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Motion of discrete particles in a turbulent fluid

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Summary

Various approximations to Basset's equation for the motion of a particle in a viscous fluid have been applied to the complex phenomenon of dispersion in a turbulent fluid. The deviations of the particle motion from the fluid motion, as predicted by the various approximations, is explored, and the frequencies for which this deviation is large are described. The approximations are found to be invalid for such cases as sediment transport and motion of gas bubbles in liquids. For small, 7 micron, liquid or solid particles in air, however, all approximations are shown to be valid for turbulent frequencies below 812 cps.

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Abbreviations

a :

parameter in equation (2.3)

b :

parameter in equation (2.3)

c :

parameter in equation (2.3)

d :

diameter of sphere

E f :

energy spectrum of the fluid

E p :

energy spectrum of the particle

F :

frequency of oscillation

f 1 :

parameter defined by equation (2.10)

f 2 :

parameter defined by equation (2.10)

g :

acceleration of gravity

N S :

\(\sqrt {{v \mathord{\left/ {\vphantom {v {(\omega d^2 )}}} \right. \kern-\nulldelimiterspace} {(\omega d^2 )}}}\), Stokes number

s :

density ratio

t :

time

t 0 :

initial time

u f :

fluid velocity

u p :

particle velocity

V :

velocity of sphere

β :

phase angle

λ :

parameter in equation (2.8)

η :

amplitude ratio

ϕ :

parameter in equation (2.8)

μ :

dynamic viscosity

ν :

kinematic viscosity

ρf:

density of the fluid

ρp:

density of the particle

σ :

parameter in equation (2.8)

ς :

parameter in equation (2.8)

ω :

circular frequency of the motion

References

  1. Basset, A. B., A Treatise on hydrodynamics, v. 2, ch. 5, Deighton, Bell and Co., Cambridge, 1888.

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  4. Friedlander, S. K., A.I.Ch.E. Journal 3 (1957) 381.

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  5. Hinze, J. O., Turbulence, McGraw-Hill, New York, 1959.

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  6. Liu, V. C., J. of Meterology 13 (1956) 399.

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  7. Lumley, J., “Some Problems Connected with the Motion of Small Particles in Turbulent Fluid”, Ph.D. Thesis, Johns Hopkins University, Baltimore, 1957.

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  8. Soo, S. L., Chem. Engg. Science 5 (1956) 57.

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  9. Tchen, C. M., “Mean Values and Correlation Problems Connected with the Motion of Small Particles Suspended in a Turbulent Fluid”, Ph.D. Thesis, Delft, 1947

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Author notes

  1. A. T. Hjelmfelt Jr.

    Present address: University of Missouri, Columbia, Missouri, USA

Authors and Affiliations

  1. Northwestern University, Evanston, Illinois, USA

    A. T. Hjelmfelt Jr. & L. F. Mockros

Authors
  1. A. T. Hjelmfelt Jr.
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  2. L. F. Mockros
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Hjelmfelt, A.T., Mockros, L.F. Motion of discrete particles in a turbulent fluid. Appl. Sci. Res. 16, 149–161 (1966). https://doi.org/10.1007/BF00384062

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  • DOI: https://doi.org/10.1007/BF00384062

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