The article investigates liquid oxygen (LOx)–methane supercritical combustion dynamics in a multi-element rocket-scale combustor using large eddy simulation (LES). A complex framework of real gas thermodynamics and flamelet-generated manifold (FGM) combustion model is invoked to simulate transcritical oxygen injection and supercritical methane combustion. A benchmark Mascotte chamber, rocket combustion Modeling (RCM) test case, i.e., RCM-3 (V04)/G2 test case, is used to validate the real gas FGM model in the LES framework. The validation study accurately reproduces experimental flame structure and OH concentration, demonstrating the FGM model's importance in incorporating finite rate kinetics in LOx–methane combustion. Subsequently, the numerical framework investigates a specially designed multi-element combustion chamber featuring seven bidirectional swirl coaxial injectors. The analyses capture the complex hydrodynamics and combustion dynamics associated with multiple swirl injectors operating at supercritical pressure, effectively demonstrating the initiation of transverse acoustic waves and examining the effect of local sound speed on the evolution of acoustic modes in the combustor. The dominant frequency modes shed light on understanding the role of injectors in enhanced combustor dynamics. Spectral analysis reveals the interplay of the upstream injector and chamber acoustics due to possible frequency coupling. The results also highlight the effect of fuel injection temperature on the stability of the combustor, revealing a violent dynamic activity for lower fuel injection temperature associated with the longitudinal acoustic mode of the combustor. The investigation appropriately reproduces self-sustained limit-cycle oscillations at lower fuel injection temperatures and corroborates the conventional understanding of combustor instability.
