Abstract
Interblade vortices can greatly influence the stable operations of Francis turbines. As visible interblade vortices are essentially cavitating flows, i.e., the ones to cause interblade vortex cavitations, an unsteady simulation with a method using the RNG k-ε turbulence model and the Zwart-Gerber-Belamri (ZGB) cavitation model is carried out to predict the pressure fluctuations induced. Modifications of the turbulence viscosity are made to improve the resolutions. The interblade vortices of two different appearances are observed from the numerical results, namely, the columnar and streamwise vortices, as is consistent with the experimental results. The pressure fluctuations of different frequencies are found to be induced by the interblade vortices on incipient and developed interblade vortex lines, respectively, on the Hill diagram of the model runner’s parameters. From the centrifugal Rayleigh instability criterion, it follows that the columnar interblade vortices are stable and the streamwise interblade vortices are unstable in the model Francis turbine.
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HUANG Yuan-fang, LIU Guang-ning and FAN Shi-ying. Research on prototype hydro-turbine operation[M], Beijing, China, China Electric Power Press, 2010(in Chinese).
SHI Qing-hua, XU Wei-wei and GONG Li. Noise reduction in a low head Francis turbine caused by runner inter-blade vortices[J]. Dongfang Electrical Machine, 2008, (1): 42–46(in Chinese).
GRINDOZ B. Lois de similitudes dans les essays de cavitation des turbines Francis[D]. Doctoral Thesis, Lausanne, Switzerland: EPFL, 1991.
PENG Zhong-nian, CHEN Rui and JIANG Xue-yun. Experimental investigation of flow pattern observation and water pressure pulsation performed on the Three Gorges model turbine[J]. Water Resources and Hy-dropower Engineering, 1999, 30(11): 8–14(in Chinese).
CHEN Rui, PENG Zhong-nian. An experimental study on water pressure fluctuation at Francis turbine runner blade outlet[J]. Water Resources and Hydropower Engineering, 1999, 30(11): 30–32(in Chinese).
CHEN Jin-xia, LI Guo-wei and LIU Sheng-zhu. The occurrence and the influence of the interblade vortex on the hydraulic turbine instability[J]. Large Electric Machine and Hydraulic Turbine, 2007, (3): 42–46(in Chinese).
ZHANG Peng-yuan, ZHU Bao-shan and ZHANG Le-fu. Numerical investigation on pressure fluctuations induced by interblade vortices in a runner of Francis turbi-ne[J]. Large Electric Machine and Hydraulic Turbine, 2009, (6): 35–39(in Chinese).
STEIN P., SICK M. and DOERFLER P. et al. Numerical simulation of the cavitating draft tube vortex in a Francis turbine[C]. IAHR Section Hydraulic Machinery, Equipment, and Cavitation, 23rd Symposium. Yokohama, Japan, 2006.
AVELLAN F. Introduction to cavitation in hydraulic machinery[C]. 6th International Conference on Hydraulic Machinery and Hydrodynamics. Timisoara, Romania, 2004.
KUROSAWA S., LIM S. M. and ENOMOTO Y. Virtual model test for a Francis turbine[C]. 25th IAHR Symposium on Hydraulic Machinery and Systems. Timisoara, Romania, 2010.
ZHANG R., CAI Q. and WU J. et al. The physical origin of severe low-frequency pressure fluctuations in giant Francis turbines[J]. Modern Physics Letters B, 2005, 19(28–29): 1527–1530.
WU J., CHEN S. and WU Y. et al. Characteristics and control of the draft-tube flow in part-load Francis turbine[J]. Journal of Fluids Engineering, 2009, 131(2). 021101.
SENOCAK I., SHYY W. A pressure-based method for turbulent cavitating flow computations[J]. Journal of Computational Physics, 2002, 176(2): 363–383.
MERKLE C., FENG J. and BUELOW P. Computational modeling of the dynamics of sheet cavitation[C]. Proceeding of Third International Symposium on Cavitation. Grenoble, France, 1998, 307–311.
KUNZ R. F., BOGER D. A. and CHYCZEWSKI T. S. et al. Multi-phase CFD analysis of natural and ventilated cavitation about submerged bodies[C]. ASME Fluid Engineering Division Summer Meeting, FEDSM99-7364. San Francisco, USA, 1999.
KUNZ R., BOGER D. and STINEBRING D. A Preconditioned Navier-Stokes method for two-phase flows with application to cavitation prediction[J]. Computers and Fluids, 2000, 29(8): 849–875.
SINGHAL A. K., ATHAVALE M. M. and LI H. et al. Mathematical basis and validation of the full cavitation model[J]. Journal of Fluids Engineering, 2002, 124(3): 617–624.
SENOCAK I., SHYY W. Interfacial dynamics-based modeling of turbulent cavitating flows, model development and steady-state computations[J]. International Journal for Numerical Methods in Fluids, 2004, 44(9): 975–995.
ZWART P., GERBER A. and BELAMRI T. A two-phase flow model for predicting cavitation dynamics[C]. Fifth International Conference on Multiphase Flow. Yokohama, Japan, 2004.
LIU Yan, ZHAO Peng-fei and WANG Qiang et al. URANS computation of cavitating flows around skewed propellers[J]. Journal of Hydrodynamics, 2012, 24(3): 339–346.
COUTIER-DELGOSHA O., REBOUD J. Numerical simulation of unsteady cavitation flows[J]. International Journal for Numerical Methods in Fluids, 2003, 42(5): 527–548.
COUTIER-DELGOSHA O., FORTES-PATELLA R. and REBOUD J. Evaluation of the turbulence model influence on the numerical simulations of unsteady cavi-tation[J]. Journal of Fluids Engineering, 2003, 125(1): 38–45.
COUTIER-DELGOSHA O., REBOUD J. and ALBANO G. Numerical simulation of the unsteady cavitation behavior of an inducer blade cascade[C]. ASME Proceedings of ASME Fluids Engineering Division Summer Meeting. Boston, Massachusetts, USA, 2000.
Hydraulic turbines, storage pumps and pump-turbines-Model acceptance tests[S]. International Standard IEC 60193, 1999.
HANSEN C. D., JOHNSON C. R. Visualization Handbook[M]. Burlington, Canada: Butterworth-Heinemann, 2005, 295–309.
RAYLEIGH L. On the dynamics of revolving fluids[J]. Proceedings of the Royal Society of London, Series A, 1917, 93(648): 148–154.
DRAZIN P. G., REID W. H. Hydrodynamic stability[M]. 2nd Edition, Cambridge, UK: Cambridge university Press, 2004.
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Project supported by the National Natural Science Foundation of China (Grant No. 51476083), the National Science and Technology Ministry of China (Grant No. 2011BAF03B01).
Biography: ZUO Zhi-gang (1977-), Male, Ph. D.
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Zuo, Zg., Liu, Sh., Liu, Dm. et al. Numerical analyses of pressure fluctuations induced by interblade vortices in a model Francis turbine. J Hydrodyn 27, 513–521 (2015). https://doi.org/10.1016/S1001-6058(15)60511-X
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DOI: https://doi.org/10.1016/S1001-6058(15)60511-X