2D-SIMULATION OF DEPTH FILTRATION IN PLEATED FILTER Nathalie BARDIN-MONNIER*, Pierre-Colin GERVAIS & Dominique THOMAS Reactions & Chemical Engineering Laboratory LRGP, CNRS, Nancy University, 1 rue Grandville, BP20401, 54001 Nancy Cedex, France ABSTRACT Pleated filters are widely used for many industrial applications in air treatments due to their high effective surface area for a low overall dimension. Experimentally, Del Fabbro et al. (2002) observed that pleated filter pressure drop evolution with solid particles could be described by 3 periods. Among these is a period of depth filtration when particles are mostly collected within the fibrous medium. The aim of the work described in this paper is to characterize the filtration step numerically using the GeoDict code. We present general ideas how the depth filtration is taken into account and results on a specific pleat case. KEYWORDS Air filters, Filter media design, Simulation, Aerosol filtration, Hepa-/mini pleating machines 1. Introduction Pleated filters are widely used for many industrial applications in air treatments due to their high effective surface area for a low overall dimension. Nevertheless, their lifetime still needs to be controlled. In fact, during clogging, the pressure drop considerably increases with cake deposition. Consequently the filtration flow is no longer maintained and a deterioration of the media may occur. It is crucial to characterize the evolution of pressure drop regarding to the operating conditions (particle diameter, mean velocity and particle collected mass) and the filter characteristics (pleat geometry) in order to best design these filtration equipments. Experimentally, Del Fabbro et al. (2002) observed that pleated filter pressure drop evolution with solid particles could be described by 3 periods. In a first time, a period of depth filtration occurs where most particles are collected within the fibrous medium. This step is followed by a surface filtration period, with the formation of a cake at the medium surface. The last period corresponds to the decrease of the available filtration area due to the cake deposition. Our numerical approach is firstly based on a study of the air velocity local distribution. A two-phase flow approach with variable pleat geometry is then conducted. However, no computer code is available to simulate directly the depth filtration in the pleat. To overcome this problem, the use of GeoDict code is considered (developed by Fraunhofer ITWM, www.geodict.com).
2. Method and results Geodict is a voxel-based code in which each voxel is empty or filled. In this study, the domain size is 29mm×2mm corresponding to the real configuration of a pleat. The resolution is 10 microns per voxel. All the simulations were run on a computing station 12 GB of RAM with a dual-processor quad-core AMD at 2.1 GHz. The simulation of depth filtration in the pleat is implemented thanks to the following numerical procedure: •
creation of a 2D pleat as a porous layer thanks to the PleatGeo modulus. The design is performed by setting the pleat height, length, depth, radius at the top, at the bottom and opening angle. The material of which the pleat is made of is assigned a permeability value (Figure 1).
Figure 1. 2D Design of a pleat with given porosity. •
The flow field (equations 1 and 2) is then computed by calling Geodict (PleatDict modulus) in order to run the flow solver on the porous pleat (Figure 2). −µΔu + ∇p + κ −1u = f
(1)
∇.u = 0
(2)
κ is the porous voxel permeability, u the velocity, µ the fluid viscosity and p the pressure.
Figure 2. Velocity field in a pleat
•
The appropriate filter solver runs afterwards by tracking particles in the previously computed flow field on an empty structure. This assumption means that a particle can penetrate through any voxel of the pleat. A Lagrangian description of the particle motion is adopted. Inertia is considered via friction and diffusion via Brownian motion. (equations 3 to 6).
dv = −γ v ( x ) − v 0 ( x ) dt + σ .dW (t ) dx =v dt R γ = 6πρµ m 2k Tγ σ2 = B m dWi (t )dW j (t ) = δij dt
(
)
(3) (4) (5) (6) (7)
x is the particle position, v the particle velocity, R the particle radius, m its mass. T is the ambient temperature, kB the Boltzmann constant, dW a 3D probability Wiener measure and v0 the fluid velocity. •
The crossings of the particle trajectories and pleat structures are found. The voxel resistivity (µ/κ) where the crossings locate are increased by proportional to volume fraction.
Example of particle tracking. •
The loop goes to the second step for more batches (the maximum number is set by the user).
• 3. Conclusion A quite innovative method is implemented in Geodict in order to characterize the depth filtration in a pleat. The work under progress at present consists in simulating the whole filtration operation in order characterize the three different steps. The influence of the operating parameters (pleat geometry, fluid velocity and particle size, density) will be studied in a second time. 4. Reference: Del Fabbro L. et al. (2002). Air flows modelling and pressure drop modelling for different pleated industrial filters. Filt. Sep., 39(1) :35-40.
