http://www.cfd-online.com/W/index.php?title=Special:Contributions/Kett&feed=atom&limit=50&target=Kett&year=&month=CFD-Wiki - User contributions [en]2016-08-27T14:10:29ZFrom CFD-WikiMediaWiki 1.16.5http://www.cfd-online.com/Wiki/Yap_correctionYap correction2010-11-09T18:55:55Z<p>Kett: Elaboration on calculating <math>y_n</math> needed for the Yap correction</p>
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<div>{{Turbulence modeling}}<br />
The Yap correction [[#References|[Yap. C. J. (1987)]]] consists of a modification of the epsilon equation in the form of an extra source term, <math>S_\epsilon</math>, added to the right hand side of the epsilon equation. The source term can be written as:<br />
<br />
:<math>\rho S_\epsilon \equiv 0.83 \, \rho \, \frac{\epsilon^2}{k} \, \left(\frac{k^{1.5}}{\epsilon \, l_e} - 1 \right) \, \left(\frac{k^{1.5}}{\epsilon \, l_e} \right)^2</math><br />
<br />
Where<br />
<br />
:<math>l_e \equiv c_\mu^{-0.75} \, \kappa \, y_n</math><br />
<br />
<math>y_n</math> is the normal distance to the nearest wall.<br />
<br />
This source term should be added to the epsilon equation in the following way:<br />
<br />
:<math><br />
\frac{\partial}{\partial t} \left( \rho \epsilon \right) +<br />
\frac{\partial}{\partial x_j} <br />
\left[<br />
\rho \epsilon u_j - \left( \mu + \frac{\mu_t}{\sigma_\epsilon} \right) <br />
\frac{\partial \epsilon}{\partial x_j}<br />
\right]<br />
=<br />
\left( C_{\epsilon_1} f_1 P - C_{\epsilon_2} f_2 \rho \epsilon \right)<br />
\frac{\epsilon}{k}<br />
+ \rho E<br />
+ \rho S_\epsilon<br />
</math><br />
<br />
Where the epsilon equation has been written in the same way as is in the CFD-Wiki article on [[low-Re k-epsilon models]].<br />
<br />
The Yap correction is active in nonequilibrium flows and tends to reduce the departure of the turbulence length scale from its local equilibrium level. It is an ad-hoc fix which seldom causes any problems and often improves the predictions.<br />
<br />
Yap showed strongly improved results with the k-epsilon model in separated flows when using this extra source term. The Yap correction has also been shown to improve results in a stagnation region. Launder [[#References|[Launder, B. E. (1993)]]] recommends that the Yap correction should always be used with the epsilon equation.<br />
<br />
==Implementation issues==<br />
<br />
The Yap source term contains the explicit distance to the nearest wall, <math>y_n</math>. This distance is sometimes difficult to efficiently calculate in complex geometries. In structured grids, the coordinate distance to the nearest wall can be used as an approximation. Otherwise, a brute force calculation must be used which greatly benefits from a multi grid approach. In topologies with domain boundaries that are not walls the problem becomes more complex, because the non-wall boundaries will block the direct path to the wall boundaries. A simple loop over length must now be accompanied by topological path checking. This makes the Yap correction most suitable for use in a structured code where some normal wall distance is readily available. There are several alternative formulations that can be used instead though ''(anyone have the references??)''.<br />
<br />
When implementing the Yap correction it is common to use it only if the source term is positive. Hence:<br />
<br />
:<math>\rho S_\epsilon^{implemented} = max(\rho S_\epsilon, 0)</math><br />
<br />
==References==<br />
<br />
{{reference-paper|author=Launder, B. E.|year=1993|title=Modelling Convective Heat Transfer in Complex Turbulent Flows|rest=Engineering Turbulence Modeling and Experiments 2, Proceedings of the Second International Symposium, Florence, Italy, 31 May - 2 June 1993, Edited by W. Rodi and F. Martelli, Elsevier, 1993, ISBN 0444898026}}<br />
<br />
{{reference-book|author=Yap, C. J.|year=1987|title=Turbulent Heat and Momentum Transfer in Recirculating and Impinging Flows|rest=PhD Thesis, Faculty of Technology, University of Manchester, United Kingdom}}</div>Kett