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7th International Conference on Multiphase Flow
ICMF 2010, Tampa, FL USA, May 30-June 4, 2010
Generation of three dimensional nonwoven structures for simulation of fluid flow
and particle deposition
Tobias Warth, Manfred Piesche
University of Stuttgart, Institute of Mechanical Process Engineering (IMVT)
Bdblinger Str. 72, 70199 Stuttgart, Germany
warth~,imvt.uni-stuttgart. de
Keywords: CFD, Nonwovens, Particle separation, Filtration efficiency,
Pressure drop, Lattice-Boltzmann-Method
Abstract
In the first part of this study the results of the solution of the Navier-Stokes-Equations using the Lattice Boltzmann
Method and the Finite Volume Method for the flow through regular fiber structures are compared and opposed to
measurements. In the second part virtually generated nonwoven structures based on geometrical parameters like
porosity, fiber diameters, media thickness and anisotropy of real metal nonwovens as an alternate to the costly
digitalization of cutouts of the real media is reviewed. The resulting flow field serves as a basis for a Lagrangian
particle simulation and their initial deposition in the media. Pressure drop and collection efficiency are compared to
measurements. The importance of proper consideration of particle bouncing off the fibers for simulation of filter
efficiency and lifetime is illustrated by additional comparison with approximations from literature.
Introduction
There are various options to generate a digital three
dimensional image of a nonwovens geometric
structure. Time-consuming methods like CT-scanning
or Digital Volumetric Imaging (DVI), which are often
used in literature [2, 3], are capable of converting the
real stochastic structure into CAD data. Alternatively,
the model geometry can be generated by random
algorithms [4, 5]. Virtually generated structures allow
the fast replication of nonwovens based on geometric
properties like porosity, fiber diameter, anisotropy and
the thickness of the media and therefore examination
of their influences on pressure drop and filtration
efficiency using numerical simulation methods.
Due to the highly stochastic character of nonwoven
filter media and the resulting complex flow field,
examination of a representative cutout of an assembly
of randomly arranged fibers is necessary. Especially
for filter efficiency simulations, when the relevant
particle sizes are comparable to the pore sizes of the
nonwovens and hence the filtration is dominated by
inertia effects, a reproduction of the pore size
distribution within the nonwoven and the knowledge
of the flow field is required. Nevertheless, the flow
field has an influence on particle capture for smaller
particles as well, even when Brownian motion is the
dominant filtration mechanism. With today's
increasing available computing power the numerical
simulation of complex cutouts of nonwoven structures
offers a way for a better understanding of filtration
mechanisms. Besides the common Navier-Stokes
solvers using the Finite Volume Method (FVM), the
Lattice Boltzmann Method (LBM) is a powerful
technique for the simulation of single and multiphase
flows in such complex geometries, owing to its
numerical stability and constitutive versatility [6].
For both methods flow simulations were carried out.
This was done in a first step for a regular arrangement
of single fibers to compare the methods to each other.
In a second step a square mesh filter cloth was used to
verify the simulations with pressure drop
measurements. Finally LBM simulations for virtual
nonwovens based on real filter media are compared to
measurements regarding pressure drop and filter
efficiency.
7th International Conference on Multiphase Flow
ICMF 2010, Tampa, FL USA, May 30-June 4, 2010
resolution of 10 pm (grid: Gl, shown in figure 1)
respective 5 pm (G2, FVM) and a fiber with smooth
surface using an unstructured, locally refined grid (G3,
FVM) with a resolution of about 1 pm in the fiber's
proximity. In that way, differences in the calculated
flow field due to the different numerical methods and
different surface structures can be detected.
Nomenclature
d Diameter (pm)
p Pressure (Pa)
w Velocity (ms ?)
W Width (m)
H Height (m)
R Restitution
A Hamaker's Parameter (J)
Greek letters
6 Media thickness (p~m)
E Porosity (1)
p Density (Kg m-3)
Viscosity (Kg ml s )
Subsripts
f Fiber
fl Fluid
0 Undisturbed
p Particle
Dimensionless N~umbers
Re Reynolds Number
St Stokes Number
Pil -d, -wo
Re =
.. .. .. .. .. .. .. .. .. .. .. .. .. .
W = 1240 pum
x***************
H = 1500 p~m
all boundaries of
periodic type
Pp d~ w, 1
St -
18-gy,-d, Cu
Regular Structures
Validation of the simulations is conducted for the FVM
implemented in the commercial software Fluent" and
the LBM implemented in the GeoDIct code. In a first
step the airflow through a regular arrangement of single
fibers is carried out. The simulation domain is shown in
figure 1 (top). All boundaries are of periodic type. As
the LBM uses a structured grid with equilateral
hexahedrons for discretisation (voxels), a high
resolution is required for a good mapping of the
structures' surfaces resulting in high memory
requirement in case of large simulation areas. The
Finite Volume Method also allows the usage of an
unstructured, locally refined grid. Thus a smoother
surface of rounded structures like fibers is possible and
high resolution is only used where required, resulting in
lower total cell numbers. Therefore the influence of
different resolutions and surface mapping were
examined. Exemplarily shown in figure 2 are the results
for an identical structure for both methods with a mesh
Figure 1: top: Simulation area of an arrangement of
single fibers; bottom: discretisation schemes
(examples)
As the results in figure 2 show, there are only marginal
differences in the calculated flow fields. Therefore
maximum pressure drop deviation is 1.2 % for
Reynolds numbers from Re = 1 to Re = 20 as shown
in figure 3.
7th International Conference on Multiphase Flow
ICMF 2010, Tampa, FL USA, May 30-June 4, 2010
- - - + - - - - - -
cutout for
simulation
0.10
0.05
- .0
65 pm
0.90 -
0.45
Figure 2: Simulated flow field for single fiber
arrangement: velocity contours left: LBM, structured
grid Gl: velocity contours right: FVM, refined
structured grid G2 (top), unstructured grid G3
(bottom); velocities in m/s
200
100 Ip
Figure 4: Left square mesh dimensions; right: cuout
for simulation, structured grid (top) used in LBM with
2 pm voxel size, locally refined grid used by FVM:
150 0FVM
r LBM
& 100 -
1.5 3.0
velocity magnitude \ m/s
Figure 5: comparison of simulated flow fields using
FVM respective LBM
Re [1]
2.2 8.9
13.3 17.8
0 10 20
Re [1 ]
Figure 3: Simulated pressure drop per unit length
over periodic fiber arrangements using LBM
respective FVM:
The validation of the numerical simulations requires
the aligmnent with experimental data. For easier
comparison with measurements, a woven square mesh
filter medium with its well defined geometry is taken
as a basis. The precondition for the simulation of
virtually generated nonwovens is given for good
agreement between these validation simulations and
the measurements. The diameter of warp and weft of
the square mesh is 65 pm, the aperture size is 100 pm.
a Measurement
4 FVM
A LB-Method
80
60 -
-
20
0 ~
0 1 2
wo [m/s ]
3 4
Figure 6: Comparison of the simulated pressure drop
over a woven square mesh filter medium with
experiments for varying filter face velocities we
FVM
0.0
Media de [pm] e [%] 6 [pm]
filter #1 7 77 170
filter #2 8 80 190
filter #3 13 84 230
7th International Conference on Multiphase Flow
ICMF 2010, Tampa, FL USA, May 30-June 4, 2010
In figure 5 the comparison of numerical results of the
flow fields for both methods shows again good
accordance for this more complex flow field. The
difference of the simulated pressure drop is therefore
low at about 3 % and the measurement results that are
also shown in the chart (fig. 6) align the simulation
data.
These pre examinations show that both numerical
methods provide good results in the examined range
for Re < 20.
Nonwovens
Based on three different real metal fiber nonwovens,
varying in their geometric parameters shown in table 1,
the virtual structures for the simulation with the LBM
1000 -
800
e 600
0- 400 -
200
O
ii
.
0123456
wo \m/s
Figure 8: Comparison of simulated and measured
pressure drop for three nonwovens
For the simulation of particle deposition a Lagrangian
formulation for particle movement implemented in the
GeoDIct code [1] is used. A model regarding
adhesion and restitution is provided for consideration
of bouncing effects. Attraction between particle and
fiber due to van der Waals forces can be adjusted via
Hamaker's parameter A. Restitution R governs the loss
of kinetic energy of a particle during the collision with
a fiber, whereas R = 0 means a total loss of kinetic
energy (plastic deformation) and R = 1 a completely
elastic deformation without loss of kinetic energy.
Particles adhere to the fiber if the kinetic energy after
the collision is not sufficient to exceed the attraction
forces. The results of these calculations are compared
to measurements of the initial grade efficiency of the
metal fiber nonwovens. The considered Stokes
numbers range from St = 0.01 to st = 20. The filter test
rig consists of an aerosol generator, an electrical
Corona discharging unit, a light-scattering
spectrometer (Welas"), the filter housing for circular
blanks of the test medium and a vacuum pump. SAE
coarse test dust was used at a filter face velocity of
0.167 m/s. Simulated efficiencies in figure 9 show
clear dependency of the resolution of the numerical
grid on particle deposition, especially for particles in
the same scale as the grid resolution. This is already
observed elsewhere [7]. A finer resolution could not
be realized so far due to the high memory
requirements. For larger particles, i.e. higher Stokes
numbers, the simulated filter efficiency is too high as
particle bouncing is not considered here. A model for
the consideration of particle bouncing behavior is
required for simulations at higher Stokes numbers. In
figure 10 simulation results based on the adhesion/
restitution model implemented in GeoDIct show the
influences of the parameters Hamaker A and
restitution R on filtration efficiency cp. Used values
are generated
GeoDIct [41.
using the algorithm implemented in
geometrical data for three nonwoven
Table 1:
structures
Figure 7: Comparison of real (left, SEM image) and
virtually generated fiber structure (right) for filter #2
Based on the three generated fiber structures,
simulations of the flow field are carried out using
LBM. The simulation area is chosen large enough to
avoid influences of fiber length since it is regarded as
infinite. The results show a good accordance to the
pressure drop measurements for the three reviewed
media (fig. 8).
*------ Filter #1
---- Filter #2
- Filter #3
Simulation
were A = 5e-19 J [9] respective A = le-19 J and a
restitution of R = 0.6 [10]. The peak of the curves
using the adhesion/restitution model marks the point,
where particles predominantly bounce off the fibers
until finally sieving effects dominate and filter
efficiency increases again. The abrupt, sensible change
to particle bouncing shows the complexity of finding
one set of parameters for a complete inhomogeneous
particle size distribution, due to the influences of
surface roughness, particle shape and material
properties on the bouncing behavior.
d [pm ]
Figure 9: Filter #1; influence of grid resolution on
simulated filtration efficiency cp
1
-A=1e-19/R=0.6
-A=5e-19/R=0.6
- Experirrent
0.1 d m 10
Figure 10: influence of simulated bouncing effects,
particles are caught on first touch (COFT) or bounce
off with a restitution of 0.6 and values of Hamaker s
parameter of A = le~' J respective A = 5e~' J
Figure 11 shows the comparison of calculated filter
7th International Conference on Multiphase Flow
ICMF 2010, Tampa, FL USA, May 30-June 4, 2010
efficiencies cp using approximations from literature
with the simulation and experimental data.
Approximations for single fiber efficiencies 77
considering diffusion (Lee and Liu, [11]), inertia and
interception effects (Yeh and Liu, [12]) are used and
filter efficiency is then calculated via equation (3).
11 E df ]IU1 3
The calculated and simulated curve progressions show
the same tendency. The filter efficiency for larger
particles is calculated too high as particle bouncing is
not considered here.
-Theoretical approx.
-Simulation
- -Experiment
0.1 1 10
d [plm ]
Figure 11: Comparison of theoretical calculation
(diffusion: Lee and Liu [11], inertia and interception:
Yeh and Liu [12]) and simulation (COFT, resolution
0.4 pm) for filter #1
Conclusion
The numerical simulation of air flow through a regular
fiber arrangement using the two simulation techniques
Finite Volume Method and Lattice Boltzmann Method
for the solution of the Navier-Stokes-Equations
showed good accordance regarding the velocity
distribution and pressure drop. Measurements could
verify both simulation results for pressure drop.
Simulated flow through virtually generated nonwoven
structures showed good conformity to measurements
as well. Therefore the virtual structures can provide an
alternative to the costly, three dimensional
digitalisation of real nonwovens. Nevertheless,
extensive inhomogeneities in real fiber media cannot
be represented in the comparatively small simulation
area.
- Resolution 1.33 plm
- Resolution 0.66 pm
- Resolution 0.4 plm
- Extperiment
Resolution
7th International Conference on Multiphase Flow
ICMF 2010, Tampa, FL USA, May 30-June 4, 2010
A. Latz, "Simulation studies of deposition
mechanisms for aerosol particles in fibrous filters
including slip flow", 10th World Filtration Congress,
Leipzig, Germany (2008)
[8] A. Latz and A. Wiegmann, "Simulation of fluid
particle separation in realistic three dimensional fiber
structures", Filtech Europa, Diisseldorf, Germany
(2003)
[9] R. Hiller, F. Ldffler, "Der Einfluss von
Auffreffgrad und Haftanteil auf die
Partikelabscheidung in Faserfiltern", Staub-Reinhalt.
Luft 40, pp. 405-411 (1980)
[10] R. Hiller, "Der Einfluss von Partikelstol) und
Partikelhaftung auf die Abscheidung in Faserfiltern",
PhD Thesis, Universitiit Karlsruhe (1981)
[11] K. W. Lee, Liu B. Y. H. "Theoretical Study of
Aerosol Filtration by Fibrous Filters", Aerosol Science
and Technology 1, pp. 147-161 (1982)
[12] H. C. Yeh, Liu B. Y. H. "Aerosol Filtration by
Fibrous Filters", Aerosol Sci. 5, pp. 191-217 (1974)
The simulation of the particle transport to the fibers
seems to provide good results as can be observed by
the good accordance for separation efficiency of
particles at low Stokes numbers. However, for
increasing Stokes numbers, when particle rebound has
to be taken into account, it seems that the quite simple
adhesion/restitution model used in this work is not
sufficient to represent the more complex behavior of
the test dust. This is probably due to further
parameters like surface roughness, particle shape and
material properties of the real particle system, which
are not considered in the implemented collision model.
Further work will be necessary to expand the
implemented model via User Defined Functions
(UDF) and to compare these simulations to
experimental results of the filtration efficiencies using
spherical polystyrene particle standards for example.
A proper simulation of such a simplified setup is the
basis for the simulation of a real and more complex
particle system. Covering these details is challenging
but seems to be essential for the prediction of filter
efficiency and lifetime.
References
[1] A. Latz and A. Wiegmann, "Simulation of fluid
particle separation in realistic three dimensional fiber
structures", Filtech Europa, Diisseldorf, Germany
(2003)
[2] S. Jaganathan, H. Vahedi Tafreshi, B. Pourdeyhimi,
"A realistic approach for modeling permeability of
fibrous media: 3-D imaging coupled with CFD
simulation", Chemical Engineering Science, Volume
63, Issue 1, January 2008, pp. 244-252
[3] Gernot Boiger, Marianne Mataln, Bernhard
Gschaider, "Large particle modelling in realistic
filtration fibre geometry", OpenFoam WS, Milan
(2008)
[4] A. Wiegmann, S. Rief and A. Latz, "Computer
Models of Nonwoven Geometry and Filtration
Simulation", International Nonwoven Technical
Conference, Houston, Texas (2006)
[5] Q. Wang, B. Maze, H. Vahedi Tafreshi, B.
Pourdeyhimi, "Simulating through-plane permeability
of fibrous materials with different fiber lenghts",
Modeling and Simulation in Materials Science and
Engineering, 15 (2007), pp. 855-868
[6] D. Raabe, "Overview of the lattice Boltzmann
method for nano- and microscale fluid dynamics in
materials science and engineering", Modeling and
Simulation in Materials Science and Engineering, 12
(~lrl14) pp. R13-R46
[7] A. Wiegmann, K. Schmidt, S. Rief, L. Cheng and
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