Lattice Boltzmann method simulations of Stokes number effects on particle trajectories in a wall-bounded flow

Experimental studies of particle-laden flows in a pipe show that the spatial distribution of the particles across the radius of the pipe is dependent on the Stokes number [Timothy C. W. Lau & Graham J. Nathan, J. Fluid Mech. 2014]. It has been suggested that the Saffman lift effect [Saffman, 1965] makes a significant contribution to this spatial distribution. The Saffman lift effect has been studied in prior works by several authors and the relative contribution of the lift force has been studied within the context of various forces acting on particles in a flow. The lift force depends on the particle size and the velocity of the particle relative to the gas phase. In this study, the lattice Boltzmann method is employed to study the mechanism of particle migration of an isolated particle moving in a wall-bounded flow. The boundary condition proposed by Bouzidi et al. [2001][23], which involves the bounce-back scheme modified to account for fractional link distances between the wall and the fluid node, is used for the particles. The force acting on the particle is found by adding the momentum lost by all the fluid molecules as they bounce back from the particle surface along the link joining the particle and the fluid boundary nodes. This force is used to update the position of the particle after every streaming step. The torque acting on the particle is determined similarly and is used to update the angular velocity of the particle. It is found that at low Stokes number the particle behaves like a neutrally buoyant particle and exhibits the Segré-Silberberg effect. With increasing Stokes number, the particle exhibits an oscillatory behavior about its mean position. For large Stokes number, the particle oscillations are significant. If the ratio of channel height to particle diameter is increased, the particle moves closer to the wall and the oscillatory behavior is evident at lower Stokes number.Anand Samuel Jebakumar, Kannan N.Premnath, John Abraha

On the Three-dimensional Central Moment Lattice Boltzmann Method

A three-dimensional (3D) lattice Boltzmann method based on central moments is derived. Two main elements are the local attractors in the collision term and the source terms representing the effect of external and/or self-consistent internal forces. For suitable choices of the orthogonal moment basis for the three-dimensional, twenty seven velocity (D3Q27), and, its subset, fifteen velocity (D3Q15) lattice models, attractors are expressed in terms of factorization of lower order moments as suggested in an earlier work; the corresponding source terms are specified to correctly influence lower order hydrodynamic fields, while avoiding aliasing effects for higher order moments. These are achieved by successively matching the corresponding continuous and discrete central moments at various orders, with the final expressions written in terms of raw moments via a transformation based on the binomial theorem. Furthermore, to alleviate the discrete effects with the source terms, they are treated to be temporally semi-implicit and second-order, with the implicitness subsequently removed by means of a transformation. As a result, the approach is frame-invariant by construction and its emergent dynamics describing fully 3D fluid motion in the presence of force fields is Galilean invariant. Numerical experiments for a set of benchmark problems demonstrate its accuracy.Comment: 55 pages, 8 figure

Lattice-Boltzmann Studies of Droplet Deformation

In this paper, three-dimensional computations, using the lattice Boltzmann method (LBM), of droplets involving deformation when sujected to shear flow are reported. The influence of shear rate on the droplet deformation of single and pairs of droplets, which is characterized in terms of the capillary number, is discussed. It is found that the larger the capillary number, the greater the deformation and rotation of the droplet. In the case of a pair of droplets, during the early stages of their deformation, shear-induced coalescence is observed that leads to the formtion of a ligament