Slip with friction boundary conditions for the Navier–Stokes-[formula omitted] turbulence model and the effects of the friction on the reattachment point

Abstract

The main purpose of this study is to apply the slip with friction boundary condition on a turbulence model, namely the Navier–Stokes-α model (NS-α). To achieve this, the appropriate friction coefficient is calculated using the power law and the slip with friction boundary condition. Then its asymptotic behavior is analyzed as the averaging radius δ→0 and as the Reynolds number Re→∞. Numerical tests are performed on two dimensional channel flows across a step. This is done by using the slip with friction boundary condition on the top and bottom wall as well as on the step. The effects of Reynolds numbers and friction coefficients on reattachment points are investigated. All numerical tests reveal that the reattachment points prediction is improved by the proposed boundary conditions. The fact that the presented model is nearly identical to the real-world problem is a contributing factor to this study.