Group Title: 7th International Conference on Multiphase Flow - ICMF 2010 Proceedings
Title: 5.3.2 - Numerical and experimental investigation of the pressure and velocity field inside a pleat of an air filter during loading
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Title: 5.3.2 - Numerical and experimental investigation of the pressure and velocity field inside a pleat of an air filter during loading Industrial Applications
Series Title: 7th International Conference on Multiphase Flow - ICMF 2010 Proceedings
Physical Description: Conference Papers
Creator: Kopf, P.
Piesche, M.
Publisher: International Conference on Multiphase Flow (ICMF)
Publication Date: June 4, 2010
Subject: air filtration
Lagrangian simulations
particle-laden gas
Abstract: A numerical model has been developed to simulate the loading of pleated filter elements in order to determine separation efficiency and dust holding capacity. The model is based on a commercial CFD code which is coupled with a depth and surface filtration model. To validate the model pressure and flow velocity inside a single model pleat of a filter medium are measured and compared to the numerical results.
General Note: The International Conference on Multiphase Flow (ICMF) first was held in Tsukuba, Japan in 1991 and the second ICMF took place in Kyoto, Japan in 1995. During this conference, it was decided to establish an International Governing Board which oversees the major aspects of the conference and makes decisions about future conference locations. Due to the great importance of the field, it was furthermore decided to hold the conference every three years successively in Asia including Australia, Europe including Africa, Russia and the Near East and America. Hence, ICMF 1998 was held in Lyon, France, ICMF 2001 in New Orleans, USA, ICMF 2004 in Yokohama, Japan, and ICMF 2007 in Leipzig, Germany. ICMF-2010 is devoted to all aspects of Multiphase Flow. Researchers from all over the world gathered in order to introduce their recent advances in the field and thereby promote the exchange of new ideas, results and techniques. The conference is a key event in Multiphase Flow and supports the advancement of science in this very important field. The major research topics relevant for the conference are as follows: Bio-Fluid Dynamics; Boiling; Bubbly Flows; Cavitation; Colloidal and Suspension Dynamics; Collision, Agglomeration and Breakup; Computational Techniques for Multiphase Flows; Droplet Flows; Environmental and Geophysical Flows; Experimental Methods for Multiphase Flows; Fluidized and Circulating Fluidized Beds; Fluid Structure Interactions; Granular Media; Industrial Applications; Instabilities; Interfacial Flows; Micro and Nano-Scale Multiphase Flows; Microgravity in Two-Phase Flow; Multiphase Flows with Heat and Mass Transfer; Non-Newtonian Multiphase Flows; Particle-Laden Flows; Particle, Bubble and Drop Dynamics; Reactive Multiphase Flows
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Volume ID: VID00126
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Resource Identifier: 532-Kopf-ICMF2010.pdf

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7th International Conference on Multiphase Flow,
ICMF 2010, Tampa, FL, May 30 -June 4, 2010

Numerical and experimental investigation of pressure and flow velocity inside a
pleat of an air filter during loading

P. Kopf* and M. Piesche*

Institute of Mechanical Process Engineering, University of Stuttgart, 70178 Stuttgart, Germany
Keywords: air filtration, lagrangian simulations, particle-laden gas, LDA


A numerical model has been developed to simulate the loading of pleated filter elements in order to determine
separation efficiency and dust holding capacity. The model is based on a commercial CFD code which is coupled
with a depth and surface filtration model. To validate the model pressure and flow velocity inside a single model pleat
of a filter medium are measured and compared to the numerical results.


Roman symbols
C Cunningham correction (1)
D particle diffusional coeff. (m2s 1)
E efficiency (1)
H hydrodynamic factor (1)
d diameter (m)
d32 Sauter mean diameter (m)
h thickness (m)
k constant (m)
u velocity (ms 1)
Greek symbols
6 porosity (1)
r/ single fiber efficiency (1)
A mean free path (m)
P viscosity (Pas)
p density (kgm-1)
0 sphericity (1)
D diffusion
I inertia
R interception
b bulk
f fiber
fm filter medium
fc filter cake
1 labyrinth
p particle
r real
Dimensionless numbers

Knudsen number (2Adp 1)
Peclet number (udfD 1)
Stokes number (d'ppC(18,pdf) 1)
interception parameter (ddf 1)


Specifications for modem filter systems concerning e.g.
dust holding capacity and pressure drop are more and
more challenging to comply with. This is due to tech-
nical progress, higher emission standards and limited
space especially for air intake filters of combustion en-
gines. To meet the requirements, the capacity of the fil-
ter medium must be utilized completely. This can be
reached by an optimization of the incident flow of the
filter element and the geometry of the element itself, e.g.
pleat density and depth. Latter is done mainly by exten-
sive and costly experiments and it would be a great ben-
efit to reduce the number of experiments via numerical
simulations of the loading process.
Unfortunately CFD in the field of filtration is difficult
mainly for two reasons. Firstly, the dimensions consid-
ered span some orders of magnitude. Inside the filter
medium separation of particles takes place on fibers with
diameters of some micrometers while flow through the
medium is influenced by the pleat geometry and the filter
housing with dimensions of several centimeters. Even
by using high performance computers it is not possible
to resolve the smallest scales in detail when looking at
the macroscopic flow at the same time. Secondly, prop-
erties of the filter medium are changing significantly dur-

7th International Conference on Multiphase Flow,
ICMF 2010, Tampa, FL, May 30 -June 4, 2010

ing dust loading. Pressure drop rises and strongly affects
the upstream flow. Thus, kinetics of filtration must be
considered in order to simulate the behavior of the filter
during its life time.
To handle the difficulties mentioned above, a simula-
tion model has been developed which solves the scale
problem by the use of analytical filtration models from
literature. They replace the simulation of flow on the mi-
cro scale and are coupled with a commercial CFD code
(FLUENT) via user defined functions (UDF). These
analytical filtration models contain various parameters
from which some have to be determined by filtration
experiments. In order to validate the coupled simula-
tion model the velocity field on the upstream side of
a single model pleat of filter medium is measured dur-
ing loading with a Laser Doppler Measurement tech-
nique(LDA). Additionally the overall pressure drop and
the local pressure at different positions on the down-
stream side of the pleat is measured.

Numerical model

SFlow field calculation

Calculation of dust mass distribution

Depth filtration model

Surface filtration model

Calculation of momentum sink terms

Figure 1: Simulation sequence.

When the filter medium is loaded the flow field in-
side the filter apparatus changes because of the rising
pressure drop due to particle deposition. This is a tran-
sient process and thus the numerical simulation has to be
transient, too. But if the dust concentration is low, pres-
sure drop changes slowly compared to the flow velocity
and the flow field can be approximated by a quasisteady
solution during a certain time interval. The steady so-
lution has to be updated only if the particle depositions
are large enough to change the flow field significantly.
By the help of this simplification it is possible to sim-
ulate the loading process of the filter medium during
its lifetime with acceptable computational costs. Using
this simplification the simulation can be divided into five

main parts shown in Fig.1, which forms a quasisteady
time step. The five parts are repeated until a certain load-
ing state of the filter is reached.
Flow field calculation. The flow field is calculated by
solving the Navier-Stokes equations under consideration
of additional momentum sink terms which account for
the pressure drop due to the flow through porous regions
like the filter medium and the filter cake. These pressure
drops are calculated using analytical filtration models,
which were explained later on.
Calculation of dust mass distribution. Since the
dust loading of the filter medium is not homogeneous
in pleated filters because of inertial effects and an un-
equal perfusion of the filter it has to be determined via a
two phase CFD simulation. The dust considered in this
work is the standard Arizona test dust (A2 fine) com-
plying with ISO 12103-1. It is characterized by a very
broad particle size distribution ranging from some hun-
dret nanometers to 120 micrometers. While the smaller
particles follow the flow with negligible slip the bigger
particles show considerable inertia effects which have to
be considered. Therefore the particle size distribution is
divided into two fractions which are treated in a different
The small particles with negligible inertia (in our case
< 1 pm ) are treated like massless particles which are
homogeneously distributed in the flow. This small parti-
cle phase is characterized by a concentration and a par-
ticle size distribution. The mass flow of these particles
through the surface of the filter medium is simply calcu-
lated by a multiplication of the air volume flow and the
concentration of small particles.
To account for inertia effects in the separation of the
bigger particles, an Euler-Lagrange method is used to
calculate the particle trajectories. For each size class
of the particle size distribution of bigger particles some
hundred particle tracks are calculated in order to de-
termine the location where particles penetrate the filter
In each control volume on top of the filter medium the
particle size distribution of the deposited particle mass
is calculated based on the results of the particle tracking
for the bigger particles and the mass flow balance for the
smaller particles.
Depth filtration model. The depth filtration model is
based on the widely used model of Konstandopoulos et
al (1). It has been developed to describe the filtration of
soot particles in diesel particulate traps but is also capa-
ble to describe the filtration in fibrous filter media. Ba-
sis of the model is the "unit collector" filtration theory,
in which the complex three dimensional filter structure
is described by a regular arrangement of equivalent unit
collectors. A detailed summary of unit collector filtra-
tion theory could be found for example in (2). The unit

collectors could be spherical or cylindrical depending on
the real filter medium. In our case the filter medium con-
sists of cellulose fibers so we chose cylindrical collec-
tors. The separation of dust particles in the real com-
plex fiber arrangement is simplified to the well described
separation of particles on a single fiber. The deposition
mechanisms considered in this work are diffusion, inter-
ception and inertia which are combined by a summation:

1l = /D + IR + l/ (1)
For the single fiber efficiency due to diffusion an ex-
pression of Stechkina and Fuchs (3) was used.

riD = 2.9H 1/3pe2/3 + 0.624Pe (2)

It is a function of the dimensionless Peclet number Pe
and a hydrodynamic factor H after Kuwabara (4) which
accounts for the porosity ef, of the fiber arrangement.

H 0.51n( m)- + (1
(1 Ejm)2


Single fiber efficiency due to interception is modeled af-
ter Kirsch and Stechkina (5) as a function of interception
parameter R and the Knudsen number Kn.

2k- -l1 + R)
(2 + R)R (4)
+2(1 + R) ln(1 + R) + 2.86Kn (2+ RR


k 0.51og(1 E ,)
0.52 + 0.64(1 c) + 1.43cfmKn.

Inertial deposition is described with the following em-
pirical equation after Davies (6),

ri [0.16 + 10.9(1 em)
[R + (0.5 + 0.1R)Sto -

-17(1 et,)2]

wherein the Stokes number Sto describes inertia of the
particles. The constants of the original equation have
been adapted to represent our experimental results.
As the unit collector theory assumes an equal spatial
distribution of collectors inside the filter medium, which
is not the case in a real filter medium, it over predicts
the filtration efficiency. Therefore Benarie (7) suggests
a correction of the efficiency which depends on the pore
size distribution of the filter medium. If the pore size dis-
tribution follows a logarithmic normal distribution with
the standard deviaton arg, the average single fiber effi-
ciency of the real filter medium rT, can be approximated

7th International Conference on Multiphase Flow,
ICMF 2010, Tampa, FL, May 30 -June 4, 2010

from the single fiber efficiency of the ideal filter medium
after the following equation.

logl0 Ti

To calculate the separation efficiency E of the whole
filter medium, a differential mass balance around a sin-
gle collector has to be integrated over the depth of the
filter medium hf, under consideration of its structural
parameters fiber diameter df and porosity cf, and its
single fiber efficiency ri. This leads to

E 1 exp 4(1


With the classical single fiber theory only the effi-
ciency of a clean filter medium can be calculated, not the
change of it during loading. Therefore Konstandopoulos
introduces in his model a modification of the unit collec-
tor size which depends on the deposited particle mass.
The diameter of the collector grows while the porosity
is reduced. As a consequence collection efficiency and
pressure drop rises.
In order to reproduce the dust distribution in the depth
of the filter medium Konstandopoulos divides it into
slabs of equal thickness and calculates the deposition
of dust mass in each slab according to equation (8).
The buildup of a filter cake on top of the filter medium
is realized by a partition coefficient which determines
the amount of dust mass that stays on top of the filter
medium. This coefficient is proportional to the fraction
of surface area that is blocked by the dust loaded fibers
in the first slab. The details of the depth filtration model
can be found in (1). The implementation of the depth
filtration model into the CFD Code is outlined in Fig.2.
The control volumes of the CFD grid inside the filter
medium are subdivided into slabs needed for the depth
filtration model. This is necessary since the amount of
computational cells inside the filter medium is typically
much lower than the amount of slabs for the filtration
Surface filtration model. During the loading process
of the pleated filter medium a filter cake builds up on the
surface of the filter medium and narrows the pleat. Pres-
sure drop rises mainly because of two reasons: firstly
due to the flow through the filter cake and secondly due
to the reduction of the open channel inside the pleat.
While the first effect leads to a nearly linear increase
of pressure drop with the cake height, the second effect
goes ahead with a quadratic increase. Hence the spatial
extent of the filter cake inside the pleat must be consid-
ered in the simulation model.
Pressure drop due to flow through the cake is de-

-4.61ogno( g)

CFD grid

Figure 2: Subgrid for the depth filtration model.

scribed by the Carman-Kozeny equation (8):

Apf, -72kl2 vthf,. (9)
6f3c (Od32)2

Therein ki is a constant which accounts for the wounded
flow path through the filter cake, y is the sphericity of
the dust particles and d32 is the Sauter mean diameter
of the particles which form the cake. It is inverse pro-
portional to the specific surface area and therefore ac-
counts for the particle size distribution. Based on the
Carman-Kozeny equation the pressure drop respectively
the momentum sink term is calculated in each control
volume of the computational domain, that contains de-
posited dust. If the dust volume exceeds the control vol-
ume the dust is distributed into neighboring control vol-
umes. Hence the growth of the filter cake is realized.

Experimental setup

The experimental work is divided into two parts. In the
first part the filtration properties of the filter medium are
determined in order to fit the parameters of the filtration
model. In the second part the filter medium is folded
and embedded in a filter housing which holds the single
pleat in a stable and well defined position. Overall pres-
sure drop as well as flow velocity and local pressure at
selected positions on the up- und downstream side of the
pleat are measured as a function of deposited dust mass.
The aim of these measurements is to evaluate the capa-
bility of the model to predict the influence of the pleat
geometry on filtration performance. The filter medium
and the test dust chosen for the studies are a common

y= 0

7th International Conference on Multiphase Flow,
ICMF 2010, Tampa, FL, May 30 -June 4, 2010

cellulose medium and a standard test dust, so no sim-
plification was done compared to common filter tests.
Model pleat.

filter medium


Figure 3: Sectional view of the filter housing with
model pleat

Filter test rig. In the filter test rig the plane medium
is loaded with a standard test dust (A2 fine) while the
evolution of pressure drop and the particle concentra-
tion and size distribution on the downstream side is mea-
sured. The test rig is equipped with a powder dispersion
generator (Palas RBG1000), a Corona discharge unit
(Palas CD 2000) and an optical particle counter (Palas
Welas 3000). The filter medium has a circular shape
with a surface area of 100 cm2. Volume flow is set to 50
1/min and concentration to approximately 100 mg/mr3.
The filter is weighed before and after the test to deter-
mine its dust load. Each measurement is repeated three
times. In figure 3 a sectional view of the filter housing
which holds the model pleat is shown. The filter medium
is clamped between the upper and the lower part of the
housing and sealed with glue. The permeable part of it
has a surface area of 112 cm2. The front side of the up-
per part consists of acrylic glass to allow optical access
for the laser. The side walls of the housing are equipped
with pressure taps to measure overall pressure drop as
well as local pressure along the downstream side of the
pleat. Figure 4 shows a flow chart of the experimental
setup. The test dust is dispersed in the dispersion gen-
erator and neutralized in a Corona discharge unit before
it enters the filter housing and loads the filter medium.

Air mass flow is measured downstream with a long ra-
dius nozzle. The flow velocity inside the pleat is mea-

7th International Conference on Multiphase Flow,
ICMF 2010, Tampa, FL, May 30 -June 4, 2010

three parts, a very short part where depth filtration dom-
inates, a broad transition region and a nearly linear part
of pure surface filtration. During depth filtration and the
transition to surface filtration the separation efficiency
rises until it reaches values near one in the surface filtra-
tion region. The development of efficiency can be seen



Traverse z

Figure 4: Flow chart of the model pleat test rig.

sured with a 1-D laser doppler anemometer (Dantec Dy-
namics) with a focal length of 400mm. It measures the
velocity of particles in the air by a non-contact optical
method. If particles are small enough the particle veloc-
ity meets the flow velocity. As tracer particles the test
dust itself is used. Due to its broad particle size distribu-
tion it is in the strict sense not suitable for LDA measure-
ments, because the bigger particles follows the flow with
a certain slip. Since the flow velocity inside the pleat is
low and the fraction of particles with considerable slip is
small the error is acceptable. A detailed description of
the measurement technique can be found in (9).
In two measurement series the volume flow was var-
ied from 50 1/min to 70 1/min. Particle concentration was
kept as low as possible in order to resolve the change
from depth filtration to surface filtration. Each measure-
ment was repeated three times.


In figure 5 the evolution of pressure drop as a function
of the dust load is shown. The curve can be divided into

0 001 002 003 004 005 006
dust loading ( kgm2 )

Figure 5: Pressure drop of the plane filter medium at 50
1/min as a function of dust load, simulation and experi-

c 07
0 06 *
0 4 Exp 0 kgm-2
SExp 0 01 kgm2
S0 3 Exp 0 02 kgm2
02 S Sm 0kgm 2
0'2 Sim 0 01 kgm-2
01 -- Sim 0 02 kgm 2
n . . . . i -. . . . i . .. .

d Im

Figure 6: Fractional efficiency of the plane filter
medium at 50 1/min at different loading, simulation and

in figure 6, where the measured fractional efficiency is
depicted as a function of the particle diameter and dust
loading. At the beginning the clean filter medium shows
a very bad efficiency for particles smaller than one mi-
crometer, but after a short period of loading it rises sig-
nificantly and reaches values near one at a load of ap-
proximately 0.02 kg/m2. These curves were used to fit
the parameters of the numerical model. In table 1 all

7th International Conference on Multiphase Flow,
ICMF 2010, Tampa, FL, May 30 -June 4, 2010

variables for the model are listed together with a remark
if they were measured (m) or fitted (f). The simulation
results can be seen in figure 5 and 6. The model de-
scribes the filtration behavior well but overestimates the
depth filtration phase.
In figure 7 the measured evolution of pressure drop for
the pleated filter is compared to the numerical results.
A satisfying accordance can be seen, but the phase of
depth filtration is again overestimated. The profile of the





j 1000
Exp 50 Imin1
Exp 70 Imin'
500 --- Sim 50 Imin
Sim 70 Imin1
0 002 004 006 008 01
dust loading/ ( kgm2)

Figure 7: Pressure drop of the model pleat as a function
of dust load for 50 1/min and 70 1/min, simulation and

y-velocity in the center of the pleat is displayed in figure
8 at three different loading states. Again, the measure-
ments and the simulation results are shown. The sharp
rise of y-velocity is caused by an acceleration of the flow
in the inlet area of the pleat. Afterwards velocity is re-
duced continuously due to the flow through the porous
walls. The shape of the decay is influenced strongly by
the loading of the filter medium. This change in the
shape of the velocity profile is predicted well by the nu-
merical model. In figure 9 the simulated and measured
pressure values at different positions on the downstream
side of the pleat are depicted. The values are scaled by
the overall pressure drop Apo of the pleat at the corre-
sponding loading. The numerical model describes the
evolution of pressure in the outlet channel qualitatively
well, but the pressure gradients are two low. A possi-
ble reason for this could be, that the filter medium is
deformed due to the higher pressure on the upstream
side. This deformation rises with increasing pressure
drop and the outlet channels becomes more and more
narrow which leads to a higher pressure gradient. At the
moment such a deformation of the filter medium can't
be reflected by the model.

5 +

S- Exp 0 kgm2
SExp 0 0026 kgm-2
2 Exp 0 01 kgm2
Sim 0 kgm-2
1 / Sim 0 0026 kgm2
-- Sim 0 01 kgm-2
0 002 004 0.06 008 01 012 014 016

Figure 8: Profile of y-velocity in the upstream channel
at 70 1/min at different loading, simulation and experi-

0 002 004 006 008 01


Figure 9: Profile of relative pressure in the downstream
channel at 70 1/min at different loading, simulation and


The comparison of the experimental investigations with
the numerical results show that the model is able to de-
scribe the filtration behavior of pleated filters. All pa-
rameters of the model can be determined in less ex-
pensive standard filter tests on the plane filter medium.
Hence the numerical model can be used to perform vari-
ations for example of the pleat geometry and other pa-
rameters which could hardly be varied in experiments.
Furthermore it gives interesting insights in details of the
loading process like the unequal mass distribution on
the filter surface or the fractioning of particles sizes in-
side the pleat due to inertia of particles. Nevertheless
the model has to be developed further in order to pre-

' Exp 0 kgm2
Exp 0 0026 kgm 2

Sim 0 0026 kgm-2
SSi, 0 01 kgm

7th International Conference on Multiphase Flow,
ICMF 2010, Tampa, FL, May 30 -June 4, 2010

dict more accurately the transition between depth and [8] Carman, P.C.: The flow of gases through porous
surface filtration. Furthermore the deformation of the media. Academic Press, New York, 1956.
filter medium with rising pressure drop should be inves-
tigated. [9] Albrecht, H.E. et al: Laser Doppler and Phase
Doppler Measurement Techniques. Springer-
Verlag, Berlin Heidelberg, 2003.
Table 1: Summary of parameters used in the numerical
model. Measured values are marked with an (m), fitted
ones with an (f).
Variable Value Units
hfm (m) 450 p/m
EfJ (m) 0.81 1
df (m) 15 / t
og (f) 2.2 1
(aft (f) le11 m2
pp(m) 2650 kg/m3
efc (m) 0.85 1
ki (f) 13 1
y (f) 0.85 1
Pp,b (f) 250 kg/m3


[1] Konstandopoulos, A. G.; Kostoglou, M.: Funda-
mental Studies of Diesel Particulate Filters: Tran-
sient Loading, Regeneration and Aging. SAE-
Paper Series, 2000-01-1016, 2000.

[2] Ldffler, F:Staubabscheiden, Chemieingenieur-
wesen/Verfahrenstechnik, Georg Thieme Verlag
Stuttgart, 1988.

[3] Stechkina,I.B.; Fuchs, N.A.: Studies on Fibrous
Aerosol Filters I Calculation of Diffusional De-
position of Aerosols in Fibrous Filters. The An-
nuals of Occupational Hygiene, 9,2,59-64,1966.

[4] Kuwabara, S.: The force experienced by ran-
domly distributed parallel circular cylin-ders or
spheres in viscous flow at small Reynolds num-
bers. Journal of the Physical So-ciety of Japan,
14, 4, 527-532, 1959.

[5] Kirsch, A.A.; Stechkina, I.B.: The Theory
of Aerosol Filtration with Fibrous Filters, In:
D.T.Shaw (Ed.), Fundamentals in Aerosol Sci-
ence, John Wiley & Sons, New York, pp. 165-256

[6] Davies, C. N.: Air filtration. Academic Press,
London, New York, 171, 1973.

[7] Benarie, M.: Einfluss der Porenstruktur auf den
Abscheidegrad in Faserfilter, Staub Reinhal-
tung der Luft 29, 2, 74-78, 1969.

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