Numerical simulations of the effect of leading edge cavitation on the vibration characteristics of an elastic hydrofoil
YAO Zhifeng1,2, LAI Guihua1, LIU Jing3, ZENG Yongshun1
1. College of Water Resources and Civil Engineering, China Agricultural University, Beijing 100083, China; 2. Beijing Engineering Research Center of Safety and Energy Saving Technology for Water Supply Network System, China Agricultural University, Beijing 100083, China; 3. AECC Commercial Aircraft Engine Co., Ltd., Shanghai 200241, China
Abstract:When hydraulic machinery operating conditions differ from the design conditions, leading edge cavitation can significantly disrupt the flow field and increase fluid-solid interactions (FSI) between the flow and the blade which change the system vibration characteristics. The flow around a NACA0009 elastic hydrofoil was simulated using the shear stress transfer (SST) turbulence model and the Zwart-Gerber-Belamri (ZGB) cavitation model in the three dimensional Reynolds average numerical simulation (RANS) method.The damped natural frequency and the added damping ratio were then calculated using a two-way FSI numerical method. The results were verified against existing experimental data. The computational results show that both the length and thickness of the cavitation region expand and the boundary layer on the hydrofoil leading edge grows thicker as the cavitation number decreases. The increasing cavitation length then reduces the shedding vortex frequency from the hydrofoil trailing edge. The leading edge cavity has little influence on the vibration shape of the bending mode, but greatly influences the vibration shape of the torsional mode. Enlarging the cavitation region increases the natural frequencies of the bending and torsional modes of the elastic hydrofoil in the same way, while the effects of the added damping ratio depend on the vibration mode. At an attack angle of 2° and a flow rate of 14 m/s, the natural frequency of the hydrofoil in the bending mode with leading edge cavitation increases up to 2.25% and the added damping ratio decreases by 9.00%, while the natural frequency in the torsional mode increases by 20.12% and the added damping ratio increases by 165.70%.
姚志峰, 赖桂桦, 刘婧, 曾永顺. 前缘空化对弹性水翼振动特性影响数值模拟[J]. 清华大学学报(自然科学版), 2021, 61(11): 1325-1333.
YAO Zhifeng, LAI Guihua, LIU Jing, ZENG Yongshun. Numerical simulations of the effect of leading edge cavitation on the vibration characteristics of an elastic hydrofoil. Journal of Tsinghua University(Science and Technology), 2021, 61(11): 1325-1333.
[1] TRIVEDI C. A review on fluid structure interaction in hydraulic turbines:A focus on hydrodynamic damping[J]. Engineering Failure Analysis, 2017, 77:1-22. [2] 胡秀成, 张立翔. 水泵水轮机增减负荷过程三维流动特性大涡模拟分析[J]. 水利学报, 2018, 49(4):492-500. HU X C, ZHANG L X. Numerical simulation of unsteady flow for a pump-turbine in transition cases with large-eddy simulation[J]. Journal of Hydraulic Engineering, 2018, 49(4):492-500. (in Chinese) [3] DÖRFLER P, SICK M, COUTU A. Flow-induced pulsation and vibration in hydroelectric machinery[M]. London, UK:Springer, 2013. [4] DEHKHARQANI A S, AIDANPÄÄ J O, ENGSTRÖM F, et al. A review of available methods for the assessment of fluid added mass, damping, and stiffness with an emphasis on hydraulic turbines[J]. Applied Mechanics Reviews, 2018, 70(5):050801. [5] DUPONT P. Study of the dynamics of a partial cavitation in view of hydraulic turbomachines[D]. Lausanne, Swiss:Swiss Federal Institute of Technology in Lausanne, 1993. [6] DE LA TORRE O, ESCALER X, EGUSQUIZA E, et al. Experimental investigation of added mass effects on a hydrofoil under cavitation conditions[J]. Journal of Fluids and Structures, 2013, 39:173-187. [7] YAO Z F, WANG F J, DREYER M, et al. Effect of trailing edge shape on hydrodynamic damping for a hydrofoil[J]. Journal of Fluids and Structures, 2014, 51:189-198. [8] 朱文若, 高忠信, 陆力, 等. 离心泵叶轮水中固有频率经验下降系数分析及优化[J]. 水利学报, 2013, 44(12):1455-1461. ZHU W R, GAO Z X, LU L, et al. Analysis and optimization on natural frequencies depreciation coefficient of centrifugal pump impeller in water[J]. Journal of Hydraulic Engineering, 2013, 44(12):1455-1461. (in Chinese) [9] LINDHOLM U S, KANA D D, CHU W H. Elastic vibration characteristics of cantilever plates in water[J]. Journal of Ship Research, 1965, 9(2):11-36. [10] BLEVINS R D, PLUNKETT R. Formulas for natural frequency and mode shape[J]. Journal of Applied Mechanics, 1980, 47(2):461-462. [11] SEELEY C, COUTU A, MONETTE C, et al. Characterization of hydrofoil damping due to fluid-structure interaction using piezocomposite actuators[J] Smart Materials and Structures, 2012, 21(3):035027. [12] BERGAN C W, TENGS E O, SOLEMSLIE B W, et al. An experimental investigation of the hydrodynamic damping of vibrating hydrofoils[C]//29th IAHR Symposium on Hydraulic Machinery and Systems. Kyoto, Japan, 2018:16-21. [13] LIU X, ZHOU L J, ESCALER X, et al. Numerical simulation of added mass effects on a hydrofoil in cavitating flow using acoustic fluid-structure interaction[J]. Journal of Fluids Engineering, 2017, 139(4):041301. [14] HU S L, LU C J, HE Y S. Fluid-structure interaction simulation of three-dimensional flexible hydrofoil in water tunnel[J]. Applied Mathematics and Mechanics, 2016, 37(1):15-26. [15] 曾永顺, 姚志峰, 杨正军, 等. 非对称尾部形状水翼水力阻尼识别方法研究[J]. 水利学报, 2019, 50(7):864-873. ZENG Y S, YAO Z F, YANG Z J, et al. Study on hydrodynamic damping identification for an asymmetrical trailing edge shape hydrofoil[J]. Journal of Hydraulic Engineering, 2019, 50(7):864-873. (in Chinese) [16] 曾卓雄. 稠密两相流动湍流模型及其应用[M]. 北京:机械工业出版社, 2012. ZENG Z X. Turbulence models in dense two-phase flow and its application[M]. Beijing:China Machine Press, 2012. (in Chinese) [17] ZWART P J, GERBER A G, BELAMRI T. A two-phase flow model for predicting cavitation dynamics[C]//Proceedings of the 5th International Conference on Multiphase Flow. Yokohama, Japan, 2004. [18] LIANG Q W, RODRIGUEZ C G, EGUSQUIZA E, et al. Numerical simulation of fluid added mass effect on a Francis turbine runner[J]. Computers & Fluids, 2007, 36(6):1106-1118. [19] GAUTHIER J P, GIROUX A M, ETIENNE S, et al. A numerical method for the determination of flow-induced damping in hydroelectric turbines[J]. Journal of Fluids and Structures, 2017, 69:341-354. [20] ACUPR P, ŠTEFAN D, HABÁN V, et al. FSI analysis of Francis-99 hydrofoil employing SBES model to adequately predict vortex shedding[J/OL]. Journal of Physics:Conference Series, 2019, 1296(1):012002. DOI:10. 1088/1742-6596/1296/1/012002. [21] ZENG Y S, YAO Z F, GAO J Y, et al. Numerical investigation of added mass and hydrodynamic damping on a blunt trailing edge hydrofoil[J]. Journal of Fluids Engineering, 2019, 141(8):081108. [22] DE LA TORRE O, ESCALER X, EGUSQUIZA E, et al. Numerical and experimental study of a nearby solid boundary and partial submergence effects on hydrofoil added mass[J]. Computers & Fluids, 2014, 91:1-9. [23] CELIK I B, GHIA U, ROACHE P J, et al. Procedure for estimation and reporting of uncertainty due to discretization in CFD applications[J]. Journal of Fluids Engineering, 2008, 130(7):078001.