Simulations of filter media performances from microtomography-based calculation domain. P.-C. Gervaisa, S. Bourrousa,b,c,d, F. Danya, L. Bouillouxa and L. Ricciardia a

Institut de Radioprotection et de Sûreté Nucléaire (IRSN), PSN-RES, SCA, Gif-surYvette, 91192, France (E-mail: [email protected]) b Université de Lorraine, LRGP, UMR 7274, Nancy, 54001, France c CNRS, LRGP, UMR 7274, Nancy, 54001, France d Camfil Farr, Z.I. de Saint-Martin-Longueau, Pont-Sainte-Maxence, 60722, France Abstract In this work, synchrotron X-ray microtomography was applied to produce high spatial resolution images of fibrous media, used in aerosol filtration. Based on these images, representative calculation domains were created with the GeoDict code. Flow as well as collection efficiency simulations were then carried out. In parallel, experimental measurements were realized on the same media for providing an experimental validation.

Keywords. Fibrous filter - Synchrotron tomography - Collection efficiency - Permeability - GeoDict INTRODUCTION In addition to being easy to use and maintain, fibrous media are the most efficient filters among the different existing devices. They are therefore implemented in many applications such as engine intake, cleanroom and in the nuclear industry to contain radioactive particles, in normal operation or accidental situation. The physical mechanisms involved in aerosol filtration, governing flows in porous structures and particles transport and deposition, are now fully described. Nevertheless, the development of predictive models, used for design optimization or lifetime determination, is hardly achievable due to the wide range of operating conditions as well as aerosol and media characteristics. The initial performances of fibrous media are characterized by the filtration efficiency E and the pressure drop ΔP. Among the studies devoted to the modelling of such performances, numerical approaches, consisting in designing fibrous micro-geometries together with solving transport equations, seem to be relevant tools to investigate all parameters (Gervais, 2012). Recent improvements allow to import and process images from computed-tomography (CT) in order to compute flows and particles transport on real structures (Soltani, 2014). The objective of this study is to use the synchrotron X-ray microtomography as a mean to create representative calculation domains and also provide an experimental validation.

MATERIALS AND METHODS Simulations were performed with the GeoDict code (from Math2Market GmbH, www.geodict.com). GeoDict is a voxelbased code dedicated to predict materials properties by solving transport equations on a virtual material. Through an interface dedicated to images analysis, GeoDict allows to import and process images from CT. The studied filter media is provided by Bernard Dumas (Creysse, France). It is made of fiberglass and binderless. The nominal fiber diameter (df) is 2.7 µm. The given grammage is 74 g/m², thickness (Z) and solid volume fraction (SVF) are unknown. Images were acquired on the ID19 beamline of the European Synchrotron Radiation Facility (ESRF, Grenoble, France). In addition to being non-invasive and non-destructive, synchrotron X-ray Figure 1: Illustration of the steps for structure microtomography has a high spatial resolution, which may in our case represent the diameter of nominal fibers by at least importation in GeoDict. 9 voxels. The experimental setup consists of a high resolution microtomograph with a sample-to-detector distance of 5 mm. The FReLoN CCD camera with a 2048×2048 pixel chip, associated to the ×20 objective, were used in order to obtain a pixel size of 0.28 µm. Five overlapped scans were carried out to visualize the entire sample thickness. Each of them consists of 1995 projections on 360 degrees with an exposure time of 0.2 second. The protocol of images importation is

shown in Fig. 1. The 4351 tomograms (a) are firstly read thanks to the ImportGeo-Vol interface (b). 3D processing parameters are then applied to the images. The resize step defines a 1024×1024 voxels square area in the centred area to avoid edge effects (c). A median filter, with a sphere radius of 2 voxels, is used to reduce noise (d). The choice of the relevant threshold value, in order to binarize the images, is the final step of the importation (e). Moreover, structure was cleansed by reassigning the objects comprised under 500 voxels to fluid zone. The resulting 3D microstructure (f) consists of a fibrous core, more than 1.2 mm length and 0.08 mm² of filtration surface. Four non-overlapping subvolumes (SV) were created from the original structure. This choice was made in order to save memory when the simulation domain is handled and to have reasonable computational time. SV considered in this paper are 512×512×4351 voxels with a resolution of 0.28 µm per voxel. Mesh number 9 is therefore greater than 1.1×10 . The air flow through the microstructure is governed by the Stokes' equation and the continuity equation. It was computed relative to thickness direction by setting a velocity inlet and pressure outlet condition. The fluid velocity was set to 4 cm/s and periodic boundary conditions were imposed in tangential directions. Simulation was performed thanks to a Lagrangian description of the spherical particles motion, and described by a forces balance acting on each of them. The particle size 3 distribution ranges from 0.03 to 0.84 µm with 28 size classes. Density was fixed to 1550 kg/m and 1000 particles per size classes were simulated. The results were obtained using a cluster with 512 GB of RAM and a 4-hexa-core AMD CPU with a speed of 3.0 GHz.

RESULTS Table 1: Summary of the structural parameters and results. σdf (µm) 3.19 2.19 1.74 1.65 -

k×10-11 (m²) 3.25 3.44 3.07 3.27 3.26

The Tab. 1 summarizes the structural parameters obtained by image 1 analyses for each SV as well as the 2 permeability (k) and efficiency (E) 3 simulations results. A set of pressure 4 Mean drop measurement, for a large rate of flow, was performed on a flat filter. The Darcy’s law is then used to calculate the experimental value of -11 permeability of 3.36×10 m². Based on the very low value of the average of relative errors (RE), we note a very good agreement between experimental and simulated values of k. Simulated values of averaged efficiency are also very close to the value given by the manufacturer, around 65-70% at 4 cm/s. Fig. 2 allows visualizing pressure field, computed with GeoDict, in the case of one of the 4 subvolumes. On the same structure, trajectories of filtered or non-filtered particle can be presented, as shown on Fig. 3. SV.

SVF (%) 3.66 3.34 3.46 3.39 3.46±0.14

Z (µm) 999 863 1002 970 989±65

df (µm) 2.92 2.63 2.51 2.40 2.62±0.22

Figure 2: Visualization of the pressure field computed with GeoDict in one of the subvolume.

RE (%) 3.2 2.3 8.7 2.7 4.2

E (%) 65.6 63.8 67.5 65.9 65.7

Figure 3: Visualization of the filtered 0.3 µmdiameter particles trajectories (a) as well as the non-filtered ones (b).

CONCLUSION A very good agreement is found between the experimental value of permeability and the simulated results from microtomography-based calculation domain. An average difference less than 5% is observed, which allows us to validate the representativeness of the subvolume. In order to overcome the value given by the manufacturer, filtration efficiency measurements are in progress. They are based on fluorescein spherical aerosol generation as well as the determination of the particle size distribution upstream and downstream from the tested filter thanks to a scanning mobility particle sizer.

REFERENCES Gervais P.C., Bardin-Monnier N., Thomas D., Permeability modeling of fibrous media with bimodal fiber size distribution (2012), Chemical Engineering Science, Vol. 73, Pages 239-248 Soltani P., Johari M.S., Zarrebini M., Effect of 3D fiber orientation on permeability of realistic fibrous porous networks (2014), Powder Technology, Vol. 254, Pages 44-56.