A theoretical study of three-dimensional combustion instability in liquid-propellant rocket engines

Abstract

A theoretical study of three-dimensional linear combustion instability in liquid-propellant rocket motors is presented. A concentrated combustion model is used, and the mathematical analysis is presented as a boundary-value problem in which the solutions describing the flow oscillations in the combustor are required to satisfy a combustion-zone boundary condition at one end of the chamber and a Nozzle Admittance Relation at the other end. Crocco's time-lag hypothesis is used to describe the combustion process, and an analysis of the nonsteady nozzle flow is used to derive the Nozzle Admittance Relation. The model used in this study can predict stability behavior of combustors with low and high Mach number flows over a wide frequency range. An investigation of stability behavior over a wide frequency range predicts the possibility of spontaneous combustion instability with respect to the pure transverse mode and the mixed acoustic modes (which are associated with a given pure transverse mode). In addition, this study predicts that each of the following effects: (a) increasing the combustor's length, (b) decreasing the Mach number of the mean flow, and (c) “smoothing” the convergence of the nozzle are destabilizing with respect to the pure transverse modes. No general conclusions regarding the stability of the combustor with respect to the various mixed acoustic modes can be drawn. It appears that the stability behavior of each of these modes should be considered separately. Experimental evidence supporting some of these theoretical predictions is presented.