Etude de la combustion de gaz de synthèse issus d'un processus de ...

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Appendix C -Rivère model Appendix C – RIVÈRE MODEL The heat flux received by the wall is modelled using an original heat conduction approach in the fluid-wall boundary based on the kinetic theory of gases developed by Rivère, (2005), from Renault. The heat flux appears as a statistic result of the gas molecules over the wall. Random reflection is assumed in direction, not in module. Each gas molecule yields kinetic energy ΔE c when collides with the wall, characterized by the kinetic energy fraction K: ' 2 '2 ' 1 2 '2 Ec − Ec V −V Δ Ec = Ec − Ec = mg cos( θ )( V − V ) K = = 2 (C.1) 2 E V With m g the molecular mass, θ the impact angle, V and V’ the impact and reflection speeds (Figure C.1). c tel-00623090, version 1 - 13 Sep 2011 Figure C.1 – Fraction of energy received by the wall. In order to know the kinetic energy fraction K yielded by one molecule of gas during rebound, the wall is modelled by a linear chain of atoms vibrating by translation along x only. The calculus shows that n=2 atoms are enough to take into account the phenomenon (Figure C.2). The cases of harmonic and non-harmonic systems are considered. Figure C.2 – Molecules translation movement. As a result of this calculation, the transfer coefficient K is obtained with error of about 2%. This coefficient is dependent of the gas temperature, which in turns determines the thickness of the thermal boundary layer. χ λ K = η + − T T (C.2) g g With η,λ, and χ the integration constants to be determined using experimental results. 220
Appendix C -Rivère model Heat flux The gases, with a mean speed U 0 along X, are supposed to follow the speed distribution of Maxwell-Boltzmann. The particles volume density dn g , which the thermal stirring speed is in the range [V; V+dV] is then: 3 2 2 2 −ag ( V−U0 ) 4π ⎛ag ⎞ dng = ng ⎜ ⎟ V e dV ⎝ π ⎠ (C.3) With a = M 2RT , M is the gas molar mass and R the ideal gases constant. The g number of particles dN g with impact speed V on a surface dS during dt is: tel-00623090, version 1 - 13 Sep 2011 dN g 1 = sin θ cos θ . V . dt . dng . dS . dθ (C.4) 2 The elementary heat flux is then: 2 3 ⎛ag ⎞ 5 −ag ( V−U0 ) dQ =Δ EcdNg = ρg sin( θ)cos ( θ). ⎜ ⎟π. K. V e dV. dt. dS. dθ (C.5) ⎝ π ⎠ Heat flux integration Back to the heat flux actually received by the wall, the elementary flux dQ must be integrated on the thermal boundary layer thickness δ (Figure C.3) . This thickness is discretized with a step equal to the mean gas molecules path λ . T 2 T 1 T g T k-1 Wall Q k Q 1 Gas δ T W λ Figure C.3 – Thermal boundary layer. The thickness can be estimated based on the mean free path λ : 221
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THÈSE Pour l’obtention du Grade
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Acknowledgements Acknowledgements T
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Résumé __________________________
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Nomenclature Nomenclature Roman tel
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Nomenclature Subscripts tel-0062309
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Contents tel-00623090, version 1 -
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Contents 6.4. SYNGAS FUELLED-ENGINE
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Introduction CHAPTER 1 INTRODUCTION
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Introduction proves to have higher
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Introduction Chapter 3 - Experiment
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Bibliographic revision CHAPTER 2 BI
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Bibliographic revision point today
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Bibliographic revision - Boudouard
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Bibliographic revision Table 2.1 -
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Bibliographic revision Biomass Dryi
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Bibliographic revision Circulating
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Bibliographic revision or eliminate
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Bibliographic revision established
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Bibliographic revision Hydrogen Hyd
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Bibliographic revision of low moist
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Bibliographic revision scrubbing an
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Bibliographic revision suggests tha
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Bibliographic revision 1 d( δ A) 1
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Bibliographic revision Since n is
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Bibliographic revision 2 ( rsr ) 2
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Bibliographic revision This evoluti
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Bibliographic revision The burning
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Bibliographic revision δVG = − a
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Bibliographic revision 2 1 − −
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Bibliographic revision where the su
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Bibliographic revision the stretche
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Bibliographic revision burning velo
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Experimental set ups and diagnostic
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Chapter 4 CHAPTER 4 EXPERIMENTAL AN
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Chapter 4 4.1 Laminar burning veloc
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Chapter 4 4.1.1.1 Flame morphology
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Chapter 4 P i = 1.0 bar, Ti = 293 K
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Chapter 4 Figure 4.5 shows schliere
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Chapter 4 P i = 2.0 bar, T i = 293
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Chapter 4 Sn (m/s) 3.0 2.5 2.0 1.5
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Chapter 4 5 ms 10 ms 15 ms 20 ms 25
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Chapter 4 behaviour of the curves r
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Chapter 4 1.50 Sn (m/s) 1.25 1.00 0
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Chapter 4 0.5 0.4 φ =1.0 Su (m/s)
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Chapter 4 variation of the normaliz
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Chapter 4 4.1.1.6 Comparison with o
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Chapter 4 The values of laminar bur
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Chapter 4 Pressure (bar) 7 6 5 4 3
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Chapter 4 0.5 0.4 φ=1.2 Su (m/s) 0
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Chapter 4 0.3 φ=0.8 Su (m/s) 0.2 0
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Chapter 4 a minimum pressure to exp
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Chapter 4 Notice the similar behavi
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Chapter 4 A very good agreement bet
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Chapter 4 ( ) Q = h T − T (4.21)
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Chapter 4 tel-00623090, version 1 -
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Chapter 4 are tested and discussed.
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Chapter 4 7 500 Pressure (bar) 6 5
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Chapter 4 Pressure (bar) 7 6 5 4 3
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Chapter 4 4.2.3.4 Quenching distanc
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Chapter 4 10000 Quenching distance
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Chapter 5 CHAPTER 5 EXPERIMENTAL ST
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Chapter 5 30 10 25 8 Pressure (bar)
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Chapter 5 30 Piston position (mm) 2
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Chapter 5 5.1.1.4 In-cylinder press
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Chapter 5 estimation of various par
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Chapter 5 TDC 1.25 ms 2.5 ms 3.75 m
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Chapter 5 Piston position (mm) 500
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Chapter 5 tel-00623090, version 1 -
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Chapter 5 From figure 5.15 is possi
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Chapter 5 From figure 5.16 is obser
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Chapter 5 80 Pressure (bar) 70 60 5
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Chapter 5 80 10 Pmax (bar) 70 60 50
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Chapter 5 -5.0 ms -3.75 ms -2.5 ms
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Chapter 5 observation emphasis the
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Chapter 6 CHAPTER 6 NUMERICAL SIMUL
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Chapter 6 centered at the spark plu
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Page 199 and 200: Conclusions CHAPTER 7 CONCLUSIONS 7
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Page 221 and 222: Appendix A - Overdetermined linear
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Page 229 and 230: Appendix C -Rivère model The work
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