Effect of subgrid-scale anisotropy on wall-modeled large-eddy simulation of separated flow

TL;DR

This work investigates how subgrid-scale (SGS) anisotropy affects wall-modeled large-eddy simulations (WMLES) of flow over a spanwise-uniform Gaussian bump, focusing on separation onset. By comparing isotropic eddy-viscosity SGS closures (Smagorinsky) with an anisotropic MSM closure and using an ideal wall boundary to fix the mean wall-shear, the study isolates SGS effects and reveals that anisotropic SGS stress, especially normal components near the wall under a favorable pressure gradient, crucially shapes Reynolds-stress distributions and downstream separation. A targeted a posteriori analysis shows the critical influence of anisotropic SGS stress on the windward, FPG-dominated region, where backscatter and redistribution of energy enhance inner-wall stress peaks and drive upstream-to-downstream history effects that determine bubble size. An a priori analysis with filtered DNS confirms strong near-wall anisotropy under FPG, supporting the need for anisotropic SGS formulations in WMLES of non-equilibrium wall-bounded turbulence. The results provide mechanistic insight and practical guidance for developing robust SGS models that can predict separation across mesh resolutions, highlighting the role of Reynolds-stress budgets and anisotropic dissipation/diffusion in enabling reliable WMLES of complex separated flows.

Abstract

We examine the role of anisotropic SGS stress in WMLES of flow over a spanwise-uniform Gaussian-shaped bump, with particular 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 across mesh resolutions. To identify where SGS anisotropy is most critical, we selectively introduce anisotropic SGS terms in different regions of the computational domain. The results reveal that the windward side near the bump peak, where a strong FPG occurs, plays a crucial role in determining downstream flow separation. Analysis of the Reynolds stress transport equation shows that fluctuations of anisotropic SGS stress directly modify SGS dissipation and diffusion in this region, thereby altering the Reynolds stress distributions and the onset of downstream 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. As the grid is refined, however, resolved Reynolds stresses increasingly govern the near-wall momentum transport, and the influence of SGS stress fluctuations becomes more pronounced, 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. Finally, an a priori study using filtered DNS of turbulent Couette-Poiseuille flow confirms that wall-bounded turbulence under FPG is highly anisotropic and that anisotropic SGS models provide a more realistic representation of SGS stress anisotropy than eddy-viscosity-based models.

Figures (33)

• Figure 1: Simulation set-up for flow over a Guassian-shaped bump.
• Figure 2: Isocontours of mean velocity $\overline{u}_x/U_{\infty}$ from the medium-mesh simulations with the SM (a) and MSM (b) and from the reference DNS uzun2022high (c).
• Figure 3: Isocontours of mean eddy viscosity $\overline{\nu}_t/\nu$ from the medium-mesh simulations with the SM (a) and MSM (b).
• Figure 4: Mean pressure coefficient on the bottom surface from the medium-mesh simulations with the SM and MSM along with the reference DNS uzun2022high.
• Figure 5: The profiles of mean streamwise velocity at $x/L = -0.7$ (a), $x/L = -0.2$ (b), $x/L = -0.1$ (c), $x/L = 0$ (d), $x/L = 0.05$ (e), $x/L = 0.1$ (f) and $x/L = 0.2$ (g) for the SM, MSM, and the reference DNS uzun2022high.