K–omega turbulence model

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).

Standard (Wilcox) k–ω turbulence model

The eddy viscosity ν_T, as needed in the RANS equations, is given by: Template:Nowrap, while the evolution of k and ω is modelled as:

$\begin{array}{cc}& \frac{\partial (\rho k)}{\partial t}+\frac{\partial (\rho u_{j}k)}{\partial x_j}=\rho P-{\beta }^{\ast }\rho \omega k+\frac{\partial }{\partial x_j}\left[(\mu +{\sigma }_k\frac{\rho k}{\omega })\frac{\partial k}{\partial x_j}\right],\text{with }P={\tau }_{ij}\frac{\partial u_i}{\partial x_j},\\ & \frac{\partial (\rho \omega )}{\partial t}+\frac{\partial (\rho u_j\omega )}{\partial x_j}=\frac{\alpha \omega }{k}\rho P-\beta \rho {\omega }^2+\frac{\partial }{\partial x_j}\left[(\mu +{\sigma }_{\omega }\frac{\rho k}{\omega })\frac{\partial \omega }{\partial x_j}\right]+\frac{\rho {\sigma }_d}{\omega }\frac{\partial k}{\partial x_j}\frac{\partial \omega }{\partial x_j}.\end{array}$

For recommendations for the values of the different parameters, see Template:Harvtxt.

References

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External links

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