Drag and lift forces on a stationary cylinder in a linear shear flow at a low Reynolds number

Abstract

In this study, the fluid forces on a stationary circular cylinder placed in a shear flow, the velocity of which varies linearly along the span of the cylinder, are investigated through numerical simulation. The Reynolds number varies in the laminar region as the shear rate, λ, changes. A rough prediction of the lift force on sectional cylinders is first built based on predefined assumptions. These assumptions indicate that the shedding frequency of the vortex in a specific region should be constant if the total lift force in this region does not become zero as t→∞. This conclusion is supported by numerical results, which show the existence of two end cells with a dominant Strouhal number of St0 (low-velocity side) and St1 (high-velocity side), respectively. Numerical results illustrate that St0 varies linearly with respect to λ, whereas St1 is less sensitive to λ. The detailed formation process of the two end cells versus time is characterised using wavelet analysis. In shear flow, on encountering the same dominant Strouhal number, the length of the effective shear layer can increase or decrease with rising shear rates, resulting in the lift coefficients being much different from those in a uniform flow. The end boundaries play an important role in the behaviour of fluid in the whole computation domain, however, they are not crucial for the existence of the end cell at the high-velocity side. When the aspect ratio is sufficiently small, the end cell corresponding to St1 disappears and the dominant Strouhal numbers at different heights are identical.