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TECHNICAL PAPERS

Direct Numerical Simulation of Flow and Heat Transfer From a Sphere in a Uniform Cross-Flow

[+] Author and Article Information
P. Bagchi, S. Balachandar

Department of Theoretical & Applied Mechanics, University of Illinois, Urbana, IL 61801-2935

M. Y. Ha

School of Mechanical Engineering, Pusan National University, South Korea

J. Fluids Eng 123(2), 347-358 (Nov 17, 2000) (12 pages) doi:10.1115/1.1358844 History: Received January 10, 2000; Revised November 17, 2000
Copyright © 2001 by ASME
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References

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Natarajan,  R., and Acrivos,  A., 1993, “The Instability of the Steady Flow Past Spheres and Disks,” J. Fluid Mech., 254, pp. 323–344.
Tomboulides, A. G., Orszag, S. A., and Karniadakis, G. E., 1993, “Direct and large-eddy simulation of axisymmetric wakes,” AIAA Paper 93-0546.
Johnson,  T. A., and Patel,  V. C., 1999, “Flow past a sphere up to a Reynolds number of 300,” J. Fluid Mech., 378, pp. 19–70.
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Bagchi, P., and Balachandar, S., 2000, “Unsteady motion and forces on a spherical particle in nonuniform flows,” Proceedings of FEDSM 2000, Boston, MA.
Sayegh,  N. N., and Gauvin,  W. H., 1999, “Numerical Analysis of Variable Property Heat Transfer to a Single Sphere in High Temperature Surroundings,” AIChE J., 25, pp. 522–534.
Ranz,  W. E., and Marshall,  W. R., 1952, “Evaporation From Drops,” Chem. Eng. Prog., 48, pp. 141—146.
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Renksizbulut,  M., and Yuen,  M. C., 1983, “Numerical Study of Droplet Evaporation in a High-Temperature Stream,” ASME J. Heat Transfer, 105, pp. 389–397.
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Yuge,  T., 1960, “Experiments on Heat Transfer From Spheres Including Combined Natural and Forced Convection,” ASME J. Heat Transfer, 82, pp. 214–220.
Chiang,  C. H., Raju,  M. S., and Sirignano,  W. A., 1992, “Numerical Analysis of Convecting, Vaporizing Fuel Droplet With Variable Properties,'Numerical Analysis of Convecting, Vaporizing Fuel Droplet With Variable Properties,'’ Int. J. Heat Mass Transf., 35, No. 5, pp. 1307–1324.
Xin,  J., and Megaridis,  C. M., 1996, “Effects of Rotating Gaseous Flows on Transient Droplet Dynamics and Heating,” Int. J. Heat Fluid Flow, 17, pp. 52–62.
Dandy,  D. S., and Dewyer,  H. A., 1990, “A Sphere in Shear Flow at Finite Reynolds Number: Effect of Shear on Particle Lift, Drag, and Heat Transfer,” J. Fluid Mech., 216, pp. 381–410.
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Figures

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Axisymmetric flow at Re=200. (a) Streamlines; (b) azimuthal vorticity (ωϕ) contours at an interval of 0.5; dashed lines indicate negative values; (c) dimensionless temperature at an interval of 0.1.
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Variation of Nusselt number for axisymmetric flow over the sphere: ——, Re=50; – – –, Re=100, —⋅—⋅—, Re=200.
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Contours of Nusselt number on the sphere surface for Re=200.
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Contours of azimuthal vorticity (ωϕ) (left panel) and dimensionless temperature (right panel) at Re=250. ωϕ contours are plotted at an interval of 0.5 while temperature contours are plotted at an interval of 0.1. Dashed lines indicate negative values. (a) Results from axisymmetric simulation; (b) results from 3-D simulation.
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Variation of Nusselt number for Re=250. ——, Nu obtained from axisymmetric simulation. Nu obtained from 3-D simulations are shown at three different ϕ locations: – – –, ϕ=0; —⋅—⋅—, ϕ=π; [[dotted_line]], ϕ=π/2. The thick line represents ϕ-averaged Nusselt number 〈Nu〉 obtained from 3-D simulation.
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Contours of local Nusselt number on the surface of the sphere for Re=250. (a) Results from axisymmetric simulation; (b) results from 3-D simulation.
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Contours of azimuthal vorticity (ωϕ) (left panel) and dimensionless temperature (right panel) at Re=350. ωϕ contours are plotted at an interval of 0.5 while temperature contours are plotted at an interval of 0.1. Dashed lines indicate negative values. (a) Results from axisymmetric simulation. Results of 3-D simulation are presented in (b), (c), (d), and (e) at four different time instants approximately at equal interval in a shedding cycle.
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Variation of Nusselt number for Re=350. (a), (b), (c), and (d) represent four different time instants in the shedding cycle corresponding to Fig. 7. ——, Nu obtained from axisymmetric simulation. Local Nu obtained from 3-D simulations are shown at three different ϕ locations: – – –, ϕ=0; —⋅—⋅—, ϕ=π; [[dotted_line]], ϕ=π/2. The thick line represents ϕ-averaged Nusselt number 〈Nu〉 obtained from 3-D simulation.
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Contours of Nusselt number on the surface of the sphere for Re=350 from the 3D simulations. Four different time instants are shown and they are the same as in Figs. 7 and 8.
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Instantaneous pathlines for Reynolds number (a) 250 and (b) 350. Figures in the left panel show the pathlines that originate on two sides of the x-y plane. In the right panel, the x-y view, two particle paths coincide.
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Time evolution of drag and lift coefficients and surface-averaged Nusselt number Nu for Re=350. (a) Vertical axis on the left is for CD and that on the right is for CL. ——, CD obtained from 3-D simulation; – – –, mean (time-averaged) drag coefficient; —⋅—⋅—, CD obtained from axisymmetric simulation; [[dotted_line]], CL obtained from 3-D simulation; – – –, mean (time-averaged) lift coefficient. (b) ——, Nu obtained from 3-D simulation; – – –, mean (time-averaged) Nu; —⋅—⋅—, Nu obtained from axisymmetric simulation.
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ϕ-averaged surface pressure coefficient 〈CP〉 for (a) Re=350 and (b) Re=500. Dashed line is the result from axisymmetric simulations and solid line is the result from 3-D simulations.
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Same as Fig. 7 but for Re=500. Time instants for the unsteady simulations (b, c, d and e) are at approximately equal interval in a shedding cycle.
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Variation of Nusselt number for Re=500 at four different time instants: a, b, c and d represent same time instants as in Fig. 13 corresponding to the unsteady simulation. Symbols used here are same as in Fig. 8.
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Same as Fig. 9 but for Re=500. Results from 3D simulations are shown at four different time instants that are same as in Fig. 14.
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Same as Fig. 11 but for Re=500
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Comparison of computational CD and Nu with experimental correlations. Symbols are computational results ranging from Re=50–500. Correlation for drag is from Clift et al. 1 and the Nu correlation is from Ranz and Marshall 11.
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The mean (time-averaged) lift coefficient versus Reynolds number for flow past a sphere. • symbols are the results from present simulations. ⋄ symbols correspond to simulation results of Johnson and Patel 6.

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