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Symmetrical flow past an accelerated circular cylinder

Published online by Cambridge University Press:  26 April 2006

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

The development of the two-dimensional flow of a viscous incompressible fluid around a circular cylinder which suddenly starts to move with the velocity U = U0 + U1t + U2t2 is studied. Equations for the flow in terms of the stream function and vorticity in boundary-layer coordinates are presented. A perturbation series solution for small times is developed. The flow for longer times is computed numerically using an accurate implicit time-integration procedure. The numerical method is checked for small times by comparison with the results of the analytical solution. Reynolds numbers R in the range 200 to 104 (based on the diameter of the cylinder) are considered. One particularly interesting result is that for certain values of U1 and U2 at R = 500 and R = 103 it is found that two co-rotating vortices and three co-rotating vortices develop with time in each half of the wake in the two respective cases.

Type
Research Article
Information
Journal of Fluid Mechanics , Volume 308 , 10 February 1996 , pp. 97 - 110
Copyright
© 1996 Cambridge University Press

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References

Badr, H. M. & Dennis, S. C. R. 1985 Time-dependent viscous flow past an impulsively started rotating and translating circular cylinder. J. Fluid Mech. 158, 447–488.Google Scholar
Blasius, H. 1908 Grenzschichten in Flüssigkeiten mit kleiner Reibung. Z. Angew. Math. Phys. 56, 1–37. (Translated as ‘The boundary layers in fluids with little friction’. Tech. Mem. Nat. Adv. Comm. Aero., WA No. 1256.)Google Scholar
Collins, W. M. & Dennis, S. C. R. 1973a The initial flow past an impulsively started circular cylinder. Q. J. Mech. Appl. Maths 26, 53–75.Google Scholar
Collins, W. M. & Dennis, S. C. R. 1973b Flow past an impulsively started circular cylinder. J. Fluid Mech. 60, 105–127.Google Scholar
Collins, W. M. & Dennis, S. C. R. 1974 Symmetrical flow past a uniformly accelerated circular cylinder. J. Fluid Mech. 65, 461–480.Google Scholar
Davidson, B. J. & Riley, N. 1972 Jets induced by oscillatory motion. J. Fluid Mech. 53, 287–303.Google Scholar
Justese, P. 1991 A numerical study of oscillating flow around a circular cylinder. J. Fluid Mech. 222, 157–196.Google Scholar
Riley, N. 1965 Oscillating viscous flows. Mathematika. 12, 161–175.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
Vasantha, R. & Riley, N. 1988 On the initiation 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
Williamson, C. H. K. 1985 Sinusoidal flow relative to circular cylinders. J. Fluid Mech. 155, 141–174.Google Scholar