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

Chapter 6
centered at the spark plug (Verhelst and Sheppard, 2009). The multi-zone approach is
retained throughout the expansion phase, i.e. from the end of combustion until the
EVO.
6.1.1 Conservation and state equations
The governing equations are presented for the combustion process. During
compression and expansion the same equations are retained, with adaptations
regarding the number of zones included.
Assuming that ‘n’ is the number of the current burned zones, with the latest-generated
burned zone indicated by subscript ‘n’, the energy conservation equation is applied for
the unburned zone, the n-1 already burned zones and the total cylinder charge,
yielding, respectively.
tel-00623090, version 1 - 13 Sep 2011
dQu dUu dVu dmb
= + p + hu
(6.1)
dθ dθ dθ dθ
dQbi ,
dUbi ,
dVbi
,
= + p ( i = 1,..., n−1)
(6.2)
dθ dθ dθ
dQ dU dV
= + p
(6.3)
dθ dθ dθ
Zero blow-by rate is assumed during the whole closed cycle period. The instantaneous
cylinder volume is equal to the sum of the volumes of the unburned and burned zones,
resulting in the following relation after differentiating with respect to crank angle:
dV dV dV
dθ dθ dθ
n
= ∑
bi ,
+
u
(6.4)
i = 1
where V is the instantaneous cylinder volume, calculated from the engine geometric
characteristics as a function of crank angle:
2
( sin )
⎧ rc
−1 ⎡ 1
⎤⎫
V = VTDC
⎨1+ 1− cosθ + 1− 1−ϕ θ
2
⎢
⎬
ϕ
⎥
⎩ ⎣
⎦⎭
(6.5)
with ϕ being the crank radius to piston rod length ratio. The rate of change of the
instantaneous cylinder volume against crank angle is
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