Untitled - Aerobib - Universidad Politécnica de Madrid

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8.4. QUENCHING 227 8.4 Quenching So far studies have dealt with flames propagating through unlimited mixtures, not taking into account the influence of the proximity of walls, A set of phenomena exist, of great importance, relative to the behavior of flames close to walls which have been the subject of such attention in recent years. Among those phenomena are quenching, blow-off and flash-back. Experiments prove that when the diameter of a tube full of a combustible gas is sufficiently small, it is impossible for a flame to propagate through it. This phenomenon, which has been recognized for a long time and which has been applied to the prevention of explosions, is known as “quenching”. The way in which the walls of the tube act to prevent flame propagation is not well understood at present, The most direct explanation is to attach the effect to the cooling of the flame due to the proximity of the walls. However, it is though that chemical action of the wall when acting as chain breaker may also be significant. Analogously to what happened for some time with flame theory, if one considers either cooling or diffusion as the only acting effect, a “thermal” or “diffusive” theory will be obtained. Examples of thermal theories are those by Lewis-von Elbe [1] and by Kármán-Millán [18], and on diffusion theories the one by Simon-Bellos [19]. The difference between this case and the unlimited flame theory lies on the fact that both the formulation of the equation and boundary conditions and their solution are far more difficult. Hence, the solutions may only be attempted through drastic simplifications. A great number of measurements have been carried out with the purpose of determining the quenching distance in ducts of different cross-sections and the influence on it, of the mixture. For an additional study of this question as well as on the phenomena of blow-off and flash-back we refer the reader to Refs. [20] through [23]. In particular references [20] and [23] include an extensive bibliography. References [1] Lewis, B. and von Elbe, G.: Combustion, Flames and Explosions of Gases. Academic Press, New York, 1951. [2] Lewis, B, Pease, R. N. and Taylor, H,S.: Combustion Processes. Vol. II of High Speed Aerodynamics and Jet Propulsion, Princeton University Press, 1956.
228 CHAPTER 8. IGNITION, FLAMMABILITY AND QUENCHING [3] Lewis, B. and von Elbe, G.: Fundamental Principles of Flammability and Ignition. Selected Combustion Problems, Vol. II, AGARD, 1956, pp. 63-72. [4] Fenn, J. B.: Lean Inflammability Limit and Minimum Spark Ignition Energy. Industrial and Engineering Chemistry. Vol. Dec., 1951, pp. 2865-68. [5] Swott, C. C.: Spark Ignition of Flowing Gases. IV. Theory of Ignition in Nonturbulent and Turbulent Flow Using Long Duration Discharges. NACA Research Memorandum No. R M E54F29a, 1954. [6] Wigs. L. D.: The Ignition of Flowing Gases. Selected Combustion Problems, Vol. II, AGARD, 1956, pp. 73-82. [7] Spalding, D. B.: Some Fundamentals of Combustion. Butterworths Scientific Publications, 1955. [8] Olsen, E. L., Gayhart, E. L. and Edmoneon, R. B.: Propagation of Incipient Spark–Ignited Flames in Hydrogen–Air and Propane–Air Mixtures. Fourth Symposium (International) on Combustion, Williams and Wilkins Co., Baltimore, 1953, pp. 144-148. [9] Coward, H. F. and Jons, G. W.: Limits of Flammability of Gases and Vapors. U.S. Bureau of Mines. Bull., 503, 1952. [10] Egerton, A. C.: Limits of Inflammability. Fourth Symposium (International) on Combustion, Williams and Wilkins Co., Baltimore, 1953, pp. 4-13. [11] Linnet, J. W. and Simpson, O. J. S.: Limits of Inflammability. Sixth Symposium (International) on Combustion, Reinhold Publishing Corp., New York, 1957. [12] Richardson, J. M.: The Existence and Stability of Simple One–Dimensional, Steady–State Combustion Waves. Fourth Symposium (International) on Combustion, Williams and Wilkins Co., Baltimore, 1953, pp. 182-189. [13] Layzer, D.: Journal of Chemical Physics, Vol. 22, 1954, p. 222. [14] Wehner, J. F. and Rosen, J. B.: Temperature Stability of the Laminar Combustion Wave. Combustion and Flame, Sept. 1957, pp. 339-345 . [15] Rosen, J. B.: Stability of the Ozone Flame Propagation. Sixth Symposium (International) on Combustion, Reinhold Publishing Corp., New York, 1957. [16] Streng, A. G. and Grosse, A. V.: The Ozone to Oxygen Flame. Sixth Symposium (International) on Combustion, Reinhold Publishing Corp., New York, 1957. [17] Spalding, D. B.: A Theory of Inflammability Units and Flame–Quenching . Proc. Roy, Soc. London, Ser. A, Vol. 240, No. 1220, 1957, pp. 83-100. [18] von Kármán, Th. and Millán, G.: Thermal Theory of Laminar Flame Front near a Cold Wall. Fourth Symposium (International) on Combustion, Williams and Wilkins Co., Baltimore, 1953, pp. 173-177.
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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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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
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Page 294 and 295: 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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