Wall Treatment

Walls are a source of vorticity in most flow problems of practical importance. Therefore, an accurate prediction of flow and turbulence parameters across the wall boundary layer is essential.

The inner region of the boundary layer can be split up into three sublayers. In each of them the flow has different characteristics:

• Viscous sublayer

  The fluid layer in contact with the wall is dominated by viscous effects and is almost laminar. The mean flow velocity only depends on the fluid density, viscosity, distance from the wall, and the wall shear stress.

• Log layer

  The turbulent log layer is dominated equally by viscous and turbulent effects.

• Buffer layer

  The buffer layer is a transitional layer between the viscous sublayer and the log layer.

Each of the sublayers can be modeled using different empirical approaches. The non-dimensional wall distance $y^{\text{+}}$ , see Eqn. (1584), can be used to define the extents of the sublayers. The following plot shows the non-dimensional velocity $u^{\text{+}}$ , see Eqn. (1585), as a function of $y^{\text{+}}$ across the three sublayers:

Simcenter STAR-CCM+ provides the following types of wall treatment:

High- $y^{\text{+}}$

The high- $y^{\text{+}}$ wall treatment is equivalent to the traditional wall-function approach. This approach uses algebraic relations based on the assumed distribution of velocity, temperature, and turbulence quantities across the boundary layer to provide boundary conditions for the continuum equations. The accuracy of the wall-function approach depends on the degree to which the assumptions and approximations embodied in the functions correspond with the reality of the application. Most standard wall functions apply only to equilibrium conditions. However, Simcenter STAR-CCM+ extends the wall functions to include non-equilibrium effects.

This approach assumes that the near-wall cell lies within the log layer of the boundary layer at $y^{\text{+}}$ > 30. The main advantage of the high- $y^{\text{+}}$ wall treatment is therefore the significant savings in the number of near-wall cells.

Low- $y^{\text{+}}$

In general, the low- $y^{\text{+}}$ wall treatment is equivalent to the traditional low Reynolds number approach, where the boundary layer is resolved with a fine layered mesh and no modeling beyond the assumption of laminar flow is necessary to predict the flow across the wall boundary.

However, for robustness reasons, Simcenter STAR-CCM+ does not apply this approach but applies standard wall functions to obtain boundary conditions when the centroid of a near-wall cell lies in the viscous sublayer of the boundary layer.

To resolve the viscous sublayer, these models require a sufficiently fine mesh with near-wall cells located at $y^{\text{+}}$ of around unity. The computational expense that is associated with this approach can be significant, particularly for large Reynolds number flows where the viscous sublayer can be very thin. Therefore this wall treatment is suitable only for low Reynolds number flows.

All- $y^{\text{+}}$

The all- $y^{\text{+}}$ wall treatment uses blended wall functions that emulate the low- $y^{\text{+}}$ wall treatment for fine meshes, and the high- $y^{\text{+}}$ wall treatment for coarse meshes.

It is also formulated with the desirable characteristic of producing reasonable answers for meshes of intermediate resolution, that is, when the wall-cell centroid falls within the buffer region of the boundary layer. Therefore, this wall treatment is suitable for a wide range of near-wall mesh densities.

Two-layer all- $y^{\text{+}}$

The two-layer all- $y^{\text{+}}$ wall treatment, which is available for the two-layer turbulence models, uses an approach that is identical to the all- $y^{\text{+}}$ wall treatment. However, specific values of the turbulence dissipation rate $\epsilon$ are imposed at the centroids of the near-wall cells to make it consistent with the two-layer formulation of the underlying turbulence model.