Multi-environment models

The basis idea behind multi-environment models is that the mixture fraction at any location in the reactor can be approximated by a distribution function in the form of a sum of delta functions as follows ... 

The multi-environment model for the joint PDF generalizes Eq. (33) by writing... 

The multi-environment model for turbulent transport of the bi-variate moments in the absence of moment source terms has the form... 

Note that the correction terms are proportional to fT and result from turbulent velocity fluctuations (represented by a gradient-diffusion model). For the multi-environment model the composition vector is defined by... 

As shown in Section 5.10, it is possible to reformulate multi-environment models in terms of a multi-peak presumed joint PDF. In this case, it is possible to specify the... 

A more sophisticated scalar-flux model could be employed in place of the gradient-diffusion model. However, given the degree of approximation inherent in the multi-environment model, it is probably unwarranted. 

As noted earlier, it is possible to use JVe < Ns by choosing a linearly independent set of higher-order moments. For example, the multi-environment models discussed in Section 5.10 use jVe = 2-4. 

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