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

Numerical simulation of a syngas-fuelled engine
The rate of internal energy change for a mixture is given by:
dh dm dT
= u + mc
dθ dθ dθ
∑ ∑ (6.15)
i
i
i i vi
i
where m i is the mass of species i (O 2 , N 2 , CO 2 ,H 2 O, N, NO, OH, H, O, etc.) and c v is
the specific heat under constant volume (a function of temperature only c v =du/dT), with
⎡⎛
n 1 ⎞ ⎤
cvi( T)
= Rsi ⎢⎜
∑ ai,
nT −
⎟−1⎥
⎣⎝
n ⎠ ⎦
(6.16)
with the values of m i , dm i , T, dT found from the corresponding first-law analysis of the
cylinder contents. The rate of entropy change is:
tel-00623090, version 1 - 13 Sep 2011
dS dm
m dT V dp
= + −
dθ dθ T dθ T dθ
i
i
∑ Si ( T,
xip)
∑ cpi
(6.17)
i
i
With
'
⎛xi
p ⎞
Si ( T, xip) = Si ( T, pi)
−Rsi
ln⎜ ⎟
(6.18)
⎝ pi
⎠
'
and S ( T,
p )
i
i
the standard state entropy of species i, which is a function of temperature
only, with x i the molar fraction of species i in the mixture (Ferguson, 1986; Heywood,
1988), given by the following property relation:
5 n−1
⎡
'
⎛ T ⎞ ⎤
si( T, pi) = Rsi ⎢ai1lnT ⎜ ∑ ai,
n ⎟+
ai7⎥
⎣ ⎝ n=
2 n −1⎠
⎦
(6.19)
For the Gibbs free enthalpy or energy:
dG dm
= ∑ (6.20)
i
i
dθ
i dθ
μ
where μ i =g i (T,p i ) is the chemical potential of species i in the mixture, with
gi( T, pi) = gi( T, xip) = hi( T) −Tsi( T, xip)
⎡
⎛xi
p ⎞⎤
= hi( T) −T ⎢si( T, pi) −Rsi
ln⎜
⎟⎥
⎢⎣
⎝ pi
⎠⎥⎦
(6.21)
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