LINEAR AND NONLINEAR 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 techn iques. The formulation is based on a generalized wave equation derived from the conservation equations for a two-phase mixture, and accommod ates all influences of non-linear gas dynamics and combustion response s. Several specific effects of baffles are presented as mechanisms by which baffles eliminate combustion instabilities. Included are longitu dinalization of transverse waves inside baffle compartments, restricti on of velocity fluctuations near the injector face, and decreased osci llation frequency. A potential destabilizing influence of baffles is f ound to be the concentration of acoustic pressure at the injector face . Primary aspects of limit cycles are examined by considering second o rder non-linear acoustics for both two- and three-dimensional cases. C onditions for the existence of limit cycles were obtained, as well as explicit formulas for the oscillation amplitudes and frequencies in te rms of linear and non-linear parameters. Important features of the ene rgy cascade among acoustic modes are elucidated, including the energy balance during limit cycles and transfer of energy by non-linear gas d ynamics. (C) 1995 Academic Press Limited