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

Abstract

Transcritical turbulent flows are governed by the compressible Navier–Stokes equations along with a real-gas 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 subfilter-scale 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.