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

摘要

A predictive model for assessing the stabilization impact of radial blades, hub blades, and acoustic cavities in liquid-propellant rocket engines was developed, including nozzle, mean flow, and distributed combustion effects. A full three-dimensional linear stability analysis was couched in terms of a pseudovelocity potential formulation, and the solution was found through an integral Fourier series eigenfunction expansion. The nonhomogeneous terms of the governing equation are dependent on the velocity potential and the derivatives of the potential; therefore, a successive approximation technique 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 solutions for each compartment and a matching technique that allows for the velocity potential as well as the gradient of the potential to match at these interfaces. It will be shown that noniterative 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 of the potential field by mean flow, combustion, and cavity effects.