On the magnitude of the subgrid-scale eddy coefficient in large-eddy simulations of turbulent channel flow

Abstract

A series of large-eddy simulations of plane Poiseuille flow are discussed. The subgrid-scale motions are represented by an eddy viscosity related to the flow deformation — the ‘Smagorinsky’ model. The resolution of the computational mesh is varied independently of the value of the coefficient Cs which determines the magnitude of this subgrid eddy viscosity. To ensure that results are from a statistically steady state unrealistic initial conditions are used and sufficient time is allowed for the flow to become independent of the initial conditions. In keeping with previous work it is found that for large Cs the resolved-scale motions are damped out; however, this critical value of Cs is found to depend on the mesh resolution. Only with a fine mesh does the value of Cs previously found to be appropriate for homogeneous turbulence (≈ 0.2) give simulations with sustained resolved-scale motions. The ratio l0/δ of the channel width 2δ to the scale of the ‘Smagorinsky’ mixing length, l0 = Cs Δ where Δ is a typical mesh spacing), is found to be the key parameter determining the ‘turbulent’ eddy-viscosity ‘Reynolds number’ of the resolved-scale motions. A fixed value of 10 is regarded as determining the separation of scales into resolved and subgrid. The value of l0 is regarded as a measure of numerical resolution and values of Cs less than about 0.2 correspond to inadequate resolution.