## Abstract

Pump operating as turbine (PAT) is an effective source of reducing the equipment cost in small hydropower plants. However, the manufacturers provide poor information on the PAT performance thus representing a limit for its wider diffusion. Additional implementation difficulties arise under variable operating conditions, characteristic of water distribution networks (WDNs). WDNs allow to obtain widespread and globally significant amount of produced energy by exploiting the head drop due to the network pressure control strategy for leak reductions. Thus a design procedure is proposed that couples a parallel hydraulic circuit with an overall plant efficiency criteria for the market pump selection within a WDN. The proposed design method allows to identify the performance curves of the PAT that maximizes the produced energy for an assigned flow and pressure-head distribution pattern. Finally, computational fluid dynamics (CFD) is shown as a suitable alternative for performance curve assessment covering the limited number of experimental data.

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## Acknowledgements

The authors would like to thank Caprari s.p.a. and Eng. Lauro Antipodi for having provided both the experimental performance curves and the 3D-geometry of the two machines.

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## Appendix

### Appendix

In 1966 Suter introduced two parameters (see also Wylie et al. 1993):

where

represents the operating condition of the machine and

Being *T* the torque applied to the runner. The two functions *WH*(*θ*) and *WT*(*θ*) are unique for similar machines. Thus, once they are available for a prototype machine, they can be used to calculate the head drop *H*
^{T} and the efficiency *η*
^{T} of similar PATs in any operating condition *θ*

where \(\eta_B^T\) is the efficiency of the machine at the BEP. In Fig. 9 the Suter parameters of the machines A and B are shown for the turbine operating mode.

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Carravetta, A., Del Giudice, G., Fecarotta, O. *et al.* Energy Production in Water Distribution Networks: A PAT Design Strategy.
*Water Resour Manage* **26, **3947–3959 (2012). https://doi.org/10.1007/s11269-012-0114-1

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### Keywords

- Pump as Turbine (PAT)
- Water Distribution Networks (WDNs)
- Computational Fluid Dynamics (CFD)
- Pressure Reducing Valve (PRV)
- Leak reduction