Untitled - Aerobib - Universidad Politécnica de Madrid

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1.1. INTRODUCTION 3 GAS ε/k (K) σ (Ȧ) b 0 (cm 3 /mol) Air 99.2 3.522 55.11 N 2 95.05 3.698 63.78 O 2 117.5 3.580 57.75 CO 100.2 3.763 67.22 CO 2 189 4.468 113.90 NO 131 3.170 40.00 N 2 O 189 4.590 122.00 CH 4 148.2 3.817 70.16 CH-CH 185 4.221 94.86 CH 2=CH 2 199.2 4.523 116.70 C 2H 6 243 3.954 78.00 C 3H 8 242 5.367 226.00 n-C 4 H 10 297 4.971 155.00 i-C 4 H 10 313 5.341 192.18 n-C 5 H 12 345 5.769 242.19 n-C 6 H 14 413 5.909 260.25 n-C 7 H 16 282 8.880 884.00 n-C 8 H 18 320 7.451 521.79 n-C 9H 20 240 8.448 760.53 Cyclohexane 324 6.093 285.33 C 6H 6 440 5.270 84.62 CH 3 OH 507 3.585 58.12 C 2 H 5 OH 391 4.455 111.53 CH 3 Cl 855 4.455 48.49 CH 2 Cl 2 406 4.759 135.96 CHCl 3 327 5.430 201.95 C 2 N 2 339 4.380 105.99 COS 335 4.130 88.86 CS 2 488 4.438 110.26 Table 1.1: Force constants for the Lennard-Jones potential. and T ∗ = kT ε . (1.6) Table 1.1, taken from Ref. [3], gives the values of b 0 and ε/k for several gases. These values have been determined from experimentation. Fig. 1.2 gives the values for B ∗ (T ∗ ) taken from the same reference. 3 To get an idea on the order of magnitude of coefficients B (T ) and C (T ), and, consequently, on the deviations that are to be expected in the actual behavior of gases respect to their ideal model, Figs. 1.3 and 1.4 give the values of these coefficients for some gases. As can be observed B (T ) is first negative and then becomes positive, tending slowly to zero for T → ∞. Such behavior of B (T ) is common for all gases. It is seen, for example, that in nitrogen for p = 25 kg/cm 2 and T = 800 K, B (T ) = 1 cm 3 /gr. Therefore, the error made 3 Ref. [3] also includes a table for the calculation of C (T ).
4 CHAPTER 1. THERMOCHEMISTRY with the assumption that in such a state nitrogen behaves as an ideal gas is one per cent. Therefore under the conditions of the present study it is justified to consider the gases as ideal. Hereinafter, unless the contrary is made explicit, such an assumption is adopted. 0.5 0.0 T * = 100ξ T * = 10ξ −0.5 T * = ξ B * (T * ) −1.0 −1.5 −2.0 −2.5 0.5 1.0 1.5 2.0 2.5 3.0 3.5 4.0 4.5 5.0 ξ Figure 1.2: B ∗ as a function of T ∗ . Note the two changes of scale. 8 H 2 C 7 H 16 4 O 2 N 2 B(T) (cm 3 /gr) 0 −4 CH 4 CO 2 −8 −12 0 400 800 1200 1600 2000 2400 2800 3200 3600 T(K) Figure 1.3: Virial coefficient B (cm 3 /gr) , as function of temperature for several gases.
Page 2 and 3: Aerothermochemistry Gregorio Millá
Page 4 and 5: PRESENTACIÓN Amable Liñán Es un
Page 6 and 7: que no cambiaron los resultados, y
Page 8: INSTITUTO NACIONAL DE TÉCNICA AERO
Page 11 and 12: aim to become acquainted with Aerot
Page 13 and 14: Tarifa, Manuel de Sendagorta and Ig
Page 15 and 16: 3.4 Energy equation . . . . . . . .
Page 17 and 18: 8.4 Quenching . . . . . . . . . . .
Page 20 and 21: Chapter 1 Thermochemistry 1.1 Intro
Page 24 and 25: 1.1. INTRODUCTION 5 14 12 10 N 2 CH
Page 26 and 27: 1.2. THERMODYNAMIC FUNCTIONS OF AN
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Page 30 and 31: 1.3. MIXTURE OF GASES 11 Helmholtz
Page 32 and 33: 1.3. MIXTURE OF GASES 13 is the par
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Page 36 and 37: 1.4. CALCULATION OF THE THERMODYNAM
Page 38 and 39: 1.4. CALCULATION OF THE THERMODYNAM
Page 40 and 41: 1.5. CHEMICAL REACTIONS IN A MIXTUR
Page 42 and 43: 1.6. CHEMICAL EQUILIBRIUM 23 Since
Page 44 and 45: ∆G 0 j = ∑ i 1.7. CASE OF A MIX
Page 46 and 47: 1.7. CASE OF A MIXTURE OF IDEAL GAS
Page 48 and 49: 1.8. CHEMICAL KINETICS 29 1.8 Chemi
Page 50 and 51: 1.8. CHEMICAL KINETICS 31 Mechanics
Page 52 and 53: 1.8. CHEMICAL KINETICS 33 This stru
Page 54 and 55: 1.8. CHEMICAL KINETICS 35 [3] Hirsc
Page 56 and 57: Chapter 2 Transport phenomena in ga
Page 58 and 59: 2.2. DIFFUSION 39 Hereinafter, nota
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Page 66 and 67: 2.2. DIFFUSION 47 coefficients. 14
Page 68 and 69: 2.3. VISCOSITIES 49 2.3 Viscosities
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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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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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