Application of biharmonic equation in impeller profile optimization design of an aero-centrifugal pump

Abstract

Purpose The purpose of this paper is to improve the hydraulic efficiency without changing the overall dimension. The blade profile optimization design of the aero-centrifugal pump based on the biharmonic equation surrogate model has been studied. Design/methodology/approach First of all, Bezier curves and linear function are used to control the annular angle distribution and the stacking angle of blade profile under the MATLAB platform. Grid independence analysis has been studied to find the finest mesh scheme. After the precision comparison of test data and computation fluid dynamics 15 sets of design parameters are carried out as the boundary condition of the biharmonic equation. The efficiency surrogate model of the biharmonic equation is constructed via iteratively solving of a discrete difference equation. The other two surrogate models of response surface model (RSM) and radial basis function neural network surrogate model (RBFNNSM) are compared with the biharmonic equation surrogate model by the standard of modified complex correlation coefficient R2 and root mean square deviation (RSME). Finally, the artificial fish swarm algorithm has been used to find the global optimal design parameters with the objective function of highest efficiency. Findings The results show that the design parameters code conversion method can reduce the number of optimization parameters from five to three, makes the design space become a cube, and compared with RSM and RBFNNSM, the biharmonic equation surrogate model has higher precision with R2 is 0.8958, RSME is 0.1382. The final optimum result of AFSA is at the point of [1 −1 −1]. The internal flow field analysis shows that after optimization the outlet relative velocity becomes more uniform and the wake effect has been significantly decreased. The hydraulic efficiency of the optimized pump is about 59.45 per cent increasing 5.4 per cent compared with a prototype pump. Originality/value This study developed a new method to optimize the design parameters of aero-centrifugal pump impeller based on biharmonic equation surrogate model, which had a good agreement with experimental values within just 15 sets of the original design. The optimization results shows that the method can improve the hydraulic efficiency significantly.

Centrifugal Pump Design: An Optimization

“…Box and Wilson presented the Reaction Surface Methodology (RSM) in 1951; it is a technique for estimating the combined effect of several independent variables that do not require the performance of factorial design experiments for all of the independent variables at each level. RSM (Liu et al, 2019;Meng et al, 2022)is a technique that can be found in the field of chemical engineering.…”

Many-Objective Hybrid Optimization Method for Impeller Profile Design of Low Specific Speed Centrifugal Pump in District Energy Systems

“…[10] Impeller high-pressure and low-pressure side diameter, impeller low-pressure side hub diameter, impeller high-pressure side exit width Hydraulic efficiency in differient mass flow rate CFD and Experiment MOGA Wang et al [11] Hub inlet angle, hub exit angle, hub wrap angle, leading-edge wrap angle at hub, shroud inlet angle, shroud exit angle, shroud wrap angle, and the leading edge wrap angle at the shroud Efficiency and NPSHr CFD and Experiment MOGA Derakhshan et al [7] Hub diameter, suction diameter, impeller diameter, impeller width, inlet, and outlet blade angles Efficiency and total pressure difference CFD and Experiment ABC Derakhshan and M. Bashiri. [12] Hub diameter, suction diameter, impeller diameter, impeller width, and inlet and outlet blade angles Efficiency and total pressure difference CFD and Experiment ES Liu et al [13] Hub streamline and shroud streamline Hydraulic efficiency CFD and Experiment AFSA Wang et al [14] Four angles for the sweep and lean Efficiencies at two working points and total pressure ratio CFD NSGA-II Zhao et al [5] Blade outlet angle, blade inlet angle, splitter offset angle, impeller meridional section Anti-cavitation ability and the hydraulic efficiency CFD and Experiment NSGA-II Pei et al [15] The shroud radius, the hub radius, the shroud angle, and the hub angle As can be seen in Table 1, a problem that existed in the past research is that major parameters affecting the performance of LSSCP, namely head, efficiency, shaft power, and suction capability, have not been fully considered as the optimization objectives. This is due to the shortcomings of the global optimization algorithm, such as encoding complexity and long iterations.…”

“…It is preferred in the design of pumps in previous research because of its advantage in reaching the global optimum. Table 1 summarizes the global optimization method used for the performance optimization of pumps commonly in recent years, including multi-objective genetic algorithm (MOGA) [9][10][11], artificial bee colony (ABC) [7], eagle strategy (ES) [12], artificial fish swarm algorithm (AFSA) [13], and non-dominated sorting genetic algorithm-II (NSGA-II) [14][15][16][17]. Pei et al used the particle swarm optimization algorithm to arrange the optimal solution of the impeller parameters and efficiency of LSSCP, and performance of LSSCP was improved after optimization [3].…”

Multi-Objective Optimization Design of Low Specific Speed Centrifugal Pumps Based on Genetic Algorithm

“…It can be seen from the table that the outlet diameter of the optimized centrifugal pump impeller is significantly reduced, and the number of blades is reduced. This is beneficial to reduce the friction loss of centrifugal pump impeller disk, thus reducing the energy loss of centrifugal pump [32][33]. At the same time, the outlet angle of the optimized centrifugal pump blade is obviously reduced.…”