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

Appendix C -Rivère model
4 λ Tw
δ = (C.6)
3 K T
g
The temperature profile of the thermal boundary layer is linearly fitted. The integration
of the wall heat flux Q w based on the elementary heat flux dQ shows a temperature
difference between the gas and wall ΔT=T g -T w :
⎛ η χ λ ⎞ ⎛ aϖ
Tg
15 ⎛ αΔT
⎞⎞
Qw
= ρg. a⎜ + − ⎟. + U
3/2
0
1+ ΔT
⎜ ϖ ϖ T ϖ T ⎟ ⎜
g
4π
32 ⎜ 4ϖT
⎟⎟
g
⎝
g
⎝
⎠ ⎝
⎠⎠
(C.7)
With a, α and ω calcul parameters.
tel-00623090, version 1 - 13 Sep 2011
A heat transfer coefficient is then defined as Q w =h.ΔT. As the term U 0 is representative
of the overall movement, is negligible compared with the term related to the thermal
agitation in T g , the expression simplifies as follows:
3
2
2 ⎛ R ⎞ ⎛ χ λ ⎞
h = ρg.
Tg
η
π
⎜ M
⎟ + −
(C.8)
⎝ ⎠ ⎜ T T ⎟
⎝ ⎠
Where ρ g , T g and M are, respectively, the density, the temperature and molar mass of
the gases, T w the wall temperature, χ and λ material constants and η a function of the
aerodynamic conditions.
Integration constants evaluation
w
w
χ , λ and η are determined based on engine experimental results for several running
conditions and combustion modes: spark ignition, compression ignition, controlled
auto-ignition, etc.
χ and λ are constants wall related, hence identical for every engine experiments. On
the other hand, η is flow dependent and follows a variation law under the conditions of
operation. After the engine experiments, the evolution of η is linear in function of
engine regime, e.g. mean piston speed:
η
engine
= a+ b < Vpiston
> (C.9)
With a=7×10 -4 , b=7×10 -5 (m/s) -1 , the mean piston speed around 2-10 m/s.
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