Hostname: page-component-cd9895bd7-gvvz8 Total loading time: 0 Render date: 2024-12-19T13:02:03.615Z Has data issue: false hasContentIssue false
  • English
  • Français

The Stokes-flow drag on prolate and oblate spheroids during axial translatory accelerations

Published online by Cambridge University Press:  29 March 2006

Robert Y. S. Lai  and
Lyle F. Mockros
Robert Y. S. Lai
Affiliation:
Department of Civil Engineering, The Technological Institute, Northwestern University, Evanston, Illinois Present address: Department of Energetics, University of Wisconsin, Milwaukee.
Lyle F. Mockros
Affiliation:
Department of Civil Engineering, The Technological Institute, Northwestern University, Evanston, Illinois
Get access Rights & Permissions [Opens in a new window]

Abstract

Stokes's linearized equations of motion are used to calculate the flow field generated by a spheroid executing axial translatory oscillations in an infinite, otherwise still, incompressible, viscous fluid. The flow field, expressed in terms of spheroidal wave functions of order one, is used to develop general expressions for the drag on oscillating prolate and oblate spheroids. Formulae for the approximate drag, useful in making calculations, are obtained for small values of an oscillation parameter. These formulae reduce to the Stokes result in the limit when the spheroid becomes a sphere and the steady-state drag for a spheroid as the frequency of oscillation becomes zero. The fluid forces on spheroids of various shapes are compared graphically. The approximate formulae for the drag are integrated over all frequencies to obtain formulae for the drag on spheroids executing general axial translatory accelerations. The fluid resistance on the spheroid is expressed as the sum of an added mass effect, a steady-state drag and an effect due to the history of the motion. A table of added mass, viscous and history coefficients is given.

Type
Research Article
Information
Journal of Fluid Mechanics , Volume 52 , Issue 1 , 14 March 1972 , pp. 1 - 15
Copyright
© 1972 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

Aoi, T. 1955 The steady flow of viscous fluid past a fixed spheroidal obstacle at small Reynolds numbers. J. Phys. Soc. Japan, 10, 119.Google Scholar
Basset, A. B. 1888. A Treatise on Hydrodynamics, vol. 2 Dover.
Breach, D. R. 1961 Slow flow past ellipsoids of revolution. J. Fluid Mech. 10, 306.Google Scholar
Carstens, M. R. 1952 Accelerated motion of a spherical particle. Tram. Am. Geophys. Un. 33, 713.Google Scholar
Flammer, C. 1957 Spheroidal Wave Functiom. Stanford University Press.
Happel, J. & Brenner, H. 1965 Low Reynolds Number Hydrodynamics. Prentice-Hall.
Kanwal, R. P. 1955 Rotatory and longitudinal oscillations of axi-symmetric bodies in a viscous fluid. Q. J. Mech. Appl. Math. 8, 146.Google Scholar
Lai, R. Y. S. 1969 Stokes flow solution for an accelerating spheroid. Ph.D. dissertation, Northwestern University, Illinois.
Lamb, H. 1932 Hydrodynamics, 6th edn. Cambridge University Press.
Landau, L. D. & Lifshitz, E. M. 1959 FZuid Mechanics (trans. Sykes & Reid). Pergamon.
Mockros, L. F. & LAI, R. Y. S. 1969 Limit of validity of Stokes flow theory for a falling sphere. J. Engng. Mech. Div., Am. Soc. Civ. Engrs. 95, 87.Google Scholar
Oberbeck, A. 1876 Über Stationare Flussigkeitsbewegungen mit Berucksiohtigung der inner Reibung. 2. angew. Math. Phys. 81, 62.Google Scholar
Odar, F. 1962 Forces on a sphere accelerating in a viscous fluid. Ph.D. dissertation, Northwestern University, Illinois.
Payne, L. E. & Pell, W. H. 1960 The Stokes flow problem for a class of axially symmetric bodies. J. Fluid Mech. 7, 529.Google Scholar
Stokes, G. G. 1851 On the effect of the internal friction of fluids on pendulums. Trana. Camb. Phil. Soc. 9, 8
Yih, C.-S. 1969 Fluid Mechanics. McGraw-Hill.