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

Bibliographic revision
burning velocity at reference conditions, S u0 (P 0 ,T 0 ). The reference temperature, T 0 ,
must be set equal to 291 K and the reference pressure, P 0 , is 1 atm.
⎛T
⎞ ⎡ ⎛ P ⎞⎤
⎜ ⎟ 1 β ln⎜ ⎟⎥
⎝ ⎠ ⎢⎣
⎝ ⎠⎥⎦
Su
= Su
⎢ +
0
T
0 P
0
Metghalchi and Keck (1980) found that
α
α
⎛T
⎞ ⎛ P ⎞
= ⎜ ⎟ ⎜ ⎟
⎝ ⎠ ⎝ ⎠
Su
Su0
T
0 P
0
β
(2.88)
(2.89)
Where, T 0 and P 0 , are the reference temperature and pressure, respectively. The
influence of the equivalence ratio is incorporated through the temperature and pressure
exponents, α and β, as a linear function and through the reference burning velocity S u0
as a square function.
tel-00623090, version 1 - 13 Sep 2011
Only the last two correlations are general, and the latter has been used extensively,
namely by: Bradley et al., (1998); Gu et al., (2000); Dahoe and Goey, (2003); Liao et
al., (2004), due to its simplicity and will also be used in this in work to correlate the
laminar burning velocity obtained the constant volume method.
The determination of the coefficients of Eq. (2.89) is made as follows. Applying Neper
logarithmic, we have:
⎛T
⎞ ⎛ P ⎞
Ln Su
= LnSu
+ αLn⎜ ⎟+
βLn⎜ ⎟
0
T P
⎝ 0 ⎠ ⎝ 0 ⎠
(2.90)
Rewriting Eq. (2.90) into the form of linear equation system AX=b, the coefficients
matrix A is defined to be rectangular with 3 columns and n lines as follows:
( T T )
( )
( P P )
( )
⎡1 ln
1 0
ln
1 0
⎤
⎢
⎥
⎢1 ln T2 T0 ln P1 P0
⎥
⎢
⎥
A = ⎢
. . . ⎥
⎢. . . ⎥
⎢
⎥
⎢1 ln( Tn
T0)
ln( Pn
P0)
⎣
⎥
⎦
(2.91)
The vector b is represented by:
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