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
kopf@imvt.unistuttgart.de
Keywords: air filtration, lagrangian simulations, particleladen gas, LDA
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.
Nomenclature
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 (kgm1)
0 sphericity (1)
Subscripts
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)
Introduction
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 NavierStokes 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 121031. 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
way.
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 EulerLagrange 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
medium.
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.
3
H 0.51n( m) + (1
4
(1 Ejm)2
Efm)
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
with
k 0.51og(1 E ,)
(5)
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]
0.805RSto]
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
fl
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
iV

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
model.
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 CarmanKozeny 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
CarmanKozeny 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
taps
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
1000
Model
pleat
Traverse z
Figure 4: Flow chart of the model pleat test rig.
sured with a 1D laser doppler anemometer (Dantec Dy
namics) with a focal length of 400mm. It measures the
velocity of particles in the air by a noncontact 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.
Results
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
ment
09
08
c 07
0 06 *
os4
0 4 Exp 0 kgm2
SExp 0 01 kgm2
S0 3 Exp 0 02 kgm2
02 S Sm 0kgm 2
0'2 Sim 0 01 kgm2
01  Sim 0 02 kgm 2
n . . . . i . . . . i . .. .
d Im
P
Figure 6: Fractional efficiency of the plane filter
medium at 50 1/min at different loading, simulation and
experiment
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
3000
2500
S2000
1500
j 1000
Exp 50 Imin1
Exp 70 Imin'
500  Sim 50 Imin
Sim 70 Imin1
0
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
experiment
yvelocity 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 yvelocity 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 +
54
S Exp 0 kgm2
SExp 0 0026 kgm2
2 Exp 0 01 kgm2
Sim 0 kgm2
1 / Sim 0 0026 kgm2
 Sim 0 01 kgm2
0
0 002 004 0.06 008 01 012 014 016
y/m
Figure 8: Profile of yvelocity in the upstream channel
at 70 1/min at different loading, simulation and experi
ment
0 002 004 006 008 01
y/m
012
Figure 9: Profile of relative pressure in the downstream
channel at 70 1/min at different loading, simulation and
experiment
Conclusions
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 kgm2
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
References
[1] Konstandopoulos, A. G.; Kostoglou, M.: Funda
mental Studies of Diesel Particulate Filters: Tran
sient Loading, Regeneration and Aging. SAE
Paper Series, 2000011016, 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, 9,2,5964,1966.
[4] Kuwabara, S.: The force experienced by ran
domly distributed parallel circular cylinders or
spheres in viscous flow at small Reynolds num
bers. Journal of the Physical Society of Japan,
14, 4, 527532, 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. 165256
[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, 7478, 1969.
