WALL-MODEL FOR LARGE-EDDY SIMULATION AND ITS APPLICATIONS

doi:10.6052/0459-1879-18-071

Abstract

Abstract:

Large-eddy simulation (LES) is an important method to investigate unsteady turbulent flows. The cost of the wall-resolved LES is comparable to that of direct numerical simulation, which prevents the applications of the LES to wall-bounded turbulences at high Reynolds numbers. The grid length would be of the order of the viscous length to resolve the near-wall flow structures, which causes the prohibitive computational cost of the wall-resolved LES. Wall-models circumvent the flow details near the wall to avoid resolving all the flow structures near the wall, which significantly reduce the computation cost and have been successfully combined with the LES for turbulent flows. We discuss the basic idea of wall-models for LES and review the wall-stress models with implementation details. The construction and characteristics of the equilibrium models and the two-layer models are discussed in detail. The limitations of the wall-stress models and their improvements to account for the non-equilibrium effects are also discussed. We review the state of the art of the wall shear stress models and provide a hierarchical diagram for the current models. Finally, we present the applications of the Werner-Wengle model to the LES of flows over periodic hills.

Key words: Large-eddy simulation, wall-model, wall-stress model, two-layer model, flows over periodic hills

CLC Number:

O357

Wu Ting, Shi Beiji, Wang Shizhao, Zhang Xing, He Guowei. WALL-MODEL FOR LARGE-EDDY SIMULATION AND ITS APPLICATIONS[J]. Chinese Journal of Theoretical and Applied Mechanics, 2018, 50(3): 453-466.

Figures/Tables 11

Fig. 1 Diagrammatic sketch of the LES region and the wall-model. If meshes near the wall is too coarse to resolve the flow structure, the viscous stress obtained by the usual finite difference operator is not correct. Wall-models can guarantee the momentum conservation on coarse meshes near the wall, obtaining correct velocity profiles (modified based on the Fig.2 of Ref.[9])

Fig. 2 Schematic of the staggered mesh and the boundary

Fig. 3 Wall-models for LES of wall-bounded turbulence. Wall-stress models are widely used in LES. The equilibrium models and the two-layer models are the two main branches of the wall-stress models. The equilibrium models compute the wall-stress based on the equilibrium boundary layer near the wall. The two-layer models compute the wall-stress by solving the simplified equations near the wall. The improved versions of the equilibrium models have the capability of accounting for the non-equilibrium effects

Fig. 4 The streamlines and the profiles of the mean streamwise velocities at different streamwise locations

Fig. 5 A two-dimensional slice of the grid used for LES of the flows over periodic hills

Fig. 6 The profiles of the mean streamwise velocities

Fig. 7 The profiles of the mean wall-normal velocities

Fig. 8 The variance of streamwise velocities

Fig. 9 The variance of wall-normal velocities

Fig. 10 The profiles of Reynolds stresses

Fig. 11 The friction and the pressure coefficients along the bottom wall

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