A generalization of the Thickened Flame model for stretched flames

The Thickened Flame (TF) model is a widely used approach for Large Eddy Simulation of premixed flames. It is based on a “mapping” transformation where all diffusivities are multiplied by a thickening factor F while reaction terms are divided by F. Theory shows and 1D flame simulations confirm that this mapping preserves the unstretched laminar flame speed sL0 while increasing its thickness δL0 by F, allowing to resolve the flame on a coarse grid. However this property is not satisfied anymore when the TF model is applied to stretched flames: the burning velocity sc(k) of a thickened flame submitted to a stretch k is not conserved compared to the non-thickened solution. A new diffusion-reaction transformation, named Stretched-Thickened Flame (S-TF) model, is developed here to conserve the burning velocity of stretched flames, proposing a generalization of the classical diffusion-reaction transformation which the TF model is based on. Thermal and mass diffusion zones are thickened differently and the laminar unstretched properties are preserved by modifying the chemical source terms. The S-TF model is applied on canonical 1D strained flames and validated for a cylindrical expanding flame configuration to prove its applicability to recover both strain and curvature effects. Results show that the Stretched-Thickened Flame model is an effective solution to correct the deficiency of the classical approach for stretched flames and can be easily implemented in CFD codes relying on the TF model.