(354f) Direct Numerical Investigation of a Sphere Interaction with Neighboring Particles and Wall

Abstract:

Direct Numerical Simulations (DNS) are performed on a single sphere settling freely under the action of gravity in a variety of situations such as a Hele-Shaw cell, vertical and inclined walls. The simulations are based on a non-Lagrange multiplier based fictitious-domain method, which has been developed and validated by Veeramani et al. (2007) [J. Comp. Physics 224, 867-879].  Simulations have been carried out in the range of Reynolds number from 43.5 to 315 (based on terminal settling velocity of an isolated sphere) for understanding the effect of the nearby walls on the settling velocity and the wake dynamics of flow behind a sphere. In the case of a Hele-Shaw cell, the gap between the parallel plates was varied from 1.5d_p to 1.2d_p, where d_p is the particle diameter, similar to those used in the experimental work of Lee et al. (2007) [J Fluid Mech.  586, 449-464].

At Re of 43.5 and at the gap of 1.2d_p the settling velocity of sphere in a Hele-Shaw cell is only 68% of its free terminal settling velocity and our simulation results show a good agreement with the experimental results of the Lee et al. (2007). Further the closely bounded walls also affect the wake structure. The reflective symmetry in the wake is broken at Re = 163, which causes a complex dynamical migration pattern of the sphere. In contrast, an isolated sphere in an infinite medium loses its axisymmetry in the wake at Re=210, also initiating a complex three-dimensional migration patter. These oscillation frequencies of the sphere are quantified in terms of Strouhal number (St = f d_pV_s) and they compare favorably with the experimental work of Lee et al. (2007) under certain conditions.

This numerical study and other recent experimental studies, show that the dynamics of a freely falling sphere is much more complicated than that of a fixed sphere at intermediate Reynolds numbers, past the primary bifurcation point due to the complex interaction that is possible between the sphere and the fluid. Neighboring objects embellish these complex dynamics with a much richer physical response. Fictitious domain methods, with carefully refined dynamic meshing techniques to compute the surface forces accurately, provide a realistic picture of the evolving complex dynamics of such particles, setting the stage for multi-particle investigations.