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The article investigates liquid oxygen (LOx)-methane supercritical combustiondynamics in a multi-element rocket scale combustor using large eddy simulation(LES). A complex framework of real gas thermodynamics and flamelet generatedmanifold (FGM) combustion model is invoked to simulate transcritical oxygeninjection and supercritical methane combustion. A benchmark Mascotte chamber,Rocket Combustion Modelling (RCM) Test Case, i.e. RCM-3 (V04)/G2 test case, isused to validate the real gas FGM model in the LES framework. The validationstudy accurately reproduces experimental flame structure and OH concentration,demonstrating the FGM model's importance in incorporating finite rate kineticsin LOx-methane combustion. Subsequently, the numerical framework investigates aspecially designed multi-element combustion chamber featuring sevenbidirectional swirl coaxial injectors. The analyses capture the complexhydrodynamics and combustion dynamics associated with multiple swirl injectorsoperating at supercritical pressure, effectively demonstrating the initiationof transverse acoustic waves and examining the effect of local sound speed onthe evolution of acoustic modes in the combustor. The dominant frequency modesshed light on understanding the role of injectors in enhanced combustordynamics. Spectral analysis reveals the interplay of the upstream injector andchamber acoustics due to possible frequency coupling. The results alsohighlight the effect of fuel injection temperature on the stability of thecombustor, revealing a violent dynamic activity for lower fuel injectiontemperature associated with the longitudinal acoustic mode of the combustor.The investigation appropriately reproduces self-sustained limit cycleoscillations at lower fuel injection temperatures and corroborates theconventional understanding of combustor instability.

Numerical Investigation of Supercritical Combustion Dynamics in a Multi-Element LOx-Methane Combustor Using Flamelet-Generated Manifold Approach