Large-eddy simulations of high-pressure shear coaxial flows relevant for H2/O2 rocket engines
Masquelet, Matthieu Marc
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The understanding and prediction of transient phenomena inside Liquid Rocket Engines (LREs) have been very difficult because of the many challenges posed by the conditions inside the combustion chamber. This is especially true for injectors involving liquid oxygen LOX and gaseous hydrogen GH₂. A wide range of length scales needs to be captured from high-pressure flame thicknesses of a few microns to the length of the chamber of the order of a meter. A wide range of time scales needs to be captured, again from the very small timescales involved in hydrogen chemistry to low-frequency longitudinal acoustics in the chamber. A wide range of densities needs to be captured, from the cryogenic liquid oxygen to the very hot and light combustion products. A wide range of flow speeds needs to be captured, from the incompressible liquid oxygen jet to the supersonic nozzle. Whether one desires to study these issues numerically or experimentally, they combine to make simulations and measurements very difficult whereas reliable and accurate data are required to understand the complex physics at stake. This thesis focuses on the numerical simulations of flows relevant to LRE applications using Large Eddy Simulations (LES). It identifies the required features to tackle such complex flows, implements and develops state-of-the-art solutions and apply them to a variety of increasingly difficult problems. More precisely, a multi-species real gas framework is developed inside a conservative, compressible solver that uses a state-of-the-art hybrid scheme to capture at the same time the large density gradients and the turbulent structures that can be found in a high-pressure liquid rocket engine. Particular care is applied to the implementation of the real gas framework with detailed derivations of thermodynamic properties, a modular implementation of select equations of state in the solver. and a new efficient iterative method. Several verification cases are performed to evaluate this implementation and the conservative properties of the solver. It is then validated against laboratory-scaled flows relevant to rocket engines, from a gas-gas reacting injector to a liquid-gas injector under non-reacting and reacting conditions. All the injectors considered contain a single shear coaxial element and the reacting cases only deal with H₂-O₂ systems. A gaseous oyxgen-gaseous hydrogen (GOX-GH₂) shear coaxial injector, typical of a staged combustion engine, is first investigated. Available experimental data is limited to the wall heat flux but extensive comparisons are conducted between three-dimensional and axisymmetric solutions generated by this solver as well as by other state-of-the-art solvers through a NASA validation campaign. It is found that the unsteady and three-dimensional character of LES is critical in capturing physical flow features, even on a relatively coarse grid and using a 7-step mechanism instead of a 21-step mechanism. The predictions of the wall heat flux, the only available data, are not very good and highlight the importance of grid resolution and near-wall models for LES. To perform more quantitative comparisons, a new experimental setup is investigated under both non-reacting and reacting conditions. The main difference with the previous setup, and in fact with most of the other laboratory rigs from the literature, is the presence of a strong co-flow to mimic the surrounding flow of other injecting elements. For the non-reacting case, agreement with the experimental high-speed visualization is very good, both qualitatively and quantitatively but for the reacting case, only poor agreement is obtained, with the numerical flame significantly shorter than the observed one. In both cases, the role of the co-flow and inlet conditions are investigated and highlighted. A validated LES solver should be able to go beyond some experimental constraints and help define the next direction of investigation. For the non-reacting case, a new scaling law is suggested after a review of the existing literature and a new numerical experiment agrees with the prediction of this scaling law. A slightly modified version of this non-reacting setup is also used to investigate and validate the Linear-Eddy Model (LEM), an advanced sub-grid closure model, in real gas flows for the first time. Finally, the structure of the trans-critical flame observed in the reacting case hints at the need for such more advanced turbulent combustion model for this class of flow.