Surrogate modeling method for multi-objective optimization of the inlet channel and the basin of a gravitational water vortex hydraulic turbine

Abstract

This work presents a high-fidelity surrogate model for generating a multi-objective genetic algorithm to allow the search for the optimal geometry of the inlet channel and the basin of a gravitational water vortex hydraulic turbine. Six parameters were considered for the optimization: the relations between the basin diameter (D) and the basin height (H), H/D; the wrap-around angle (γ), the outlet diameter (d) and D, d/D; the inlet channel width (w) and D, w/D; the inlet channel height (h) and D, h/D; and the inlet channel length (L) and D, L/D. Two conflicting objectives were studied: maximizing the vortex strength (Γ) and minimizing the volume flow rate (Q). The multi-objective optimization problem was resolved by applying the gamultiobj function in Matlab R2018b software. The optimization combines the genetic algorithm with Kriging interpolation to obtain the Pareto front. To train the gamultiobj function, an initial population of 40 individuals was used. As a stopping criterion, the maximum generation of 500 individuals was established. To improve the Pareto front, 20 optimization cycles (60 new samples) were required, reaching a final population of 100 individuals. It was found from the Pareto front that the values of the six variables providing the compromise solution, between Γ and Q, were H/D=1.572, L/D=1.518, h/D=0.565, w/D=0.361, d/D=0.108, and γ=92.141°. This solution reaches a Q of 0.00305 m3/s and a Γ of 1.699 m2/s. The results of this study were compared with the results reported by other authors, who optimized this type of turbine by applying the response surface methodology. The difference between these results was less than 9.61%.