Statistical Analysis of Cross Scalar Dissipation Rate Transport in Turbulent Partially Premixed Flames: A Direct Numerical Simulation Study

Statistically planar turbulent partially premixed flames for different initial intensities of decaying turbulence have been simulated for global equivalence ratios <????> = 0.7 and <????> = 1.0 using three-dimensional simplified chemistry based Direct Numerical Simulations (DNS). The simulation parameters are chosen such that the combustion situation belongs to the thin reaction zones regime and a random bi-modal distribution of equivalence ratio ?? is introduced in the unburned gas ahead of the flame to account for mixture inhomogeneity. The DNS data has been used to analyse the statistical behaviour of the transport of the cross-scalar dissipation rate based on the fuel mass fraction Y _F and the mixture fraction ?? fluctuations $\,\tilde{\varepsilon}_{Y\xi}={\overline{\rho D\nabla Y_{F}^{\prime\prime}.\nabla \xi^{\prime\prime}} } \big/ {\bar {\rho }}$ (where $\bar{q}$ , $\tilde{q}={\overline{\rho q} } \big/ {\bar {\rho }}$ and $q^{\prime\prime} =q-\tilde {q}$ are Reynolds average, Favre mean and Favre fluctuation of a general quantity q) in the context of Reynolds Averaged Navier?CStokes simulations where ?? is the gas density and D is the gas diffusivity. The statistical behaviours of the unclosed terms in the $\tilde{\varepsilon }_{Y\xi } $ transport equation originating from turbulent transport T ₁, density variation T ₂, scalar?Cturbulence interaction T ₃, chemical reaction rate T ₄ and the molecular dissipation rate D ₂ have been analysed in detail. It has been observed that the contributions of T ₂, T ₃, T ₄ and D ₂ play important roles in the $\tilde{\varepsilon }_{Y\xi } $ transport for the globally stoichiometric cases, but in the globally fuel-lean cases the contributions of T ₂ and T ₄ become relatively weaker in comparison to the contributions of T ₃ and D ₂. The term T ₁ remains small in comparison to the leading order contributions of T ₃ and D ₂ for all cases, but the contribution of T ₁ plays a more important role in the low Damköhler combustion cases. The term T ₂ behaves as a sink term towards the unburned gas side but becomes a source term towards the burned gas side. The scalar?Cturbulence interaction term T ₃ has been found to be generally positive throughout the flame brush, but in globally stoichiometric cases the contribution of T ₃ becomes negative in regions of intense heat release. The combined contribution of (T ₄ ?C D ₂) remains mostly as a sink in all cases studied here. Models are proposed for the unclosed terms of the $\tilde{\varepsilon }_{Y\xi } $ transport equation in the context of Reynolds Averaged Navier?CStokes simulations, which are shown to satisfactorily predict the corresponding quantities extracted from the DNS data for all cases.