Response of turbulent premixed flames to harmonic acoustic forcing

Abstract

The objective of this paper is to compare the response of laminar and turbulent premixed flames to harmonic forcing. This work is motivated by the growing body of work on the laminar flame problem, much of it with corresponding experimental validation. However, the relevance of these results to turbulent flames, and the degree to which turbulent and laminar flames exhibit similar quantitative and qualitative responses is currently unclear. This paper addresses this problem by solving the nonlinear G-equation in its implicit form, so that highly turbulent flame features are included, such as multi-valued front position and pocket formation. In particular, it analyzes the response of the flame to an imposed harmonic velocity disturbance of amplitude u a ′ / S L , superposed upon a background turbulent velocity field of varying intensity, u T ′ / S L . The results are compared with those obtained for flames forced by a harmonic velocity field without background turbulence. It is shown that the qualitative dynamics of the flames remain similar, with significant quantitative differences. This is due to the following: in the absence of background turbulence, harmonic forcing generates sinusoidal wrinkles on the flame which convect downstream. The amplitude of these wrinkles decrease with downstream distance due the propagation of the flame normal to itself. The rate of this flame area destruction grows nonlinearly with amplitude of forcing, so that the flame area perturbation amplitude does not grow linearly with amplitude of u a ′ . Background turbulence enhances the destruction rate of these harmonic wrinkles. Thus, there is a net decrease in the ensemble averaged flame area fluctuation at the harmonic forcing frequency, causing a reduction in the coherent response of the turbulent flame relative to its laminar value.