AP/HTPB combustion response simulation with a new equivalent linear system method

In the study of solid rocket motor (SRM) combustion instability, modeling and analyzing the combustion response of the solid propellant is a laborious task. We propose a new idea, an equivalent linear system method, for modeling solid propellant combustion response with three steps: first, simulating the transient combustion process under pulse pressure excitation for only one CFD case; then, treating the combustion process as a black-box and obtaining the transfer function of the combustion process from the CFD result; finally, predicting and analyzing the combustion response based on the transfer functions. For the AP/HTPB sandwich propellant withp¯=3MPa, the amplitude, duration, and direction of excitation pulses are studied. The new method is also verified, with a maximum relative error of 4.3% for burning rate response under p˜≤1MPa (as high as one-third of the pressure DC). Applicability of this new method is demonstrated for another two AP/HTPB sandwich propellants with different configuration under p¯=8MPa and p¯=10MPa, showing that the system-simulated combustion responses of burning surface temperature and burning rate are consisted well with the CFD results and the maximum relative error of burning rate response is 2.1%. Asymmetric combustion response for positive and negative pressure perturbations is a new finding based on the CFD and simulation results. Besides, a new approach using dual transfer functions is proposed to ensure high accuracy for the simulation of solid propellant combustion. The pressure-coupled response function is predicted by this method for the sandwich propellant under p¯=5MPa and p˜=20kPa within a wide continuous frequency range (0–3000 Hz). The comparison with CFD results indicates that the relative bias of R_p is less than 2%. With the proposed method, the combustion response to arbitrary pressure excitations can be simulated with high accuracy, high time-resolution, and high speed. The method shows great advantage and potential in simulating and predicting combustion instability.