The Lagrangian Coherent Structure-based Investigation of Cavitating Flows around a Disc

doi:10.3969/j.issn.1000-1093.2014.03.011

Abstract

Abstract: The cavitating flows around a disc is analyzed based on finite-time Lyapunov exponents (FTLE) and Lagrangian coherent structure (LCS). The inhomogeneous model is utilized to predict the interaction between vapour and water flows in the simulation. The simulation results are confirmed by the experimental data. The analytical result shows that LCS defined by the ridges of FTLE can be divided into straight and circular LCSs. The straight LCS reflects that the disc hinders the motion of fluid, and the circular LCS distinguishes the large-scale vortex and identifies the center of vortex accurately. The vortex is intensified and the distribution is concentrated with the development of cavity. It is the periodic change in the intensity of re-entrant flow that causes the periodic expansion and contraction of cavity. A low FTLE region emerges near the support-rod with the increase in re-entrant flow, and there exists a corresponding relationship between the region and the start point of streamline.

Key words: fluid mechanics, Lagrangian coherent structure, finite-time Lyapunov exponent, inhomogenous model, cavitating flow

CLC Number:

TV131.32

BAI Ze-yu, WANG Guo-yu, WU Qin, HUANG Biao. The Lagrangian Coherent Structure-based Investigation of Cavitating Flows around a Disc[J]. Acta Armamentarii, 2014, 35(3): 362-370.

References

［1］黄海龙, 王聪, 黄文虎等. 变攻角圆盘空化器生成自然超空泡数值模拟[J]. 北京理工大学学报, 2008, 28(2): 100-103.
HUANG Hai-long, WANG Cong, HUANG Wen-hu, et al. Numerical simulation on natural supercavity based on disk-cavitator with variable attack angle[J]. Transactions of Beijing Institute of Technology, 2008, 28(2): 100-103.(in Chinese)
［2］隗喜斌, 王聪, 荣吉利等. 锥体空化器非定常超空泡形态分析[J]. 兵工学报, 2007, 28(7): 863-866.
WEI Xi-bin, WANG Cong, RONG Ji-li, et al. Unsteadysupercavitating flow on cone cavitator[J]. Acta Armamentarii, 2007, 28(7): 863-866. (in Chinese)
［3］孟庆昌, 张志宏, 刘巨斌等. 压缩性对亚声速圆盘空化器超空泡流动的影响[J]. 华中科技大学学报：自然科学版, 2011, 39(3): 51-54.
MENG Qing-chang, ZHANG Zhi-hong, LIU Ju-bin,et al. Effect of the compressibility over supercavitating flow on subsonic disk cavitators[J]. Journal of Huazhong University of Science and Technology: Natural Science Edition, 2011, 39(3): 51-54. (in Chinese)
［4］孟庆昌, 张志宏, 刘巨斌等. 超声速圆盘空化器超空泡流动数值计算方法[J]. 上海交通大学学报, 2011, 45(10): 1435-1439.
MENG Qing-chang, ZHANG Zhi-hong, LIU Ju-bin,et al. Numerical method for supercavitating flow over disk cavitator of underwater supersonic projectile[J]. Journal of Shanghai Jiaotong University, 2011, 45(10): 1435-1439. (in Chinese)
［5］袁绪龙, 张宇文, 杨武刚. 高速超空化航行体典型空化器多相流CFD分析[J]. 弹箭与制导学报, 2005, 25(1): 53-59.
YUAN Xu-long, ZHANG Yu-wen, YANG Wu-gang. Multi-phase CFD analysis of typical cavitator for high-speed supercavitating underwater vehicle[J]. Journal of Projectiles, Rockets. Missiles and Guidance, 2005, 25(1): 53-59. (in Chinese)
［6］时素果, 王国玉, 权晓波，等. 当地均相介质模型在通气超空化流动计算中的应用[J]. 兵工学报, 2011, 32(2): 147-154.
SHI Su-guo, WANG Guo-yu, QUAN Xiao-bo,et al. The application of a local homogenous medium model in the ventilated-supercavitation flow computations[J]. Acta Armamentarii, 2011, 32(2): 147-154. (in Chinese)
［7］ Johansen S T, Wu J, Shyy W. Filter-based unsteady RANS computations[J]. International Journal of Heat and Fluid Flow, 2004, 25(1): 10-21.
［8］黄彪, 王国玉, 袁海涛，等. 基于密度分域的混合湍流模型的应用与评价[J]. 北京理工大学学报, 2010, 30(10): 1170-1174.
HUANG Biao, WANG Guo-yu, YUAN Hai-tao,et al. Assessment of a density modify based turbulence closure for unsteady cavitating flows[J]. Transactions of Beijing Institute of Technology, 2010, 30(10): 1170-1174. (in Chinese)
［9］ Boisson N, Malin M R. Numerical prediction of two-phase flow in bubble columns[J]. International Journal for Numerical Methods in Fluids, 1996, 23(12): 1289-1310.
［10］Chahed J, Roig V, Masbernat L. Eulerian-Eulerian two-fluid model for turbulent gas-liquid bubbly flows[J]. InternationalJournal of Multiphase Flow, 2003, 29(1): 23-49.
［11］Arakeri V H, Acosta A J. Viscous effects in the inception of cavitation on axisymmetric bodies[J]. Journal of Fluids Engineering, 1973, 95(4): 519-527.
［12］Belahadji B, Franc J P, Michel J M. Cavitation in the rotational structures of a turbulent wake[J]. Journal of Fluid Mechanics, 1995, 287(1): 383-403.
［13］Hunt J C R, Wray A A, Moin P. Eddies, streams, and convergence zones in turbulent flows[C]//Studying Turbulence Using Numerical Simulation Databases.Washington:NASA,1988: 193-208.
［14］Chong M S, Perry A E, Cantwell B J. A general classification of three-dimensional flow fields[C]// Topological Fluid Mechanics. Cambridge:IUTAM, 1990: 408-420.
［15］Jeong J, Hussain F. On the identification of a vortex[J]. Journal of Fluid Mechanics, 1995, 285(69): 69-94.
［16］Haller G, Yuan G. Lagrangian coherent structures and mixing in two-dimensional turbulence[J]. Physica D: Nonlinear Phenomena, 2000, 147(3): 352-370.
［17］Haller G. Distinguished material surfaces and coherent structures in three-dimensional fluid flows[J]. Physica D: Nonlinear Phenomena, 2001, 149(4): 248-277.
［18］Shadden S C, Lekien F, Marsden J E. Definition and properties of Lagrangian coherent structures from finite-time Lyapunov exponents in two-dimensional aperiodic flows[J]. Physica D: Nonlinear Phenomena, 2005, 212(3): 271-304.
［19］Green M A, Rowley C W, Haller G. Detection of Lagrangian coherent structures in three-dimensional turbulence[J]. Journal of Fluid Mechanics, 2007, 572(1): 111-120.
［20］O’Farrell C, Dabiri J O. A lagrangian approach to identifying vortex pinch-off[J].An Interdisciplinary Journal of Nonlinear Science, 2010, 20(1):1-9.
［21］Tang J N, Tseng C C, Wang N F. Lagrangian-based investigation of multiphase flows by finite-time Lyapunov exponents[J]. Acta Mechanica Sinica, 2012, 28(3): 612-624.
［22］Launder B E, Spalding D B. The numerical computation of turbulent flows[J]. Computer Methods in Applied Mechanics and Engineering, 1974, 3(2): 269-289.
［23］Kubota A, Kato H, Yamaguchi H, et al. Unsteady structure measurement of cloud cavitation on a foil section using conditional sampling technique[J]. Journal of Fluids Engineering, 1989, 111(2): 204-210.
［24］张敏弟, 郭善刚, 邵峰，等. 绕空化器自然空化流动的研究[J]. 工程热物理学报, 2010, 31(8): 1319-1323.
ZHANG Min-di, GUO Shan-gang, SHAO Feng, et al. Study on natural cavitation around a cavitator[J]. Journal of Engineering Thermophysics, 2010, 31(8): 1319-1323. (in Chinese)
［25］胡子俊, 张楠, 姚惠之，等. 涡判据在孔腔涡旋流动拓扑结构分析中的应用[J]. 船舶力学, 2012, 16(8): 839-846.
HU Zi-jun, ZHANG Nan,YAO Hui-zhi, et al. Vortex identification in the analysis on the topology structure of vortical flow in cavity[J]. Journal of Ship Mechanics, 2012, 16(8): 839-846.(in Chinese)

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