Simulations of two sedimenting-interacting spheres with different sizes and initial configurations using immersed boundary method

Abstract

Numerical investigations are carried out for the drafting, kissing and tumbling (DKT) phenomenon of two freely falling spheres within a long container by using an immersed-boundary method. The method is first validated with flows induced by a sphere settling under gravity in a small container for which experimental data are available. The hydrodynamic interactions of two spheres are then studied with different sizes and initial configurations. When a regular sphere is placed below the larger one, the duration of kissing decreases in pace with the increase in diameter ratio. On the other hand, the time duration of the kissing stage increases in tandem with the increase in diameter ratio as the large sphere is placed below the regular one, and there is no DKT interactions beyond threshold diameter ratio. Also, the gap between homogeneous spheres remains constant at the terminal velocity, whereas the gaps between the inhomogeneous spheres increase due to the differential terminal velocity.

Size and thermal effects on sedimentation behaviors of two spheres

“…The observation is consistent with that reported in Ref. [12]. When α=0.7, the smaller particle settles slowly than the larger one and thus distance between the two particles is increased before drafting.…”

“…As pointed out by Ref. [12], for the sedimentation of two isothermal particles with initial vertical position arrangement, there is no DKT process beyond a threshold size ratio. Here we study the effects of heat transfer on this threshold size ratio for the first time.…”

“…Recently, Liao et al [12] numerically investigated the hydrodynamic interactions of two spheres with different sizes and initial configurations using lattice Boltzmann method-immersed boundary method (LB-IB). When a regular sphere was placed below the larger one, the duration of kissing decreased against increasing diameter ratio.…”

An approach of dynamic mesh adaptation for simulating 3‐dimensional unsteady moving‐immersed‐boundary flows

“…In the experiment, Ten Cate et al obtained the trajectory and velocity of the falling sphere. Using an immersed boundary method, Liao et al carried out a numerical simulation of this problem.…”

“…In the experiment, Ten Cate et al obtained the trajectory and velocity of the falling sphere. Using an immersed boundary method, Liao et al 29,30 carried out a numerical simulation of this problem. In the simulation of Liao et al, 29 the domain is discretized by a mesh of 91 × 215 × 91 = 1 780 415 nodes.…”