https://orcid.org/0000-0001-7781-3526
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ABSTRACT
Undershot water wheels are hydropower converters for head differences between 0.5 and 1.5 m. The Zuppinger and Sagebien types are the most used and efficient. Optimal rotational speeds depend on the head difference and on the flow rate: hence, in variable flow rate applications, the variable rotational speed is needed to optimize the performance, requiring expensive power take-off systems. In light of this, the use of adjustable inflow weirs was tested on Zuppinger and Sagebien wheels. Different flow rates were tested, each one with an inflow weir height chosen to maintain the upstream water level constant through the tests. The first aim was to increase the power at very low flows. The second aim was to maintain the range of optimal rotational speeds as narrow as possible over the flow rate range. The maximum acceptable weir height ranged between 1:15 and 1:10 of the wheel’s radius.
Notation
| b | = | width of the wheel (m) |
| D | = | diameter of the wheel (m) |
| g | = | gravity acceleration (m s−²) |
| hu | = | upstream water depth (m) |
| hd | = | downstream water depth over the base plate of the wheel (m) |
| hs | = | downstream water depth (m) |
| P | = | mechanical power output (N m s−1) |
| Pin | = | mechanical power input (N m s−1) |
| Qin | = | total inflow rate (l s−1) |
| T | = | torque (N m) |
| u | = | wheel tangential speed (m s−1) |
| u* | = | normalized wheel tangential speed (–) |
| vu | = | upstream flow velocity (m s−1) |
| vs | = | downstream flow velocity (m s−1) |
| ΔH | = | head difference (m) |
| ΔP | = | power output error (W) |
| η | = | efficiency (–) |
| ρ | = | water density (kg m−3) |
| ω | = | wheel rotational speed (rad s−1) |
ORCID
Emanuele Quaranta http://orcid.org/0000-0001-7781-3526
