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Turbulent dispersion of particles in self-generated homogeneous turbulence

Published online by Cambridge University Press:  26 April 2006

R. N. Parthasarathy  and
G. M. Faeth
R. N. Parthasarathy
Affiliation:
Department of Aerospace Engineering, The University of Michigan, Ann Arbor, MI 48109–2140, USA Present address: Institute of Hydraulic Research, University of Iowa, Iowa City, IO, USA.
G. M. Faeth
Affiliation:
Department of Aerospace Engineering, The University of Michigan, Ann Arbor, MI 48109–2140, USA
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Abstract

Turbulent dispersion of particles in their self-generated homogeneous turbulent field was studied both experimentally and theoretically. Measurements involved nearly monodisperse spherical glass particles (nominal diameters of 0.5, 1.0 and 2.0 mm) falling with uniform particle number fluxes in a nearly stagnant water bath. Particle Reynolds numbers based on terminal velocities were 38, 156, and 545 for the three particle sizes. The flows were dilute with particle volume fractions less than 0.01%. Measurements included particle motion calibrations, using motion-picture shadowgraphs; and streamwise and cross-stream mean and fluctuating particle velocities, using a phase-discriminating laser velocimeter. Liquid-phase properties were known from earlier work. Particle properties were predicted based on random-walk calculations using statistical time-series methods to simulate liquid velocities along the particle path.

Calibrations showed that particle drag properties were within 14% of estimates based on the standard drag correlation for spheres, however, the particles (particularly the 1.0 and 2.0 mm diameter particles) exhibited self-induced lateral motion even in motionless liquid due to eddy-shedding and irregularities of shape. Particle velocity fluctuations were primarily a function of the rate of dissipation of kinetic energy in the liquid since this variable controls liquid velocity fluctuations. Streamwise particle velocity fluctuations were much larger than cross-stream particle velocity fluctuations (2–5:1) largely due to varying terminal velocities caused by particle size variations. Cross-stream particle and liquid velocity fluctuations were comparable owing to the combined effects of turbulent dispersion and self-induced motion. Predicted mean and fluctuating particle velocities were in reasonably good agreement with the measurements after accounting for effects of particle size variations and self-induced motion. However, the theory must be extended to treat self-induced motion and to account for observations that this motion was affected by the turbulent environment.

Type
Research Article
Information
Journal of Fluid Mechanics , Volume 220 , November 1990 , pp. 515 - 537
Copyright
© 1990 Cambridge University Press

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References

Al Taweel, A. M. & Landau, J. 1977 Turbulence modulation in two-phase jets. Intl J. Multiphase Flow 3, 341–351.Google Scholar
Anand, M. A. & Pope, S. B., 1985 Diffusion behind a line source in grid turbulence. Fourth Symposium on Turbulent Shear Flows, pp. 17.11–17.17.Google Scholar
Batchelor, G. K.: 1972 Sedimentation in a dilute dispersion of spheres. J. Fluid Mech. 52, 245–268.Google Scholar
Box, G. E. P. & Jenkins, G. M. 1976 Time Series Analysis, rev. edn. pp. 47–84. Holden Day.
Clift, R., Grace, J. R. & Weber, M. E., 1978 Bubbles, Drops and Particles, pp. 266–269, 296–302. Academic.
Crowe, C. T.: 1982 Review – numerical models for dilute gas particle flows. J. Fluids Engng 104, 297–303.Google Scholar
Csanady, G. T.: 1963 Turbulent diffusion of heavy particles in the atmosphere. J. Atmos. Sci. 20, 201–208.Google Scholar
Desjonqueres, P., Gouesbet, G., Berlemont, A. & Picart, A., 1986 Dispersion of discrete particles by continuous turbulent motions: new results and discussions. Phys. Fluids 29, 2147–2151.Google Scholar
Durbin, P. A.: 1980 A random flight model of inhomogeneous turbulent dispersion. Phys. Fluids 23, 2151–2153.Google Scholar
Faeth, G. M.: 1987 Mixing, transport and combustion in sprays. Prog. Energy Combust. Sci. 13, 293–345.Google Scholar
Ferguson, J. R. & Stock, D. E., 1986 Particle dispersion in decaying isotropic homogeneous turbulence. Gas–Solid Flows (ed. J. J. Jurewicz), pp. 9–14. ASME.
Gouesbet, G., Berlemont, A. & Picart, A., 1984 Dispersion of discrete particles by continuous turbulent motions. Extensive discussion of the Tchen's theory using a two-parameter family of Lagrangian correlation functions. Phys. Fluids 27, 827–837.Google Scholar
Katz, E. J.: 1966 Atmospheric diffusion of settling particles with sluggish response. J. Atmos. Sci. 23, 159–166.Google Scholar
Kraichnan, R. H.: 1970 Diffusion by a random velocity field. Phys. Fluids 13, 22–31.Google Scholar
Maxey, M. R.: 1987 The gravitational settling of aerosol particles in homogeneous turbulence and random flow fields. J. Fluid Mech. 174, 441–465.Google Scholar
Meek, C. C. & Jones, B. G., 1973 Studies of the behavior of heavy particles in a turbulent fluid flow. J. Atmos. Sci. 30, 239–244.Google Scholar
Nakamura, I.: 1976 Steady wake behind a sphere. Phys. Fluids 19, 5–8.Google Scholar
Nir, A. & Pismen, L. M., 1979 The effect of a steady drift on the dispersion of a particle in a turbulent fluid. J. Fluid Mech. 94, 369–381.Google Scholar
Odar, F. & Hamilton, W. S., 1964 Force on a sphere accelerating in a viscous fluid. J. Fluid Mech. 18, 302–314.Google Scholar
Parthasarathy, R. N.: 1989 Homogeneous dilute turbulent particle-laden water flows. PhD thesis, The University of Michigan.
Parthasarathy, R. N. & Faeth, G. M., 1987 Structure of particle-laden turbulent water jets in still water. Intl J. Multiphase Flow 13, 699–716.Google Scholar
Parthasarathy, R. N. & Faeth, G. M., 1900 Turbulence modulation in homogeneous dilute particle-laden flows. J. Fluid Mech. 220, 485–514.Google Scholar
Picart, A., Berlemont, A. & Gouesbet, G., 1986 Modelling and predicting turbulence fields and dispersion of discrete particles transported by turbulent flows. Intl J. Multiphase Flow 12, 237–261.Google Scholar
Pismen, L. M. & Nir, A., 1978 On the motion of suspended particles in stationary homogeneous turbulence. J. Fluid Mech. 84, 193–206.Google Scholar
Putnam, A.: 1961 Integrable form of droplet drag coefficient. Am. Rocket Soc. J. 31, 1467–1468.Google Scholar
Reeks, M. W.: 1977 On the dispersion of small particles suspended in an isotropic turbulent fluid. J. Fluid Mech. 83, 529–546.Google Scholar
Reeks, M. W.: 1980 Eulerian direct interaction applied to the statistical motion of particles in a turbulent fluid. J. Fluid Mech. 97, 569–590.Google Scholar
Sawford, B. L. & Hunt, J. C. R. 1986 Effects of turbulence structure, molecular diffusion and source size on scalar fluctuations in homogeneous turbulence. J. Fluid Mech. 165, 373–400.Google Scholar
Snyder, W. H. & Lumley, J. L., 1971 Some measurements of particle velocity auto-correlation functions in a turbulent flow. J. Fluid Mech. 48, 41–71.Google Scholar
Viets, H.: 1971 Accelerating sphere–wake interaction. AIAA J. 9, 2087–2089.Google Scholar
Wells, M. R. & Stock, D. E., 1983 The effects of crossing trajectories on the dispersion of particles in turbulent flow. J. Fluid Mech. 136, 31–62.Google Scholar
Yudine, M. I.: 1959 Physical considerations on heavy-particle diffusion. Adv. Geophys. 6, 185–191.Google Scholar