A multidimensional combustion model for oblique, wrinkled premixed flames

Abstract

A new premixed turbulent combustion model is proposed, which is based on one-dimensional (1D) filtering of density times progress variable and reaction source term of laminar premixed flame profiles using a filter kernel that reflects the variation of the area of planar flame fronts moving through filter volumes. It is shown that these genuinely multidimensional effects qualitatively change the relation between the filtered reaction source term and the Favre-filtered reaction progress variable compared to strictly 1D models, particularly at large filter widths. Analytical results for the filtered quantities are obtained by approximating the laminar flame profiles by suitable ansatz functions. Filtered data from Direct Numerical Simulations (DNS) of statistically planar turbulent premixed flames at a range of turbulence levels of the unburnt mixture and for two different heat release parameters is used to optimize and validate the model. For filter widths smaller than the laminar flame thickness, minor effects from subgrid flame folding are observed. For larger filters, the effect of subgrid flame folding can be represented well through a wrinkling factor, which reduces the effective filter width used in the 1D filtering operation. Two wrinkling factor models are proposed, using fractal dimensions patterned on literature models. The modelled reaction source term written as function of Favre averaged progress variable and filter width shows excellent agreement with filtered DNS data conditioned on the Favre averaged progress variable for all investigated turbulence levels, filter widths and both heat release parameters.