Environmental Engineering Reference
In-Depth Information
G
b
¼
b
l
t
r
t
ðr
T
g
Þ
ð
14
Þ
2
3
q
k
2
3
l
t
ðr
v
Þ
2
2
G
k
¼
l
t
S
r
v
ð
15
Þ
where
r
v is the velocity divergence, S is the strain parameter, and S is the strain
rate tensor given in Eqs. (
16
) and (
17
).
p
2S
p
2S
S
T
S ¼
jj
¼
S
¼
S
ð
16
Þ
:
:
And
1
2
ðr
v
T
v
þr
Þ
ð
Þ
S
¼
17
Also, the product of two tensors is described in Eq. (
18
).
s
:
s
¼
s
ij
s
ji
ð
18
Þ
4.3 SST k-
ˉ
Model
The shear
model was addressed by Menter (
1994
) and can be
expressed as Eqs. (
19
) and (
20
):
stress transport k-
ˉ
-
Z
Z
Z
dt
q
kd
V
þ
q
k
ð
v
v
g
Þ
d
a
¼
ðl þ r
k
l
t
Þr
k
d
a
V
A
A
Z
ðc
eff
G
k
c
0
qb
f
b
ðx
k
þ
x
0
k
0
ÞÞ
d
V
V
ð
19
Þ
Z
Z
Z
d
dt
qx
d
V
þ
qxð
v
v
g
Þ
d
a
¼
ðl þ r
x
l
t
Þrx
d
a
V
A
A
Z
2
2
0
þ
ð
G
x
qb
f
b
ðx
x
Þþ
D
x
Þ
d
V
V
ð
20
Þ
where k
0
are the ambient turbulence values in source terms that counteract turbu-
lence decay,
c
eff
is the effective intermittency provided by the Gamma Theta
Transition model, and
c
0
¼
½
ðc
eff
;
:
Þ;
. The turbulent production G
k
and
G
x
can be written as follows in Eqs. (
21
) and (
22
).
min
max
0
1
1
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