Etude de la combustion de gaz de synthèse issus d'un processus de ...
Etude de la combustion de gaz de synthèse issus d'un processus de ... Etude de la combustion de gaz de synthèse issus d'un processus de ...
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
- 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
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- 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
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Bibliographic revision<br />
the stretched f<strong>la</strong>me velocity, S n , reflecting the f<strong>la</strong>me propagation speed, is <strong>de</strong>rived from<br />
the f<strong>la</strong>me radius versus time data as:<br />
S<br />
n<br />
dr<br />
u<br />
= (2.84)<br />
dt<br />
where r u is the radius of the f<strong>la</strong>me in schlieren photographs and t is the time. S n can be<br />
directly obtained from the f<strong>la</strong>me photo.<br />
For expanding spherical f<strong>la</strong>me with instantaneous surface area A= 4πr u 2 , the f<strong>la</strong>me<br />
stretch rate is solely due to the change in curvature with time. From Eq. (2.2) and<br />
(2.29) the stretch rate can be simplified as<br />
tel-00623090, version 1 - 13 Sep 2011<br />
1 dA 2 dru<br />
2<br />
α = = = Sn<br />
(2.85)<br />
Adt r dt r<br />
u<br />
Where r u is the instantaneous radius of the f<strong>la</strong>me. Asymptotic analyses of Matalon and<br />
Matkowsky, (1982) and <strong>de</strong>tailed mo<strong>de</strong>lling of Warnatz and Peters, (1984) show a linear<br />
re<strong>la</strong>tionship between stretch rate and burning velocity in the low-stretch regime. Thus, it<br />
is assumed that,<br />
0<br />
n n b<br />
u<br />
S − S = L κ<br />
(2.86)<br />
0<br />
where Sn<br />
is the unstretched f<strong>la</strong>me speed, and L b is the Markstein length of burned<br />
gases. From Eqs. (2.84) and (2.85), the stretched f<strong>la</strong>me speed, S n , and f<strong>la</strong>me stretch<br />
rate, κ, can be calcu<strong>la</strong>ted.<br />
The unstretched f<strong>la</strong>me speed is obtained as the intercept value at κ = 0, in the plot of<br />
S n against κ, and the burned gas Markstein length is the slope of S n –κ curve. Markstein<br />
length can reflect the stability of f<strong>la</strong>me (Liao et al., 2004). Positive values of L b indicate<br />
that the f<strong>la</strong>me speed <strong>de</strong>creases with the increase of f<strong>la</strong>me stretch rate. In this case, if<br />
any kind of perturbation or small structure appears on the f<strong>la</strong>me front (stretch<br />
increasing), this structure tends to be suppressed during f<strong>la</strong>me propagation, and this<br />
makes the f<strong>la</strong>me stability. In contrast to this, a negative value of L b means that the<br />
f<strong>la</strong>me speed increases with the increase of f<strong>la</strong>me stretch rate. In this case, if any kinds<br />
of protuberances appear at the f<strong>la</strong>me front, the f<strong>la</strong>me speed in the f<strong>la</strong>me protruding<br />
position will be increased, and this increases the instability of the f<strong>la</strong>me.<br />
58
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