Multi-objective optimization of a mixed-flow pump impeller using modified NSGA-II algorithm

Abstract

In order to maintain a uniform distribution of pareto-front solutions, a modified NSGA-II algorithm coupled with a dynamic crowding distance (DCD) method is proposed for the multi-objective optimization of a mixed-flow pump impeller. With the pump meridional section fixed, ten variables along the shroud and hub are selected to control the blade load by using a three-dimensional inverse design method. Hydraulic efficiency, along with impeller head, is applied as an optimization objective; and a radial basis neural network (RBNN) is adopted to approximate the objective function with 82 training samples. Local sensitivity analysis shows that decision variables have different impacts on the optimization objectives. Instead of randomly selecting one solution to implement, a technique for ordering preferences by similarity to ideal solution (TOPSIS) is introduced to select the best compromise solution (BCS) from pareto-front sets. The proposed method is applied to optimize the baseline model, i.e. a mixed-flow waterjet pump whose specific speed is 508 min 1 m 3 s 1 m. The performance of the waterjet pump was experimentally tested. Compared with the baseline model, the optimized impeller has a better hydraulic efficiency of 92% as well as a higher impeller head at the design operation point. Furthermore, the off-design performance is improved with a wider highefficiency operation range. After optimization, velocity gradients on the suction surface are smoother and flow separations are eliminated at the blade inlet part. Thus, the authors believe the proposed method is helpful for optimizing the mixed-flow pumps.mixed-flow pump, waterjet pump, multi-objective optimization, numerical simulation, modified NSGA-II Citation: Huang R F, Luo X W, Ji B, et al. Multi-objective optimization of a mixed-flow pump impeller using modified NSGA-II algorithm.

Derivation of the Mathematical Approach to the Radial Pump’s Meridional Channel Design Based on the Controlment of the Medial Axis

“…where ( ) can be got from (8) or (9). In [14,15], the distribution of the cross section area ( ) can be taken as a previous settled variable, so that the variable ( ) can still be taken as a known variable before the meridional channel design in this study.…”

“…To design the pump, two aspects, namely, the blade shape and the meridional channel, can be considered [5]. Though many inverse design methods about the blade shape have already been conducted by former studies [6][7][8], little attention has been paid to the meridional channel design. Nevertheless, the meridional shape is the foundation for the pump design, and Bing et al [9] had proven that the meridional shape has great effects on the pump performance, so that the related design method about the meridional channel should be treated seriously.…”

Application of the Modified Inverse Design Method in the Optimization of the Runner Blade of a Mixed-Flow Pump

“…In this inverse design approach, the blade shape was represented as sheets of blade loading with the approximate distribution controlled by specific variables at the hub and shroud sides, such a design method has already been adopted in the TURBODesign software. Using this sequential design method in the software, several optimal pumps have been successfully obtained [8,9]. However, some problems still remain waiting to be solved.…”

Optimization of Pump Hydraulic Performance Based on the Response Surface Method

“…The results show that the radial basis function has high accuracy and computational efficiency. Huang [2] combined with radial basis response model and NSGA-II genetic algorithm to optimize the impeller of mixed flow pump. The hydraulic efficiency increased by 1.2% with head increased by 0.5m.…”