# Velocity coupling from pulse-test firings

Article

Triggering of nonlinear combustion instability has often been attributed to velocity coupling. The prediction of this term is often ad hoc in nature, with no accepted experimental method to obtain the velocity-coupled response function. Tubular-grain solid rocket motors have been used successfully to obtain pressure-coupled response functions. The Rousseau and Knoetze analysis is extended to calculate the velocity-coupled response function using the Burnley-Culick velocity-coupling model. This model is used due to its easy incorporation into the analysis methodology. The solid rocket motor's linear stability is calculated for the expected modes at the point where nonlinear combustion instability occurs. Decomposing the composite acoustic wave, from pulse-tested tubular-grain motor data, into its fundamental modes makes it possible to obtain the velocity-coupling response function for several frequencies. The results from this analysis return reasonable values for the velocity-coupled response. These values can then be used to predict triggering. This analysis can be applied to liquid, ram, and hybrid rockets or any system that exhibits longitudinal mode acoustic instability. The ad hoc velocity-coupling model was used here, but the analysis methodology can be used to investigate other models as well. Copyright © 2012 by the American Institute of Aeronautics and Astronautics, Inc.