# Wray-Agarwal(WA) Turbulence Model

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== Introduction == | == Introduction == | ||

- | The WA 2017m model is a one-equation model that was derived from two-equation <math>k-\omega</math> closure. It combines the most desirable characteristics of the one-equation <math>k-\epsilon</math> model and one-equation <math>k-\omega</math> model, analogous to the SST <math>k-\omega</math> model which combines best features of two-equation <math>k-\epsilon</math> and <math>k-\omega</math> models. | + | The Wray-Agarwal (WA 2017m) model is a one-equation linear eddy viscosity model that was derived from two-equation <math>k-\omega</math> closure. It combines the most desirable characteristics of the one-equation <math>k-\epsilon</math> model and one-equation <math>k-\omega</math> model, analogous to the SST <math>k-\omega</math> model which combines best features of two-equation <math>k-\epsilon</math> and <math>k-\omega</math> models. |

- | ==WA Model== | + | ==WA Model (WA 2017m) == |

'''The turbulent eddy viscosity is given by:''' | '''The turbulent eddy viscosity is given by:''' | ||

Line 22: | Line 22: | ||

- | ''' | + | '''where''' |

Line 67: | Line 67: | ||

:<math> | :<math> | ||

{{\sigma }_{k\varepsilon }}=1.0 | {{\sigma }_{k\varepsilon }}=1.0 | ||

+ | </math> | ||

+ | |||

+ | :<math> | ||

+ | {{\sigma}_{R}}={{f}_{1}}\left( {{\sigma}_{k\omega }}-{{\sigma}_{k\varepsilon }} \right)+{{\sigma}_{k\varepsilon }} | ||

</math> | </math> | ||

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C_{m} = 8.0 | C_{m} = 8.0 | ||

</math> | </math> | ||

- | |||

==Boundary Conditions== | ==Boundary Conditions== | ||

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

- | *{{reference-paper|author=X. Han, T. J. Wray, and R. K. Agarwal | + | *{{reference-paper|author=X. Han, T. J. Wray, and R. K. Agarwal|year=2017|title=Application of a New DES Model Based on Wray-Agarwal Turbulence Model for Simulation of Wall-Bounded Flows with Separation|rest= AIAA Paper 2017-3966, June 2017}} |

[[Category:Turbulence models]] | [[Category:Turbulence models]] |

## Latest revision as of 17:19, 19 February 2021

## Contents |

## Introduction

The Wray-Agarwal (WA 2017m) model is a one-equation linear eddy viscosity model that was derived from two-equation closure. It combines the most desirable characteristics of the one-equation model and one-equation model, analogous to the SST model which combines best features of two-equation and models.

## WA Model (WA 2017m)

**The turbulent eddy viscosity is given by:**

**The model solves for the variable using the following equation:**

**where**

**and d is the minimum distance to the nearest wall.**
**The model constants are:**

## Boundary Conditions

**Solid smooth wall:**

**Freestream:**

## References

**X. Han, T. J. Wray, and R. K. Agarwal (2017)**, "Application of a New DES Model Based on Wray-Agarwal Turbulence Model for Simulation of Wall-Bounded Flows with Separation", AIAA Paper 2017-3966, June 2017.