Theoretical study of the flame describing function of AP/HTPB propellant flame based on sandwich model

The flame dynamics of ammonium perchlorate/hydroxyl-terminated polybutadiene (AP/HTPB) composite propellant subject to the acoustic oscillation in a solid rocket motor (SRM) is investigated numerically in this article. The sandwich model is suitably modified to carry out the simulations of propellant combustion under unsteady conditions and the flame response to the acoustic oscillations with different amplitudes and frequencies is investigated. Attention is focused on the heat flux to the propellant surface and the Flame Describing Function (FDF) is utilized to capture the characteristics of the heat feedback under different forcing amplitudes and frequencies. The results indicate the flame responses are non-linear for the first longitudinal mode of acoustic oscillation and the gain of the fluctuating heat feedback reaches the point saturation at the high forcing amplitude. For high forcing frequency (the third acoustic mode), the gain of the fluctuating heat feedback shows insensitivity to the acoustic oscillations with different amplitudes and varies little. The full FDF confirms the nonlinearity of the gain response and shows the trend of fluctuating heat feedback as a function of different forcing frequencies and amplitudes.