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Flow around an oscillating circular disk at low to moderate Reynolds numbers

Published online by Cambridge University Press:  12 January 2017

Xinliang Tian ,
Longfei Xiao ,
Xiangdong Zhang ,
Jianmin Yang ,
Longbin Tao  and
Dan Yang
Xinliang Tian
Affiliation:
State Key Laboratory of Ocean Engineering, Shanghai Jiao Tong University, Shanghai 200240, China Collaborative Innovation Center for Advanced Ship and Deep-Sea Exploration, Shanghai 200240, China
Longfei Xiao
Affiliation:
State Key Laboratory of Ocean Engineering, Shanghai Jiao Tong University, Shanghai 200240, China Collaborative Innovation Center for Advanced Ship and Deep-Sea Exploration, Shanghai 200240, China
Xiangdong Zhang
Affiliation:
State Key Laboratory of Ocean Engineering, Shanghai Jiao Tong University, Shanghai 200240, China Collaborative Innovation Center for Advanced Ship and Deep-Sea Exploration, Shanghai 200240, China
Jianmin Yang*
Affiliation:
State Key Laboratory of Ocean Engineering, Shanghai Jiao Tong University, Shanghai 200240, China Collaborative Innovation Center for Advanced Ship and Deep-Sea Exploration, Shanghai 200240, China
Longbin Tao
Affiliation:
School of Marine Science and Technology, Newcastle University, Newcastle upon Tyne NE1 7RU, UK
Dan Yang
Affiliation:
School of Naval Architecture and Ocean Engineering, Huazhong University of Science and Technology, Wuhan 430074, China
*
†Email address for correspondence: [email protected]
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Abstract

Direct numerical simulations of the flow induced by a circular disk oscillating sinusoidally along its axis are performed. The aspect ratio ($\unicode[STIX]{x1D712}=\text{diameter}/\text{thickness}$) of the disk is 10. The Reynolds number ($\mathit{Re}$), based on the maximum speed and the diameter of the disk, is in the range of $50\leqslant \mathit{Re}\leqslant 800$. The Keulegan–Carpenter number ($KC$) is in the range of $1\leqslant KC\leqslant 24$. Five flow regimes are observed in the considered $\mathit{Re}$–$KC$ space: (I) axisymmetric flow (AS), (II) planar symmetric flow in the low-$KC$ region (PSL), (III) azimuthally rotating flow in the low-$KC$ region (ARL), (IV) planar symmetric flow in the high-$KC$ region (PSH) and (V) azimuthally rotating flow in the high-$KC$ region (ARH). The critical boundaries between different flow regimes are identified based on the evolutions of the magnitude and direction of transverse force acting on the disk. For the non-axisymmetric flow regimes, the flow is one-sided with respect to the axis of the disk and is associated with a non-zero mean value of the transverse force acting on the disk.

JFM classification

Vortex Flows: Vortex instability Vortex Flows: Vortex interactions
Type
Papers
Information
Journal of Fluid Mechanics , Volume 812 , 10 February 2017 , pp. 1119 - 1145
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Copyright
© 2017 Cambridge University Press 

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References

An, H., Cheng, L. & Zhao, M. 2011 Direct numerical simulation of oscillatory flow around a circular cylinder at low Keulegan–Carpenter number. J. Fluid Mech. 666, 77–103.CrossRefGoogle Scholar
Auguste, F., Fabre, D. & Magnaudet, J. 2010 Bifurcations in the wake of a thick circular disk. Theor. Comput. Fluid Dyn. 24 (1), 305–313.CrossRefGoogle Scholar
Auguste, F., Magnaudet, J. & Fabre, D. 2013 Falling styles of disks. J. Fluid Mech. 719, 388–405.CrossRefGoogle Scholar
Bearman, P. W. 1984 Vortex shedding from oscillating bluff bodies. Annu. Rev. Fluid Mech. 16 (1), 195–222.CrossRefGoogle Scholar
Berger, E., Scholz, D. & Schumm, M. 1990 Coherent vortex structures in the wake of a sphere and a circular disk at rest and under forced vibrations. J. Fluids Struct. 4 (3), 231–257.CrossRefGoogle Scholar
Bohorquez, P., Sanmiguel-rojas, E., Sevilia, A., Jiménez-gonzález, J. I. & Martínez-bazán, C. 2011 Stability and dynamics of the laminar wake past a slender blunt-based axisymmetric body. J. Fluid Mech. 676, 110–144.CrossRefGoogle Scholar
Chrust, M., Bouchet, G. & Dušek, J. 2010 Parametric study of the transition in the wake of oblate spheroids and flat cylinders. J. Fluid Mech. 665, 199–208.CrossRefGoogle Scholar
Chrust, M., Bouchet, G. & Dušek, J. 2014 Effect of solid body degrees of freedom on the path instabilities of freely falling or rising flat cylinders. J. Fluids Struct. 47, 55–70.CrossRefGoogle Scholar
Chrust, M., Dauteuille, C., Bobinski, T., Rokicki, J., Goujon-Durand, S., Wesfreid, J. E., Bouchet, G. & Dušek, J. 2015 Effect of inclination on the transition scenario in the wake of fixed disks and flat cylinders. J. Fluid Mech. 770, 189–209.CrossRefGoogle Scholar
Ern, P., Risso, F., Fabre, D. & Magnaudet, J. 2012 Wake-induced oscillatory paths of bodies freely rising or falling in fluids. Annu. Rev. Fluid Mech. 44, 97–121.CrossRefGoogle Scholar
Fabre, D., Auguste, F. & Magnaudet, J. 2008 Bifurcations and symmetry breaking in the wake of axisymmetric bodies. Phys. Fluids 20, 051702.CrossRefGoogle Scholar
Fernandes, P. C., Risso, F., Ern, P. & Magnaudet, J. 2007 Oscillatory motion and wake instability of freely rising axisymmetric bodies. J. Fluid Mech. 573, 479–502.CrossRefGoogle Scholar
Ghidersa, B. & Dus̆ek, J. 2000 Breaking of axisymmetry and onset of unsteadiness in the wake of a sphere. J. Fluid Mech. 423, 33–69.CrossRefGoogle Scholar
Hunt, J. C. R., Wray, A. A. & Moin, P. 1988 Eddies, streams, and convergence zones in turbulent flows. In Center for Turbulence Research Report CTR-S88, pp. 193–208. NASA.Google Scholar
Kuo, Y. H. & Baldwin, L. V. 1967 The formation of elliptical wakes. J. Fluid Mech. 27 (02), 353–360.CrossRefGoogle Scholar
Marshall, D. & Stanton, T. E. 1931 On the eddy system in the wake of flat circular plates in three dimensional flow. Proc. R. Soc. Lond. A 130 (813), 295–301.Google Scholar
Meliga, P., Chomaz, J. M. & Sipp, D. 2009 Global mode interaction and pattern selection in the wake of a disk: a weakly nonlinear expansion. J. Fluid Mech. 633, 159–189.CrossRefGoogle Scholar
Michael, P. 1966 Steady motion of a disk in a viscous fluid. Phys. Fluids 9, 466–471.CrossRefGoogle Scholar
Morison, J. R., O’Brien, M. P., Johnson, J. W. & Schaaf, S. A. 1950 The force exerted by surface waves on piles. Petrol. Trans. AIME 189, 149–157.Google Scholar
Natarajan, R. & Acrivos, A. 1993 The instability of the steady flow past spheres and disks. J. Fluid Mech. 254, 323–344.CrossRefGoogle Scholar
OpenFOAM 2009 The Open Source CFD Toolbox, Programmer’s Guide, Version 1.6. OpenCFD Limited.Google Scholar
Rimon, Y. 1969 Numerical solution of the incompressible time-dependent viscous flow past a thin oblate spheroid. Phys. Fluids 12, II–65–75.CrossRefGoogle Scholar
Rivet, J. P., Henon, M., Frisch, U. & d’Humieres, D. 1988 Simulating fully three-dimensional external flow by lattice gas methods. Europhys. Lett. 7, 231.CrossRefGoogle Scholar
Roberts, J. B. 1973 Coherence measurements in an axisymmetric wake. AIAA J. 11, 1569–1571.CrossRefGoogle Scholar
Roos, F. W. & Willmarth, W. W. 1971 Some experimental results on sphere and disk drag. AIAA J. 9, 285–291.CrossRefGoogle Scholar
Shenoy, A. R. & Kleinstreuer, C. 2008 Flow over a thin circular disk at low to moderate Reynolds numbers. J. Fluid Mech. 605, 253–262.CrossRefGoogle Scholar
Shenoy, A. R. & Kleinstreuer, C. 2010 Influence of aspect ratio on the dynamics of a freely moving circular disk. J. Fluid Mech. 653, 463–487.CrossRefGoogle Scholar
Tchoufag, J., Fabre, D. & Magnaudet, J. 2014 Global linear stability analysis of the wake and path of buoyancy-driven disks and thin cylinders. J. Fluid Mech. 740, 278–311.CrossRefGoogle Scholar
Weller, H. G., Tabor, G., Jasak, H. & Fureby, C. 1998 A tensorial approach to computational continuum mechanics using object-oriented techniques. Comput. Phys. 12, 620–631.CrossRefGoogle Scholar
Williamson, C. H. K. & Govardhan, R. 2008 A brief review of recent results in vortex-induced vibrations. J. Wind Engng Ind. Aerodyn. 96, 713–735.CrossRefGoogle Scholar
Willmarth, W. W., Hawk, N. E. & Harvey, R. L. 1964 Steady and unsteady motions and wakes of freely falling disks. Phys. Fluids 7, 197–208.CrossRefGoogle Scholar
Yang, J., Liu, M., Wu, G., Liu, Q. & Zhang, X. 2015 Low-frequency characteristics in the wake of a circular disk. Phys. Fluids 27 (6), 064101.CrossRefGoogle Scholar
Yang, J., Liu, M., Wu, G., Zhong, W. & Zhang, X. 2014a Numerical study on coherent structure behind a circular disk. J. Fluids Struct. 51, 172–188.CrossRefGoogle Scholar
Yang, J., Tian, X. & Li, X. 2014b Hydrodynamic characteristics of an oscillating circular disk under steady in-plane current conditions. Ocean Engng 75, 53–63.CrossRefGoogle Scholar
Yang, J., Wu, G., Zhong, W. & Liu, M. 2014c Numerical study on bifurcations in the wake of a circular disk. Intl J. Comput. Fluid Dyn. 28 (5), 187–203.CrossRefGoogle Scholar
Zhong, H. J. & Lee, C. B. 2012 The wake of falling disks at low Reynolds numbers. Acta Mechanica Sin. 28, 1–5.Google Scholar

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