Modeling the equations of state using a flamelet approach in LRE-like conditions

In this study, we investigate the averaging and modeling of real fluid equations of state (EoS) used in the context of numerical simulations of flows under conditions relevant to liquid rocket engine (LRE) thrust chambers. Direct numerical simulation (DNS) data of supercritical and transcritical mixing are used, in an a-priori fashion, to glean insight on the effect of averaging the EoS in the context of Reynolds averaged Navier Stokes (RANS). The widely employed no-model approach for the EoS, which neglects residual effects, is shown to generate large errors under transcritical conditions due to the extreme non-linearity of the pseudo-boiling processes. Further a-priori analysis, performed by filtering the DNS data in a large eddy simulation (LES) context, shows that highly resolved LES mitigates such sub grid scale errors. We discuss such EoS modeling related issues in the context of flamelet based turbulent combustion approaches and low Mach number assumptions, under which they acquire an unambiguous thermodynamic consistency. We show a-posteriori that a steady laminar flamelet formulation, implemented in a low Mach number unsteady RANS solver, is capable of correctly capturing the characteristic flow field and structure of a reference liquid oxygen (LOx) - gaseous methane (GCH4) cryogenic flame at supercritical pressure.