1/2 15,700 153 4-1/2 27,100 207 7-1/2 39,400 257 13-1/2 31,800 205 The temperatures for each station as a function of tube radius are shown in Figure 53, where the inside or outside surface temperature can easily be read. A plot of the local fluxes as a function of distance along the tube from the flameholder dan be made, An integration of the area under the curve gives Qio Here, Qi = 53,400 Btu/hr. The heat absorbed by the tubeTs cooling water gives a check for the heat transferred through the wallo The net rise in, te watJer temperature is 10.2 - 0.3 = 9.90F, at a water rate of 11,4 gpm, QW = 11,4 x 9.9 x 8,33 x 1.0 x 60 = 56,400 Btu/hr The difference between the two methods is 5,4 per cent, One other heat loss is that transferred to the flameholder's cooling water. Qfh. = 24 x 27,1 x.2642 x 10-3 x 8~33 x 3600 x 1 5160 Btu/hr Reynolds Number and Fuel-to-Air Ratio The molal average viscosity for the inlet mixture is 0o0177 cpo Its density is 0.0778 lbs/ft3 under standard conditions, 60~F and 1 atm, D V -pV 4,92 x 0,0778 x 135o97 x 60 x 144 Re =; 12 x 18571 x 0,0177 x 2,42 Re = 46,900

RUN NO.48 200 2001 4 IFROMFH 0 3 150 4 2 2 wI. I \ I I | OUTSIDE TUBE SURFACE 50 INSIDE TUBE SURFACE 0.39 0.40 0.41 0.42 0.43 0.4 4 0.45 0.46 047 LOGo r Figure 53. Temperature Gradient in the Tube Wall at the Five Measuring Stations.

-147 -The ratio of the moles of air to the moles of fuel, 98 per cent propane and 2 per cent propylene, is 23.75 for a stoichiometric mixture. The ratio of the fuel-to-air ratio to that of a stoichiometric mixture, 0, is then = 23.75 x 97 = 0.901 131 Bulk Temperature and Combustion Efficiency The bulk temperature is readily evaluated, knowing the sodiumline-reversal temperature and the inside surface temperature as read from Figure 53. 13-1/2-inches from flameholder, Tb = 0.82 (3125 - 205) + 205 = 2600~F 7-1/2-inches from flameholder, Tb = 0.82 (3135 - 257) + 257 = 2615~F The composition must first be estimated to evaluate Cp2 before the combustion efficiency can be calculated. So the combustion efficiency is assumed to be 75 per cent and the compositon is calculated assuming complete combustion to C02 and H20. The basis for calculation is 18075 moles of nitrogen, Five moles of oxygen, 0ol2 moles of H20, and, moles of propane, i.e., 0.901, are present with this nitrogen in the unburned gases. For the burned gases,

-148 -moles ~ mole fraction y M yM Cp 600-26000F yCp N2 18.75 0.7370 x 28 = 20.63 0.0198 o.0146 02 1.62 0.0637 x 32 = 2.04 0.0198 0.00126 C H8 0.22 0.0087 x 44 0.38 0.080 0.0007 C02 2.03 0.0798 x 44 3.51 0.0319 0.00255 20 2,82 0.1108 x 18 = 1.99 0.0261 0.00289 25.44 1.0000 = 28p55 Cp2 = 0.02200 The heat capacities in this table are the mean heat capacities from 60~F to 2600~F obtained from Perry(59) in the units of Btu/ft3~F, with the volume measured at 60~F. The density of the burned gases at 60~F is 0.0752 lb/ft3 and thus Cp2 in mass units is 0.293 Btu/lb~F. 2 (Tb - Ti)+ Qt E= (14) Qt is the heat lost from the flame to the point of flame temperature measurement. Integration of the local fluxes from the flameholder to the 13-1/2-inch distance gives 41,100 Btu/hr. The loss to the flameholder is added on giving 46,300 Btu/hr. =t = Q/W = 46,300/635.6 = 73 Btu/lb mixture The heat of combustion of the fuel, 98 per cent propane and 2 per cent propylene, is 19,924 Btu/lb fuel. Since at the stoichiometric point there are 15.7 lbs of air per lb of fuel, then o.91o QR = 19,924 x 15.7 + 0.901 = 1082 Btu/lb mixture 0.293 (2600 - 85) + 73 x 100 = 75 per cent 1082

-149 -Since this value agrees with the estimated one, the heat capacity does not have to be reevaluated. Similarly, at 7-1/2-inches from the flameholder Qt 36, Cp2 = 0.292 and 0.292(2615 - 85) + 36 x 100 72 per cent 1082 Radiant Heat Fluxes Radiant heat transfer is calculated from the method presented by McAdams, (48) using the SLR temperature measurement. The mean beam length for the core gases is 0.61 D or 0.25 feet. At the 13-1/2-inch distance, the partial pressure of C02 is 0.08 atm and that of H20 is 0.111 atm from the composition determined earlier for E = 75. For C02, PcL = 0.020 and for 120, PwiL 0,028, At 3585~R, TSLRy eg = 0.016 + 0.0058 = 0.022, Also by Me.Adams' m ethods. ag=:0086. 1+C T 4 T qR = 0.173( z (100 - (23; The tube emmissivity, es, is estimated to be 0.6. R= 173 x 0.8 x [ 022 — 5854.086(165 4] =R 5(35 Btu/hri0t2 qR = 5000 Btu/hrft2

-150 -Similarly for the 7-1/2-inch distance from the flameholder where E = 72 and TSLR = 3595~R, qR = 4900 Btu/hrft2 Convective Coefficient The convective heat transfer coefficient is now readily evaluated, at the 13-1/2-inch distance Q/As - qR 31,800 - 5000 h = - (24) Tb - Ts 2,600 - 205 h = 11.2 Btu/hrft2~F and at the 7-1/2-inch distance h = 14.6 Btu/hrft2oF Temperature Profile The temperature profile along the burner length is now calculated, using the data taken without combustion, i.e., the cold flow data, For the S-2 flameholder, the h /h' values are L, inches h /ht ' hx Btu/hrft2 ~F (from flameholder) 13-1/2 1.7 11.2 7-1/2 2.2 14.5 4-1/2 2.8 18,4 2-1/2 3.6 23.7 1/2 4.8 31.6 The hx values are obtained by multiplying h /h' by the factor, h at x

-151 -13-1/2-inches + 1.7 = 6.59. In this manner the coefficients have been scaled up by. a constant factor based on the coefficient measured during combustion at the 13-1/2-inch level. Radiation fluxes must be estimated before the temperatures at the four stations can be calculated from the above convective coefficients. Therefore, gas temperatures are estimated and the radiant heat transfer calculated as demonstrated earlier, L, inches Tg OF QR/As 2 Q/A/As /As (assumed) Btu/hrft2 Btu/hrft2 Btu/hrft 13-1/2 2600 5000 31, 800 26,800 7-1/2 2620 4900 39,400 34,500 4-1/2 1575 1900 27, 4oo00 25, 5oo 2-1/2 800 400 15,700 15,300 1/2 265 0 5,300 5,300 The temperature differences are now found from (= c/A s (25) hx L, Inches f Tg TS F Tg~F 13-1/2 2395 205 2600 7-1/2 2380 257 2637 4-1/2 1385 207 1592 2-1/2 646 153 799 1/2 168 103 271 Since the calculated gas temperatures are essentially those assumed to evaluate the radiant heat transfer, the calculation need not be repeated.

-152 -Pressure-Drop Combustion Efficiency The drag caused by the tube walls during combustion is calculated using friction factors for smooth tubes and the previously calculated temperature profile to evaluate the viscosity and density of the burned gases. The viscosity is evaluated using Sutherland's formula _ 273.1 + C ( T~K 3/2 -o T~K + C 273.1 (26) with C = 114 and So = 0.0171, in. H20 L, inches Re f lbsyft3,/L) in.tube 1/2 34,900 0.0058 0.0535 0.470 x 10-3 2-1/2 23,900 0.0063 0.0310 0.885 x 10-3 4-1/2 17,800 0o0068 0.0191 1.54 x 10-3 7-1/2 14,300 0.0072 0.0126 2.48 x 10-3 13-1/2 14,400 0.0072 0,0128 2.44 x 10 3 AP 4fG2 f inches 20 where AL. 2gcD- - (4,34 x 10-3) inch tube The summation of the pressure drop per unit length is made with each local value taken to represent the few inches on either side of it as shown below, AP L, inches AL L x AL 1/2 0 to 1-1/2 = 1-1/2 0.71 x 10-3 2-1/2 1-1/2 to 3-1/2 = 2 1.77 x 10 3 4-1/2 3-1/2 to 5-1/2 = 2 3.08 x 10-3 7-1/2 5-1/2 to 10-1/2 = 5 12,40 x 10-3 13-1/2 10-1/2 to 15-1/2 = 5 12.20 x 10-3 30.16 x 10-3 inches H20

-153 -Therefore~, drag of tube walls is 0.03 inches of H20. The drag of the flamqholder was measured under cold flow conditions and found to be 15.52 inches H20. The pressure drop due to the combustion then is APQ = 16.30 - 15.52 -.03 = 0,75 inches H20. A combustion efficiency of 80 per cent is assumed to evaluate M2. 2 T2 P2 M2A2 s plu ] 2 [Ape (13) Ti Pp1 P1 A1 [ + ] (13) 14.7 28,5 19.01 1 T2 = 545 x 153 x 294 x 0.749 [0.750 x 5.2 + 0.749] T2 = 32000R = 2740~F To evaluate Cp2' the combustion efficiency is estimated to be 80 per cent. Moles mole fraction y M yM Cp 600 to 2740~F yCp N2 18.8 0,736 x 28 = 20.60 0.0199 0.0147 ~2 1,4 0*055 x 32 = 1*76 0.0199 0.0011 C3H8 0,18 0,007 x 44 = 0.31 0O082 o.ooo6 C2 2:16 0.085 x 44 = 3*74 0.0322 0,0027 o20 3.00.0*117 x 18 = 2.10 0.0263 0*0031 2= 28.51 Cp2= 0.0222 Again 0p2 is in Btu/ft3OF with the volume measured at 60'F and 1 atm. The density of the burned gases at 60~F is 0!0751 lb/ft3 and Cp2 becomes 0.296 Btu/lbOF. The heat loss up to 2 inahes from the end of the burner is 52,700 Btu/hr and t = 83 Btu/hr lb. Cp2 (T2 Ti) + Qt (14 E = 2 x o00 (14) 6~1.

0.296 (2740 - 85) + 83 80 E 1082 x 100 = 80 Since M2 and Cp2 were evaluated on an estimated combustion efficiency of 80 per cent, the calculation is complete. Predicted Coefficients The coefficient for convective heat transfer, ho, predicted for fully developed turbulent f'lcw is calculated from the relation, ks 0.8 1/3 ha D= x O.G03 Fes0.8 Prsl/3 (Tb/Ts).33 (18) For the 13-1/2-inch distance, with r.i = 2050F and E = 75 per cent, the properties of the gases at the:uLtfc: were estimated using weight averages. ks, = 00171 Is = 0 0195 cp and Cps 0261 Pr 0.72 Ps s Pr./3..- (O,896 Then O0,0o7 4 92 1Xx 36 x l2 x 836 x 12 0 8 h00 4.92 X.023 19 x 0.0195 x 2.42 3060o. 33 x ( 665 h = 7.0 Btu/hrft2~F Similarly, for the 7-1/2-inch distance, h. = 7.01 Btu/hrft2oF. The cold flow ratio of coefficients is at the 13-7/2-inch distance, h /h00, 1.7 at the 7-1/2 —inch distance, / t 2 h /h 00 = 2.2

-155 -Therefore, at 13-1/2- inches, h/(hc h /ht,) = 04929 at 7-1/2 inches, h/(h h'/h' ) = 0.946 The coefficient determined from the assumption of E = 80 per cent at the 13-1/2-inch distance, i.e., the 4-inch level, is easily evaluated. QRE - Qt 1082 x 0.80 - %73 T2 = - + Ti=0293 + 85 = 27000F Cp2 Thus for E = 80 per cent, Q/A - R 31, 8 00 -5600 105 Btu/hrft F aT 2700 - 205 and h/ (how h'/h O) 10.5 =.889 6.95 x 1.7

APPENDIX C DERIVATIONS -156 -

APPENDIX C DERIVATIONS Combustion Efficiency The derivation of the equations used to evaluate the combustion efficiency from the measured pressure drops is presented. This derivation is adapted from that presented by Sundstrom.(78) The general mass, momentum, and energy relations can be reduced by reasonable assumptions to the following one-dimensional form. Mas s: Pi U1 A = P2 u2 A2 (10) 2 2 Momentum: (P1 + ) A FD = (P2 + 2 ) A2 (11) g-~ )AlFD(TTo+ )AT (11) Energy: p(T-T ) + ui + Qr -Qt 2 + 2gc ~P11~ 0~2gc r 2(T2T)g(12) The assumptions made in deriving these equations are 1) the flow is steady, 2) thermal diffusion is negligible, 3) t is negligible compared to i, 4) Cps = constant, and 5) there are no gradients in velocity temperature or pressure at either stations 1 or 2. Assumptions 1, 2, and 3 are valid. The error introduced by assumption 4 is minimized by using the average value of Cps between To and T1 or T2. In the experiments, stations 1 and 2 are located upstream of the flameholder and at 2 inches from the end of the tube, respectively. -157 -

-158 -Upstream of the flameholder, conditions are uniform, but gradients do exist at the tube exit. Since the region of most active combustion is upstream of the exit, the gradients are not severe. From the ideal gas law T P p M 2 2 1 2 P _1_ P2 Ml(27) The mass and momentum equations are combined to give P1 u2A2 c A2 A2 FD plu11 P2 U1A1= PluA [ 1[P2 FAA (28)lU Substitution of the expression for temperature ratio gives T2 P2M2 9 A2 A2 FD plU22 2T 1 1 A A A c(13) The energy equation is solved for the heat released due to chemical reaction. ~(To)= u 2U2$ U2 T~) 2 (T2-To) -pl (T1-To) +2gc Qt (29) In the experiments, Ti had an average value of 76~F with the maximum deviation being 10~F for any run, Therefore, the reference temperature, To, is conveniently chosen as 76~F. The kinetic energy terms are much smaller than the exit sensible heat and heat transfer terms and are therefore eliminated. Equation (29) is then simplified Q (T1) = CP (T2-T1) + Qt (3Q)

-159 -The combustion efficiency is defined as the ratio of the heat released by chemical reaction to the heat which would be released if combustion were complete. Q(Tl) a (T2-T1) + E= (14) QR(Tl) QR(Tl) Equation (13) is used to evaluate T2 from the pressure-drop measurements. Effect of Thermocouple Holes The error caused by the presence of the thermocouples in the tube wall on the heat flux is estimated. The case to be analyzed is one that would cause the greatest error in the heat flux. The thermocouple assembly is assumed to be a perfect insulator and the analysis employs a conformal mapping technique. The error, caused by the presence of the thermocouple, in the temperature distribution and temperature indication of the thermocouple is covered by Beck and Hurwicz(6) in a generalized manner. Since the thermocouple section is approximately one-inch wide in both the longitudinal and the circumferential directions and since the angle subtended by the section is only 20~, the two-dimensional view for the analysis may be either a longitudinal one or a circumferential one. The longitudinal plane, shown as section A-AT in Figure 54, is the easier to analyze and is used here. The analysis using the radial plane has also been done with the results agreeing within one per cent. The thermocouple hole nearest the inside tube surface will have the greatest effect and is placed at the origin of the x-y plane. The

-160 -A 0IX 1 -HOLE CHOSEN J,. FOR ANALYSIS SECTION A-A' ~~~~y /y Ti '-7 1 ~TO UNIT RADIUS X __ __ __ X I HEAT FUWX INSIDE a | | G-OUTSIDE TUBE SURFACE TUBE SURFACE Z- PLANE V Z':FZ HEAT FLUX I -Z' + Z' Figure 54. Complex Mapping Technique for Analysis of Error Caused by a Thermocouple Hole on the Heat Flux.

-161 -conditionsof the problem are 1) T = Ti at x = -0.040 inches 2) T = To at x = +0.468 inches 3) dT 0 at = 1/2inches dy 4) dT/dQ = 0 at Q = + 10 5) 0.042-inch diameter thermocouple hole at the orgin. The coordinates of the z plane are first multiplied by a factor F of 47.6 to convert the hole with a radius of 0.021 inches to one of unit radius. Then the hoJe is collapsed in the W plane by the transformation W = z + -t. The heat flux through the approximate rectangle of the W plane compared to the heat flux through the rectangle of the zt plane, ignoring the hole, will show the effect of the hole. The coordinates of the important points in the three planes are given in the following table: t I x y x y u v -0.040 0 -1.90 0 -2.43 0 +0.468 0 +22.30 0 +22,35 0 0 0.5 0 23*80 0 23.76 -0.040 0.5 -1.90 23.80 -1.90 23.76 +0.468 0o5 +22.30 23.80 +22.32 23.78 u Fx + Fx (31) (Fx) + (Fy) Fy v = Fy - (Fx)2 + ()2 (32)

The average coordinates of the approximate rectangle in the W plane are used to estimate the heat flux. The distortion of the rectangle is exaggerated in the drawing. The average coordinates are ui = -2.17, UO = 22.34, and vs = 23.76. Since the heat flow is one-dimensional, the heat fluxes are given by the relation 2 k hoey I!(33) qno holes 2 kys Axt qholes = 2 ks (34) qholes Vs Ax' _T AU (35) qno holes Ys Au 23.76 (-1.90 - 22 30) 2380 ( 1-2,17 - 22o,34) = 0.98 Therefore, tie estimated error in the heat flux caused by the presence of the thermozouple is 2 per eent,

APPENDIX D CONDUCTIVITY OF TUBE WALL AND LAMP CALIBRATION -163 -

0 190 z 0. z. Cr: 180 ICOMPOSITION OF CROLOY >- 1700 9 % CHROMIUM I % MOLYBDENUM cJ9..~~~~~~~~~~~ ~0.40/0 MANGANESE aZ~~~~~~~~~~~~~ I 0/% MAX. SILICON z o0 0.03% MAX. PHOSPHORUS -~~~~~J OI I i I /~~~~~~0.030/~MAX. SULFUR it ~~~~f ~~~~~~~~~~BALANCE IRON 150 100 300 500 700 900 IfOO0 1300 1500 1700 TEMPERATURE 0F Figure 55. Thermal Conductivity of TubeWall, Croloy, as a Function of Temperature.

3500 LL 3000.I Id Q,,i, | / ] CALIBRATION 0. 2500 LAMP VERTICAL IN 78~F AIR w/ WAVELENGTH 0.659 k VYCOR DISC, 1/8 INCH THICK (J WAS BETWEEN LAMP AND PYROMETER ZI 2000 J 1500 1000 6 7 8 9 10 11 12 13 14 LAMP CURRENT, AMPERES (d.c.) Figure 56. Calibration Curve of Tungsten Ribbon Lamp with Vycor Window in Line of Si ah+.

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