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Symmetric flow past orthotropic bodies : single and clusters Masliyah, Jacob Heskel

Abstract

Numerical solution of the Navier-Stokes equation was successfully accomplished, using an adaptation of the relaxation technique of Jenson, for axisymmetric flow past single oblate and prolate spheroids at particle Reynolds numbers up to 100. The aspect ratio of the spheroids varied between 0.999 (nearly perfect sphere) and 0.2. For low aspect ratios the surface pressure and vorticity distributions showed a marked difference from those of a sphere. The appearance of the wake bubble behind a spheroid was found to be a strong function of the particle shape. Numerical solutions were also obtained for two-dimensional symmetric flow past elliptical cylinders, with the flow parallel to the major axis for aspect ratios of 0.995 to 0.2 at Reynolds numbers up to 90, and with the flow parallel to the minor axis for an aspect ratio of 0.2 at Reynolds numbers up to 40. The numerical solution was found to be less stable than the corresponding three-dimensional axisymmetric case. The variation of the total drag coefficient with Reynolds number for the spheroids and the elliptical cylinders of various aspect ratios was not much different from that of a sphere and a circular cylinder, respectively. The results for both the spheroids and the elliptical cylinders showed a steady trend with Reynolds number from Stokes and/or Oseen flow to boundary layer flow. Happel's free surface cell model and Kuwabara's zero vorticity cell model were employed for the study of creeping flow past swarms of aligned spheroids and clusters of aligned elliptical cylinders. Large deviations of the Kozeny constant from its commonly assumed value of 5 for packed beds were found by both models for particles which deviate significantly in shape from a sphere or a circular cylinder. In general, Happel's free surface model predicted lower total drag coefficients than did Kuwabara's zero vorticity model for both the swarms of spheroids and the clusters of elliptical cylinders. Contours of the streamlines, equi-vorticity lines and equi-velocity lines are presented.

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