Wave instabilities in combustion and thrust chambers

A new theory and computations for combustion instability analysis are presented herein. The basic theoretical foundation sterna from the concept of entropy-controlled energy growth or decay. Third order perturbation expansion is performed on the entropy-controlled acoustic energy equation to obtain the stability integrodifferential equation for the energy growth factor in terms of the linear, second, and third order energy growth rate parameters. These parameters are calculated from Navier-Stokes solutions with space and time averages performed on as many Navier-Stokes time steps as required to Navier at least one peak wave period. Applications, e made for one-dimensional Navier-Stokes solution the space shuttle main engine thrust chamber the cross section area variations taken into account. It is shown that instability occurs when the mean pressure is raised to 2000 psi with 30% disturbances for the case investigated in this analysis. Instability also arises when the mean pressure is set at 3000 psi with 20% disturbances. The system with mean pressures and disturbances more adverse than these cases has been shown to be unstable.