A reduced-order model of thermoacoustic instability in solid rocket motors

A finite-dimensional dynamical system is derived from a coupled system of partial differential equations modeling the thermoacoustic oscillations inside a solid rocket motor. The governing equations for the coupling between the chamber acoustics and combustion of the solid propellant are derived from conservation laws and existing combustion models. Model reduction is carried out for the unsteady burning rate model based on a pseudo-spectral truncation, leading to a three-dimensional dynamical system. The resulting low-dimensional dynamical system is shown to be able to capture the main bifurcation behavior of the original infinite-dimensional system. The reduced-order model can be used to predict the nonlinear thermoacoustic behavior of a solid rocket motor at reduced computation costs.