Modeling of scalar dissipation in partially premixed turbulent flames

The question of the closure of scalar dissipation terms for both passive and reactive scalars is addressed. In a first step of the analysis, modeled transport equations for the mean reactive scalar dissipation are reviewed in the two limiting cases of (i) the flamelet regime and (ii) the thickened flame regime of turbulent premixed combustion. The corresponding asymptotic algebraic closures obtained for large values of the turbulent Reynolds ReTReT, i.e., eddy breakup and linear relaxation model for scalar fluctuations decay, are recovered. These two limiting closures are then used to build a general algebraic closure of the mean dissipation of reactive scalar fluctuations. The resulting expression is applicable to modeling turbulent premixed combustion whatever the combustion regime. In a second step, the same strategy leads to the development of an algebraic closure for partially premixed situations, a situation requiring the use of at least two variables. In this process, a relationship between reactive, passive, and cross-scalar dissipations is derived. This general result is then simplified to elaborate new closed expressions of mean dissipation terms. There are applicable to a wide range of conditions, from premixed to partially premixed situations and from the flamelet to the thickened flame regime.