Discussion of 'Revisiting the Energy-Momentum Method for Rating Vertical Sluice Gates under Submerged Flow Conditions' by Oscar Castro-Orgaz, Luciano Mateos, and Subhasish Dey

摘要

The discussers really appreciated the efforts to make more solid some usual assumptions used to derive reliable stage-discharge relationships, and the confrontation with field measurements. Energy and momentum equations are generally applied in their standard form, as presented in most hydraulic engineering books. The authors are right to point out that some of these assumptions are simplistic, which introduces biases in the derived relationships. Velocity distribution is one of these assumptions, and trying to improve this distribution is commendable. Head loss is another crucial issue, especially for submerged gates where the presence of the roller above the jet induced large dissipation. The authors also neglected the friction forces and assumed that contraction coefficient (Cc) is the same in submerged flow as in free flow. This assumption was questioned by Henderson (1989), and Belaud et al. (2009) showed how to derive a continuous relationship for Cc between low submergence (Cc about 0.61) and fully open gate (Cc ¼ 1). For submerged gates, there have been a limited number of experimental studies that explored the validity of the most sensitive assumptions. Compared to free flow, much more phenomena need to be quantified, such as head loss due to jet–roller interaction, velocity distributions at the contracted section and downstream measuring section, friction forces between these two sections. The effect of submergence introduces another dimension when trying to elaborate generic relationships. As the practical objectives are to obtain accurate discharge predictions, a common approach is to calibrate corrections using measured discharges, water levels, and openings. This may not be sufficient to validate physically based improvements since several phenomena compensate for each other. The pioneer experimental works used by the authors provided very useful data sets to perform this analysis. This discussion is based on recent experimental and numerical results presented by Cassan and Belaud (2012). Experiments used acoustic Doppler velocimetry at selected locations, for three configurations in free flow and three in submerged flow. Computational fluid dynamics was used in complement, with the objective to interpolate flow characteristics between measuring points and to explore other configurations than those measured. Experiments were essential to verify the validity of the numerical results, based on Reynolds–Average Navier–Stokes simulations with the volume-of-fluid method and Reynolds stress model as turbulence closure model. Notations are those of the discussed paper.