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A Numerical Study of Viscous Flow Past a Thin Oblate Spheroid at Low and Intermediate Reynolds Numbers

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  • 1 Dept. of Meteorology, University of California, Los Angeles 90024
  • | 2 Dept. of Chemical Engineering, McMaster University, Hamilton, Ontario, Canada
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Abstract

The flow past a thin oblate spheroid falling at terminal velocity in an infinite, viscous fluid was investigated using a numerical solution of the steady-state Navier-Stokes equations of motion. The detailed streamfunction and vorticity yielded the drag, pressure distribution, and the extent of the spheroid's downstream wake. Calculations were performed for spheroids of axis ratios 0.05 and 0.2 and Reynolds numbers between 0.1 and 100. The results were compared with other numerical and analytical solutions to the Navier Stokes equations of motion for viscous flow past oblate spheroids and disks and with experimental results in the literature. Our numerical results for oblate spheroids of axis ratio 0.2 agree well with the numerical results of Masliyah and Epstein and with our own experimental results. Our results for oblate spheroids of axis ratio 0.05 agree well with the numerical computations of Michael and available experimental results on disks, but depart significantly from the numerical results of Rimon. In agreement with our earlier studies on spheres, we find that, as the Reynolds number approaches zero, the drag on an oblate spheroid of any axis ratio approaches its value at zero Reynolds number via the Oseen drag rather than via the Stokes drag. The significance of the present study to cloud physics is pointed out.

Abstract

The flow past a thin oblate spheroid falling at terminal velocity in an infinite, viscous fluid was investigated using a numerical solution of the steady-state Navier-Stokes equations of motion. The detailed streamfunction and vorticity yielded the drag, pressure distribution, and the extent of the spheroid's downstream wake. Calculations were performed for spheroids of axis ratios 0.05 and 0.2 and Reynolds numbers between 0.1 and 100. The results were compared with other numerical and analytical solutions to the Navier Stokes equations of motion for viscous flow past oblate spheroids and disks and with experimental results in the literature. Our numerical results for oblate spheroids of axis ratio 0.2 agree well with the numerical results of Masliyah and Epstein and with our own experimental results. Our results for oblate spheroids of axis ratio 0.05 agree well with the numerical computations of Michael and available experimental results on disks, but depart significantly from the numerical results of Rimon. In agreement with our earlier studies on spheres, we find that, as the Reynolds number approaches zero, the drag on an oblate spheroid of any axis ratio approaches its value at zero Reynolds number via the Oseen drag rather than via the Stokes drag. The significance of the present study to cloud physics is pointed out.

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