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Wake dynamics of external flow past a curved circular cylinder with the free stream aligned with the plane of curvature

  • A. MILIOU (a1), A. DE VECCHI (a1), S. J. SHERWIN (a1) and J. M. R. GRAHAM (a1)
Abstract

Three-dimensional spectral/hp computations have been performed to study the fundamental mechanisms of vortex shedding in the wake of curved circular cylinders at Reynolds numbers of 100 and 500. The basic shape of the body is a circular cylinder whose centreline sweeps through a quarter section of a ring and the inflow direction lies on the plane of curvature of the quarter ring: the free stream is then parallel to the geometry considered and the part of the ring that is exposed to it will be referred to as the ‘leading edge’. Different configurations were investigated with respect to the leading-edge orientation. In the case of a convex-shaped geometry, the stagnation face is the outer surface of the ring: this case exhibited fully three-dimensional wake dynamics, with the vortex shedding in the upper part of the body driving the lower end at one dominant shedding frequency for the whole cylinder span. The vortex-shedding mechanism was therefore not governed by the variation of local normal Reynolds numbers dictated by the curved shape of the leading edge. A second set of simulations were conducted with the free stream directed towards the inside of the ring, in the so-called concave-shaped geometry. No vortex shedding was detected in this configuration: it is suggested that the strong axial flow due to the body's curvature and the subsequent production of streamwise vorticity plays a key role in suppressing the wake dynamics expected in the case of flow past a straight cylinder. The stabilizing mechanism stemming from the concave curved geometry was still found to govern the wake behaviour even when a vertical extension was added to the top of the concave ring, thereby displacing the numerical symmetry boundary condition at this point away from the top of the deformed cylinder. In this case, however, the axial flow from the deformed cylinder was drawn into the wake of vertical extension, weakening the shedding process expected from a straight cylinder at these Reynolds numbers. These considerations highlight the importance of investigating flow past curved cylinders using a full three-dimensional approach, which can properly take into account the role of axial velocity components without the limiting assumptions of a sectional analysis, as is commonly used in industrial practice. Finally, towing-tank flow visualizations were also conducted and found to be in qualitative agreement with the computational findings.

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Barkley, D., Tuckerman, L. S. & Golubitsky, M. 2000 Bifurcation theory for three-dimensional flow in the wake of a circular cylinder. Phys. Rev. E 61, 52475252.
Bearman, P. W. 1967 The effect of base bleed on the flow behind a two-dimensional model with a blunt trailing edge. Aeronaut. Q. 18, 207224.
Bearman, P. W. & Owen, J. C. 1998 a Special brief note: reduction of bluff-body drag and suppression of vortex shedding by the introduction of wavy separation lines. J. Fluids Struct. 12, 123130.
Bearman, P. W. & Owen, J. C. 1998 b Suppressing vortex shedding from bluff bodies by the introduction of wavy separation lines. In 1998 Conference on Bluff Body Wakes and Vortex-Induced Vibration, ASME Fluids Engineering Division (Annual Summer Meeting), Washington, DC.
Bearman, P. W. & Takamoto, M. 1988 Vortex shedding behind rings and discs. Fluid Dyn. Res. 3, 214218.
Blackburn, H. M., Marques, F. & Lopez, J. M. 2005 Symmetry breaking of two-dimensional time-periodic wakes. J. Fluid Mech. 522, 395411.
Darekar, R. M. & Sherwin, S. J. 2001 Flow past a square-section cylinder with a wavy stagnation face. J. Fluid Mech. 426, 263295.
Gaster, M. 1969 Vortex shedding from slender cones at low Reynolds numbers. J. Fluid Mech. 38, 565576.
Gerich, D. & Eckelmann, H. 1982 Influence of end plates and free ends on the shedding plates of circular cylinders. J. Fluid Mech. 122, 109121.
Jeong, J. & Hussain, F. 1995 On the identification of a vortex. J. Fluid Mech. 285, 6994.
Karniadakis, G. E. & Sherwin, S. J. 1999 Spectral/hp Element Methods for CFD. Oxford University Press.
Karniadakis, G. E., Israeli, M. & Orszag, S. A. 1991 High-order splitting methods for the incompressible Navier–Stokes equations. J. Comput. Phys. 97, 414443.
Lear, C. J. 2003 Controlling the break-up distance of aircraft trailing vortices. PhD thesis, University of London.
Leweke, T. & Provansal, M. 1995 The flow behind rings–bluff-body wakes without end effects. J. Fluid Mech. 288, 265310.
Maskell, E. C. 1963 A theory of blockage effect on bluff-bodies and stalled wings in a closed wind tunnel. ARC R&M 3400.
Meneghini, J. R., Saltara, F., de Andrade Fergonesi, R., Yamamoto, C. T., Casaprima, E. & Ferrari, J. A. JR 2004 Numerical simulations of viv on long flexible cylinders immersed in complex flow fields. Eur. J. Fluid Mech. B/Fluids 23, 5163.
Miliou, A., Sherwin, S. J. & Graham, J. M. R. 2003 Fluid dynamic loading on curved riser pipes. Trans. ASME J. Offshore Mech. Arctic Engng 125, 176182.
Owen, J. C. 2001 Passive control of vortex shedding in the wakes of bluff bodies. PhD thesis, University of London.
Peiró, J. & Sayma, A. I. 1995 A 3-d unstructured multigrid Navier–Stokes solver. In Numerical Methods for Fluid Dynamics, V (ed. Morton, K. W. & Baines, M. J.). Oxford University Press.
Peiró, J., Peraire, J. & Morgan, K. 1994 Felisa Manual. Department of Aeronautics, Imperial College of Science, Technology and Medicine.
Peraire, J., Peiró, J. & Morgan, K. 1993 Multigrid solution of the 3-d compressible Euler equations on unstructured tetrahedral grids. Intl J. Numer. Meth. Engng 36, 10291044.
Sherwin, S. J. & Karniadakis, G. E. 1996 Tetrahedral hp finite elements: algorithms and flow solutions. J. Comput. Phys. 124, 1445.
Sherwin, S. J. & Peiró, J. 2002 Mesh generation in curvilinear domains using high-order elements. Intl J. Numer. Meth. Engng 53, 207223.
Slaouti, A. & Gerrard, J. H. 1981 An experimental investigation of the end effects on the wake of a circular cylinder towed through water at low Reynolds numbers. J. Fluid Mech. 112, 297314.
Takamoto, M. & Izumi, K. 1981 Experimental observation of stable arrangement of vortex rings. Phys. Fluids 24, 15821583.
Willden, R. H. J. & Graham, J. M. R. 2004 Multi-modal vortex-induced vibrations of a vertical riser pipe subject to a uniform current profile. Eur. J. Fluid Mech. B/Fluids 23, 209218.
Williamson, C. H. K. 1988 The existence of two stages in the transition to three dimensionality of a cylinder wake. Phys. Fluids 31, 31653168.
Williamson, C. H. K. 1989 Oblique and parallel modes of vortex shedding in the wake of a circular cylinder at low Reynolds numbers. J. Fluid Mech. 206, 579627.
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Journal of Fluid Mechanics
  • ISSN: 0022-1120
  • EISSN: 1469-7645
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