with the boundary conditions (28), the ODE (30) can be analytically solved for mixture fraction as a function of x 。
Rich Lean Rich Lean
narrower as the mixture becomes more homogeneous。
Recently, it is proposed that the conditional dissipation rate can be determined by solving a PDF transport equation for mixture fraction [18]。 However, this method would incur additional computational cost and might not be appropriate for engine simulations。
2 2
Furthermore, according to equation (2), the functional form for scalar dissipation rate will be obtained by differentiating equation (31) with respect to x:
Hergart has proposed a new model for the conditional scalar dissipation rate applied to diesel combustion [19]。 This approach fits into a single flamelet RIF model in that the model determines an averaged scalar
dissipation rate over the whole cylinder after the end of the fuel injection。 However, this model is not suitable for
Substituting Equation (32) into Equation (2):
the flamelet combustion models with spatially resolved flamelets, for example, the Flamelet Time Scale model used here。
(Lean Rich )2
Equation (31) is used to solve for x in terms of :
Rich Lean
These boundaries in mixture vary with time and space and represent the local boundary conditions feeding an instantaneous flamelet。
In connection to the flamelet time scale combustion
The functional form of is subsequently obtained by substituting Equation (34) into Equation (33) for x and organized as:
Lean Rich
model, the flamelet equation can be understood as a result of the asymptotic expansion around the stoichiometric mixture fraction surface [17]。 In this sense, the instantaneous scalar dissipation rate should be that at stoichiometric position, namely st 。 Thus, st predicted by Equation (39) should be used as in
Equation (4) to evaluate species mass fractions。
where 0 is the maximum scalar dissipation and functionf has the form:
The turbulence and combustion models discussed above are implemented into the KIVA-3V code, as
f (;Lean,Rich) exp2 erf 1 2
modified by the University of Wisconsin Engine
Research Center [20]。 The governing equations are
It should be noted that erf-1 is the inverse error function other than reciprocal of the error function。 can thus
be related to its value at the stoichiometric condition using Equation (35):
f (; Lean , Rich )
solved by standard KIVA numerical methods including quasi second-order upwinding for convection terms, central differencing for diffusion terms, and time split scheme with inner and outer iterations for implicit terms plus pressure coupling [21]。 柴油机大涡中小火焰模型模拟英文文献和中文翻译(5):http://www.youerw.com/fanyi/lunwen_100459.html