Study Of The Flow Mechanism Of Parabolic Flume And Piano Key Weir

Parabolic flumes has the advantages of better discharge capacity, smaller water head loss, higher accuracy under conditions of low water depth, and simpler structure, when used in U-shaped channels. However a flat parabolic flume requires a long horizon-leveled approach channel, according to the design demands, when installed in a channel with bottom slope. This design increases construction difficulty, leads to drop sills and results in greater water head loss.Three-dimensional flow fields in parabolic flumes, Parshall flumes and long-throated flumes, are simulated using the volume-of-fluid (VOF) model. The hydraulic model was validated by using data of physical model testing. The velocity and turbulent kinetic energy dissipation rate in typical sections of the three measuring flumes are analyzed and the total head curves of the three flumes are obtained. The results indicate that the Parshall flume installed in a U-shaped channel leads to a high water head loss, whereas the water head loss for the parabolic flume is only 35% of that of the long-throated flume or 30% of the Parshall flume, which makes parabolic flumes more suitable for U-shaped channels. A formula for calculating discharge that is applicable to channels of slope ranging between 1/1000-1/100 is theoretically derived. Which, are demonstrated to be accurate enough to satisfy the demands of water discharge measurement. Using this formula, the parabolic flumes are suitable for wider slope of channels.Piano Key Weirs have obvious advantages in enhancing the spillway discharge capacity. Compared with the traditional sharp-crested weir, ogee-crested weir, under the same conditions, the Piano Key Weir can provide at most four times the discharge capacity.Three-dimensional flow fields in Piano Key Weirs (PKW) are simulated using the volume-of-fluid model. The hydraulic model was validated by comparing with data of Lemperiere’s model test. On this basis, the flow pattern of PKW in different conditions of various upstream head are analyzed. Then, the mechanism of PKW’s discharge efficiency decrease with the increasing of the upstream head are revealed based on the theory of fluid mechanics:the change of lateral flow direction, due to the longitudinal flow velocity along the inlet key, leads to the decrease of the side weir discharge; the influence of the critical section along the inlet key, interaction between side nappes, and the head loss at the inlet key entrance are also neglectable. Based on orthogonal numerical test for 25 different PKW structures, the geometric parameters which importantly impact the PKW discharge efficiency were determined. Numerical simulations and theoretical analysis were processed according to these geometric parameters. New formulas for calculating PKW discharge are then derived, and the precision is verified. Based on the mechanism of PKW’s changing discharge efficiency and flow calculation formula, this paper provides a reliable method for PKW design and engineering applications.