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

CHAPTER 2. TURBULENCE MODELS 24
ˆε is required in order to calculate ε for use in the k transport equation
(Equation 2.16). ˆε is defined as
ˆε = 2ν
∂ √ 2 k
∂y
(2.30)
Thus, ˆε does not require a transport equation, but may be solved from local
quantities.
νt is modified according to
where
2.2.2 Yap Correction
νt = Cµfµ
fµ = exp
⎡
2 k
˜ε
⎣ −2.5
1 + ˜ Ret
50
⎤
(2.31)
⎦
(2.32)
The ‘Yap correction’ refers to an additional source term in the ˜ε transport
equation of the low-Reynolds-number k-ε model. The Yap correction was
originally introduced by Yap [92] to improve the performance of the k-ε
model in impinging and recirculating flows. Yap correction is often implicitly
included in standard k-ε modelling, so it has been included in the present
UMIST-N wall function for completeness.
Using Yap correction, the ˜ε transport equation becomes
2
D˜ε ν + νt
˜ε
˜ε
= ▽ ·
▽ ˜ε + Cε1f1 Pk − Cε2f2 + E + Y (2.33)
Dt σε
k
k
with the additional Y source term defined as
⎛⎡
Y = max ⎝⎣0.83
k 3
2
− 1
2.5˜εy
k 3
2
2.5˜εy
2 2 ˜ε
k
⎤ ⎞
⎦ , 0⎠
(2.34)