Comparing the Behavior of Ogee and Piano Key Weirs under Unsteady Flows

Analysis of the unsteady flow on the weir end sill is fundamental to determining the passing flow's exact flow discharge and height. Due to the difference between the steady and unsteady flows and the effect of different terms of the Saint-Venant equation, the weirs' stage-discharge curves under the two types of flows are different. In the present study, 3D free-surface flow on the Ogee and the Piano-key weirs under steady and unsteady flows was modeled using the FLOW-3D numerical model, and the effect of different input hydrographs for multiple time bases was investigated. Based on the obtained results, the steady flow condition's unit stage-discharge curve turned into a circular curve in the case of the unsteady flow condition. In both types of the weirs, by increasing the hydrograph time base, the stage-discharge curve changed from a circular curve into a unit curve and finally conformed to the steady-state's stage-discharge curve. In both types of studied weirs, for a constant flow discharge, the water head difference was more considerable for the hydrograph with smaller base-time, i.e. the hydrograph with steeper ascending and descending branches. The amount of head difference in the ogee weir due to your hydrographs with time steps of 4, 10, and 40 seconds is 0.023, 0.013, and 0.008, respectively, and for the piano key weir is 0.024, 0.019, and 0.009. In other words, for steeper input hydrographs on the end-sill of the weirs located on the channels or the weirs used as a diversion, an unsteady flow analysis should be performed. For a fixed weir height and a fixed input hydrograph, water head changes of the Piano key weir were greater than the Ogee weir.