The UMIST-N Near-Wall Treatment Applied to Periodic Channel Flow

CHAPTER 2. TURBULENCE MODELS 25
y is the distance from the wall.
2.3 The k-ω Model
The k-ω model is like the k-ε model in being dubbed a two-equation model,
because it demands the solution of two additional transport equations in
order to characterise turbulence. Like most two-equation models, the k-ω
model tracks turbulent kinetic energy, k. However, the dissipation rate, ε is
not tracked using its own transport equation, as in the k-ε model. Instead, a
transport equation is solved for ω. ω is sometimes referred to as the specific
dissipation rate.
The Wilcox 1988 k-ω model [89] uses the following transport equation for k:
Dk ν + νt
= ▽ ·
▽ k + Pk − ωkβ
Dt σkω
∗
(2.35)
so that ω is defined as
ω ≡ ε
kβ ∗
(2.36)
Pk is defined in the same way as for the k-ε model, as shown in Equation
2.20.
The equation for νt becomes
νt = γ ∗
The transport equation for ω is
Dω ν + νt
= ▽ ·
Dt σω
k
ω
▽ ω + γ
ω
Pk − βω
k
2
(2.37)
(2.38)