Numerical Study of the Effect of the Bed Roughness on Discharge Coefficient and Energy Dissipation on Ogee Spillway

The diversion dams are used to increase the water level and diversion flow from the river to intakes. Increasing the water level in the river will increase the potential flow energy upstream of the dam, as a result, the flow velocity on the overflow increases. Flow at the toe of a spillway is supercritical. If the high energy of water does not dissipated, causing scouring of the river's materials. Therefore, stilling basins are usually used to dissipate the energy of water exiting the spillway of a dam. If the flow energy is high in the toe, the stilling basins will have a larger dimension and the cost of the design will increase. Information about how to change the speed and depth of the flow during the spillway and calculating the flow characteristics in the in the toe of a dam is the most important factor in determining the type and dimensions of the stilling basins. Few studies have been conducted on the amount of energy loss and the flow characteristics in the toe of the dam. One of the objectives of this study is to provide an appropriate Formula for determining the amount of energy depreciation on the spillway that can be used to calculate the amount of depth and flow velocity in the toe of the dam. Investigation of the effect of surface roughness on discharge coefficient, flow velocity profile and the energy dissipation rate are other goals of this research.

In this paper, Savage and Johnson’s (2001) experimental data were used for evaluating the accuracy of the FLUENT model results. A physical model of a typical ogee spillway, with a design head Hd of 301 mm was fabricated and tested at the UWRL. The model was constructed of Plexiglas and was fabricated to conform to the distinctive shape of an ogee crest. The model also included a tangent section and a typical flip bucket. Plexiglas was chosen because it could be fabricated with smooth curves and easily instrumented with pressure taps. The model was 1.83 m wide and approximately 0.80 m high. The P/Hd ratio (height of crest/design head) was 2.7. Wall boundary condition was applied to the spillway body and vertical walls and floor of reservoir. Zero pressure boundary condition is applied in output and upper flow field. Zero pressure is applied in air inlet and velocity inlet in upstream boundary. VOF (volume of fluid) was used to determine free surface for solving flow field and to determine boundary condition of two-phase flow. The value of volume fraction is considered equal to zero on all boundaries, except that the water inlet flow value is applied equal to one. Using available experimental data, the depth of water on the weir crest and the pressure on the overflow body were calculated and compared with the observed results. In order to study the effect of bed roughness on velocity profile, flow coefficient and energy loss, the values of 0.01, 1 and 3 mm were considered for roughness and the FLUENT model was again applied for these values. By performing some simulations, relation to energy loss over ogee spillway was presented.

Based on the simulations carried out by the FLUENT model, the k-ε RNG turbulence model and the PISO algorithm are suitable for separating the governing equations. The water depth and pressure on spillway calculated by the FLUENT model is very close to the observed data. The average relative errors of the numerical model in estimating the water depth is 3.35% and average errors in estimating pressure on spillway are 0.88, 1.22 and 1.51cm for Q/Qd=1.33,1,0.625 respectively, which are suitable for predicting the characteristics of flow passing through a ogee spillway. Comparison of the results of the numerical model and observational values shows that the correlation coefficient of the pressure data is about 97.5%, which indicates the proper accuracy for simulating the flow through the overflow. One of the factors influencing the characteristics of the flow through the overflow is the body roughness. The discharge flow rate decreases slightly as surface roughness height and maximum velocity at any section is slightly decreasing as the surface roughness.

The results show that with increasing roughness of the weir crest at low discharge, about 6% of the discharge coefficient decreases compared to the smooth state. Also, with an increase in roughness at low discharge, about 50 percent of the energy in the toe of a spillway is reduced. In this study, a relationship was also proposed for the amount of energy loss over ogee spillway, which provides an accurate precision for calculating the amount of energy at the beginning of the stilling basins.