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

Chapter 4
( )
Q = h T − T
(4.21)
c g w
with T g and T w , respectively, the temperature of the gases and wall and, h, the
convective heat transfer coefficient. T w is considered constant as it varies less than 10
K during combustion as reported by Boust, (2006). T g is the local temperature of the
gases. The determination of the convective heat transfer coefficient is case sensitive
and several models are available in the literature [Annand (1963), Woschni (1967), or
Hohenberg (1979)]. In this code the Woschni, (1967) model, which is based on the
hypotheses of forced convection is applied and compared with the recent heat transfer
model of Rivère, (2005) based on the gases kinetic theory (see appendix C). The
Woschni (1967) heat transfer correlation is given as:
02 08 055 08
= 130 − . . − . .
hg () t B P() t T() t v()
t (4.22)
tel-00623090, version 1 - 13 Sep 2011
where B is the bore (m), P and T are the instantaneous cylinder pressure (bar) and gas
temperature (K), respectively. The instantaneous characteristic velocity, v is defined as:
⎛
VT ⎞
s r
v = ⎜2. 28Sp
+ 0. 00324 ( P −Pmot)
⎟
(4.23)
⎝
Pr
Vr
⎠
Where P mot =P r (V r /V) γ is the motored pressure. S p is mean piston speed (m/s), V s is
swept volume (m 3 ), V r , T r and P r are volume, temperature and pressure (m 3 , K, bar)
evaluated at any reference condition, such as inlet valve closure, V is instantaneous
cylinder volume (m 3 ) and γ is the specific heat ratio. The second term in the velocity
expression allows for movement of the gases as they are compressed by the
advancing flame.
In the model of Rivère, (2005) the heat transfer coefficient is obtained as follows:
3
2
2 ⎛ R ⎞ ⎛ χ λ ⎞
h = ρg.
Tg
η
π
⎜
M
⎟ + −
(4.24)
⎝ ⎠ ⎜ T T ⎟
⎝ ⎠
w
w
where ρ g , T g and M are, respectively, the density, the temperature and molar mass of
the gases. The last parenthesis in the right side of the Eq. (4.26) represents the heat
transfer coefficient that depends on the gases temperature that determines the length
of the boundary layer. χ and λ are the material constants and η a function of the
aerodynamic conditions equal to zero in the advection absence.
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