Three-Equation Eddy Viscosity Models
v2-f Model
In order to account for the near wall turbulence anisotropy and non local pressure strain effects, Durbin (1995) introduced a velocity scale v2 and the elliptic relaxation function f to the standard k-ε turbulence model.
The velocity scale v2 represents the velocity fluctuation normal to the streamline and represents a proper scaling of the turbulence damping near the wall, while the elliptic relaxation function f is used to model the anisotropic wall effects. Compared to the k-ε turbulence models, the v2-f model produces more accurate predictions of wall-bounded flows dominated by separation but suffers from numerical stability issues.
Transport Equations
Elliptic Relation for the relaxation function f
- : the length scale,
- : the time scale.
Production Modeling
Dissipation Modeling
Modeling of Turbulent Viscosity
Model Coefficients
= 1.44, = 1.92, = 0.22, = 1.0, = 1.3. = 1.4, = 0.45, = 6.0, = 0.25, = 85, = 1.0.
Zeta-F Model
The base model of the zeta-f model is the v2f model described by Durbin (1995).
However, by introducing a normalizing velocity scale, the numerical stability issues found in the v2f model have been improved (Hanjalic et al., 2004; Laurence et al., 2004; Popovac and Hanjalic, 2007).
Transport Equations
Elliptic Relation for the Relaxation Function f
where : the length scale, : the time scale.
Production Modeling
Velocity Scale
Dissipation Modeling
Modeling of Turbulent Viscosity
Model Coefficients
= 1.44, = 1.92, = 0.22, = 1.0, = 1.3. = 1.4, = 0.65, = 6.0, = 0.36, = 85, = 1.2.