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Two-dimensional numerical study of vortex shedding regimes of oscillatory flow past two circular cylinders in side-by-side and tandem arrangements at low Reynolds numbers

  • Ming Zhao (a1) and Liang Cheng (a2) (a3)

Abstract

Oscillatory flow past two circular cylinders in side-by-side and tandem arrangements at low Reynolds numbers is simulated numerically by solving the two-dimensional Navier–Stokes (NS) equations using a finite-element method (FEM). The aim of this study is to identify the flow regimes of the two-cylinder system at different gap arrangements and Keulegan–Carpenter numbers (KC). Simulations are conducted at seven gap ratios $\def \xmlpi #1{}\def \mathsfbi #1{\boldsymbol {\mathsf {#1}}}\let \le =\leqslant \let \leq =\leqslant \let \ge =\geqslant \let \geq =\geqslant \def \Pr {\mathit {Pr}}\def \Fr {\mathit {Fr}}\def \Rey {\mathit {Re}}G$ ( $G=L/D$ where $L$ is the cylinder-to-cylinder gap and $D$ the diameter of a cylinder) of 0.5, 1, 1.5, 2, 3, 4 and 5 and KC ranging from 1 to 12 with an interval of 0.25. The flow regimes that have been identified for oscillatory flow around a single cylinder are also observed in the two-cylinder system but with different flow patterns due to the interactions between the two cylinders. In the side-by-side arrangement, the vortex shedding from the gap between the two cylinders dominates when the gap ratio is small, resulting in the gap vortex shedding (GVS) regime, which is different from any of the flow regimes identified for a single cylinder. For intermediate gap ratios of 1.5 and 2 in the side-by-side arrangement, the vortex shedding mode from one side of each cylinder is not necessarily the same as that from the other side, forming a so-called combined flow regime. When the gap ratio between the two cylinders is sufficiently large, the vortex shedding from each cylinder is similar to that of a single cylinder. In the tandem arrangement, when the gap between the two cylinders is very small, the flow regimes are similar to that of a single cylinder. For large gap ratios in the tandem arrangement, the vortex shedding flows from the gap side of the two cylinders interact and those from the outer sides of the cylinders are less affected by the existence of the other cylinder and similar to that of a single cylinder. Strong interaction between the vortex shedding flows from the two cylinders makes the flow very irregular at large KC values for both side-by-side and tandem arrangements.

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Corresponding author

Email address for correspondence: m.zhao@uws.edu.au

References

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Alam, M. M., Moriya, M. & Sakamoto, H. 2003 Aerodynamic characteristics of two side-by-side circular cylinders and application of wavelet analysis on the switching phenomenon. J. Fluids Struct. 18, 325346.
An, H., Cheng, L. & Zhao, M. 2009 Steady streaming around a circular cylinder in an oscillatory flow. Ocean Engng 36, 10891097.
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, 77103.
Anagnostopoulos, P. & Minear, R. 2004 Blockage effect of oscillatory flow past a fixed cylinder. Appl. Ocean Res. 26, 147153.
Bao, Y., Zhou, D. & Tu, J. 2011 Flow interference between a stationary cylinder and an elastically mounted cylinder arranged in proximity. J. Fluids Struct. 27, 14251446.
Bearman, P. W., Downie, M. J., Graham, J. M. R. & Obasaju, E. D. 1985 Forces on cylinders in viscous oscillatory flow at low Keulegan–Carpenter numbers. J. Fluid Mech. 154, 337356.
Bearman, P. W., Graham, J. M. R., Naylor, P. & Obasaju, D. E.1981 The role of vortices in oscillatory flow about bluff cylinders International Symposium on Hydrodynamics in Ocean Engineering, Norwegian Hydrodynamics Laboratories, Trondheim, pp. 621–635.
Bearman, P. W. & Wadcock, A. J. 1973 The interaction between a pair of circular cylinders normal to a stream. J. Fluid Mech. 61, 499511.
Borazjani, I. & Sotiropoulos, F. 2009 Vortex-induced vibrations of two cylinders in tandem arrangement in the proximity-wake interference region. J. Fluid Mech. 621, 321364.
Brooks, A. N. & Hughes, T. J. R. 1982 Streamline upwind/Petrov–Galerkin formulations for convection dominated flows with particular emphasis on the incompressible Navier–Stokes equations. Comput. Meth. Appl. Mech. Engng 32, 199259.
Chern, M. J., Kanna, P. R., Lu, Y. J., Cheng, I. C. & Chang, S. C. 2010 A CFD study of the interaction of oscillatory flows with a pair of side-by-side cylinders. J. Fluids Struct. 26, 626643.
Coenen, W. & Riley, N. 2009 Oscillatory flow about a cylinder pair. Q. J. Mech. Appl. Maths 62 (1), 5366.
Dütsch, H., Durst, F. & Becker, S. 1998 Low-Reynolds-number flow around an oscillating circular cylinder at low Keulegan–Carpenter numbers. J. Fluid Mech. 360, 249271.
Elston, J. R., Blackburn, H. M. & Sheridan, J. 2006 The primary and secondary instabilities of flow generated by an oscillating circular cylinder. J. Fluid Mech. 550, 359389.
Elston, J. R., Sheridan, J. & Blackburn, H. M. 2004 Two-dimensional Floquet stability analysis of the flow produced by an oscillating circular cylinder in quiescent fluid. Eur. J. Mech. (B/Fluids) 23, 99106.
Hall, P. 1984 On the stability of the unsteady boundary layer on a cylinder oscillating transversely in a viscous fluid. J. Fluid Mech. 146, 347367.
Honji, H. 1981 Streaked flow around an oscillating circular cylinder. J. Fluid Mech. 107, 507520.
Hover, F. S., Techet, A. H. & Triantafyllou, M. S. 1998 Forces on oscillating uniform and tapered cylinders in cross flow. J. Fluid Mech. 363, 97114.
Iliadis, G. & Anagnostopoulos, P. 1998 Numerical visualization of oscillatory flow around a circular cylinder at $\mathit{Re}=200$ and $\mathit{KC}=20$ – an aperiodic flow case. Commun. Numer. Meth. Engng 14, 181194.
Jester, W. & Kallinderis, Y. 2004 Numerical study of incompressible flow about transversely oscillating cylinder pairs. J. Offshore Mech. Arctic Engng 126 (4), 310317.
Justensen, P. 1991 A numerical study of oscillating flow around a circular cylinder. J. Fluid Mech. 222, 157196.
Kim, H. J. & Durbin, P. A. 1988 Investigation of the flow between a pair of cylinders in the flopping regime. J. Fluid Mech. 196, 431448.
Kühtz, S.1996 Experimental investigation of oscillatory flow around circular cylinders at low beta numbers. PhD thesis, University of London.
Lin, X. W., Bearman, P. W. & Graham, J. M. R. 1996 A numerical study of oscillatory flow about a circular cylinder for low values of beta parameters. J. Fluids Struct. 10, 501526.
Meneghini, J. R., Saltara, F., Siqueira, C. L. R. & Ferrari, J. J. A. 2001 Numerical simulation of flow interference between two circular cylinders in tandem and side-by-side arrangements. J. Fluids Struct. 15 (2), 327350.
Mittal, S. & Kumar, V. 2001 Flow-induced oscillations of two cylinders in tandem and staggered arrangements. J. Fluids Struct. 15 (5), 717736.
Mittal, S. & Kumar, V. 2004 Vortex induced vibrations of a pair of cylinders at Reynolds number 1000. Intl J. Comput. Fluid Dyn. 18, 601614.
Mizushima, J. & Suehiro, N. 2005 Instability and transition of flow past two tandem circular cylinders. Phys. Fluids 17 (10), 104107.
Morison, J. R., O’Brien, M. P., Johnson, J. W. & Schaaf, S. A. 1950 The force exerted by surface waves on piles. J. Petrol. Tech. 2 (5), 149154.
Morse, T. L., Govardhan, R. N. & Williamson, C. H. K. 2008 The effect of end conditions on the vortex-induced vibration of cylinders. J. Fluids Struct. 24, 12271239.
Nehari, D., Armenio, V. & Ballio, F. 2004 Three-dimensional analysis of the unidirectional oscillatory flow around a circular cylinder at low Keulegan–Carpenter and $\beta $ numbers. J. Fluid Mech. 520, 157186.
Nemes, A., Zhao, J., Jacono, D. L. & Sheridan, J. 2012 The interaction between flow-induced vibration mechanisms of a square cylinder with varying angles of attack. J. Fluid Mech. 710, 102130.
Obasaju, E. D., Bearman, P. W. & Graham, J. M. R. 1988 A study of forces, circulation and vortex patterns around a circular cylinder in oscillating flow. J. Fluid Mech. 196, 467494.
Sarpkaya, T. 1986 Force on a circular cylinder in viscous oscillatory flow at low Keulegan–Carpenter numbers. J. Fluid Mech. 165, 6171.
Sarpkaya, T. 2002 Experiments on the stability of sinusoidal flow over a circular cylinder. J. Fluid Mech. 457, 157180.
Sarpkaya, T. 2005 On the parameter $\beta =\mathit{Re}/\mathit{KC} =D^{2}/\nu T$ . J. Fluids Struct. 21, 435440.
Sarpkaya, T. 2006 Structures of separation on a circular cylinder in periodic flow. J. Fluid Mech. 567, 281297.
Scandura, P., Armenio, V. & Foti, E. 2009 Numerical investigation of the oscillatory flow around a circular cylinder close to a wall at moderate Keulegan–Carpenter and low Reynolds numbers. J. Fluid Mech. 627, 259290.
Tasaka, Y., Kon, S., Schouveiler, L. & Gal, P. L. 2006 Hysteretic mode exchange in the wake of two circular cylinders in tandem. Phys. Fluids 18, 084101.
Tatsuno, M. & Bearman, P. W. 1990 A visual study of the flow around an oscillating circular cylinder at low Keulegan–Carpenter numbers and low Stokes numbers. J. Fluid Mech. 211, 157182.
Uzunoglu, B., Tan, M. & Price, W. G. 2001 Low-Reynolds-number flow around an oscillating circular cylinder using a cell viscous boundary element method. Intl J. Numer. Meth. Engng 50, 23172338.
Williamson, C. H. K. 1985a Sinusoidal flow relative to circular cylinders. J. Fluid Mech. 155, 141174.
Williamson, C. H. K. 1985b Evolution of a single wake behind a pair of bluff bodies. J. Fluid Mech. 159, 118.
Yang, K., Cheng, L., An, H., Bassom, A. P. & Zhao, M. 2013 The effect of a piggyback cylinder on the flow characteristics in oscillatory flow. Ocean Engng 62, 4555.
Zdravkovich, M. M. 1987 The effects of interference between circular cylinders in cross flow. J. Fluids Struct. 1, 239261.
Zdravkovich, M. M. 1988 Review of interference-induced oscillations in flow past two parallel circular cylinders in various arrangements. J. Wind Engng Ind. Aerodyn. 28, 183200.
Zdravkovich, M. M. & Pridden, D. L. 1977 Interference between two circular cylinders, series of unexpected discontinuities. J. Ind. Aerodyn. 2, 255270.
Zhao, M. 2013 Flow induced vibration of two rigidly coupled circular cylinders in tandem and side-by-side arrangements at a low Reynolds number of 150. Phys. Fluids 25, 123601.
Zhao, M., Cheng, L., Teng, B. & Dong, G. 2007 Hydrodynamic forces on dual cylinders of different diameters in steady flow. J. Fluids Struct. 23, 5983.
Zhao, M., Cheng, L. & Zhou, T. 2009 Numerical simulation of three-dimensional flow past a yawed circular cylinder. J. Fluids Struct. 25, 831847.
Zhao, M., Thapa, J., Cheng, L. & Zhou, T. 2013 Three-dimensional transition of vortex-shedding flow around a circular cylinder at right and oblique attacks. Phys. Fluids 25, 014105.
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Two-dimensional numerical study of vortex shedding regimes of oscillatory flow past two circular cylinders in side-by-side and tandem arrangements at low Reynolds numbers

  • Ming Zhao (a1) and Liang Cheng (a2) (a3)

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