Low-Order Modeling and High-Fidelity Simulations for the Prediction of Combustion Instabilities in Liquid Rocket Engines and Gas Turbines

Combustion instabilities are a major concern in the design of Liquid Rocket Engines (LREs) and gas turbines. During this PhD work, several directions were explored to understand and mitigate their effects. First, more efficient and robust numerical methods for their prediction in complex combustors were designed. In this matter, a novel type of modal expansion, named a frame expansion and comparable to the classical Galerkin expansion, was introduced to build more accurate acoustic Low-Order Models (LOMs), able to account for the full geometrical complexity of industrial combustors. In particular, the frame expansion is able to accurately represent the acoustic velocity field near non-rigid-wall boundaries, a crucial ability that the Galerkin method lacks. An entire class of novel numerical methods, based on the frame expansion, were then designed and combined with the state-space formalism to build acoustic networks of complex systems. The second ingredient in the prediction of thermoacoustic instabilities is the flame dynamics modeling. This work dealt with this problem, in the specific case of a cryogenic coaxial jet-flame characteristic of a LRE. Flame dynamics driving phenomena were identified thanks to three-dimensional Large Eddy Simulations (LES) of the Mascotte experimental test rig where both reactants (CH4 and O2) are injected in transcritical conditions. Several LES with harmonic modulation of the fuel inflow at various frequencies and amplitudes were performed in order to evaluate the flame response to acoustic oscillations and compute a Flame Transfer Function (FTF). The stabilization of this flame in the near-injector region, which is of primary importance on the overall flame dynamics, was also investigated thanks to multi-physics two-dimensional Direct Numerical Simulations (DNS), where a conjugate heat transfer problem is resolved at the injector lip.