The improvement in energy saving aspects in water systems is currently a topic of major interest. The utilization of pumps working as turbines is a relevant strategy in water distribution networks consisting of pressurized pipes, using these machines to recover energy, generate green energy and reduce leakages in water systems. The need to develop energy studies, prior to the installation of these facilities, requires the use of simulation tools. These tools should be able to define the operation curves of the machine as a function of the flow rate. This research proposes a new strategy to develop a mathematics model for pumps working as turbines (PATs), considering the modified affinity laws. This proposed model, which can be input into hydraulic simulation tools (e.g., Epanet, WaterGems), allows estimation of the head, efficiency, and power curves of the PATs when operating at different rotational speeds. The research used 87 different curves for 15 different machines to develop the new model. This model improves the results of the previously published models, reducing the error in the estimation of the height, efficiency, and power values. The proposed model reduced the errors by between 30 and 50% compared to the rest of the models.

The present research depicts an analysis of the implementation of computational fluid dynamics (CFD) in the study of pumps such as turbines and PATs. To highlight the benefits of CFDs for PAT studies, results from both experimental tests have been compared to better understand the reproduction error phenomena. For this, data analysis used in successful models has been applied to determine variables and parameters, and to report a low relative error. The results show that most of the studies focused on fixed speed rotation with some cases of variable speed rotation. Furthermore, there is not enough information in the academic literature for PAT of axial and mixed flows with fixed and variable speed. Finally, turbulence models based on Reynolds average Navier–Stokes (RANS) have been used to simulate PATs with fixed speed rotation in most cases.

The selection of pumps as turbines (PATs) for their respective use in energy optimisation systems is a complicated task, because manufacturers do not provide the characteristic curves. For this reason, some research has been carried out to predict them with computational fluid dynamics (CFD) and mathematical models. The purpose of this study is to validate these two prediction methodologies of flow (Q) vs. head (H) curves through numerical modelling using the computational package OpenFOAM, together with a comparison with the experimental data obtained from a PAT for the case in which the nominal rotation speed of the machine varies. Depending on the configuration and working conditions of the PAT, the simulation performed with OpenFOAM was validated by calibrating it with the nominal curve of the pump and with another simulation performed with CFD workbench SOLIDWORKS FloEFD. Subsequently, the second methodology related to the analyses and mathematical models proposed to predict the Q vs. H curves were also validated with new models in OpenFOAM and the experimental data. The results show that these prediction methods are effective when a machine’s operating point is close to the BEP (best efficient point). The absolute error ranges obtained with these two prediction methodologies for rotation speeds of 880 rpm, 1020 rpm, 1200 rpm, and 1500 rpm are between 5 and 24%, 2 and 17%, 0 and 12%, and 1 and 24%, respectively.

Pump as turbine (PAT); computational fluid dynamics; variable rotational nominal speed; OpenFoam.

This study evaluates, through a comparative statistical analysis, the predictive performance of empirical equations for estimating peak discharge during earthen pond failures, using a curated dataset of 78 reliable historical failure cases covering the documented period of available records, selected from an initial international database of 1893 cases. The analysis focuses on reservoirs with storage volumes below 6 hm³, a range that remains insufficiently addressed by existing breach-outflow models despite its importance for hydraulic, mining, and agricultural infrastructures. The procedure established a key comparative evaluation between equations to define the fit volume intervals. The results indicate that predictive uncertainty and error dispersion increase significantly as reservoir volume decreases, with a critical high-variability interval identified between 3.5 and 6 hm³ for both overtopping and piping failure mechanisms. A key finding is that predictive performance is strongly dependent on stored volume segmentation, as no single empirical formulation dominates the entire volume range; instead, 10 of 63 different equations achieve optimal accuracy within 5 specific storage intervals considering the RMSE, MAD and MAE error values. These findings emphasize the necessity of volume-dependent equation selection, based on comparative performance evaluation, and the development of specialized predictive models for small earthen reservoirs to ensure reliable risk assessment.