##
**A fast numerical method for flow analysis and blade design in centrifugal pump impellers.**
*(English)*
Zbl 1237.76079

Summary: A numerical methodology is developed to simulate the turbulent flow in a 2-dimensional centrifugal pump impeller and to compute the characteristic performance curves of the entire pump. The flow domain is discretized with a polar, Cartesian mesh and the Reynolds-averaged Navier-Stokes (RANS) equations are solved with the control volume approach and the k-\(\epsilon \) turbulence model. Advanced numerical techniques for adaptive grid refinement and for treatment of grid cells that do not fit the irregular boundaries are implemented in order to achieve a fully automated grid construction for any impeller design, as well as to produce results of adequate precision and accuracy. After estimating the additional hydraulic losses in the casing and the inlet and outlet sections of the pump, the performance of the pump can be predicted using the numerical results from the impeller section only. The regulation of various energy loss coefficients involved in the model is carried out for a commercial pump, for which there are available measurements. The predicted overall efficiency curve of the pump was found to agree very well with the corresponding experimental data. Finally, a numerical optimization algorithm based on the unconstrained gradient approach is developed and combined with the evaluation software in order to find the impeller geometry that maximizes the pump efficiency, using as free design variables the blade angles at the leading and the trailing edge. The results verified that the optimization process can converge very fast and to reasonable optimal values.

### MSC:

76M12 | Finite volume methods applied to problems in fluid mechanics |

76U05 | General theory of rotating fluids |

76D05 | Navier-Stokes equations for incompressible viscous fluids |

PDF
BibTeX
XML
Cite

\textit{J. S. Anagnostopoulos}, Comput. Fluids 38, No. 2, 284--289 (2009; Zbl 1237.76079)

Full Text:
DOI

### References:

[1] | Zangeneh, M.; Goto, A.; Takemura, T., Suppression of secondary flows in a mixed-flow pump impeller by application of three-dimensional inverse design method: part 1 - design and numerical validation, ASME trans J turbomach, 118, 536-543, (1996) |

[2] | Xu, J.Z.; Gu, C.W., A numerical procedure of three-dimensional design problem in turbomachinery, ASME trans J turbomach, 114, 548-582, (1992) |

[3] | Borges, J.E., A three-dimensional inverse method for turbomachinery: part-1 theory, ASME trans J turbomach, 112, 346-354, (1994) |

[4] | Peng, G.; Cao, S.; Ishizuka, M.; Hayama, S., Design optimization of axial flow hydraulic turbine runner: part I - an improved Q3D inverse method, Intl J num meth fluids, 39, 517-531, (2002) · Zbl 1101.76314 |

[5] | Benra, F.K., Economic development of efficient centrifugal pump impellers by numerical methods, World pumps, May, 48-53, (2001) |

[6] | Yulin W, Jianming Y, Shuliang C. Advanced design for large hydraulic turbine runner. In: ASME/JSME FEDSM’ 99, San Francisco, California, Paper S-287, July 18-23, 1999. |

[7] | Garrison LA, Richard KF, Sale MJ, Cada G. Application of biological design criteria and computational fluid dynamics to investigate fish survival in Kaplan turbines. In: HydroVision 2002, Portland, Oregon, July 29-August 2, 2002. |

[8] | Cao, S.; Peng, G.; Yu, Z., Hydrodynamic design of rotodynamic pump impeller for multiphase pumping by combined approach of inverse design and CFD analysis, ASME trans J fluids engin, 127, 330-338, (2005) |

[9] | Asuaje, M.; Bakir, F.; Kouidri, S.; Rey, R., Inverse design method for centrifugal impellers and comparison with numerical simulation tools, Int J comput fluid dynamics, 18, 2, 101-110, (2004) · Zbl 1063.76637 |

[10] | Gehrer A, Schmidl R, Sadnik D. Kaplan turbine runner optimization by numerical flow simulation (CFD) and an evolutionary algorithm. In: 23rd IAHR symposium on hydraulic machinery and systems, Yokohama, Japan. Paper F125; 2006. |

[11] | Miyauchi S, Kasai N, Fukutomi J. Optimization of meridional shape design of pump impeller. In: 23rd IAHR symposium on hydraulic machinery and systems, Yokohama, Japan. Paper F310; 2006. |

[12] | Mazzouji F, Couston M, Ferrando L, Garcia F, Debeissat F. Multicriteria optimization: viscous fluid analysis – mechanical analysis. In: 22nd IAHR symposium on hydraulic machinery and systems, Stockholm, Sweden, June 29- July 2. Paper A04-1; 2004. |

[13] | Kueny JL, Lestriez R, Helali A, Dmeulenaere A, Hirsch C. Optimal design of a small hydraulic turbine. In: 22nd IAHR symposium on hydraulic machinery and systems, Stockholm, Sweden, Paper A02-2, 2004. |

[14] | Ye, T.; Mittal, R.; Udaykumar, H.S.; Shyy, W., An accurate Cartesian grid method for viscous incompressible flows with complex immersed boundaries, J comput phys, 156, 209-240, (1999) · Zbl 0957.76043 |

[15] | Fadlun, E.A.; Verzicco, R.; Orlandi, P.; Mohd-Yusof, J., Combined immersed-boundary finite-difference methods for three-dimensional complex flow simulations, J comput phys, 161, 35-60, (2000) · Zbl 0972.76073 |

[16] | Anagnostopoulos, J.; Mathioulakis, D., Numerical simulation and hydrodynamic design optimization of a tesla-type valve for micropumps, IASME trans, 2, 6, 1846-1852, (2005) |

[17] | Anagnostopoulos, J., Discretization of transport equations on 2D Cartesian unstructured grids using data from remote cells for the convection terms, Intl J num meth fluids, 42, 297-321, (2003) · Zbl 1143.76493 |

[18] | Anagnostopoulos, J.; Mathioulakis, D., A flow study around a time-dependent 3-D asymmetric constriction, J fluids struct, 19, 49-62, (2004) |

[19] | Neumann, B., The interaction between geometry and performance of a centrifugal pump, (1991), Mechanical Engineering Publications London |

[20] | Pfleiderer, C., Die kreiselpumpen, (1961), Springer-Verlag Berlin |

This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.