k - ω Model
Historically, Kolmogorov (1942) proposed the first two equation model. Kolmogorov chose the kinetic energy of turbulence as one of the parameters, while the other parameter as the dissipation per unit turbulence kinetic energy, ω . Wilcox (1988) and Speziale et al. (1990) also regard ω as the ratio of ε and k . Here we present the model due to Wilcox as
The turbulent viscosity is related to k and ω by the expression
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(28.1) |
The transport equations for turbulent kinetic energy (k) and its dissipation rate per unit turbulence kinetic energy (ω) are
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(28.2) |
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(28.3) |
The coefficients have the following empirically derived values
α = 5/9, β = 3/40, β* = 9/100, σk = 2.0, σω = 2.0
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The equation for ω may also be derived from the ε equation using variable transformation
This tranformation relates α and β coefficients to Cε1 and Cε2
 and 
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Thus the turbulent diffusion term from the transformed k-ε model will, however, contain additional terms
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(28.4) |
which is the major difference between k-ε and k-ω model. Also σk=2.0 compared with σk=1.0 in the k-ε model |
