Zeta-f model
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(Difference between revisions)
Mirzapopovac (Talk | contribs) (→The normalized fluctuating velocity normal to the streamlines <math>\zeta</math>) |
Mirzapopovac (Talk | contribs) (→The elliptic relaxation function <math>f</math>) |
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<math>\frac{\partial \zeta}{\partial t} + U_j \frac{\partial \zeta}{\partial x_j} = f - \frac{\zeta}{k} P_k + \frac{\partial}{\partial x_j} \left[ \left( \nu + \frac{\nu_t}{\sigma_{\zeta}} \right) \frac{\partial \zeta}{\partial x_j} \right]</math> | <math>\frac{\partial \zeta}{\partial t} + U_j \frac{\partial \zeta}{\partial x_j} = f - \frac{\zeta}{k} P_k + \frac{\partial}{\partial x_j} \left[ \left( \nu + \frac{\nu_t}{\sigma_{\zeta}} \right) \frac{\partial \zeta}{\partial x_j} \right]</math> | ||
- | == | + | == Elliptic relaxation function <math>f</math> == |
<math>L^2 \nabla^2 f - f = \frac{1}{T} \left( C_1 - 1 + C'_2 \frac{P_k}{\varepsilon} \right) \left( \zeta - \frac{2}{3} \right)</math> | <math>L^2 \nabla^2 f - f = \frac{1}{T} \left( C_1 - 1 + C'_2 \frac{P_k}{\varepsilon} \right) \left( \zeta - \frac{2}{3} \right)</math> | ||
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== The production of the turbulent kinetic energy <math>P_k</math> == | == The production of the turbulent kinetic energy <math>P_k</math> == |
Revision as of 12:28, 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
Normalized velocity scale
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.