# Near-wall treatment for k-omega models

(Difference between revisions)
 Revision as of 22:26, 1 November 2011 (view source)m← Older edit Revision as of 11:59, 2 November 2011 (view source)mNewer edit → Line 4: Line 4: Main page: [[Two equation models#Near-wall treatments| Two equation near-wall treatments]] Main page: [[Two equation models#Near-wall treatments| Two equation near-wall treatments]] - For $k$ the boundary conditions imposed are + For $k$ the boundary conditions imposed at the solid boundary are: :$:[itex] - \frac{\partial k}{\partial y} = 0 + \begin{matrix} + \frac{\partial k}{\partial n} = 0 & & \frac{\partial \omega}{\partial n} = 0 + \end{matrix}$ [/itex] + where $n$ is the normal to the boundary. + Moreover the centroid values in cells adjacent to solid wall are specified as Moreover the centroid values in cells adjacent to solid wall are specified as :$:[itex] - k_p = \frac{u^2_\tau}{\sqrt{C_\mu}y_p} + \begin{matrix} -$ + k_p = \frac{u^2_\tau}{\sqrt{C_\mu}y_p}, - :$+ && - \omega_p = \frac{u_\tau}{\sqrt{C_\mu}\kappa y_p} = \frac{\sqrt{k_p}}{{C_\mu^{1/4}}\kappa y_p}, + \omega_p = \frac{u_\tau}{\sqrt{C_\mu}\kappa y_p} = \frac{\sqrt{k_p}}{{C_\mu^{1/4}}\kappa y_p}. + \end{matrix}$ [/itex] In the alternative approach $k$ production terms is modified. In the alternative approach $k$ production terms is modified.

## Revision as of 11:59, 2 November 2011

As described in Two equation turbulence models low and high reynolds number treatments are possible.

## Standard wall functions

Main page: Two equation near-wall treatments

For $k$ the boundary conditions imposed at the solid boundary are:

$\begin{matrix} \frac{\partial k}{\partial n} = 0 & & \frac{\partial \omega}{\partial n} = 0 \end{matrix}$

where $n$ is the normal to the boundary.

Moreover the centroid values in cells adjacent to solid wall are specified as

$\begin{matrix} k_p = \frac{u^2_\tau}{\sqrt{C_\mu}y_p}, && \omega_p = \frac{u_\tau}{\sqrt{C_\mu}\kappa y_p} = \frac{\sqrt{k_p}}{{C_\mu^{1/4}}\kappa y_p}. \end{matrix}$

In the alternative approach $k$ production terms is modified.

## Automatic wall treatments

Menter suggested a mechanism that switches automatically between HRN and LRN treatments.

The full description to appear soon. The idea is based on blending:

$\omega_\text{vis} = \frac{6\nu}{\beta y^2}$
$\omega_\text{log} = \frac{u_\tau}{C_\mu^{1/4} \kappa y}$
$\omega_p = \sqrt{\omega_{\text{vis}}^2 + \omega_{\text{log}}^2},$

$u_\tau = \sqrt[4]{(u_\tau^{\text{vis}})^4 + (u_\tau^{\text{log}})^4},$

## FLUENT

Both k- omega models (std and sst) are available as low-Reynolds-number models as well as high-Reynolds-number models.

The wall boundary conditions for the k equation in the k- omega models are treated in the same way as the k equation is treated when enhanced wall treatments are used with the k- epsilon models.

This means that all boundary conditions for
- wall-function meshes will correspond to the wall function approach, while for the
- fine meshes, the appropriate low-Reynolds-number boundary conditions will be applied.

In Fluent, that means:

If the Transitional Flows option is enabled in the Viscous Model panel, low-Reynolds-number variants will be used, and, in that case, mesh guidelines should be the same as for the enhanced wall treatment
(y+ at the wall-adjacent cell should be on the order of y+ = 1. However, a higher y+ is acceptable as long as it is well inside the viscous sublayer (y+ < 4 to 5).)

If Transitional Flows option is not active, then the mesh guidelines should be the same as for the wall functions.
(For [...] wall functions, each wall-adjacent cell's centroid should be located within the log-law layer, 30 < y+ < 300. A y+ value close to the lower bound y+ = 30 is most desirable.)

## References

• Menter, F., Esch, T. (2001), "Elements of industrial heat transfer predictions", 'COBEM 2001, 16th Brazilian Congress of Mechanical Engineering.'.
• ANSYS (2006), "FLUENT Documentation", .