Untitled - Aerobib - Universidad Politécnica de Madrid

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5.7. TRANSITION FROM DEFLAGRATION TO DETONATION 127 O A B P P n ϕ 2 1 P v p − v p = (n−1)ϕ v p1 3 1 2 P 3 P 2 P, v (n−1)ϕ P 1 Figure 5.7: Schematic diagram of the flame propagation in a closed tube. gases after the wave, with respect to the tube, is v p1 −v p2 . The condition that the burnt gases must be at rest is v p1 − v p2 = (n − 1)ϕ, (5.53) as it can easily be verified. The velocity v a at which the flame travels along the tube is v a = nϕ, (5.54) where ϕ is the propagation velocity of the flame throughout the gases in their state after the pressure wave. Such propagation velocity differs from that corresponding to the state of the gases before the flame. This state of affairs can be maintained unchanged along the tube. For the detonation to occur it is necessary to activate the combustion, increasing the burnt mass per second. Such an increase is necessary in order to increase the intensity of the pressure jump across the pressure wave, up to the point of self-ignition of the mixture after the wave, needed to maintain the detonation. The slight compression of the mixture, produced by the compression wave, is not sufficient to increase, appreciably, the propagation velocity of the flame. Therefore, the increase of burnt mass per second must be due to other effects. The explanation can be found in the influence of the tube walls. In fact, due to friction, the distribution of velocities in the cross-section of a tube is not uniform but maximum at the axis and zero on the walls. Due to this non-uniformity of the velocity distribution, the flame front curves increasing its surface. Due to this surface increase, the burnt mass per second increases and therewith the velocity of the gases and the intensity of the pressure jump, producing an interaction of both effects such that when the tube is sufficiently long it leads to the establishment of the detonation wave. This standpoint is corroborated by the fact that for tubes with rough walls or small diameter the
128 CHAPTER 5. STRUCTURE OF THE COMBUSTION WAVES detonation is soon establish because both effects increase the influence of friction. On the other hand, if the mixture is ignited at the open end of the tube, the detonation is established with greater difficulty as the burnt gases can escape through the open end and the pressure wave that precedes the combustion wave is much weaker. In this case, a longer tube is necessary so that the pressure wave may reach the required intensity for the detonation to occur. For the case previously analyzed, A.K. Oppenhein [15] has studied the succession of intermediate states that must be produced in the transition from deflagration to detonation by acceleration of the deflagration wave up to the point where it overtakes the shock wave. He demonstrated his results by means of a hydraulic analogy. References [1] Backer, R.: Stosswelle und Detonation. Zeitschrift für Physic, Vol. 8, 1922. [2] von Kármán, Th.: Aerothermodynamics and Combustion Theory. L’Aerotecnica, Vol. XXXIII, Fasc. 1st., 1953, pp. 80-86. [3] Friedrichs, K. O.: On the Mathematical Theory of Deflagrations and Detonations. NAVORD Report 79-46, Institute for Mathematics and Mechanics, New York University, 1946. [4] Hirschfelder, J. O., Curtiss, C. F. and Campbell, D.E.: The Theory of Flames and Detonations. Fourth Symposium (International) on Combustion, Williams and Wilkins Co., Baltimore, 1953, pp. 190-211. [5] Vieille, P.: Rôle des Discontinuites dans la Propagation des Phénomènès Explosifs. Comptes Rendus des Séances de 1’Académie des Sciences, Vol. CXXXI, 1900, p. 413. [6] Jouguet, E.: Mecanique des Explosifs, Paris, 1917, p. 325. [7] Neumann, J. von: Progress Report on the Theory of Detonation Waves. N D R C, Division B, 0 S R D, No. 549, 1942. [8] Zeldovich, Y. B.: On the Theory of Propagation of Detonation. Journal of Experimental and Theoretical Physics, Vol. 10, 1940, p. 542, Translated as NACA Technical Memorandum No. 1261, 1950. [9] Döring, W.: Annalen der Physic, Vol. 43, 1943, p. 421. [10] Zeldovich, Y. B.: Theory of Combustion and Detonation of Gases. A9-T-45, Air Documents Division, Air Material Command, U S A F .
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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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Page 108 and 109: Chapter 4 Combustion Waves 4.1 Deto
Page 110 and 111: 4.2. KINDS OF DETONATIONS AND DEFLA
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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
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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 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 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 188 and 189: 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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9.2. CONDITIONS THAT MUST BE SATISF
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9.3. NORMAL FLAME FRONT 235 9.3 Nor
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9.4. INCLINED FLAME FRONT 237 60 50
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9.5. ENTROPY JUMP ACROSS THE FLAME
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9.5. ENTROPY JUMP ACROSS THE FLAME
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9.6. VORTICITY ACROSS THE FLAME 243
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Chapter 10 Aerothermodynamic field
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10.1. INTRODUCTION 247 form numeric
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10.1. INTRODUCTION 249 ∆ P /∆ P
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10.2. TSIEN METHOD 251 As aforesaid
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10.2. TSIEN METHOD 253 1.0 λ=6.0 M
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10.3. METHOD OF FABRI-SIESTRUNCK-FO
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10.3. METHOD OF FABRI-SIESTRUNCK-FO
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10.5. CHAMBER WITH SLOWLY VARYING C
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Chapter 11 Similarity in combustion
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11.2. DIMENSIONLESS PARAMETERS OF A
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11.2. DIMENSIONLESS PARAMETERS OF A
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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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