Environmental Engineering Reference
In-Depth Information
z
β
θ
(
z
)
dz
=
(
z
)
−
θ
e
(
z
)
(2.7)
z
−
l
down
Therry and Lacarrère (1983) proposed a relation between
l
k
and
l
ε
1
l
ε
w
θ
c
ε
e
3
/
2
l
ε
g
θ
l
k
=
+
(2.8)
Bélair et al. (1999) used the budget equation for the TKE to derive the rela-
tion neglecting the turbulent transport contribution and assuming steady-state. This
leads to
1
l
B
e
D
e
l
k
=
+
(2.9)
ε
or
2
B
e
+
l
ε
G
e
l
k
=
(2.10)
B
e
+
G
e
where
B
e
,
D
e
and
G
e
are the buoyancy, the dissipation and the gradient terms of
the TKE budget equation.
l
k
is determined as the minimum between
l
up
and
l
down
(Bougeault and Lacarrère, 1989).
The turbulent transport T of (2.1) can be written as
K
z
u
i
c
2
∂
∂
=−
∂
∂
Pr
∂
c
2
∂
(2.11)
x
i
z
z
The dissipation D of (2.1) can be written as
c
2
τ
c
2
ε
c
2
=
(2.12)
Verver et al. (1997) used the TKE dissipation timescale divided by 2.5 as vari-
ance dissipation timescale to be inserted in the expression of the scalar variance
dissipation. Using this expression with (2.5) leads to
e
3
/
2
l
c
2
ε
c
2
=
2.5
c
(2.13)
ε
ε
C
and
C
k
are set to 0.125 and 0.7 and the Prandtl number
Pr
is 1/1.3. Boundary con-
ditions for the TKE and the variances are calculated assuming no gradients across
the surface.
ε
Search WWH ::
Custom Search