Multi-objective Optimization of Draft Tube in Francis Turbine Using DOE, RBF and NSGA-II

Abstract

Abstract:In order to improve the performance of the draft tube in hydraulic turbine, a multi-objective optimization method for the draft tube is developed by combining the design of experiment (DOE), the radial basis function (RBF) and the non-dominated sorting genetic algorithm (NSGA-II) in this paper. The geometrical design variables of the median section in the draft tube and the cross section in its exit diffuser are considered as design parameters in this optimization, which objective function is to maximize the pressure recovery factor (Cp) and minimize the energy loss coefficient (ζ). The limited numbers of design matrix required for the shape optimization of the draft tube is generated by optimal Latin hypercube (OLH) method of the DOE technique, of which performances are evaluated through computational fluid dynamic (CFD) numerical simulation. For reducing of the computational consumption, the approximate model is used based on the RBF. The Pareto optimal solutions are finally performed using the NSGA-II for obtaining the best geometrical parameters of the draft tube. The optimization result of the draft tube shows a marked performance improvement over the original, which verifies the theoretical validity and feasibility of the proposed method in this paper.

Optimization of a Draft Tube using Statistical Techniques- DOE and 2D Computational Fluid Dynamic Analysis

“…The Cp indicates the amount of conversion of kinetic energy into static pressure, therefore, a higher value indicates a greater efficiency of the turbine, due to the performance of the draft tube (Mun et al 2017).…”

“…As a result, the method that Nelder-Mead applied to the third-order Bezier curve achieved the best Cp result with 0.813706, compared with 0.812354 obtained by Adjoint Solver. Mun et al (2017), presents a multi-objective optimization method to improve the performance of draft tubes in hydraulic turbines where the design of the experiment (DOE), radial base functions (RBF) and genetic algorithm of non-dominated ordering (NSGA-II) are combined with CFD modelling. The objective-function used in the process corresponds to the maximization of the Cp, based on a problem governed by 9 design variables.…”