Untitled - Aerobib - Universidad Politécnica de Madrid

More documents

Recommendations

Info

7.2. TURBULENT COMBUSTION THEORIES 215 valid for which also contradicts (7.16). v ′ u l ≪ 1, Wohl has shown that (7.22) can also be deduced from (7.13) through purely geometric considerations by assuming that the distortion of the flame front consists in the formation of a system of prisms instead of the cones proposed by Shelkin. Scurlock and Graver [17] calculate σ l by assuming with Shelkin that the laminar surface is formed by a set of cones whose base is proportional to the square l 2 of the scale of turbulence and whose height is proportional to the root mean square displacement ¯X of the turbulent oscillations suffered by a flame element. Therefore, as in Eq. (7.14), u t is given by expression √ u t = 1 + k ¯X 2 u l l 2 . (7.25) The problem lies in computing ¯X. Its magnitude, according to Scurlock, is governed by three different mechanisms: 1) Turbulent diffusivity tends to increase indefinitely the value of ¯X as time elapses. Figure 7.5 shows two consecutive positions of the flame front in Scurlock’s model after the instant at which the flame was plane. Initial flat flame Flame after passage of short time Flame after passage of longer time Figure 7.5: Schematic diagram showing wrinkling with passage of time of an initially flat flame element exposed to turbulence. 2) Laminar combustion tends to absorb oscillations reducing the value of ¯X. Karlovitz and his collaborators [19] were the first to acknowledge this fact which is represented in Fig. 7.6 3) The flame generates turbulence 2 and this tends to increase the value of ¯X. 2 See §4.
216 CHAPTER 7. TURBULENT FLAMES ARBITRARY WAVY FLAME FRONT BURNED GAS FRESH GAS FLAME FRONT AFTER ∆t TIME Figure 7.6: The effect of laminar flame propagation on the evolution of a turbulent flame front. Since the locus of an element of the flame at two different instants are related to two different particles of the mixture, when calculating the influence of turbulent diffusivity on ¯X, a combined time-space coefficient of correlation R tx should be used substituting coefficient time-correlation R t in Taylor’s formula [17]. The influence of the laminar propagation of the flame in the value of ¯X may be obtained through purely geometric considerations. Finally, the influence of the turbulence generated by the flame is taken into consideration by substituting into the expression of ¯X, the intensity v ′ of turbulence of the unburnt gases flow by the resultant of it, plus the intensity of the turbulence originated by the flame. The combination of these three effects gives a differential equation which in turn supplies the law of variation for ¯X as a function of time t during which the particle has been exposed to turbulent oscillations. This differential equation replaces Taylor’s equation (7.18) for this case. Through integration of this equation the value for ¯X is obtained, and when taken into Eq. (7.22) it gives a formula for the propagation velocity of the turbulent flame. Now we must determine the time t that each element of the flame has been exposed to the action of turbulence. Scurlock considers only flames inclined respect to the flow such as the one obtained with a flame-holder or from the ring of a bunsen burner. He identifies t with the time taken by a gas particle to cross the flame front from the holders section to the point under consideration. Let v t by the component tangential to the flame front of the velocity of the unburnt gases and s the distance to the flame-holder measured along the flame front. The following expression is obtained for t t = ∫ s 0 ds v t . (7.26)
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 100 and 101:
Page 102 and 103:
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 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: 6.12. GENERAL EQUATIONS FOR THE COM
Page 186 and 187: 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
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

You also want an ePaper? Increase the reach of your titles

Delete template?

Save as template?