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Viscous oscillatory flow about a circular cylinder at small to moderate Strouhal number

Published online by Cambridge University Press:  26 April 2006

H. M. Badr ,
S. C. R. Dennis ,
S. Kocabiyik  and
P. Nguyen
H. M. Badr
Affiliation:
Departent of Applied Mathmatics, University of Western Ontario, London, Ontario N6A 5B7, Canada Permanent address: Mechanical Engineering Department, King Fahd University of Petroleum and Minerals, Dhahran 31261 Saudi Arabia.
S. C. R. Dennis
Affiliation:
Departent of Applied Mathmatics, University of Western Ontario, London, Ontario N6A 5B7, Canada
S. Kocabiyik
Affiliation:
Departent of Applied Mathmatics, University of Western Ontario, London, Ontario N6A 5B7, Canada Present address: Department of Applied Mathematics, University of Manitoba, Winnipeg, Manitoba R3T 2N2, Canada.
P. Nguyen
Affiliation:
Departent of Applied Mathmatics, University of Western Ontario, London, Ontario N6A 5B7, Canada
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Abstract

The transient flow field caused by an infinitely long circular cylinder placed in an unbounded viscous fluid oscillating in a direction normal to the cylinder axis, which is at rest, is considered. The flow is assumed to be started suddenly from rest and to remain symmetrical about the direction of motion. The method of solution is based on an accurate procedure for integrating the unsteady Navier–Stokes equations numerically. The numerical method has been carried out for large values of time for both moderate and high Reynolds numbers. The effects of the Reynolds number and of the Strouhal number on the laminar symmetric wake evolution are studied and compared with previous numerical and experimental results. The time variation of the drag coefficients is also presented and compared with an inviscid flow solution for the same problem. The comparison between viscous and inviscid flow results shows a better agreement for higher values of Reynolds and a Strouhal numbers. The mean flow for large times is calculated and is found to be in good agreement with previous predictions based on boundary-layer theory.

Type
Research Article
Information
Journal of Fluid Mechanics , Volume 303 , 25 November 1995 , pp. 215 - 232
Copyright
© 1995 Cambridge University Press

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References

Badr, H. M. 1994 Oscillating inviscid flow over elliptic cylinders with plates and circular cylinders as spccial cases. Ocean Engng 21, 105–113.Google Scholar
Badr, H. M. & Dennis, S. C. R. 1985 Time-dependent viscous flow past an implusively started rotating and translating circular cylinder. J. Fluid Mech. 158, 447–488.Google Scholar
Badr, H. M.Dennis, S. C. R. & Kocabiyik, S. 1995 Initial oscillatory flow past a circular cylinder. J. Engng Maths. 29, 255–269.Google Scholar
Collins, W. M. & Dennis, S. C. R. 1973a The intial flow past an implusively started circular cylinder. Q. J. Mech. Appl. Maths 26, 53–75.Google Scholar
Collins, W. M. & Dennis, S. C. R. 1973b Flow past an implusively started circular cylinder. J. Fluid Mech. 60, 105–127.Google Scholar
Davidson, B. J. & Riley, N. 1972 Jets induced by oscillatory motion. J. Fluid Mech. 53, 287–303.Google Scholar
Fettis, H. E. 1955 On the integration of a class of defferential equations occurring in the boundary layer and other hydrodynamic problems. Proc. 4th Midwestern Conf. on Fluid Mech., Purdue University, pp. 93–114.
Justesen, P. 1991 A numerical study of oscillating flow around a circular cylinder. J. Fluid Mech. 222, 157–196.Google Scholar
Obasaju, E. D.Bearman, P. W. & Graham, J. M. R. 1988 A study of forces, circulations and vortex patterns around a circular cylinder is oscillating flow. J. Fluid Mech. 196, 467–494.Google Scholar
Riley, N. 1965 Oscillating viscous flows. Mathematika 12, 161–175.Google Scholar
Sarpkayam T. 1986 Force on a circular cylinder in viscous oscillatory flow at low Keulegan-Carpenter numbers. J. Fluid Mech. 165, 61–71.Google Scholar
Schlichting, H. 1932 Berechnung ebener periodischer Grenzschichtströmungen. Phys. Z. 33, 327–335.Google Scholar
Stuart, J. T. 1966 Double boundary-layers in oscillatory viscous flows. J. Fluid Mech. 24, 673–687.Google Scholar
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, 157–182.Google Scholar
Dyke, Van M. 1982 An Album of Fluid Motion, fig, 31. pp. 23 Stanford: The Parabolic Press.
Vasantah, R, & Riley, N. 1988 On the initation of jets in oscillatory viscous flows. Proc. R. Soc. Lond. A 419, 363–378.Google Scholar
Wang, C.-Y. 1965 The resistance on a circular cylinder in an oscillating stream. Q. Appl. Maths 23, 305–312.Google Scholar
Wang, C-Y. 1968 On high-frequency oscillatory viscous flows. J. Fluid Mech. 312, 55–68.Google Scholar
Wang, X. & Dalton, C. 1991 Oscillating flow past a rigid circular cylinder: A finite difference calculation. Trans. ASME I: J. Fluids Engng 113, 377–383.Google Scholar
Williamson, C. H. K. 1985 Sinusoidal flow relative to circular cylinders. J. Fluid Mech. 155, 141–174.Google Scholar