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Steady separated flow past a circular cylinder at low Reynolds numbers. (English) Zbl 1156.76381
Summary: The steady two-dimensional laminar flow around a stationary circular cylinder has been investigated via a stabilized finite-element method. The Reynolds number $$Re$$ is based on the cylinder diameter and free-stream speed. The results have been presented for $$6 \leqslant Re \leqslant 40$$ and the blockages between 0.000125 and 0.80. The blockage $$B$$ is the ratio of the cylinder diameter to the domain width. There is large scatter in the value of $$Re_s$$, reported in the literature, marking the onset of the flow separation. From the present study the $$Re_s$$ is found to be 6.29, approximately for $$B = 0.005$$. The effect of the blockage on the characteristic flow parameters is found to be insignificant for $$B \leqslant 0.01$$. The bubble length, separation angle and $$Re_s$$ exhibit non-monotonic variation with the blockage. It is for the first time that such a behaviour for the separation angle and $$Re_s$$ is being reported. Two types of boundary conditions at the lateral walls have been studied: the slip wall and towing tank. In general for high blockage, the results from the slip boundary condition are closer to the ones for the unbounded flow. In that sense, the use of the slip boundary condition as opposed to the towing tank boundary condition on the lateral walls is advocated. The bubble length, separation angle, base suction, total drag, pressure drag, viscous drag and maximum vorticity on the cylinder surface for the steady flow are found to vary as $$Re, Re^{-0.5}, Re^{-1} Re^{-0.5}, Re^{-0.64}, Re^{-0.60}$$ and $$Re^{0.5}$$, respectively. The extrapolated results for the steady flow, for higher Re, are found to match quite well with the other results from the literature.

MSC:
 76D25 Wakes and jets 76M10 Finite element methods applied to problems in fluid mechanics
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