Hydromechanics of the Asymmetric Trapezoidal Piano Key and Labyrinth Weirs

Abstract

This paper presents the results of experimental measurements and numerical simulations on the hydromechanics of trapezoidal asymmetric piano key weirs and compares the performance of piano key weirs and labyrinth weirs with the same crest lengths and layouts. The results show that gradually increasing the sidewall angle from 0° to 6° for labyrinth weirs continuously increases the discharge capacity of the weir. In contrast, for piano key weirs, increasing the sidewall angle from 0° to 3° significantly increases the efficiency of the weir at low to medium heads, but further increasing the sidewall angle does not significantly change the efficiency of the hydraulically optimal asymmetric piano key weir. The high angle of the lateral spilling jet to the outlet keys, along the downstream half of the side crests and the widening of the outlet keys increase the discharge efficiency of the trapezoidal piano-key weir with 3° of sidewall angle and 4 unit keys, compared to the identical weir with 6° of sidewall angle. Despite the wider outlet keys at the downstream of the trapezoidal piano key weir with 6° of sidewall angle, the narrower width of the inlet key, results in a higher streamwise inertia and thus the lower discharge at the outlet keys. Discretization of the discharge along the crest of the tested weirs confirms these results. In this research, the discharge capacity of trapezoidal piano key and labyrinth weirs were examined under various conditions and their performance was compared. The authors suggest an optimal ratio of weir height to unit width for rectangular piano key weirs, which increases the discharge coefficient by 6%. This finding can be applied to new dam projects to design cost-effective and highly efficient weirs. The study also showed that increasing the sidewall angle from 0° to 6° in trapezoidal labyrinth weirs improves the discharge coefficient by an average of 10.3%. However, in trapezoidal piano key weirs, increasing the sidewall angle from 0° to 3° has a significant impact on discharge coefficient, but further increase reverses the trend. Overall, piano key weirs perform better than their labyrinth counterparts.