No-slip consistent immersed boundary particle tracking to simulate impaction filtration in porous media

In this paper, we present a new method for simulating the motion of a disperse particle phase in a carrier gas through porous media. We assume a sufficiently dilute particle-laden flow and compute, independently of the disperse phase, the steady laminar fluid velocity using the immersed boundary method. Given the velocity of the carrier gas, the equations of motion for the particles experiencing the Stokes drag force are solved to determine their trajectories. The no-slip consistent' particle tracking algorithm avoids possible numerical filtration of very small particles due to the nonzero velocity field at the solid-fluid interface introduced by the immersed boundary method. This physically consistent tracking allows a reliable estimation of the filtration efficiency of porous filters due to inertial impaction. We illustrate and test our new approach for model porous media consisting of a structured array of aligned rectangular fibers, arranged in line and staggered. In the staggered geometry, the effect of the residual velocity at the solid-fluid interface is significant for particles with low inertia. Without adopting the developed no-slip consistent numerical method, an artificial numerical filtration is observed, which becomes dominant for small enough particles. For both the in line and the staggered geometries, the filtration rate depends quite strongly and non monotonically on the particle inertia. This is expressed most clearly in the staggered arrangement in which a very strong increase in the filtration efficiency is observed at a well-defined critical droplet size, corresponding to a qualitative change in the dominant particle paths in the porous medium. Copyright (c) 2013 John Wiley & Sons, Ltd.