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

CHAPTER 3. CHANNEL FLOW 42
〈u 2 〉 +
k +
+ 1/4
y
= 1.46 − 0.542 ∗ +
Reτ
⎛
y +
⎜
⎝
1.5 +
7
2 y +
7
⎞
⎟
⎠ (3.42)
Figure 3.5 shows the profile for 〈u 2 〉 + obtained by multiplying Equation 3.42
by Equation 3.41. This is plotted against DNS results.
Table 3.2 offers qualitative descriptions of the contributions of the various
terms in Equation 3.42.
Table 3.2: Qualitative behaviour of terms in Equation 3.42
„ y +
«
7
“ ”
y + 2
1.5+ 7
y + 1/4
−0.542 ∗
Reτ
fits the peak value of 〈u2 〉 +
k +
shifts the curve at higher y + to account for some
Reynolds number dependence of 〈u2 〉 +
3.4.5 Empirical Profile for v 2 +
This profile for 〈v2 〉 +
k +
was originally fitted by Alexander Davroux and Do-
minique Laurence at Electricité de France. The profile is
〈v 2 〉 +
k +
where
=
y + 2
+
20
y
0.08 ∗ 2 + 0.8 ∗ 1λR + λR ∗ 0.06 ∗ + 1
y +
Reτ
2 + 20
+ 2
+ 2
−1
y y
∗ 1 − exp −
∗ 1 − exp −
(3.43)
20
3
λR = exp − 100
Reτ
k +