Abstract
A piano key weir (PKW) is a solution for improving the efficiency and safety of reservoirs and simplifying their management. To investigate the influence of the inlet/outlet width ratio on the discharge efficiency of PKWs, a three-dimensional numerical model based on a standard turbulence model and volume-of-fluid (VOF) method is employed, and the flow characteristics of nine laboratory-scale PKWs with different ratios are studied numerically. The results confirm that PKW configurations with are generally superior to those with in terms of discharge capacity. However, as the water head rises, the discharge efficiency of the PKW with a greater decreases more rapidly. By decomposing the total discharge into inlet, lateral and outlet components, according to the flow features of each overflow crest and their contributions to the total discharge, the intrinsic influencing mechanism of on the discharge performance of PKWs is revealed.
Acknowledgements
The authors are grateful to the Taylor & Francis Group for providing highly valuable information and new ideas for future research.
Notation
= | streamwise length () (mm) | |
= | footprint length (mm) | |
= | inlet key overhang length (mm) | |
= | outlet key overhang length (mm) | |
= | upstream /downstream overhang ratio (–) | |
= | water head of PKW (upstream flow depth measured relative to the weir crest) (mm) | |
= | water head of sharp-crested weir (mm) | |
= | total length of the PKW’s spillway front (developed crest length) () (mm) | |
= | pressure (Pa) | |
= | vertical height of PKW (mm) | |
= | vertical height of sharp-crested weir (mm) | |
= | unit discharge (l s−1 m−1) | |
= | discharge (l s−1) | |
= | discharge amplification ratio (–) | |
= | discharge amplification ratio per unit width (–) | |
= | wall thickness (mm) | |
= | transverse width (mm) | |
= | inlet key width (mm) | |
= | outlet key width (mm) | |
= | inlet/outlet key width ratio (–) | |
= | coordinate along flow direction (mm) | |
= | coordinate along water depth (mm) | |
= | coordinate in the direction of the transverse width (mm) |