Heat Release Response Function during Self-Sustained Combustion Instability in a High-Pressure Rocket Combustor

The heat release response function during thermo-acoustic combustion instability can provide valuable insights into the instability mechanisms in rocket combustors. It also enables low-fidelity modeling for parametric studies and facilitates the development of control strategies for mitigating instabilities at reduced computational costs. In this study, we examine both local and global response functions during self-sustained longitudinal combustion instability observed within a high-pressure shear-coaxial rocket combustor. The combustor configuration, referred to as the Continuously Variable Resonance Combustor (CVRC), has been extensively studied in the past, where longitudinal instabilities of different amplitudes have been reported to occur with different lengths of the oxidizer injector. We consider the dataset obtained from large-eddy simulation (LES) of a configuration with a 12 cm injector length, which has predicted the presence of longitudinal instability in agreement with the experiments. LES is performed using a well-established adaptive mesh refinement (AMR)-CutCell-based approach employing detailed finite-rate kinetics (21 species and 84 steps). The response functions are extracted from two-dimensional snapshots of the reacting flow field in the central symmetry plane that are saved at high frequency over multiple cycles of instability. Apart from conventional approaches to determine both local and global response functions, akin to flame transfer and flame describing functions, we also employ the dynamic mode decomposition technique to obtain the response functions. The results are examined in terms of the frequency-dependent phase and amplitude relationships of heat release and acoustic fluctuations. While the analysis of the local response function identifies flame regions that are most sensitive to acoustic fluctuations, the global response function yields overall growth rates and frequencies of the underlying acoustic modes.