Hostname: page-component-cd9895bd7-8ctnn Total loading time: 0 Render date: 2024-12-18T21:18:53.706Z Has data issue: false hasContentIssue false
  • English
  • Français

On the formation and suppression of vortex ‘shedding’ at low Reynolds numbers

Published online by Cambridge University Press:  26 April 2006

P. J. Strykowski  and
K. R. Sreenivasan
P. J. Strykowski
Affiliation:
Department of Mechanical Engineering, University of Minnesota, Minneapolis, MN 55455, USA
K. R. Sreenivasan
Affiliation:
Mason Laboratory, Yale University, New Haven, CT 06520, USA
Get access Rights & Permissions [Opens in a new window]

Abstract

Vortex ‘shedding’ behind circular cylinders can be altered and suppressed altogether (or ‘controlled’) over a limited range of Reynolds numbers, by a proper placement of a second, much smaller, cylinder in the near wake of the main cylinder. This new and dramatic suppression of vortex ‘shedding’ is the subject of this paper. Details of the phenomenon are documented through parallel experimental and numerical investigations, including flow visualization. Temporal growth rate measurements of the velocity fluctuations reveal that the presence of the smaller cylinder reduces the growth rate of the disturbances leading to vortex ‘shedding’, and that its suppression, accompanied by the disappearance of sharp spectral peaks, coincides with negative temporal growth rates. It is argued that the presence of the secondary cylinder has the effect of altering the local stability of the flow by smearing and diffusing concentrated vorticity in the shear layers behind the body; a related effect is that the secondary cylinder diverts a small amount of fluid into the wake of the main cylinder. A unified explanation of the formation and suppression of the vortex street is attempted, and it is suggested that the vortex ‘shedding’ is associated with temporally unstable eigenmodes which are heavily weighted by the near field. It is also shown that absolute instability is relevant, up to a point, in explaining vortex shedding, whose suppression can similarly be associated with altering the instability in the near wake region from absolute to convective.

Type
Research Article
Information
Journal of Fluid Mechanics , Volume 218 , September 1990 , pp. 71 - 107
Copyright
© 1990 Cambridge University Press

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

Abernathy, F. H. & Kronauer, R. E., 1961 The formation of vortex sheets. J. Fluid Mech. 13, 1–20.Google Scholar
Ahlborn, B. & Lefrancois, M., 1985 Constructive and destructive interference of drag forces in turbulent wakes. 38th meeting of the Fluid Dyn. Div. of the Am. Phys. Soc., Paper CN3, p. 1727 (abstract only).Google Scholar
Bearman, P. W.: 1967 The effect of base bleed on the flow behind a two-dimensional model with a blunt trailing edge. Aero. Q. 18, 207–224.Google Scholar
Bechart, D. W.: 1985 Excitation of instability waves. Z. Flugwiss. W. 9, 356–361.Google Scholar
Berger, E.: 1964 Bestimmung der hydrodynamischen Grössen einer Karmanschen Wirbelstrasse aus Hitzdrahtmessungen bei Kleinen Reynolds-Zahlen. Z. Flugwiss. W. 12, 41–59.Google Scholar
Berger, E.: 1967 Suppression of vortex shedding and turbulence behind oscillating cylinders. Phys. Fluids Suppl. 10, 191–193.Google Scholar
Berger, E. & Wille, R., 1972 Periodic flow phenomena. Ann. Rev. Fluid Mech. 4, 313–340.Google Scholar
Cimbala, J. M., Nagib, H. & Roshko, A., 1988 Large structure in the far wakes of two-dimensional bluff bodies. J. Fluid Mech. 190, 265–298.Google Scholar
Dennis, S. C. R. & Chang, G.-Z. 1970 Numerical solutions for steady flow past a circular cylinder at Reynolds numbers up to 100. J. Fluid Mech. 42, 471–489.Google Scholar
Fage, A. & Johansen, F. C., 1927 On the flow of air behind an inclined flat plate of infinite span. Proc. R. Lond. Soc. A. 166, 170–197.Google Scholar
Fage, A. & Johansen, F. C., 1928 The structure of the vortex street. Phil. Mag. 5, 417–441.Google Scholar
Fornberg, B.: 1980 A numerical study of steady viscous flow past a circular cylinder. J. Fluid Mech. 98, 819–855.Google Scholar
Gaster, M.: 1969 Vortex shedding from slender cones at low Reynolds numbers. J. Fluid Mech. 38, 565–576.Google Scholar
Gaster, M.: 1971 Vortex shedding from circular cylinders at low Reynolds numbers. J. Fluid Mech. 46, 749–756.Google Scholar
Gerich, D. & Eckelmann, H., 1982 Influence of end plates and free ends on the shedding frequency of circular cylinders. J. Fluid Mech. 122, 109–121.Google Scholar
Gerrard, J. H.: 1966 The mechanics of the formation region of vortices behind bluff bodies. J. Fluid Mech. 25, 401–413.Google Scholar
Grassberger, P. & Procaccia, I., 1983 Characterization of strange attractors. Phys. Rev. Lett. 50, 346–349.Google Scholar
Hannemann, K.: 1987 Numerische Simulation und Stabilitätstheoretische Untersuchung des absolut und konvektiv instabilen Nachlaufs. Ph.D. thesis, Universität Karlsruhe.
Hannemann, K., Gilbert, N., Schwamborn, D. & Gentzsch, W., 1985 A finite-difference Galerkin method for the solution of the Navier-Stokes equations. In Proc. 6th GAMM Conference on Numerical Methods in Fluid Mechanics, Göttingen, 25–27 September.
Hannemann, K. & Oertel, H., 1989 Numerical simulation of the absolutely and convectively unstable wake. J. Fluid Mech. 199, 55–88.Google Scholar
Hirota, I. & Miyakoda, K., 1965 J. Met. Soc. Japan II 43, 30–36.
Huerre, P. & Monkewitz, P. A., 1985 Absolute and convective instabilities in free shear flows. J. Fluid Mech. 159, 151–161.Google Scholar
Jackson, C. P.: 1987 A finite-element study of the onset of vortex shedding in flow past variously shaped bodies. J. Fluid Mech. 182, 23–45.Google Scholar
von Kármán, Th. 1911 Über den Mechanismus des Widerstandes, den ein bewegter Körper in einer Flussigkeit erzeugt. Nacht. Wiss. Ges. Göttingen. Math. Phys. Klasse. 509–517.Google Scholar
von Kármán, Th. & Rubach, H. 1912 Über den Mechanismus des Flüssigkeits-und Luftwiderstandes. Phys. Z. 13, 49–59.Google Scholar
Koch, W.: 1985 Local instability characteristics and frequency determination of self-excited wake flows. J. Sound Vib. 99, 53–83.Google Scholar
Kovasznay, L. S. G.: 1949 Hot-wire investigation of the wake behind cylinders at low Reynolds numbers. Proc. R. Soc. Lond. A 198, 174–190.Google Scholar
Mair, W. A. & Maull, D. J., 1971 Bluff bodies and vortex shedding - a report on Euromech 17. J. Fluid Mech. 45, 209–224.Google Scholar
Mathis, C., Provansal, M. & Boyer, L., 1984 The Bénard–von Kármán instability: an experimental study near the threshold. J. Phys. Lett. 45, L483–491.Google Scholar
Monkewitz, P. A.: 1988 The absolute and convective nature of instability in two-dimensional wakes at low Reynolds numbers. Phys. Fluids 31, 999–1006.Google Scholar
Monkewitz, P. A. & Nuygen, L. N., 1987 Absolute instability in the near-wake of two-dimensional bluff bodies. J. Fluids Structures 1, 165–184.Google Scholar
Monkewitz, P. A. & Sohn, K. D., 1986 Absolute instability in hot jets and their control. AIAA Paper 86–1882, presented at the 10th AIAA Aeroacoustics Conference, July 9–11, Seattle.Google Scholar
Nishioka, M. & Sato, H., 1974 Measurements of velocity distributions in the wake of a circular cylinder at low Reynolds numbers. J. Fluid Mech. 65, 97–112.Google Scholar
Nishioka, M. & Sato, H., 1978 Mechanism of determination of the shedding frequency of vortices behind a cylinder at low Reynolds numbers. J. Fluid Mech. 89, 49–60.Google Scholar
Olinger, D. J. & Sreenivasan, K. R., 1988a Nonlinear dynamics of the wake of an oscillating cylinder. Phys. Rev. Lett. 60, 797–800.Google Scholar
Olinger, D. J. & Sreenivasan, K. R., 1988b Low Reynolds number dynamics in the wake of an oscillating cylinder. In Proc. ASME Intl Symp. Flow-Induced Vibrations and Noise, pp. 1–27.Google Scholar
Provansal, M., Mathis, C. & Boyer, L., 1987 Bénard–von Kármán instability: transient and forced regimes. J. Fluid Mech. 182, 1–22.Google Scholar
Roshko, A.: 1954 On the development of turbulent wakes from vortex streets. NACA Rep. 1191.Google Scholar
Roshko, A.: 1955 On the wake and drag of bluff bodies. J. Aero. Sci. 22, 124–132.Google Scholar
Shair, F. H., Grove, A. S., Petersen, E. E. & Acrivos, A., 1963 The effect of confining walls on the stability of the steady wake behind a circular cylinder. J. Fluid Mech. 17, 547–550.Google Scholar
Sreenivasan, K. R.: 1985 Transition and turbulence in fluid flows and low-dimensional chaos. In Frontiers of Fluid Mechanics (ed. S. H. Davis & J. L. Lumley), pp. 41–67. Springer.
Sreenivasan, K. R.: 1986 Chaos in open flow systems. In Dimensions and Entropies in Chaotic Systems (ed. G. Mayer-Kress), pp. 222–230. Springer.
Sreenivasan, K. R., Raghu, S. & Kyle, D., 1989 Absolute instability in variable density jets. Exps. Fluids 7, 309–317.Google Scholar
Sreenivasan, K. R., Strykowski, P. J. & Olinger, D. J., 1986 Hopf bifurcation, Landau equation and vortex shedding behind circular cylinders. In Proc. Forum on Unsteady Flow Separation (ed. K. N. Ghia), pp. 1–13. ASME.
Stansby, P. K.: 1974 The effects of end plates on the base pressure coefficient of a circular cylinder. Aero. J. 78, 36–37.Google Scholar
Stephens, A. B., Bell, J. B., Solomon, J. M. & Hackerman, L. B., 1984 A finite-difference Galerkin formulation for the incompressible Navier–Stokes equations, J. Comput. Phys. 53, 152–172.Google Scholar
Strouhal, V.: 1878 Über eine besondere Art der Tonerregung. Ann. Phys. Chemie (New series) 5, 216–251.Google Scholar
Strykowski, P. J.: 1986 The control of absolutely and convectively unstable shear flows. Ph.D. thesis, Engineering and Applied Science, Yale University.
Strykowski, P. J. & Sreenivasan, K. R., 1985a The control of transitional flows. AIAA Shear Flow Control Conf. Boulder, Colorado, Paper 85–0559.Google Scholar
Strykowski, P. J. & Sreenivasan, K. R., 1985b The control of vortex shedding behind circular cylinders at low Reynolds numbers. Proc. 5th Symp. on Turb. Shear Flows, Cornell Univ., Ithaca.Google Scholar
Thoman, D. C. & Szewczyk, A. A., 1969 Time-dependent viscous flow over a circular cylinder. Phys. Fluids Suppl. 12, II 76–86.Google Scholar
Triantafyllou, G. S. & Karniadakis, G. Em., 1990 Computational reducability of unsteady viscous flow. Phys. Rev. Lett. (submitted).Google Scholar
Triantafyllou, G. S., Triantafyllou, M. S. & Chryssostomidis, C., 1986 On the formation of vortex streets behind stationary cylinders. J. Fluid Mech. 170, 461–477.Google Scholar
Tritton, D. J.: 1959 Experiments on the flow past a circular cylinder at low Reynolds numbers. J. Fluid Mech. 6, 547–567.Google Scholar
Wehrmann, O. H.: 1967 Influence of vibrations on the flow field behind a cylinder. Phys. Fluids Suppl. 10, 187–190.Google Scholar
Zabib, A.: 1987 Stability of viscous flow past a circular cylinder. J. Engng Maths 21, 155–165.Google Scholar