K–omega turbulence model

Short description: Tool in computational fluid dynamics

In computational fluid dynamics, the k–omega (k–ω) turbulence model is a common two-equation turbulence model, that is used as an approximation for the Reynolds-averaged Navier–Stokes equations (RANS equations). The model attempts to predict turbulence by two partial differential equations for two variables, k and ω, with the first variable being the turbulence kinetic energy (k) while the second (ω) is the specific rate of dissipation (of the turbulence kinetic energy k into internal thermal energy).

## Contents

* 1 Standard (Wilcox) k–ω turbulence model
* 2 Notes
* 3 References
* 4 External links

## Standard (Wilcox) k–ω turbulence model

The eddy viscosity νT, as needed in the RANS equations, is given by: νT = k/ω, while the evolution of k and ω is modelled as:[1]

∂(ρk)∂t+∂(ρujk)∂xj=ρP−β*ρωk+∂∂xj[(μ+σkρkω)∂k∂xj],with P=τij∂ui∂xj,∂(ρω)∂t+∂(ρujω)∂xj=αωkρP−βρω2+∂∂xj[(μ+σωρkω)∂ω∂xj]+ρσdω∂k∂xj∂ω∂xj.

For recommendations for the values of the different parameters, see (Wilcox 2008).

## Notes

1. ↑ (Wilcox 2008)

## References

* Wilcox, D. C. (2008), "Formulation of the k–ω Turbulence Model Revisited", AIAA Journal 46 (11): 2823–2838, doi:10.2514/1.36541, Bibcode: 2008AIAAJ..46.2823W
* Wilcox, D. C. (1998), Turbulence Modeling for CFD (2nd ed.), DCW Industries, ISBN 0963605100
* Bradshaw, P. (1971), An introduction to turbulence and its measurement, Pergamon Press, ISBN 0080166210
* Versteeg, H.; Malalasekera, W. (2007), An Introduction to Computational Fluid Dynamics: The Finite Volume Method (2nd ed.), Pearson Education Limited, ISBN 978-0131274983

## External links

* CFD Online Wilcox k–omega turbulence model description, http://www.cfd-online.com/Wiki/Wilcox's_k-omega_model, retrieved May 12, 2014

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