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Excitation of shear layer instability in flow past a cylinder at low Reynolds number. (English) Zbl 1284.76178
Summary: The instability of the separated shear layer for flow past a cylinder, in two dimensions, is investigated for low Reynolds numbers (\(Re\leq 350\)). The line of symmetry, downstream of the cylinder, in the wake is forced to be a streamline. This hypothetical situation allows slip of velocity along the wake centreline but prevents any flow normal to it. With this arrangement the flow is completely stable for \(Re\leq 250\). It suppresses the primary instability of the wake that is responsible for the von Karman vortex shedding. Unlike the conventional splitter plate such an arrangement does not have a wake of its own. At \(Re = 300\) and above the wake instability and the shear layer instability are observed. The fluctuations due to the instabilities are intermittent in nature. The shear layer frequency is smaller than the frequency of the von Karman vortex shedding for the regular flow past a cylinder. It is also found that flow past half a cylinder, with symmetry conditions at the wake centreline, at \(Re = 300\) is stable. However, when a secondary cylinder with one-fifth the diameter of the half-cylinder is placed close to it, the vortex shedding from the smaller cylinder again leads to instability of the separated shear layer of the half-cylinder. This suggests that although the separated shear layer is stable, at such low \(Re\), the shear layer instability can be excited by some other disturbances. It is found that even at such low \(Re\), the normalized shear layer frequency follows the \(Re^{0.67}\) power law. All the computations have been carried out using a stabilized finite element formulation.

MSC:
76E99 Hydrodynamic stability
76M10 Finite element methods applied to problems in fluid mechanics
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