Citation: Barbarelli, S.; Pisano, V.;
Amelio, M. Development of a
Predicting Model for Calculating the
Geometry and the Characteristic
Curves of Pumps Running as
Turbines in Both Operating Modes.
Energies 2022, 15, 2669. https://
doi.org/10.3390/en15072669
Academic Editors: Luis
Hernández-Callejo, Sergio
Nesmachnow and Sara Gallardo
Saavedra
Received: 28 February 2022
Accepted: 31 March 2022
Published: 6 April 2022
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Article
Development of a Predicting Model for Calculating the
Geometry and the Characteristic Curves of Pumps Running as
Turbines in Both Operating Modes
Silvio Barbarelli * , Vincenzo Pisano and Mario Amelio
Department of Mechanical, Energy and Management Engineering, University of Calabria,
Via Ponte P. Bucci Cubo 44/C, 87036 Rende, Italy; vincent88kr@hotmail.it (V.P.); mario.amelio@unical.it (M.A.)
* Correspondence: silvio.barbarelli@unical.it
Abstract:
This article is part of a scientific research project dedicated to the study of plants generating
electricity from hydraulic sources by exploiting the technology of inverted flow centrifugal pumps,
also known as PAT. The main purpose is to provide a contribution to the methodologies already
existing in the literature, creating a one-dimensional model capable of predicting the characteristic
curves of the machine, in both operating modes, without knowing its geometry. The first part of
the work is therefore focused on the description of the fluid dynamic model, capable of determin-
ing the losses in the various sections of the machine, using different calculation approaches. The
development of this model was carried out using a set of six centrifugal pumps, measured at the
DIMEG Department of the University of Calabria and at the University of Trento. For this range of
pumps, the characteristic curves were therefore obtained, both in pump and turbine operation. The
second part of this work focuses on the description of the geometric model, useful as generally few
data are provided in the manufacturer’s catalog, which is necessary for the correct installation of
the machine. The geometric model can determine, using these parameters and through good design
techniques and statistical diagrams, the entire geometry of the machine. This model refers to a pump
prototype, having a simplified geometry, for which the characteristic curves of the PAT are obtained
in pump operation. These curves are compared with those present in the manufacturer’s catalog, and
if they show too high deviations, it is possible to act on some geometric parameters, chosen based
on a sensitivity analysis. Once satisfactory results have been obtained, it is possible to obtain the
characteristic curves also in turbine operation. This procedure has been finally applied to another
PAT, taken as an example.
Keywords: pumps as turbines; predicting model; experimental test; optimization procedure
1. Introduction
Over the years, world energy consumption has drastically increased, with different
trends in various countries based on the degree of wealth and development and the
availability of raw materials and resources. Consequently, as regards the water sector, the
idea of using inverted flow pumps, also known as PAT [
1
,
2
], has begun to make its way
into the market. The first researchers who realized the actual potential in exploiting a pump
used as a turbine were Thoma and Kittredge [
3
]. They began experimenting in laboratories
on this technology around the 1930s. There are also traces of the use of this technology in
the 1970s; however, it failed to play an important role as energy was cheap and there was
still no sensitivity towards recycling and saving. It was therefore more convenient to buy
energy directly from the grid, and few tended to invest in new plants to produce a small
number of kilowatt-hours. However, in the 1980s, some factors prompted a re-evaluation
of the use of this technology, favoring its development and its establishment on the market,
including the following:
Energies 2022, 15, 2669. https://doi.org/10.3390/en15072669 https://www.mdpi.com/journal/energies
