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Settling velocity and concentration distribution of heavy particles in homogeneous isotropic turbulence

  • Lian-Ping Wang (a1) (a2) and Martin R. Maxey (a1)

The average settling velocity in homogeneous turbulence of a small rigid spherical particle, subject to a Stokes drag force, has been shown to differ from that in still fluid owing to a bias from the particle inertia (Maxey 1987). Previous numerical results for particles in a random flow field, where the flow dynamics were not considered, showed an increase in the average settling velocity. Direct numerical simulations of the motion of heavy particles in isotropic homogeneous turbulence have been performed where the flow dynamics are included. These show that a significant increase in the average settling velocity can occur for particles with inertial response time and still-fluid terminal velocity comparable to the Kolmogorov scales of the turbulence. This increase may be as much as 50% of the terminal velocity, which is much larger than was previously found. The concentration field of the heavy particles, obtained from direct numerical simulations, shows the importance of the inertial bias with particles tending to collect in elongated sheets on the peripheries of local vortical structures. This is coupled then to a preferential sweeping of the particles in downward moving fluid. Again the importance of Kolmogorov scaling to these processes is demonstrated. Finally, some consideration is given to larger particles that are subject to a nonlinear drag force where it is found that the nonlinearity reduces the net increase in settling velocity.

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Auton, T. R., Hunt, J. C. R. & Prud’Homme, M. 1988 The force exerted on a body in inviscid unsteady nonuniform rotational flow. J. Fluid Mech. 197, 241257.

Balachandar, S. & Maxey, M. R.1989Methods for evaluating fluid velocities in spectral simulations of turbulence. J. Comput. Phys.83, 96125.

Chung, J. N. & Troutt, T. R. 1988 Simulations of particle dispersion in an axisymmetric jet. J. Fluid Mech. 186, 199222.

Comte-Bellot, G. & Corrsin, S. 1971 Simple Eulerian time correlation of full- and narrow-band velocity signals in grid-generated, ‘isotropic’ turbulence. J. Fluid Mech. 48, 273337.

Crowe, C. T., Gore, R. & Troutt, T. R.1985Particle dispersion by coherent structures in free shear flows. Particulate Sci. Tech.3, 149158.

Csanady, G. T.1963Turbulent diffusion of heavy particles in the atmosphere. J. Atmos. Sci.20, 201208.

Davis, R. H. & Acrivos, A.1985Sedimentation of noncolloidal particles at low Reynolds numbers. Ann. Rev. Fluid Mech.17, 91118.

Eswaran, E. & Pope, S. B.1988An examination of forcing in direct numerical simulations of turbulence. Comput. Fluids16, 257278.

Fung, J. C. H., Hunt, J. C. R., Malik, N. A. & Perkins, R. J. 1992 Kinematic simulation of homogeneous turbulence by unsteady random Fourier modes. J. Fluid. Mech. 236, 281318.

Hwang, P. A.1985Fall velocity of particles in oscillating flow. J. Hydraul. Engng ASCE111 (3), 485502.

Lázaro, B. J. & Lasheras, J. C.1992Particle dispersion in the developing free shear layer. Part 2. Forced flow. J. Fluid Mech.235, 179221.

Longmire, E. K. & Eaton, J. K. 1992 Structure of a particle-laden round jet. J. Fluid Mech. 236, 217257.

Maxey, M. R. & Corrsin, S.1986Gravitational settling of aerosol particles in randomly oriented cellular flow fields. J. Atmos. Sci.43, 11121134.

Maxey, M. R. & Riley, J. J.1983Equation of motion for a small rigid sphere in a nonuniform flow. Phys. Fluids26, 883889.

Meek, C. C. & Jones, B. G.1973Studies of the behavior of heavy particles in a turbulent fluid flow. J. Atmos. Sci.30, 239244.

Mei, R., Adrian, R. J. & Hanratty, T. J. 1991 Particle dispersion in isotropic turbulence under Stokes drag and Basset force with gravitational settling. J. Fluid Mech. 225, 481495.

Nir, A. & Pismen, L. M. 1979 The effect of a steady drift on the dispersion of a particle in turbulent fluid. J. Fluid Mech. 94, 369381.

Odar, F. & Hamilton, W. S. 1964 Forces on a sphere accelerating in a viscous fluid. J. Fluid Mech. 18, 302314.

Reeks, M. W. 1977 On the dispersion of small particles suspended in an isotropic turbulent fluid. J. Fluid Mech. 83, 529546.

Riley, J. J. & Paterson, G. S.1974Diffusion experiments with numerically integrated isotropic turbulence. Phys. Fluids17, 292287.

Schöneborn, P.-R.1975The particle interaction between a single particle and an oscillating fluid. Intl J. Multiphase Flow2, 307317.

She, Z.-S., Jackson, E. & Orszag, S. A.1990Intermittent vortex structures in homogeneous turbulence. Nature344, 226.

Squires, K. D. & Eaton, J. K. 1991a Measurements of particle dispersion from direct numerical simulations of isotropic turbulence. J. Fluid Mech. 226, 135.

Tunstall, E. B. & Houghton, G.1968Retardation of falling spheres by hydraulic oscillations. Chem. Engng Sci.23, 10671081.

Wang, L.-P. & Stock, D. E.1993On the dispersion of heavy particles by turbulent motion. J. Atmos. Sci.50, 18971913.

Yeung, P. K. & Pope, S. B. 1989 Lagrangian statistics from direct numerical simulations of isotropic turbulence. J. Fluid Mech. 207, 531586.

Yudine, M. I.1959Physical considerations on heavy-particle dispersion. Adv. Geophys.6, 185191.

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Journal of Fluid Mechanics
  • ISSN: 0022-1120
  • EISSN: 1469-7645
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