Environmental Engineering Reference
In-Depth Information
Q
m
;
w
;
b
Q
m
;
w
;
i
¼
Q
m
;
w
;
e
Q
m
;
w
;
i
B ¼
1
ð
11
Þ
Which describes the ratio of breakup volumetric
fl
flow rate to water supply
fl
ow rate,
and a higher B indicates higher breakup level of water into the two-phase
fl
ow.
4 Numerical Analysis
4.1 Numerical Models
In this study, STAR-CCM+ was applied to perform
fl
flow simulations by solving the
unsteady Reynolds-Averaged Navier
Stokes (URANS) equations. The system of
equations was solved in an Eulerian multiphase state with an implicit unsteady solver
applying the volume of
-
fl
uid (VOF) approach which is a multiphase model simulating
several
fl
fluid interfaces between various
fl
fluid phases (Hirt and Nichols
1981
).
4.2 k-
ʵ
Model
The standard two-layer k-
ε
model combines the standard k-
ε
model with two-layer
approach introduced by Rodi (
1991
). The k-
ε
model can be expressed as in
Eqs. (
12
) and (
13
).
Z
Z
Z
r
k
d
a
d
dt
l
t
r
k
q
k d
V
þ
q
k v
v
g
d
a
¼
l þ
V
A
Z
þ
½G
k
þ
G
nl
þ
G
b
qðð
0
Þþc
M
Þ
d
V
V
ð
12
Þ
r
Z
Z
Z
d
dt
l
t
r
q
d
V
þ
qð
v
v
g
Þ
d
a
¼
l þ
d
a
V
A
Z
1
T
½C
1
ð
G
k
þ
G
nl
þ
C
3
G
b
Þ
C
2
qð
0
Þþqc
y
þ
d
V
V
ð
13
Þ
G
nl
in nonlinear production term for nonlinear model, G
b
is the production due to
buoyancy and de
ned as in Eq. (
14
), G
k
is the turbulent production and evaluated
as in Eq. (
15
).
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