TABLE OF CONTENTS In Section 5.6, Lagrangian micromixing models based on 'mixing environments' were introduced. In terms of the joint composition PDF, nearly all such models can be expressed mathematically as a multi-peak delta function. The principal advantage of this type of model is the fact that the chemical source term is closed, and thus it is not necessary to integrate with respect to the joint composition PDF in order to evaluate the Reynolds-averaged chemical source term. [137] However, the multi-peak form of the presumed PDF requires particular attention to the definition of the micromixing terms when the model is extended to inhomogeneous flow (Fox 1998), or to homogeneous flows with uniform mean scalar gradients. [138] In this section, we first develop the general formulation for multi-environment presumed PDF models in homogeneous flows, and then extend the model to inhomogeneous flows for the particular cases with two and four mixing environments. Tables summarizing all such models that have appeared in the literature are given at the end of this section.
In a multi-environment micromixing model, the presumed composition PDF has the following form:
| (5.341) |  |
where N e is the number of environments, p n( x, t) is the probability [139] of environment n, and ? ? ? n ( x, t) is the mean [140] composition vector in environment n. For a homogeneous flow in the absence of mean scalar gradients, the...
