Modeling the Response of Turbulent Flames to Harmonic Forcing

Abstract

This article analyzes the response of a turbulent, premixed flame to harmonic forcing. This problem has been worked extensively for laminar flames, and the key parameters influencing the flame transfer function are well understood. For turbulent flames, several prior studies have utilized a quasi-laminar approach, by utilizing the time-averaged flame position and ensemble-averaged disturbance field, as inputs to what is otherwise identical to the laminar problem. More generally, the manner in which turbulent flames respond to harmonic disturbances is not amenable to analytical solutions because of the nonlinear interactions between stochastic flow disturbances and harmonic flame wrinkling. We utilize a turbulent burning velocity closure proposed by Shin and Lieuwen (2013), who showed that the ensemble-averaged turbulent burning rate for a harmonically forced flame is proportional to the ensemble-averaged flame curvature. Shin and Lieuwen (2013) previously used it to analyze the ensemble-averaged space-time flame wrinkle characteristics. Here, we extend these results to analyze the spatial variation of ensemble-averaged flame surface area and burning rate and then compare these results to computations. These results show that, for low stochastic forcing amplitudes, wrinkling of the front exerts quantitative differences between those predicted by a quasi-laminar and the actual flame response (e.g., reducing peak values of the flame transfer function and eliminating nodes), but does not change the key qualitative features. While this result needs to be considered for strongly turbulent flames, it does suggest why good agreement has been observed between quasi-laminar approaches and experimental data for harmonically excited, turbulent flames. Two results for model problems showing the linearized flame transfer functions are also presented, which explicitly demonstrate qualitative turbulence effects on harmonically excited flames.