# Realisable k-epsilon model

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where <math> \overline{\Omega_{ij}} </math> is the mean rate-of-rotation tensor viewed in a rotating reference frame with the angular velocity <math> \omega_k </math>. The model constants <math> A_0 </math> and <math> A_s </math> are given by: <br> | where <math> \overline{\Omega_{ij}} </math> is the mean rate-of-rotation tensor viewed in a rotating reference frame with the angular velocity <math> \omega_k </math>. The model constants <math> A_0 </math> and <math> A_s </math> are given by: <br> | ||

- | <math> A_0 = 4.04, \; \; A_s = \sqrt{6} \cos \phi </math> | + | <math> A_0 = 4.04, \; \; A_s = \sqrt{6} \cos \phi </math> <br> |

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+ | <math> \phi = \frac{1}{3} \cos^{-1} (\sqrt{6} W), \; \; W = \frac{S_{ij} S_{jk} S_{ki}}{{\tilde{S}} ^3}, \; \; \tilde{S} = \sqrt{S_{ij} S_{ij}}, \; \; S_{ij} = \frac{1}{2}\left(\frac{\partial u_j}{\partial x_i} + \frac{\partial u_i}{\partial x_j} \right) </math> | ||

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+ | ==Model Constants == | ||

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+ | <math> C_{1 \epsilon} = 1.44, \;\; C_2 = 1.9, \;\; \sigma_k = 1.0, \;\; \sigma_{\epsilon} = 1.2 </math> |

## Revision as of 23:09, 18 September 2005

## Transport Equations

Where

In these equations, represents the generation of turbulence kinetic energy due to the mean velocity gradients, calculated in same manner as standard k-epsilon model. is the generation of turbulence kinetic energy due to buoyancy, calculated in same way as standard k-epsilon model.

## Modelling Turbulent Viscosity

where

;

;

where is the mean rate-of-rotation tensor viewed in a rotating reference frame with the angular velocity . The model constants and are given by:

## Model Constants