Hostname: page-component-78c5997874-mlc7c Total loading time: 0 Render date: 2024-11-10T03:23:10.095Z Has data issue: false hasContentIssue false
  • English
  • Français

Unsteady flow about a sphere at low to moderate Reynolds number. Part 2. Accelerated motion

Published online by Cambridge University Press:  26 April 2006

Eugene J. Chang  and
Martin R. Maxey
Eugene J. Chang
Affiliation:
Center for Fluid Mechanics, Turbulence and Computation, Brown University, Box 1966, Providence, RI 02912, USA Present Address: Naval Research Laboratory, Code 6410, Washington, DC 20375, USA.
Martin R. Maxey
Affiliation:
Center for Fluid Mechanics, Turbulence and Computation, Brown University, Box 1966, Providence, RI 02912, USA
Get access Rights & Permissions [Opens in a new window]

Abstract

A full numerical simulation based on spectral methods is used to investigate linearly accelerating and decelerating flows past a rigid sphere. Although flow separation does not occur at Reynolds numbers below 20 for a steady flow, in the linearly decelerating flow separation is observed at much lower Reynolds numbers with complete detachment of vorticity possible in certain cases. The existence of a large recirculation region contributes to the result that a negative viscous force on the sphere is possible. The contribution of the pressure to the force includes a component that is well described by the inviscid added-mass term in both the accelerating and decelerating cases. The force on the sphere is found in general to initially decay in a power law manner after acceleration or deceleration ends followed by rapid convergence at later times to the steady state. For the cases examined this convergence is found to be exponential except for those in which the sphere is brought to rest in which case the convergence remains algebraic. This includes the special case of an infinite acceleration or deceleration where the free stream velocity is impulsively changed.

Type
Research Article
Information
Journal of Fluid Mechanics , Volume 303 , 25 November 1995 , pp. 133 - 153
Copyright
© 1995 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

Bassett, A. B. 1888 A Treatise in Hydrodynamics, Vol. II. Cambridge: Deighton, Bell, and Co.
Batchelor, G. K. 1967 An Introduction to Fluid Dynamics. Cambridge University Press.
Bentwich, M. & Miloh, T. 1978 The unsteady matched Stokes-Oseen solution for the flow past sphere. J. Fluid Mech. 88, 17–32.Google Scholar
Chang, E. J. 1992 Accelerated motion of rigid spheres in unsteady flow at low to moderate Reynolds numbers PhD Thesis, Brown University.
Change, E. J. & Maxey, M. R. 1994 Accelerated motion of rigid spheres in unsteady flow at low to moderate Reynolds numbers. Part 1. Oscillatory motion. J. Fluid Mech. 277, 347–379.Google Scholar
Dennis, S. C. R. & Walker, J. D. A. 1971 Calculation of the steady flow past sphere at low and moderate Reynolds numbers. J. Fluid Mech. 48 771–789.Google Scholar
Dennis, S. C. R. & Walker, J. D. A. 1972 Numerical solutions for time-dependent flow past an impulsively started sphere. Phys. Fluids 15, 517–525.Google Scholar
Lawrence, C. J. & Mei, R. 1995 Long-time behaviour of the drang on a body in implusive motion. J. Jluid Mech. 283, 307–327.Google Scholar
Lovalenti, P. M. & Brady, J. F. 1993a The hydrodynamic force on a rigid particle undergoing arbitrary time-dependent motion at small Reynolds umber. J. Fluid Mech. 256, 607–614.Google Scholar
Marcus, P. S. & Tuckerman, L. S. 1987 Simulation of flow between concentric rotating spheres. Part 1. Steady states. J. Fluid Mech. 185, 1–30.Google Scholar
Maxey, M. R. & Riley, J. J. 1983 Equation of motion for a small rigid sphere in a nonuniform flow. Phys. Fluids 26, 863–889.Google Scholar
Mei, R. 1993 History force on a sphere due to a step change in the free-stream velocity. Intl J. Multiphase Flow 19, 509–525.Google Scholar
Mei, R. & Adrian, R. J. 1992 Flow past a sphere with an oscillation in the free-stream velocity and unsteady drag at finite Reynolds number. J. Fluid Mech. 237, 323–341.Google Scholar
Mei, R., Lawrence, C. J. & Adrian, R. J. 1991 Drag on a sphere with fluctuations in the free stream velocity. J. Fluid Mech. 233, 613–631.Google Scholar
Orszag, S. A. 1974 Fourier series on spheres. Mon. Weather Rev. 102, 56–75.Google Scholar
Rivero, M. 1991 Etude par simulation numerérique des forces exercé sur une inclusion sphérique par un écoulement accéléré. Thése de Doctorat, INPT.
Rivero, M., Magnaudet, J. & Fabre, J. 1991 Quelques résultants nouveaux concernant les forces exercées sur une inclusion sphérique par en éoulement accéléré. Acad. Sci. Paris 312 (II), 1499–1506.Google Scholar
Sono, T. 1981 Unsteady flow past a sphere at low Reynolds number. J. Fluid Mech. 112, 433–441.Google Scholar
Torobin, L. B. & Gauvin, W. H. 1959 Fundamental aspects of solids-gas flow. Part III. Accelerated motion of a particle in a fluid. Can. J. Chem. Engng 38, 224–236.Google Scholar