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Streaming flow induced by an oscillating cascade of circular cylinders

Published online by Cambridge University Press:  26 April 2006

B. Yan ,
D. B. Ingham  and
B. R. Morton
B. Yan
Affiliation:
Department of Applied Mathematical Studies, University of Leeds, Leeds, LS2 9JT, UK
D. B. Ingham
Affiliation:
Department of Applied Mathematical Studies, University of Leeds, Leeds, LS2 9JT, UK
B. R. Morton
Affiliation:
Department of Mathematics, Monash University, Clayton 3168, Victoria, Australia
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Abstract

The fluid flow induced by a cascade of circular cylinders which oscillates harmonically in an unbounded, incompressible, viscous fluid which is otherwise at rest is investigated both numerically and experimentally. Attention in this paper is mainly concentrated on the induced steady streaming flow which occurs when the ratio of the amplitude of the oscillation of the cascade to the size of the cylinder, ε, is very small. The leading-order flow is then governed by the steady Navier-Stokes equations. In order to solve these equations numerically we first generate numerically a grid system using the boundary element method and then use a finite-difference scheme on the newly generated rectangular grid system. Numerical results show that for small values of the streaming Reynolds number Rs there are four recirculating flows of equal strength around each circular cylinder of the cascade. At large values of Rs symmetry breaks down and numerical solutions are found for asymmetrical flows. Numerically, a critical value of Rs, Rso say, is identified such that the flow is symmetrical when Rs < Rso and asymmetrical when Rs > Rso and these results are in reasonable agreement with experimental results, which are also presented in this paper.

Type
Research Article
Information
Journal of Fluid Mechanics , Volume 252 , July 1993 , pp. 147 - 171
Copyright
© 1993 Cambridge University Press

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References

Bertelsen, A. F. 1974 An experimental investigation of high Reynolds number steady streaming generated by oscillating cylinders. J. Fluid Mech. 64, 589–597.Google Scholar
Bertelsen, A., Svardal, A. & Tjotta, S. 1973 Nonlinear streaming effects associated with oscillating cylinders. J. Fluid Mech. 59, 493–511.Google Scholar
Davidson, B. J. & Riley, N. 1972 Jet induced by oscillating motion. J. Fluid Mech. 53, 287–303.Google Scholar
Dennis, S. C. R. & Hudson, J. D. 1978 A difference method for solving the Navier—Stokes equations. In Proc. 1st Intl Conf. Numer. Methods in Laminar & Turbulent Flow, pp. 69–80. Swansea: Pineridge.
Fearn, R. M., Mullin, T. & Cliffe, K. A. 1990 Nonlinear flow phenomena in a symmetric sudden expansion. J. Fluid Mech. 211, 595–608.Google Scholar
Haddon, E. W. & Riley, N. 1979 The steady streaming induced between oscillating circular cylinders. Q. J. Mech. Appl. Maths 32, 265–282.Google Scholar
Ingham, D. B., Tang, T. & Morton, B. R. 1990 Steady two-dimensional flow through a row of normal flat plates. J. Fluid Mech. 210, 281–302.Google Scholar
Ingham, D. B. & Yan, B. 1989 The fluid flow induced by an oscillating cascade. In Proc. 6th Conf. Numer. Methods in Laminar & Turbulent Flow, pp. 723–733. Swansea: Pineridge.
Ingham, D. B. & Yan, B. 1992 Fluid flow induced by a small amplitude harmonically oscillating cascade. Acta Mechanica 91, 27–46.Google Scholar
Ingham, D. B., Yan, B. & Morton, B. R. 1992 The fluid flow induced by large amplitude oscillations of a cascade. Computers Fluids 21, 305–321.Google Scholar
Irani, M. B. 1982 Finite element analysis of viscous flow and rigid body interaction. Masters thesis, University of British Columbia.
Kim, S. K. & Troesch, A. W. 1989 Streaming flows generated by high-frequency small-amplitude oscillations of arbitrarily shaped cylinders. Phys. Fluids A 1, 975–985.Google Scholar
Manzoor, M. 1984 Heat Flow Through Extended Surface Heat Exchangers. Lecture Notes in Engineering, vol. 5. Springer.
Pattani, P. G. & Olson, M. D. 1987 Rigid body-viscous interaction. Intl J. Numer. Meth. Fluids 7, 653–695.Google Scholar
Pattani, P. G. & Olson, M. D. 1988 Force on oscillating bodies in viscous fluids. Intl J. Numer. Meth. Fluids 8, 519–563.Google Scholar
Riley, N. 1965 Oscillating viscous flows. Mathematika 12, 161–175.Google Scholar
Riley, N. 1967 Oscillatory viscous flows, review and extension. J. Inst. Maths Applics. 3, 419–434.Google Scholar
Sobey, I. J. & Drazin, P. G. 1986 Bifurcations of two-dimensional channel flows. J. Fluid Mech. 171, 263–287.Google Scholar
Stansby, P. K. & Smith, P. A. 1991 Viscous forces on a circular cylinder in orbital flow at low Keulegan—Carpenter numbers. J. Fluid Mech. 229, 159–171.Google Scholar
Stuart, J. T. 1963 Unsteady boundary layers. In Laminar Boundary Layers (ed. L. Rosenhead), pp. 347–408. Oxford University Press.
Stuart, J. T. 1966 Double boundary layers in oscillating viscous flows. J. Fluid Mech. 24, 673–687.Google Scholar
Tabakova, S. & Zapryanov, Z. 1982 On the hydrodynamic interaction of two spheres oscillating in a viscous fluid —I. Axisymmetrical case. J. Appl. Maths. Phys. 33, 344–357.Google Scholar
Tatsuno, M. & Bearman, P. W. 1990 A visual study of the flow around an oscillatory circular cylinder at low Keulegan—Carpenter numbers and low Stokes numbers. J. Fluid Mech. 211, 157–182.Google Scholar
Thompson, J. F., Thames, F. C. & Mastin, C. W. 1974 Automatic numerical grid generation of body fitted curvilinear coordinate systems for fields containing any number of arbitrary two dimensional bodies. J. Comput. Phys. 15, 299–319.Google Scholar
Wang, C. Y. 1967 On high frequency oscillatory viscous flows. J. Fluid Mech. 32, 55–68.Google Scholar
Williamson, C. H. K. 1985 Sinusoidal flow relative to circular cylinders. J. Fluid Mech. 155, 141–174.Google Scholar
Zapryanov, Z., Kozhoukharova, Zh. & Iordanova, A. 1988 On the hydrodynamic interaction of two circular cylinders oscillating in a viscous fluid. Z. Angew. Maths. Phys. 39, 204–220.Google Scholar