Selection Rules for Resonant Longitudinal Injector-Coupling in Experimental Rocket Combustors

Abstract

This paper investigates different types of longitudinal mode coupling in subscale rocket combustion chambers using experimental data and numerical simulations. Based on a one-dimensional planar wave acoustic model of coupled cavity resonators with two acoustic inlet boundary conditions, mode selection rules are derived, providing a simple way of predicting which injector and combustion chamber modes have matching frequencies. Longitudinal mode coupling of an injector with an acoustically open inlet boundary condition has been reported in the literature for the start-up transient of a research combustor experiment. In this experiment, every third injector mode couples to a corresponding chamber longitudinal mode, which is explained in terms of the selection rules derived in this paper. Numerical simulation results for a different combustor experiment show an unexpected mode coupling behavior when an acoustically closed injector inlet is used. Theoretical analysis by using the one-dimensional wave model and applying the derived selection rules shows that in this setup, the injector acoustic mode can accommodate two different acoustic boundary conditions at the injector-chamber interface simultaneously. This results in different acoustic mode shapes in the injector, explaining the unexpected behavior for the resonant coupling with an acoustically closed injector inlet.