http://www.cfd-online.com/W/index.php?title=Special:Contributions/Baldy&feed=atom&limit=50&target=Baldy&year=&month=CFD-Wiki - User contributions [en]2016-07-01T22:11:55ZFrom CFD-WikiMediaWiki 1.16.5http://www.cfd-online.com/Wiki/Near-wall_treatment_for_k-omega_modelsNear-wall treatment for k-omega models2009-07-29T05:09:40Z<p>Baldy: spelling</p>
<hr />
<div>{{Turbulence modeling}}<br />
Both k- omega models (std and sst) are available as low-Reynolds-number models as well as high-Reynolds-number models. <br><br />
<br />
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. <br><br />
<br />
This means that all boundary conditions for <br><br />
- '''wall-function meshes''' will correspond to the wall function approach, while for the <br><br />
- '''fine meshes''', the appropriate low-Reynolds-number boundary conditions will be applied. <br><br />
<br />
that means:<br />
<br />
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 <br><br />
''(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).)''<br><br />
<br />
If '''Transitional Flows option is not active''', then the mesh guidelines should be the same as for the wall functions.<br><br />
''(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.)''<br />
<br />
<br><br />
<br />
Reference: <br />
FLUENT 6.2 Documentation, 2006 <br></div>Baldyhttp://www.cfd-online.com/Wiki/LES_filtersLES filters2009-06-29T18:56:42Z<p>Baldy: Undo revision 9784 by Baldy (Talk)</p>
<hr />
<div>In [[Large eddy simulation]] (LES) only the large scale motions of the flow are solved for by filtering out the small and [[universal]] eddies. In practical applications of some [[SGS models]], implicit filtering is done by the grid itself and programmers need not worry about the filtering operation. The values of velocity on the grid are the filtered values of velocity. However, for some SGS models, such as the [[Dynamic subgrid-scale model]] an explicit filtering step is required to compute the [[SGS stress]] tensor. Additionally, in the theoretical analysis of LES, filtering a function is defined as convoluting the function with a filtering kernel, just as is typically done in electrical engineering.<br />
<br />
Some of the commonly used filters are defined below. In all cases, <math> \Delta </math> is the filter width, <math> G(x) </math> is the filtering kernel in physical space and <math>\widehat{G(k)}</math> is the filtering kernel in [[Fourier transform|Fourier]]-[[wavenumber]] space.<br />
<br />
== Box filter ==<br />
<br />
The Box filter is the same as the "grid filter" whereby the filter cuts off the values of the function beyond a half filter width away.<br />
<br><br />
:<math><br />
G(x) = \frac{1}{\Delta} H\left( \frac{1}{2}\Delta -|x| \right)<br />
</math><br />
where H is the [[Heaviside function]],<br />
<br><br />
:<math><br />
\widehat{G(k)} = \frac{\sin \left (\frac{1}{2} k \Delta \right)}{ \frac{1}{2} k \Delta}<br />
</math><br />
<br />
== Gaussian filter ==<br />
<br />
The Gaussian filter is a normalized [[Gaussian function]]. The Fourier transform of a Gaussian function is also a Gaussian, hence the G(x) and <math>\widehat{G(k)}</math> have very similar forms,<br />
<br><br />
:<math><br />
G(x) = \left( \frac{6}{\pi \Delta^2} \right)^{1/2} e^{ \frac{-6 x^2}{\Delta^2}}<br />
</math><br />
<br><br />
:<math><br />
\widehat{G(k)} = e^{ \frac{-k^2 \Delta^2}{24} }<br />
</math></div>Baldyhttp://www.cfd-online.com/Wiki/LES_filtersLES filters2009-06-29T18:53:39Z<p>Baldy: </p>
<hr />
<div>In [[Large eddy simulation]] (LES) only the large scale motions of the flow are solved for by filtering out the small and [[universal]] eddies. In practical applications of some [[#Subgrid-scale models|SGS models]], implicit filtering is done by the grid itself and programmers need not worry about the filtering operation. The values of velocity on the grid are the filtered values of velocity. However, for some SGS models, such as the [[Dynamic subgrid-scale model]] an explicit filtering step is required to compute the [[SGS stress]] tensor. Additionally, in the theoretical analysis of LES, filtering a function is defined as convoluting the function with a filtering kernel, just as is typically done in electrical engineering.<br />
<br />
Some of the commonly used filters are defined below. In all cases, <math> \Delta </math> is the filter width, <math> G(x) </math> is the filtering kernel in physical space and <math>\widehat{G(k)}</math> is the filtering kernel in [[Fourier transform|Fourier]]-[[wavenumber]] space.<br />
<br />
== Box filter ==<br />
<br />
The Box filter is the same as the "grid filter" whereby the filter cuts off the values of the function beyond a half filter width away.<br />
<br><br />
:<math><br />
G(x) = \frac{1}{\Delta} H\left( \frac{1}{2}\Delta -|x| \right)<br />
</math><br />
where H is the [[Heaviside function]],<br />
<br><br />
:<math><br />
\widehat{G(k)} = \frac{\sin \left (\frac{1}{2} k \Delta \right)}{ \frac{1}{2} k \Delta}<br />
</math><br />
<br />
== Gaussian filter ==<br />
<br />
The Gaussian filter is a normalized [[Gaussian function]]. The Fourier transform of a Gaussian function is also a Gaussian, hence the G(x) and <math>\widehat{G(k)}</math> have very similar forms,<br />
<br><br />
:<math><br />
G(x) = \left( \frac{6}{\pi \Delta^2} \right)^{1/2} e^{ \frac{-6 x^2}{\Delta^2}}<br />
</math><br />
<br><br />
:<math><br />
\widehat{G(k)} = e^{ \frac{-k^2 \Delta^2}{24} }<br />
</math></div>Baldyhttp://www.cfd-online.com/Wiki/Smagorinsky-Lilly_modelSmagorinsky-Lilly model2009-06-19T19:42:12Z<p>Baldy: Grammatical correction</p>
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<div>The Smagorinsky model could be summarised as:<br />
:<math><br />
\tau _{ij} - \frac{1}{3}\tau _{kk} \delta _{ij} = - 2\left( {C_s \Delta } \right)^2 \left| {\bar S} \right|S_{ij} <br />
</math> <br><br />
<br />
In the Smagorinsky-Lilly model, the eddy viscosity is modeled by <br><br />
<br />
<br />
:<math><br />
\mu _{sgs} = \rho \left( {C_s \Delta } \right)^2 \left| {\bar S} \right|<br />
</math> <br />
<br><br />
<br />
Where the filter width is usually taken to be<br />
:<math><br />
\Delta = \left( \mbox{Volume} \right)^{\frac{1}{3}} <br />
</math> <br />
<br><br />
and <br />
:<math><br />
\bar S = \sqrt {2S_{ij} S_{ij} } <br />
</math><br />
<br />
The effective viscosity is calculated from <br><br />
:<math><br />
\mu _{eff} = \mu _{mol} + \mu _{sgs} <br />
</math><br />
The Smagorinsky constant usually has the value: <br />
:<math><br />
C_s = 0.1 - 0.2<br />
</math></div>Baldy