A priori analysis for high-fidelity large-eddy simulation of wall-bounded transcritical turbulent flows

Transcritical turbulent flows are governed by the compressible Navier-Stokes equations along with a realgas equation of state. Their computation is strongly susceptible to numerical instabilities and requires kinetic -energy- and pressure -equilibrium -preserving schemes to yield stable and non -dissipative scale -resolving simulations. Building upon a recently developed kinetic -energy- and pressure -equilibrium -preserving discretization framework based on transporting a pressure equation, the objectives of this paper are to (i) derive a filtered set of equations suitable for large -eddy simulation, and (ii) characterize the properties of the resulting subfilterscale terms by performing a priori analyses of transcritical wall -bounded turbulence direct numerical simulation data. The filtering operation leads to three unconventional subfilter-scale terms that emerge from the pressure equation and require dedicated modeling. The subfilter-scale stress tensor is dissected in terms of magnitude, shape and orientation based on an eigendecomposition analysis, and compared with existing subfilter-scale models. A priori analyses confirm that models of eddy -viscosity type are favorable for this framework, although the tensor shape is not fully captured. Closure expressions are finally proposed and tested for the novel subfilter terms, showing acceptable performances.