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

Published online by Cambridge University Press:  26 April 2006

Lian-Ping Wang  and
Martin R. Maxey
Lian-Ping Wang
Affiliation:
Center for Fluid Mechanics, Turbulence, and Computation, Box 1966, Brown University, Providence, RI 02912, USA Present address: Department of Mechanical Engineering, Pennsylvania State University, University Park, PA 16802, USA.
Martin R. Maxey
Affiliation:
Center for Fluid Mechanics, Turbulence, and Computation, Box 1966, Brown University, Providence, RI 02912, USA
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Abstract

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.

Type
Research Article
Information
Journal of Fluid Mechanics , Volume 256 , November 1993 , pp. 27 - 68
Copyright
© 1993 Cambridge University Press

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References

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, 241–257.Google Scholar
Balachandar, S. & Maxey, M. R. 1989 Methods for evaluating fluid velocities in spectral simulations of turbulence. J. Comput. Phys. 83, 96–125.Google Scholar
Bendat, J. S. & Piersol, A. G. 1971 Random Data: Analysis and Measurement Procedures. Wiley-Interscience.
Brasseur, J. G. & Lin, W.-Q. 1991 Structure and statistics of intermittency in homogeneous turbulent shear flow. Advances in Turbulence 3, pp. 3–12. Springer.
Chang, E. J. 1992 Accelerated motion of rigid spheres in unsteady flows at low to moderate Reynolds numbers. Ph.D. thesis, Brown University, Providence.
Chung, J. N. & Troutt, T. R. 1988 Simulations of particle dispersion in an axisymmetric jet. J. Fluid Mech. 186, 199–222.Google Scholar
Clift, R., Grace, J. R. & Weber, M. E. 1978 Bubble, Drops, and Particles. Academic Press.
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, 273–337.Google Scholar
Crowe, C. T., Gore, R. & Troutt, T. R. 1985 Particle dispersion by coherent structures in free shear flows. Particulate Sci. Tech. 3, 149–158.Google Scholar
Csanady, G. T. 1963 Turbulent diffusion of heavy particles in the atmosphere. J. Atmos. Sci. 20, 201–208.Google Scholar
Davis, R. H. & Acrivos, A. 1985 Sedimentation of noncolloidal particles at low Reynolds numbers. Ann. Rev. Fluid Mech. 17, 91–118.Google Scholar
Domaradzki, J. A. 1992 Nonlocal triad interactions and the dissipation range of isotropic turbulence. Phys. Fluids A 4, 2037–2045.Google Scholar
Eswaran, E. & Pope, S. B. 1988 An examination of forcing in direct numerical simulations of turbulence. Comput. Fluids 16, 257–278.Google Scholar
Fung, J. C. H. 1990 Kinematic simulation of turbulent flow and particle motions. PhD dissertation, University of Cambridge.
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, 281–318.Google Scholar
George, W. K. 1992 The decay of homogeneous isotropic turbulence. Phys. Fluids A 4, 1492–1509.Google Scholar
Hinze, J. O. 1975 Turbulence. McGraw-Hill.
Hunt, J. C. R., Buell, J. C. & Wray, A. A. 1987 Big whorls carry little whorls. Proc. 1987 Summer Program, Rep. CTR-S87, Stanford University, California.
Hwang, P. A. 1985 Fall velocity of particles in oscillating flow. J. Hydraul. Engng ASCE 111 (3), 485–502.Google Scholar
Lázaro, B. J. & Lasheras, J. C. 1992 Particle dispersion in the developing free shear layer. Part 2. Forced flow. J. Fluid Mech. 235, 179–221.Google Scholar
Longmire, E. K. & Eaton, J. K. 1992 Structure of a particle-laden round jet. J. Fluid Mech. 236, 217–257.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
Maxey, M. R. & Corrsin, S. 1986 Gravitational settling of aerosol particles in randomly oriented cellular flow fields. J. Atmos. Sci. 43, 1112–1134.Google Scholar
Maxey, M. R. & Riley, J. J. 1983 Equation of motion for a small rigid sphere in a nonuniform flow. Phys. Fluids 26, 883–889.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
Mei, R. 1990 Particle dispersion in isotropic turbulence and unsteady particle dynamics at finite Reynolds number. PhD thesis, University of Illinois at Urbana-Champaign, Urbana, Illinois.
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, 481–495.Google Scholar
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, 369–381.Google Scholar
Odar, F. & Hamilton, W. S. 1964 Forces on a sphere accelerating in a viscous fluid. J. Fluid Mech. 18, 302–314.Google Scholar
Pruppacher, H. R. & Klett, J. D. 1978 Microphysics of Clouds and Precipitation, pp. 464–541. Dordrecht: The Netherlands.
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
Riley, J. J. & Paterson, G. S. 1974 Diffusion experiments with numerically integrated isotropic turbulence. Phys. Fluids 17, 292–287.Google Scholar
Rivero, M. 1991 A numerical investigation of the forces exerted on a spherical body by an accelerated flow. PhD thesis, Institut National Polytechnique de Toulouse.
Ruetsch, G. R. & Maxey, M. R. 1991 Small-scale features of vorticity and passive scalar fields in homogeneous isotropic turbulence. Phys. Fluids A 3, 1587–1597.Google Scholar
Ruetsch, G. R. & Maxey, M. R. 1992 The evolution of small-scale structures in homogeneous isotropic turbulence. Phys. Fluids A 4, 2747–2760.Google Scholar
Schöneborn, P.-R. 1975 The particle interaction between a single particle and an oscillating fluid. Intl J. Multiphase Flow 2, 307–317.Google Scholar
She, Z.-S., Jackson, E. & Orszag, S. A. 1990 Intermittent vortex structures in homogeneous turbulence. Nature 344, 226.Google Scholar
Snyder, W. H. & Lumley, J. L. 1971 Some measurements of particle velocity autocorrelation functions in a turbulent flow. J. Fluid Mech. 48, 41–71.Google Scholar
Squires, K. D. & Eaton, J. K. 1991a Measurements of particle dispersion from direct numerical simulations of isotropic turbulence. J. Fluid Mech. 226, 1–35.Google Scholar
Squires, K. D. & Eaton, J. K. 1991b Preferential concentration of particles by turbulence. Phys. Fluids A 3, 1169–1178.Google Scholar
Stewart, R. W. & Townsend, A. A. 1951 Similarity and self-preservation in isotropic turbulence. Phil. Trans. R. Soc. Lond. 243 A, 359.Google Scholar
Tunstall, E. B. & Houghton, G. 1968 Retardation of falling spheres by hydraulic oscillations. Chem. Engng Sci. 23, 1067–1081.Google Scholar
Van Atta, C. W. & Antonia, R. A. 1980 Reynolds number dependence of skewness and flatness factors of turbulent velocity derivatives. Phys. Fluids A 23, 252–257.Google Scholar
Wang, L.-P., Maxey, M. R., Burton, T. D. & Stock, D. E. 1992 Chaotic dynamics of particle dispersion in fluids. Phys. Fluids A 4, 1789–1804.Google Scholar
Wang, L.-P. & Stock, D. E. 1993 On the dispersion of heavy particles by turbulent motion. J. Atmos. Sci. 50, 1897–1913.Google Scholar
Wells, M. R. & Stock, D. E. 1983 The effects of crossing trajectories on the dispersion of particles in a turbulent flow. J. Fluid Mech. 136, 31–62.Google Scholar
Yeh, F. & Lei, U. 1991 On the motion of small particles in a homogeneous isotropic turbulent flow. Phys. Fluids A 3, 2571–2586.Google Scholar
Yeung, P. K. & Pope, S. B. 1989 Lagrangian statistics from direct numerical simulations of isotropic turbulence. J. Fluid Mech. 207, 531–586.Google Scholar
Yudine, M. I. 1959 Physical considerations on heavy-particle dispersion. Adv. Geophys. 6, 185–191.Google Scholar