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SUMMARYIn 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 © 2013 John Wiley & Sons, Ltd.

We present a new numerical approach for estimating filtration through porous media from first principles. We numerically simulate particle motion as arises in a carrier gas flow. The filtration we look at occurs due to impaction of particles with obstructing surfaces that are contained in the solid filter. We consider the case when the motion of particles is governed by linear Stokes-drag, which is characterized by the particle relaxation time. The gas-particle interaction is modeled by using the Eulerian-Lagrangian approach and one-way coupling of the phases. In this case the carrier flow drags along the particles, without being affected by the motion of the particles. The gas flow is governed by Navier-Stokes equations for incompressible fluids and is calculated numerically using finite-volume discretization that is based on an energy conserving skew-symmetric discretization. We apply an immersed boundary (IB) method to capture the detailed flow in the porous filter, in which we explicitly incorporate flow around all small-scale features that make up the inner structure of the porous filter. To validate and develop our method we consider a porous medium composed of a staggered arrangement of square rods in 3D, which was already extensively considered in the literature for flow computation. This is a stepping-stone case on the way of simulating filtration of aerosol particles in complex, realistic filters. Based on results of our simulations we investigate the decay of the number of particles as a function of time. We focus on the dependence of the decay-rate on the Reynolds number of the gas and the inertial effects of the particles. For a range of particle relaxation times we observe a strong influence of the Reynolds number on filtration rate. A non-monotonic dependence of the filtration efficiency on Stokes number at different flow conditions is observed, hinting at qualitative differences in the motion of the aerosol ensemble through the structured filter.

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