Abstract
We studied the effect of wall boundary conditions on the statistics in a wall-modeled large-eddy simulation (WMLES) of turbulent channel flows. Three different forms of the boundary condition based on the mean stress-balance equations were used to supply the correct mean wall shear stress for a wide range of Reynolds numbers and grid resolutions applicable to WMLES. In addition to the widely used Neumann boundary condition at the wall, we considered a case with a no-slip condition at the wall in which the wall stress was imposed by adjusting the value of the eddy viscosity at the wall. The results showed that the type of boundary condition utilized had an impact on the statistics (e.g., mean velocity profile and turbulence intensities) in the vicinity of the wall, especially at the first off-wall grid point. Augmenting the eddy viscosity at the wall resulted in improved predictions of statistics in the near-wall region, which should allow the use of information from the first off-wall grid point for wall models without additional spatial or temporal filtering. This boundary condition is easy to implement and provides a simple solution to the well-known log-layer mismatch in WMLES.
Highlights
We introduced three different boundary conditions for applying wall shear stress derived from the mean stress-balance equations for a turbulent channel flow with a nopenetration boundary condition (v|w = 0)
The Neumann boundary condition with nonzero eddy viscosity computed from the SGS model (N-EV)
The mean stress-balance equation can be satisfied by changing the eddy-viscosity be nonzero at the wall while applying a Dirichlet boundary condition for the velocities, which we call the Dirichlet boundary condition with eddy viscosity augmentation (D-EV)
Summary
Publisher’s Note: MDPI stays neutral with regard to jurisdictional claims in published maps and institutional affiliations. By modeling the near-wall flow such that only the large-scale motions in the outer region of the boundary layer are resolved, the grid-point requirement for wall-modeled LES scales at most linearly with increasing Reynolds number. Using the eddy viscosity at the wall as a wall-modeling term provides various options in imposing the correct wall shear stress through the stress-balance equation One such option is to impose a boundary condition on the eddy viscosity at the wall rather than the wallnormal derivative of the streamwise velocity [20]. We will show that augmenting the eddy-viscosity at the wall, rather than imposing a Neumann boundary condition for the wall-parallel velocities, provides a better prediction of the mean velocity profile and turbulence statistics in the first few grid points off the wall.
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