Linear and non-linear pressure oscillations in baffled combustion chambers

Linear and non-linear analyses of acoustic waves in baffled combustion chambers have been developed by means of perturbation-expansion techniques. The formulation is based on a generalized wave equation derived from the conservation equations for a two-phase mixture, and accommodates all influences of non-linear gas dynamics and combustion responses. Several specific effects of baffles are presented as mechanisms by which baffles eliminate combustion instabilities. Included are longitudinalization of transverse waves inside baffle compartments, restriction of velocity fluctuations near the injector face, and decreased oscillation frequency. A potential destabilizing influence of baffles is found to be the concentration of acoustic pressure at the injector face. Primary aspects of limit cycles are examined by considering second order non-linear acoustics for both two- and three-dimensional cases. Conditions for the existence of limit cycles were obtained, as well as explicit formulas for the oscillation amplitudes and frequencies in terms of linear and non-linear parameters. Important features of the energy cascade among acoustic modes are elucidated, including the energy balance during limit cycles and transfer of energy by non-linear gas dynamics.