Formulation of combustion acoustic coupling using multiple time and length scales

The governing equations for combustion acoustic interaction in a generalized multiple time and length scale regime is derived from the full compressible Navier Stokes equations. The equations are shown to reduce to their counterparts for single-time-multiple-length scale and multiple-time-single- length scale regimes reported in the literature. The acoustics is driven by the divergence of the base-flow velocity in the multi-time-length scale whereas it is the heat release rate fluctuations in the single-time-multiple-length scale regimes. The acoustics is not driven by the flow in the multiple-time-single- length scale regime. The acoustics in turn affects the base-flow through the acoustic Reynolds stress in the multipletime- single-length scale and multiple-time-length scale regimes and through the gradient in acoustic pressure in the single-time-multiple-length scale regime. The behaviour of the coupled system is predicted numerically in the present work for a laminar non-premixed flame at a backward facing step in the multiple-time-length scale regime. The acoustic Reynolds stress is observed to play a key role in the evolution of the coupled system, as it gradually evolves towards a single-time-multiple-length scale leading to combustion instability. Copyright © 2010 by C. Balaji and S. R. Chakravarthy.