Scale and Reynolds Dependence of the Two-Phase Flow Properties Downstream of Piano Key Weirs

Abstract

Piano key weirs in horizontal channels exhibit highly complex air–water flow characteristics; however, the influence of scale and Reynolds number ( R e ) on their two-phase flow behavior remains insufficiently understood. This study experimentally investigates the downstream air–water flow properties and associated scale effects under Froude similitude. Measurements were conducted across three geometrically similar models for inflow R e ranging from 3.47 × 10 4 to 3.08 × 10 5 . Key parameters, including void fraction, particle (bubble) count rate, and interfacial velocity, exhibited pronounced scale effects for R e < 10 5 , with the stronger deviations appeared in particle count rates. Turbulence intensity remained high near jet impact zones, followed by rapid downstream decay with diminishing Reynolds dependence. The mean air-chord length showed strong sensitivity to both Reynolds and Weber numbers, particularly below 10 5 and 2,112, respectively, reflecting higher turbulence effect on bubble breakup at larger scales. In addition, a characteristic aeration length, derived from longitudinal detrainment trends, indicated that the extent of the aerated core cannot be described by Froude similarity alone. Furthermore, interfacial velocity profiles transitioned from quasi-wall-jet behavior near the jet impact region to classical power-law distributions downstream, with the transition occurring at approximately six times the upstream flow depth above the crest. Overall, the results demonstrate that the air–water flow parameters of piano key weirs, particularly near jet impact regions, are strongly scale-dependent if R e < 1 × 10 5 , underscoring the importance of incorporating Reynolds effects when extrapolating laboratory findings to prototype conditions.