Influence of the Damköhler number on turbulence-scalar interaction in premixed flames. II. Model development

The modeling of Damköhler number, Da, effects on the interaction of turbulence and scalar fields in premixed flames is studied using two freely propagating statistically planar flames calculated by direct numerical simulation (DNS). One flame having Da>1 shows attributes of turbulent combustion in the corrugated flamelets regime while the other having Da<1 depicts characteristics of the thin reaction zones regime. The interaction process is characterized by the tensor inner product of the scalar and velocity gradients. It is found that the interaction process dissipates the scalar gradients in the Da>1 flame whereas it produces the scalar gradients in the Da<1 flame. It is argued and also shown that the Damköhler number dependence should explicitly appear in the models for the turbulence-scalar interaction in order to represent the above physics correctly. Simple unified models, in the Reynolds averaged Navier-Stokes (RANS) framework, for the interaction processes involving a local Damköhler number dependence are proposed and validated against the DNS data. The proposed models are shown to degenerate simply to passive scalar models when there are no chemical reactions in the flow or when the chemical reactions are passive. The predictions of these models are also compared to the values obtained using the models available in the literature. It is found that the explicit Da dependence is required to capture the DNS results correctly. Extension of the proposed RANS models to large eddy simulation is also discussed.