# Shuai-Agarwal turbulence Model

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

- | One-equation k-kL turbulence model was developed from two-equation k-kL closure of Abdol-Hamid et al | + | One-equation k-kL turbulence model was developed from two-equation k-kL closure of Abdol-Hamid et al. Improvements to the original formulation of one-equation k-kL model (AIAA 2019-1879) were made by optimizing the model constants (AIAA 2020-1075). The new improved model has been validated by simulating several benchmark canonical wall-bounded turbulent flows with small regions of separation from NASA TMR (https://turbmodels.larc.nasa.gov/). The model needs further investigations by the scientific community to evaluate its potential. |

==Shuai – Agarwal One Equation k-kL Turbulence Model == | ==Shuai – Agarwal One Equation k-kL Turbulence Model == | ||

- | '''The turbulent viscosity is given by:''' | + | '''The turbulent kinematic viscosity is given by:''' |

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

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

- | P=\frac{\tau_{ij}}{\rho} \frac{\partial u_{i}}{\partial | + | P=\frac{\tau_{ij}}{\rho} \frac{\partial u_{i}}{\partial x_{j}} |

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

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

- | S_{i j}=\frac{1}{2}\left(\frac{\partial u_{i}}{\partial | + | S_{i j}=\frac{1}{2}\left(\frac{\partial u_{i}}{\partial x_{j}} + \frac{\partial u_{j}}{\partial x_{i}} \right) |

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

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- | '''The | + | '''The parameters of the model are:''' |

:<math> | :<math> |

## Latest revision as of 19:43, 10 April 2021

## Introduction

One-equation k-kL turbulence model was developed from two-equation k-kL closure of Abdol-Hamid et al. Improvements to the original formulation of one-equation k-kL model (AIAA 2019-1879) were made by optimizing the model constants (AIAA 2020-1075). The new improved model has been validated by simulating several benchmark canonical wall-bounded turbulent flows with small regions of separation from NASA TMR (https://turbmodels.larc.nasa.gov/). The model needs further investigations by the scientific community to evaluate its potential.

## Shuai – Agarwal One Equation k-kL Turbulence Model

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

**The final form of the new Shuai-Agarwal one-equation k-kL model is obtained as: **

**Where is the production term:**

**The following Bradshaw relation is used to express the relationship between and k and kL:**

**The parameters of the model are:**

**The model constants are:**

## References

**S. Shuai and R. K. Agarwal (2020)**, "A New Improved One-Equation Turbulence Model Based on k-kL Closure", AIAA Paper 2020-1075, January 2020.**K. S. Abdol-Hamid, J. R. Carlson, and C. L. Rumsey (2016)**, "Verification and Validation of the k-kL Turbulence Model in FUN3D and CFL3D Codes", AIAA 2016-3941, 2016.