Hostname: page-component-8448b6f56d-c4f8m Total loading time: 0 Render date: 2024-04-19T12:00:34.986Z Has data issue: false hasContentIssue false
  • English
  • Français

A numerical study of the dynamics of a particle settling at moderate Reynolds numbers in a linearly stratified fluid

Published online by Cambridge University Press:  30 May 2014

A. Doostmohammadi ,
S. Dabiri  and
A. M. Ardekani
A. Doostmohammadi
Affiliation:
Department of Aerospace and Mechanical Engineering, University of Notre Dame, Notre Dame, IN 46556, USA
S. Dabiri
Affiliation:
Department of Aerospace and Mechanical Engineering, University of Notre Dame, Notre Dame, IN 46556, USA School of Mechanical Engineering, Purdue University, 585 Purdue Mall, West Lafayette, IN 47907, USA
A. M. Ardekani*
Affiliation:
Department of Aerospace and Mechanical Engineering, University of Notre Dame, Notre Dame, IN 46556, USA School of Mechanical Engineering, Purdue University, 585 Purdue Mall, West Lafayette, IN 47907, USA
*
†Email address for correspondence: aardekan@nd.edu
Get access Rights & Permissions [Opens in a new window]

Abstract

In this paper, the transient settling dynamics of a spherical particle sedimenting in a linearly stratified fluid is investigated by performing fully resolved direct numerical simulations. The settling behaviour is quantified for different values of Reynolds, Froude and Prandtl numbers. It is demonstrated that the transient settling dynamics is correlated to the induced Lagrangian drift of flow around the settling particle. A simplified model is provided to predict the maximum velocity of the settling particle in linearly stratified fluids. The peak velocity can be followed by the oscillation of the settling velocity and the particle can even reverse its direction of motion before reaching to its neutrally buoyant level. The frequency of oscillation of settling velocity scales with the Brunt–Väisälä frequency and the motion of the particle can lead to the formation of secondary and tertiary vortices following the primary vortex.

JFM classification

Geophysical and Geological Flows: Stratified flows
Type
Papers
Information
Journal of Fluid Mechanics , Volume 750 , 10 July 2014 , pp. 5 - 32
Copyright
© 2014 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

Abaid, N., Adalsteinsson, D., Agyapong, A. & McLaughlin, R. M. 2004 An internal splash: levitation of falling spheres in stratified fluids. Phys. Fluids 16, 1567–1580.CrossRefGoogle Scholar
Alldredge, A. L. & Gotschalk, C. C. 1989 Direct observations of the mass flocculation of diatom blooms: characteristics, settling velocities and formation of diatom aggregates. Deep-Sea Res. A 36, 159–171.CrossRefGoogle Scholar
Ardekani, A. M., Dabiri, S. & Rangel, R. H. 2008 Collision of multi-particle and general shape objects in a viscous fluid. J. Comput. Phys. 227, 10094–10107.CrossRefGoogle Scholar
Ardekani, A. M., Dabiri, S. & Rangel, R. H. 2009 Deformation of a droplet in a particulate shear flow. Phys. Fluids 21, 093302.CrossRefGoogle Scholar
Ardekani, A. M. & Rangel, R. H. 2008 Numerical investigation of particle–particle and particle–wall collisions in a viscous fluid. J. Fluid Mech. 596, 437–466.CrossRefGoogle Scholar
Ardekani, A. M. & Stocker, R. 2010 Stratlets: low Reynolds number point-force solutions in a stratified fluid. Phys. Rev. Lett. 105, 084502.CrossRefGoogle Scholar
Blanchette, F. & Shapiro, A. 2012 Drops settling in sharp stratification with and without Marangoni effects. Phys. Fluids 24, 042104.CrossRefGoogle Scholar
Camassa, R., Falcon, C., Lin, J., McLaughlin, R. M. & Mykins, N. 2010 A first-principle predictive theory for a sphere falling through sharply stratified fluid at low Reynolds number. J. Fluid Mech. 664, 436–465.CrossRefGoogle Scholar
Camassa, R., Falcon, C., Lin, J., McLaughlin, R. M. & Parker, R. 2009 Prolonged residence times for particles settling through stratified miscible fluids in the Stokes regime. Phys. Fluids 21, 031702.CrossRefGoogle Scholar
Doostmohammadi, A., Stocker, R. & Ardekani, A. M. 2012 Low-Reynolds number swimming at pycnoclines. Proc. Natl Acad. Sci. U.S.A. 109, 3856–3861.CrossRefGoogle ScholarPubMed
Eames, I. & Hunt, J. C. R. 1997 Inviscid flow around bodies moving in weak density gradients without buoyancy effects. J. Fluid Mech. 353, 331–355.CrossRefGoogle Scholar
Gottlieb, S. & Shu, C. W. 1998 Total variation diminishing Runge–Kutta schemes. Maths Comput. 67 (221), 73–85.CrossRefGoogle Scholar
Graf, G. 1989 Benthic–pelagic coupling in a deep-sea benthic community. Nature 341, 437–439.CrossRefGoogle Scholar
Greenslade, M. D. 2000 Drag on a sphere moving horizontally in a stratified fluid. J. Fluid Mech. 418, 339–350.CrossRefGoogle Scholar
Hanazaki, H. 1988 A numerical study of three-dimensional stratified flow past a sphere. J. Fluid Mech. 192, 393–419.CrossRefGoogle Scholar
Hanazaki, H., Konishi, K. & Okamura, T. 2009 Schmidt-number effects on the flow past a sphere moving vertically in a stratified diffusive fluid. Phys. Fluids 21, 026602.CrossRefGoogle Scholar
Hunt, J. C. R. & Snyder, W. H. 2006 Experiments on stably and neutrally stratified flow over a model three-dimensional hill. J. Fluid Mech. 96, 671–704.CrossRefGoogle Scholar
Jacobson, M. Z. 1998 Aerosol scattering and absorption. In Fundamentals of Atmospheric Modelling, Cambridge University Press.Google Scholar
Kellogg, W. W. 1980 Aerosols and climate. In Interactions of Energy and Climate (ed. Bach, W., Pankrath, J. & Williams, J.), pp. 281–296. Kluwer Academic.CrossRefGoogle Scholar
Leonard, B. P. 1979 A stable and accurate convective modelling procedure based on quadratic upstream interpolation. Comput. Meth. Appl. Mech. Engng 19, 59–98.CrossRefGoogle Scholar
MacIntyre, S., Alldredge, A. L. & Gotschalk, C. C. 1995 Accumulation of marine snow at density discontinuities in the water column. Limnol. Oceanogr. 40, 449–468.CrossRefGoogle Scholar
Magnaudet, J. & Eames, I. 2000 The motion of high-Reynolds-number bubbles in inhomogeneous flows. Annu. Rev. Fluid Mech. 32 (1), 659–708.CrossRefGoogle Scholar
Mordant, N. & Pinton, J. F. 2000 Velocity measurement of a settling sphere. Eur. Phys. J. B 18, 343–352.CrossRefGoogle Scholar
Mowbray, D. E. & Rarity, B. S. H. 1967 The internal wave pattern produced by a sphere moving vertically in a density stratified liquid. J. Fluid Mech. 30 (03), 489–495.CrossRefGoogle Scholar
Schlichting, H. 1968 Boundary-Layer Theory. McGraw-Hill.Google Scholar
Sharma, N. & Patankar, N. A. 2005 A fast computation technique for direct numerical simulation of rigid particulate flows. J. Comput. Phys. 205, 439–457.CrossRefGoogle Scholar
Srdić-Mitrović, A. N., Mohamed, N. A. & Fernando, H. J. S. 1999 Gravitational settling of particles through density interfaces. J. Fluid Mech. 381, 175–198.CrossRefGoogle Scholar
Torres, C. R., Hanazaki, H., Ochoa, J., Castillo, J. & van Woert, M. 2000 Flow past a sphere moving vertically in a stratified diffusive fluid. J. Fluid Mech. 417, 211–236.CrossRefGoogle Scholar
White, F. M. 2006 Viscous Fluid Flow. McGraw-Hill Higher Education.Google Scholar
Yick, K. Y., Torres, C. R., Peacock, T. & Stocker, R. 2009 Enhanced drag of a sphere settling in a stratified fluid at small Reynolds numbers. J. Fluid Mech. 632, 49–68.CrossRefGoogle Scholar