Equilibrium-chemistry limit means

In a CFD calculation, one is usually interested in computing only the reacting-scalar means and (sometimes) the covariances. For binary mixing in the equilibrium-chemistry limit, these quantities are computed from (5.154) and (5.155), which contain the mixture-fraction PDF. However, since the presumed PDF is uniquely determined from the mixture-fraction mean and variance, (5.154) and (5.155) define mappings (or functions) from (I>- space ... 

In the equilibrium-chemistry limit, the turbulent-reacting-flow problem thus reduces to solving the Reynolds-averaged transport equations for the mixture-fraction mean and variance. Furthermore, if the mixture-fraction field is found from LES, the same chemical lookup tables can be employed to find the SGS reacting-scalar means and covariances simply by setting x equal to the resolved-scale mixture fraction and x2 equal to the SGS mixture-fraction variance.88... 

An ad hoc extension of the method presented above can be formulated for complex chemistry written in terms of yip and . In the absence of chemical reactions, y>rp = 0. Thus, if a second limiting case can be identified, interpolation parameters can be defined to be consistent with the unconditional means. In combusting flows, the obvious second limiting case is the equilibrium-chemistry limit where yip = y>eq( ) (see Section 5.4). The components of the conditional reacting-progress vector can then be approximated by (no summation is implied on a)... 

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