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12.1. INTRODUCTION 283 In fact, otherwise, some of the species would diffuse across the flame and react with those on the other side. In order to judge the validity of this model Hottel and Hawthorne [3] performed some experiments to determine the composition of the gases in a diffusion flame of hydrogen burning in the open atmosphere, taking samples of the gas at different points of the flame by means of a special sound. Details of these experiments can be found in the said work. Figure 12.2, taken from it, shows the results of the sounding made in three cross sections of the flame. The results of such measurements prove the correctness of Burke and Schumann’s model. 100 75 50 25 H 2 flame front distance from port= 30.5 cm Percentage in dry sample 0 100 75 50 25 0 100 O 2 H 2 N 2 N 2 axis of flame flame front O 2 distance from port= 22.85 cm 75 50 25 H 2 N 2 flame front distance from port= 15.25 cm 0 O 2 0 10 20 30 40 Radial distance (mm) Figure 12.2: Gas composition in a hydrogen diffusion flame Burke and Schumann have successfully applied their model to the calculation of the shape and height of laminar diffusion flames for the case where the fuel jet discharges within a tube where an air stream moves with the same velocity than the fuel jet, Fig. 12.3. This device eliminates the difficulties originating from momentum transfer between the fuel and the surrounding air when their velocities are not equal. Furthermore, for this reason it is easier to obtain a stable flame. By introducing several drastic simplifications, to be considered further on, Burke and Schumann were able to calculate the shape of the flame. Some of their results are outlined in Fig. 12.3. Fig. 12.3 (a) corresponds to an overventilated flame, which closes at the axis of the
284 CHAPTER 12. DIFFUSION FLAME air fuel air air fuel air (a) overventilated (b) underventilated Figure 12.3: Confined laminar diffusion flames. tube, and Fig. 12.3 (b) to an underventilated flame, which ends at the wall of the exterior tube. The fuel-air ratio can be changed by varying the diameters ratio of both tubes. Both types of flames were experimentally observed by Burke and Schumann. The flame length is proportional to the amount of fuel burnt per second and does not depend on the diameter of the burner. Burke and Schumann’s analysis on confined flames has been extended by J. Barr, [4] and [5], to the case where air and fuel velocities are different. He has experimentally analyzed the appearance of the flames that form when the streams of air and fuel change within limits far more extended than those covered by any previous investigation. As a result he concludes that the length of a laminar diffusion flame is proportional to the fuel consumption not only for the case of short flames, as stated by Lewis and von Elbe [6], but also for flames of a length as much as a hundred times the diameter of the burner. The results of his work are summarized in Fig. 12.4, taken from Ref. [5], which shows the different types of flames observed when the flow rates of air and fuel are changed. In the same figure, regions 1 and 2 correspond to flames with excess of air and fuel respectively, of the type studied by Burke and Schumann. In between these regions a zone of carbon formation exists. Region 3 corresponds to meniscus flames for which diffusion in the axial direction is important. A meniscus flame blows-out when the fuel flow rate is reduced. Region 4 corresponds to the socalled convective or Lambent flames. Within this region, where the fuel and air ratios are small, buoyancy forces are important and oscillating flames are obtained. Region 5, where fuel flow rate is very large, corresponds to tilted flames preceding blow-off. Region 6, where the fuel and air streams are very strong, corresponds to lifted flames
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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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Chapter 9 Flows with combustion wav
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Page 268 and 269: 10.1. INTRODUCTION 249 ∆ P /∆ P
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Page 288 and 289: 11.3. SCALING OF ROCKETS 269 From h
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Page 322 and 323: 13.2. ATOMIZATION 303 lem has been
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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
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Page 338 and 339: 13.11. NUMERICAL APPLICATION 319 wh
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Page 346 and 347: 13.15. DROPLET EVAPORATION 327 4 0.
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13.16. APPENDIX: APPLICATION OF PRO
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13.16. APPENDIX: APPLICATION OF PRO
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Untitled - Aerobib - Universidad Politécnica de Madrid

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