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.

跨临界湍流由可压缩纳维-斯托克斯方程和真实气体状态方程控制。它们的计算非常容易受到数值不稳定性的影响，并且需要动能和压力平衡保持方案来产生稳定且非耗散的尺度解析模拟。基于最近开发的基于传递压力方程的动能和压力保持平衡离散化框架，本文的目标是 (i) 推导一组适用于大涡流模拟的过滤方程组，以及 (ii) ）通过对跨临界壁面湍流直接数值模拟数据进行先验分析来表征所得子滤波器尺度项的属性。滤波操作会产生三个非常规的子滤波器尺度项，这些项是从压力方程中出现的，需要专门的建模。基于特征分解分析，对子滤波器尺度应力张量的大小、形状和方向进行剖析，并与现有的子滤波器尺度模型进行比较。先验分析证实，涡粘性模型有利于该框架，尽管张量形状尚未完全捕获。最终针对新颖的子过滤器项提出并测试了闭包表达式，显示出可接受的性能。