Drag Coefficients of Viscous Spheres at Intermediate and High Reynolds Numbers

[+] Author and Article Information
Zhi-Gang Feng, Efstathios E. Michaelides

School of Engineering and Center for Bioenvironmental Research, Tulane University, New Orleans, LA 70118

J. Fluids Eng 123(4), 841-849 (May 20, 2001) (9 pages) doi:10.1115/1.1412458 History: Received October 05, 2000; Revised May 20, 2001
Copyright © 2001 by ASME
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Lovalenti,  P. M., and Brady,  J. F., 1995, “Force on a Body in Response to an Abrupt Change in Velocity at Small but Finite Reynolds Number,” J. Fluid Mech., 293, pp. 35–46.
Mei,  R., Lawrence,  C. J., and Adrian,  R. J., 1991, “Unsteady Drag on a Sphere at Finite Reynolds Number with Small Fluctuations in the Free-Stream Velocity,” J. Fluid Mech., 233, pp. 613–631.
Mei,  R., and Adrian,  R. J., 1992, “Flow past a Sphere with an Oscillation in the Free-Stream and unsteady Drag at Finite Reynolds Number,” J. Fluid Mech., 237, pp. 323–341.
Feng, Z.-G., 1996, “Heat Transfer from Small Particles at Low Reynolds Numbers,” Sc. D. Dissertation, Tulane Univ.
Feng,  Z. G., and Michaelides,  E. E., 1998, “Transient Heat Transfer from a Particle with Arbitrary Shape and Motion,” ASME J. Heat Transfer, 120, pp. 674–681.
Michaelides,  E. E., and Feng,  Z.-G., 1995, “The Equation of Motion of a Small Viscous Sphere in an Unsteady Flow with Interface Slip,” Int. J. Multiphase Flow, 21, pp. 315–321.
Sirignano, W. A., 1999, Fluid Dynamics and Transport of Droplets and Sprays, Cambridge Univ. Press, Cambridge.
Leal, L. G., 1992, Laminar Flow and Convective Transport Processes, Butterworth-Heineman, Boston.
Kim, S., and Karrila, S. J., 1991, Microhydrodynamics: Principles and Selected Applications, Butterworth-Heineman, Boston.
Clift, R., Grace, J. R., and Weber, M. E., 1978, Bubbles, Drops and Particles, Academic Press, New York.
Happel,  J., and Moore,  D. W., 1968, “The motion of a spherical liquid drop at high Reynolds number,” J. Fluid Mech., 32, part 2, pp. 367–391.
Le Clair,  B. P., and Hamielec,  A. E., 1972, “A theoretical and experimental study of the internal circulation in water drops falling at terminal velocity in air,” J. Atmos. Sci., 29, No. 2, pp. 728–740.
Rivkind,  V. Y., Ryskin,  G. M., and Fishbein,  G. A., 1976, “Flow around a spherical drop in a fluid medium at intermediate Reynolds numbers,” Appl. Math. Mech., 40, pp. 687–691.
Oliver,  D. L., and Chung,  J. N., 1987, “Flow about a fluid sphere at low to moderate Reynolds numbers,” J. Fluid Mech., 177, pp. 1–18.
El-Shaarawi,  M. A. I., Al-Farayedhi,  A., and Antar,  M. A., 1997, “Boundary layer flow about and inside a liquid sphere,” ASME J. Fluids Eng., 119, pp. 42–49.
Briley,  W. R., 1971, “A numerical study of laminar separation bubbles using the Navier-Stokes equations,” J. Fluid Mech., 47, pp. 713–736.
Rivkind,  V. Y., and Ryskin,  G. M., 1976, “Flow structure in motion of a spherical drop at intermediate Reynolds numbers,” Translated from Russian, Fluid Mechanics, 11, No. 1, pp. 5–12.
Elzinga,  E. R., and Banchero,  J. T., 1961, “Some Observations on the Mechanics of Drops in Liquid-Liquid Systems,” AIChE J., 7, No. 3, pp. 394–399.
Brabston,  D. C., and Keller,  H. B., 1975, “Viscous flows past spherical gas bubbles,” J. Fluid Mech., 69, No. 1, pp. 179–189.
Winnikow,  S., and Chao,  B. T., 1966, “Droplet Motion in Purified Systems,” Phys. Fluids, 9, pp. 50–61.
Harper,  J. F., 1972, “The Motion of Bubbles and Drops through Liquids,” Adv. Appl. Mech., 12, pp. 59–129.


Grahic Jump Location
Schematic diagram of the viscous sphere translating in a fluid.
Grahic Jump Location
(a) Streamlines and vorticity field for λ=7 and Re=10; (b) streamlines and vorticity field for λ=7 and Re=100; (c) streamlines and vorticity field for λ=7 and Re=500.
Grahic Jump Location
The vorticity field for Re=500,λ=0.1, with mesh size 120×40 for the internal and 120×180 for the external flow field. The upper half shows the results from the conventional method and the lower half from the method presented here.
Grahic Jump Location
Drag coefficients for the whole range of λ in terms of log(Re)
Grahic Jump Location
The effect of the computational grid used on the vorticity field developed at Re=500: (a) Conventional method, (b) 40 internal grid points, (c) 120 internal grid points




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