In the past fifty years, most design parameters of the combustion chamber of Liquid Rocket Engines (LREs) have been adjusted without a detailed understanding of combustion phenomena, because of both limited experimental diagnostics and numerical capabilities. The objective of the present thesis work is to conduct high-fidelity unsteady numerical simulations of transcritical reacting flows, in order to improve the understanding of flame dynamics in LRE, and eventually provide guidelines for their improvement. First real-gas thermodynamics and its impact on numerical schemes are presented. As Large-Eddy Simulation (LES) involves filtered equations, the filtering effects induced by real-gas thermodynamics are then highlighted in a typical 1D transcritical configuration and a specific real-gas artificial dissipation is proposed to smooth transcritical density gradients in LES. Then, a Direct Numerical Simulation (DNS) study of turbulent mixing and combustion in the near-injector region of LREs is conducted. In the non-reacting case, vortex shedding in the wake of the lip of the injector is shown to play a major role in turbulent mixing, and induces the formation of finger-like structures as observed experimentally in similar operating conditions. In the reacting case, the flame is attached to the injector rim without local extinction and the finger-like structures disappear. The flame structure is analyzed and various combustion modes are identified. Finally, a LES study of a transcritical H2/O2 jet flame, issuing from a coaxial injector with and without inner recess, is conducted. Numerical results are first validated against experimental data for the injector without recess. Then, the recessed configuration is compared to the reference solution and to experimental results, to scrutinize the effects of this design parameter on combustion efficiency.
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