High-frequency combustion instabilities represent the main technical risk faced by design engineers when developing new chemical rocket propulsion systems. Such instabilities are driven by the coupling between the flames’ heat release rate and the combustion chamber’s acoustic field. As such, they can only be assessed during detailed design phases, making design iterations costly. Despite constant efforts being invested in developing numerical tools for their analysis, their reliable prediction remains a major issue. Furthermore, with the advent of the New Space industry, a need to cost-effectively analyze the stability of Hydrocarbon-based systems is stressed. As a result, this work contributes towards the development of a reliable numerical framework to predict the onset of high-frequency combustion instabilities in liquid rocket engines by ameliorating their acoustic modeling. More specifically, the performance of a novel Linearized Navier-Stokes (LNS) solver in COMSOL is benchmarked against its established Helmholtz solver and validated against the data of two hot-fires of DLR’s LOX/CH4 LUMEN engine. Following a step-wise increase in modeling complexity and by investigating how the background flow description influences the results, sub-5% eigenfrequency errors were obtained. The results also showed that the moving background flow in rocket engines significantly reduces the eigenfrequencies, and that its influence can be accounted for by prescribing varying flow properties to the acoustic solvers. Besides achieving the most accurate eigenfrequency results for a LOX/CH4 system, a more representative velocity disturbance distribution is also attained with the LNS simulation, allowing future studies to better account for the influence of velocity fluctuations on the heat release rate driving the instabilities.

The German Aerospace Centre (DLR) has in the past years been performing test runs with their experimental sub-scale combustion chambers to measure and investigate the effects of unstable combustion. Some of these investigations are focused on the heat flux to the chamber walls, changes in which can cause a significant shift in chamber wall strength and even melting, and can thus lead to structural failures. As a continuation of research regarding this phenomenon, the DLR combustion chamber version D (BKD) is used to investigate changes in heat flux, and its test data have been made available for this research. Using the test data, finding a relation between measured steady state heat flux and controlled chamber conditions became feasible, and changes in heat flux related to combustion instabilities can be identified. However, although these changes in heat flux are often observed and are described in literature as a known effect of combustion instabilities, there are currently no validated explanations as to why these effects take place. In an effort to provide this explanation, the results of a previously completed investigation regarding the DLR combustion chamber version H (BKH) are evaluated, as they allowed determination of a relation between combustion length and magnitudes of acoustic pressure oscillations. In this research, the results obtained for combustion length are converted to a model regarding varying heat flux profiles and modified as to implement them for BKD. Finally, the model predicted increases in heat flux during time periods when increases are observed experimentally, showing agreement with the experimental data. Besides this, a conversion in the model allowed reconstruction of a localised heat flux profile, which showed an increase in local heat flux near the injector face plate. This matches effects described in literature and observed in the experimental set-up after a test run with combustion instabilities. With this validation of the model, the theory developed and tested in this thesis work could prove a significant advancement in the understanding of effects of combustion chamber instabilities and their impact on the engine integrity and performance.

The prediction of high-frequency combustion instabilities is of relevance for liquid propellant rocket engines, to prevent risks or damages caused by overpressure and increased heat transfer to the walls. The main prediction method in rocket engines is through CFD simulations, which are computationally expensive, and require a significant set up process. This document presents a low-order tool capable of providing predictions in significantly less time than CFD simulations, with little to no setup time required by the user. The tool has the capability to predict stability, as well as computing the acoustic resonant frequencies of the system with an accuracy comparable to higher order models. The tool employs what is known as a "network model" and linear acoustics. The model includes new developments that improve its prediction capabilities with respect to the existing network model approaches present in literature. This includes acoustic elements capable of describing any isentropic flow, as well as distributed flame models that asses the stability of the combustion chambers of rocket engines. The document describes these new models in detail as well as their derivations. The new models are validated using experimental data from various rocket engines and load points tested at DLR Lampoldshausen. The validation shows that the acoustic resonant frequencies are predicted with an average error less than 5%. Furthermore, no single validation case presents an error over 10%. The tool is capable of predicting stability based on two parameters, the time lag and gain between perturbations in pressure and the flame response. Given these parameters the tool adequately predicts stability of the engines used for validation.