A Multi-scale, Multi-domain Approach to Wall-Modelling for LES of High Reynolds Number Wall-Bounded Turbulence

Abstract

Application of LES to high Reynolds number wall-bounded turbulent flows of practical interest requires new methods for overcoming the large resolution requirement of the near-wall region, as well as subgrid-scale (SGS) models which remain robust regardless of the type of filter employed. To address these issues, a SGS model based on direct approximation of the nonlinear terms in the filtered Navier-Stokes equations has been developed. The resulting Nonlinear Interactions Approximation Model (NIAM) uses deconvolution to parameterize the local triadic interactions across the LES filter, and an eddy-viscosity term to represent the distant interactions. Tests of NIAM in LES of decaying isotropic turbulence at Re λ [approximate] 720, turbulent channel flow at Re τ [approximate] 210 and 570, and rotating turbulent channel flow at Re τ [approximate] 190 and rotation number Ro = 0.15 show that NIAM gives more accurate predictions of the skin-friction coefficient and turbulence statistics compared to popular existing models at comparable resolution. The near-wall resolution requirements are addressed by a novel multi-scale multi-domain (MSMD) approach. This method utilizes the quasi-periodicity of the near-wall turbulence structures to solve the flow in the near-wall region at fine resolution in a minimal flow unit large enough to accommodate only one packet of vortical structures. This flow unit is then repeated periodically or quasi-periodically and matched to a coarse-resolution but full-domain solution in the outer layer. The performance of the MSMD approach is found to be largely dependent on the size of the near-wall units employed. For near-wall units of spanwise size fixed in outer variables, ∼δ, accurate predictions can be obtained in both the near-wall region and outer layer. However, the resolution requirements of the method scale as O ([Special characters omitted.] Re$^{\textrm{2}}$ t ), which limits its applicability to Re τ ≤ 5000. For near-wall units of spanwise size fixed in inner variables, ∼ 1000 wall units, the method yields accurate predictions in the outer layer but only approximate results in the near-wall region. In this case, simulations can be performed with a resolution of 32 × 64 × 17 in the near-wall region and 32 × 64 × 33 in the outer layer for 1000 ≤ Re τ ≤ 10,000, independent of Re τ . At higher Reynolds numbers, the resolution requirements scale as O ( Re τ ).