Void Fraction Distribution Downstream of Nonlinear Weirs: An Experimental Investigation Using Trapezoidal A-Type Piano Key Weirs, a Labyrinth Weir, and a Linear Weir

Abstract

This experimental study investigates the behavior of void fraction distribution downstream of nonlinear weirs. Systematic air concentration measurements were performed in a 3D array for two model pairs: (1) a piano key weir and a labyrinth weir, and (2) a piano key weir and a reference linear weir. For the labyrinth and piano key weirs tested herein, the results revealed a significant variation of depth-averaged void fraction within the channel cross-section. Under limited tailwater conditions, interaction of spreading plunging jet shockwaves from the inlet keys remained significant, leading to higher void fractions along the adjacent outlet keys due to the formation of standing waves. However, this cross-sectional variation is moderated as the effect of plunging jets reduces with increasing tailwater depth. Alignment of an inlet key with the sidewall also induced standing waves that further contributed to the lateral variability of air concentrations. The findings further indicated that the labyrinth weir yields higher void fraction compared to the piano key weir under similar hydraulic conditions, highlighting the role of weir type and geometry. Additionally, 3D surfaces and contour profiles of depth-averaged void fraction were derived using high-resolution measurements downstream of the second model pair that showed substantial differences between nonlinear and linear weirs. Furthermore, a simplified relationship was established using the upstream and downstream flow depths to parameterize the behavior of the depth-averaged void fraction. Exponential detrainment trends were observed in all cases along the flow, and classic depth-concentration profiles were found to replicate the observations in these experiments.