Low-Order Modeling of Combustion Instability: A Comprehensive Analysis of the BKD Test Case

This paper investigates the use of an in-house low-order numerical tool for the analysis and prediction of transverse high-frequency combustion instability in multi-injector rocket engines. To this aim, a non-linear multi-dimensional low-order Eulerian model for multi-species reactive flows is employed. The numerical tool makes use of a physics-based response function formulation that mimics the behavior of shear coaxial injectors, characterized by cyclic fuel accumulation and release in response to acoustic perturbations. Pressure waves are in this framework connected to unsteady fuel mass flow rate, preserving a possible physical causality between acoustic waves and unsteady heat release, whose relationship is at the base of thermo-acoustic phenomena. In the present work, the unstable load point of the BKD test case, featuring combustion instability at the first transverse mode of the chamber (1T), is used as benchmark. Results show a remarkable agreement with the experimental data in terms of both limit cycle frequency and peak-to-peak amplitude. The model is able to provide valuable information regarding the phenomenology underlying the analyzed instability and is also capable of identifying its key features, including the standing nature of pressure oscillations, and the injection-coupled dynamics. Lastly, a sensitivity analysis of the solution with respect to the model free parameters is performed. Most of the results are well in line with physical expectations, further emphasizing the validity of the numerical tool.