Mixture-fraction vector filtered

The procedure followed above can be used to develop a multi-environment conditional LES model starting from (5.396). In this case, all terms in (5.399) will be conditioned on the filtered velocity and filtered compositions,166 in addition to the residual mixture-fraction vector = - . In the case of a one-component mixture fraction, the latter can be modeled by a presumed beta PDF with mean f and variance (f,2>. LES transport equations must then be added to solve for the mixture-fraction mean and variance. Despite this added complication, all model terms carry over from the original model. The only remaining difficulty is to extend (5.399) to cover inhomogeneous flows.167 As with the conditional-moment closure discussed in Section 5.8 (see (5.316) on p. 215), this extension will be non-trivial, and thus is not attempted here. 

In this case, the filtered compositions are partitioned into the filtered mixture-fraction vector and the filtered reaction-progress variables. 

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