Zeta-f model
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<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> | ||
- | == | + | == Turbulent kinetic energy dissipation rate <math>\varepsilon</math> == |
<math>\frac{\partial \varepsilon}{\partial t} + U_j \frac{\partial \varepsilon}{\partial x_j} = \frac{C_{\varepsilon 1} P_k - C_{\varepsilon 2} \varepsilon}{T} + \frac{\partial}{\partial x_j} \left[ \left( \nu + \frac{\nu_t}{\sigma_{\varepsilon}} \right) \frac{\partial \varepsilon}{\partial x_j} \right]</math> | <math>\frac{\partial \varepsilon}{\partial t} + U_j \frac{\partial \varepsilon}{\partial x_j} = \frac{C_{\varepsilon 1} P_k - C_{\varepsilon 2} \varepsilon}{T} + \frac{\partial}{\partial x_j} \left[ \left( \nu + \frac{\nu_t}{\sigma_{\varepsilon}} \right) \frac{\partial \varepsilon}{\partial x_j} \right]</math> | ||
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== The normalized fluctuating velocity normal to the streamlines <math>\zeta</math> == | == The normalized fluctuating velocity normal to the streamlines <math>\zeta</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
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.