Integral equation approach for analyzing acoustic interactions with wrinkled flame fronts

Abstract

Flame-acoustic wave interactions play an important role in the characteristic unsteadiness of turbulent combustion processes. They arise because acoustic waves incident from other parts of the flame or from external sources impinge upon the flame and are scattered because of the significant change in sound speed and density at the flame front. The characteristics of the scattered waves are complex, due to the fact that they are interacting with a dynamic flame surface that is convoluted over a broad range of length and time scales. Over a wide range of frequencies (e.g., up to about 20 kHz), such turbulent flames may be treated as nonpassive (i.e., the flame acts as a source of acoustic energy) temperature discontinuities. We describe here an integral equation approach, similar to the development of the Ffowcs Williams–Hawking (FWH) equation, that is suitable for analysis of acoustic-flame interactions. This FWH equation is generalized for the case of interest where the surface is penetrable, not passive, and whose area varies in time. The integration surface consists of the time varying flame front that divides two homogeneous regions. The wave motions in these two regions are coupled by appropriate mass, momentum, and energy conservation conditions.