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9.2. CONDITIONS THAT MUST BE SATISFIED BY THE JUMP ACROSS A FLAME FRONT. 233 and v t are the normal and tangential components of this velocity. Moreover ρ and p are, as usual, the density and pressure of the gases, and h is the total specific enthalpy, that is, (as seen in chapter 1), the thermal enthalpy h T plus the formation enthalpy h f , h = h T + h f , (9.5) where h T is expressed, in terms of the heat capacity c p at constant pressure and the absolute temperature T , as follows h T = ∫ T 0 which, for the special case c p = constant reduces to c p dT, (9.6) h T = c p T. (9.7) At each side of the flame front, the pressure, density and temperature are related by the state equation, which is assumed to be that of the perfect gases, that is p 1 ρ 1 = R 1 T 1 and p 2 ρ 2 = R 2 T 2 , (9.8) where R 1 = R M u and R 2 = R M b (9.9) are the specific constants of the unburnt and burnt gases, respectively, and M u and M b their respective average molecular masses. Since the tangential component of the velocity is continuous throughout the flame, there results that the incoming and outgoing velocities and the vector normal to the combustion front are coplanar. When the state of the unburnt gases and the incline α 1 of the incident flow relative to the flame front, see Fig. 9.2, are known, the system of equations (9.1), (9.2), (9.3), (9.4) and (9.8) determines the state of the burnt gases. Let ϕ be the flame propagation velocity corresponding to the composition of the unburnt gas mixture in the thermodynamic state defined by the values p 1 and ρ 1 of pressure and density. Obviously we have ϕ = v n1 , (9.10) and for the incline α 1 of the flame front relative to the incident flow sin α 1 = v n1 v 1 = ϕ v 1 . (9.11)
234 CHAPTER 9. FLOWS WITH COMBUSTION WAVES V t1 V n1 α 2 ϕ = − V n1 α 1 V 1 α 1 δ V n2 V 2 V t2 = Vt1 Figure 9.2: Velocity components at both sides of the front. Therefore, α 1 is determined by the velocity v 1 of the incident flow relative to the front and by the burning velocity ϕ of the mixture. This velocity depends only on the composition, pressure and density or temperature, and must be considered as a datum, determined either theoretically or experimentally (see chapter 6). In order to simplify calculations, it is assumed in the following that the thermal enthalpy can be expressed as indicated in (9.7). Let q = h f1 − h f2 (9.12) be the difference between the formation enthalpies of the unburnt and burnt gases. By substituting equations (9.7) and (9.12) into (9.4), this equation can be written 1 2 v2 1 + c p1 T 1 + q = 1 2 v2 2 + c p2 T 2 . (9.13) Let T s1 and T s2 be the stagnation temperatures of the unburnt and burnt gases respectively. By virtue of equation (9.13) they are related by c p1 T s1 + q = c p2 T s2 , (9.14) and their ratio n is given by For the particular case c p1 = c p2 , we have n = T ( s2 = 1 + q ) cp1 . (9.15) T s1 c p1 T s1 c p2 n = 1 + q c p1 T s1 . (9.16)
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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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6.10. 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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Page 228 and 229: 7.1. INTRODUCTION 209 300 250 TURBU
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Page 240 and 241: Chapter 8 Ignition, flammability an
Page 242 and 243: 8.2. IGNITION 223 comparison betwee
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Page 248 and 249: 8.4. QUENCHING 229 [19] Simon, D. M
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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
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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
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Page 272 and 273: 10.2. TSIEN METHOD 253 1.0 λ=6.0 M
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Page 288 and 289: 11.3. SCALING OF ROCKETS 269 From h
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Page 294 and 295: 11.5. FLAME STABILIZATION 275 Flame
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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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