The effect of the energy head and the inlet and outlet key width on discharge coefficient of Piano key weir

Introduction

Piano key weir is a form of nonlinear weir designed to improve the discharge capacity of spillway structures. Due to the increase in effective length, they can be used in dam spillways or water regulation structures. It is modified form of labyrinth weir which easy to place on the existing spillway or newly constructed dam with less base area. There is no standard method available for PK weir design, and the amount of published information is insufficient for the design of PK weir. A large number of geometric and hydraulic parameters affect the discharge capacity of PK weir, and their effect on the hydraulic performance of the weir can be investigated with a numerical model or laboratory data. Simulation of flow over PKW using FLOW-3D software and the effect of the turbulence model on the accuracy of the numerical model is one of the goals of this study. Also, in this research, the effect of the ratio of the inlet key width to the outlet key width (Wi/Wo) and the effect of the energy head on the discharge capacity are investigated.

Methodology
Laboratory data from Anderson (2011) were used to validate the numerical model. The total length and height of the weir are 4.848 and 0.197 m respectively, the floor slope in inlet and outlet key are 1:1.8, and number of keys is 4. The inlet and outlet key width are 0.116 and 0.925 m respectively, and the Wi/Wo ratio is 1.25. Selection of boundary conditions for the numerical model is one of the most basic stages of simulation. In order to define the boundary conditions, in the inflow point (Xmin) volume flow rate, in the sides of the weir (Ymin, Ymax) and bed (Zmin) wall condition, on the upper border (Zmax) symmetry condition and in the outflow section of the weir, outflow condition was used.

Results and discussion
The numerical model results were compared with the laboratory data. The results showed that if the second order scheme and RNG k-ε turbulence model are used in the numerical model, the simulation accuracy of the flow over PKW increases. Also, the results show that increasing the He/P decreases the discharge coefficient. So that the discharge coefficient for He/P=0.92 decreases by about 50% compared to He/P=0.24. With the increase of the water depth on the weir, the interference of the flow takes place at the breaking point of the weir cycles, and as a result, the discharge coefficient decreases. Another factor affecting the flow coefficient of the piano key is the ratio of the inlet key width to the outlet key width. By increasing the Wi/Wo, the flow coefficient has increased, and then it becomes maximum at Wi/Wo=1.5.

Conclusions
In this research, the simulation of the flow over piano key and labyrinth weir was done using a numerical model. The results showed that for a fixed depth, the piano key weir passes more discharge than the labyrinth weir, and the ratio of flow through the piano key weir to the labyrinth weir is about 1.08. In other words, at a constant depth, the piano key weir passes 8% more flow. In this research, the effect of head energy on the discharge coefficient of the piano key weir was also investigated. The results show that increasing the He/P decreases the discharge coefficient. The results showed that if the Wi/Wo equal to 1.5, the highest discharge coefficient occurs for the piano key weir.