The effects of shear flow on the unsteady wakes behind a sphere at moderate Reynolds numbers

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Abstract
Numerical simulations to investigate the effects of shear flow on wakes behind a sphere were carried out using a three-dimensional finite element method. The time-dependent Navier–Stokes equations were solved by a modified explicit time integration scheme. The Reynolds number, defined by the sphere diameter and oncoming velocity at its center, ranged from 20 to 500. Linear shear is assumed, and the dimensionless shear rate, defined as the vertical gradient of oncoming shear flow, was varied from 0.0 to 0.2. Extensive comparisons were made between the present computed results and available experimental and numerical investigations, and showed that they are in close agreement. Computed lift force was directed toward the low velocity side for Re > 50 whereas it was toward the high velocity side for Re < 50. In addition, drag forces showed slight increases compared to those in a uniform flow. The Reynolds number, at which vortex shedding begins, was found to be lower than that in a uniform flow and was a function of the shear rate. Vortex shedding frequency also increases with the Reynolds number and the shear rate. The irregularity of the vortex shedding and the oscillation of the vortex detachment location appearing in uniform and low shear flows at Re = 500 vanishes when high shear was present.

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