K–omega turbulence model - Alchetron, the free social encyclopedia

In computational fluid dynamics, the k–omega (k–ω) turbulence model is a common two-equation turbulence model, that is used as a closure 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: ν_T = k/ω, while the evolution of k and ω is modelled as:

∂ ( ρ k ) ∂ t + ∂ ( ρ u j k ) ∂ x j = ρ P − β ∗ ρ ω k + ∂ ∂ x j [ ( μ + σ k ρ k ω ) ∂ k ∂ x j ] , with P = τ i j ∂ u i ∂ x j , ∂ ( ρ ω ) ∂ t + ∂ ( ρ u j ω ) ∂ x j = γ ω k P − β ρ ω 2 + ∂ ∂ x j [ ( μ + σ ω ρ k ω ) ∂ ω ∂ x j ] + ρ σ d ω ∂ k ∂ x j ∂ ω ∂ x j .

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

References

K–omega turbulence model Wikipedia

(Text) CC BY-SA