The effect of the inlet/outlet width ratio on the discharge of piano key weirs

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 $W_i/W_o$ on the discharge efficiency of PKWs, a three-dimensional numerical model based on a standard $k-\epsilon$ turbulence model and volume-of-fluid (VOF) method is employed, and the flow characteristics of nine laboratory-scale PKWs with different $W_i/W_o$ ratios are studied numerically. The results confirm that PKW configurations with $W_i/W_o>1$ are generally superior to those with $W_i/W_o<1$ in terms of discharge capacity. However, as the water head rises, the discharge efficiency of the PKW with a greater $W_i/W_o$ 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 $W_i/W_o$ on the discharge performance of PKWs is revealed.

Keywords:

• Discharge efficiency
• hydraulic characteristics
• numerical simulation
• parameter optimization
• piano key weirs

Acknowledgements

The authors are grateful to the Taylor & Francis Group for providing highly valuable information and new ideas for future research.

Notation

$B$	=	streamwise length ($B_i\text{ + }{B}_b\text{ + }{B}_o$) (mm)
$B_b$	=	footprint length (mm)
$B_i$	=	inlet key overhang length (mm)
$B_o$	=	outlet key overhang length (mm)
$B_i/B_o$	=	upstream /downstream overhang ratio (–)
$h$	=	water head of PKW (upstream flow depth measured relative to the weir crest) (mm)
$H$	=	water head of sharp-crested weir (mm)
$L$	=	total length of the PKW’s spillway front (developed crest length) ($L=W+4B$) (mm)
$p$	=	pressure (Pa)
$P$	=	vertical height of PKW (mm)
$P_1$	=	vertical height of sharp-crested weir (mm)
$q$	=	unit discharge (l s−1 m−1)
$Q$	=	discharge (l s−1)
$r$	=	discharge amplification ratio (–)
$R$	=	discharge amplification ratio per unit width (–)
$T_S$	=	wall thickness (mm)
$W$	=	transverse width (mm)
$W_i$	=	inlet key width (mm)
$W_o$	=	outlet key width (mm)
$W_i/W_o$	=	inlet/outlet key width ratio (–)
$X$	=	coordinate along flow direction (mm)
$Y$	=	coordinate along water depth (mm)
$Z$	=	coordinate in the direction of the transverse width (mm)

Additional information

Funding

This study was partly supported by a National Natural Science Foundation of China-sponsored project [grant number 51579206], a Public Service Scientific Research Special Project funded by the Ministry of Water Resources [grant number 201301063], and a Shaanxi Province Natural Science Fundamental Research Project [grant number 2015JM5201].