Hostname: page-component-7c8c6479df-r7xzm Total loading time: 0 Render date: 2024-03-27T06:05:26.777Z Has data issue: false hasContentIssue false

Large structure in the far wakes of two-dimensional bluff bodies

Published online by Cambridge University Press:  21 April 2006

John M. Cimbala
Affiliation:
Mechanical Engineering Department, Pennsylvania State University, University Park, PA 16802, USA
Hassan M. Nagib
Affiliation:
Mechanical and Aerospace Engineering, Illinois Institute of Technology, Chicago, IL 60616, USA
Anatol Roshko
Affiliation:
Graduate Aeronautical Labs, California Institute of Technology, Pasadena, CA 91125, USA

Abstract

Smoke-wire flow visualization and hot-wire anemometry have been used to study near and far wakes of two-dimensional bluff bodies. For the case of a circular cylinder at 70 < Re < 2000, a very rapid (exponential) decay of velocity fluctuations at the Kármán-vortex-street frequency is observed. Beyond this region of decay, larger-scale (lower wavenumber) structure can be seen. In the far wake (beyond one hundred diameters) a broad band of frequencies is selectively amplified and then damped, the centre of the band shifting to lower frequencies as downstream distance is increased.

The far-wake structure does not depend directly on the scale or frequency of Kármán vortices shed from the cylinder; i.e. it does not result from amalgamation of shed vortices. The growth of this structure is due to hydrodynamic instability of the developing mean wake profile. Under certain conditions amalgamation can take place, but is purely incidental, and is not the driving mechanism responsible for the growth of larger-scale structure. Similar large structure is observed downstream of porous flat plates (Re ≈ 6000), which do not initially shed Kármán-type vortices into the wake.

Measured prominent frequencies in the far cylinder wake are in good agreement with those estimated by two-dimensional locally parallel inviscid linear stability theory, when streamwise growth of wake width is taken into account. Finally, three-dimensionality in the far wake of a circular cylinder is briefly discussed and a mechanism for its development is suggested based on a secondary parametric instability of the subharmonic type.

Type
Research Article
Copyright
© 1988 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

Aref, H. & Siggia, E. 1981 Evolution and breakdown of a vortex street in two dimensions. J. Fluid Mech. 109, 435463.Google Scholar
Berger, E. & Wille, R. 1972 Periodic flow phenomena. Ann. Rev. Fluid Mech. 4, 313340.Google Scholar
Bevilaqua, P. 1975 Intermittency, the entrainment problem. ARL Tech. Rep. 75–0095, USAF.
Breidenthal, R. E. 1980 Response of plane shear layers and wakes to strong three-dimensional disturbances. Phys. Fluids 23, 19291934.Google Scholar
Cantwell, B. J. 1979 Coherent turbulent structures as critical points in unsteady flow. Arch. Mech. 31, 707721.Google Scholar
Castro, I. 1971 Wake characteristics of two-dimensional perforated plates normal to an air-stream. J. Fluid Mech. 46, 599609.Google Scholar
Cimbala, J. 1984 Large structure in the far wakes of two-dimensional bluff bodies. Ph.D. Thesis, California Institute of Technology, Pasadena, California.
Cimbala, J., Nagib, H. & Roshko, A. 1981 Wake instability leading to new large scale structures downstream of bluff bodies. Bull. Am. Phys. Soc. 26, 1256.Google Scholar
Champagne, F., Marasli, I. & Wygnanski, I. 1982 A turbulent wake of a cylinder - some recent observations. Bull. Am. Phys. Soc. 27, 1163.Google Scholar
Corke, T., Koga, D., Drubka, R. & Nagib, H. 1977 A new technique for introducing controlled sheets of streaklines in wind tunnels. IEEE Publication 77-CH 1251–8 AES.
Desruelle, D. 1983 Beyond the Kármán vortex street. M.S. thesis, Illinois Institute of Technology, Chicago, Illinois.
Durgin, W. & Karlsson, S. 1971 On the phenomenon of vortex street breakdown. J. Fluid Mech. 48, 507527.Google Scholar
Gaster, M. 1965 The role of spatially growing waves in the theory of hydrodynamic stability. Prog. Aero. Sci. 6, 251270.Google Scholar
Gaster, M., Kit, E. & Wygnanski, I. 1985 Large-scale structures in a forced turbulent mixing layer. J. Fluid Mech. 150, 2339.Google Scholar
Gerrard, H. 1966 The three-dimensional structure of the wake of a circular cylinder. J. Fluid Mech. 25, 143164.Google Scholar
Grant, H. L. 1958 The large eddies of turbulent motion. J. Fluid Mech. 4, 149198.Google Scholar
Gupta, A., Laufer, J. & Kaplan, R. 1971 Spatial structure in the viscous sublayer, J. Fluid Mech. 50, 493512.Google Scholar
Kama, F. R. 1962 Streaklines in a perturbed shear flow. Phys. Fluids 5, 644650.Google Scholar
Herbert, T. 1983 Secondary instability of plane channel flow to subharmonic three-dimensional disturbances. Phys. Fluids 26, 871874.Google Scholar
Herbert, T. 1984 Analysis of subharmonic route to transition in boundary layers. AIAA Paper 84–0009.
Ho, C.-M. & Huerre, P. 1984 Perturbed free shear layers. Ann. Rev. Fluid Mech. 16, 365424.Google Scholar
Hooker, S. 1936 On the action of viscosity in increasing the spacing ratio of a vortex street. Proc. R. Soc. Lond. A 154, 6789.Google Scholar
Hussain, A. K. M. F. & Ramjee, V. 1976 Periodic wake behind a circular cylinder at low Reynolds numbers. Aero. Q. 27, 123142.Google Scholar
Keffer, J. 1985 The uniform distortion of a turbulent wake. J. Fluid Mech. 22, 135159.Google Scholar
Lapple, C. E. 1961 The little things in life. Stanford Res. Inst. J. 5, 94102.Google Scholar
Lessen, M. & Singh, P. J. 1974 Stability of turbulent jets and wakes. Phys. Fluids 17, 13291330.Google Scholar
Matsui, T. & Okude, M. 1980 Rearrangement of Kármán vortex street at low Reynolds numbers. XVth International Congress of Theoretical and Applied Mechanics, University of Toronto, August, pp. 127.
Matsui, T. & Okude, M. 1981 Vortex pairing in a Kármán vortex street. In Proc. Seventh Biennial Symposium on Turbulence, Rolla, Missouri.
Matsui, T. & Okude, M. 1983 Formation of the secondary vortex street in the wake of a circular cylinder. In Structure of Complex Turbulent Shear Flow, IUTAM Symposium, Marseille, 1982. Springer.
Mattingly, G. E. & Criminale, W. O. 1972 The stability of an incompressible two-dimensional wake. J. Fluid Mech 51, 233272.Google Scholar
Meiburg, E. 1987 On the role of subharmonic perturbations in the far wake. J. Fluid Mech. 177, 83107.Google Scholar
Morkovin, M. 1964 Flow around circular cylinders - a kaleidoscope of challenging fluid phenomena. In Proc. ASME Symposium on Fully Separated Flows, Philadelphia, pp. 102118.
Mumford, J. C. 1983 The structure of the large eddies in fully developed turbulent shear flows. Part 2. The plane wake. J. Fluid Mech. 137, 44756.Google Scholar
Nagib, H. & Desruelle, D. 1982 Controlled excitation of the far wake instability, Bull. Am. Phys. Soc. 27, 1193.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, 4960.Google Scholar
Payne, F. & Lumley, J. 1967 Large eddy structure of the turbulent wake behind a circular cylinder. Phys. Fluids Suppl. 10, S194196.Google Scholar
Pierrehumbert, R. & Widnall, S. 1982 The two- and three-dimensional instabilities of a spatially periodic shearlayer. J. Fluid Mech. 114, 5982.Google Scholar
Robinson, A. C. & Saffman, P. G. 1982 Three-dimensional stability of vortex arrays. J. Fluid Mech 125, 411427.Google Scholar
Roshko, A. 1953 On the development of turbulent wakes from vortex streets. NACA TN 2913 (see also, NACA Rep. 1191 (1959)).
Roshko, A. 1976 Structure of turbulent shear flows: a new look. AIAA J. 14, 13491357.Google Scholar
Saffman, P. & Schatzman, J. 1982 An inviscid model for the vortex-street wake. J. Fluid Mech. 122, 467486.Google Scholar
Saric, W. & Thomas, A. 1984 Experiments on the subharmonic route to turbulence in boundary layers. In Turbulence and Chaotic Phenomena in Fluids, (ed. T. Tatsumi), pp. 117122. Elsevier.
Schatzman, J. 1981 A model for the von Kármán vortex street. Ph.D. Thesis, California Institute of Technology, Pasadena, California.
Taneda, S. 1959 Downstream development of wakes behind cylinders. J. Phys. Soc. Japan 14, 843848.Google Scholar
Townsend, A. A. 1956 The Structure of Turbulent Shear Flow. Cambridge University Press.
Townsend, A. A. 1966 The mechanism of entrainment in free turbulent flows. J. Fluid Mech. 26, 689715.Google Scholar
Townsend, A. A. 1970 Entrainment and the structure of turbulent flow. J. Fluid Mech. 41, 136.Google Scholar
Townsend, A. A. 1979 Flow patterns of large eddies in a wake and in a boundary layer. J. Fluid Mech. 95, 515537.Google Scholar
Tritton, D. J. 1959 Experiments on the flow past a circular cylinder at low Reynolds numbers. J. Fluid Mech. 6, 547567.Google Scholar
Tritton, D. J. 1977 Physical Fluid Dynamics, p. 23. International Student Edition, Van Nostrand Reinhold.
Valensi, J. 1974 On the aerodynamic of porous sheets. In Omaggio a Carlo Ferrari.: Libreria Editrice Universitaria Levrotto & Bella, Torino.
Weihs, D. 1973 On the existence of multiple Kármán vortex-street modes. J. Fluid Mech. 61, 199205.Google Scholar
Winant, C. D. & Browand, F. K. 1974 Vortex pairing: the mechanism of turbulent mixing-layer growth at moderate Reynolds number. J. Fluid Mech. 63, 237255.Google Scholar
Williamson, C. H. 1985 Evolution of a single wake behind a pair of bluff bodies. J. Fluid Mech. 159, 118.Google Scholar
Wlezien, R. 1981 The evolution of the low-wavenumber structure in a turbulent wake. Ph.D. Thesis, Illinois Institute of Technology, Chicago, Illinois.
Wygnanski, I., Champagne, F. & Marasli, B. 1986 On the large-scale structures in two-dimensional small-deficit, turbulent wakes. J. Fluid Mech. 168, 3171.Google Scholar
Zdravkovich, M. M. 1968 Smoke observations of the wake of a group of three cylinders at low Reynolds number. J. Fluid Mech. 32, 339351.Google Scholar
Zdravkovich, M. M. 1969 Smoke observations of the formation of a Kármán vortex street. J. Fluid Mech. 37, 491496.Google Scholar