# Zeta-f model

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<math>\nu_t = C_\mu \, \zeta \, k \, T</math> | <math>\nu_t = C_\mu \, \zeta \, k \, T</math> | ||

- | == | + | == Turbulent kinetic energy <math>k</math> == |

<math>\frac{\partial k}{\partial t} + U_j \frac{\partial k}{\partial x_j} = P_k - \varepsilon + \frac{\partial}{\partial x_j} \left[ \left( \nu + \frac{\nu_t}{\sigma_{k}} \right) \frac{\partial k}{\partial x_j} \right]</math> | <math>\frac{\partial k}{\partial t} + U_j \frac{\partial k}{\partial x_j} = P_k - \varepsilon + \frac{\partial}{\partial x_j} \left[ \left( \nu + \frac{\nu_t}{\sigma_{k}} \right) \frac{\partial k}{\partial x_j} \right]</math> | ||

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== The turbulent kinetic energy dissipation rate <math>\varepsilon</math> == | == The turbulent kinetic energy dissipation rate <math>\varepsilon</math> == |

## Revision as of 12:26, 22 January 2007

The *zeta-f* model is a robust modification of the elliptic relaxation model. The set of equations, for the incompressible Newtonian fluid, constituting the model is given below.

## Turbulent viscosity

## Turbulent kinetic energy

## The turbulent kinetic energy dissipation rate

## The normalized fluctuating velocity normal to the streamlines

## The elliptic relaxation function

## The production of the turbulent kinetic energy

## The modulus of the mean rate-of-strain tensor

## The turbulence time scale

## The turbulence length scale

## The coefficients

, , , , , , , , , and .

## References

**Popovac, M., Hanjalic, K.**Compound Wall Treatment for RANS Computation of Complex Turbulent Flows and Heat Transfer, Flow, Turbulence and Combustion, DOI 10.1007/s10494-006-9067-x, 2007.

**Hanjalic, K., Popovac, M., Hadziabdic, M.**A robust near-wall elliptic-relaxation eddy-viscosity turbulence model for CFD, Int. J. Heat Fluid Flow, 25, 1047–1051, 2004.