Numerical Investigating the Effect of Trapezoidal Sharp-Crested Sideweir Geometric Parameters on Discharge Coefficient

Background and Objectives
Weirs are the most important structures for measuring and regulating flow rate. They are also simple hydraulic structures used to control the water level and measure the flow rate in canals. Lateral weirs are sometimes known as side weirs. Side weirs are usually made in various geometric shapes such as rectangular, arched, trapezoidal and triangular. A complete analytical solution of the equations governing the side weir discharge is not possible as there are many parameters influencing the flow phenomenon. An accurate computation of lateral discharge mainly depends on the proper estimation of its discharge coefficient. Investigation of the discharge coefficient has been the main focus by many researchers. In trapezoidal side weirs, weir height, hydraulic head, and weir wall angle affect the discharge coefficient. Although many researchers have done studies on the theoretical and practical applications of simple side weirs, there are only limited investigations on compound sharp-crested side weirs. Recently, some experimental works have been done in order to understand flow hydraulics of compound sharp- and broad- crested normal weirs, which are built across the channel. In this study, the effect of the mentioned parameters on the discharge coefficient, hydraulic characteristics of the flow including flow rate, the water surface profile and energy variations were investigated numerically.
Methodology
Numerical simulation geometry which is composed of a rectangular channel and installed side weir, created and meshed using GAMBIT (ANSYS) . The experimental domain length is 2 m in order to avoid large mesh numbers. A quad-map mesh was generated for all models. In the present study, 3-dimensional numerical simulation of  flow over  trapezoidal sharp-crested side weir was evaluated using three turbulence models of  standard k-ε, RNG k-ε and  Realizable k-ε. The free surface was determined using the VOF method. The results showed that the RNG k-ε turbulence model and VOF method are suitable for predicting the discharge coefficient in trapezoidal plan side weirs. The studied models for trapezoidal side weirs were meshed using different node values to determine the optimum number of nodes to generate mesh and to perform a mesh independence test , a negligible difference was observed by increasing the number of nodes in simulated and measured the discharge coefficient of flow over trapezoidal side weir. Therefore, a mesh composed of approximately 25000 elements was considered as an optimum mesh for all created models to resolve flow characteristics. The boundary conditions were defined for all models. At the channel inlet and outlet, pressure inlet and outlet boundary conditions were used. For free surface, pressure inlet boundary condition was defined
and wall boundary condition was assigned at the channel bed, side walls and the structure of weir. The comparison of the discharge coefficient of flow that data obtained from numerical simulation agreed well with the experimental data. Also results showed that VOF method can simulate free surface variations accurately enough given that the average relative error values of measured and simulated the discharge coefficient were 2 - 6% for all considered turbulence models. For sharp-crested side weirs in subcritical flow conditions, the equation  of  De Marchi (1934)was used to compute  the flow discharge coefficient of the side weirs.
Finding
In this study the water surface and flow patterns were analyzed using contour plots at different horizontal and vertical planes.  Using a non-linear regression model, they proposed a dimensionless relationship for prediction of the discharge coefficient in trapezoidal side weirs in subcritical flow conditions. In this study, the effect of weir wall angle, weir height and the hydraulic head on the discharge coefficient  of trapezoidal side weirs was investigated numerically using FLUENT software and also the numerical results were compared with the experimental data. The results of the simulation were in a good agreement with the experimental data. The discharge coefficient (C_m) is not dependent on any single hydraulic or geometric parameter, but several parameters affect it. The results also showed that the side weir with a wall slope of  z = 1 has better performance compared to the other two angles. Because it has the highest amount of the discharge coefficient among different weirs.
Conclusion
As a result of the flow passing through the side weir, the main channel's flow rate and longitudinal velocity decrease. It can be concluded that the velocity values near the side weir decrease with a greater slope, and the velocity variations decrease downstream in the main channel.