Flow past a circular cylinder at low Reynolds number: Oblique vortex shedding

Abstract

Oblique shedding in the laminar regime for the flow past a nominally two-dimensional circular cylinder has been investigated numerically via a stabilized finite element method. No-slip condition on one of the sidewalls leads to the formation of a boundary layer which promotes oblique vortex shedding. Computations are carried out for three values of Reynolds number (Re): 60, 100, and 150. Cellular shedding is observed in all cases. Three cells are observed along the span for the Re=60 flow while only two cells are formed at Re=100 and 150. Spotlike vortex dislocations form at the junction of the cells. The frequency of the appearance of the dislocations increases with Re. Cellular shedding leads to low frequency modulation in the time histories of aerodynamic coefficients. Lowest value of drag is achieved at a time instant corresponding to the appearance of a new dislocation in the near wake. The vortex shedding frequency as well as the oblique angle of the primary vortices is found to vary with time for the Re=60 flow. Their variation is also related to the appearance of dislocations in the near wake. It is found that the vortex shedding frequency (Stθ) is related to the frequency observed for parallel shedding (St0) and the angle of the oblique vortices (θ) by the relation: Stθ=St0 cos θ. This relationship was proposed earlier for the case when the vortex shedding frequency and the oblique angle do not change with time. The velocity fluctuations are found to decrease with increase in θ. For the Re=100 and 150 flow, the oblique angle of the vortices and the shedding frequency outside the end cell do not change with time. However, θ and Stθ depend on the aspect ratio of the cylinder. The oblique shedding angle, for various lengths of endplate and Re, is found to vary linearly with the thickness of the boundary layer on the side wall.