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Chapter 12 Diffusion flames 12.1 Introduction So far we have considered combustion problems dealing with premixed reactant gases. Yet, it can also happen that species are initially separated, and mixing and combustion take place simultaneously. Thus, a new type of flame is obtained which Burke and Schumann [1] called diffusion flame. In these flames the reaction zone separates the two reacting species which diffuse through inert gases and combustion products from each side towards the flame. A flame of this type is obtained, for example, when a jet of combustible gas discharges from a burner into the open atmosphere or into an air stream parallel to the jet burning at the outlet of the burner, see Fig. 12.1. Such flames, are largely used in industrial applications. The flame length needed to burn a given x Flame Air Air o r Fuel Figure 12.1: An open diffusion flame. 281
282 CHAPTER 12. DIFFUSION FLAME quantity of fuel per unit time under given conditions is highly interesting in these applications, since the dimensions of burners and furnaces depend on it. The reacting species burn very rapidly as they reach the reaction zone. Thereby, the combustion velocity is generally conditioned by the accessibility of the species to the flame. In other words, by their facility to diffuse across the inert gases and combustion products. Diffusion can be either laminar or turbulent depending on the conditions of the phenomenon, originating the flames accordingly. The actual state of knowledge on diffusion flames is by far less advanced than on premixed flames The fundamental work by Burke and Schumann [1] has been the starting point for practically all the later studies. Even though considerably ahead the publication of this work a correct qualitative idea on diffusion flames was held, 1 Burke and Schumann were the first to achieve a quantitative study of the phenomenon. For the purpose they used a highly simplified model that enabled an analytical solution of the problem. This model retains the essential factors of the process and can be summarized in the following two assumptions: 1) The thickness of the reaction zone is zero. 2) The reacting species burn instantaneously upon reach the flame. This simple model eliminates chemical kinetics from the process thus making available its computation. This simplification is justified when the reaction rate is very large compared to the diffusion velocities of the species towards the flame. Thereby it is not applicable, for example, to the study of flames rarefied or very diluted by inert gases where the time of reaction can appreciably influence the process. The model disregards the structure of the reaction zone as was done in Chap. 6 for premixed flames. The difference between both cases lies upon the fact that while in the case of premixed flames the combustion front is a discontinuity surface for velocity, temperature, composition, etc., in diffusion flames such magnitudes change continuously across the front. The first assumption reduces the reaction zone to a surface called the flame front, which acts as a sink for reacting species and as a source for combustion products. The second assumption implies the following consequences: a) Concentrations of reactants at the flame must be zero. b) Reactants must diffuse towards the flame in the stoichiometric ratio corresponding to the produced reactions. 1 See, i.e., Barr’s review paper [2] where data and bibliography on the subject can be found.
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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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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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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
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Page 262 and 263: 9.6. VORTICITY ACROSS THE FLAME 243
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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
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
Page 296 and 297: 11.5. FLAME STABILIZATION 277 Flame
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Page 312 and 313: 12.4. SIMPLIFIED EQUATIONS 293 As f
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Page 322 and 323: 13.2. ATOMIZATION 303 lem has been
Page 324 and 325: 13.4. COMBUSTION 305 solution corre
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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
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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.
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13.16. APPENDIX: APPLICATION OF PRO
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Untitled - Aerobib - Universidad Politécnica de Madrid

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