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12.3.1 Near-Wall Mesh Guidelines

Wall Functions

The log-law, which is valid for equilibrium boundary layers and fully developed flows, provides upper and lower limits on the acceptable distance between the near-wall cell centroid and the wall. The distance is usually measured in the dimensionless wall units, $y^+$ ( $\equiv \rho u_{\tau} y/\mu$), or $y^*$. Note that $y^+$ and $y^*$ have comparable values when the first cell is placed in the log-layer but are different by $C_{\mu}^{1/4}$ i.e. $\approx$ 0.5.

Enhanced Wall Treatment

Although the enhanced wall treatment is designed to extend the validity of the near-wall modeling beyond the viscous sublayer, it is still recommended that you construct a mesh that will be sufficient to resolve the viscosity-affected near-wall region. In such case, the two-layer component of the enhanced wall treatment will be dominant and the following mesh requirements are recommended (note that, here, the mesh requirements are in terms of $y^+$, not $y^*$):

Spalart-Allmaras Model

The Spalart-Allmaras model in its complete implementation is a low-Reynolds-number model. This means that it is designed to be used with meshes that properly resolve the viscosity-affected region, and the damping functions have been built into the model to attenuate the turbulent viscosity in the viscous sublayer. Therefore, to obtain the full benefit of the Spalart-Allmaras model, the near-wall mesh spacing should be as described in Section  12.3.1.

The boundary conditions for the Spalart-Allmaras model (see this section in the separate Theory Guide) have been implemented so that the model is capable to work on coarser meshes, that are suitable for the wall function approach. If you are using a coarse mesh, you should follow the guidelines described in Section  12.3.1.

In summary to achieve the best results with the Spalart-Allmaras model, one should use either a very fine near-wall mesh (on the order of $y_{\rho}^+ = 1$ for the first near-wall cell center) or a mesh with $y^+ \geq 30$.

$k$- $\omega$ Models

Both $k$- $\omega$ models available in ANSYS FLUENT are available as low-Reynolds-number models as well as high-Reynolds-number models. Therefore, the mesh guidance should be the same as for the enhanced wall treatment. However if the Low-Re Corrections option in Viscous Model dialog box is enabled, then the intention is to resolve the laminar sublayer. For cases where the laminar sublayer is adjacent to wall cells, it should be constructed so as to result in $y^+$ being in the range of 1.

Transition Models ( $k$- $kl$- $\omega$ or SST Based Model)

Proper mesh refinement and specification of inlet turbulence levels is crucial for accurate transition prediction. In general, there is some additional effort required during the mesh generation phase because a low-Re mesh with sufficient streamwise resolution is needed to accurately resolve the transition region. Furthermore, in regions where laminar separation occurs, additional mesh refinement is necessary in order to properly capture the rapid transition due to the separation bubble. Finally, the decay of turbulence from the inlet to the leading edge of the device should always be estimated before running a solution as this can have a large effect on the predicted transition location.

Large Eddy Simulation

For the LES in ANSYS FLUENT, the wall boundary conditions have been implemented using a law-of-the-wall approach (see this section in the separate Theory Guide). This means that there are no computational restrictions on the near-wall mesh spacing. However, for best results, it might be necessary to use a very fine near-wall mesh spacing (on the order of $y^+ = 1$).

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