Environmental Engineering Reference
In-Depth Information
Ta b l e 2
Study cases
Flow (m
3
s
−
1
)
10
5
)
Spillway
Reynolds (
×
A1
5,000
2,088
A2
6,500
2,714
A3
8,000
3,341
B1
16,655
3,222
B2
18,155
3,512
B3
19,655
3,808
one simulation were used to validate Eq.
2
. The operating conditions given for each
of the six cases are indicated in Table
2
.
Three scenarios for each case (A and B) were simulated. The two types of spillways
were taken with the same specifications as the ones mentioned in Mercado et al.
(
2013
) with the same operating conditions that were included as case A2 and B2.
A RANS (Reynolds Averaged Navier-Stokes) model was used (Eq.
3
).
∂
u
j
φ
∂
∂
∂
φ
∂
φ
∂
x
j
=
+
S
(3)
φ
x
j
x
j
where
is the variable of interest (velocity in the j direction, turbulent kinetic
energy and dissipation kinetic energy).
φ
φ
is the diffusion coefficient and
S
is
φ
the source term. Through the two-equation approach (
ʺ
−
ʵ
), the turbulence effects
were included. The model
realizable was used and additional parameters were
defined based on Eq.
4
(Fluent
2013
).
ʺ
−
ʵ
3
2
(
2
0
.
75
1
.
5
l
t
−
1
16Re
−
1
/
8
ʺ
=
uI
)
;
=
c
μ
ʺ
;
I
=
0
.
and l
t
=
0
.
07L
(4)
where Re is the Reynolds number, I is the turbulence intensity, in percent (%). l
t
is the
turbulence length scale in m.
are the turbulent kinetic and dissipation energy,
respectively, in m
2
s
−
2
.c
u
is equal to 0.09. L is the characteristic length of the spill-
way, in m. Additional parameters for the same model were defined as C
1
−
=
ʺ
and
1
.
44
and C
2
−
=
92.
This problem demands a free water surface simulation between the two phases
(air and water) under the presence of instabilities during the spillway water fall.
The model used the VOF approach in order to represent simultaneously in the same
domain the interaction of air and water phases. The VOF method is followed since it
has been successfully utilized in previous investigations (Ferrari
2010
; Chakib
2013
;
Mohammadpour et al.
2013
).
1
.
3 Results and Discussion
A series of grids with different number of cells were created. Each grid was evaluated
in order to verify stability of the results. The process to obtain a convenient grid
consisted of incrementing the number of cells uniformly at the whole domain with
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