Airflow and particle transport simulations for predicting permeability and aerosol filtration efficiency in fibrous media

Chemical Engineering Science 165 (2017) 154–164

Contents lists available at ScienceDirect

Chemical Engineering Science journal homepage: www.elsevier.com/locate/ces

Airflow and particle transport simulations for predicting permeability and aerosol filtration efficiency in fibrous media P.-C. Gervais a,⇑, D. Bémer b, S. Bourrous a, L. Ricciardi a a b

Institut de Radioprotection et de Sûreté Nucléaire (IRSN), PSN-RES, SCA, Saclay, 91192 Gif-sur-Yvette, France Institut National de Recherche et de Sécurité, rue du Morvan, CS 60027, 54519 Vandœuvre-lès-Nancy Cedex, France

h i g h l i g h t s
Synchrotron X-ray microtomography is used to produce images of fibrous filter media. Ò


Representative domains are created using Matlab .

Ò


Flow and efficiency simulations are carried out thanks to GeoDict .
Good agreement is found between experimental and simulated values of permeability.
Simulated values of efficiency give a good approximation of experiments.

a r t i c l e

i n f o

Article history: Received 26 October 2016 Received in revised form 10 February 2017 Accepted 1 March 2017 Available online 3 March 2017 Keywords: Aerosol filtration Fibrous media Permeability Collection efficiency CFD simulation GeoDictÒ

a b s t r a c t In this work, synchrotron X-ray microtomography was used to produce high spatial resolution images of two kinds of binderless and monodisperse fibrous filter media, made of fiberglass and sintered stainless steel respectively. Representative computational domains were created based on these images. Both flow and collection efficiency simulations were then carried out using the flow and particle transport modules of the GeoDictÒ code. An image analysis program based on MatlabÒ was used to determine the structural properties of the computational domain, namely the thickness, the solid volume fraction and the fiber size distribution. In parallel, permeability and collection efficiency measurements were performed on the same media, to provide an experimental comparison. Very good agreement was found between the experimental and the simulated permeability values. We showed that, in order to compare collection efficiency from experiments with those simulated with GeoDictÒ, it was necessary to take into account the difference between the thickness of the fibrous structures that were used to create the calculation domain, and the averaged experimental thickness characterized by SEM. Using this way of comparison, we obtained the first experimental validation of the GeoDictÒ code on both permeability and efficiency aspects for aerosols filtration. Ó 2017 Elsevier Ltd. All rights reserved.

1. Introduction Improving the knowledge of the performance of High Efficiency Particulates Air (HEPA) filters, used in the nuclear industry to contain radioactive particles in normal operation or in an accident situation, is a key factor in nuclear safety. This knowledge is crucial because HEPA filters represent the last containment barrier for aerosols, which constitute the main source of contamination. As a part of this research, one specific topic relates to the experimental and

⇑ Corresponding author at: IFTS, Institut de la Filtration et des Techniques Séparatives, Rue Marcel Pagnol, Foulayronnes, France. E-mail addresses: [email protected] (P.-C. Gervais), laurent. [email protected] (L. Ricciardi). http://dx.doi.org/10.1016/j.ces.2017.03.002 0009-2509/Ó 2017 Elsevier Ltd. All rights reserved.

numerical characterization of the intrinsic performance of filter media, in terms of pressure drop (DP) and collection efficiency (E), depending on the operating conditions (filtration velocity and particles size). While the physical mechanisms involved in aerosol filtration by fibrous media have been fully described in the literature (Fuchs and Stechkina, 1963; Stechkina and Fuchs, 1966; Kirsch and Fuchs, 1967; Kirsch and Fuchs, 1968; Stechkina et al., 1969), the development of predictive models remains hardly achievable due to the wide range of operating conditions as well as aerosol and media characteristics. Given the multiplicity of parameters, the use of a numerical tool is often considered and many studies have been conducted to determine the influence of geometric parameters like fiber diameter and the solid volume fraction (SVF) (Tafreshi et al., 2009; Fotovati et al., 2010a; Hosseini and Tafreshi, 2010;

155

P.-C. Gervais et al. / Chemical Engineering Science 165 (2017) 154–164

Gervais et al., 2012), fiber orientation (Fotovati et al., 2010b), or fiber length (Wang et al., 2007) on initial filtration performances. The primary objective of this work is to validate, by comparison with experimental results, the CFD software GeoDictÒ, specialized in air filtration. Initial contributions of IRSN for qualifying GeoDictÒ have been conducted on model fibrous structures, representing ideal fibrous media (monodisperse fibers, without binder) a priori well characterized from literature (Gougeon et al., 1995, 1996). The data provided by the manufacturer were used in geometry models (fibers diameter, medium thickness, SVF and isotropic orientation). Our results have shown a major gap for the pressure drop. In the case of a laminar flow, the pressure drop allows the medium permeability, an intrinsic property of the material, to be calculated. If values are not consistent with experiments, this may probably come from the creation of the computational domain from the overall characteristics of the fibrous medium. In order to avoid assumptions such as the use of overall values for fiber anisotropy, fiber diameter and SVF as well as the design of the fibers as long straight cylinders, we chose to create images from real fibrous media for use as a geometrical support for the calculation of flow and particle transport. In one of our previous papers, X-ray synchrotron microtomography had already been used to create computational domains to simulate the performances of a fiberglass fibrous medium (Gervais et al., 2015). One of the conclusions of this study was that very good agreement was found between the experimental value of permeability and the simulated results from the microtomography-based computational domains. An average difference of less than 5% was observed, which allowed us to validate the representativeness of the computational domains. Nevertheless, a significant gap was found between the experimental and simulated values of efficiency. From our point of view, this was due to not taking into account the electrostatic effects. This work should make possible to use neutralized aerosol and conductor media, such as metallic filter, to be free of any charge effect during the experiments. A completely new experimental set-up was used in the present study. This was the subject of collaboration with the Process Engineering Department of the Occupational Safety and Health Institut (INRS). In a first time, it allowed us to highlight the influence of electrostatic effects. Moreover, these effects were annihilated using an electrostatic precipitator and we obtained the overall range of particle size which are relevant for aerosols filtration using a SMPS and an APS and not only the SMPS. We also use another kind of fibrous media, to enlarge the range of our study. The experimental set-up and the operating protocols to determine experimental permeability and collection efficiency are presented in Section 2. Section 3 of this paper presents the methods used to acquire and process the images, as well as the simulation settings. The structural properties of the computational domains, determined from the image analysis, are also given in this section. Finally, a new interpretation of the comparison of numerical calculations and experiments, especially for the fractional collection efficiency, is presented in the last part of this work. We now take into account the limitation of X-ray microtomography as a mean to create the calculation domain from real media.

2. Experimental determination of filtration performance

dedicated to fundamental research in the past (Gougeon et al., 1995, 1996). So, we first focused on a binderless monodisperse fiberglass medium, provided by the Bernard Dumas company (Creysse, France). The initial results we obtained (Gervais and Ricciardi, 2014) have led us to consider the use of a metallic medium to overcome potential electrostatic effects in collection efficiency measurements. A sintered stainless steel fibrous medium has been provided by the Bekaert company (Zwevegem, Belgium). Table 1 summarizes the target properties of the filter media samples tested. It contains the values of nominal fiber diameters (df), thicknesses (Z) and solid volume fractions (SVF). Fig. 1 illustrates the surfaces of both fibrous media obtained by Scanning Electron Microscopy (SEM). As a qualitative comment, we can observe the best monodispersity for the sintered stainless steel medium. For both media, we take note that the fibers are cylindrical and that the tortuosity of the fibers seems to be negligible. Melting points between fibers, resulting from sintering, are readily visible in the case of the stainless steel medium. 2.2. Thickness characterization The thicknesses of both media were determined by SEM visualization. A fixation method followed by sanding and polishing steps was applied in the same way as the method used by Bourrous et al. (2014) for the samples. Fig. 2 illustrates the slices of both fibrous media as well as examples of the measurements. Table 2 summarizes the experimental thicknesses characterization of the filter media samples tested. It contains the number of measurements for each medium and the values of experimental thicknesses (Z exp ). While the thickness of the sintered stainless steel fibrous medium, measured experimentally, is very close to the target value required by the manufacturer, a major difference is observed for the fiberglass medium. It reveals the difficulty of designing samples based on target properties due to the technical resources of the manufacturers. However, the experiments and simulations will be performed using the same samples and not the manufacturer’s data. 2.3. Experimental set-up Permeability as well as fractional collection efficiency measurements were conducted at the French Institute for Occupational Safety and Health (INRS, Nancy, France), using a dedicated experimental bench. The set-up (Fig. 3) is based on an pressurized cylindrical pipe (diameter 40 mm) made of stainless steel, electrically grounded. An aerosol of solid sodium-chloride particles is generated using an AGK 2000 nebulizer (Palas GmbH, Germany), supplied with compressed, dry and filtered air and with a 8% solution of NaCl, followed by a drying chamber. The aerosol generated is then transferred to an electrical charging zone. The bipolar Electrostatic Aerosol Neutralizer EAN 581 (Topas GmbH, Germany) is used to control the particle charge. It is based on the corona discharge principle and consists of a mixing chamber with two separate ionization heads and a control unit (Topas, 2014). An electrostatic precipitator (ESP), home designed, can then be used in order to separate charged particles to obtain neutralized aerosol. The airflow, absolute pressure and temperature are directly checked using a mass flowmeter (TSI, USA). Pressure tappings on both sides of the

2.1. Tested media As this study aims to complete experimental validation of a simulation tool, we focused on simplified fibrous systems. The idea was to study some media exclusively composed of monodisperse fibers, without binder. In nuclear filtration, glass fibers are most commonly used and ideal fiberglass fibrous media were often

Table 1 Target properties of the fibrous structures required by manufacturers. Medium

SVF (%)

Z (lm)

df (lm)

Fiberglass Stainless steel

10 20

300 200

2.6 2

156

P.-C. Gervais et al. / Chemical Engineering Science 165 (2017) 154–164

Fig. 1. Illustrations of the surfaces of the fibrous media in fiberglass (left/top) and in sintered stainless steel (right/bottom).

Fig. 2. Illustrations of the thickness characterization of the fibrous media in fiberglass (left/top) and in sintered stainless steel (right/bottom).

fluid flow through a length Z of porous media in a stationary laminar flow, permeability is given by Darcy’s law (Darcy, 1856):

Table 2 Summary for the characterization of experimental thicknesses. Medium

# measurements

Z exp (lm)

Fiberglass Stainless steel

27 55

1185  91 212  31

filter holder allow a differential pressure sensor to be connected, in order to monitor the filter pressure drop. To determine particle size distribution and then fractional efficiency, a Scanning Mobility Particle Sizer (SMPS), provided by Grimm technologies (Germany), is used. It consists of a Differential Mobility Analyzer (DMA) used to select particles of known size, followed by a Condensation Particle Counter (CPC). The DMA is the Vienna type electrostatic classifier, which is able to select particles between 10 and 1100 nm depending on the applied voltage. For larger particles, an Aerodynamic Particle Sizer APS 3321 spectrometer (TSI, USA) provides high-resolution and real-time aerodynamic measurements of particles from 0.5 to 20 lm. A VKL 100 (Palas GmbH, Germany) is used upstream from the analyzing instruments, as a dilution system, in order to reduce the aerosol concentration. To respect isokinetic sampling, a nozzle with a suitable diameter is used in the aerosol sampling line. Commercial software is used for temporal registration and particle size analysis. 2.4. Experimental results 2.4.1. Permeability The permeability k is the ability of a material to be passed through by a fluid under a pressure gradient DP. For incompressible

k¼l

Z U DP

ð1Þ

where l and U are the dynamic viscosity and the fluid face velocity respectively. For both kinds of medium, series of pressure drop was measured for filtration velocities between 0 and 0.3 m/s on flat filter samples. The selected flow rate was randomized for each measurement to overcome experimental bias. Using the medium thicknesses determined by SEM, Zexp, Darcy’s law was then used to calculate the experimental value of permeability, kexp , as follows:

kexp ¼ l  Z exp 

U DP

ð2Þ

The dynamic viscosity is chosen as follows: l = 1.834105 kg/ms. The ratio U=DP is deduced from the value of the linear best fit slope for the experimental pressure drop measurements as a function of the filtration velocity. Table 3 summarizes experimental results for the determination of experimental permeability. 2.4.2. Fractional collection efficiency For both kinds of medium, a series of aerosol concentration measurements were performed upstream and downstream from flat filter samples. For each of them, 3 upstream and 3 downstream aerosol concentrations were alternately measured, using the fast scans routine of the SMPS. Moreover, 8 measurements of 30 s each, alternating upstream and downstream from the samples, were performed with the APS. Note that in this work, only the aerosol with no charge can be compared with simulations. For each of both media, 2 experiments were performed for this configuration. As the

P.-C. Gervais et al. / Chemical Engineering Science 165 (2017) 154–164

157

Fig. 3. Schematic diagram of the experimental setup.

Table 3 Summary for the determination of experimental permeability. Media

kexp  1011 (m2)

Fiberglass Stainless steel

3.24  0.25 0.185  0.027

SMPS provides results based on the electrical mobility diameter while those of the APS are based on the aerodynamic diameter, it was necessary to harmonize diameters. Using the aerodynamic diameter (da ), we first determined the sphere diameter which has an equivalent volume (dv e ), using the following equation (Hinds, 1999):

1 dv e ¼ da  qffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi 1 qp Cuðdv e Þ v  q  Cuðda Þ

ð3Þ

0

where v is the dynamic shape factor (DSF) for NaCl aerosols. The DSF for cubic form of NaCl particles is size dependent, increasing from 1.06 to 1.17 as particle size increases from 200 to 800 nm (Zelenyuk et al., 2006). To be representative of the sizes of the most penetrating particles (200–300 nm), we chose to set a DSF value equal to 1.08. qp and q0 are the particle and standard densities. They are fixed to 2.16 and 1 g/cm3 respectively. The ratio of Cunningham numbers is calculated using Eq. (12) (see Section 3.5) applied to both diameters. Determining the equivalent diameter therefore requires an iterative calculation initialized with the ratio of Cunningham numbers equal to 1. The loop is stopped when the convergence error parameter is less than 105 . Using the previously calculated equivalent volume diameter, the electrical mobility diameter, db , is deduced using the Eq. (4) (Carlo et al., 2004):

db ¼ dv e  v 

Cuðdb Þ Cuðdv e Þ

ð4Þ

The choice of the DSF is also subject to the above mentioned assumptions and the same iterative method is used to calculate the ratio of Cunningham numbers. As we first focused on a binderless monodisperse fiberglass medium, four aerosol charge state configurations were investigated for this medium with a filtration velocity of 3.1 cm/s:
Natural charge: the NaCl aerosol generated is taken upstream and downstream of the filter holder into the sampling line for analysis. This configuration is dependent on the environment as well as the measurement conditions. It only ensures that other configurations give consistent results. Charged configurations should give higher efficiencies while the efficiency of the neutralized configuration should be lower.
Neutralized: firstly, the NaCl aerosol generated is charged by the EAN. Both electrodes deliver a voltage of several kilovolts (about 5–6 kV), which ionize the air in the surrounding area and establish positive and negative electric charges. When the aerosol flows through, particles accumulate the charges. Downstream from the charger, the ESP delivers 7 kV in voltage, and deflects the trajectory of particles with an unbalanced electrical charge. Thus, only the particles with an overall charge of zero will be analyzed.
Positive charge: In this case, only the positive electrode of the charger supplies a voltage of about 6 kV.
Negative charge: In this case, only the negative electrode of the charger supplies a voltage of about 5 kV. Fig. 4 shows the concentrations of particles measured upstream (left/top) and downstream (right/bottom) from the fiberglass fibrous medium as a function of the particle diameter, for each configuration. The number of charges per particle, for the positive and negative configurations, are deduced from the online characterization of current using an electrometer.

158

P.-C. Gervais et al. / Chemical Engineering Science 165 (2017) 154–164

Fig. 4. Concentrations of particles measured upstream (left/top) and downstream (right/bottom) from the fiberglass fibrous medium as a function of the particle diameter, for each configuration (2 neutralized, 1 natural charge, 1 positively charged and 1 negatively charged). Filtration velocity is fixed at 3.1 cm/s.

For each particle class size, the experimental collection efficiencies, Eexp ðdp Þ, of the fiberglass fibrous medium, are then calculated as follows:

Eexp ðdp Þ ¼ 1 

C downstream ðdp Þ C upstream ðdp Þ

ð5Þ

Fig. 5 shows the collection efficiencies of the fiberglass fibrous medium, as a function of particle diameter, for each configuration. As expected, for charged configurations, collection efficiencies are substantially higher than the natural charge configuration. The positive configuration leads to an higher efficiency than the negative configuration since the number of charges per particle is higher. This collection efficiency increase is due to the electrostatic effects combined with the classical physical mechanisms governing particles transport (Brownian diffusion, interception and inertial impaction). Neutralized configurations for both samples are similar. They lead to a lower efficiency than the others. This suggests that only classical physical mechanisms are responsible for the particle capture. To eliminate residual electrostatic or triboelectric effects due to air friction on the glass fibers, the use of a conductive metallic material was considered. Only the neutralized and the positive configurations were investigated for the sintered stainless steel fibrous medium for a filtration velocity of 5.8 cm/s. If only neutralized configurations are compared with simulations, comparisons

with a charged configuration will confirm that any residual charges are conducted to the ground. Fig. 6 shows the concentrations of particles measured upstream (left/top) and downstream (right/bottom) from the sintered stainless steel fibrous media as a function of the particle diameter, for each configuration. For each particle class size, experimental collection efficiencies are calculated using Eq. (5). Fig. 7 shows the collection efficiencies of the sintered stainless steel fibrous mediim, as a function of particle diameter, for each configuration. Neutralized configurations for both samples are similar. As expected, positive charged configuration is also similar to the neutralized ones, which confirms that residual charges are conducted to the ground.

3. Numerical calculations of filtration performance GeoDictÒ software (Math2Market GmbH, www.geodict.com) was used for simulations. GeoDictÒ is a voxel-based code dedicated to predicting material properties by solving transport equations for a virtual material. The properties of the code and its use to model aerosol filtration by fibrous media were described in our previous paper (Gervais et al., 2012, 2015).

3.1. Image acquisition Through an interface dedicated to image analysis, GeoDictÒ allows data to be imported and processed from computed tomography. Synchrotron X-ray microtomography was used as a way to create representative computational domains, in order to simulate filter media performances. Images of the filter media studied were acquired on the ID19 beamline of the European Synchrotron Radiation Facility (ESRF, Grenoble, France).

3.2. Image import for the creation of computational domains

Fig. 5. Collection efficiencies for the fiberglass fibrous medium as a function of particle diameter for each configuration (2 neutralized, 1 natural charge, 1 positively charged and 1 negatively charged). Filtration velocity is fixed at 3.1 cm/s.

3.2.1. Fiberglass fibrous medium How to produces and import images for the fiberglass fibrous medium was explained in a previous paper (Gervais et al., 2015). As a reminder, to save memory when handling the computational domain and to have reasonable computational times, four nonoverlapping subvolumes (SV) were created from the original structure. They consist of 512  512  4351 voxels with a resolution of 0.28 lm per voxel. An example of one of the computational domains is shown in Fig. 8.

P.-C. Gervais et al. / Chemical Engineering Science 165 (2017) 154–164

159

Fig. 6. Concentrations of particles measured upstream (left/top) and downstream (right/bottom) from the sintered stainless steel fibrous medium as a function of the particle diameter, for each configuration (2 neutralized and 1 positively charged). Filtration velocity is fixed at 5.8 cm/s.

Fig. 7. Collection efficiencies for the sintered stainless steel fibrous medium as a function of particle diameter, for each configuration (2 neutralized and 1 positively charged). Filtration velocity is fixed at 5.8 cm/s.

3.2.2. Sintered stainless steel fibrous medium Images are produced from a sample with a diameter of 500 lm (about 20 times smaller than the sample size for fiberglass fibrous sample -9 mm-, X-rays have more difficulty crossing the stainless steel). In order to pass through the material, the energy of the light line is 35 keV. A sCMOS camera with a 2048  2048 pixel chip, associated with a 40 objective were used in order to obtain a pixel size of 0.16 lm. One single scan is sufficient to visualize the entire sample thickness. The scan consists of 1500 projections over 360 degrees with an exposure time of 0.2 s. The method used for phase extraction is based on the single distance phase retrieval approach (Paganin et al., 2002). The import protocol is shown in Fig. 9. Given the heterogeneities between tomograms (a), it was necessary to determine, in advance of importation, the area of interest that had not been affected by the sampling (cutting, bending). This work was performed by image analysis using MatlabÒ software. First, edge detection (b) was used to isolate the images to be analyzed, throughout the entire thickness (c, d). A square area of variable size is created from the original image (e). Solid volume fraction is determined based on the size of the square. The graph (f) demonstrates the size where solid volume fraction begins to increase (f1, dense area) and the area where solid volume fraction decreases (f2, end of the fiber area). Tomograms were then cut according to the value of f1. The choice of the threshold value for the binarization of images was optimized thanks to MatlabÒ. The binary images were then read through the ImportGeo-Vol

Fig. 8. An example of one of the computational domains created with GeoDictÒ. The thickness of the medium is along the z direction (1218 lm), the ðxyÞ plane (143 lm  143 lm) corresponds to the filtration surface.

interface. Finally, the structure is cleaned by reallocating objects with a volume of less than 5000 voxels in fluid area. The 3D microstructure (g) consists of a fibrous mass 1500 voxels thick, containing upstream and downstream flow zones, with a filtration surface of 950  950 voxels. Resolution is equal to 0.16 lm per voxel. 3.3. The properties of computational domains properties The method used to determine the structural properties of the fibrous structures acquired by microtomography, using an image analysis program based on MatlabÒ image processing, has also been explained in our previous paper (Gervais et al., 2015). For ease of understanding, it is detailed below. Based on 2D-slices in the ðxzÞ plane (see Fig. 8), the medium thickness Z was determined in two steps:
The first step involved detecting the maximum medium thickness. The criterion to determine the thickness is the presence of at least one solid voxel in the domain. At this step, the minimum SVF and the maximum thickness were extracted. These values are not representative of the real medium, but they will be used as a basis for applying the second criterion.

160

P.-C. Gervais et al. / Chemical Engineering Science 165 (2017) 154–164

Fig. 9. Illustration of the steps for importing the stainless steel fibrous sample into GeoDictÒ, based on microtomography images.


The second step to evaluate the efficient characteristics of the real medium was the application of a more restrictive criterion. We estimated that the bulk of the medium begins when the local SVF corresponds to 5% of the mean minimal SVF of the  medium. Using this criterion, the effective thickness and SVF

the value determined by analyzing the stainless steel fibrous medium. As regards the fiberglass medium, we take note that the significant difference in SVF compensates for the gap revealed in terms of thickness (see Section 2.2) if the weight G of the medium is calculated.

were estimated. 3.4. Flow simulation These two steps were necessary in order to avoid some effects due to the small surface acquired using microtomography, like single fibers appearing in the 3D volume. The mean diameter df was measured on 2D-slices in the ðxyÞ plane. Each picture was crossed by six horizontal lines, on which two points on the fiber edge were detected. From these two points, a third was found, also on the fiber edge on a vertical axis, then the fiber diameter was determined by trigonometric calculation. As a hypothesis, we considered that the fibers are cylindrical and that the tortuosity of the fibers over a length equal to twice the diameter is negligible. This assumption was easily confirmed by the SEM pictures (see Fig. 1) of the real medium, as well as the 3D structure. The structural properties of the fibrous structures acquired by microtomography, resulting from the image analysis, are summarized in Table 4. Note that in the case of fiberglass medium, the properties are the average of the four subvolumes. For each medium, a difference of about 20% can be noted between the thicknesses determined in the analysis of the images acquired by microtomography, Z, and the averaged thickness value Z exp measured from the SEM pictures (see Table 2). This difference can be attributed to the restricted area treated using X-ray microtomography. Moreover, the fiber diameter values are very close to the value given by the manufacturer. Regarding solid volume fractions, good agreement is found between manufacturer values and

Table 4 Properties of the fibrous structures resulting from image analysis. Media

 (%) SVF

Z (lm)

df (lm)

Fiberglass Stainless steel

3.46 19.45

959.0 163.5

2.62 2.06

Flow simulation options are controlled with the FlowDict module. The air flow through the microstructure is governed by the Stokes equations, which consist of the momentum balance equation:

rp ¼ lDu

ð6Þ

and the continuity equation:

ru¼0

ð7Þ

where u is the velocity vector, p is the pressure and l is the dynamic viscosity. In order to compare with the experiments, the mean velocity U was set to 3.1 cm/s for fiberglass and 5.8 cm/s for the sintered stainless steel fibrous medium. Explicit finite volume solver was used to calculate flow in the computational subvolumes representing the fiberglass fibrous medium. Velocity inlet and pressure outlet boundary conditions were used in the flow direction. Periodic boundary conditions were imposed in tangential directions. LIR solver was used to calculate flow calculation in the computational domain representing the sintered stainless steel fibrous medium. This solver, only used for solving Stokes equations, allows the computational domain to be decomposed into an adaptive space. This is one way to refine the mesh in solving PDE using local linear systems (Linden et al., 2015). Use of this solver involves imposing periodic boundary conditions in the flow direction, requiring the incorporation of upstream/downstream areas. Conditions for symmetry were applied in tangential directions. The maximum number of iterations and the maximum computing time were set to 106 and 240 h respectively. Permeability was chosen as the stopping criterion. In each iteration, permeability is calculated from the current flow field using Darcy’s law. The solver

P.-C. Gervais et al. / Chemical Engineering Science 165 (2017) 154–164

accuracy was set to 104 . To decide whether the accuracy has been reached or not, the current permeability value is compared to the value obtained 100 iteration steps previously. The physical parameters are chosen as follows; air density: 1.204 kg/m3 and dynamic viscosity: 1:834  105 kg/ms. The results are obtained using a hardware configuration with 512 GB of RAM and a 4-hexa-core AMD CPU with a speed of 3.0 GHz. The local computation is executed on 32 processors. Note that the calculation time is around 40 h with the Explicit finite volume solver (on 1:16  109 meshes) whereas it decreases to 1h using LIR solver (on 1:35  109 meshes). 3.5. Particle transport simulation Particle transport settings are checked using the FilterDict module. Filtration simulations are performed using a Lagrangian description of the particle motion and are described by a force balance acting on each of them (Wiegmann et al., 2012):

X

F¼ma

ð8Þ

where m is the particle mass and a is the acceleration. The particle motion results from inertia, friction with the fluid and Brownian diffusion. Electrostatic effects are not considered. Thus, Eq. (8) can be expressed as follows:

dx ¼ v dt

ð9Þ

dv ¼ cðv ðxÞ  uðxÞÞdt þ D  dWðtÞ

ð10Þ

where t is the time, x is the position and v is the particle velocity. Brownian diffusion is calculated using the particle diffusivity D and a 3D Wiener process W. The latter is a mathematical model that describes a continuous-time stochastic process. Practically, in the time step discretization, a Gaussian distributed random value is added to the equation (Wiegmann et al., 2012). In the case of a Stokes flow and spherical particles, the friction coefficient is given by the following equation:

c¼

3pqldp Cu  m

ð11Þ

Cu, the Cunningham slip correction factor, is used to take the non-continuum effects into account when the drag force is calculated for a small particle:

"



Cu ¼ 1 þ Knp 1:17 þ 0:525e

1:56 Knp

#

ð12Þ

The experimental coefficient values are given by the GeoDictÒ user guide and come from Crowe (2006). Knp is the Knudsen number for particles in air. Here, it is defined as the ratio of the mean free path in air (k = 66 nm) to the particle radius in question. We consider that a particle is caught when its trajectory encounters a solid voxel. GeoDict does not directly simulate the real particle distribution. These latest are treated as points moving along their trajectory and are randomly arranged at the inlet according to a random seed. Initially, all particles have the velocity of the surrounding fluid at their start position. So the velocity depends on the position, but not the diameter. During the tracking, GeoDict ensure that a particle does not move more than a tenth of the voxel length in one-time step. This step size seems reasonably small given the fact that the flow field and the 3D structure data only has a resolution of one voxel. In order to compare the simulations with experimental data, simulated particles are created to mimic experiments. It should be noted that the morphology of the particles constituting the aerosol cannot be specified in GeoDictÒ. In addition, it is not

161

possible to simulate agglomerates or aggregates. Only singular spherical particles can be simulated. With the NaCl aerosol, the particles are considered to be cubic. In the deposit model, if for a given position, the radius of the particle is smaller than the distance separating it from the nearest solid voxel, the particle is collected. For each time step, the description of the particle motion allows GeoDict to compute mathematically the number of voxel which separate trajectory and solid voxel. Thus, to mimic the behavior of a cubic aerosol regarding the interception phenomenon, we determined the diameters of the spheres circumscribed in cubic particles (dcs ) from electrical mobility diameters (db ) classes of the SMPS. We used a 2-step process for this purpose:
using the electrical mobility diameter, we determined the sphere diameter, which has an equivalent volume (dv e ) in order to calculate the particle volume, using the following equation:

dv e ¼

db Cuðdv e Þ  v Cuðdb Þ

ð13Þ

The choice of the DSF and the iterative method used to calculate the ratio of Cunningham numbers are the same as those described in the Section 2.4.2.
The edge, a, of the cube which has the same volume as the sphere, is found by equalizing the volume:

a3 ¼

p 6

3

 dv e

ð14Þ

Finally, the diameter of the sphere circumscribed in the cube is calculated:

dcs ¼ a 

pffiffiffi 3

ð15Þ

Thus, for the collection efficiency confrontation between GeoDictÒ and the experiments, two X-axes will be used in graphical representations. For electrical mobility diameters between 0.0111 and 2.4686 micrometers, the diameters of the spheres circumscribed will be between 0.0149 and 3.2069 micrometers. 4. Comparison of numerical calculations and experiments 4.1. Permeability The error relative to the experimental data has been calculated in order to quantitatively compare the simulation with experimental data. We used the average values for relative errors, called the Mean Relative Error (MRE), as a qualitative criterion (Green and Margerison, 1978):

MREexp=sim ¼

N j yexp  ysim j 1X j j N j¼1 yexp j

ð16Þ

where y is the parameter of interest. Table 5 summarizes flow simulation results. For each medium, the simulated pressure drop DP, the resulting permeability values ksim and the mean relative error are indicated. Note that with the fiberglass medium, the results are the average of the four subvolumes. The flow simulations, in the structures created from microtomographies for each of the two media, have yielded very good results for permeability, since the MRE between GeoDictÒ values and the experiments are very low (see Table 5). From these results, it is fair to assert that the internal structures of the samples are representative of reality since permeability is an intrinsic property of the material. In the case of fibrous filters, permeability only depends on the solid volume fraction and on the fiber size, the shape and the arrangement.

162

P.-C. Gervais et al. / Chemical Engineering Science 165 (2017) 154–164

Table 5 Summary of the comparison of numerical calculations and experiments for permeability. Media

DP (Pa)

ksim  1011 (m2)

kexp  1011 (m2 )

MREexp=sim (%)

Fiberglass Stainless steel

21.29 (U ¼ 3:1 cm=s) 143.8 (U ¼ 5:8 cm=s)

3.26 0.178

3.24  0.25 0.185  0.027

0.6 4.2

Table 6 Summary regarding the values of thicknesses. Medium

Z (lm)

Z exp (lm)

Zþ (lm)

Z (lm)

Fiberglass Stainless steel

959.0 163.5

1185  91 212  31

1276 243

1094 181

Fig. 10. Collection efficiencies as a function of neutralized particle diameter. Comparison between the experiments and the averaged results computed with GeoDictÒ.

4.2. Fractional collection efficiency While X-ray microtomography can be used to create the calculation domain from real media, this technique is limited to a few selected samples. This can present some problems in terms of representativeness of thickness, however this parameter is critical to precisely simulate the collection efficiency. So, in order to compare collection efficiency from experiments with that was simulated using GeoDictÒ in a fair manner, it is necessary to take into account the difference between the thickness of the fibrous structures that were used to create the calculation domain, resulting from image analysis Z (see Table 4), with the averaged experimental thickness characterized by SEM Z exp (see Table 2). This difference may be taken into account by modeling the single fiber capture efficiency. Indeed, it is possible to calculate the filtration efficiency of fibrous media from the single fiber capture efficiency, gðdp Þ. The modeling takes into account air flow and particle characteristics as well as the structural properties of the filter. Calculation results from the particle concentration (C p ) balance on a thickness element dZ of the media:

dC p ¼ C p ðZÞ  gðdp Þ  df  Lv  dZ

ð17Þ

where Lv , the specific length, is the total length of the fiber by the bulk volume of the fibrous media. Knowing that the filtration efficiency is based on the upstream and downstream particle concentration ratio as shown in relation (5), the integration between 0 and Z of Eq. (17), gives the following expression for filtration efficiency (Dorman, 1974):



Eðdp Þ ¼ 1  e

a  Z 4gðdp Þ1 a pd

f



ð18Þ

The single fiber capture efficiency depends on the physical mechanisms governing the particle collection. Using the properties of the fibrous structures (computational domains) obtained from image analysis (see Table 4), the values of Eðdp Þ determined by simulation are used to find the single fiber capture efficiency using Eq. (18). Then, the thickness values determined experimentally Z exp (see Table 2), are used to calculate adapted values of Eðdp Þ. To ensure the representativeness of the thickness distribution, we chose to present the numerical results as an area limited by the extreme values of experimental thicknesses Zþ and Z (see Table 6). Fig. 10 shows the experimental and numerical collection efficiencies as a function of neutralized particle diameter, for the fiberglass (left/top) and sintered stainless steel (right/bottom) fibrous medium. The gray lines are the simulation results obtained from the calculation domains, without taking into account the correction in thicknesses between Z and Z exp . Both black lines for each graph are the corrected results (dashed in the Z case), which illustrates the influence of medium thickness on efficiency. We can see that the experimental points are properly bounded by the numerical curves determined from the extreme values of experimental thicknesses. Table 7 summarizes the comparison of numerical calculations with experiments for the collection efficiency. For each medium, the mean relative error is indicated. Note that MRE are only calculated for particle diameters in the SMPS range since the diameters of the spheres circumscribed have been for these diameters. Nevertheless, it seems that the MRE are slightly increased since the range of SMPS integrates MPPS. The gap between the experimental and numerical collection efficiencies is most important for this particle size. Based on the low mean relative errors, we note a good agreement between the experimental and simulated values of collection efficiency, especially for the extreme values of experimental

P.-C. Gervais et al. / Chemical Engineering Science 165 (2017) 154–164 Table 7 Summary of the comparison of numerical calculations and experiments for the collection efficiency. Media

MREexp=sim Zþ (%)

MREexp=sim Z (%)

Fiberglass Filter 1 Fiberglass Filter 2

0.7 0.7

3.6 3.7

Stainless steel Filter 1 Stainless steel Filter 2

1.4 1.5

7.0 6.2

thicknesses Zþ. While the deviations with the Z curves are slight, the best results obtained for Zþ can be explained by the filter holder type. Indeed, the samples are compressed over their circumference, which can induce the elastic swelling of the fibrous mass in the flow area. As with the permeability, the comparison of numerical calculations and experiments for the stainless steel samples is slightly less good than for the fiberglass samples. From our point of view, this may be due to the sintering process. Indeed, the modeling step necessary to take into account the different thicknesses involves the specific length. To calculate the total length of the fiber by the bulk volume of the fibrous media, it has been assumed that the fibers are cylindrical, which is not exactly the case for the medium in stainless steel since it contains some melting points between fibers (see Fig. 1).

163

The flow simulations have yielded very good results for permeability, since an average difference of less than 5% is observed. So, the internal structures of the samples are representative of reality since permeability is an intrinsic property of the material. While X-ray microtomography can be used to create calculation domains from real media, this technique is limited to a few selected samples. To compare collection efficiency from experiments with that simulated using GeoDictÒ, we have taken into account the difference between the thickness of the fibrous structures that were used to create the calculation domain, obtained from image analysis and the averaged experimental thickness characterized by SEM. Single fiber capture efficiency modeling was used for this purpose. The experimental points are properly bounded by the numerical curves determined from the extreme values of experimental thicknesses. Given these results, we can conclude with the first validation of the GeoDict code on both permeability and efficiency aspects, in the same study, for aerosols filtration by fibrous structures. Parametric simulations are envisaged to expand the validity range of the code. In the future, synchrotron X-ray nanotomography will be considered for producing images from H13 and H14 media, used for the design of High Efficiency Particulate Air filters and constituted of much finer fibers, with a wider fiber size distribution. The permeability, collection efficiency and penetration profile will be studied using GeoDictÒ.

5. Conclusion Acknowledgements The development of predictive models for the filter lifetime remains hardly achievable due to the wide range of operating conditions as well as aerosol and media characteristics. Given the multiplicity of parameters, the numerical approach is ideal. The main objective of this work was to validate, by comparison with experimental results, the CFD software GeoDictÒ, specialized in air filtration. As the purpose of this study is to complete the experimental validation of a simulation tool, we focused on simplified fibrous systems. The idea was to study some media exclusively composed of fibers whose diameter was more monodisperse. We focused on a fiberglass medium, widely used in general industry and particularly in the nuclear field. A sintered stainless steel fibrous medium has been also used to overcome potential electrostatic effects in collection efficiency measurements. First of all, the thicknesses of both media were characterized using MEB analysis. The thickness of the sintered stainless steel fibrous medium is very close to the target value required by the manufacturer, but a major difference is observed for the fiberglass medium. Experimental measurements were then performed for both kinds of medium. A series of pressure drop were measured for filtration velocities between 0 and 0.3 m/s on flat filter samples in order to determine the experimental value of permeability, kexp . In parallel, aerosol concentrations were measured, upstream and downstream from flat filter samples, for different aerosol state of charge configurations, in order to calculate experimental collection efficiency. The computational domain is the basis for the simulation, and virtual fibrous geometry design involves a lot of assumptions, even if the structural parameters are well-known. Through an interface dedicated to image analysis, GeoDictÒ allows data to be imported and processed from computed tomography. Synchrotron X-ray microtomography was used as a way to create representative computational domains, in order to simulate filter media performances. Images of the filter media studied were acquired on the ID19 beamline of the European Synchrotron Radiation Facility (ESRF, Grenoble, France). An image analysis program based on MatlabÒ was used to determine the structural properties of the fibrous structures, namely thickness, solid volume fraction and fiber size distribution.

The authors are grateful to the companies Bernard Dumas (Creysse, France) and Bekaert (Zwevegem, Belgium), for the design of fibrous media samples. The authors are grateful to the NOVITOM company, in Grenoble, France, (www.novitom.com) for the acquisition and reconstruction of the microtomography. References Bourrous, S., Bouilloux, L., Ouf, F.-X., Appert-Collin, J.-C., Thomas, D., Tampère, L., Morele, Y., 2014. Measurement of the nanoparticles distribution in flat and pleated filters during clogging. Aerosol Sci. Technol. 48 (4), 392–400. http://dx. doi.org/10.1080/02786826.2013.878453. Carlo, P.F.D., Slowik, J.G., Worsnop, D., Davidovits, P., Jimenez, J.L., 2004. Particle morphology and density characterization by combined mobility and aerodynamic diameter measurements. Part 1: theory. Aerosol Sci. Technol. 38, 1185–1205. Crowe, C.T., 2006. Multiphase Flow Handbook. Taylor and Francis. Darcy, H., 1856. Les Fontaines Publiques de la Ville de Dijon. Victor Dalmont, France (in French). Dorman, R., 1974. Dust control and air cleaning. International Series of Monographs in Heating, Ventilation, and Refrigeration, vol. 9. Pergamon Press. Fotovati, S., Tafreshi, H.V., Ashari, A., Hosseini, S.A., Pourdeyhimi, B., 2010a. Analytical expressions for predicting capture efficiency of bimodal fibrous porous media. J. Aerosol Sci. 41 (3), 295–305. http://dx.doi.org/10.1016/ j.jaerosci.2010.01.002. Fotovati, S., Tafreshi, H.V., Pourdeyhimi, B., 2010b. Influence of fiber orientation distribution on performance of aerosol filtration media. Chem. Eng. Sci. 65 (18), 5285–5293. http://dx.doi.org/10.1016/j.ces.2010.06.032. Fuchs, N.A., Stechkina, I.B., 1963. A note on the theory of fibrous aerosol filters. Ann. Occup. Hyg. 6 (1), 27–30. Gervais, P.-C., Ricciardi, L., 2014. Air flow and particle transport simulations in fibrous media. In: Aerosol Technology 2014, Karlsruhe, Abstract T290A13. Gervais, P.-C., Bardin-Monnier, N., Thomas, D., 2012. Permeability modeling of fibrous media with bimodal fiber size distribution. Chem. Eng. Sci. 73, 239–248. http://dx.doi.org/10.1016/j.ces.2012.01.040. Gervais, P.-C., Bourrous, S., Dany, F., Bouilloux, L., Ricciardi, L., 2015. Simulations of filter media performances from microtomography-based computational domain. Experimental and analytical comparison. Comput. Fluids 116, 118– 128. Gougeon, R., Boulaud, D., Renoux, A., 1995. Experimental study of stationary filtration with model fiber filters. Comparison with different deposition models. J. Aerosol Sci. 26 (Suppl. 1), S913–S914. Gougeon, R., Renoux, A., Boulaud, D., 1996. Comparison of data from model fiber filters with diffusion, interception and inertial deposition models. Chem. Eng. Commun. 151 (1), 19–39.

164

P.-C. Gervais et al. / Chemical Engineering Science 165 (2017) 154–164

Green, J.R., Margerison, D., 1978. Statistical Treatment of Experimental Data. Elsevier, Amsterdam. Hinds, W.C., 1999. Aerosol Technology: Properties, Behavior, and Measurement of Airborne Particles. Wiley, New York. Hosseini, S.A., Tafreshi, H.V., 2010. 3-D simulation of particle filtration in electrospun nanofibrous filters. Powder Technol. 201 (2), 153–160. http://dx. doi.org/10.1016/j.powtec.2010.03.020. Kirsch, A.A., Fuchs, N.A., 1967. Studies on fibrous aerosol filters-II. Pressure drops in systems of parallel cylinders. Ann. Occup. Hyg. 10 (1), 23–30. Kirsch, A.A., Fuchs, N.A., 1968. Studies on fibrous aerosol filters-III. Diffusional deposition of aerosols in fibrous filters. Ann. Occup. Hyg. 11 (4), 299–304. Linden, S., Wiegmann, A., Hagen, H., 2015. The LIR space partitioning system applied to the Stokes equations. Graph. Models 82 (c), 58–66. Paganin, D., Mayo, S.C., Gureyev, T.E., Miller, P.R., Wilkins, S.W., 2002. Simultaneous phase and amplitude extraction from a single defocused image of a homogeneous object. J. Microsc. 206 (Pt 1), 33–40. http://dx.doi.org/10.1046/ j.1365-2818.2002.01010.x. Stechkina, I.B., Fuchs, N.A.F., 1966. Studies on fibrous aerosol filters-I. Calculation of diffusional deposition of aerosols in fibrous filters. Ann. Occup. Hyg. 9 (2), 59–64.

Stechkina, I.B., Kirsch, A.A., Fuchs, N.A., 1969. Studies on fibrous aerosol filters-IV. Calculation of aerosol deposition in model filters in the range of maximum penetration. Ann. Occup. Hyg. 12 (1), 1–8. Tafreshi, H.V., Rahman, M.S.A., Jaganathan, S., Wang, Q., Pourdeyhimi, B., 2009. Analytical expressions for predicting permeability of bimodal fibrous porous media. Chem. Eng. Sci. 64 (6), 1154–1159. http://dx.doi.org/10.1016/j. ces.2008.11.013. Topas, 2014. Topas Electrostatic Aerosol Neutralizer EAN 581, Topas GmbH. Wang, Q., Maze, B., Tafreshi, H.V., Pourdeyhimi, B., 2007. Simulating through-plane permeability of fibrous materials with different fiber lengths. Modell. Simul. Mater. Sci. Eng. 15 (8), 855–868. http://dx.doi.org/10.1088/0965-0393/15/8/ 003. Wiegmann, A., Cheng, L., Rief, S., Latz, A., Wagner, C., Wersterteiger, R. 2012. Simulating filter efficiency and lifetime with FilterDict, GeoDict User Guide. Zelenyuk, A., Cai, Y., Imre, D., 2006. From agglomerates of spheres to irregularly shaped particles: determination of dynamic shape factors from measurements of mobility and vacuum aerodynamic diameters. Aerosol Sci. Technol. 40 (3), 197–217.