Numerical and Simplified Analytical Solutions for Typical Spillways - Selected Topics of Computational and Experimental Fluid Mechanics - page 438

a rate of 1.65. An evaluation of each one of the grids has been performed with
Fluent ( 2013 ) by implementing the momentum equation until the water velocity at
the spillway had stable results and it was found a variation of less than 5 % between
the previous and current grid. The settings followed during the test of each grid
correspond to the cases A2 and B2, for the spillway type A and B, respectively. The
grid chosen was made of structured tetrahedral cells with a maximum ratio between
cells of 22, y+ values to be less than 300 and skewness less than 0.9 as recommended
by Fluent ( 2013 ). The grids evaluated and chosen were for the cases A and B with
540,000 and 740,000 cells, respectively.
In both cases the water velocity inlet was assumed to be a constant. No slip
conditions were fixed at any wall with a roughness coefficient of 0.5. The turbulence
model was also defined in Fluent ( 2013 ) according to Eqs. 3 and 4 . The SIMPLE
method (Semi Implicit Pressure Linked Equation) linking pressure and velocity was
used in conjunction with the second order upwind scheme for the discretization of
Eq. 3 . The solution was found when the residuals were less than 10 − 5 . This condition
was imposed to the x and y velocity, kinetic energy, turbulence energy dissipation,
air phase and continuity.
The numerical results were found for each of the six cases indicated in Table 2 .
For instance, Fig. 2 indicates the numerical solution of the water fall profile indi-
cating the water velocity and additionally how the spillway water discharge creates
water recirculation at the downstream zone of the spillway. This water recirculation
modifies the water fall profile based on the spillway operating conditions.
For all the operating conditions shown in Table 2 the water fall profile was
obtained. Then, coefficient (a) of Eq. 2 was found using n equal to 1.84 and con-
sidering all the cases but not the case A2. The water fall profile predicted by Eq. 2
was adjusted by means of the coefficient (a) until it was similar for at least 90 %
of the water fall profile found in the numerical solution. The summary of the five
cases were plotted in Fig. 3 where it was easy to identify a correlation between the
coefficient (a) and (Re).
The linear regression from five numerical solutions and indicated in Fig. 2 was
then used to estimate the corresponding value of the coefficient (a) for the case A2
by means of the Reynolds number. The prediction obtained of Eq. 2 in the case A2
Fig. 2 Velocity gradient of
the water fall profile of
spillway B2