Investigation of the influence of finocyl grain structure on solid rocket motor damping characteristics

Nozzle is one of the primary sources of acoustic energy loss in the combustion instability of solid rocket motors. Previous studies have shown that nozzle damping is related to throat-to-port diameter ratio and Mach number. However, for variable cross-section grain configurations—such as finocyl grains, conical grains, and dual-thrust motors with two-stage grain designs—it is difficult to directly define throat-to-port diameter ratio and calculate the corresponding damping. To address this issue, the present study investigates the damping characteristics of finocyl-grain solid rocket motors through both experimental and numerical methods. In the experiments, inert grains were used to form motors with different cavity configurations, and the pulse decay method was applied under non-combustion conditions to obtain the damping coefficients of the first to fourth longitudinal modes. The results indicate that the damping coefficient depends on both modal frequency and propellant grain configuration. To further elucidate the underlying mechanisms, numerical simulations were performed to obtain the pressure and velocity fields. Dynamic mode decomposition (DMD) was then used to analyze the energy variation process of incident and reflected waves for different modes. The results reveal that the aft cavity of the finocyl grain strongly suppresses the transmission of the second longitudinal mode compared to the first mode. This leads to higher damping coefficients for the first mode compared with the second. Finally, the damping coefficients under actual motor operation condition were computed. The results show that, while the damping coefficients under firing conditions are higher than those in non-combustion tests, the relation between damping and modal frequency remains consistent. This confirms that non-combustion experiments can be used for qualitative investigations of the influence of grain geometry on damping coefficients.