Low-order modeling approach for the prediction of transverse combustion instabilities in multi-injector engines

This paper addresses the prediction of spontaneous self-sustained transverse combustion instabilities in multi-injector engines using a multi-dimensional non-linear low-order Eulerian model. The approach utilizes a physically aware response function that directly links pressure oscillations to fuel mass flow rate, independent of external data. This enables accurate capture of the behavior of shear coaxial injectors that have been proven to show a peculiar dynamics of cyclic fuel accumulation and release in response to acoustic waves. A NASA test case is employed as a reference, and a comprehensive analysis is conducted to investigate the behavior of the model. Firstly, a preliminary analysis is performed within a quasi-one-dimensional framework for a reduced single-injector configuration. This analysis provides insights into the influence of key parameters on the instability onset. Subsequently, the full-scale geometry is considered in a multi-dimensional framework, and the low-order solver is employed to analyze the thermo-acoustic behavior of the engine. The model successfully captures the instability dynamics, including temporal evolution, dominant frequency, and mode shapes. Sensitivity analyses are conducted to examine the impact of the model free parameters on the unstable modes. Additionally, the effect of introducing baffles as damping devices within the combustion chamber is investigated. The results highlight the model predictive capabilities and its potential for guiding the design and optimization of liquid rocket engines.