Untitled - Aerobib - Universidad Politécnica de Madrid

More documents

Recommendations

Info

4.2. KINDS OF DETONATIONS AND DEFLAGRATIONS 93 p C E’ p 1 p p 1 P B J α α min E A P τ 0 1 (a) Detonation branch τ τ J’ D τ 1 τ 3 τ (b) Deflagration branch Figure 4.3: Chapman-Jouguet points in the detonation and deflagration branches of the Hugoniot curve. These properties can immediately be translated into properties for the propagation velocity of the detonation. In fact, we have 2 tan α = p 2 − p 1 τ 1 − τ 2 . (4.12) Taking this value into Eq. (4.8), the following expression for the propagation velocity is obtained v 1 = τ 1 √ tan α. (4.13) Therefore, it results that the propagation velocity of a detonation is minimum at point J, where the straight line P J is tangent to H. This property was observed by Chapman in 1899 [2]. Point J is called the Chapman-Jouguet point and the corresponding detonation the Chapman-Jouguet detonation. The Chapman-Jouguet detonation is important since it is the one usually observed. Hence, one concludes that of all the possible detonations, compatible with the given initial conditions, the Chapman-Jouguet detonation is the one which propagates at a minimum velocity. 2 To account for dimensions a constant should be included. Hereinafter it is omitted for simplicity.
94 CHAPTER 4. COMBUSTION WAVES The detonations corresponding to the upper part JC of H, for which the pressure of the burnt gases is greater than the pressure of the Chapman-Jouguet detonation, have been called by Courant and Friedrichs strong detonations and those corresponding to the lower part AJ, weak detonations. In the same manner it can be proven, Fig. 4.3(b), that in the deflagration branch there exists a point J ′ in which H and P J ′ are tangent and the corresponding deflagration, also called Chapman-Jouguet, propagates with a maximum velocity. Point J ′ divides the deflagration branch in two parts, one J ′ D of strong deflagrations and the other BJ ′ of weak deflagrations. 4.3 Velocity of the burnt gases It is interesting to determine the subsonic or supersonic character of the velocity v 2 of the burnt gases with respect to the wave front, since the stability of the detonation wave depends on the character of this velocity, that is, the possibility for this wave to propagate unchanged through the gas. In order to determine the character of v 2 it is necessary to compare this velocity with the sound velocity a 2 in the burnt gases. Let us see how this can be attained. Gas Dynamics shows 3 that the sound velocity a in a gas is given by the expression a = τ √ − ( ) ∂p , (4.14) ∂τ S where subscripts S means differentiation along the isentropic that passes through the representative point of the gas state. Let α S , Fig. 4.4, be the angle between the tangent to the isentropic that passes through the point (p 2 , τ 2 ) of the detonation branch, and the negative direction of x axis. From Eq. (4.14) we have a 2 = τ 2 √ tan αS . (4.15) On the other hand, the velocity v 2 of the burnt gases with respect to the flame front, in virtue of Eq. (4.1), is v 2 = τ 2 τ 1 v 1 . Then, because of Eq. (4.13), this velocity can be expressed as v 2 = τ 2 √ tan α , (4.16) where α is the previously defined angle. If α is larger, equal to or smaller than α s , then v 2 will be larger, equal to or smaller than a 2 ; and the flow of the burnt gases 3 See Courant-Friedrichs: Supersonic Flow and Shock Waves. Intersciences Pub. Inc., New York, 1948.
Page 2 and 3:
Aerothermochemistry Gregorio Millá
Page 4 and 5:
PRESENTACIÓN Amable Liñán Es un
Page 6 and 7:
que no cambiaron los resultados, y
Page 8:
INSTITUTO NACIONAL DE TÉCNICA AERO
Page 11 and 12:
aim to become acquainted with Aerot
Page 13 and 14:
Tarifa, Manuel de Sendagorta and Ig
Page 15 and 16:
3.4 Energy equation . . . . . . . .
Page 17 and 18:
8.4 Quenching . . . . . . . . . . .
Page 20 and 21:
Chapter 1 Thermochemistry 1.1 Intro
Page 22 and 23:
1.1. INTRODUCTION 3 GAS ε/k (K) σ
Page 24 and 25:
1.1. INTRODUCTION 5 14 12 10 N 2 CH
Page 26 and 27:
1.2. THERMODYNAMIC FUNCTIONS OF AN
Page 28 and 29:
1.2. THERMODYNAMIC FUNCTIONS OF AN
Page 30 and 31:
1.3. MIXTURE OF GASES 11 Helmholtz
Page 32 and 33:
1.3. MIXTURE OF GASES 13 is the par
Page 34 and 35:
1.3. MIXTURE OF GASES 15 Entropy Si
Page 36 and 37:
1.4. CALCULATION OF THE THERMODYNAM
Page 38 and 39:
1.4. CALCULATION OF THE THERMODYNAM
Page 40 and 41:
1.5. CHEMICAL REACTIONS IN A MIXTUR
Page 42 and 43:
1.6. CHEMICAL EQUILIBRIUM 23 Since
Page 44 and 45:
∆G 0 j = ∑ i 1.7. CASE OF A MIX
Page 46 and 47:
1.7. CASE OF A MIXTURE OF IDEAL GAS
Page 48 and 49:
1.8. CHEMICAL KINETICS 29 1.8 Chemi
Page 50 and 51:
1.8. CHEMICAL KINETICS 31 Mechanics
Page 52 and 53:
1.8. CHEMICAL KINETICS 33 This stru
Page 54 and 55:
1.8. CHEMICAL KINETICS 35 [3] Hirsc
Page 56 and 57:
Chapter 2 Transport phenomena in ga
Page 58 and 59:
2.2. DIFFUSION 39 Hereinafter, nota
Page 60 and 61:
2.2. DIFFUSION 41 where r is the di
Page 62 and 63: 2.2. DIFFUSION 43 T ∗ Ω (1,1)∗
Page 64 and 65: 2.2. DIFFUSION 45 Gas Pair σ 12 (
Page 66 and 67: 2.2. DIFFUSION 47 coefficients. 14
Page 68 and 69: 2.3. VISCOSITIES 49 2.3 Viscosities
Page 70 and 71: 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 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 122 and 123: 4.7. INDETERMINACY OF THE SOLUTION
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:
Page 172 and 173:
Page 174 and 175:
Page 176 and 177:
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 184 and 185:
Page 186 and 187:
Page 188 and 189:
6.13. OZONE DECOMPOSITION FLAME 169
Page 190 and 191:
Page 192 and 193:
Page 194 and 195:
Page 196 and 197:
6.14. HYDRAZINE DECOMPOSITION FLAME
Page 198 and 199:
Page 200 and 201:
Page 202 and 203:
Page 204 and 205:
Page 206 and 207:
6.15. FLAME PROPAGATION IN HYDROGEN
Page 208 and 209:
Page 210 and 211:
Page 212 and 213:
Page 214 and 215:
Page 216 and 217:
Page 218 and 219:
Page 220 and 221:
Page 222 and 223:
Page 224 and 225:
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
Page 232 and 233:
Page 234 and 235:
Page 236 and 237:
Page 238 and 239:
7.4. COMPARISON WITH EXPERIMENTAL R
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
Page 272 and 273:
10.2. TSIEN METHOD 253 1.0 λ=6.0 M
Page 274 and 275:
10.3. METHOD OF FABRI-SIESTRUNCK-FO
Page 276 and 277:
10.3. METHOD OF FABRI-SIESTRUNCK-FO
Page 278 and 279:
10.5. CHAMBER WITH SLOWLY VARYING C
Page 280 and 281:
Chapter 11 Similarity in combustion
Page 282 and 283:
11.2. DIMENSIONLESS PARAMETERS OF A
Page 284 and 285:
11.2. DIMENSIONLESS PARAMETERS OF A
Page 286 and 287:
11.3. SCALING OF ROCKETS 267 Furthe
Page 288 and 289:
11.3. SCALING OF ROCKETS 269 From h
Page 290 and 291:
11.4. SCALING OF ROCKETS FOR NON-ST
Page 292 and 293:
11.4. SCALING OF ROCKETS FOR NON-ST
Page 294 and 295:
11.5. FLAME STABILIZATION 275 Flame
Page 296 and 297:
11.5. FLAME STABILIZATION 277 Flame
Page 298 and 299:
11.5. FLAME STABILIZATION 279 which
Page 300 and 301:
Chapter 12 Diffusion flames 12.1 In
Page 302 and 303:
12.1. INTRODUCTION 283 In fact, oth
Page 304 and 305:
12.1. INTRODUCTION 285 which preced
Page 306 and 307:
12.1. INTRODUCTION 287 remains appr
Page 308 and 309:
12.2. GENERAL EQUATIONS FOR LAMINAR
Page 310 and 311:
12.3. BOUNDARY CONDITIONS ON THE FL
Page 312 and 313:
12.4. SIMPLIFIED EQUATIONS 293 As f
Page 314 and 315:
12.4. SIMPLIFIED EQUATIONS 295 whil
Page 316 and 317:
12.5. SOLUTIONS OF THE SIMPLIFIED S
Page 318 and 319:
12.5. SOLUTIONS OF THE SIMPLIFIED S
Page 320 and 321:
Chapter 13 Combustion of liquid fue
Page 322 and 323:
13.2. ATOMIZATION 303 lem has been
Page 324 and 325:
13.4. COMBUSTION 305 solution corre
Page 326 and 327:
13.5. NOTATION 307 2) The phenomeno
Page 328 and 329:
13.6. CONTINUITY EQUATIONS 309 Chem
Page 330 and 331:
13.7. ENERGY EQUATION 311 The value
Page 332 and 333:
13.8. DIFFUSION EQUATIONS 313 13.8
Page 334 and 335:
13.9. COMBUSTION VELOCITY OF THE DR
Page 336 and 337:
13.10. INTEGRATION OF THE EQUATIONS
Page 338 and 339:
13.11. NUMERICAL APPLICATION 319 wh
Page 340 and 341:
13.11. NUMERICAL APPLICATION 321 10
Page 342 and 343:
13.12. COMPARISON WITH EXPERIMENTAL
Page 344 and 345:
13.14. COMBUSTION OF FUEL SPRAYS 32
Page 346 and 347:
13.15. DROPLET EVAPORATION 327 4 0.
Page 348 and 349:
13.15. DROPLET EVAPORATION 329 1 0.
Page 350 and 351:
13.16. APPENDIX: APPLICATION OF PRO
Page 352 and 353:
Page 354 and 355:
show all

Untitled - Aerobib - Universidad Politécnica de Madrid

Create successful ePaper yourself

Delete template?

Save as template?