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

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Chapter 2 γb−1 Tu γu −γb ( γ 1) ( 1 ) u − Ti γu − γb−1 Tu γu −γ ⎡ b ( γ −1) ( γ −1 ) p− p ⎡ i + x = ⎣ p − p + ⎣ e i u Ti u ⎤ ⎦ ⎤ ⎦ (2.79) As a final step, the above result is written fully in terms of pressure using Eq. (2.62). For later use, the result is given in a more concise form: p − pf i ( p) x = p − pf( p) e i (2.80) Where ⎛γb −1⎞ ⎛γu −γ ⎞⎛ b p ⎞ f( p) = ⎜ ⎟+ ⎜ ⎟⎜ ⎟ ⎝γu −1⎠ ⎝ γu −1 ⎠⎝ pi ⎠ ( γ −1/ ) γ u u (2.81) tel-00623090, version 1 - 13 Sep 2011 Differentiation is straightforward, yielding Where '( )[ − i ( )] [ − ] 2 dx 1 − pf i '( p) pif p p pf p = + dp p − p f ( p) p pf( p) e i e i ⎛γu − γ ⎞⎛ b p ⎞ pf i '( p) = ⎜ ⎟⎜ ⎟ ⎝ γ u ⎠⎝pi ⎠ −1/ γu (2.82) (2.83) The above methodology was extended to multiple zones by Luijten et al., (2009) without considerable improvement in the results. The linear approximation, introduced by Lewis and Von Elbe, is still the most widespread analytical relation to interpret burning velocity data. Differences in laminar burning velocities between the varieties of x(p) were quantified by Luijten et al., (2009) for the example case of stoichiometric methane–air combustion, demonstrating that deviations between burning velocities from bomb data and other methods can at least partly be ascribed to the limited accuracy of the linear approximation. For the example case, differences up to 8% were found. 2.5.2.4 Constant pressure method Laminar burning velocity and Markstein length can be deduced from schlieren photographs as described by Bradley et al., (1998). For a spherically expending flame, 57
Bibliographic revision the stretched flame velocity, S n , reflecting the flame propagation speed, is derived from the flame radius versus time data as: S n dr u = (2.84) dt where r u is the radius of the flame in schlieren photographs and t is the time. S n can be directly obtained from the flame photo. For expanding spherical flame with instantaneous surface area A= 4πr u 2 , the flame stretch rate is solely due to the change in curvature with time. From Eq. (2.2) and (2.29) the stretch rate can be simplified as tel-00623090, version 1 - 13 Sep 2011 1 dA 2 dru 2 α = = = Sn (2.85) Adt r dt r u Where r u is the instantaneous radius of the flame. Asymptotic analyses of Matalon and Matkowsky, (1982) and detailed modelling 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, 0 n n b u S − S = L κ (2.86) 0 where Sn is the unstretched flame speed, and L b is the Markstein length of burned gases. From Eqs. (2.84) and (2.85), the stretched flame speed, S n , and flame stretch rate, κ, can be calculated. The unstretched flame speed is obtained as the intercept value at κ = 0, in the plot of S n against κ, and the burned gas Markstein length is the slope of S n –κ curve. Markstein length can reflect the stability of flame (Liao et al., 2004). Positive values of L b indicate that the flame speed decreases with the increase of flame stretch rate. In this case, if any kind of perturbation or small structure appears on the flame front (stretch increasing), this structure tends to be suppressed during flame propagation, and this makes the flame stability. In contrast to this, a negative value of L b means that the flame speed increases with the increase of flame stretch rate. In this case, if any kinds of protuberances appear at the flame front, the flame speed in the flame protruding position will be increased, and this increases the instability of the flame. 58
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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
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 and 50: Bibliographic revision 2 ( rsr ) 2
Page 51 and 52: Bibliographic revision This evoluti
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: Bibliographic revision where the su
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
Page 103 and 104: Chapter 4 5 ms 10 ms 15 ms 20 ms 25
Page 105 and 106: Chapter 4 behaviour of the curves r
Page 107 and 108: Chapter 4 1.50 Sn (m/s) 1.25 1.00 0
Page 109 and 110: 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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