Numerical optimization and experimental validation of the runner of a gravitational water vortex hydraulic turbine with a spiral inlet channel and a conical basin

This paper describes the use of the response surface methodology for the numerical optimization of the runner of a gravitational water vortex hydraulic turbine with a conical basin and a spiral inlet channel. The effect of the relative position of the runner (p), the number of blades (n), and the relation between the mean diameter of the blades (Db), and the diameter of the basin (D), (Db/D) on the efficiency of the turbine was evaluated, and the optimum runner was determined. A second-order regression model representing the efficiency of the turbine was developed. From this model, it was found that the highest efficiency of 65.18% was reached when all the independent variables were set to their higher values, i.e., Db/D, n, and p equal to 0.45, 6, and 0.6, respectively. Experiments were performed using the optimal runner (Db/D=0.45, n=6) and four values for p (0.4, 0.45, 0.50, and 0.55). It was not possible to test the optimal condition with p=0.6, due to the final quality of the acrylic model, the runner collided with the walls of the cone. The experimental efficiencies for the p values were 30.13, 38.35, 53.19, and 60.77%, respectively. According to the response model, these efficiencies correspond to 28.84, 40.46, 50.80, and 59.99%, respectively.