Optimization of the basin and inlet channel of a gravitational water vortex hydraulic turbine using the response surface methodology

The gravitational water vortex hydraulic turbine is an appropriate turbine to be used under from a small to medium water flow rate and at a low head. This turbine extracts energy from an induced vortex in a basin, using a coaxial rotor with a vertical axis. The gravitational turbine has efficiencies that vary between 17 and 85%. Increasing the circulation was required in order to achieve the highest efficiency. The circulation is a function of some geometric parameters of the turbine, such as the ratios between the basin diameter (D) and the outlet diameter (d), d/D; the basin height (H) and D, H/D; the inlet channel width (w) and D, w/D; the inlet channel height (h) and D, h/D; the inlet channel long (L) and D, L/D; and the wrap-around angle (gamma). Response surface methodology was utilized to determine the optimal geometry that results in the highest circulation. The values of the six variables that give the highest circulation of 2.089 m(2)/s were d/D = 0.167, H/D = 1.840, w/D = 0.2, h/D = 0.599, L/D = 0.500 and gamma= 179.97 degrees. In addition, an exponential equation was proposed for calculating the inlet velocity for each treatment. This equation is a function of d/D and the coefficient of discharge, C-d. The results of the exponential function were compared with experimental data from other investigations. (C) 2022 Elsevier Ltd. All rights reserved.