Direct numerical simulations of a freely falling sphere using fictitious domain method: breaking of axisymmetric wake

Abstract

In the present paper, numerical simulations of the wake generated by a freely falling sphere, under the action of gravity, are performed. Simulations have been carried out in the range of Reynolds numbers from 1 to 210 for understanding the formation, growth and breakup of the axisymmetric wake. The in-house code used is based on a non-Lagrange multiplier fictitious-domain method, which has been developed and validated by Veeramani et al. (2007). The onset of instability in the wake and its growth along with the dynamic behavior of a settling sphere is examined at Reynolds number (Re) of 210. It is found that at the onset of instability the sphere starts to rotate and gives rise to a lift force due to the break of the axisymmetry in the wake which in turns triggers a lateral migration of the sphere. The lift coefficient of a freely falling sphere is 1.8 times that of a fixed sphere at a given sphere density of 4000 kg m⁻³ and sphere to fluid density ratio of 4. This is attributed to the Robin's force which arises due to the rotation of the sphere. At this Reynolds number (Re=210) a double threaded wake is observed, which resembles the experimental observations of Magarvey and MacLatchy (1965).