# Yap correction

### From CFD-Wiki

m (Elaboration on calculating <math>y_n</math> needed for the Yap correction) |
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- | The Yap correction consists of a | + | {{Turbulence modeling}} |

+ | 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: | ||

- | :<math>\rho S_\epsilon | + | :<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> |

Where | Where | ||

Line 7: | Line 8: | ||

:<math>l_e \equiv c_\mu^{-0.75} \, \kappa \, y_n</math> | :<math>l_e \equiv c_\mu^{-0.75} \, \kappa \, y_n</math> | ||

- | + | <math>y_n</math> is the normal distance to the nearest wall. | |

- | + | This source term should be added to the epsilon equation in the following way: | |

- | The Yap source term contains the explicit distance to the nearest wall, <math>y_n</math>. | + | :<math> |

+ | \frac{\partial}{\partial t} \left( \rho \epsilon \right) + | ||

+ | \frac{\partial}{\partial x_j} | ||

+ | \left[ | ||

+ | \rho \epsilon u_j - \left( \mu + \frac{\mu_t}{\sigma_\epsilon} \right) | ||

+ | \frac{\partial \epsilon}{\partial x_j} | ||

+ | \right] | ||

+ | = | ||

+ | \left( C_{\epsilon_1} f_1 P - C_{\epsilon_2} f_2 \rho \epsilon \right) | ||

+ | \frac{\epsilon}{k} | ||

+ | + \rho E | ||

+ | + \rho S_\epsilon | ||

+ | </math> | ||

+ | |||

+ | Where the epsilon equation has been written in the same way as is in the CFD-Wiki article on [[low-Re k-epsilon models]]. | ||

+ | |||

+ | 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. | ||

+ | |||

+ | 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. | ||

+ | |||

+ | ==Implementation issues== | ||

+ | |||

+ | 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??)''. | ||

+ | |||

+ | When implementing the Yap correction it is common to use it only if the source term is positive. Hence: | ||

+ | |||

+ | :<math>\rho S_\epsilon^{implemented} = max(\rho S_\epsilon, 0)</math> | ||

==References== | ==References== |

## Latest revision as of 18:55, 9 November 2010

The Yap correction [Yap. C. J. (1987)] consists of a modification of the epsilon equation in the form of an extra source term, , added to the right hand side of the epsilon equation. The source term can be written as:

Where

is the normal distance to the nearest wall.

This source term should be added to the epsilon equation in the following way:

Where the epsilon equation has been written in the same way as is in the CFD-Wiki article on low-Re k-epsilon models.

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.

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 [Launder, B. E. (1993)] recommends that the Yap correction should always be used with the epsilon equation.

## Implementation issues

The Yap source term contains the explicit distance to the nearest wall, . 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??)*.

When implementing the Yap correction it is common to use it only if the source term is positive. Hence:

## References

**Launder, B. E. (1993)**, "Modelling Convective Heat Transfer in Complex Turbulent Flows", 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.

**Yap, C. J. (1987)**, *Turbulent Heat and Momentum Transfer in Recirculating and Impinging Flows*, PhD Thesis, Faculty of Technology, University of Manchester, United Kingdom.