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A sphere in shear flow at finite Reynolds number: effect of shear on particle lift, drag, and heat transfer

Published online by Cambridge University Press:  26 April 2006

David S. Dandy  and
Harry A. Dwyer
David S. Dandy
Affiliation:
Combusion Research Facility, Sandia National Laboratories, Livermore, CA 94551. USA
Harry A. Dwyer
Affiliation:
Department of Mechanical Engineering, University of California, Davis. CA 95616, USA
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Abstract

Three-dimensional numerical solutions have been obtained for steady, linear shear flow past a fixed, heated spherical particle over a wide range of Reynolds number (0.1 [les ] R [les ] 100) and dimensionless shear rates (0.005 [les ] α [les ] 0.4). The results indicate that at a fixed shear rate, the dimensionless lift coefficient is approximately constant over a wide range of intermediate Reynolds numbers, and the drag coefficient also remains constant when normalized by the known values of drag for a sphere in uniform flow. At lower values of the Reynolds number, the lift and drag coefficients increase sharply with decreasing R, with the lift coefficient being directly proportional to R−½. For the range of shear rates studied here, the rate of heat transfer to the particle surface was found to depend only on the Reynolds number, that is, it was insensitive to the shear rate. The dimensionless rate of heat transfer, the Nussel number Nu, was seen to increase monotonically with R.

Type
Research Article
Information
Journal of Fluid Mechanics , Volume 216 , July 1990 , pp. 381 - 410
Copyright
© 1990 Cambridge University Press

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References

Acrivos, A. & Taylor, T. D. 1962 Heat and mass transfer from single spheres in Stokes flow. Phys. Fluids 5, 387–394.Google Scholar
Beard, K. V. & Pruppacher, H. R. 1971 A wind tunnel investigation of the rate of evaporation of small water drops falling at terminal velocity in air. J. Atmos. Sci. 28, 1455–1464.Google Scholar
Brabston, D. C. & Keller, H. B. 1975 Viscous flows past spherical gas bubbles. J. Fluid Mech. 69, 179–189.Google Scholar
Bretherton, F. P. 1962 The motion of rigid particles in a shear flow at low Reynolds number. J. Fluid Mech. 14, 284–304.Google Scholar
Brignell, A. S. 1973 The deformation of a liquid drop at small Reynolds number. Q. J. Mech. Appl. Maths 26, 99–107.Google Scholar
Brown, S. N. & Stewartson, K. 1969 Laminar separation. Ann. Rev. Fluid Mech. 1, 45–72.Google Scholar
Chorin, A. J. 1967 A numerical method for solving incompressible viscous flow problems. J. Comput. Phys. 2, 12–26.Google Scholar
Chorin, A. J. 1968 Numerical solution of incompressible flow problems. Studies in Numerical Analysis 2, pp. 64–70. Philadelphia: SIAM.
Christov, C. I. & Volkov, P. K. 1985 Numerical investigation of the steady viscous flow past a stationary deformable bubble. J. Fluid Mech. 158, 341–364.Google Scholar
Chuchottaworn, T. 1984 Numerical analysis of heat and mass transfer from a sphere with surface mass injection or suction. J. Chem. Engng Japan 17, 1–7.Google Scholar
Clift, R., Grace, J. R. & Weber, M. E. 1978 Bubbles, Drops, and Particles. Academic.
Cox, R. G. & Brenner, H. 1968 The lateral migration of solid particles in Poiseuille flow—I. Theory. Chem. Engng Sci. 23, 147–173.Google Scholar
Dandy, D. S. & Leal, L. G. 1989 Buoyancy-driven motion of a deformable drop through a quiescent liquid at intermediate Reynolds numbers. J. Fluid Mech. 208, 161–192.Google Scholar
Dwyer, H. A. 1989 Calculations of droplet dynamics in high temperature environments. Prog. Energy Combust. Sci. 15, 131–158.Google Scholar
Fornberg, B. 1988 Steady viscous flow past a sphere at high Reynolds numbers. J. Fluid Mech. 190, 471–489.Google Scholar
Harper, J. F. 1972 The motion of bubbles and drops through liquids. Adv. Appl. Mech. 12, 59–129.Google Scholar
Harper, J. F. & Moore, D. W. 1968 The motion of a spherical liquid drop at high Reynolds number. J. Fluid Mech. 32, 367–391.Google Scholar
Ho, B. P. & Leal, L. G. 1974 Intertial migration of rigid spheres in two-dimensional unidirectional flows. J. Fluid Mech. 65, 365–400.Google Scholar
LeClair, B. P., Hamielec, A. E., Pruppacher, H. R. & Hall, W. D. 1972 A theoretical and experimental study of the internal circulation in water drops falling at terminal velocity in air. J. Atmos. Sci. 29, 728–740.Google Scholar
Masliyah, J. H. 1970 Symmetric flow past orthotropic bodies: single and clusters. Ph.D. thesis, University of British Columbia, Vancouver.
Moore, D. W. 1959 The rise of a gas bubble in a viscous liquid. J. Fluid Mech. 6, 113–130.Google Scholar
Moore, D. W. 1963 The boundary layer on a spherical gas bubble. J. Fluid Mech. 16, 161–176.Google Scholar
Moore, D. W. 1965 The velocity of rise of distorted gas bubbles in a liquid of small viscosity. J. Fluid Mech. 23, 749–766.Google Scholar
Oliver, D. L. R. & Chung, J. N. 1987 Flow about a fluid sphere at low to moderate Reynolds numbers. J. Fluid Mech. 177, 1–18.Google Scholar
O'Neill, M. E. 1968 A sphere in contact with a plane wall in a slow linear shear flow. Chem. Engng Sci. 23, 1293–1298.Google Scholar
Peacemann, D. W. & Rachford, H. H. 1955 The numerical solution of parabolic and elliptic differential equations. J. Soc. Indust. Appl. Maths 3, 28–41.Google Scholar
Proudman, I. & Pearson, J. R. A. 1957 Expansions at small Reynolds numbers for the flow past a sphere and a circular cylinder. J. Fluid Mech. 2, 237–262.Google Scholar
Ranz, W. E. & Marshall, W. R. 1952a Evaporation from drops: Part I. Chem. Engng Prog. 48, 141–146.Google Scholar
Ranz, W. E. & Marshall, W. R. 1952b Evaporation from drops: Part II. Chem. Engng Prog. 48, 173–180.Google Scholar
Rimmer, P. L. 1968 Heat transfer from a sphere in a stream of small Reynolds number. J. Fluid Mech. 32, 1–19.Google Scholar
Rimon, Y. & Cheng, S. I. 1969 Numerical solution of a uniform flow over a sphere at intermediate Reynolds numbers. Phys. Fluids 12, 949–959.Google Scholar
Rivkind, V. Y. & Ryskin, G. 1976 Flow structure in motion of a spherical drop in a fluid medium at intermediate Reynolds numbers. Fluid Dyn. 11, 5–12.Google Scholar
Roache, P. J. 1972 Computational Fluid Dynamics. Albuquerque: Hermosa.
Rubinow, S. I. & Keller, J. B. 1961 The transverse force on a spinning sphere moving in a viscous fluid. J. Fluid Mech. 11, 447–459.Google Scholar
Ryskin, G. & Leal, L. G. 1984a Large deformations of a bubble in axisymmetric steady flows. Part 1. Numerical techniques. J. Fluid Mech. 148, 1–17.Google Scholar
Ryskin, G. & Leal, L. G. 1984b Large deformations of a bubble in axisymmetric steady flows. Part 2. The rising bubble. J. Fluid Mech. 148, 19–35.Google Scholar
Saffman, P. G. 1965 The lift on a small sphere in a slow shear flow. J. Fluid Mech. 22, 385–400, and Corrigendum. J. Fluid Mech. 31 (1968), 624.Google Scholar
Sayegh, N. N. & Gauvin, W. H. 1979 Numerical analysis of variable property heat transfer to a single sphere in high-temperature surroundings. AIChE J. 25, 522–534.Google Scholar
Schonberg, J. A., Drew, D. A. & Belfort, G. 1986 Viscous interactions of many neutrally buoyant spheres in Poiseuille flow. J. Fluid Mech. 167, 415–426.Google Scholar
Schonberg, J. A. & Hinch, E. J. 1989 Inertial migration of a sphere in Poiseuille flow. J. Fluid Mech. 203, 517–524.Google Scholar
Taneda, S. 1956 Experimental investigation of the wake behind a sphere at low Reynolds numbers. J. Phys. Soc. Japan 11, 1104–1108.Google Scholar
Taylor, T. D. & Acrivos, A. 1964 On the deformation and drag of a falling viscous drop at low Reynolds number. J. Fluid Mech. 18, 466–476.Google Scholar
Whitaker, S. 1972 Forced convection heat transfer correlations for flow in pipes, past flat plates, single cylinders, single spheres, and for flow in packed beds and tube bundles. AIChE J. 18, 361–371.Google Scholar
White, B. R., Greeley, R., Iversen, J. D. & Pollack, J. B. 1976 Estimated grain saltation in a Martian atmosphere. J. Geophys. Res. 81, 5643–5650.Google Scholar
Williams, J. C. 1977 Incompressible boundary-layer separation. Ann. Rev. Fluid Mech. 9, 113–144.Google Scholar
Woo, S.-W. 1971 Simultaneous free and forced convection around submerged cylinders and spheres. Ph.D. thesis, McMaster University, Hamilton, Ontario.
Woo, S. E. & Hamielec, A. E. 1971 A numerical method of determining the rate of evaporation of small water drops falling at terminal velocity in air. J. Atmos. Sci. 28, 1448–1454.Google Scholar