Nonlinear Periodic Oscillations in Rocket Motors with Distributed Combustion

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Abstract
In this paper high frequency combustion chamber oscillations of two different types are studied analytically. The first kind of oscillation treated is the purely transverse mode found in an annular motor. The second type of oscillation studied is the longitudinal mode in a cylindrical chamber. For both types of oscillation the combustion processes are represented using the sensitive time lag model. The sources of mass and energy due to combustion are taken to be distributed in a more or less arbitrary way in the axial direction. A nonlinear perturbation analysis, employing the technique of coordinate stretching is carried out and results, for both types of oscillation, in a nonlinear ordinary differential equation governing the shape of the nonlinear periodic waves. In both cases the governing equation can be transformed into an equation that has been previously solved in studies of concentrated combustion. In the case of the transverse oscillations both standing and travelling waves are considered and the configuration of the shock in the case of discontinuous oscillations is determined.