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4.7. INDETERMINACY OF THE SOLUTION 103 y 125 100 x =1/6 0 (a) Detonation branch 75 50 J 25 0 P A 0.0 0.2 0.4 0.6 0.8 1.0 y 1.0 0.8 P B (b) Deflagration branch x 0.6 0.4 J’ 0.2 0.0 0 20 40 60 80 100 x Figure 4.7: Hugoniot curve (x = τ/τ 1, y = p/p 1) corresponding to p 1 = 1 atm, τ 1 = 1000 cm 3 /gr, T 1 = 300 K, γ 1 = γ 2 = 1.4, Q = 1000 cal gr −1 , c p2 = 0.46 cal gr −1 K −1 , ν = 1. 4.7 Indeterminacy of the solution The study performed in this chapter allows the establishment of the different types of combustion waves that are compatible with the principles of the conservation of mass, momentum and energy. This has been attained by comparison between the initial and final state of the gases. In order to obtain this result it has not been necessary to take into account the intermediate states undergone by the gas, within the wave. Thus, the problem is essentially simplified. However, if the influence of the intermediate states is neglected the result obtained is incomplete, since the propagation velocity of the combustion wave remains undetermined, whilst experience shows that it takes a well defined value for each different case. In order to eliminate the said indeterminacy and select among the combustion waves obtained herein those that will actually occur, it is necessary to analyze the internal structure of the wave and see the mechanism that
104 CHAPTER 4. COMBUSTION WAVES propagates the reaction to the unburnt gases. This study will be the subject of the following chapter. Therein, it will be seen that: 1) The weak detonations and strong deflagrations are impossible. 2) The detonations physically observed must be of the Chapman-Jouguet type. 3) Deflagrations propagate with a well defined velocity. References [1] Crussard, L.: Ondes de choc et onde explosive. Bulletin de la Société de l’Industrie Minérale, Vol. VI, 1907. [2] Chapman, D. L.: On the rate of explosion in gases. Phylosophical Magazine, Jan. 1899. [3] Jouguet, E.: Sur la propagation des réactions chimiques dans les gaz. Journal de Mathématiques Pures et Appliquées, 1905-6. [4] Taylor, J.: Detonation in Condensed Explosives. Oxford University Press, 1952.
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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
Page 72 and 73: 2.3. VISCOSITIES 53 Its value depen
Page 74 and 75: 2.4. THERMAL CONDUCTIVITY 55 2000 1
Page 76 and 77: 2.4. THERMAL CONDUCTIVITY 57 4000 3
Page 78 and 79: Chapter 3 General equations 3.1 Int
Page 80 and 81: 3.2. EQUATION OF CONTINUITY 61 The
Page 82 and 83: 3.2. EQUATION OF CONTINUITY 63 A i
Page 84 and 85: 3.4. ENERGY EQUATION 65 where the s
Page 86 and 87: 3.4. ENERGY EQUATION 67 The energy
Page 88 and 89: 3.5. GENERAL EQUATIONS 69 obtained
Page 90 and 91: 3.6. ENTROPY VARIATION 71 Taking in
Page 92 and 93: 3.7. ONE-DIMENSIONAL MOTIONS 73 red
Page 94 and 95: 3.8. STATIONARY, ONE-DIMENSIONAL MO
Page 96 and 97: 3.9. THE CASE OF ONLY TWO CHEMICAL
Page 98 and 99: 3.10. STATIONARY, ONE-DIMENSIONAL M
Page 104 and 105: 3.11. APPENDIX: NOTATION AND REPERT
Page 106 and 107: 3.11. APPENDIX: NOTATION AND REPERT
Page 108 and 109: Chapter 4 Combustion Waves 4.1 Deto
Page 110 and 111: 4.2. KINDS OF DETONATIONS AND DEFLA
Page 112 and 113: 4.2. KINDS OF DETONATIONS AND DEFLA
Page 114 and 115: 4.3. VELOCITY OF THE BURNT GASES 95
Page 116 and 117: 4.3. VELOCITY OF THE BURNT GASES 97
Page 118 and 119: 4.4. PROPAGATION VELOCITY 99 p H’
Page 120 and 121: 4.5. APPLICATIONS 101 By substituti
Page 124 and 125: Chapter 5 Structure of the combusti
Page 126 and 127: 5.2. WAVE EQUATIONS 107 of diffusio
Page 128 and 129: 5.2. WAVE EQUATIONS 109 2) Burnt ga
Page 130 and 131: 5.4. LIMITING FORM OF THE WAVE EQUA
Page 132 and 133: 5.4. LIMITING FORM OF THE WAVE EQUA
Page 134 and 135: 5.5. DETONATIONS 115 Of these two v
Page 136 and 137: 5.5. DETONATIONS 117 waves. Such th
Page 138 and 139: 5.5. DETONATIONS 119 This relation
Page 140 and 141: 5.5. DETONATIONS 121 curves, repres
Page 142 and 143: 5.6. DEFLAGRATIONS 123 mum temperat
Page 144 and 145: 5.6. DEFLAGRATIONS 125 8 7 v/v 1 =T
Page 146 and 147: 5.7. TRANSITION FROM DEFLAGRATION T
Page 148 and 149: 5.7. TRANSITION FROM DEFLAGRATION T
Page 150 and 151: Chapter 6 Laminar flames 6.1 Introd
Page 152 and 153: 6.1. INTRODUCTION 133 papers presen
Page 154 and 155: 6.3. BOUNDARY CONDITIONS 135 c) Dif
Page 156 and 157: 6.4. MODIFICATION OF THE CONDITIONS
Page 158 and 159: 6.4. MODIFICATION OF THE CONDITIONS
Page 160 and 161: 6.6. EXAMPLE 141 generally impossib
Page 162 and 163: 6.6. EXAMPLE 143 Two more relations
Page 164 and 165: 6.7. REACTION VELOCITY 145 1.0 0.8
Page 166 and 167: 6.8. FLAME EQUATIONS 147 6.8 Flame
Page 168 and 169: 6.9. SOLUTION OF THE FLAME EQUATION
Page 170 and 171: 6.9. SOLUTION OF THE FLAME EQUATION
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6.9. SOLUTION OF THE FLAME EQUATION
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6.10. STRUCTURE OF THE COMBUSTION W
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6.11. IGNITION TEMPERATURE 161 6.11
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6.12. GENERAL EQUATIONS FOR THE COM
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6.13. OZONE DECOMPOSITION FLAME 169
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6.14. HYDRAZINE DECOMPOSITION FLAME
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6.15. FLAME PROPAGATION IN HYDROGEN
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Chapter 7 Turbulent flames 7.1 Intr
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7.1. INTRODUCTION 209 300 250 TURBU
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7.2. TURBULENT COMBUSTION THEORIES
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7.4. COMPARISON WITH EXPERIMENTAL R
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Chapter 8 Ignition, flammability an
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8.2. IGNITION 223 comparison betwee
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8.3. FLAMMABILITY LIMITS 225 The pr
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8.4. QUENCHING 227 8.4 Quenching So
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8.4. QUENCHING 229 [19] Simon, D. M
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Chapter 9 Flows with combustion wav
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9.2. CONDITIONS THAT MUST BE SATISF
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9.3. NORMAL FLAME FRONT 235 9.3 Nor
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9.4. INCLINED FLAME FRONT 237 60 50
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9.5. ENTROPY JUMP ACROSS THE FLAME
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9.5. ENTROPY JUMP ACROSS THE FLAME
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9.6. VORTICITY ACROSS THE FLAME 243
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Chapter 10 Aerothermodynamic field
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10.1. INTRODUCTION 247 form numeric
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10.1. INTRODUCTION 249 ∆ P /∆ P
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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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