Modeling of Hybrid Rocket Low Frequency Instabilities

A comprehensive dynamic model of a hybrid rocket has been developed to understand and predict the transient behavior including instabilities. A linearized version of the transient model predicted the low-frequency chamber pressure oscillations that are commonly observed in hybrids. The source of the instabilities is based on a complex coupling of thermal transients in the solid fuel, the wall heat transfer blocking due to fuel regression rate, and the transients in the boundary layer that forms on the fuel surface. The oscillation frequencies predicted by the linearized theory are in very good agreement with 43 motor test results obtained from the hybrid propulsion literature. The motor test data used in the comparison cover a very wide spectrum of parameters including 1) four separate research and development programs; 2) three different oxidizers (liquid oxygen, gaseous oxygen, and nitrous oxide); 3) a wide range of motor dimensions, that is, from 5 in. (12.7 cm) diameter to 72 in. (182.9 cm) diameter, and operating conditions; and 4) several fuel formulations. A simple universal scaling formula for the frequency of the primary oscillation mode is also suggested.