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Near-wall treatment for k-omega models

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Turbulence modeling
RANS-based turbulence models
  1. Linear eddy viscosity models
    1. Algebraic models
      1. Cebeci-Smith model
      2. Baldwin-Lomax model
      3. Johnson-King model
      4. A roughness-dependent model
    2. One equation models
      1. Prandtl's one-equation model
      2. Baldwin-Barth model
      3. Spalart-Allmaras model
    3. Two equation models
      1. k-epsilon models
        1. Standard k-epsilon model
        2. Realisable k-epsilon model
        3. RNG k-epsilon model
        4. Near-wall treatment
      2. k-omega models
        1. Wilcox's k-omega model
        2. Wilcox's modified k-omega model
        3. SST k-omega model
        4. Near-wall treatment
      3. Realisability issues
        1. Kato-Launder modification
        2. Durbin's realizability constraint
        3. Yap correction
        4. Realisability and Schwarz' inequality
  2. Nonlinear eddy viscosity models
    1. Explicit nonlinear constitutive relation
      1. Cubic k-epsilon
      2. EARSM
    2. v2-f models
      1. \overline{\upsilon^2}-f model
      2. \zeta-f model
  3. Reynolds stress model (RSM)
Large eddy simulation (LES)
  1. Smagorinsky-Lilly model
  2. Dynamic subgrid-scale model
  3. RNG-LES model
  4. Wall-adapting local eddy-viscosity (WALE) model
  5. Kinetic energy subgrid-scale model
  6. Near-wall treatment for LES models
Detached eddy simulation (DES)
Direct numerical simulation (DNS)
Turbulence near-wall modeling
Turbulence free-stream boundary conditions
  1. Turbulence intensity
  2. Turbulence length scale

As described in Two equation turbulence models low and high reynolds number treatments are possible.


Standard wall functions

Main page: Two equation near-wall treatments

For k the boundary conditions imposed are

\frac{\partial k}{\partial y} = 0

Moreover the centroid values in cells adjacent to solid wall are specified as

  k_p = \frac{u^2_\tau}{\sqrt{C_\mu}y_p}

  \omega_p = \frac{u_\tau}{\sqrt{C_\mu}\kappa y_p} = \frac{\sqrt{k_p}}{{C_\mu^{1/4}}\kappa y_p},

In the alternative approach k production terms is modified.

Automatic wall treatments

Menter suggested a mechanism that switches automatically between HRN and LRN treatments.

The full description to appear soon. The idea is based on blending:

  \omega_\text{vis} = \frac{6\nu}{\beta y^2}

  \omega_\text{log} = \frac{u_\tau}{C_\mu^{1/4} \kappa y}

  \omega_p = \sqrt{\omega_{\text{vis}}^2 + \omega_{\text{log}}^2},

  u_\tau = \sqrt[4]{(u_\tau^{\text{vis}})^4 + (u_\tau^{\text{log}})^4},


Both k- omega models (std and sst) are available as low-Reynolds-number models as well as high-Reynolds-number models.

The wall boundary conditions for the k equation in the k- omega models are treated in the same way as the k equation is treated when enhanced wall treatments are used with the k- epsilon models.

This means that all boundary conditions for
- wall-function meshes will correspond to the wall function approach, while for the
- fine meshes, the appropriate low-Reynolds-number boundary conditions will be applied.

In Fluent, that means:

If the Transitional Flows option is enabled in the Viscous Model panel, low-Reynolds-number variants will be used, and, in that case, mesh guidelines should be the same as for the enhanced wall treatment
(y+ at the wall-adjacent cell should be on the order of y+ = 1. However, a higher y+ is acceptable as long as it is well inside the viscous sublayer (y+ < 4 to 5).)

If Transitional Flows option is not active, then the mesh guidelines should be the same as for the wall functions.
(For [...] wall functions, each wall-adjacent cell's centroid should be located within the log-law layer, 30 < y+ < 300. A y+ value close to the lower bound y+ = 30 is most desirable.)


  • Bredberg, J. (2000), "On the Wall Boundary Condition for Turbulence Models", 'Internal Report, Department of Thermo and Fluid Dynamics, Chalmers University of Tecyhnology Gotebord, Sweden'.
  • Menter, F., Esch, T. (2001), "Elements of industrial heat transfer predictions", 'COBEM 2001, 16th Brazilian Congress of Mechanical Engineering.'.
  • ANSYS (2006), "FLUENT Documentation", .
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