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

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Chapter 2 taken into account here. In this relation the proportionality of the burning velocity to the flame stretch is represented by a parameter that was considered as a characteristic length scale of the flame. This parameter is now generally known as the Markstein length, which denotes the sensitivity of a flame to flame stretch. Asymptotic analyses of Clavin and Williams, (1982) and Matalon and Matkowsky, (1982) and detailed modeling of Warnatz and Peters, (1984) show a linear relationship between stretch rate and burning velocity in the low-stretch regime. Thus, it is assumed that, S − S = L κ (2.33) 0 n n b Where gases. 0 S n is the unstretched flame speed and L b is the Markstein length of burned tel-00623090, version 1 - 13 Sep 2011 When the observation is limited to the initial part of the flame expansion where the pressure does not vary yet, then a simple relationship links the unstretched flame speed to the unstretched burning velocity. S S 0 n 0 u ρ u = = (2.34) ρ b σ Where σ is the expansion factor and ρ u and ρ b are, respectively, the unburned and burned densities. The same behavior of the unstretched burning velocity regarding the stretch can be observed (Lamoureux et al., 2003): S − S = L κ (2.35) 0 u u u where L u represents the unburned Markstein length, which is obtained dividing the burned Markstein length by the expansion factor. The normalization of the laminar burning velocity by the unstretched one introduces two numbers which characterize the stretch that is applied to the flame, the Karlovitz number (Ka), and its response to it, the Markstein Number (Ma): S MaKa S = − (2.36) u 1 0 u δ Ka = κ (2.37) S 0 u L u Ma = (2.38) δ where δ is the flame thickness defined, in this work, using the thermal diffusivity, α: α δ = (2.39) 0 S u 47
Bibliographic revision This evolution of the laminar flame velocity with the stretch rate was verified by Aung et al., (1997) for moderate stretch rate. As one can see, different definitions of a characteristic flame thickness lead to different Karlovitz and Markstein numbers. Bradley et al., (1996) use the kinematic viscosity of the unburned mixture to derive the flame thickness while Aung et al., (1997) use the mass diffusivity of the fuel in the unburned gas. However, this effect disappears in Eq. (2.36) since the flame thickness cancels out. tel-00623090, version 1 - 13 Sep 2011 Clavin and Joulin, (1989) proposed a phenomenological law to take the effects of curvature and strain in flame stretch into account separately, thereby introducing a Markstein length for the curvature part of the flame and another one for the flow straining through the flame. This separation is used by several workers as Bradley et al., (1996) or Gu et al., (2000). However, Groot et al., (2002) investigated theoretically these separate contributions demonstrating that the Markstein number for curvature and the combined one for both curvature and strain are unique. However, it is not possible to introduce a separate and unique Markstein number for the flow straining that can be used to describe its influence in different combustion situations. Therefore, the modification of the burning velocity is characterized by the total stretch rate, and it is impossible to introduce the separate contributions into an arbitrary combustion situation. A new methodology based on the resolution of Clavin’s equation, linking the flame speed and the stretch linearly, was recently proposed by Tahtouh et al. (2009). This methodology is based on the following. Combining Eqs. 2.33-2.29 leads to: dr dt 0 dr = Sn − 2Lb (2.40) rdt Which exact solution, allows avoiding noise generation due to the differentiation process. The function that solves Eq. (2.40) is: rt () = 2 LW( Z) (2.41) b 0 With W the Lambert function and: 0 Sn t+ C1 2Lb e Z = (2.42) 2L b 48
Page 1 and 2: THÈSE Pour l’obtention du Grade
Page 3 and 4: Acknowledgements Acknowledgements T
Page 5 and 6: Résumé __________________________
Page 7 and 8: Nomenclature Nomenclature Roman tel
Page 9 and 10: Nomenclature Subscripts tel-0062309
Page 11 and 12: Contents tel-00623090, version 1 -
Page 13 and 14: Contents 6.4. SYNGAS FUELLED-ENGINE
Page 15 and 16: Introduction CHAPTER 1 INTRODUCTION
Page 17 and 18: Introduction proves to have higher
Page 19 and 20: Introduction Chapter 3 - Experiment
Page 21 and 22: Bibliographic revision CHAPTER 2 BI
Page 23 and 24: Bibliographic revision point today
Page 25 and 26: Bibliographic revision - Boudouard
Page 27 and 28: Bibliographic revision Table 2.1 -
Page 29 and 30: Bibliographic revision Biomass Dryi
Page 31 and 32: Bibliographic revision Circulating
Page 33 and 34: Bibliographic revision or eliminate
Page 35 and 36: Bibliographic revision established
Page 37 and 38: Bibliographic revision Hydrogen Hyd
Page 39 and 40: Bibliographic revision of low moist
Page 41 and 42: Bibliographic revision scrubbing an
Page 43 and 44: Bibliographic revision suggests tha
Page 45 and 46: Bibliographic revision 1 d( δ A) 1
Page 47 and 48: Bibliographic revision Since n is
Page 49: Bibliographic revision 2 ( rsr ) 2
Page 53 and 54: Bibliographic revision The burning
Page 55 and 56: Bibliographic revision δVG = − a
Page 57 and 58: Bibliographic revision 2 1 − −
Page 59 and 60: Bibliographic revision where the su
Page 61 and 62: Bibliographic revision the stretche
Page 63 and 64: Bibliographic revision burning velo
Page 65 and 66: Experimental set ups and diagnostic
Page 89 and 90: Chapter 4 CHAPTER 4 EXPERIMENTAL AN
Page 91 and 92: Chapter 4 4.1 Laminar burning veloc
Page 93 and 94: Chapter 4 4.1.1.1 Flame morphology
Page 95 and 96: Chapter 4 P i = 1.0 bar, Ti = 293 K
Page 97 and 98: Chapter 4 Figure 4.5 shows schliere
Page 99 and 100: Chapter 4 P i = 2.0 bar, T i = 293
Page 101 and 102:
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 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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Chapter 6 H 2 O, (3) N 2 , (4) O 2
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Chapter 6 For all the above express
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Chapter 6 motions within the cylind
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Chapter 6 Heat transfer Wei et al.,
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Chapter 6 The calibration coefficie
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Chapter 6 6.3.2.2 In-cylinder volum
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Chapter 6 40 Experimental 30 Numeri
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Chapter 6 80 70 60 Numerical Experi
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Chapter 6 downdraft syngas than for
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Chapter 6 80 23º BTDC 60 29.5º BT
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Chapter 6 with experimental results
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Conclusions CHAPTER 7 CONCLUSIONS 7
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Conclusions radius and time for syn
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Conclusions conditions, therefore s
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Conclusions tel-00623090, version 1
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References References tel-00623090,
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References tel-00623090, version 1
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Appendix A - Overdetermined linear
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Appendix A - Overdetermined linear
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Appendix B- Syngas-air mixtures pro
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Appendix C -Rivère model Heat flux
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Appendix C -Rivère model The work
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tel-00623090, version 1 - 13 Sep 20
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