Improved Response Function for Low-Order Modeling of Longitudinal Combustion Instabilities

This paper investigates longitudinal high-frequency combustion instabilities using a low-order numerical solver to provide fast, reliable predictions intended to support the preliminary design of new liquid rocket engines at low computational cost. A physics-based response function is employed to model thermoacoustic interactions, linking acoustic waves in the injector recess to unsteady fuel mass flow rate. This approach mimics the cyclic fuel accumulation and release characteristic of shear coaxial injectors, as documented in experimental and numerical studies. The objective of this work is to present a significant update to a low-order model previously developed by the present research group. This update is made by introducing a new response function capable of detecting the direction of acoustic waves, and by introducing an additional transport equation for the fuel released at the injector. This new approach eliminates spurious numerical oscillations observed in the previous version of the model and leads to improved predictive capabilities. A detailed comparative analysis and validation of the updated solver are performed using the continuously variable resonance combustor test case as the benchmark. The study assesses the predictive capabilities of the solver by evaluating computed limit-cycle features against experimental data. A phenomenological investigation of fuel release events and a sensitivity analysis of model parameters shows the physical consistency and robustness of the solution, which are critical aspects for predictive modeling applications.