Turbulence Models

You can calculate the effective turbulent viscosity in a fluid system based on the eddy viscosity model. There are two models in the eddy viscosity model:

• Standard K-Epsilon Model

The Standard K-Epsilon model is a Turbulence model available in Creo Flow Analysis.

formulation for the Turbulent Kinetic Energy k is:

formulation for the Turbulent Dissipation Rate ε is:

where,

c1=1.44 | constants C1 |

c2=1.92 | constants C2 |

σk=1 | turbulence kinetic energy Prandtl number |

σz=1 | turbulence dissipation rate Prandtl number |

turbulent kinetic energy | |

v’ | turbulent fluctuation velocity |

turbulent energy dissipation rate | |

strain tensor | |

u’i(i=1,2,3) | components of the turbulent fluctuation velocity |

turbulent viscosity, with Cμ=0.09 and E=9.793 | |

turbulence generation term | |

turbulence Reynolds stress | |

the Boussinesq approximation to the Reynolds Stress |

References: Launder, B.E. & Spalding, D.B. (1974) “The numerical computation of turbulent flows,” Computer Methods, Applied Mechanics and Engineering, vol. 3, pp. 269-289

• Renormalization Group (RNG) K-Epsilon Model

The Renormalization Group (RNG) K-Epsilon model is a Turbulence model available in Creo Flow Analysis. This model is similar to the Standard K-Epilson model but with an expression involving two new constants that are used to modify the C2 RNG term in the equation below:

where,

η0=4.38 | RNG constant (a hard-coded constant in Flow Analysis ) |

β=1.92 | RNG constant (a hard-coded constant in Flow Analysis ) |

P | local pressure |

c1=1.44 | constants C1 |

c2=1.92 | constants C2 |

σk=1 | turbulence kinetic energy Prandtl number |

σz=1 | turbulence dissipation rate Prandtl number |

turbulent kinetic energy | |

v’ | turbulent fluctuation velocity |

turbulent energy dissipation rate | |

strain tensor | |

u’i(i=1,2,3) | components of the turbulent fluctuation velocity |

turbulent viscosity, with Cμ=0.09 | |

turbulence generation term | |

turbulence Reynolds stress | |

Boussinesq approximation to the Reynolds stress |

References: Yakhot, V., Orszag, S.A., Thangam, S., Gatski, T.B. & Speziale, C.G. (1992), "Development of turbulence models for shear flows by a double expansion technique", Phys. of Fluids A, Vol. 4, No. 7, pp1510-1520