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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

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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