To improve the accuracy and reduce the calculation cost for the inverse problem of centrifugal pump impeller, the new inverse method based on proper orthogonal decomposition (POD) is proposed. The pump blade shape is parameterized by quartic Bezier curve, and the initial snapshots is generated by introducing the perturbation of the blade shape control parameters. The internal flow field and its hydraulic performance is predicted by CFD method. The snapshots vector includes the blade shape parameter and the distribution of blade load. The POD basis for the snapshots set are deduced by proper orthogonal decomposition. The sample vector set is expressed in terms of the linear combination of the orthogonal basis. The objective blade shape corresponding to the objective distribution of blade load is obtained by least square fit. The Iterative correction algorithm for the centrifugal pump blade inverse method based on POD is proposed. The objective blade load distributions are corrected according to the difference of the CFD result and the POD result. The two dimensional and three dimensional blade calculation cases show that the proposed centrifugal pump blade inverse method based on POD have good convergence and high accuracy, and the calculation cost is greatly reduced. After two iterations, the deviation of the blade load and the pump hydraulic performance are limited within 4.0% and 6.0% individually for most of the flow rate range. This paper provides a promising inverse method for centrifugal pump impeller, which will benefit the hydraulic optimization of centrifugal pump.
Ren-Hui Zhang
,
Rong Guo
,
Jun-Hu Yang
,
Jia-Qi Luo
. Inverse Method of Centrifugal Pump Impeller Based on Proper Orthogonal Decomposition (POD) Method[J]. Chinese Journal of Mechanical Engineering, 2017
, 30(4)
: 1025
-1031
.
DOI: 10.1007/s10033-017-0137-x
[1] C Hornsby. CFD—driving pump design forward. World Pumps, 2002, 2002(431): 18–22.
[2] H Sun, R F Xiao, F J Wang, et al. Analysis of the pump-turbine S characteristics using the detached eddy simulation method. Chinese Journal of Mechanical Engineering, 2015, 28(1): 115–122.
[3] W D Shi, L Zhou, W G Lu, et al. Numerical prediction and performance experiment in a deep-well centrifugal pump with different impeller outlet width. Chinese Journal of Mechanical Engineering, 2013, 26(1): 46–52.
[4] J Wu, K Shimmei, K Tani, et al. CFD-based design optimization for hydro turbines. Journal of Fluids Engineering, 2007, 129(2): 159–168.
[5] J H Kim, K Y Kim. Optimization of Vane diffuser in a mixedflow pump for high efficiency design. International Journal of Fluid Machinery & Systems, 2011, 4(1): 172–178.
[6] A Goto, M Nohmi, T Sakurai, et al. Hydrodynamic design system for pumps based on 3-D CAD, CFD, and inverse design method. Journal of Fluids Engineering, 2002, 124(2): 329–335.
[7] A Goto, M Zangeneh. Hydrodynamic design of pump diffuser using inverse design method and CFD. Journal of Fluids Engineering, 2002, 124(2): 319–328.
[8] M Zangeneh, A Goto, H Harada. On the role of three-dimensional inverse design methods in turbomachinery. Journal of Mechanical Engineering, 1999, 213(1): 27–42.
[9] M Zangeneh, A Goto, T Takemura. Suppression of secondary flows in a mixed-flow pump impeller by application of threedimensional inverse design method: part 1—design and numerical validation. Journal of Turbomachinery, 1996, 118(3): 536–543.
[10] A Goto, T Takemura, M Zangeneh. Suppression of secondary flows in a mixed-flow pump impeller by application of threedimensional inverse design method: Part 2—Experimental Validation. Journal of Turbomachinery, 1996, 118(3): 544–551.
[11] M Zangeneh. A Compressible three-dimensional design method for radial and mixed flow turbomachinery blades. International Journal for Numerical Methods in Fluids, 1991, 13(5): 599–624.
[12] G Peng, S Cao, M Ishizuka, et al. Design optimization of axial flow hydraulic turbine runner: Part Ⅰ—an improved Q3D inverse method. International Journal for Numerical Methods in Fluids, 2002, 39(6): 517-531.
[13] M Zangeneh. Inviscid-viscous interaction method for threedimensional inverse design of centrifugal impellers. Journal of Turbomachinery, 1994, 116(2):280–290.
[14] C H Wu. A General theory of three-dimensional flow in subsonic and supersonic turbomachines of axial, radial, and mixed-flow types. Technical Report Archive & Image Library, 1952, 1(1).
[15] S Cao, G Peng, Z Yu. Hydrodynamic design of rotodynamic pump impeller for multiphase pumping by combined approach of inverse design and CFD analysis. Journal of Fluids Engineering, 2005, 127(2): 330–338.
[16] H Y Fan. An inverse design method of diffuser blades by genetic algorithms[J]. Proceedings of the Institution of Mechanical Engineers, Part A: Journal of Power and Energy, 1998, 212(4): 261–267.
[17] J S Kim, W G Park. Optimized inverse design method for pump impeller. Mechanics Research Communications, 2000, 27(4): 465–473
[18] A Chatterjee. An introduction to the proper orthogonal decomposition. Current Science, 2000, 78(7): 808–817.
[19] P Holmes, J L Lumley, G Berkooz. Turbulence, coherent structures, dynamical systems and symmetry. London: Cambridge University Press, 1998.
[20] B F Feeny, R Kappagantu. On the physical interpretation of proper orthogonal modes in vibrations. Journal of Sound and Vibration, 1998, 211(4): 607–616.
[21] L Sirovich, M Kirby. Low-dimensional procedure for the characterization of human faces. Journal of the Optical Society of America A, 1987, 4(3): 519–524.
[22] S G Raben, J J Charonko, P P Vlachos. Adaptive gappy proper orthogonal decomposition for particle image velocimetry data reconstruction. Measurement Science and Technology, 2012, 23(2): 025303.
[23] T Bui-thanh, M Damodaran, E Willcoxk. Aerodynamic data reconstruction and inverse design using proper orthogonal decomposition. AIAA journal, 2004, 42(8): 1505–1516.
[24] A Oyama, T Nonomura, K Fujii. Data mining of Pareto-optimal transonic airfoil shapes using proper orthogonal decomposition. Journal of Aircraft, 2010, 47(5): 1756–1762.
[25] D J J Toal, N W Bressloff, A J Keane. Geometric filtration using POD for aerodynamic design optimization//Collection of Technical Papers—26th AIAA Applied Aerodynamics Conference, Honolulu, HI, USA. 2008: 18–21.
[26] X Cai, F Ladeinde. A comparison of two POD methods for airfoil design optimization. AIAA Paper, 2005, 4912: 2005.
[27] J Luo, Y Duan, X Tang, et al. An iterative inverse design method of turbomachinery blades by using proper orthogonal decomposition. ASME Paper GT2015-42876, 2015.
[28] R H Zhang, J H Yang, R N Li. Investigation on parametric design of centrifugal pump blade. Drainage and Irrigation Machinery, 2009, 27(5):310–313.(in Chinese)
