Assessment of a prototype of gravitational water vortex turbine: experimental validation of efficiency

The present work focuses on the evaluation, by best efficient point (BEP), Nash–Sutcliffe efficiency (NSE), mean square relative error (MSRE), relative mean error (RME) and residual bias (BIAS) of a prototype of a gravitational water vortex turbine. The analysis performed using computational fluid dynamics was experimentally validated to quantify the accuracy of the mathematical model. The estimation of the statistical parameters mentioned was made for different response variables, such as vortex height \(H_{v}\), torque \(T_{s}\), mechanical power \(P_{m}\) and efficiency \(\eta_{t}\), in order to identify biases in different areas of the simulation. The BEP was determined for a flow rate of \(6.0 {l \mathord{\left/ {\vphantom {l s}} \right. \kern-0pt} s}\) with an efficiency of 58.13% in the experimental part and 54.62% in the numerical modeling, with the vortex height as the critical parameter of the system due to its influence on performance. The NSE and MSRE indicators were positioned as the functions with the best adaptability for the response parameters by criteria and sensitivity. Meanwhile, the RME, MSRE and BIAS presented significant differences for the values of mechanical power and torque. Regarding the electrical efficiency of the generator, it was estimated at 27.68% for the BEP with an average decrease of 3.1% per unit of flow supplied from this point. Therefore, the turbine is subject to the conditions of the generator (torque and number of revolutions per minute) and vortex height, which control the optimization of the system.