Analytical and Numerical Development of a Baffled Liquid Rocket Combustion Stability Code

Abstract

A predictive model for assessing the stabilization impact of radial blades, hub blade, and acoustic cavities in liquid propellant rocket engin es was developed, including nozzle, mean flow, and distributed combustion effects. A full t hree dimensional linear stability analysis was couched in terms of a pseudo velocity potential formulation, and the solution found through an integral Fourier series eigenfunction ex pansion. The non-homogeneous terms of the governing equation are dependent on the velocit y potential and the derivatives of the potential; therefore a successive approximation tec hnique was employed using the acoustic wave shape as the zeroth level approximation. The complex geometry that arises from the inclusion of the blade system requires separate sol utions for each compartment and a matching technique that allows for the velocity pot ential as well as the gradient of the potential to match at these interfaces. It will be shown that non-iterative techniques that do not allow for distortion of the wave shape from the acoustic solution may predict stable operation for a given combustion response while the iterative technique presented in this paper predicts an instability due to modification o f the potential field by mean flow, combustion, and cavity effects.