Numerical study of triggered thermoacoustic instability driven by linear and nonlinear combustion response in a solid rocket motor

Thermoacoustic instability (TAI) has consistently presented challenges to the development of solid rocket motors (SRMs), making the prediction of TAI critically important. Most existing TAI predictions rely on linear instability theory, which is inadequate for predicting certain nonlinear TAI, such as triggered TAI. To address this challenge, this study has constructed the nonlinear response model for the burning rate, known as the nonlinear pressure-coupled response function (PCR). The nonlinear PCR is capable of considering the effects of both frequency and amplitude of pressure oscillations. By integrating the PCR into the computational fluid dynamics framework, this study successfully replicated the nonlinear triggered TAI. When exclusively employing the linear PCR, the model demonstrates typical multi-order resonant modes, and the stability map exhibits either persistent stability or persistent instability, contingent upon the distribution of the linear PCR function. However, by incorporating the nonlinear PCR, this study effectively reproduces nonlinear pulse-triggered instability. This instability arises only when the pulse intensity surpasses the threshold value due to SRM damping. The nonlinear response framework allows for the identification of the instability boundary, facilitating a more comprehensive assessment of SRM performance. This study fills a critical gap in predicting triggered TAI in SRMs, providing insights into nonlinear TAI mechanisms.