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TECHNICAL PAPERS

Numerical Simulations of Flows Inside a Partially Filled Centrifuge

[+] Author and Article Information
Fang Yan, Bakhtier Farouk

Department of Mechanical Engineering, Drexel University, Philadelphia, PA 19104

J. Fluids Eng 125(6), 1033-1042 (Jan 12, 2004) (10 pages) doi:10.1115/1.1627832 History: Received March 20, 2002; Revised July 03, 2003; Online January 12, 2004
Copyright © 2003 by ASME
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References

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Benton,  E. R., and Clark,  A., 1974, “Spin-up,” Annu. Rev. Fluid Mech., 6, pp. 259–280.
Duck,  P., and Foster,  M., 2001, “Spin-up of Homogeneous and Stratified Fluids,” Annu. Rev. Fluid Mech., 33, pp. 231–263.
Wedemeyer,  E. H., 1964, “The Unsteady Flow Within a Spinning Cylinder,” J. Fluid Mech., 20, pp. 383–399.
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Kitchens,  C. W., 1980, “Navier-Stokes Equations for Spin-up in a Filled Cylinder,” AIAA J., 18, pp. 929–934.
Hyun,  J. M., Leslie,  F., Fowlis,  W. W., and Warn-Varnas,  A., 1983, “Numerical Solutions for Spin-up From Rest in a Cylinder,” J. Fluid Mech., 127, pp. 263–281.
Watkins,  W. B., and Hussey,  R. G., 1977, “Spin-up From Rest in a Cylinder,” Phys. Fluids, 20, pp. 1596–1604.
Goller,  H., and Ranov,  T., 1968, “Unsteady Rotating Flow in a Cylinder With a Free Surface,” ASME J. Basic Eng., 90, pp. 445–454.
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Homicz,  G. F., and Gerber,  N., 1987, “Numerical Model for Fluid Spin-up From Rest in a Partially Filled Cylinder,” ASME J. Fluids Eng., 109, pp. 194–197.
Choi,  S., Kim,  J. W., and Hyun,  J. M., 1989, “Transient Free Surface Shape in an Abruptly Rotating, Partially Filled Cylinder,” ASME J. Fluids Eng., 111, pp. 439–443.
Choi,  S., Kim,  J. W., and Hyun,  J. M., 1991, “Experimental Investigation of the Flow With a Free Surface in an Impulsively Rotating Cylinder,” ASME J. Fluids Eng., 113, pp. 245–249.
Shadday,  M. A., Ribando,  R. J., and Kauzlarich,  J. J., 1983, “Flow of an Incompressible Fluid in a Partially Filled, Rapidly Rotating Cylinder With a Differentially Rotating Endcap,” J. Fluid Mech., 130, pp. 203–218.
Wang,  C. Y., and Cheng,  P., 1996, “A Multiphase Mixture Model for Multiphase, Multicomponent Transport in Capillary Porous Media—I. Model Development,” Int. J. Heat Mass Transfer, 39, pp. 3607–3618.
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Figures

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(a) Schematic diagram of the spinup problem, (b) schematic diagram of the “overrotating” lid problem
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Comparison of the transient free-surface shapes for the spinup case, –, experimental data; [[dashed_line]], numerical results
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Comparison of the predicted steady free-surface shape with analytic solution
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The effect of mesh sizes on the numerical results at nondimensional time, Ωt=400; (a) development of free surface, (b) radial velocity along the r direction at section z=0.25 mm
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The effect of time-step sizes on the numerical results at instant Ωt=400
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(a) Streamlines at time Ωt=200 for the spinup case; (b) details of streamlines near the bottom end at time Ωt=200 for the spinup case
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Streamlines at time Ωt=400 for the spinup case
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The effect of mesh size on axial velocity profile at z/H=0.438 in the liquid region for the “overrotating” lid case (the origin of the horizontal axis indicates the free surface)
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Nonuniform grid generated for the overrotating case
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Streamlines in the liquid region for the overrotating case (the vertical left side indicates the free surface) (the stream function values along each stream lines in the figure are equally distributed between 1×10−6 and 6×10−6)
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(a) Streamlines in the gas region for the overrotating case (the dashed line on the right indicates the free surface); (b) details of streamlines near the top end in the air flow region for the overrotating case (the dashed line on the right indicates the free surface)
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Computed radial profiles of (a) axial (b) and relative azimuthal velocity at z/H=0.438 in the liquid region for the overrotating case
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Computed radial profiles of (a) axial and relative azimuthal velocity at z/H=0.83 in the liquid region for the overrotating case
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Computed radial profiles of (a) axial and (b) relative azimuthal velocity at z/H=0.438 in gas and liquid phases for the overrotating case (the dashed line indicates the free surface)
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Computed radial profiles of axial (a) and azimuthal (b) velocity at z/H=0.83 in gas and liquid phases for the overrotating case (the dashed line indicates the free surface)

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