Analytical modeling of the one-dimensional acoustic field in hybrid rocket combustion chamber

Abstract

An analytical model to predict the longitudinal acoustic modes of hybrid rocket combustion chambers is presented. In the classical motor configuration, a dump plenum and an aft-mixing chamber are mated to the solid fuel grain; this arrangement produces cross-sectional discontinuities that vary over the motor firing because of the widening of the fuel port. This feature mainly, in conjunction with mixture-ratio shift in the motor operation to a much lesser degree, usually induces a change of the frequency of longitudinal modes during combustion. Furthermore, in the combustion chamber there is an axial gradient of the speed of sound, which has an influence on the mode characteristics. The model developed here accounts for both the cross-sectional area discontinuities and the axial variations of temperature and gas composition, assuming a linear trend of the squared speed of sound from the injection head to the exhaust nozzle entrance, and zero mean flow. Comparison with the results computed with a comprehensive one-dimensional model, which considers also the effects of the vaporizing fuel mass injection and of the actual temperature variation in the chamber, reveals maximum deviations around 3%. Finally, the model has been employed to predict the first longitudinal acoustic mode frequency measured versus time in a couple of firing tests of a laboratory-scale rocket showing fairly good agreement.