Environmental Engineering Reference
In-Depth Information
Mercado et al. (
2013
) proved that Eq.
1
was properly derived from the Navier-Stokes
equations after a series of assumptions and simplifications. The deduced Eq.
1
takes
care only of inertial forces; however, spillways operate under turbulent conditions,
which mean that viscous and inertial forces determine the flow behavior. Furthermore,
phenomena occurring at the spillway water discharge can certainly change the water
dynamics significantly, such as the conversion of kinetic to potential energy at the
moment of the spillway discharge; the air entrainment at the boundary layer between
air and water; the surface ondulation; free surface instabilities and others. Thus, Eq.
1
can be improved by considering the Reynolds number (Re) and the coefficient (a)
that incorporate the phenomena that occur in the water fall profile within turbulence
regime.
The proposal in this work suggests a methodology that allows the improvement in
the prediction of Eq.
1
after a limited number of numerical solutions in two spillways
with similar design but different dimensions. Then, the term k in Eq.
1
can be replaced
by a/Re in Eq.
2
in order to increase the accuracy of those calculations.
a
Re
x
n
=
×
.
y
(2)
This investigation evaluates two types of spillways as study cases (A and B) but
similar characteristics in the design. The numerical solution of each case was found
through Fluent (
2013
). The dimensions in each case are specified in Table
1
and
indicated in Fig.
1
. Six simulations in total were performed in steady state conditions.
Five simulations were used to identify the coefficient (a) in Eq.
2
and the results of
Ta b l e 1
Spillway specifications
Symbol
Cases
Units
A
B
Width
L
35.8
86.4
m
Head
H
o
var
var
m
Height of domain
H
1
2(H
o
+P)
2(H
o
+P)
m
Length of upstream spillway
W
1
1.5(H
o
+P)
1.5(H
o
+P)
m
Length of downstream spillway
W
2
5(H
o
+P)
5(H
o
+P)
m
Height of dam
P
3.5
34.2
m
m
3
s
−
1
Discharge
Q
var
var
Hydraulic ratio
h
r
var
var
m
Fig. 1
Dimensions of the
spillway
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