Hostname: page-component-cd9895bd7-jkksz Total loading time: 0 Render date: 2024-12-27T13:37:41.242Z Has data issue: false hasContentIssue false
  • English
  • Français

Particle dispersion in isotropic turbulence under Stokes drag and Basset force with gravitational settling

Published online by Cambridge University Press:  26 April 2006

Renwei Mei ,
Ronald J. Adrian  and
Thomas J. Hanratty
Renwei Mei
Affiliation:
Department of Theoretical and Applied Mechanics, University of Illinois at Urbana-Champaign, IL 61801, USA Present address: Department of Aerospace Engineering, Mechanics & Engineering Science, University of Florida, Gainesville, FL 32611, USA.
Ronald J. Adrian
Affiliation:
Department of Theoretical and Applied Mechanics, University of Illinois at Urbana-Champaign, IL 61801, USA
Thomas J. Hanratty
Affiliation:
Department of Chemical Engineering, University of Illinois at Urbana-Champaign, IL 61801, USA
Get access Rights & Permissions [Opens in a new window]

Abstract

An analysis that includes the effects of Basset and gravitational forces is presented for the dispersion of particles experiencing Stokes drag in isotropic turbulence. The fluid velocity correlation function evaluated on the particle trajectory is obtained by using the independence approximation and the assumption of Gaussian velocity distributions for both the fluid and the particle, formulated by Pismen & Nir (1978). The dynamic equation for particle motion with the Basset force is Fourier transformed to the frequency domain where it can be solved exactly. It is found that the Basset force has virtually no influence on the structure of the fluid velocity fluctuations seen by the particles or on particle diffusivities. It does, however, affect the motion of the particle by increasing (reducing) the intensities of particle turbulence for particles with larger (smaller) inertia. The crossing of trajectories associated with the gravitational force tends to enhance the effect of the Basset force on the particle turbulence. An ordering of the terms in the particle equation of motion shows that the solution is valid for high particle/fluid density ratios and to 0(1) in the Stokes number.

Type
Research Article
Information
Journal of Fluid Mechanics , Volume 225 , April 1991 , pp. 481 - 495
Copyright
© 1991 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

AutoN, T. R., Hunt, J. C. R. & Prud'homme, M. 1988 J. Fluid Mech. 197, 241–257.
Basset, A. B.: 1888 A Treatise on Hydrodynamics, vol. 2. Dover.
Chao, B. T.: 1964 Osterreichisches Ingenieur-Archiv. 18, 7–21.
Corrsin, S.: 1959 Adv. Geophys. 6, 161–184.
Gouesbet, G., Berlemont, A. & Picart, A., 1984 Phys. Fluids 27 (4), 827–837.
Hinze, J. O.: 1975 Turbulence. McGraw-Hill.
Kraichnan, R. H.: 1970 Phys. Fluids 13, 22–31.
Landau, L. E. & Lifshitz, E. M., 1959 Fluid Mechanics. Pergamon.
Lumley, J. L.: 1957 Some problems connected with the motion of small particles in turbulent fluid. PhD thesis, The Johns Hopkins University, Baltimore, MD.
Lundgren, T. S. & Pointin, Y. B., 1976 Phys. Fluids 19, 355–358.
Maxey, M. R.: 1987 J. Fluid Mech. 174, 441–465.
Maxey, M. R. & Riley, J., 1983 Phys. Fluids 26 (4), 863–889.
Mei, R., Lawrence, C. J. & Adrian, R. J., 1990 Unsteady drag on a sphere at finite Reynolds number with small fluctuations in the free-stream velocity. Submitted.
Nir, A. & Pismen, L. M. 1979 J. Fluid Mech. 94, 369–381.
Phythian, R.: 1975 J. Fluid Mech. 67, 145–153.
Pismen, L. M. & Nir, A., 1978 J. Fluid Mech. 84, 193–206.
Reeks, M. W.: 1977 J. Fluid Mech. 83, 529–546.
Reeks, M. W. & Mckee, S., 1984 Phys. Fluids 27 (7), 1573–1582.
Sano, T.: 1981 J. Fluid Mech. 112, 433–441.
Shlien, D. J. & Corrsin, S., 1974 J. Fluid Mech. 62, 255–271.
Tchen, C. M.: 1947 Mean value and correlation problems connected with the motion of small particles suspended in a turbulent fluid. PhD thesis, Delft University, Netherlands.