Semi-analytical validation of a dynamic large-eddy simulation procedure for turbulent premixed flames via the G-equation

The performance of a dynamic subgrid model for the turbulent burning speed of a premixed flame is investigated for a series of idealized test cases where the flame front is wrinkled by a multiple-scale shear flow; a rigorous asymptotic subgrid model is also implemented for comparison. Explicit formulae for the flame wrinkled shape and turbulent speed are available to generate a reference database. The role of the subgrid wrinkling models is to achieve the same overall flame shape and propagation speed in a simulation where only the largest scales of the flow are explicitly accounted for. Very good results are obtained when the subgrid burning speed enhancement is estimated using the asymptotic subgrid model. On the other hand, the dynamic model attempts to exploit the scaling observable in the simulation to extrapolate the turbulent burning speed enhancement in the original system The performance of this strategy is adequate for some regimes but poor for others; the source of the problem is traced back to the existence of a scaling transition that occurs as the flame propagating speed is adjusted during the large-eddy simulation. A modification to the scaling of the enhanced burning is implemented to account for the existence of the two distinct scaling ranges; it improves significantly the predictions of the dynamic model away from the transition, but results in the near-critical range remain predictably very poor compared with the rigorous asymptotic model results. These conclusions based on apriori performance for the reference steady data are confirmed by comparing unsteady large-eddy and direct simulations. Results based on rigorous mathematical tools are possible here because of the separation of length scales in the special class of idealized flow fields used in this study: their relevance to more realistic flows is also discussed.