*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 determining 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
