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A numerical study of oscillating flow around a circular cylinder

Published online by Cambridge University Press:  26 April 2006

Peter Justesen
Peter Justesen
Affiliation:
Institute of Hydrodynamics and Hydraulic Engineering, Technical University of Denmark, DK-2800 Lyngby, Denmark
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Abstract

This paper presents results obtained from a numerical solution to a stream function–vorticity formulation of the Navier–Stokes equations for the flow around a circular cylinder in planar oscillating flow at small Keulegan–Carpenter numbers (KC) in the subcritical Reynolds number (Re) range. The equations are solved by finite-difference methods. For very small KC ([les ] 1), the numerical results coincide with analytical solutions. As KC is increased, the incipient separation and instability leading to an asymmetrical flow with vortex shedding are predicted. Computed flow fields at small KC values are compared to flow visualizations, and good agreement is found for moderate β-values (≈ 250). The well-documented flow regimes with the transverse vortex street, single-, double- and three-pair shedding, are predicted by the model. Although the flow is not fully resolved for the highest Re values, comparisons of calculated drag and inertia coefficients with experimental data for three different values of the frequency parameter β in the range 196–1035 for 0 < KC < 26 show good agreement.

Type
Research Article
Information
Journal of Fluid Mechanics , Volume 222 , January 1991 , pp. 157 - 196
Copyright
© 1991 Cambridge University Press

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References

Baba, N. & Miyata, H., 1987 Higher-order accurate difference solutions of vortex generation from a circular cylinder in an oscillatory flow. J. Comput. Phys. 69, 362–396.Google Scholar
Bearman, P. W.: 1985 Vortex trajectories in oscillatory flow. In Proc. Intl Symp. on Separated Flow round Marine Structures, Trondheim, pp. 133–153. Norwegian Institute of Technology, Trondheim.
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, 337–356.Google Scholar
Bearman, P. W., Graham, J. M. R., Naylor, P. & Obasaju, E. E., 1981 The role of vortices in oscillatory flow about bluff bodies. In Proc. Intl Symp. on Hydrodynamics in Ocean Engng, Trondheim, Norway, August, pp. 621–635.Google Scholar
Borthwick, A.: 1986 Comparison between two finite-difference schemes for computing the flow around a cylinder. Intl J. Numer. Meth. Fluids 6, 275–290.Google Scholar
Bouard, R. & Coutanceau, M., 1980 The early stage of development of the work behind an impulsively started cylinder for 40 Re 104. J. Fluid Mech. 101, 583–607.Google Scholar
Braza, M., Chassaing, P. & Ha Minh, H. 1986 Numerical study and physical analysis of the pressure and velocity fields in the near wake of a circular cylinder. J. Fluid Mech. 165, 79–130.Google Scholar
Graham, J. M. R. & Djahansouzi, B. 1989 Hydrodynamic damping of structural elements. In Proc. Eighth Intl Conf. Offshore Mech. and Arctic Engng, The Hague, The Netherlands, vol. 2, pp. 289–293.Google Scholar
Hall, P.: 1984 On the stability of unsteady boundary layer on a cylinder oscillating transversely in a viscous fluid. J. Fluid Mech. 146, 347–367.Google Scholar
Honji, H.: 1981 Streaked flow around an oscillating circular cylinder. J. Fluid Mech. 107, 509–520.Google Scholar
Leonard, B. P.: 1979 A survey of finite differences of opinion on numerical muddling of the incomprehensible defective confusion equation. In Proc. ASME Winter Annual Meeting, Publ. AMD-34.Google Scholar
Martinez, G.: 1979 Charactéristiques dynamiques et thermiques de l'ecoulement autour d'un cylindre circulaire à nombres de Reynolds moderés. Thèse docteur-Ingénieur, I. N. P. Toulouse.
Maull, D. J. & Milliner, M. C., 1978 Sinusoidal flow past a circular cylinder. Coastal Engrg 2, 149–168.Google Scholar
Morison, J. R., O'Brien, M. P., Johnson, J. W. & Schaff, S. A., 1950 The force exerted by surface waves on piles. Petrol. Trans. 189, 149–157.Google Scholar
Murashige, S., Hinatsu, M. & Kinoshita, T., 1989 Direct calculations of the Navier—Stokes equations for forces acting on a cylinder in oscillatory flow. In Proc. Eighth Intl Conf. Offshore Mech. and Arctic Engng, The Hague, vol. 2, pp. 411–418.Google Scholar
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, 467–494.Google Scholar
Patankar, S. V.: 1980 Numerical Heat Transfer and Fluid Flow. McGraw-Hill.
Rosenhead, L. (ed.) 1963 Laminar Boundary Layers. Clarendon.
Sarpkaya, T.: 1986 Forces on a circular cylinder in viscous oscillatory flow at low Keulegan—Carpenter numbers. J. Fluid Mech. 165, 61–71.Google Scholar
Sarpkaya, T.: 1989 Computational methods with vortices – The 1988 Freeman Scholar Lecture. Trans. ASME I: J. Fluids Engrg 111, 5–52.Google Scholar
Skomedal, N. G., Vada, T. & Sortland, B., 1989 Viscous forces on one and two circular cylinders in planar oscillatory flow. Appl. Ocean Res. 11, 114–34.Google Scholar
Smith, P. A. & Stansby, P. K., 1988 Impulsively started flow around a circular cylinder by the vortex method. J. Fluid Mech. 194, 45–77.Google Scholar
Sortland, B.: 1986 Force measurements in oscillating flow on ship sections and circular cylinders in a U-tube water tank. Dr.- Ing. thesis, Norwegian Institute of Technology, Trondheim.
Stansby, P. K.: 1979 Mathematical modelling of vortex shedding from circular cylinders in planar oscillatory flows, including effects of harmonics. In Mechanics of Wave-Induced Forces on Cylinders (ed. T. L. Shaw), pp. 450–460. Pitman.
Stansby, P. K. & Smith, P. A., 1989 Flow around a cylinder by the random vortex method. In Proc. Eighth Intl Conf. Offshore Mech. and Arctic Eng., The Hague, The Netherlands, vol. 2, pp. 419–426.Google Scholar
Stokes, G. G.: 1851 On the effect of the internal friction of fluids on the motion of pendulums. Trans. Camb. Phil. Soc. 9, 8–106.Google Scholar
Ta Phuoc, Loc & Bouard, R. 1985 Numerical solution of the early stage of the unsteady viscous flow around a circular cylinder: a comparison with experimental visualization and measurements. J. Fluid Mech. 160, 93–117.Google Scholar
Van Der Vegt, J. J. W. & De Boom, W. C. 1985 Numerical simulation of flow round circular cylinders at high Reynolds numbers. In Proc. Behaviour of Offshore Structures, Delft 1985, pp. 227–238. Elsevier.
Wang, C.-Y.: 1968 On the high-frequency oscillating viscous flows. J. Fluid Mech. 32, 55–68.Google Scholar
Williamson, C. H. K.: 1985 Sinusoidal flow relative to circular cylinders. J. Fluid Mech. 155, 141–174.Google Scholar
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, 579–627.Google Scholar