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Periodic Wake Behind a Circular Cylinder at Low Reynolds Numbers

Published online by Cambridge University Press:  07 June 2016

A K M F Hussain  and
V Ramjee
A K M F Hussain
Affiliation:
University of Houston, Texas
V Ramjee
Affiliation:
University of Houston, Texas
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Summary

The effects of free-stream turbulence and of sinusoidal free-stream pulsations of controlled frequencies and amplitudes on the periodic wake of a circular cylinder are investigated experimentally by employing hot-wire and smoke visualisation techniques. In addition, the effects of cylinder yaw and mild favourable and adverse pressure gradients on the vortex shedding mechanism have been explored.

The data relating frequency to mean velocity follow Berger’s relation; this relation is uninfluenced by free-stream turbulence intensities up to 8 per cent. As the longitudinal turbulence intensity increases from 0.3 to 8 per cent, the downstream distance Lp behind the cylinder over which the hot-wire signal is periodic decreases progressively, indicating that the otherwise steady periodic wake interacts non-linearly with the three-dimensional free-stream turbulence and undergoes either transition or rapid diffusion by turbulence, depending on both the Reynolds number and the turbulence intensity. For a given turbulence intensity, Lp decreases also with increasing Reynolds number.

The shedding frequency behind a yawed cylinder does not vary as the cosine of the yaw angle ϕ for ϕ < 50°; the signal switches intermittently between periodic and irregular form as the yaw is increased from 0 to 70°. Mild pressure gradients (favourable as well as adverse) do not affect the shedding frequency; this is confirmed by smoke visualisation, which also shows that the pressure gradient changes the longitudinal vortex spacing downstream; the measured frequency is that determined by the local Reynolds number corresponding to the Berger relation.

Sinusoidal streamwise pulsations of controlled frequencies, and of amplitudes up to 10 per cent of free-stream velocity, have no effect on the natural shedding frequency; this is confirmed by smoke visualisation of the cylinder wake. However, the wake signal is amplitude-modulated at a frequency equal to the difference between the pulsation frequency and the natural shedding frequency corresponding to the free-stream mean velocity. The vortices are diffused faster in the presence of pulsation. When the pulsation amplitude is increased beyond 20 per cent, the hot-wire signal frequency in the wake equals the driving frequency; the frequency in the wake centre is also that of the pulsation. The effect of free-stream pulsation on the periodic wake is different from that due to longitudinal or transverse cylinder vibration, when lock-in has been observed.

It appears that free-stream disturbances – random or periodic – cannot account for the “Tritton jump”.

Type
Research Article
Information
Aeronautical Quarterly , Volume 27 , Issue 2 , May 1976 , pp. 123 - 142
Copyright
Copyright © Royal Aeronautical Society. 1976

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References

1 Perry, A E Morrison, G L Static and dynamic calibrations of constant temperature hot-wire systems. Journal of Fluid Mechanics, Vol 47, pp 765–777, 1971.CrossRefGoogle Scholar
2 Berger, E Wille, R Periodic flow phenomena. Annual Reviews of Fluid Mechanics, Vol 4, pp 313–340, 1972.CrossRefGoogle Scholar
3 Goldstein, S (Editor) Modern Developments in Fluid Mechanics, Vol II, Dover Publications, 1965.Google Scholar
4 Roshko, A On the development of turbulent wakes from vortex streets. NACA Report 1191, 1954.Google Scholar
5 Tritton, D J Experiments on the flow past a circular cylinder at low Reynolds numbers. Journal of Fluid Mechanics, Vol 6, pp 547–567, 1959.CrossRefGoogle Scholar
6 Morrow, T B Kline, S J The evaluation and use of hot-wire and hot-film anemometers in liquids. Stanford University Report MD-25, 1971.Google Scholar
7 Kohan, S Schwarz, W H Low speed calibration formula for vortex shedding from cylinders. Physics of Fluids, Vol 16, pp 1528–1529, 1973.CrossRefGoogle Scholar
8 Kovasznay, L S G Hot-wire investigations of wake behind cylinders at low Reynolds numbers. Proc Roy Soc A, Vol 198, pp 174–190, 1949.Google Scholar
9 Collis, D C Williams, M J Two-dimensional convection from heated wires at low Reynolds number. Journal of Fluid Mechanics, Vol 6, pp 357–384, 1959.CrossRefGoogle Scholar
10 Nishioka, M Sato, H Measurements of velocity distributions in the wake of a circular cylinder at low Reynolds numbers. Journal of Fluid Mechanics, Vol 65, pp 97–112, 1974.CrossRefGoogle Scholar
11 Gaster, M Vortex shedding from slender cones at low Reynolds numbers. Journal of Fluid Mechanics. Vol 38, pp 565–576, 1969.CrossRefGoogle Scholar
12 Tritton, D J A note on vortex streets behind circular cylinders at low Reynolds numbers. Journal of Fluid Mechanics, Vol 45, pp 203–208, 1971.CrossRefGoogle Scholar
13 Gaster, M Vortex shedding from circular cylinders at low Reynolds numbers. Journal of Fluid Mechanics, Vol 46, pp 749–756, 1971.CrossRefGoogle Scholar
14 Bloor, M Susan Transition to turbulence in the wake of a circular cylinder. Journal of Fluid Mechanics, Vol 19, pp 290–304, 1964.CrossRefGoogle Scholar
15 Gerrard, J H The mechanics of the formation region of vortices behind bluff bodies. Journal of Fluid Mechanics, Vol 25, pp 401–413, 1966.CrossRefGoogle Scholar
16 Wille, R On unsteady flows and transient motions. Progress in Aeronautical Sciences, Vol 7, pp 195–207, Pergamon, 1966.Google Scholar
17 Webster, C A G An experimental study of turbulence in a density-stratified shear flow. Journal of Fluid Mechanics, Vol 19, pp 221–245, 1964.CrossRefGoogle Scholar
18 Lighthill, M J The response of laminar skin friction and heat transfer to fluctuations in the stream velocity. Proc Roy Soc A, Vol 224, pp 1–23, 1954.Google Scholar
19 Chen, C F Ballengee, D B Vortex shedding from circular cylinders in an oscillating free-stream. AIAA Journal, Vol 9, pp 340–342, 1971.CrossRefGoogle Scholar
20 Hatfield, H M Morkovin, M V Effect on an oscillating free stream on the unsteady pressure on a circular cylinder. Journal of Fluids Engineering, pp 249–254, June 1973.CrossRefGoogle Scholar
21 Comte-Bellot, G Corrsin, S The use of a contraction to improve the isotropy of grid-generated turbulence. Journal of Fluid Mechanics, Vol 25, pp 657–682, 1966.CrossRefGoogle Scholar
22 Crow, S C Champagne, F H Orderly structure in jet turbulence. Journal of Fluid Mechanics, Vol 48, pp 547–591, 1971.CrossRefGoogle Scholar
23 Brown, G L Roshko, A On density effects and large structure in turbulent mixing layers. Journal of Fluid Mechanics, Vol 64, pp 775–816, 1974.CrossRefGoogle Scholar
24 Winant, C D Browand, F K Vortex pairing: the mechanism of turbulent mixing layer growth at moderate Reynolds number. Journal of Fluid Mechanics, Vol 63, pp 237–255, 1974.CrossRefGoogle Scholar
25 Sato, H The stability and transition of a two-dimensional jet. Journal of Fluid Mechanics, Vol 7, pp 53–80, 1959.CrossRefGoogle Scholar
26 Moore, D W Saffman, P G The density of organized vortices in a turbulent mixing layer. Journal of Fluid Mechanics, Vol 69, pp 465–473, 1975.CrossRefGoogle Scholar
27 Sato, H An experimental study of non-linear interaction of velocity fluctuations in the transition region of a two-dimensional wake. Journal of Fluid Mechanics, Vol 44, pp 741–765, 1970.CrossRefGoogle Scholar
28 Michalke, A The instability of free shear layers. Progress in Aerospace Sciences, Vol 12, pp 213–239, Pergamon, 1972.Google Scholar
29 Van Atta, C W Experiments on vortex shedding from yawed circular cylinders. AIAA Journal, Vol 6, pp 931–933, 1968.CrossRefGoogle Scholar
30 Koopman, G H The vortex wakes of vibrating cylinders at low Reynolds numbers. Journal of Fluid Mechanics, Vol 28, pp 501–512, 1967.CrossRefGoogle Scholar
31 Tanida, Y Okajima, A Watanabe, Y Stability of a circular cylinder oscillating in uniform flow or in a wake. Journal of Fluid Mechanics, Vol 61, pp 769–784, 1973.CrossRefGoogle Scholar
32 Hussain, A K M F Zaman, K B M Q Effect of acoustic excitation on the turbulent structure of a circular jet. Proceedings of Third Interagency Symposium on University Research in Transportation Noise, pp 314–325, University of Utah, November 1975.Google Scholar