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7.2. TURBULENT COMBUSTION THEORIES 217 The selection of t, which is arbitrary to a certain extent, is justified by the theoretical and experimental studies carried out by Markstein [20] on the propagation of disturbance along inclined flame fronts. These studies show that such disturbances propagate with the tangential velocity of the flow as they become amplified. BURNED GASES BURNED GASES BURNED GASES MEAN POSITION OF FLAME MEAN POSITION OF FLAME MEAN POSITION OF FLAME β INSTANTANEOUS FLAME FRONT INSTANTANEOUS FLAME FRONT INSTANTANEOUS FLAME FRONT UNBURNED GASES UNBURNED GASES UNBURNED GASES U U U BURNER RIM BURNER RIM BURNER RIM Figure 7.7: Cross section of stabilized unconfined Bunsen flames constructed on basis of theory to demonstrate under typical conditions the predicted individual effects of eddy diffusion, flame propagation and flame generated turbulence. Figure 7.7 taken from the work by Scurlock and Grover, shows the influence of the above mentioned facts for the case of an open flame stabilized in a bunsen burner. The following values were adopted for computations: diameter of the burner = 5 cm, velocity on the gases in the burner= 200 cm/s, u 1 = 10 cm/s, v ′ = 10 cm/s, intensity of turbulence 5%, scale of turbulence= 0.25 cm, and width of the flame= 2 ¯X.
218 CHAPTER 7. TURBULENT FLAMES 7.3 Turbulence generated by the flame Markstein [21] has shown that the disturbances originated at a certain point of an incline flame propagate and amplify along the same and eventually generate turbulence. In their studies of turbulent flames stabilized in tubes, Willians, Hottel and Scurlock [5] recognized the existence of turbulence originated by the flame. They considered this turbulence as a consequence of the strong gradients of velocity which originate through the flame in this case. 3 Scurlock and Grove have given a formula for the maximum intensity v ′ of the possible turbulence. Such formula was deduced from elementary considerations on mass and momentum conservation across the flame before and after the mixing of burnt gases. This formula is √ ( ) v m ′ K m ρ u = (vu 3 ρ 2 − u 2 l ) ρu − 1 . (7.27) b ρ b Here, K m = ∆p ∆p −1, where is the relation between pressure jumps across ∆p ′ ∆p ′ the flames before and after the turbulent mixing, v u is the velocity of the unburnt gases normal to the mean flame front and ρ u /ρ b is the ratio between densities of unburnt and burnt gases. Formula (7.27) gives a maximum limit to the turbulence that could be originated in the flame but does not allow the computation of the possible turbulence for each case. This arises the problem of introducing an additional undetermined element in the theory which adds difficulties to the comparison between theoretical and experimental results. In practice v ′ m can be considerably larger than the turbulence of the incident stream. Karlovitz [16] when comparing the values for u t predicted by his theory with those obtained from experimenting with flames stabilized in bunsen burner verified that experimental velocities were much larger than those calculated and he considered this discrepancy to be due to the influence of the turbulence originated by the flame. Karlovitz explains the production of turbulence as follows: through the laminar front an increase in velocity takes place of the order of magnitude of ρ u ρ b − 1. In a laminar flame this increase has a constant direction but in a turbulent flame it oscillates since it must be normal to the temporary position of the flame front at all instants which is variable. The statistic oscillations of this increase are the source of the turbulence. Through a not too legitimate calculation Karlovitz deduces the following expression for the maximum intensity of turbulence produced by the flame v m ′ = √ 1 ( ) ρu − 1 u l . (7.28) 3 ρ b 3 See chapter 10.
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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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6.12. GENERAL EQUATIONS FOR THE COM
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Page 188 and 189: 6.13. OZONE DECOMPOSITION FLAME 169
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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
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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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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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Untitled - Aerobib - Universidad Politécnica de Madrid

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