Numerical study of effect of Crest shape on Discharge Coefficient of Trapezoidal Arced Labyrinth Weir

Weirs have important roles in dam safety in which they should spill floods with high return period. Designers generally enhance width of the weirs to increase their discharge capacity. This procedure involves topography as well as economic limitations. Here, arced weirs can be considered as an alternative. In plan view, arced weir is part of a circle that increases the crest length for a given channel width. This increases the flow capacity at a similar heads. Such structures are also recommended for modification and increasing the capacity of the existing spillways. Discharge capacity of labyrinth weirs is a function of flow height, effective crest length, height of weir and shape of the crest. Discharge coefficient is also a function of height of flow, height of weir, weir thickness and crest shape. In this study, hydraulic characteristics of arced labyrinth spillways are numerically investigated. Here, the effect of crest shape on the discharge coefficient of the labyrinth spillway is included. In the first step, dimensionless parameters affecting the performance of arced weirs are introduced using Buckingham π theorem. To analyze this problem, a commercially available CFD code; Flow 3D by Flow Science; was selected. Flow 3D is known for its ability to accurately tracking free surface using Volume of Fluid (VOF) method. A similar method called Fractional Area to Volume Ratio (FAVOR) is used to define labyrinth within the model. Also, Reynolds averaged Navier Stokes (RANS) equations are solved using a finite volume method. Besides, The Renormalized Group Theory (RNG) model was implemented for turbulent simulations. The laboratory data of Crookston and Tullis (2012a) is used to validate the numerical model. These researchers conducted experiments on physical modeling of the labyrinth spillways at the Utah Water Research Laboratory at Utah State University. Comparison of numerical simulations with those of experimental results validates the ability of this software to simulate the complex flow over labyrinth spillways with an acceptable accuracy. In this study, result of 16 geometry models was used to develop a hydraulic design and analysis formulation for arced labyrinth weirs. Discharge coefficient data for Half-Round, Quarter-Round, Sharp-crest and Flat-crest arced labyrinth weirs are presented for 6̊ ≤ sidewall angles ≤ 24̊ and various head water ratio (0.1≤ H0/P ≤ 0.9). The study has shown that half round crest shape could increase the discharge coefficient about 22% compared to other crest shapes. Also, the results show that factors such as local submergence and nappe interference near an upstream apex has a negative impact on performance of arced labyrinth weirs. The local submergence area is directly related to the flow head, crest shape and sidewall angle. For high head conditions, the local submergence may decrease the efficiency of a labyrinth spillway. Efficiency parameter is defined as the ratio of discharge of arced weir to that of liner weir with the same width. From efficiency curves indicates that reduce of sidewall angle can improve efficiency. As a result, the highest efficiency related to arced labyrinth spillway with sidewall angle (α = 6̊ ).