Inverse Design and Optimization of Low Specific Speed Centrifugal Pump Blade Based on Adaptive POD Hybrid Model

Document Type : Regular Article

Authors

1 School of Energy and Power Engineering, Lanzhou University of Technology, Lanzhou, Gansu, 730050, China

2 Key Laboratory of Fluid machinery and Systems, Lanzhou University of Technology, Lanzhou, Gansu, 730050, China

Abstract

To improve the prediction accuracy of the surrogate model and reduce the calculation cost for hydraulic optimization design of centrifugal pump impeller, an inverse design and optimization method based on adaptive proper orthogonal decomposition (APOD) hybrid model was proposed. Initial samples were designed by perturbing blade control parameters of the original model. The samples were classified using the K-means clustering algorithm, and the adaptive samples were selected according to the category of the objective sample. The snapshot set is composed of blade shape parameters and the CFD flow field data in impeller, which is decomposed into a linear combination of orthogonal bases by the proper orthogonal decomposition (POD) method to predict the objective parameters. According to the objective load distribution, the low specific speed centrifugal pump was inversely designed by using the APOD model, and its initial blade was obtained. And then, the flow field corresponding to disturbed blade shape was predicted using the APOD method, so as to evaluate the gradient of the objective function to design variables. Finally, the initial blade was optimized by the gradient descent method. The results show that the APOD hybrid model method can be employed to accomplish the blade inverse design and the flow field prediction in the optimization design of centrifugal impeller, which significantly reduces the numerical calculation cost and improves the accuracy of the flow field prediction.

Keywords


Buithanh, T., M. Damodaran and K. Willcox (2004). Aerodynamic Data Reconstruction and Inverse Design Using Proper Orthogonal Decomposition. AIAA Journal 42 (8), 1505–1516.##
Chatterjee, A. (2000). An Introduction to the Proper Orthogonal Decomposition. Current Science 78 (7), 808–817.##
Chen, X. B., R. H. Zhang, L. J. Jiang and W. F. Yang (2021). Adaptive POD surrogate model method for centrifugal pump impeller flow field reconstruction based on clustering algorithm. Modern Physics Letters B 35 (7), 2150126.##
Derakhshan, S., M. Pourmahdavi, E. Abdolahnejad, A. Reihani and A. Ojaghi (2013). Numerical Shape Optimization of a Centrifugal Pump Impeller Using Artificial Bee Colony Algorithm. Computers & Fluids 81, 145–151.##
Duan, Y. H., W. H.  Wu, P. H. Zhang, F. L. Tong, Z. L. Fan, G. Y. Zhou and J. Q. Luo (2019). Performance Improvement of Optimization Solutions by POD-Based Data Mining. Chinese Journal of Aeronautics 32 (4), 826–838.##
Guénot, M., I. Lepot, C. Sainvitu, J. Goblet and R. F. Coelho (2013). Adaptive Sampling Strategies for Non-Intrusive POD-Based Surrogates. Engineering Computations 30 (4), 521–547.##
Guo, G. Q., R. H. Zhang, X. B. Chen and R. N. Li (2019). Optimization method for low specific speed centrifugal impeller based on POD surrogate model. Journal of Huazhong University of Science and Technology (Natural Science Edition) 47 (7), 50–55.##
Holmes, P., J. L. Lumley and G. Berkooz (1996). Turbulence, Coherent Structures, Dynamical Systems and Symmetry. London, UK: Cambridge University Press.##
Huang, R. F., X. W. Luo, B. Ji, P. Wang, A. Yu, Z. H. Zhai and J. J. Zhou (2015). Multi-Objective Optimization of a Mixed-Flow Pump Impeller Using Modified NSGA-II Algorithm. Science China Technological Sciences 58 (12), 2122–2130.##
Han, X. D., Y. Kang, J. P. Sheng, Y. Hu and W. G. Zhao (2020). Centrifugal Pump Impeller and Volute Shape Optimization Via Combined NUMECA, Genetic Algorithm, and Back Propagation Neural Network. Structural and Multidisciplinary Optimization 61 (1), 381–409.##
Jameson, A. (1988). Aerodynamic Design via Control Theory. Journal of Scientific Computing 3 (3), 233–260.##
Kim, J. H., K. T. Oh, K. B. Pyun, C. K. Kim, Y. S.  Choi and J. Y. Yoon (2012). Design Optimization of a Centrifugal Pump Impeller and Volute Using Computational Fluid Dynamics. IOP Conference Series: Earth Environmental Science 15, 032025.##
Kato, H. and K. I. Funazak (2014, June). POD-Driven Adaptive Sampling for Efficient Surrogate Modeling and Its Application to Supersonic Turbine Optimization. In Proceedings of ASME Turbo Expo 2014: Turbine Technical Conference and Exposition, Düsseldorf, Germany.##
Luo, J. Q., X. Tang, Y. H. Duan and F. Liu (2015, June). An Iterative Inverse Design Method of Turbomachinery Blades by Using Proper Orthogonal Decomposition. In Proceedings of ASME Turbo Expo 2015: Turbine Technical Conference and Exposition, Montreal, Canada.##
Luo, J. Q., Y. L. Zhu, X. Tang and F. Liu (2017). Flow Reconstructions and Aerodynamic Shape Optimization of Turbomachinery Blades by POD-Based Hybrid Models. Science China Technological Sciences 60 (11), 1658–1673.##
Li, X. J., Y. J. Zhao and Z. X. Liu (2019). A Novel Global Optimization Algorithm and Data-Mining Methods for Turbomachinery Design. Structural and Multidisciplinary Optimization 60 (2), 581–612.##
Mohammadi, B. (2010). Hadamard Incomplete Sensitivity and Shape Optimization. Control and Cybernetics 39 (3), 615–626.##
Pei, J., W. J. Wang and S. Q. Yuan (2014). Statistical Analysis Of Pressure Fluctuations During Unsteady Flow For Low-Specific-Speed Centrifugal Pumps. Journal of Central South University 21 (3), 1017–1024.##
Qiu, Y. S., J. Q. Bai, N. Liu and C. Wang (2018). Global Aerodynamic Design Optimization Based on Data Dimensionality Reduction. Chinese Journal of Aeronautics 31 (4), 643–659.##
Sirovich, L. (1986). Turbulence and the Dynamics of Coherent Structures. Part I: Coherent Structures. Quarterly of Applied Mathematics 45 (3), 561–571.##
Sirovich, L. and M. Kirby (1987). Low-Dimensional Procedure for the Characterization of Human Faces. Journal of the Optical Society of America A 4 (3), 519–524.##
Shim, H. S. and K. Y. Kim (2020). Design Optimization of the Impeller and Volute of a Centrifugal Pump to Improve the Hydraulic Performance and Flow Stability. ASME Journal of Fluids Engineering 142 (10), 101211.##
Siddiqui, M. S., S. T. M. Latif, M. Saeed, M. Rahman, A. W.  Badar and S. M. Hasan (2020). Reduced Order Model of Offshore Wind Turbine Wake by Proper Orthogonal Decomposition. International Journal of Heat and Fluid Flow 82, 108554.##
Tan, L., S. L. Cao, S. B. Gui and B. S. Zhu (2010). Centrifugal pump impeller inverse design by using direct inverse problem iteration. Transactions of the Chinese Society of Agricultural Machinery 41 (7), 30–35.##
Tong, S. G., H. Zhao, H. Q. Liu, Y. Yu, J. F. Li and F. Y. Cong (2020). Multi-Objective Optimization of Multistage Centrifugal Pump Based on Surrogate Model. ASME Journal of Fluids Engineering 142 (1), 011101.##
Wang, F. J. (2016). Research Progress of Computational Model for Rotating Turbulent Flow in Fluid machinery. Transactions of the Chinese society for Agricultural Machinery 47 (2), 1–14.##
Wang, C., W. D. Shi, X. K. Wang, X. P. Jiang, Y. Yang, W. Li and L. Zhou (2017). Optimal Design of Multistage Centrifugal Pump Based on the Combined Energy Loss Model and Computational Fluid Dynamics. Applied Energy 187, 10–26.##
Yang, W., H. Long, L. H. Ma and H. F. Sun (2020). Research on Clustering Method Based on Weighted Distance Density and K-means. Procedia Computer Science 166, 507–511.##
Zangeneh, M., A. Goto and T. Takemura (1996). Suppression of Secondary Flows in a Mixed-Flow Pump Impeller by Application of Three-Dimensional Inverse Design Method: Part 1-Design and Numerical Validation. Journal of Turbomachinery 118 (7), 536–542.##
Zhang, R. H., M. Guo, J. H. Yang and Y. Liu (2014). Blade shape optimization of centrifugal pump impeller with adjoint method. Journal of Drainage and Irrigation Machinery Engineering 32 (11), 943–947.##
Zhang, R. H., R. Guo, J. H. Yang, and J. Q. Luo (2017). Inverse Method of Centrifugal Pump Impeller Based on Proper Orthogonal Decomposition (POD) Method. Chinese Journal of Mechanical Engineering 30 (4), 1025–1031.##
Zhang, R. H. and X. T. Zhao (2020). Inverse Method of Centrifugal Pump Blade Based on Gaussian Process Regression. Mathematical Problems in Engineering 2020, 4605625.##
Zhang, R. H., X. B. Chen and J. Q. Luo (2021). Knowledge Mining of Low Specific Speed Centrifugal Pump Impeller Based on Proper Orthogonal Decomposition Method. Journal of Thermal Science 30, 840–848.##