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Oscillatory flow around disks and through orifices

Published online by Cambridge University Press:  20 April 2006

B. de Bernardinis ,
J. M. R. Graham  and
K. H. Parker
B. de Bernardinis
Affiliation:
Physiological Flow Studies Unit, Department of Aeronautics, Imperial College, London
J. M. R. Graham
Affiliation:
Physiological Flow Studies Unit, Department of Aeronautics, Imperial College, London
K. H. Parker
Affiliation:
Physiological Flow Studies Unit, Department of Aeronautics, Imperial College, London
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Abstract

Two examples of unsteady, axisymmetric, separated flows are studied: unbounded oscillatory flow around a disk and bounded oscillatory flow through a sharp-edged orifice. Calculations are made assuming that the flow is inviscid and that the shed vortex sheets can be represented by sequences of discrete vortex rings. The solid bodies (i.e. the disk or the orifice and bounding tube) are also represented by a distribution of bound discrete vortex rings whose strengths are chosen to satisfy the Neumann or zero normal velocity boundary condition.

The results of flow visualization experiments and, for the orifice, pressure drop measurements are also reported. In general, the gross properties of the flows are predicted accurately.

Type
Research Article
Information
Journal of Fluid Mechanics , Volume 102 , January 1981 , pp. 279 - 299
Copyright
© 1981 Cambridge University Press

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References

Anton, L. 1939 Ausbildung eines Wirbels an der Kante einer Platte. Ingenieur-Archiv 10, 411–421. (English Translation, 1956, N.A.C.A. TM-1398.)Google Scholar
Ashurst, W. T. 1979 Piston–-cylinder fluid motion via vortex dynamics. Presented at Euromech 119, London.
Caro, C. G., Fitzgerald, J. M. & Schroter, R. S. 1971 Atheroma and arterial wall shear stress. Proc. Roy. Soc. B 17, 109–159.Google Scholar
Chaplin, H. R. 1964 A method for numerical calculation of slipstream contraction of a shrouded impulse disk in the static case with application to other axisymmetric potential flow problems. David Taylor Model Basin Rep. no. 1857.Google Scholar
Clark, C. 1976a The fluid mechanics of aortic stenosis. I. Theory and steady flow experiments. J. Biomech. 9, 521–528.Google Scholar
Clark, C. 1976b The fluid mechanics of aortic stenosis. II. Unsteady flow experiments. J. Biomech. 9, 567–573.Google Scholar
Clements, R. R. 1973 An inviscid model of two-dimensional vortex shedding. J. Fluid Mech. 57, 321–336.Google Scholar
Clements, R. R. & Maull, D. J. 1975 The representation of sheets of vorticity by discrete vortices. Prog. Aerospace Sci. 16, 129–146.Google Scholar
Davies, P. O. A. L. & Hardin, J. C. 1974 Potential flow modelling of unsteady flow. In Numerical Methods in Fluid Mechanics (ed. C. A. Brebia & J. J. Connor), pp. 42–64. London: Pantech Press.
Didolen, N. 1979 On the formation of vortex rings: rolling up and production of circulation. Z. angew. Math. Phys. 30, 101–116.Google Scholar
Djilali, N. 1978 Oscillatory flow through a sharp-edged orifice plate. M.Sc. thesis, Imperial College, Dept of Aeronautics.
Evans, R. A. & Bloor, M. I. G. 1976 The starting mechanism of wave-induced flow through a sharp-edged orifice. J. Fluid Mech. 82, 115–128.Google Scholar
Fage, A. & Johansen, F. C. 1927 The structure of the vortex sheet. Phil. Mag. 5 (7), 417–436.Google Scholar
Fink, P. T. & Soh, W. K. 1974 Calculations of vortex sheets in unsteady flow and applications in ship hydrodynamics. 10th Symp. Naval Hydrodynamics, Cambridge, Mass., pp. 463–489.
Fry, D. L. 1973 Response of the arterial wall to certain physical factors in atherogenesis. Ciba Foundation Symposium 12. Excerpta Medica, 93–125.
Giesing, J. P. 1969 Vorticity and Kutta condition for unsteady multienergy flows. Trans. A.S.M.E. E, J. Appl. Mech. 36, 608–613.Google Scholar
Graham, J. M. R. 1977 Vortex shedding from sharp edges. Imperial College Aero. Rep. 77–06.Google Scholar
Graham, J. M. R. 1980 The forces on sharp-edged cylinders in oscillatory flow at low Keulegan-Carpenter numbers. J. Fluid Mech. 97, 331–346.Google Scholar
Hess, J. L. & Smith, A. M. O. 1966 Calculations of potential flow about arbitrary bodies. Prog. Aero. Sci. 8.Google Scholar
Knott, G. F. & Mackley, M. R. 1980 On eddy-motions near plates and ducts, induced by water waves and periodic flows. Proc. Roy. Soc. (in press).Google Scholar
Lamb, H. 1957 Hydrodynamics, 6th edn, pp. 202–249. Cambridge University Press.
Mangler, K. W. & Smith, J. H. 1956 A theory of slender delta wing with leading edge separation. R.A.E. Rep. 2442.Google Scholar
Mates, R. E., Gupta, R. L., Bell, A. C. & Klocke, F. J. 1978 Fluid dynamics of coronary artery stenosis. Circulation Res. 42, 152–162.Google Scholar
Moore, D. W. 1974 A numerical study of the roll-up of a finite vortex sheet. J. Fluid Mech. 63, 225.Google Scholar
Prandtl, L. 1924 Über die Entstehung von Wirbeln in der idealen Flüssigkeit. Vorträge aus dem Gebiete der Hydro- und Aerodynamik, Innsbruck, 1922 (ed. von Kármán & Levi-Civita). Springer.
Rosenhead, L. 1931 The formation of vortices from a surface of discontinuity. Proc. Roy. Soc. A 134, 170–192.Google Scholar
Saffman, P. G. 1978 The number of waves on unstable vortex rings. J. Fluid Mech. 84, 625–639.Google Scholar
Sarpkaya, T. 1975 An inviscid model of two-dimensional vortex shedding for transient and asymptotically separated flow over an inclined plate. J. Fluid Mech. 68, 109–128.Google Scholar
Sarpkaya, T. & Schoaff, R. L. 1979 Inviscid model of two-dimensional vortex shedding by a circular cylinder. A.I.A.A. J. 17, 1193–1200.Google Scholar
Singh, S. 1979 Forces on bodies in an oscillatory flow. Ph.D. thesis, University of London.
Smith, A. M. O. & Pierce, J. 1958 Exact solution of the Neumann problem –- calculation of plane and axially symmetric flows about or within arbitrary boundaries. Douglas Aircraft Co. Rep. 26988.
Tomm, D. 1977 Model investigation of sound generation in vessel stenosis. INSERM –- Euromech 92, Cardiovascular and pulmonary dynamics 71, 179–192.Google Scholar
Wedermeyer, E. 1961 Ausbildung eines Wirbelpaares an den Kanten einer Platte. Ingenieur-Archiv 30, 187–200.Google Scholar
Young, D. F. 1979 Fluid mechanics of arterial stenoses. J. Biomech. Engng 101, 157–175.Google Scholar
Young, D. F. & Tsai, F. Y. 1973a Flow characteristics in models of arterial stenoses. J. Biomech. 6, 395–410.Google Scholar
Young, D. F. & Tsai, F. Y. 1973b Flow characteristics in models of arterial stenoses. J. Biomech. 6, 547–559.Google Scholar