Environmental Engineering Reference
In-Depth Information
1 Introduction
The representation of water flow in spillways is widely studied due to the outnumbered
scenarios that their design and operation bring. The necessity to analyze simultane-
ously the water properties, the operating conditions and the design of interest can
demand a significant amount of time and computational resources in order to obtain
successful solutions. Particular projects of high impact justify the detailed investi-
gation to improve the design and efficient operation of spillways. However, in many
other cases, a quick calculation through simplified equations can give an acceptable
and meaningful outcome in advance.
The aim of this work is to improve the suggested equation presented by Arreguin
(
2000
) and analyzed by Mercado et al. (
2013
) that describes the water fall profile
of a spillway. Mercado et al. (
2013
) points out that the simplified analytical equa-
tion is adequately determined and considers the more significant variables: head of
water arrival and the slope of the facing. The same equation has also been studied in
Iniguez-Covarrubias et al. (
2012
) by summarizing various investigations. Both stud-
ies (Iniguez-Covarrubias et al.
2012
; Mercado et al.
2013
) bring the interest to further
comparisons of the simplified analytical equation with results of a set of numerical
solutions.
Furthermore, a proposal for a modification of the simplified analytical solution
presented by Arreguin (
2000
) and originally introduced by the USBR (US Bureau of
Reclamation) is presented. The modification suggested takes into account the results
obtained in a series of numerical solutions using Computational Fluid Dynamics
(CFD) through Fluent (
2013
). An exemplary set of two spillways that were previously
studied in Mercado et al. (
2013
) is provided. CFD results served as a demonstration
of the benefits in a suitable modification of the simplified analytical solution.
2 Problem Formulation
The water crossing a spillway forms a crest that has been studied using different
techniques. For instance, the Navier-Stokes equations covering the inertial, viscous
and external forces are capable to reproduce the water dynamics in a spillway includ-
ing the turbulence phenomena. Nonetheless, difficulties related to the free boundary
layer (Hirt et al.
1970
), between the two phases: air and water, require the use of Vol-
ume of Fluid (VOF) approach to get the numerical solution. This kind of simulations
in large domains may imply intensive use of computational resources; consequently,
simplified analytical solutions have been used for prediction of the water fall profile
avoiding the turbulence phenomena. In this prospect, the present work finds a relation
between the numerical and simplified analytical solutions to enhance the prediction.
The simplified analytical solution (Eq.
1
) deals with coefficients such as the head
of arrival and the slope of the facing to determine the water fall profile; and values
can be found in Arreguin (
2000
)
x
n
y
=
k
×
.
(1)
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