The computation of turbulent natural convection flows - Turbulence ...

Wall Functions 104
In the case of prescribed wall heat flux, the wall temperature can be calcu-
lated by:
where
Θwall = Θn − Prny ∗ n
µn
Cthy∗ n
2 +Ath
Prny
+bµ
∗2
n
2µ
Ath = − qwall
cp
µn
ρn kp
Cthy∗ n
3 +Ath
(4.46)
(4.47)
In the case of prescribed wall temperature, the wall heat flux can be calcu-
lated as:
where
qwall = − ρncp
kp
µn
Ath
Ath = (Θn −Θwall) µn Cth − Prn 2 y∗2 n +bµ
y ∗ n
− 1
2
bµy ∗2
n
Cthy ∗3
n
6
(4.48)
(4.49)
4.2.4 Hydrodynamic Wall Function When the Near Wall Cell
Is Thicker Than the Viscous Sublayer
We now integrate the simplified wall-parallel momentum equation over
the near-wall cell in a similar manner to that just outlined for the temperature
equation. First we convert the simplified differential transport equation for
momentum into y ∗ coordinates:
or
where
∂
∂y∗
(µ+µt) ∂U
∂y∗
= µ2 υ
ρ 2 υ kP
+ µ2 υ
ρ 2 υ kP
∂(ρUU)
∂x
+ ∂(ρVU)
∂y
+ dP
dx P
[−ρrefgβ(Θ−Θref)] (4.50)
∂
∂y∗
(µ+µt) ∂U
∂y∗
= C +b(Θ−Θref) (4.51)
b = − µ2υ ρ2 ρrefgβ (4.52)
υkP