Abstract: The three-dimensional flow fields in a piano key weir were simulated using the volume-of-fluid (VOF) model, and the reliability of VOF model result was verified according to Lempérière’s test result. An orthogonal numerical test revealed major geometric parameters that affect the discharge efficiency of piano key weir. Numerical simulations and theoretical analysis were conducted to analyse the effects of these geometric parameters. New formula for the discharge of piano key weir was then derived and verified. The maximum relative error of the proposed formula is 6.7%, and the mean relative error 3.7%. The proposed formula improves the accuracy of the design and structural optimization of piano key weir.

Key words: piano key weir, hydraulic characteristics, numerical simulation, VOF model, orthogonal numerical experiment, discharge efficiency, geometric parameters, discharge calculation formula