Zeta-f model
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- | The ''zeta-f'' model is a robust modification of the elliptic relaxation model. | + | The ''zeta-f'' model is a robust modification of the elliptic relaxation model. For the incompressible Newtonian fluid the final set of equations constituting the <math>\zeta-f</math> model is given below. |
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<math>S \equiv \sqrt{2S_{ij} S_{ij}}</math> | <math>S \equiv \sqrt{2S_{ij} S_{ij}}</math> | ||
- | == | + | == Turbulence time scale <math>T</math> == |
- | <math>T = max \left[ min \left( \frac{k}{\varepsilon},\, \frac{0.6}{\sqrt{6} C_{\mu} |S|\zeta} \right), C_T \left( \frac{\nu | + | <math>T = max \left[ min \left( \frac{k}{\varepsilon},\, \frac{0.6}{\sqrt{6} C_{\mu} |S|\zeta} \right), C_T \left( \frac{\nu}{\varepsilon} \right)^{1/2} \right]</math> |
- | + | == Turbulence length scale <math>L</math> == | |
- | == | + | |
<math>L = C_L \, max \left[ min \left( \frac{k^{3/2}}{\varepsilon}, \, | <math>L = C_L \, max \left[ min \left( \frac{k^{3/2}}{\varepsilon}, \, | ||
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\left( \frac{\nu^3}{\varepsilon} \right)^{1/4} \right]</math> | \left( \frac{\nu^3}{\varepsilon} \right)^{1/4} \right]</math> | ||
- | + | == Model coefficients == | |
- | == | + | |
<math>C_\mu = 0.22</math>, <math>\sigma_{k} = 1</math>, <math>\sigma_{\varepsilon} = 1.3</math>, <math>\sigma_{\zeta} = 1.2</math>, <math>C_{\varepsilon 1} = 1.4 (1 + 0.012 / \zeta)</math>, <math>C_{\varepsilon 2} = 1.9</math>, <math>C_1 = 1.4</math>, <math>C_2' = 0.65</math>, <math>C_T = 6</math>, <math>C_L = 0.36</math> and <math>C_{\eta} = 85</math>. | <math>C_\mu = 0.22</math>, <math>\sigma_{k} = 1</math>, <math>\sigma_{\varepsilon} = 1.3</math>, <math>\sigma_{\zeta} = 1.2</math>, <math>C_{\varepsilon 1} = 1.4 (1 + 0.012 / \zeta)</math>, <math>C_{\varepsilon 2} = 1.9</math>, <math>C_1 = 1.4</math>, <math>C_2' = 0.65</math>, <math>C_T = 6</math>, <math>C_L = 0.36</math> and <math>C_{\eta} = 85</math>. | ||
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== References == | == References == | ||
- | *<b>Popovac, M., Hanjalic, K.</b> Compound Wall Treatment for RANS Computation of Complex Turbulent Flows and Heat Transfer, Flow | + | *<b>Popovac, M., Hanjalic, K.</b> Compound Wall Treatment for RANS Computation of Complex Turbulent Flows and Heat Transfer, Flow Turbulence and Combustion, 78, 177-202, 2007. |
*<b>Hanjalic, K., Popovac, M., Hadziabdic, M.</b> A robust near-wall elliptic-relaxation eddy-viscosity turbulence model for CFD, Int. J. Heat Fluid Flow, 25, 1047–1051, 2004. | *<b>Hanjalic, K., Popovac, M., Hadziabdic, M.</b> A robust near-wall elliptic-relaxation eddy-viscosity turbulence model for CFD, Int. J. Heat Fluid Flow, 25, 1047–1051, 2004. | ||
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+ | [[Category:Turbulence models]] | ||
{{stub}} | {{stub}} | ||
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Latest revision as of 10:06, 17 December 2008
The zeta-f model is a robust modification of the elliptic relaxation model. For the incompressible Newtonian fluid the final set of equations constituting the model is given below.
Turbulent viscosity
Turbulent kinetic energy
Turbulent kinetic energy dissipation rate
Normalized velocity scale
Elliptic relaxation function
Production of the turbulent kinetic energy
Modulus of the mean rate-of-strain tensor
Turbulence time scale
Turbulence length scale
Model coefficients
, , , , , , , , , and .
References
- Popovac, M., Hanjalic, K. Compound Wall Treatment for RANS Computation of Complex Turbulent Flows and Heat Transfer, Flow Turbulence and Combustion, 78, 177-202, 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.