Numerical investigation of the velocity-coupled response of propellant burning rate in a solid rocket motor

Serving as one of the primary gain sources in solid rocket motors, the burning rate response crucially determines the properties of combustion instability, which, however, still remains largely unexplored, particularly velocity-coupled burning rate response. This numerical study integrates a microscopic sandwich flame model with a macroscopic rocket internal flow field, considering the gas-solid coupling process, to investigate the velocity-coupled burning rate response of solid propellants subjected to transverse acoustic forcing in a solid rocket motor. The oscillatory flow field and flame dynamics are first analyzed, examining the variation pattern of velocity fluctuation amplitude with frequency near the burning surface and the disturbance source characteristics of the flame. Subsequently, both the pressure-coupled response function ($R_p$) and the velocity-coupled response function ($R_v$) are derived to investigate the frequency response of the burning rate. $R_v$ peaks in the second acoustic mode, potentially clarifying why the second harmonic frequently exhibits the highest amplitude in the combustion instability of real solid rocket motors. The phase relationship between velocity and flame heat release fluctuations in space is analyzed, explaining the response mechanism of burning rate to the velocity oscillation frequency. The impact of oxidizer particle sizes on $R_v$ is also explored. Smaller oxidizer particle sizes lead to a shift in the peak of $R_v$ towards higher harmonics, emphasizing the crucial role of reaction diffusion distance in velocity-coupled responses. Our work introduces a novel approach to studying propellant burning responses, particularly addressing the gap in numerical studies of velocity-coupled responses, potentially leading to enhanced understanding and control of combustion instability.