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Viscous flow over a sphere with
fluctuations in the free-stream velocity
Alassar, R.S.
, Badr, H.M.,
Allayla, R.
King Fahd Univ. Petrol. and
Minerals,
Abstract
The
problem of viscous flow over a sphere with fluctuations in the free-stream
velocity is considered. The governing conservation equations are expressed
terms of the stream function and vorticity and solved
using the series truncation method where the stream function and vorticity are approximated using finite series of Legendre
and first associated Legendre functions. The effects of the Reynolds number, Strouhal number, and the amplitude of the fluctuations on
the flow characteristics are studied. Results are presented for periodic
variation of the drag coefficient, surface vorticity
and pressure distributions for Reynolds numbers ranging from 5 to 100, Strouhal numbers ranging from π/4 to π, and
amplitude of fluctuations from 0.0 to 0.5. The time variation of the velocity
field during one complete cycle is presented in the form of streamline and equi-vorticity patterns. The periodic variation
of the angle of separation as well as the length of the separation region are
also presented.