Low-Order Approach for Investigating Thermoacoustic Instabilities in Multi-Injector Rocket Engines

This paper presents a novel low-order approach for the investigation of self-sustained high-frequency combustion instabilities in multi-injector rocket engines. The proposed methodology is developed as a multidimensional, multi-injector extension of a low-order model previously introduced by the present research group for the analysis of longitudinal instabilities in single-injector configurations. The formulation also accounts for engine configurations employing cryogenic propellants under supercritical conditions. Thermoacoustic interactions at the injector level are modeled using a physics-based response function that links acoustic perturbations to unsteady fuel mass flow rate. This modeling strategy is designed to reproduce the experimentally and numerically observed dynamics of shear coaxial injectors. The resulting low-order framework is intended to provide fast and cost-effective predictions of the unsteady behavior of engine configurations. The well-documented unstable BKD test case is employed for validation. The model successfully captures the expected instability dynamics, including limit-cycle characteristics and mode shapes, while also providing useful insights into the underlying thermoacoustic phenomenology. Sensitivity analyses are also conducted, assessing the influence of model parameters and demonstrating the robustness of the predictions.