Can a One-dimensional Strained Flame Model Combustion in Flame-vortex Interactions?

We present a study of the flame-embedding concept, introduced in [1] as an efficient approach for large-eddy simulation of turbulent combustion at high Reynolds and Damköhler numbers. In flame embedding, the combustion zone is modeled as an unsteady flame modified by the local tangential strain rate, with the latter extracted every time step from the flow field simulations. The flame structure is approximated locally as being one-dimensional, evolving in the flow field generated by a stagnation-point flow whose characteristic parameter is the applied flow strain. Two-dimensional flame-vortex interaction simulations are used as the benchmark for this study. The time-dependent strain rate at the flame front is extracted from the two-dimensional simulations and used in the one-dimensional, unsteady strained flame structure calculations. We present results for a matrix of parameters that define the impact of the flow on the flame in a flame-vortex interaction—the vortex pair size, separation and circulation—and use the instantaneous burning rate to determine the accuracy of the model. We show that the onedimensional unsteady flame calculation can capture the impact of the applied flow strain on the burning rate if the former is taken as the corresponding “non-reacting” flow strain rate at the flame reaction zone, and not the applied flow strain at the flame leading edge. The distinction is important in cases where the flame front thickness approaches that of the flow field, a situation that is likely to be encountered when small vortices interact with lean flames.