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Low specific speed centrifugal pumps (LSSCP) are widely utilized in district energy systems to promote the integration of renewable energy. However, the performance of LSSCP becomes inefficient due to harsh operating conditions resulting in substantial increase in energy consumption. Many-objective optimization is significant in improving the performance of LSSCP and promoting the sustainability of district energy systems. Among the existing optimization methods, global optimization methods are limited by high computational cost when solving many-objective optimization problems, and gradient-based optimization methods face difficulties in locating the global optimum. In the present study, a hybrid optimization method was developed for solving many-objective optimization problems of LSSCP. The LSSCP optimization result of the hybrid algorithm was compared with that of the non-dominated sorting genetic algorithm (NSGA), so as to demonstrate the capacity of the proposed method. In the designed flow condition without cavitation, the hydraulic efficiency obtained by the hybrid optimization algorithm was found to be 9.5%, 5.4%, and 4.7% higher than those of the original, NSGA-II, and NSGA-III optimized results, respectively. The shaft power was 10.3%, 8.7% and 5.1% less than said three optimized results. The maximum turbulent kinetic energy in the flow passage obtained from the hybrid optimization was only 2.2 J/kg, which was 67% and 46% less than that of the NSGA-II and NSGA-III optimized results, respectively. In the designed flow condition with cavitation, the net positive suction head critical optimized by the hybrid model was 0.857 m, which was substantially reduced compared with the original and NSGA- II optimized results.

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Particle image velocimetry (PIV) technology, which performs the full-field velocity measurement on the laser plane, plays a crucial role in the study of complex flow structures in centrifugal pumps. In particle image cross-correlation analysis, the flow field could be corrupted with outliers, due to the background Gaussian noise of imaging, insufficient illumination caused by optical obstruction, and particle slip caused by centrifugal forces, etc. Here we propose a patch-based flow field reconstruction (PFFR) method for PIV data of centrifugal pump. Particularly, inspired by the fact that natural images contain a large number of mutually similar patches at different locations, the instantaneous PIV data with symmetric property are segmented to multiple patches. Flow field reconstruction is achieved by low-rank sparse decomposition, which exploiting the information of similar flow characteristics present in patches. To evaluate the effectiveness of PFFR, we illustrated PFFR on large eddy simulation (LES) vorticity field and experimental data of centrifugal pump, and three other data analysis methods were performed. We have demonstrated that for the instantaneous flow field with outliers, PFFR has faithful reconstruction ability to improve the reliability of data. When the outliers account for 20% of the total flow vectors, the average normalized root mean square error of PFFR-reconstructed data is 0.143, which is lower than three other data methods by 21.9% ~ 48.1%. The structural similarity is 0.702, which is higher than three other data methods by 2.1% ~ 9%.