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Lift exerted on stationary spheres in turbulent flow

Published online by Cambridge University Press:  20 April 2006

Brian B. Willetts  and
Colin G. Murray
Brian B. Willetts
Affiliation:
Department of Engineering, University of Aberdeen
Colin G. Murray
Affiliation:
Department of Engineering, University of Aberdeen
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Abstract

The purpose of the study was to examine the influence of a nearby wall on the lift experienced by spheres fixed in a fluid stream, and the decay of this influence with increasing separation from the wall. For gaps less than one quarter of the sphere diameter, wall effects were found to dominate all dependencies other than that on Reynolds number. At larger gap ratios the lift vector rotates around the flow axis, sometimes this way and sometimes that but only occasionally changes direction abruptly. The rotation seems to be associated with free-stream turbulence and is inhibited by shear or by uneven surface roughness. These effects are not influenced by sphere mounting, and sphere rotation does not seem important.

Three series of experiments are described, each using different apparatus. In a Reynolds number range 3000–50000, calculated from sphere diameter and relative local velocity, repeatable lift values were observed in zones close to a flow boundary (the wind-tunnel wall), and remote from a boundary for smooth spheres. For rough spheres, results were erratic remote from the boundary.

Large persistent lift forces away from the boundary were found when the gap was less than 0·02 diameters and when it lay between 0·1 and 0·2 diameters (all these fractions being approximate). For larger gaps the lift force was strongly time-dependent and time-averaged values were smaller than those for gap ratios less than 0·2.

Lift forces are related to localized downstream displacements of the separation line round the sphere whose origin seems to lie in the response of the sphere's boundary layer to turbulent structures in the free stream. Weak regularities of the lift record are related not only to the incidence of such features but also to a natural time-scale of response of the boundary layer. Separation line disturbances do not propagate in a predictable fashion but do develop sharp boundaries as a result of recirculation in the wake.

In one series of experiments considerable pains were taken to allow the sphere to rotate freely about an axis parallel to the local tunnel wall and normal to the flow direction. No significant rotation occurred and the effects reported are not associated with sphere rotation. In shear flow remote from a boundary mean lift acted down the gradient of relative velocity.

Type
Research Article
Information
Journal of Fluid Mechanics , Volume 105 , April 1981 , pp. 487 - 505
Copyright
© 1981 Cambridge University Press

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References

Achenbach, E. 1974 The effects of surface roughness and tunnel blockage on the flow past spheres. J. Fluid Mech. 65, 113–125.Google Scholar
Bagnold, R. A. 1974 Fluid forces on a body in shear flow; experimental use of stationary flow. Proc. Roy. Soc. A 340, 147–171.Google Scholar
Coleman, N. L. 1967 A theoretical and experimental study of drag and lift forces acting on a sphere resting on a hypothetical stream-bed. Proc. 12th Cong. I.A.H.R., Fort Collins, paper C22.Google Scholar
Kiya, M., Arie, M. & Tamura, H. 1979 Forces acting on circular cylinders placed in a turbulent plane mixing layer. J. Ind. Aerodynamics 5, 13–33.Google Scholar
Lee, K. C. 1979 Aerodynamic interaction between two spheres at Reynolds Numbers around 104. Aero Quart. 15, 371–385.Google Scholar
Maxworthy, T. 1969 Experiments on the flow around a sphere at high Reynolds numbers. Trans A.S.M.E. E, J. Appl. Mech. 36, 598–607.Google Scholar
Milne-Thomson, L. M. 1968 Theoretical Hydrodynamics, 5th edn, $18.61. Macmillan.
Murray, C. G. & Willetts, B. B. 1978 Lift forces on spheres in air flow between Reynolds Numbers 5000 and 80000. Proc. 4th Int. Conf. on Pneumatic Transport of Solids in Pipes. BHRA.
Saffman, P. G. 1965 The lift on a small sphere in a slow shear flow. J. Fluid Mech. 22, 385–400.Google Scholar
Scoggins, J. R. 1967 Sphere behaviour and the measurement of wind profiles. N.A.S.A. Tech. Note TND-3994.Google Scholar
Swanson, W. M. 1961 The Magnus effect: a summary of investigations to date. Trans. A.S.M.E. D, J. Basic Engng 83, 461–470.Google Scholar
Szechenyi, E. 1974 Simulation de nombres de Reynolds élevés sur un cylindre en soufflerie. La Recherche Aerospatiale 3, p. 155.Google Scholar
Taneda, S. 1978 Visual observations of the flow past a sphere at Reynolds numbers between 104 and 106. J. Fluid Mech. 85, 187–192.Google Scholar
Thomschke, H. 1971 An experimental investigation of the flow around spheres and cylinders close to a wall. Doctoral thesis, Karlsruhe University.
Willmarth, W. W. & Enlow, R. L. 1969 Aerodynamic lift and moment fluctuations of a sphere. J. Fluid Mech. 36, 417–432.Google Scholar