Testing of logarithmic-law for the slip with friction boundary condition

Abstract

Large eddy simulation (LES) seeks to predict the dynamics of the organized structures in the flow, that is, local spatial averages u ̄ $\bar{u}$ of the velocity u of the fluid. Although LES has been extensively used to model turbulent flows, very often, the model has difficulty predicting turbulence generated by interactions of a flow with a boundary. A critical problem in LES is to find appropriate boundary conditions for the flow averages, which depend on the behavior of the unknown flow near the wall. In the light of the works of Navier and Maxwell, we use boundary conditions on the wall. We compute the appropriate friction coefficient β for channel flows and investigate its asymptotic behavior as the averaging radius δ → 0 and as the Reynolds number Re → ∞. No-slip conditions are recovered in the first limit, and free-slip conditions are recovered in the second limit. This study is not intended to develop new theories of the turbulent boundary layer; we use available boundary layer theories to improve numerical boundary conditions for flow averages.

Application of a near wall model to Navier-Stokes equations with nonlinear time-relaxation model

“…There are different studies on the laminar and turbulence boundary layer theory; see, e.g., [3]. The friction coefficient can be calculated using other descriptions [14,16,21], but it is calculated for the wall law of a laminar boundary layer in this section. Consider the flat plane Ω = {(x, y), y > 0} [14].…”

“…We present a benchmark problem of two-dimensional channel flow over a backward-facing step. This problem was considered in [11,[14][15][16]21]. We investigate the dependency of the position of the reattachment point of the recirculating eddy in two-dimensional channel flow with different values of the friction parameter β .…”