Effect of subgrid-scale anisotropy on wall-modeled large-eddy simulation of turbulent flow with smooth-body separation

Abstract

We examine the role of anisotropic subgrid-scale (SGS) stress in wall-modeled large-eddy simulation (WMLES) of flow over a spanwise-uniform Gaussian-shaped bump, with emphasis on predicting flow separation. The simulations show that eddy-viscosity-based SGS models often yield non-monotonic predictions of the mean separation bubble size on the leeward side under grid refinement, whereas models incorporating anisotropic SGS stress produce more consistent results. To identify where SGS anisotropy is most critical, we introduce anisotropic SGS stress in selected regions of the domain. The results reveal that the windward side, where a strong favorable pressure gradient (FPG) occurs, is crucial in determining downstream separation. Analysis of the Reynolds stress transport equation shows that fluctuations of anisotropic SGS stress modify SGS dissipation and diffusion in this region, thereby altering the Reynolds stress and the onset of separation. Examination of the mean streamwise momentum equation indicates that at coarse resolutions, the mean SGS shear stress dominates, and the differences between the eddy-viscosity-based and anisotropic models remain minor. With grid refinement, resolved Reynolds stresses increasingly govern the near-wall momentum transport, and the influence of SGS stress fluctuations grows as they determine the SGS dissipation and diffusion of Reynolds stresses. Component-wise analysis of the SGS stress tensor further shows that the improvement arises mainly from including significant normal stress contributions. An a priori study using filtered direct numerical simulation of turbulent Couette-Poiseuille flow confirms that wall-bounded turbulence under FPG is highly anisotropic and that anisotropic SGS models provide a more realistic SGS stress representation than eddy-viscosity-based models.