Numerical investigation of aerosol deposition on a single 2D fiber

The aerosol filtration technique deserves extensive attention, due to its wide applications found in health, environment, and industry. The simulation of aerosol filtration over fibrous filters involves the numerical investigation of the motion and capture of particles (aerosols) under different fluid operating conditions.


Capture efficiency
Fibrous filters are often characterized by their pressure drop and their capture efficiency. To have a consistent idea of the capture efficiency, researchers often use the concept of single fibre efficiency E = (N in − N out )/N in , where N in is the number of incident particles on the projected area of a single 2D fibre and N out the number of particles leaving without getting captured by the fibre.
The main mechanisms of particle deposition on fibers are interception, inertial impaction, diffusion, and gravitational settling, assuming that neither the particle nor the fibers are electrically charged and thus neglecting the effect of electrostatic attraction onto particle deposition. Deposition by interception occurs for particles that follow gas streamlines when they reach a distance smaller than the particle radius from the surface of the fiber. Inertial impaction occurs when the inertial forces of the particle are dominant and, therefore, the particle can no longer follow the streamline. Diffusion caused by Brownian molecular motion provides an increased probability of deposition, because the particle can strike the fiber by the irregular movement from a non-intercepting streamline.
To determine the net filter efficiency E two approaches can be used. The first and more accurate approach is the penetration approach shown in equation (1). It is valid as long as each individual efficiency acts independently and is less than 1. It is basically the product of the penetration due to the different mechanisms shown in equation (1). The alternative efficiency approach is estimating the filter efficiency from the addition of single-fiber efficiency through each deposition mechanism. This, however, may overestimate the efficiency due to collection of the same particle by different mechanisms, i.e. the capture of the particle could be counted twice [1].
2 Modelling and implementation Since the particle concentration is well below a volume fraction of 10 −4 it can be safely assumed that the particle movement does hardly affect the bulk fluid motion. This assumption leads to a decoupling of the fluid flow calculation from the particle tracking. The fluid flow is scaled with the fibre diameter d 0 and inlet fluid velocity u 0 , and simulated with Ansys CFX using an Eulerian method. The 2D fibre, with scaled fibre diameter d * 0 = 1, is simulated using a fictitious domain model [2], using a cubic domain (which is dependent on solidity α) with an inlet area with uniform scaled velocity of u * 0 = 1, an outlet with a uniform pressure and symmetry planes as the other walls. The computed flow field is then imported to MATLAB to track the particle trajectory using an in-house MATLAB algorithm, where the particle transport is described by the second Newtonian axiom, which calculates the particle acceleration vector du p (t)/dt at each time step. Based on time and acceleration, the 2 of 2 Section 11: Interfacial flows particle position x p (t) can be determined by integration. The particle rotation differential equation is also considered if the particle rotation has an effect onto the particle movement. Hence, we engage Here, m p is the mass of the particle, I p is the torque of inertia of the particle, ω p is the angular velocity of the particle, and T is the torque acting on the particle. For the net force acting on the particle F , the following forces are considered: drag force, inertial force, pressure force from pressure gradient and buoyancy, added mass force, Saffman force, Magnus force, and diffusion force. The implementation of the scaled diffusion force into the Lagrangian formulation is unique to this work, to the extent that the Brownian force is implemented as F d = G (πS 0 )/∆t [3]. Here, G is a vector whose components are independent zero-mean, unit variance Gaussian random numbers and S 0 = 2/(π Sc St 2 ) (Sc = ν/D is the Schmidt number and St = t 0 u 0 /d 0 is the Stokes number, where t 0 is the particle relaxation time). The time scale ∆t was freely chosen until now but in this work it was taken in the range of mean free time which is the average time between collisions of gas molecules. The diffusion mechanism can be validated by observing the particle movement due to diffusion in a stagnant fluid and calculating the diffusion coefficient and comparing it to theoretical values.

Results
The MATLAB algorithm is run for various combinations of particle diameter d 0 , fluid velocity v 0 , and solidity α and compared with existing experimental results and theoretical models. It can be seen in fig.1 that the net capture efficiency E Σ predicted by the algorithm, plotted against the scaled particle diameter, also referred to as the diameter ratio (R), follows the experimental results closely. At the lowest E Σ , the values diverge considerably, which can be explained by the number of particles present within the simulation. Due to computational restrictions, a total of 1000 particles is simulated, which appears to be not sufficient to give statistically-valid results in the range E Σ < 0.01. This could be overcome by simulating more particles. Fig. 1: Comparison of theoretical single-fiber efficiency calculated according to Stechkina [4] and Lee and Liu [5] for the experiments carried by Lee and Liu with the results from the current MATLAB simulations.