Numerical analysis on combustion instabilities in end-burning-grain solid rocket motors utilizing pressure-coupled response functions

The combustion instability has been one of severe problems suffered by solid rocket motors (SRMs) for a long term. This paper proposes a burning rate model utilizing the pressure-coupled response function for description of the spatiotemporal burning of AP-HTPB composite propellant grains in SRMs. The model is successfully incorporated to the axisymmetric internal ballistic simulation by the source terms of gasphase governing equations. The prediction of propellant combustion connected with acoustic pressures can be realized by means of an in-house high-order numerical solver, in which the numerical fluxes are reconstructed by the fifth-order WENO scheme and the viscous terms are discretized by a sixth-order compact scheme. The thermoacoustic combustion instabilities in the longitudinal modes are triggered by a burning rate pulse imposed to the steady flow. The analysis indicates that the pressure oscillations grow as a primary symptom of combustion instabilities. The influences of several factors on production of the instability symptom are discussed. It is shown that the pressure-coupled response function, the pressure index, and the reaction heat of the propellant, and the specific heat ratio of the burnt gas promote the pressure oscillation growth process evidently, but the magnitude and the imposed region of burning rate pulses have less effects. (C) 2020 Elsevier Masson SAS. All rights reserved.