Low-order modeling of combustion instability using a hybrid real/ideal gas mixture model

The present work focuses on the state of development of a low-order numerical tool, specifically aimed to face combustion instability problems in liquid rocket engines employing shear coaxial injectors. Particular attention is focused on that kind of injectors, since they have been identified in the literature to have a central role in the high frequencies combustion instability dynamics. That is due to the passage of acoustic waves causing cyclic propellant pockets accumulation and release. In a low-order framework, flow field is computed using an Eulerian set of equations for three species, namely oxidizer, fuel, and combustion products mixtures. In particular, the recent improvements involved the enhancement of the employed Equation of State, from the ideal one to a hybrid cubic one, in order to deal with cryogenic test cases. The hybrid EoS approach has been specifically developed to handle a mixture of ideal and real fluids, so that the typically cold oxidizer can be handled as a real fluid while the warmer species can be approximated as ideal gases. The combustion instability driving mechanism is regarded as a response function, which links acoustic waves to fuel mass flow rate oscillations, mimicking the described behavior of the coaxial injectors. In order to predict the onset of transverse instabilities while keeping the computational load as low as possible, the chamber domain is discretized as 3D, whereas each of the injector domains as 1D. The one-dimensional tool handling the injectors can also be used as standalone, for dealing with longitudinal instabilities test cases, or in order to study the behavior of the single injector of a more complex system. In the present work the most advanced results obtainable with the full 3D ideal gas model are presented, followed by the first analyses carried out with the hybrid-real fluid 1D model. The test case of interest is a cryogenic LOX/Methane engine prone to the onset of transverse instability.