Computation of High Reynolds Number Equilibrium and Nonequilibrium Turbulent Wall-Bounded Flows Using a Nested LES Approach

Abstract

A new nested LES approach for computing high Reynolds number, wall-bounded turbulent flows is presented. The method is based on nested LES of the full-domain at coarse resolution, coupled with well-resolved LES of a minimal flow unit. The coupling between the two domains is achieved by renormalizing the kinetic energies of components of the mean velocity and the turbulent velocity fluctuations in both domains to that of the minimal flow unit in the near-wall region, and to that of the full-size domain in the outer region, at each time-step. The method can be implemented with a fixed number of grid points, independent of Reynolds number, in any given geometry, and is applicable to both equilibrium and nonequilibrium flows. The proposed method has been applied to LES of equilibrium turbulent channel flow at \(1000\le Re_\tau \le 10{,}000\) and LES of nonequilibrium, shear-driven, three-dimensional turbulent channel flow at \(Re_\tau \simeq 2000\). All computations were performed using a spectral patching collocation method, and employed resolutions of \(64\times 64\times 17/33/17\) in the full-size domain (\(L_x \times L_y = 2\pi \times \pi \)), and resolutions of \(32 \times 64 \times 17/33/17\) and \(64 \times 64 \times 17/33/17\) the minimal flow units (\(l_x^+ \,\times \, l_y^+ \approx 3200 \times 1600 \)) of equilibrium and non-equilibrium channel flows, respectively. The dynamic Smagorinsky model with spectral cutoff filter was used as the SGS model in all the simulations. The results show that the proposed nested LES approach can predict the friction coefficient to within 5 % of Dean’s correlation in equilibrium turbulent channel flow, and the one-point turbulence statistics in good agreement with DNS and experimental data in turbulent channel flow and in shear-driven, three-dimensional turbulent boundary layer.