Inverse Method of Centrifugal Pump Impeller Based on Proper Orthogonal Decomposition (POD) Method

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.

[1]  Kiyohito Tani,et al.  CFD-Based Design Optimization for Hydro Turbines , 2007 .

[2]  Mehrdad Zangeneh,et al.  Suppression of secondary flows in a mixed-flow pump impeller by application of three-dimensional inverse design method: Part 2 - Experimental validation , 1996 .

[3]  Akira Oyama,et al.  Data Mining of Pareto-Optimal Transonic Airfoil Shapes Using Proper Orthogonal Decomposition , 2010 .

[4]  M. Zangeneh,et al.  A compressible three‐dimensional design method for radial and mixed flow turbomachinery blades , 1991 .

[5]  P. Holmes,et al.  Turbulence, Coherent Structures, Dynamical Systems and Symmetry , 1996 .

[6]  Mehrdad Zangeneh,et al.  Suppression of Secondary Flows in a Mixed-Flow Pump Impeller by Application of Three-Dimensional Inverse Design Method: Part 1—Design and Numerical Validation , 1996 .

[7]  Ling Zhou,et al.  Numerical prediction and performance experiment in a deep-well centrifugal pump with different impeller outlet width , 2013 .

[8]  Mehrdad Zangeneh,et al.  Hydrodynamic Design of Pump Diffuser Using Inverse Design Method and CFD , 2002 .

[9]  Motohiko Nohmi,et al.  Hydrodynamic Design System for Pumps Based on 3-D CAD, CFD, and Inverse Design Method , 2002 .

[10]  Chung-Hua Wu.  A General Theory of Three-Dimensional Flow in Subsonic and Supersonic Turbomachines of Axial, Radial, and Mixed-Flow Types , 1952, Journal of Fluids Engineering.

[11]  Jin-Hyuk Kim,et al.  Optimization of Vane Diffuser in a Mixed-Flow Pump for High Efficiency Design , 2011 .

[12]  Feng Liu,et al.  An Iterative Inverse Design Method of Turbomachinery Blades by Using Proper Orthogonal Decomposition , 2015 .

[13]  Hui Sun,et al.  Analysis of the pump-turbine S characteristics using the detached eddy simulation method , 2015 .

[14]  K. Willcox,et al.  Aerodynamic Data Reconstruction and Inverse Design Using Proper Orthogonal Decomposition , 2004 .

[15]  Andy J. Keane,et al.  Geometric filtration using POD for aerodynamic design optimization , 2008 .

[16]  Shuliang Cao,et al.  Hydrodynamic design of rotodynamic pump impeller for multiphase pumping by combined approach of inverse design and CFD analysis , 2005 .

[17]  B. Feeny,et al.  On the physical interpretation of proper orthogonal modes in vibrations , 1998 .

[18]  Masaru Ishizuka,et al.  Design optimization of axial flow hydraulic turbine runner: Part I—an improved Q3D inverse method , 2002 .

[19]  A. Chatterjee.  An introduction to the proper orthogonal decomposition , 2000 .

[20]  H.-Y. Fan,et al.  An inverse design method of diffuser blades by genetic algorithms , 1998 .

[21]  Pavlos P. Vlachos,et al.  Adaptive gappy proper orthogonal decomposition for particle image velocimetry data reconstruction , 2012 .

[22]  Mehrdad Zangeneh,et al.  INVISCID-VISCOUS INTERACTION METHOD FOR 3-DIMENSIONAL INVERSE DESIGN OF CENTRIFUGAL IMPELLERS , 1994 .

[23]  Craig Hornsby,et al.  CFD — driving pump design forward , 2002 .

[24]  M Zangeneh,et al.  On the role of three-dimensional inverse design methods in turbomachinery shape optimization , 1999 .

[25]  Jong-Seop Kim,et al.  Optimized inverse design method for pump impeller , 2000 .

[26]  Foluso Ladeinde,et al.  A Comparison of Two POD Methods for Airfoil Design Optimization , 2005 .

[27]  L Sirovich,et al.  Low-dimensional procedure for the characterization of human faces. , 1987, Journal of the Optical Society of America. A, Optics and image science.