Abstract

Predicting the ensemble averaged heat release response of a turbulent premixed flame to acoustic forcing is a fundamental problem associated with understanding combustion instabilities. This paper describes an analysis of this problem, by modeling the response of a flame that is simultaneously perturbed by broadband, turbulent fluctuations and narrowband, acoustic fluctuations of amplitude εa and εT, respectively. It is shown that the response of the flame surface to coherent forcing and turbulent fluctuations are coupled even at linear order in coherent forcing amplitude, εa, due to flame propagation (kinematic restoration). This coupling effectively causes the local consumption and displacement speeds of the flame to vary in time over a forcing cycle. Turbulent fluctuations also provide a mechanism for destruction of coherent flame surface wrinkling at first order in εa, an effect which only occurs at O(εa2) for laminar flames.

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