# Standard k-epsilon model

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== Transport equations for standard k-epsilon model == | == Transport equations for standard k-epsilon model == | ||

- | For k <br> | + | For turbulent kinetic energy <math> k </math> <br> |

:<math> \frac{\partial}{\partial t} (\rho k) + \frac{\partial}{\partial x_i} (\rho k u_i) = \frac{\partial}{\partial x_j} \left[ \left(\mu + \frac{\mu_t}{\sigma_k} \right) \frac{\partial k}{\partial x_j}\right] + P_k + P_b - \rho \epsilon - Y_M + S_k </math> | :<math> \frac{\partial}{\partial t} (\rho k) + \frac{\partial}{\partial x_i} (\rho k u_i) = \frac{\partial}{\partial x_j} \left[ \left(\mu + \frac{\mu_t}{\sigma_k} \right) \frac{\partial k}{\partial x_j}\right] + P_k + P_b - \rho \epsilon - Y_M + S_k </math> | ||

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

- | C_{1 \epsilon} = 1.44, \;\; C_{2 \epsilon} = 1.92, \;\; C_{\mu} = 0.09, \;\; \sigma_k = 1.0, \;\; \sigma_{\epsilon} = 1.3 | + | C_{1 \epsilon} = 1.44, \;\;\; C_{2 \epsilon} = 1.92,\;\;\; C_{3 \epsilon} = -0.33, \;\; \; C_{\mu} = 0.09, \;\;\; \sigma_k = 1.0, \;\;\; \sigma_{\epsilon} = 1.3 |

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

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

## Revision as of 14:55, 22 August 2013

## Contents |

## Transport equations for standard k-epsilon model

For turbulent kinetic energy

For dissipation

## Modeling turbulent viscosity

Turbulent viscosity is modelled as:

## Production of k

Where is the modulus of the mean rate-of-strain tensor, defined as :

## Effect of buoyancy

where Pr_{t} is the turbulent Prandtl number for energy and g_{i} is the component of the gravitational vector in the ith direction. For the standard and realizable - models, the default value of Pr_{t} is 0.85.

The coefficient of thermal expansion, , is defined as