Prediction and analysis of high-frequency combustion instabilities in liquid rocket engines using low-order modeling

High-frequency combustion instability has consistently posed a significant challenge in the design of new liquid rocket engines, where the potential for engine failure remains an ever-present concern. Although this topic has been extensively studied since the 1950s through a combination of experimental and numerical methods, a comprehensive understanding of the mechanisms underlying the phenomenon and the development of reliable predictive capabilities have yet to be achieved. This thesis addresses the analysis and prediction of different types of high-frequency instability in both single- and multi-injector engines using a multi-dimensional CFD solver for multi-species reactive flows based on low-order modeling. The numerical tool developed for this purpose, known as ``K-AFFS'', incorporates several modeling choices aimed at improving computational efficiency. The approach relies on Eulerian governing equations, on the reduction of combustion products to a single species with properties of the stoichiometric mixture, on the application of a simplified single-step global reaction for the combustion process, and on the implementation of an innovative hybrid-D approach. This approach represents the combustion chamber as a three-dimensional domain, while each injector is modeled as a quasi-one-dimensional domain, with appropriate integration at their interfaces. While the use of simplified physical models may overlook certain critical aspects of thermo-acoustic phenomena, this limitation is accounted for by enforcing them through a submodel, referred to as ``response function''. Traditional response functions establish a direct link between acoustic waves and unsteady heat release, relying heavily on external calibration data and therefore lacking predictive capabilities. On the other hand, K-AFFS employs a physics-based response function that directly links acoustic waves propagating in the injector mixing zone (recess) with the unsteady fuel mass flow rate from the injectors annular gaps. This method is designed to mimic the unsteady behavior observed in shear coaxial injectors, characterized by cyclic fuel accumulation and release. The formulation preserves a possible cause-effect relationship between acoustic waves and unsteady heat release while remaining independent of external data. The approach is validated against three distinct test cases, chosen to encompass a wide range of operating conditions. The first test case, referred to as ``NASA-LeRC'', involves a 178 kN thrust-class engine equipped with 82 recessed shear coaxial injectors which exhibits a transverse spinning instability at the first tangential chamber mode (1T). The validation begins with a preliminary analysis conducted within a reduced quasi-one-dimensional framework for a single-injector configuration, and progresses to a full-scale analysis using a multi-dimensional framework. The study includes sensitivity analyses to examine the impact of model parameters on the results, and further investigates the effect of introducing baffles as damping devices within the combustion chamber. The second test case focuses on the Continuously Variable Resonance Combustor (CVRC), a simple apparatus that exhibits longitudinal instabilities at the first longitudinal mode. This single-injector system features a movable injector head that allows for extensive data collection by varying the length of the injector. Comparative analyses between experimental and numerical data are conducted within a quasi-one-dimensional framework, evaluating 17 different injector lengths. The capabilities of K-AFFS in assessing the chamber stability and in identifying various thermo-acoustic and injection-coupling mechanisms are thoroughly investigated. An in-depth analysis of a stable and of an unstable configuration to identify key factors driving the observed unsteady dynamics is also included. A parametric study is conducted to assess the physical response of the numerical tool and the dependence of the solution quality on the initial model parameter settings. The final test case involves the Brennkammer D (BKD) combustor, a well-documented and extensively studied sub-scale engine known for its transverse standing instabilities at the first tangential mode (1T). This thrust chamber features 42 recessed shear coaxial injectors fed by cryogenic supercritical oxygen and supercritical gaseous hydrogen. Comparative analyses between experimental and numerical data focus on limit cycle features and on the identification of key mechanisms driving the unstable dynamics. A sensitivity analysis is also conducted to verify the physical behavior of the solution and to ensure its minimal dependence on model parameters within a multi-injector framework. The results demonstrate a high level of agreement with experimental data across all three test cases, particularly in terms of limit cycle frequency. The findings provide valuable insights into the phenomena underlying the observed unstable dynamics. K-AFFS consistently proves its ability to accurately detect both stable and unstable conditions and to distinguish between different types of instabilities as well as different wave displacements. The comprehensive validation, together with the sensitivity analyses confirming that the tool predictive capabilities are not heavily reliant on the initial model parameter settings, establishes K-AFFS as a powerful predictive tool with significant potential for application in the design of new liquid rocket engines.