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6.15. FLAME PROPAGATION IN HYDROGEN-BROMINE MIXTURES 203 1.00 0.75 X 1 X 2 0.50 X 2 (dissociation neglected) X 3 ε 1f − ε 1 X 4 0.25 0.0 0.1 0.2 0.3 1 − θ Figure 6.18: Composition and flux profiles for X 3,0 = 0.65. Structure of the Flame The distributions of X 1 , X 2 , X 3 , X 4 and ε 1f − ε 1 corresponding to one of the cases considered are shown in Fig. 6.18. In order to show the influence of X 4 on the distribution of X 2 , the figure also indicates the values for X 2 obtained when X 4 is neglected. Obviously, the influence of X 4 is very important, especially for values of θ near 1. On the other hand, this is the most important influence of neglecting X 4 . It may be seen that small deviations of X 1 and X 3 from the linear law have little influence upon the value of u 0 , since X 1f and X 3f are different from zero, References [1] Mallard, E. and Le Chatelier, H.: Recherches sur la Combustion des Melanges Gateaux Explosives Ann. Mines, Vol. 8 series 4, 1883, p. 274. [2] Crussard, L.: Les Deflagrations on Régime Permanent dans les Mileux Conducteurs. Compt. Rend., Vol. 158, 1914, pp. 125, 340. [3] Coward H. F. and Payman W.: Chem. Rev., Vol. 21, 1937, p. 359. [4] Zeldovich, Y. B. and Semenov, N.: Kinetics of Chemical Reactions in Flames. NACA Tech. Memo. No. 1084, 1946.
204 CHAPTER 6. LAMINAR FLAMES [5] Boys, S. F. and Corner, J.: The Structure of the Reaction Zone in a Flame. J. Proc. Roy Soc. London, 1949, A1-97,90. [6] von Kármán, Th. and Penner, S. S.: Fundamental Approach to Laminar Flame Propagation. Selected Combustion Problems, Vol. I, AGARD, 1954, pp. 5-41. [7] Hirschfelder, J. O., Curtiss, C. F. and Campbell, E.: The Theory of Flames and Detonations. Fourth Symposium (International) on Combustion, Williams and Wilkins Co., Baltimore, 1953. [8] Lewis, B. and von Elbe, G.: On the Theory of Flame Propagation. Phys., Vol. 2, 1934, pp. 537-546. [9] Evans, N. W.: Current Theoretical Concepts of Steady-State Flame Propagation. Chem. Rev., Vol. 51, 1952. [10] von Kármán, Th.: The Present Status of the Theory of Laminar Flame Propagation. Sixth Symposium (International) on Combustion, Reinhold Publishing Corp., New York, 1957. [11] Tanford, C. and Pease, R.: Equilibrium Atom and Free Radical Concentrations in Carbon Monoxide Flames and Correlation with Burning Velocities. J. Chem. Phys., Vol. 15, 1947, pp. 431-433. [12] van Tiggelen, A.: Chemical Theory of the Speed of Flame Propagation. Bull. Soc. Chim. Belg., Vol. 58, 1949, p. 259. [13] Jost, W.: Explosion and Combustion Processes in Gases. McGraw-Hill, New- York-London, 1946. [14] Gaydon A. G. and Wolfhard, H. G.: Flames, Their Structure, Radiation and Temperature. Chapman Hall, London, 1953. [15] Ladenburg, R. W., Lewis, B., Pease, R. N. and Taylor, H. S.: Physical Measurements in Gas Dynamics and Combustion. Vol. IX of High Speed Aerodynamics and Jet Propulsion, Princeton University Press, 1954. [16] Linnet, J. W.: Methods of Measuring Burning Velocities. Fourth Symposium (International) on Combustion, Williams and Wilkins Co., Baltimore, 1953, pp. 20-35. [17] Emmons, H. W., Harr, J. A. and Strong, P.: Harvard University, Contract No. AT (30-1)-497, 1950. [18] Adamson, T. C.: On the Theory of One Dimensional Flame Propagation. Jet Propulsion, January-February 1952. [19] von Kármán Th. and Millán, G.: The Thermal Theory of Constant Pressure Deflagration. Biezeno’s Anniversary Volume, Delft, Holland, 1953.
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Aerothermochemistry Gregorio Millá
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PRESENTACIÓN Amable Liñán Es un
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que no cambiaron los resultados, y
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INSTITUTO NACIONAL DE TÉCNICA AERO
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aim to become acquainted with Aerot
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Tarifa, Manuel de Sendagorta and Ig
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3.4 Energy equation . . . . . . . .
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8.4 Quenching . . . . . . . . . . .
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Chapter 1 Thermochemistry 1.1 Intro
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1.1. INTRODUCTION 3 GAS ε/k (K) σ
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1.1. INTRODUCTION 5 14 12 10 N 2 CH
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1.2. THERMODYNAMIC FUNCTIONS OF AN
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1.2. THERMODYNAMIC FUNCTIONS OF AN
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1.3. MIXTURE OF GASES 11 Helmholtz
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1.3. MIXTURE OF GASES 13 is the par
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1.3. MIXTURE OF GASES 15 Entropy Si
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1.4. CALCULATION OF THE THERMODYNAM
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1.4. CALCULATION OF THE THERMODYNAM
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1.5. CHEMICAL REACTIONS IN A MIXTUR
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1.6. CHEMICAL EQUILIBRIUM 23 Since
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∆G 0 j = ∑ i 1.7. CASE OF A MIX
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1.7. CASE OF A MIXTURE OF IDEAL GAS
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1.8. CHEMICAL KINETICS 29 1.8 Chemi
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1.8. CHEMICAL KINETICS 31 Mechanics
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1.8. CHEMICAL KINETICS 33 This stru
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1.8. CHEMICAL KINETICS 35 [3] Hirsc
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Chapter 2 Transport phenomena in ga
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2.2. DIFFUSION 39 Hereinafter, nota
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2.2. DIFFUSION 41 where r is the di
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2.2. DIFFUSION 43 T ∗ Ω (1,1)∗
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2.2. DIFFUSION 45 Gas Pair σ 12 (
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2.2. DIFFUSION 47 coefficients. 14
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2.3. VISCOSITIES 49 2.3 Viscosities
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2.3. VISCOSITIES 51 Here µ and µ
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2.3. VISCOSITIES 53 Its value depen
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2.4. THERMAL CONDUCTIVITY 55 2000 1
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2.4. THERMAL CONDUCTIVITY 57 4000 3
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Chapter 3 General equations 3.1 Int
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3.2. EQUATION OF CONTINUITY 61 The
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3.2. EQUATION OF CONTINUITY 63 A i
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3.4. ENERGY EQUATION 65 where the s
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3.4. ENERGY EQUATION 67 The energy
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3.5. GENERAL EQUATIONS 69 obtained
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3.6. ENTROPY VARIATION 71 Taking in
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3.7. ONE-DIMENSIONAL MOTIONS 73 red
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3.8. STATIONARY, ONE-DIMENSIONAL MO
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3.9. THE CASE OF ONLY TWO CHEMICAL
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3.10. STATIONARY, ONE-DIMENSIONAL M
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3.11. APPENDIX: NOTATION AND REPERT
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3.11. APPENDIX: NOTATION AND REPERT
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Chapter 4 Combustion Waves 4.1 Deto
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4.2. KINDS OF DETONATIONS AND DEFLA
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4.2. KINDS OF DETONATIONS AND DEFLA
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4.3. VELOCITY OF THE BURNT GASES 95
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4.3. VELOCITY OF THE BURNT GASES 97
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4.4. PROPAGATION VELOCITY 99 p H’
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4.5. APPLICATIONS 101 By substituti
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4.7. INDETERMINACY OF THE SOLUTION
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Chapter 5 Structure of the combusti
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5.2. WAVE EQUATIONS 107 of diffusio
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5.2. WAVE EQUATIONS 109 2) Burnt ga
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5.4. LIMITING FORM OF THE WAVE EQUA
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5.4. LIMITING FORM OF THE WAVE EQUA
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5.5. DETONATIONS 115 Of these two v
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5.5. DETONATIONS 117 waves. Such th
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5.5. DETONATIONS 119 This relation
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5.5. DETONATIONS 121 curves, repres
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5.6. DEFLAGRATIONS 123 mum temperat
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5.6. DEFLAGRATIONS 125 8 7 v/v 1 =T
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5.7. TRANSITION FROM DEFLAGRATION T
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5.7. TRANSITION FROM DEFLAGRATION T
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Chapter 6 Laminar flames 6.1 Introd
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6.1. INTRODUCTION 133 papers presen
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6.3. BOUNDARY CONDITIONS 135 c) Dif
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6.4. MODIFICATION OF THE CONDITIONS
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6.4. MODIFICATION OF THE CONDITIONS
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6.6. EXAMPLE 141 generally impossib
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6.6. EXAMPLE 143 Two more relations
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6.7. REACTION VELOCITY 145 1.0 0.8
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6.8. FLAME EQUATIONS 147 6.8 Flame
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6.9. SOLUTION OF THE FLAME EQUATION
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6.9. SOLUTION OF THE FLAME EQUATION
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Page 178 and 179: 6.10. STRUCTURE OF THE COMBUSTION W
Page 180 and 181: 6.11. IGNITION TEMPERATURE 161 6.11
Page 182 and 183: 6.12. GENERAL EQUATIONS FOR THE COM
Page 188 and 189: 6.13. OZONE DECOMPOSITION FLAME 169
Page 196 and 197: 6.14. HYDRAZINE DECOMPOSITION FLAME
Page 206 and 207: 6.15. FLAME PROPAGATION IN HYDROGEN
Page 226 and 227: Chapter 7 Turbulent flames 7.1 Intr
Page 228 and 229: 7.1. INTRODUCTION 209 300 250 TURBU
Page 230 and 231: 7.2. TURBULENT COMBUSTION THEORIES
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Page 240 and 241: Chapter 8 Ignition, flammability an
Page 242 and 243: 8.2. IGNITION 223 comparison betwee
Page 244 and 245: 8.3. FLAMMABILITY LIMITS 225 The pr
Page 246 and 247: 8.4. QUENCHING 227 8.4 Quenching So
Page 248 and 249: 8.4. QUENCHING 229 [19] Simon, D. M
Page 250 and 251: Chapter 9 Flows with combustion wav
Page 252 and 253: 9.2. CONDITIONS THAT MUST BE SATISF
Page 254 and 255: 9.3. NORMAL FLAME FRONT 235 9.3 Nor
Page 256 and 257: 9.4. INCLINED FLAME FRONT 237 60 50
Page 258 and 259: 9.5. ENTROPY JUMP ACROSS THE FLAME
Page 260 and 261: 9.5. ENTROPY JUMP ACROSS THE FLAME
Page 262 and 263: 9.6. VORTICITY ACROSS THE FLAME 243
Page 264 and 265: Chapter 10 Aerothermodynamic field
Page 266 and 267: 10.1. INTRODUCTION 247 form numeric
Page 268 and 269: 10.1. INTRODUCTION 249 ∆ P /∆ P
Page 270 and 271: 10.2. TSIEN METHOD 251 As aforesaid
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10.2. TSIEN METHOD 253 1.0 λ=6.0 M
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10.3. METHOD OF FABRI-SIESTRUNCK-FO
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10.3. METHOD OF FABRI-SIESTRUNCK-FO
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10.5. CHAMBER WITH SLOWLY VARYING C
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Chapter 11 Similarity in combustion
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11.2. DIMENSIONLESS PARAMETERS OF A
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11.2. DIMENSIONLESS PARAMETERS OF A
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11.3. SCALING OF ROCKETS 267 Furthe
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11.3. SCALING OF ROCKETS 269 From h
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11.4. SCALING OF ROCKETS FOR NON-ST
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11.4. SCALING OF ROCKETS FOR NON-ST
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11.5. FLAME STABILIZATION 275 Flame
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11.5. FLAME STABILIZATION 277 Flame
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11.5. FLAME STABILIZATION 279 which
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Chapter 12 Diffusion flames 12.1 In
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12.1. INTRODUCTION 283 In fact, oth
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12.1. INTRODUCTION 285 which preced
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12.1. INTRODUCTION 287 remains appr
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12.2. GENERAL EQUATIONS FOR LAMINAR
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12.3. BOUNDARY CONDITIONS ON THE FL
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12.4. SIMPLIFIED EQUATIONS 293 As f
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12.4. SIMPLIFIED EQUATIONS 295 whil
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12.5. SOLUTIONS OF THE SIMPLIFIED S
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12.5. SOLUTIONS OF THE SIMPLIFIED S
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Chapter 13 Combustion of liquid fue
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13.2. ATOMIZATION 303 lem has been
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13.4. COMBUSTION 305 solution corre
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13.5. NOTATION 307 2) The phenomeno
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13.6. CONTINUITY EQUATIONS 309 Chem
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13.7. ENERGY EQUATION 311 The value
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13.8. DIFFUSION EQUATIONS 313 13.8
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13.9. COMBUSTION VELOCITY OF THE DR
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13.10. INTEGRATION OF THE EQUATIONS
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13.11. NUMERICAL APPLICATION 319 wh
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13.11. NUMERICAL APPLICATION 321 10
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13.12. COMPARISON WITH EXPERIMENTAL
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13.14. COMBUSTION OF FUEL SPRAYS 32
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13.15. DROPLET EVAPORATION 327 4 0.
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13.15. DROPLET EVAPORATION 329 1 0.
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13.16. APPENDIX: APPLICATION OF PRO
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