Large eddy simulation of non-Newtonian viscous fluids with low grid dependency using an anisotropy-resolving subgrid-scale model

Abstract

Large eddy simulation (LES) is expected to be an efficient and accurate numerical method for predicting the behavior of non-Newtonian fluids. However, it has been reported that the LES results obtained using eddy viscosity subgrid-scale (SGS) models have a high dependency on the grid resolution for wall turbulence. In order to resolve this problem, in the present study, a mixed SGS model combining an isotropic eddy-viscosity model and a scale-similarity model, which is proposed by Inagaki and Abe (2017), is applied to non-Newtonian fluids obeying the power law. The model performance is tested in plane channel flows and pipe flows for the power-law index n of 0.5–1.15, using a wide range of grid resolution. The results demonstrate that, whereas conventional eddy viscosity SGS models significantly depend on the grid resolution, the present SGS model successfully prevents such grid dependency and yields accurate results even with relatively coarse grids for both pseudoplastic and dilatant fluids, where the modeled SGS shear stress consistently compensates the damped grid-scale (GS) shear stress. When decreasing the value of n (higher shear-thinning property), it has been recognized that the anisotropy of the turbulence is augmented. Since the present SGS model can express the anisotropy of the turbulence stress, the results from n=1 down to n=0.69 are in fairly good agreement with the DNS data, regardless of the grid resolution used, predicting the reduction of wall-friction drag, quantitatively. Upon further decreasing the value of n to 0.5, most eddy viscosity models do not maintain a turbulent state, whereas the present model maintains turbulence and provides results that are in reasonable agreement with the DNS data. The validity of the present model is also confirmed for high-Reynolds-number flows up to Reτ=750, where the grid independency is retained. These results demonstrate that the present model can remarkably reduce the computational cost of LES for non-Newtonian fluids.