.....
IMPROVEMENT OF FLOW UNIFORMITY AND
MODELING OF FILTRATION EFFICIENCIES
FOR AUTOMOTIVE AIR FILTER
TEST HOUSINGS
By
ROBERT DURAN
Bachelor of Science
The University of Texas
Austin, Texas
1993
Submitted to the Faculty of the
Graduate College of the
Oklahoma State University
in partial fulfillment of
the requirements for
the Degree of
MASTER OF SCIENCE
July, 1995
IMPROVEMENT OF FLOW UNIFORMITY AND
MODELING OF FILTRATION EFFICIENCIES
FOR AUTOMOTIVE AIR FILTER
TEST HOUSINGS
Thesis Approved:
/~ ~~t/  I • uesis Adviser
ULJ AJ.~
~L~
1D~
oz;tLfu&k ( ~
Dean of the Graduate College
·  .. n .. . . .. ... . l
ACKNOWLEDGMENTS
I wish to express my sincere appreciation to all of the individuals who were kind
enough to assist me in completing this project. First, I would like to thank my major
advisor, Dr. F.W. Chambers, for his guidance, support, and confidence in me. Thank
you for always finding the time. I would also like to thank my other committee
members, Dr. R.L. Dougherty, Dr. J.D. Spitler, and Dr. A.J. Johannes for their helpful
advice and encouragement throughout my graduate studies.
I would like to thank all of my colleagues and friends at the university who were
always willing to drop what they were doing to assist me. A sincere thanks goes to Dr.
Jiaqi Cai and Rich Burgess for their continual help, friendship, and encouragement
throughout my career as a graduate student. I would also like to thank my other
colleagues, R.A. Newman, F. Liang, C. Tebbutt, Dr. G. Liu, B. Natarajan, and J.
Williams for always having the time and not being afraid to get their hands dirty.
The financial support provided by Purolator Products, Inc. and the Oklahoma
Center for the Advancement of Science and Technology (OCAST) is greatly appreciated.
A special thanks goes to Dr. G. Ferrell and the personnel of Purolator Products, Inc. for
their help and insight.
I would like to express my gratefulness to my parents, Felipe and Felicitas
Duran, and to my sister and two brothers for their invaluable support and continuous
encouragement throughout my life and college endeavors.
111
TABLE OF CONTENTS
Chapter
I INTRODUCTION .............................................................................................. 1
1.1 Background ....................................................................................... 1
1. 2 Objectives, Scope, and Limitations of Present Study ......................... 3
1.3 The SAE 1726 Air Cleaner Test Code ................................................ 5
IT FIBROUS FILTRATION THEORY AND METHODOLOGY .................... 11
2.1 Fibrous Filtration ............................................................................. 11
2.2 Fiber Representation and Filtration Efficiencies ................................ 15
2. 2.1 Single Fiber Representation of a Fibrous Filter ................ 15
2.2.2 Flow Around a Fiber ......................................................... 16
2.2.3 Single Fiber Efficiency ...................................................... 17
2. 2.4 Isolated Fiber Efficiency ................................................... 19
2.2.5 Elemental Fiber Efficiency ................................................ 20
2. 2. 6 Overall Filter Efficiency ................................................... 21
2.3 Mechanisms of Particle Capture and Combined Efficiencies ............. 23
2. 3.1 Overview ........................................................................... 23
2.3.2 Interception ....................................................................... 23
IV
 ~ ~1
2. 3. 3 Inertial Impaction ............................................................. 24
2. 3. 4 Brownian Diffusion ........................................................... 24
2.3.5 Electrostatic Attraction ..................................................... 25
2.3.6 Combined Particle Collision Efficiencies .......................... 25
2.4 Kuwahara Flow Field Around a Fiber Cylinder.. ............................... 27
2.5 Filtration Efficiency Models ............................................................. 29
2.5.1 Lee and Liu Interception Model ........................................ 29
2.5.2 Landahl and Herrmann Inertial Impaction Model.. ........... 31
2. 5. 3 Combined Interception and Inertial Impaction Model ....... 32
2.5.4 Interception and Inertial Modeling
by Particle Trajectory ..................................................... 34
2.5.5 Other Collision Efficiency Models .................................... 36
2.6 Adhesion and Retention of Captured Particles .................................. 39
2. 6.1 Discussion ......................................................................... 39
2. 6. 2 Adhesion Forces ............................................................... 40
2. 6. 3 Conditions Affecting Particle Retention ............................ 43
2. 6.4 Ptak and Jaroszczyk Adhesion Model ................................ 45
2. 7 Pleated Air Filters ............................................................................ 48
2. 7.1 Discussion ......................................................................... 48
2. 7.2 Pleated Surface Area ....................................................... .49
v
.......
~ ~· · · ·· ~·
II
II
I l
2. 7.3 Air Velocities Inside Pleated Filter .................................... 50
2. 7 Methodology ................................................................................... 51
2.8.1 Typical Properties of Automotive Air Filtration Paper ...... 51
2.8.2 Fiber Diameter ................................................................. 52
2.8.3 Packing Density ................................................................ 54
2.8.4 Program "EFFMODEL.FOR" ......................................... 58
ill EXPERIMENTAL SETUP .............................................................................. 64
3 .1 Experimental Apparatus ................................................................... 64
3 .2 Laser Doppler Velocirnetry Diagnostics ........................................... 66
3.3 Principles of Laser Doppler Velocirnetry .......................................... 69
3.4 SetUp and Parameters of
Laser Doppler Velocirnetry Measurements .................................. 74
3.5 Flow Visualizations .......................................................................... 80
3.6 Equipment Listing ............................................................................ 81
IV RESULTS AND DISCUSSION OF FLOW VISUALIZATIONS
AND LASER DOPPLER VELOCIMETRY MEASUREMENTS ................. 88
4.1 Flow Visualizations .......................................................................... 88
4.2 Improvement of Flow Distribution ................................................... 92
4.2.1 Spheres Positioned Near the Housing Inlet ....................... 92
4.2.2 Spheres Positioned Upstream of the Filter Specimen ......... 96
Vl
~~
4.3 ThreeDimensional Axial Velocity Profiles ....................................... 99
4.4 Flowrate Comparison of Equally Sized Regions ............................. 106
4.5 ThreeDimensional Transverse Velocity Profiles ............................ 109
4.6 Turbulence Intensities Upstream ofFilter Specimen ....................... 113
4.7 Summary ofResults ....................................................................... 115
V FILTRATION EFFICIENCIES .................................................................... 117
5.1 General Overview .......................................................................... 117
5.2 Single Fiber Efficiencies within Pleated Air Filters .......................... 118
5.3 Elemental Efficiencies Across Pleated Air Filter Beds ..................... 122
5. 4 Overall Elemental Efficiencies for the
SAE Test Dust Particle Distributions ......................................... 131
5.5 Summary ofEfficiency Results ....................................................... 142
VI SEPARATION AND CONTROL OF THE
SAEPANELFILTER TESTHOUSING .......................................... 144
6.1 Flow Uniformity in Automotive Air Filter Test Housings ............... 144
6.2 Diffuser Performance and Characteristics ....................................... 146
6.3 'Recommended Test Housing Designs ............................................ 151
VII CONCLUSIONS AND RECOMMENDATIONS ........................................ 155
7.1 Conclusions ................................................................................... 155
7.2 Recommendations .......................................................................... 157
Vll
 ~~ .....
REFERENCES ......................................................................................................... 158
APPENDICES .......................................................................................................... 163
A. PUROLATORAF3192 AIR FILTER SPECIFICATIONS ......................... 163
B. SOURCE CODE LISTING OF EFFMODEL.FOR. .................................... 164
C. SAMPLE INPUT/OUTPUT FILES OF EFFMODEL.FOR ........................ 177
C.1 Sample Input File .......................................................................... 177
C.2 Sample VELSTRE.OUT File ........................................................ 178
C.3 Sample EFFCOMP.OUT File ........................................................ 180
C.4 Sample SINGELEM.OUT File ...................................................... 181
C.5 Sample SAEDUST.OUT File ........................................................ 183
D. SOURCE CODE LISTING OF DATAPICK.FOR FOR DSA OUTPUT .... 185
E. PRELIMINARY CALCULATIONS OF DISPLACEMENT
AND DISTORTION OF PROBE VOLUME ........................................ 188
E.1 Source Code Listing of Refraction Program .................................. 188
E.2 Plots ofProbe Volume Displacement ............................................. 190
F. SMOKEGENERATOR ............................................................................. l92
F.1 Smoke Generator Apparatus .......................................................... 192
F.2 Procedure ...................................................................................... 195
Vlll
~
LIST OF TABLES
Table Page
1.1 SAE 1726 Standard Particle Size Distribution of Test Dust ................................... 8
2.1 Average Fiber Diameter used in Automotive Air Filtration Paper ........................ 51
2.2 Typical Properties for Automotive Air Filtration Paper ....................................... 52
5.1 Overall Filter Efficiencies Assuming a Monodisperse
Particle Size Distribution ...................................................................... 131
5.2 Standard SAE Polydisperse Test Dust Distributions by Percent Weight ............ 134
5.3 Overall Filter Efficiencies for the Fine and Coarse SAE Test Dust
Polydisperse Particle Distributions ........................................................ 142
A.l Filter Specifications .......................................................................................... 163
lX
;;;;:=:.. .................................................... ~~~ ...... ==== · ·····"  · ~ ~~
LIST OF FIGURES
Figure Page
1.1 SAE (1987b) J726 Efficiency/Capacity Air Filter Element Test Setup ................. 9
1.2 SAE (1987b) J726 Panel Filter Universal Test Housing ...................................... 10
2.1 Filter Media Structure ofPacked and SingleLayer Filters:
(a) Packed Filter (dust particles not shown) and (b) SingleLayer
Filter with Dust Particles Shown in Interstitial Spaces (Crawford, 1976) ............ 13
2.2 Penetration ofMonodisperse Particles Through a Simple Filter,
20 J..lffi Fiber Diameter and 0.05 Packing Fraction, as a
Function ofParticle Size (Brown, 1993) ............................................................. 14
2.3 Section of a Filter illustrating the Scale ofParticles and Fibers (Brown, 1993) .... 14
2.4 Single Fiber Representation of Particle Capture illustrated by
a Limiting Trajectory (Crawford, 1976) ............................................................. 17
2. 5 Typical Characteristics of 11 coli, 11 adh, and 11 s
(Adapted from Stenhouse, 1975) ........................................................................ 19
2.6 Particle Capture Mechanisms: (A) Capture by Interception,
(B) Capture by Inertial Impaction, and (C) Capture by
Brownian Diffusion (Brown, 1993) .................................................................... 27
2.7 Comparison ofFlagan and Sienfeld's (1988) Exact Solution to
Sabnis' Combined Interception and Inertial Model (Newman, 1994) ................... 33
2.8 Comparison ofFlagan and Sienfeld's (1988) Exact Solution to
Isolated Collision Efficiency Models (Newman, 1994) ........................................ 39
2.9 Sphere Attached to a Plane by Capillary Forces (Brown, 1993) ......................... .43
X
~~~~1
Figure Page
2.10 Distribution of Adhesion Energies of Quartz Particles Deposited
at a Filtration Velocity of0.42 rnls on Polyamide Fibers: (1) 15.1 J..UI1
Particles; (2) I 0.3 j..lm Particles; (3) 8.3 j..lm Particles; ( 4) 5.1 j..lm
Particles (Brown, I993) ..................................................................................... 44
2.11 Filter Pleat Geometry (Newman, 1994) .............................................................. 49
2.12 Envelope Curves forf(c) Verses Packing Fraction, c, with Davies' (1973)
Very Low Packing Fraction Empirical Formula Line Curve,
Equation (2.52), (Brown, I993) ......................................................................... 57
2.13 Efficiency Curves Obtained from Program EFFMODEL at
Rp = 1.25 J..UI1, c = 0.345, and De~= 51.78 j..lm ..................................................... 62
2.I4 Efficiency Curves Obtained from Program EFFMODEL with Parameters
Used by Sabnis (I993), Rp = 1.25 !liD, c = 0.230, and Dr= 38.0 !lffi ................... 63
3 .I Experimental Apparatus ..................................................................................... 65
3.2 Schematic of the Laser Doppler Velocimetry System .......................................... 67
3.3 An Example of a Raw Doppler Burst Signal (Hiatt, I994) .................................. 73
3.4 Diagram of a Particle Passing through the Fringe Pattern .................................... 73
3. 5 Sign Convention and Coordinate System for Velocity Measurements ................. 77
3. 6 Velocity Measurement Planes ............................................................................. 78
3.7 Velocity Measurement Grid ................................................................................ 79
4.I Axial Laser Sheet Water Droplet Flow Visualization within the
SAE Test Housing (Sabnis, I993) ...................................................................... 90
XI
Figure Page
4.2 Axial Laser Sheet lntennittant Smoke Flow Visualization within
the SAE Test Housing with a 76.2 mm Dia Sphere Positioned 159 mm
from the Housing Inlet ....................................................................................... 91
4.3 Center Line Axial Velocity Profiles Measured at 13 mm Upstream of the Filter,
Plane I, with 50.8 to 76.2 mm Dia Spheres Positioned Near the Inlet .................. 94
4.4 Center Line Transverse Velocity Profiles Measured at 13 mm Upstream of the
Filter, Plane I, with 50.8 to 76.2 mm Dia Spheres Positioned Near the Inlet ........ 95
4.5 Center Line Axial Velocities Measured at 13 mm Upstream of the Filter,
Plane I, with 76.2 mm Dia Sphere Positioned at the Specified Distances
from the Housing Inlet ....................................................................................... 97
4.6 Center Line Transverse Velocities Measured at 13 mm Upstream of the Filter,
Plane I, with 76.2 mm Dia Sphere Positioned at the Specified Distances
from the Housing Inlet ....................................................................................... 98
4.7 NonDimensional Axial Velocities in the Standard SAE Test Housing
Measured at 13 mm Upstream of the Filter, Plane I .......................................... 102
4.8 NonDimensional Axial Velocities in the Test Housing Measured
at 13 mm Upstream of the Filter, Plane I, with a 76.2 mm Dia Sphere
Positioned at 159 mm Downstream from Housing Inlet .................................... 103
4.9 NonDimensional Axial Velocities in the Test Housing Measured
at 51 mm Upstream of the Filter, Plane II, with a 76.2 mm Dia Sphere
Positioned at 159 mm Downstream from Housing Inlet .................................... 104
4.10 NonDimensional Axial Velocities in the Test Housing Measured
at 13 mm Upstream of the Filter, Plane I, with a 76.2 mm Dia Sphere
Positioned at 197 mm Downstream from Housing Inlet .................................... 105
4.11 NonDimensional Flow Rate Distribution in the Standard
SAE Test Housing Measured at 13 mm Upstream of the Filter ......................... 108
Xll
~J
Figure Page
4.12 NonDimensional Flow Rate Distribution in the Test Housing Measured
at 13 mm Upstream of the Filter with a 76.2 mm Dia Sphere Positioned at
159 mm Downstream from Housing Inlet ......................................................... 108
4.13 NonDimensional Flow Rate Distribution in the Test Housing Measured
at 51 mm Upstream of the Filter with a 76.2 mm Dia Sphere Positioned at
159 mm Downstream from Housing Inlet ......................................................... 109
4.14 NonDimensional Transverse Velocities in the Standard SAE Test Housing
Measured at 13 mm Upstream of the Filter, Plane I .......................................... Ill
4.15 NonDimensional Transverse Velocities in the Test Housing Measured
at 13 mm Upstream of the Filter, Plane I, with a 76.2 mm Dia Sphere
Positioned at 159 mm Downstream from Housing Inlet .................................... Ill
4.16 NonDimensional Transverse Velocities in the Test Housing Measured
at 51 mm Upstream of the Filter, Plane II, with a 76.2 mm Dia Sphere
Positioned at 159 mm Downstream from Housing Inlet .................................... 112
4.17 NonDimensional Transverse Velocities in the Test Housing Measured
at 13 mm Upstream of the Filter, Plane I, with a 76.2 mm Dia Sphere
Positioned at 197 mm Downstream from Housing Inlet .................................... 112
4.18 Axial Turbulence Intensity in Test Housing at 13 mm Upstream of the Filter .... 114
4.19 Axial Turbulence Intensity at 13 mm Upstream of the Filter with a
76.2 mm Dia Sphere Positioned at 159 mm Downstream of the Housing Inlet .. 114
4.20 Axial Turbulence Intensity at 13 mm Upstream of the Filter with a
76.2 mm Dia Sphere Positioned at 197 mm Downstream of the Housing Inlet .. 115
5.1 Single Fiber Efficiency in Standard SAE Test Housing Assuming
Perfect Adhesion, 5 J.1Ill Particles ...................................................................... 120
5.2 Single Fiber Efficiency in Standard SAE Test Housing, 5 J.1Ill Particles ............. 120
Xl1l
Figure Page
5.3 Single Fiber Efficiency Assuming Perfect Adhesion with 76.2 mm
Dia Sphere Positioned at 159 mm Downstream of the Housing Inlet,
5 J..l.lll Particles ................................................................................................. 121
5.4 Single Fiber Efficiency with 76.2 mm Dia Sphere Positioned at
159 nun Downstream of the Housing Inlet, 5 J..lm Particles ................................ 121
5.5 Elemental Efficiency in Standard SAE Test Housing, 1.0 J..1ffi Particles .............. 125
5.6 Elemental Efficiency with 76.2 Dia Sphere Positioned at 159 mm
Downstream of the Housing Inlet, 1.0 J..lm Particles .......................................... 125
5.7 Elemental Efficiency in Standard SAE Test Housing, 2.5 J..l.lll Particles .............. 126
5.8 Elemental Efficiency with 76.2 Dia Sphere Positioned at 159 mm
Downstream of the Housing Inlet, 2.5 J..lm Particles .......................................... 126
5.9 Elemental Efficiency in Standard SAE Test Housing, 5.0 J..lm Particles .............. 127
5.10 Elemental Efficiency with 76.2 Dia Sphere Positioned at 159 mm
Downstream of the Housing Inlet, 5.0 J..1ffi Particles .......................................... 127
5.11 Elemental Efficiency in Standard SAE Test Housing, 7.5 J..lm Particles .............. 128
5.12 Elemental Efficiency with 76.2 Dia Sphere Positioned at 159 mm
Downstream of the Housing Inlet, 7.5 J..1ffi Particles .......................................... 128
5.13 Elemental Efficiency ofUnity Across Filter Assuming Perfect Adhesion
with or without 76.2 Dia Sphere Positioned Either 159 mm or
197 mm Downstream of the Housing Inlet, for Particles;;?: 15.0 J..lm .................. 129
5.14 Elemental Efficiency in Standard SAE Test Housing, 15.0 J..1ffi Particles ............ 129
5.15 Elemental Efficiency with 76.2 Dia Sphere Positioned at 159 mm
Downstream of the Housing Inlet, 15.0 J..lm Particles ........................................ 130
XIV
   ··~
Figure Page
5.16 Elemental Efficiency with 76.2 Dia Sphere Positioned at 197 mm
Downstream of the Housing Inlet, 15.0 ~m Particles ........................................ 130
5.17 Cumulative Mass Fraction Distribution of SAE
Polydisperse Fine Grade Test Dust ................................................................... 133
5.18 Cumulative Mass Fraction Distribution of SAE
Polydisperse Coarse Grade Test Dust ............................................................... 133
5.19 Overall Elemental Efficiency in Standard SAE Test Housing
Assuming Perfect Adhesion, SAE Fine Grade Test Dust Distribution ............... 136
5.20 Overall Elemental Efficiency in Standard SAE Test Housing,
SAE Fine Grade Test Dust Distribution ............................................................ 136
5.21 Overall Elemental Efficiency in Standard SAE Test Housing
Assuming Perfect Adhesion, SAE Coarse Grade Test Dust Distribution ........... 137
5.22 Overall Elemental Efficiency in Standard SAE Test Housing,
SAE Coarse Grade Test Dust Distribution ....................................................... 137
5.23 Overall Elemental Efficiency Assuming Perfect Adhesion with
76.2 mm Dia Sphere Positioned at 159 mm Downstream of the
Housing Inlet, SAE Fine Grade Test Dust Distribution ..................................... 13 8
5.24 Overall Elemental Efficiency with 76.2 mm Dia Sphere Positioned
at 159 mm Downstream of the Housing Inlet, SAE Fine
Grade Test Dust Distribution ............................................................................ 138
5.25 Overall Elemental Efficiency Assuming Perfect Adhesion with
76.2 mm Dia Sphere Positioned at 159 mm Downstream of the
Housing Inlet, SAE Coarse Grade Test Dust Distribution ................................. 139
5.26 Overall Elemental Efficiency with 76.2 mm Dia Sphere Positioned
at 159 mm Downstream of the Housing Inlet, SAE Coarse
Grade Test Dust Distribution ............................................................................ 13 9
XV
. ....  ___ .1
Figure •
5.27 Overall Elemental Efficiency Assuming Perfect Adhesion with
76.2 mm Dia Sphere Positioned at 197 mm Downstream of the
Page
Housing Inlet, SAE Fine Grade Test Dust Distribution ..................................... 140
5.28 Overall Elemental Efficiency with 76.2 mm Dia Sphere Positioned
at 197 mm Downstream of the Housing Inlet, SAE Fine
Grade Test Dust Distribution ............................................................................ 140
5.29 Overall Elemental Efficiency Assuming Perfect Adhesion with
76.2 mm Dia Sphere Positioned at 197 mm Downstream ofthe
Housing Inlet, SAE Coarse Grade Test Dust Distribution ................................. 141
5.30 Overall Elemental Efficiency with 76.2 mm Dia Sphere Positioned
at 197 mm Downstream of the Housing Inlet, SAE Coarse
Grade Test Dust Distribution ............................................................................ 141
6.1 Effect ofNonUniform Flow through a Porous Foam Filter Tested
in Layers: (a) NonUniform Flow, and (b) Uniform Flow ((Brown, 1993) ....... 145
6.2 Diffuser Geometry of a Flat Walled Diffuser (White, 1979) .............................. 149
6.3 Schematic of Flat Walled Diffuser Operating Flow Regimes (Chang, 1970) ...... 149
6.4 Flat Walled Diffuser Operating Flow Regime Map (White, 1979) ..................... 150
6.5 Shallow Angle Prototype Panel Filter Test Housing .......................................... 153
6.6 Velocity Distribution 13 mm Upstream of Filter in Prototype Test Housing ...... 154
E.1 Probe Volume Displacement for Axial (Blue) and Transverse (Green)
Beams for a 6.4 mm (0.25 in.) Plexiglas with Varying Housing Angle .............. 190
E.2 Probe Volume Displacement for Axial (Blue) and Transverse (Green)
Beams for a 9.5 mm (0.375 in.) Plexiglas with Varying Housing Angle ............ 191
F.1 Schematic of the Smoke Generator ................................................................... 197
xvi
_1
i
ae
ao, b0 , C0
A
AI
b
c
Cc
Co
Ceo
d
D1
Dp
I
f(c)
F
h
lp
Kn
Ku
NOMENCLATURE
elemental area ( m2
)
experimental parameters of adhesion model
area as specified (m2
)
Hamaker constant
radius of surrounding cell used in single fiber representation
dimensionless packing fraction or packing density of filter
Cunningham slip correction factor
particle concentration entering filter per unit volume (m"3
)
elemental particle concentration entering filter per unit volume (m"3
)
distance between interference fringes (m)
fiber diameter (m)
particle diameter (m)
frequency (Hz)
dimensionless packing density function
adhesion force (N)
filter depth (m)
interception parameter
Knudsen number
Kuwahara hydrodynamic factor
XVll
~1,
L
N
p
p
Po
Pe
q
Q
Qf
r, (}
Ra
R1
Rp
Re
Ref
Rep
SF
St
Stc
t
u
length of all fibers in a unit volume of filter media (m)
total number of samples
pitch of filter (m)
filter penetration
dimensionless porosity
elemental penetration
electrostatic charge
volumetric flow rate (m3/s)
volumetric flow rate through filter (m3/s)
Cylindrical coordinates
radius of the surface asperity
radius of fiber (m)
radius of particle (m)
Reynolds number of flow
Reynolds number based on fiber diameter
Reynolds number based on particle diameter
solidity factor
Stokes number
Stokes number corrected for slip
time (s)
velocity near filter pleats (m/s)
XV1ll
· ·· ···1.
Uo
Ucc
v
w1, w2
x,y
Yo
y
Zo
r
0
Eo
T7
T]J, T72
Tladh
Tlcoll
Tle
11!
T]J
T]R
measured axial velocity upstream of the filter media (m/s)
velocity inside filter media (rn/s)
fluid velocity (m/s)
diffuser inlet throat width (m)
Cartesian coordinates
distance between the center line of a fiber and the streamline below which
all particles are collected by inertial impaction and interception (m)
distance between the center line of a fiber and the streamline below which
all particles are collected by interception (m)
distance between particle and fiber (m)
Euler's constant
charge density depth (m)
permittivity of free space
efficiency as specified
independent collection efficiencies
adhesion efficiency
collision efficiency
elemental efficiency
overall filter efficiency
inertial impaction efficiency
interception efficiency
XlX
T/s single fiber efficiency
A. mean free path of air (m)
f.J dynamic viscosity of air (Pa s)
p density of air (kglm3
)
PP density of aerosol particle (kglm3
)
T surface tension (N/m)
If/ stream function
XX
 .. =· ___ _l
CHAPTER I
INTRODUCTION
1. 1 Background
Automotive engines require a great quantity of air to properly burn the combustion
fuel. Since engines are expected to operate under a large variety of conditions and
atmospheres, the intake air must be filtered and cleaned. Automotive air cleaners allow
intake air to pass freely while removing hannful dust and abrasive particles which may
otherwise accelerate engine wear, and thus, limit engine performance and endurance.
Most commonly used automotive air filters are round type and panel type filters that are
dry and replaceable. Critical operating characteristics of filters include (McQuiston and
Parker, 1994): filtration efficiency, air flow resistance, and dustholding capacity. The
filtration efficiency is the measure of the air cleaner's ability to remove particulate matter
from an air stream. Smaller particles are typically the most difficult to filter, resulting in
lower filtration efficiencies than larger particles. In general, the filtration efficiency of drytype
filters and filters exposed to low dust concentrations increase with dust loading. The
airflow resistance is the loss in total pressure at a specified air flow rate which typically
increases with the amount of dust loading. Dustholding capacity defines the amount of
dust that the air cleaner can hold when it is operated at a specified air flow rate to some
maximum resistance value.
1
2
To date, there are hundreds of different automotive engine air cleaners required to
service numerous makes and models of vehicles. Major United States manufacturers of
automotive air filters include Purolator Products Inc., AC Rochester, Fram, Motorcraft,
and Wix. Due to the fact that filter performance may vary from different air intake
systems and constricted housing designs dictated by limited underhood space, it is critical
that manufacturers and designers understand the filtration parameters of importance and
know how to control them. The Society of Automotive Engineers recognized the need
for standardization of air cleaners and compiled a listing of recommended air cleaners
(SAE, 1987a) and an air cleaner test code (SAE, 1987b). SAE 11141 Air Cleaner
Elements (1987a) provides a listing of recommended round type and panel type filters for
United States domestic passenger cars and light trucks. SAE J726 Air Cleaner Test Code
(1987b) provides a standardized method of detennining and reporting air cleaner
performance. However, past and present work has shown that air filters tested in the SAE
standardized test code housing experience very nonuniform flow [Sabnis, 1993; Newman,
1994; Liu et al., 1995]. For the past 3 years, in cooperation with Purolator Products Inc.,
the O.S.U. School of Mechanical and Aerospace Engineering has been working closely
with the SAE Air Cleaner Test Code Subcommittee to aid in revising the current test code
in efforts to achieve a testing system ensuring a more uniform flow throughout the filter
specimens. Such communications have contributed to the development of the recently
published SAE 11669 Passenger Compartment Air Filter Test Code (SAE, 1993).
_____ )...
3
This thesis primarily focuses on the nonuniformity effects and improvement of
flow uniformity within the "universal" standardized SAE test housing for panel type filters.
Focus is centered on pleated panel type filters, specifically, the Purolator AF3192 air filter
for which this project has already developed much investigation. Purolator specifications
for the AF3192 panel air filter are provided in Appendix A Flow visualizations, velocity
measurements, and efficiency calculations, all upstream of a pleated panel filter mounted
within the SAE standard test housing and within an altered test housing were conducted
and are presented within this thesis.
1.2 Objectives, Scope, and Limitations of Present Study
Automotive air filter testing is conducted in accordance with the SAE Air Cleaner
Test Code 1726. Past and present work in this project has shown that filters tested in the
SAE test housing experience very nonuniform flow that resembles that of an impinging
jet (Sabnis, 1993; Sabnis et al., 1994a and 1994b, Newman, 1994; Liu et al., 1995). Flow
visualizations and velocity measurements have shown that the housing provides strongly
recirculating separated flow at the walls of the housing and that the flow upstream of the
filter is channelled through the central region of the filter. A testing system ensuring
uniform flow throughout the filter would be ideal. In efforts to achieve a more uniform
flow, attention is centered on the redesigning and/or recommending modifications to the
''universal" SAE standard test housing. One alternative is to obstruct the inlet flow in
~l.
4
such a manner as to provide a more uniformly distributed flow pattern. This thesis
primarily focuses on the nonuniformity effects of the standard SAE test housing and the
improvement of the flow uniformity by obstructing the inlet flow with a sphere. The main
objectives were to analyze the flow field within the altered SAE test housing and improve
past modeling of filtration efficiency. Specifically, alternative efficiency models and
parameters, such as, packing density, nonperfect adhesion, weight averaged fiber
diameter, and effective fiber diameter, were investigated and implemented. Flow
visualizations, laser Doppler velocimetery measurements, and efficiency calculations with
· modified parameters were used to achieve these objectives.
Liang et al. (1994) developed a low angle diffuser prototype panel filter test
housing specifically designed for the Purolator AF3192 panel air filter. Due to the low
angles of the diffuser section, separation along the walls of the housing was virtually
eliminated and more uniform flows where achieved. Newman (1994) achieved similar
results using the same prototype housing and extended the study to include filtration
efficiencies. Throughout this formal report, reference to this prototype housing will be
made as a comparison. However, the reader is referred to references (Liang et al, 1994
and Newman, 1994) for a detailed discussion and analysis of the prototype test housing
flow field.
Sabnis (1993) developed a FORTRAN program incorporating a model for
collection efficiencies and utilized it to analyze the efficiencies of pleated panel filters using
measured velocity distributions within the SAE test housing. Newman (1994) developed a
..I..
5
similar C++ program for collection efficiencies and extended it to include an adhesion
model. He then utilized the program to analyze the filtration efficiency through both the
SAE test housing and the low angle prototype housing. For simplicity, a FORTRAN
program, EFFMODEL.FOR, was recently developed to incorporate the same models used
by Sabnis and Newman. Related filtration parameters were modified and added as needed
to provide a more realistic filtration efficiency model. Neither program developed by
Sabnis nor Newman was utilized in the work presented here. For our purposes, these
programs and results will not be discussed.
The scope of this thesis has been limited to (I) initially clean pleated panel filters,
(2) the nonuniformity effects of the standard SAE test housing, (3) the improvement of
the flow uniformity by obstructing the inlet flow of the housing, ( 4) related filtration
theory including perfect and nonperfect adhesion efficiency modeling, and (5)
monodisperse and polydisperse test dust distributions as specified by SAE. Past work
presented is used merely as a comparison of recent accomplishments. The reader is
referred to (Sabnis, 1993; Sabnis et al., 1994a and 1994b; Liang et al., 1994; Newman,
1994) for detailed discussions of past work.
1.3 The SAE J726 Air Cleaner Test Code
Due to variations in air intake systems and constricted housing designs dictated by
limited underhood space, performance testing under actual operating conditions is difficult
l
6
to conduct. However, by use of an ideal standard universal testing system ensuring
uniform flow throughout the filter specimen, test conditions could be controlled, and
accurate comparison of performance characteristics between different filter designs may be
made among different manufacturers and laboratories. With this in mind, the Society of
Automotive Engineers developed the SAE 1726 Air Cleaner Test Code (SAE, 1987b).
The air cleaner test code provides a uniform method of determining and reporting air
cleaner performance characteristics on the specified laboratory testing setup and
equipment. The SAE test code includes testing of automotive air cleaners for passenger
cars and light trucks, as well as, heavy trucks and industrial applications, and oil bath air
cleaners. For our purposes, we are only concerned with the first two sections of the test
code dealing with general information and automotive air cleaner test procedures.
The SAE 1726 test code allows for uniform testing procedures, conditions,
equipment, and standardized performance reports. Critical operating characteristics of the
SAE test code include: (I) dust collection efficiency, (2) airflow restriction or pressure
drop, (3) dustholding capacity, and (4) air cleaner element structure. The standardized
SAE test dust, typically comprised of 6769% of Si02 by weight, is specified in two
grades, fine and coarse. Note that a typical chemical analysis of test dust was obtained
from AC Division, General Motors Corp. and is provided in the SAE test code. The
particle size distribution is specified and described by percent volume and percent weight
as listed in Table 1.1. lllustrations and descriptions of recommended test equipment to
determine resistance to air flow, dustholding capacity, dust removal characteristics,
 _ _;..
7
sealing characteristics, and rupture/collapse characteristics are provide within the test
code. A schematic of the efficiency/capacity air filter element test setup is illustrated in
Figure 1.1. The testing setup consists of a dust metering and feeding system, a pressure
drop measuring device, the specified filter housing, an absolute filter housing downstream
of the filter specimen, a flowrate measuring system, and the required blower for induced
air flow. A detailed drawing of the panel filter universal test housing is illustrated in
Figure 1.2. Test procedures are specified for the (I) efficiency test, (2) air flow restriction
and pressure drop test, (3) dustholding capacity test, and ( 4) the three air filter element
structure tests: flow pressure collapse test, seal effectiveness test, and temperature
extreme test.
..~
8
Table 1.1
SAE J726 Standard Particle Size Distribution ofT est Dust
Particle Size distribution by Volume
Size Fine Grade Coarse Grade
[J.Lm] Volume Volume
(%less than) (%less than)
5.5 38±3 13±3
11 54±3 24±3
22 71±3 37±3
44 89±3 56±3
88 97±3 84±3
125 100 100
Particle Size Distribution by Weight
Size Range Fine Grade Coarse Grade
[J.Lm] %Weight %Weight
05 39±2 12±2
510 18±3 12±3
1020 16±3 14±3
2040 18±3 23±3
4080 9±3 30±3
80200  9±3

· .... ~··· .J..
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I. COMPRESSED t AIR
INJECTOR
AIR
OUST
FEEDER
Fi~~~R • f , I
I ... .._~ MANOMETER
FLOWMETER
_ AIR
c>
Figure 1.1 SAE (1987b) J726 Efficiency/Capacity Air Filter Element Test Setup
· ···
9
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Figure 1.2 SAE (1987b) 1726 Panel Filter Universal Test Housing
··~. · ~.1..
11
CHAPTER IT
FIBROUS FILTRATION THEORY AND METHODOLOGY
2.1 Fibrous Filtration
Fibrous filtration is a well known and accepted method for separating dry particles
from a gas stream, usually of air or combustion gases. In fibrous filtration, the dusty gas
flows into and through the filter, leaving the dust retained by the fabric. The fabric itself
does some filtering of the particles; however, it serves more as a support medium for the
layer of dust that quickly accumulates on it (Cooper and Alley, 1994). Filters can be
classified as one of two types, packed filter and singlelayer filter type, based on the way in
which fibers are held in place (Crawford, 1976). Due to their open structure, both types
offer a low resistance to airflow. In the packed filter type, the fibers are loosely and
randomly packed into a substantial volume. In the singlelayer filter, fibers are woven into
a thin layer of cloth or paper. Packed filters and singlelayer filters are commonly referred
to as nonwoven and woven fibrous filters, respectively. Refer to Figure 2.1 for an
illustration of filter elements in packed and singlelayer filters. Nonwoven filters are
typically used within the automotive and air conditioning industry, whereas, woven filters
are commonly used in large industrial applications.
__ J_
12
A useful way to think of a filter is as a large number of woven or nonwoven
layers, each sparsely populated with fibers (Brown, 1993). Even if an individual fiber
layer has a very low capture efficiency, the filter as a whole will perform well due to the
depthfiltration. Depthfiltration refers to the increase in filtration performance due to the
increase in filter depth. Figure 2.2 shows that particles with diameters less than 10 ~m are
efficiently captured by a filter with fibers of approximately 20 ~m in diameter and a
packing density of 0.05. Packing density or packing fraction is defined as the volume
fraction of the filter fibers. Even though the interfiber spaces of the filter were up to 100
~m in size, the less than 10 ~m diameter particles were able to be captured due to the
depth filtration. Points of fiberfiber contact are relatively infrequent (Brown, 1993).
Thus, it is very unlikely that the particles were captured by more than one fiber as
illustrated in Figure 2.3. Consequently, the theory of particle capture is often discussed
and analyzed in terms of a single fiber. Single Fiber Representation is discussed in the
following section. Sabnis (1993) and Newman (1994) conducted an extensive review
of relevant literature available on filtration theory through fibrous filters. Here, primary
focus is given to filtration efficiency models. A number of simple and rigorous filtration
efficiency models have been developed by different investigators over the past forty years
(Landahl and Herrmann, 1949~ Freshwater and Stenhouse, 1972~ Suneja and Lee, 1974~
First and Hinds, 1976~ Lee and Liu, 1982a and 1982b~ Flagan and Seinfeld, 1988; Ptak
and Jaroszczyk, 1990~ Wang and Kasper, 1991~ Brown, 1993). The following sections of
this chapter serve as a brief review of modern concepts of filtration which are referred to
. ·J.
13
throughout this thesis. The reader is referred to Davies, 1973; Crawford, 1976; Flagan
and Seinfeld, 1988; and Brown, 1993 for detailed discussion of filtration theory and
practice.
C)
0
C)
(4l Packed filter <dust
particles not shown)
0
(bl Singlelayer filter. with
dust particles shown in
interstitial spaces
Figure 2.1 Filter Media Structure of Packed and SingleLayer Filters:
0  ~J...
14
1.000 + ...........
+
o.soo t = ~ 0
.;.; u a
ua . +\ ;; o.oso
a .g
u
~ 0.020
""
Particle diameter (pm)
Figure 2.2 Penetration ofMonodisperse Particles Through a Simple Filter, 20 J.Lm Fiber
Diameter and 0.05 Packing Fraction, as a Function ofParticle Size (Brown, 1993)
~
o ~
o
~
o~
SOpm
Figure 2.3 Section of a Filter illustrating the Scale ofParticles and Fibers (Brown. 1993)
 '"' '' , .. ,,,  ~ _______ l
15
2.2 Fiber Representation and Filtration Efficiencies
2. 2.1 Single Fiber Representation of a Fibrous Filter
The behavior of a particle captured by a filter is often discussed and analyzed in
terms of a single fiber within the depth of a filter and then related to the overall behavior
of the filter. As discussed by Davies (1973), the dimensionless porosity, Po, and the
dimensionless packing density, c, solidity or volume fraction of the fibers, may be related
as:
c= 7!R}L= 1P0 (2.1)
assuming the media consists of fibers with unifonn radius, R.r. L represents the length of
all fibers in a unit volume of the media. The collision or collection efficiency of aerosol
particles with a fiber, Tf coil, depends on both particle and fiber parameters. Single fiber
representation considers the effects of the surrounding fibers and packing density of the
media by considering a cell surrounding the fiber. The radius of this surrounding cell, b, is
related to the packing density and to the size ofthe fibers (Crawford, 1976).
b=Ei=ic (2.2)
Figure 2.4 shows a fiber held nonnal to the flow of air at a distance b upstream from the
center of the fiber cylinder. Note that Dtis the diameter of the fiber, 2Rr, and Dp is the
diameter of the particle, 2Rp.
. ..... ··· ·~" ~· ____ ,l
16
Fiber collection of particles may also be analyzed by isolated fiber representation.
Isolated fiber representation differs from single fiber representation by not considering
surrounding fiber effects and the effects of packing density. According to Davies ( 1973 ),
this theory is accurate only for mechanisms of particle collection which operate very near
to the fiber surface; such as, Brownian diffusion and electrostatic attraction. Mechanisms
of particle collection are discussed in Section 2.3.
2.2.2 Flow Around a Fiber
In examining the flow field around the fiber cylinder, the velocity inside the filter,
uaJ , is greater than the velocity upstream of the filter media, u , due to the partial blocking
of flow by the fibers (Crawford, 1976):
u
uaJ=(lc)
(2.3)
The Reynolds number of the flow through the filter, Re 1 , is defined with respect to the
velocity inside the filter media, uaJ , and the fiber diameter, D 1 :
(2.4)
where p is the density of air, and p, is the dynamic viscosity of air. Typical Reynolds
numbers are in the order of one or smaller, for fibrous filters.
~~~e·o··· ~···1
y  Limiting particle trajectory
Dp/2 I  I 
uc:o
I X
Figure 2.4 Single Fiber Representation of Particle Capture Illustrated by
a Limiting Trajectory (Crawford, 1976)
2. 2. 3 Single Fiber Efficiency
17
Davies (1973) proposed that flow through a filter is nearly always laminar. Using
simple geometry, Davies derived and then suggested that the single fiber efficiency is equal
to the ratio of the distance between two limiting streamlines of the flow approaching a
fiber, 2y, to the diameter of the fiber, 2Rr. Refer to Figure 2.4, Single Fiber
Representation of Particle Capture illustrated by a Limiting Trajectory. Davies assumes
that all particles striking the fiber remain adhered to it, or perfect adhesion occurs. Perfect
adhesion has generally been assumed in the vast amount of work reviewed. However, due
to particle removal mechanisms such as aerodynamic drag; "blowoff', or simple rebound
after impact; "bounceoff', it is certainly not always the case that once a particle touches a
fiber it will permanently adhere to its surface (Freshwater and Stenhouse, 1972) .. Ptak and
·~  •• A• ~ ""'
18
Jaroszczyk (1990) recognized the importance of distinquishing the difference between
collection efficiency and collision efficiency. The difference is associated with momentum
of solid dust particles and their adhesion to the fiber surface. Collection efficiency refers
to the degree of particles collected, adhered, and retained by the fibers, whereas, collision
efficiency refers to the degree of particles merely making contact with a fiber. Thus, the
single fiber collection efficiency is best expressed as:
71 s = 71 coll71 adh (2.5)
where 71s is the single fiber collection efficiency, 71coll is the collision, and 77adh is the
retention or adhesion efficiency. Typical characteristics of 77 coli, 77 adh, and 77 s as
presented by Stenhouse (1975) are shown in Figure 2.5.
Much work has been devoted to collision efficiency of small particles. Refer to the
following sections. Some important parameters which determine particle adhesion and
retention efficiency have been investigated experimentally (Krupp, 1967; Dahneke, 1971,
1973, and 1974; Freshwater and Stenhouse, 1972; Walkenhorst, 1972; First and Hinds,
1976; Ptak and Jaroszczyk, 1990). However, there is a very limited presentation of
quantitative methods by which values of 77 adh may be correlated or predicted (Ptak and
Jaroszczyk, 1990; Wang and Kasper, 1991). For a more detailed discussion, refer to
Section 2.6 Adhesion and Retention of Captured Particles.
~ ·· ~·~~ J...
l .
~ c
Q)
0
~
 ........ / /~ 
Tladh' .. , / Tlcol
', /
/',
~
I ',,
I ',
I ' ',
/ ' .. ,
velocity
Figure 2. 5 Typical Characteristics of TJ coil, 17 adh , and 17 s
(Adapted from Stenhouse, 1975)
2.2.4 Isolated Fiber Efficiency
Recall from SubSection 2.2.1 that isolated fiber representation differs from single
fiber representation by not considering surrounding fiber effects and the effects of packing
density. To account for the effects of neighboring fibers on the efficiency of any given
fiber, Ptak and Jaroszczyk (1990) experimentally determined a "solidity factor," expressed
as:
0.9
SF= o.J c
(2.6)
The product of an isolated fiber efficiency, 1'/; , and the solidity factor is the single fiber
collection efficiency, T/s:
J...
20
Tfs = SF17i (2.7)
Note that the authors do not specify any limitations or conditions for Equation (2.6). It is
suggested here that possible limitations be investigated in future work.
2.2.5 Elemental Fiber Efficiency
As described by Crawford and other authors, a simple mass balance across a filter
bed and integration through the filter bed thickness, from 0 to h, yields that the particle
concentration entering a filter bed, Co, and the particle concentration leaving a filter bed,
C, are related by (Crawford, 1976):
C _( 2CTfsh J
Co = e~~ ;r( 1 c)Rf
(2.6)
Where 17 s is the single fiber efficiency and h is the filter thickness. This assumes the filter
has uniform packing density c and fiber radius Rr, and that the filter efficiency is also
uniform through the filter. Recall that for any filtering process, the ratio of particles
leaving the system to particles entering the system defines the amount of particles
penetrating through the filtering system. With this in mind, the above concentration ratio
defines the penetration of the filter bed:
P=~
co (2.9)
· . ·~~~········ ···· _ _1....
Furthermore, the efficiency of any filtering process is the ratio of particles collected to the
particles entering the filtering process. Alternatively, the filtering efficiency may be
express in terms of the fraction of particles penetrating the filter, the penetration:
1]=1P (2.10)
Thus, combining the preceding three equations gives the following expression for the
elemental fiber efficiency:
(
2c17)z J Tle = 1 ~ = 1 exp  ;r(1 c)Rr (2.11)
The elemental fiber efficiency represents the overall efficiency of a small element of a filter
having thickness h. Note that depending on how the single fiber efficiency is defined, the
elemental fiber efficiency may or may not include the various mechanisms of particle
collection or particle retention as discussed in later sections.
2.2.6 Overall Filter Efficiency
Once the individual elemental efficiencies of a filter are all determined, an overall
filter efficiency, 171 , may be calculated as a weighted average of the elemental efficiencies.
It is common to express this weighted average in terms of the elemental penetration.
From Equation (2.1 0) or (2.11 ), the elemental penetration, ~, is given by ~ = 1 17 e .
Let the elemental particle number density or the elemental dust concentration entering the
filter element be Ceo, per unit volume. The particle number density at the exit of the filter
element may then be expressed as Ceo~. If Q1 is the air volumetric flow rate through the
~J_
filter and C0 is the total particle number density entering the filter, the number rate of
particles entering the flow is simply the product of these two terms. For n elements of
elemental surface area, ae, and elemental velocity inside the pleats, u"' , the total number
n
rate of particles entering the filter flow is C0 Iaeu"'. For n elements, the overall
i=l
efficiency of the filter, 771 , is expressed as one minus the ratio of the total number rate of
particles penetrating each element to the number rate of particles entering the filter flow:
i:[( ceo~)aeucc]
jJ I 1lt = ] n
Co:L[aeu"'J
(2.12)
i=l
If we assume a uniform particle concentration per unit volume, C0 = (Ceo); for any i ,
then Equation (2.12) may be rewritten as:
f[~aeu"']
i=l '
77 ] n ]
1  :L[aeu"' ;
(2.13)
i=l
The elemental surface area ae and velocity u"' are defined specifically for a pleated air
filter element in Section 2. 7 Air Velocities of Pleated Air Filters.
l
23
2. 3 Mechanisms of Particle Capture and Combined Efficiencies
2.3.1 Overview
The basis of predicting the collision efficiency, 17coll' of a filter bed has been well
documented and investigated by several authors. The filter element is taken as a single
fiber cylinder normal to the gas flow, as illustrated in Figure 2.4. As described by Flagan
and Seinfeld (1988), there are four distinct mechanisms identified whereby particles in the
gas can reach the surface of the fiber cylinder: interception, inertial impaction, Brownian
diffusion, and electrostatic attraction. An illustration of the first three mechanisms is
provided in Figure 2.6. Particle adhesion or retention is not discussed in this section, refer
to Section 2.6 Adhesion and Retention of Captured Particles.
2. 3. 2 Interception
Particle capture due to direct interception occurs when a particle, following the
streamlines of the flow around a fiber cylinder, is of a finite size sufficiently large that it
touches the surface of the fiber cylinder. In other words, interception is said to occur if
the streamline on which the particle center lies is within a distance Dp/2 of the fiber
cylinder. This mechanism is most important only for particle sizes of Dp > 1 J.lrn (Flagan
and Seinfeld, 1988). Note that the mechanism of interception assumes the particle has size
but no mass. Without mass, there will not be any inertia effects and the particle is
understood to follow the streamline. Refer to particle A of Figure 2.6.
.1.
24
2. 3. 3 Inertial Impaction
Particle capture due to inertial impaction occurs when a particle is unable to follow
the rapidly curving streamlines because of its inertia. Inertia effects lead the particle along
a path of less curvature onto the fiber cylinder. Collision occurs due to momentum. This
mechanism is most important only for particle sizes of Dp > 1 J.lffi (Flagan and Seinfeld,
1988). Note that the mechanism of inertial impaction is based on the premise that the
particle has mass but no size. Refer to particle B of Figure 2.6.
2. 3.4 Brownian Diffusion
Particle capture due to Brownian diffusion occurs when a particle's random
motion of Brownian diffusion brings it into contact with the fiber cylinder. Brownian
diffusion is caused by collisions of submicron particles with surrounding molecules. A
concentration gradient is established once a few particle are collected. The concentration
gradient acts as a driving force to increase the rate of deposition. These effects increase
with decreasing particle size. This mechanism is most important for very small particle
sizes, Dp < 0.5 J.lffi, transported in a very low velocity flow fields (Flagan and Seinfeld,
1988). For automotive air filtering of particles greater than 0.5 J.lffi, Brownian diffusion is
understood to be negligible. Refer to particle C of Figure 2.6.
2.3.5 Electrostatic Attraction
Particle collection due to electrostatic attraction is driven by a static charge. The
J..... ~~
25
electrostatic forces may be either direct or induced. Direct electrostatic attraction refers
to both charged fibers and particles. Induced electrostatic attraction refers to either
charged fibers or charged particles. The charging is usually not present unless introduced
during the manufacture of the fiber. This mechanism is most important only for particle
sizes from 0.01 to 0.5 ~m (Flagan and Seinfeld, 1988; Gillespie, 1955). Electrostatic
attraction, is not predominantly employed in engine air filters by automotive air filter
manufacturers. However, it is being considered in designs of passenger compartment
cabin air filters (SAE, 1993). Consequently, primary focus is given to the first three
mechanisms of filtration.
2. 3. 6 Combined Particle Collision Efficiencies
The overall particle collision efficiency, rt coil, for a fiber cylinder is commonly
obtained by analyzing the mechanisms of particle collision separately and then combining
the individual efficiencies (Flagan and Seinfeld, 1988). In considering two independent
mechanisms of particle capture, the probability that a particle will escape capture by
mechanism 1 is: (1 T'/ 1) . Likewise, the probability that a particle will escape capture by
mechanism 2 is: ( 1 rt 2) . The probability that a particle will escape capture altogether is
then the product of two probabilities: (1 rt1)(1 1]2) Thus, the probability that a
particle will be captured by mechanism 1 and 2 is:
rtcoll = 1 (1 1l1X1 rt2) (2.14)
26
or for n independent particle capture mechanisms:
71coll = (1 771)(1 772}··(177n) (2.15)
Equation (2.14) may be expressed as 71coll = 771 + 772 771772. Frequently one mechanism
may dominate in a particular range of particle sizes and the third term, 771772, will approach
some small value compared to the other terms. Consequently, on occasion some authors
will express the collection efficiency by two mechanisms as simply: 77 coil = 771 + 772 .
Throughout this thesis, the overall particle collision efficiency, 71coll' for a fiber cylinder
will be defined as in Equation (2.14) or (2.15), unless otherwise stated.
This combined efficiency assumes that the mechanisms are all independent. In
other words, it assumes that collection by mechanism 1 occurred independently in series
with collection by mechanism 2 and so on. In reality, a particle may be collected due to
simultaneous effects of two mechanisms. For example, a particle of small size and mass
may not be collected due to interception or inertial impaction alone. However, with
combined effects a particle could be collected by inertial interception. Although, this
method of combining collection mechanism effects is not thoroughly rigorous, it is an
approximate approach and has been demonstrated to agree well with other efficiency
models developed from empirical data (Sabnis, 1993; Newman, 1994).
1
27
Figure 2.6 Particle Capture Mechanisms: (A) Capture by Interception, (B) Capture by
Inertial Impaction, and (C) Capture by Brownian Diffusion (Brown, 1993)
2.4 Kuwahara Flow Field Around a Fiber Cylinder
Particle capture theory requires a description of the flow field close to a fiber in a
filter element. The most popular models used today are the models published by Happel
(1959) and Kuwahara (1959) used to describe the flow pattern of a fluid through an array
of parallel cylinders. Since 1959, alternative flow fields have been published (Brinkman,
1967; and Spielman and Goren, 1968). Davies (1973) has concluded that the Kuwahara
flow solution gives the closest agreement to experimental results and makes the most
sense to use. Referring back to single fiber representation, a fiber of radius Rc is assumed
to be surrounded by an imaginary cell of radius b. NavierStokes equations for flow
J
28
transverse to the cylinders were used with the boundary condition of zero velocity at the
surface of the fibers and zero vorticity on the surface of the b cell cylinder. The Kuwahara
flow solution, as expressed by Flagan and Seinfeld (1988) in terms of the stream function
1/f lS:
1!f = u«>r [ 2ln2r 1+c+D} ( 1c) 2cr sznB
2
] .
2Ku D1 4r2 2 Dj
(2.16)
where r and B are the cylindrical coordinates. The Ku term is the Kuwahara
hydrodynamic factor given as:
3 c2 1
Ku =cIne
4 4 2
(2.17)
The radial and tangential velocity components are given in terms of the stream function
which yield the following expressions:
u =1 81/f =u«> [ 2ln2r 1+c+D} ( 1c) 2cr cosB
2
]
r r t3B 2Ku D1 4r2 2 D}
(2.18a)
81/f u«> [ 2r D} ( c) 2cr
2
u ] . 8 == 2ln+1+c 1  sznB a 2Ku D1 4r2 2 Dj
(2.18b)
Note that these equations are independent of viscosity and Reynolds number. Several
filtration efficiency models are based on this flow field model as discussed in the following
section.
''"' ·~~""""'' ~ ~.1
29
2.5 Filtration Efficiency Models
2. 5.1 Lee and Liu Interception Model
Particle capture due to direct interception occurs when a particle, following the
streamlines of the flow around a fiber cylinder, is of a finite size sufficiently large that it
touches the surface of the fiber cylinder. The single fiber collection efficiency due to
interception, TlR , as defined by Lee and Liu (1982a) is:
y
TlR = Rr
(2.19)
where Y is the distance between the center line and the streamline below which all
particles are collected. In terms of the dimensionless stream function passing through a
point at a distance of RP from the fiber surface, Equation (2.19) becomes:
"' TlR = u~Rr (2.20)
Substituting the stream function expression (2.16), as defined by the Kuwahara flow
model, Lee and Liu obtained:
TlR =
1 + lp [21n(1 +lp)1 + c+(
1]
2
(1 c) __: _(1 + IP)
2
] (2.21)
2Ku l+IP 2 2
where Ku is the Kuwahara hydrodynamic factor as expressed in Equation (2.17). IP is
the interception parameter defined as the diameter ratio of particle to fiber, or
dimensionless particle radius:
~ ""·~~~....~...
30
DP 2RP
I==
P Dr 2Rr
(2.22)
Equation (2.21) is a complete expression for the interception efficiency based on the
Kuwahara flow field model. Lee and Liu found it useful to reduce Equation (2.21) to a
simpler form using an approximate form of the stream function. As given by Lee and Liu
(1982b), the semiempirical approximation ofEquation (2.21) is:
Jc_}J_
17R = Ku l+IP
(2.23)
This approximation was compared to others obtained by other investigators. In general,
for both small c and small I P values, all approximations gave efficiency values that are
close to the value computed using Equation (2.21). However, when c becomes large,
Equation (2.23) gives much closer values to Equation (2.21) than any other approximation
equation studied (Lee and Liu, 1982b). Lee and Liu (1982b) concluded that the error for
the approximations used to obtain the simplified stream function approaches zero as c
increases and approaches 1/3.
2.5.2 Landahl and Herrmann Inertial Impaction Model
Particle capture due to inertial impaction occurs when a particle is unable to follow
the rapidly curving streamlines because of its inertia. The efficiency of inertial impaction
significantly increases with increasing filtration velocity and is a strong function of the
Stokes number for particles in the size range of approximately 1 to 80 J..1ffi (Jaroszczyk and
~~~' ~~~~~, <C ,,~~cc __ J..,
31
Wake, 1991; Landahl and Herrmann, 1949). The Stokes number as expressed by Brown
(1993) is:
R~ppu«>
St = 9pR.f
(2.24)
For small particles, the Stokes number may be corrected for slip using the Cunningham
correction factor approximated as:
Cc =I+ 1.257Kn
where Kn is the Knudsen number expressed as:
Kn=.!::_
RP
for RP >>A
(2.25)
(2.26)
and A is the mean free path of air. Thus, the Stokes number corrected for slip, Stc, is
defined as:
" C R
2
utc = CcSt = c pPpU«>
9pR.f
(2.27)
The Landahl and Herrmann (1949) model for isolated fiber efficiency due to inertial
impaction, as given by Jaroszczyk and Wake (1991) in terms of the corrected Stokes
number, is as follows:
St3
c
171 = St3 + 0.77St: + 0.22
(2.28)
Recall that the isolated fiber representation differs from the single fiber representation by
not considering surrounding fiber effects and the effects of packing density. Using the
Ptak and Jaroszczyk (1990) "solidity factor" as in Equation (2.6):
..I...
32
SF= 0.9
C0.3
the Landahl and Herrmann (1949) model may be used to obtain the single fiber efficiency
due to inertial impaction:
SF·St:
771 = st: + 0.11 st; + 0.22
(2.29)
2.5.3 Combined Interception and Inertial Impaction Model
If we consider the collision efficiency due to interception and the collision
efficiency due to inertial impaction, we can determine the combined total collision
efficiency by using Equation (2.14):
11coll = 1 (1 111X1 112)
By substituting the Lee and Liu interception mode~ Equation (2.23), and the Landahl and
Herrmann inertial impaction model, Equation (2.28), into Equation (2.14), one can obtain
the following model for combined effects of interception and inertial impaction:
(
1 c I; J( st: J 71  1 1 1 ,__..::.._:
IR  Ku 1 +I p St~ + 0.77 st; + 0.22
(2.30)
Recall that Equation (2.14) assumes that the occurrences of interception and inertial
impaction are two independent occurrences. Nonetheless, this model is an approximate
approach and has been demonstrated to agree well with other efficiency models developed
from empirical data (Sabnis, 1993; Newman, 1994). This model is plotted in Figure 2.7
for a range of Stokes numbers. An exact solution and an approximate solution presented
~~~~" .c•~• ,~ ~
33
by Flagan and Seinfeld (1988) as discussed in the following subsection are also plotted.
Note how much better this model compares to the exact solution as compared to the
approximate solution. Refer to the next subsection for a detailed description of the
Flagan and Seinfeld (1988) solutions.
1.0 =
0.1
~
0.01
· Sabnis' Approximate Method
0.001 I I , I 1 ,.,. I ! I I I'"' ' I I 1 '"" I I II II"
0.001 0.01 0.1 1.0 10
St
Figure 2.7 Comparison ofFlagan and Seinfeld's (1988) Exact Solution to Sabnis'
Combined Interception and Inertial Impaction Model (Newman, 1994)
······~. ~
34
Equation (2.30) is presented just as it was used by Sabnis (1993). The Lee and
Liu interception model used is based on the single fiber representation. However, as
mentioned earlier, the Landahl and Herrmann inertial impaction model is based on the
isolated fiber representation. Thus, to account for neighboring effects within the Landahl
and Herrmann inertial impaction model, it is proposed here to incorporate Equation (2.29)
with the solidity factor rather than Equation (2.28):
'
_ 1_ (J~_!l__J(l SF· St: J
'IIR Ku l+IP St: +0.77St; +0.22
(2.31)
One can expect slightly higher efficiencies with Equation (2.30). In general, differences
between Equations (2.30) and (2.31) should be minor except in the case of high velocities
where inertial impaction dominates.
2.5.4 Interception and Inertial Impaction Modeling by Particle Trajectory
As presented by Flagan and Seinfeld (1988), the trajectory of a particle can be
mathematically tracked by inserting the Kuwahara flow field velocities into the equation of
motion of a particle. Flagan and Seinfeld present both an approximate solution, using
average velocities, and an exact solution, using Kuwahara velocities, to obtain the isolated
collision efficiency due to interception and inertial impaction.
The "approximation solution" requires simultaneously solving the following two
equations:
I
I
____ 1
35
 2yl = _1_(1 + 2y2J
'TIIR  D 2Ku Df
f
2lrf\1 + 2DY2 J 1+c
f
+ 1 1c2/ c ( 2
2
(1+2%J 2 I+ ;:J (2.32a)
'TIIR = 2yl = (1 + DPJ + St.JC[(1 + 2yJ/ DfJ(1 + 2y2  2y]J]
D1 D1 2y2jD1 D1 D1
x{1ej_ I ( 1 + 2YJ/DtJJ]} _ (1+ 2y2 _ 2y1J
""'1'l St.JC 2y2jD1 D1 D1
(2.32b)
where y1 is the limiting streamline as in Figure 2.1 and y2 is some distance from the fiber
surface. Note that y1 and y2 are the two unknowns. There is no interest in the value of
Y2. The collision efficiency is obtained by solving for y1 .
An "exact solution" may be obtained by solving the next two secondorder
ordinary differential equations. Note that two secondorder ordinary differential equations
may be easily converted into four firstorder ordinary differential equations and solved
using an ordinary differential equation solving algorithm such as a fourthorder Runge
Kutta method:
d 2z1 dz1 St
+=
dt*2 dt* 2Ku
/·,.1' \~zf +zi}) +c2~zf +3z]}+ z2;  z2~
z1 +z2
1( ) 2 2
+ 1~ zl z2
4 2 (zf +zJt
(2.33a)
d2z2 dz2  ~[ 2zlz2  (1 c) zlz2  4czlz2]
dt*2 +dl  2Ku z2 2 2 ( 2)2 1 +z2 2 zf +z2
to be solved subject to the following boundary conditions:
1
zJ{O) = 2JC
z2(o) = )j_
Df
dz1 ux(b,y1)r
.=
dtt"=O Df
dz2 = 0 •
dtt"=O
(2.33b)
(2.34a)
(2.34b)
Figure 2. 7 shows plots of both the approximate solution and the exact solution. The
maximum difference between the two efficiencies is about 75%, occurring in the vicinity
of St = 0.1. Note how much better the model used by Sabnis follows the exact solution
curve as compared to the approximation solution.
2.5.5 Other Collision Efficiency Models
Suneja and Lee (1974) derived an equation for isolated collision efficiency due to
interception and inertial impaction:
T7 JR. = [ ( I ,2 II ]2 + ~ ~ I+ 1.53 0.23/nR£1+ O.I67( InRe1 ) I St j
(2.35)
for Re1 :5: 500. The complete NavierStokes equations were solved using a successive
overrelaxation method to obtain the flow field around a fiber (Suneja and Lee, 1974).
>> >>> 000 O> •o> _ _l
The calculated flow field was then used in computing the particle trajectories and thereby
the isolated collision efficiencies. According to this equation, the collision efficiency
increases with decrease in Stokes number, increase in Reynolds number, and increase in
the dimensionless particles size, I P .
A second model investigated for isolated collision efficiency considering combined
effects of interception and inertial impaction was the model developed by Ptak and
Jaroszczyk (1990):
(St 0.75Rer0 . 2 )2 + I2
 2 p
1JIR  (St + 0.4)
(2.36)
Ptak and Jaroszczyk used a similar approach to that used by Suneja and Lee (1974) in
deriving Equation (2.35).
A third model studied was Landahl and Herrmann's (1949) model for isolated
collision efficiency due to interception and inertial impaction:
st: I 1]  +
IR  St3 + 0.77St; + 0.22 p
(2.37)
Note that the only difference between Landahl and Herrmann's inertial impaction
efficiency model, Equation (2.28), and their interception and inertial impaction model,
Equation (2.37), is the added interception parameter, IP.
Note that the three models discussed in this subsection incorporate the relation of
two mechanisms, interception and inertial impaction, using the simplified relation of
Equation (2.14), as discussed in Section 2.3.5: 1Jcoll = 1]1 + 1]2 . Nonetheless, as illustrated
......
38
in Figure 2. 7, Equation (2.30) implements the "nonsimplified" relation of Equation (2.14)
with good agreement to the exact solution presented by Flagan and Seinfeld (1988). The
reader is reminded that both relations are approximate methods and that both relations are
accepted practices within filtration efficiency modeling.
All models discussed in this subsection are for isolated fiber efficiencies. The Ptak
and Jaroszczyk (1990) solidity factor may be used to obtain the single fiber efficiencies
accounting for neighboring fibers. A plot of these three isolated collision efficiencies
along with Flagan and Seinfeld's (1988) exact solution and the model used by Sabnis is
provided in Figure 2.8. Note that for the large range of Stokes numbers, the model used
by Sabnis, Equation (2.30), closely follows the exact solution and, for this reason, is by far
the best model to use.
""""  ""~~~" __ o_" ___  ~~Ji...
F='"
1.0
Exact
Sabnis' Approximate Method
• • • Landalll & Herrman
0.1 • Suneja & Lae
 • Ptak & Jaro$CZ'11t
0.01
0.001' I I 1 IIJIIf I I I IAI!II I 1 I 1111111 I 1 II 1111
0.001 0.01 0.1 1.0 10
St
Figure 2.8 Comparison ofFlagan and Seinfeld's (1988) Exact Solution
to Isolated Collision Efficiency Models (Newman, 1994)
2. 6 Adhesion and Retention of Captured Particles
39
2.6.1 Discussion
Most of the theory described so far has assumed that particles adhere perfectly to
fibers on contact. Now the possibility of impact without capture is considered. Although
some important parameters which determine particle adhesion and retention efficiency
have been investigated experimentally (Larsen, 1958; Krupp, 1967; Freshwater and
Stenhouse, 1972; First and Hinds, 1976; Ptak and Jaroszczyk, 1990), very limited
quantitative methods have been developed by which values of TJ adh may be correlated or
predicted (Wang and Kasper, 1991; Ptak and Jaroszczyk, 1990; Brown, 1993). There are
two primary mechanisms of particle removal after contact: "bounceoff'' or simple
rebound after initial impact and "blowoff'' or aerodynamic drag causing reentrainment
(Freshwater and Stenhouse, 1972; Brown, 1993). In the following subsections, to
provide an understanding of adhesion and retention of particles, we shall discuss the
principle forces of adhesion as applied to dry fibrous filters.
2.6.2 Adhesion Forces
By providing an understanding of adhesion forces and comparing recent
publications on adhesion theories, it is hoped here to obtain some information on the
adhesion mechanisms prevailing. As discussed by Krupp (1967), there are three types of
forces of importance in the adhesion of dust particles to filter fibers:
( 1) van der Waals forces
(2) electrostatic forces caused by excess charges
(3) surface tension or capillary forces between liquid bridges
Vander Waals forces are interaction forces based on the attraction of dipoles between the
atoms of the adhered surfaces. These interaction forces between atoms occur due to
fluctuating electric dipole moments within the atoms. An electric field is induced by an
;;;;;::==............. oiiiiiiii~~~~~ ...... ~~iiiiiiiiii~ .......................... ~~~~~~~iiiiiiiE~~ ....... ~=~~~~
41
atom which then attracts a dipole of a neighboring atom. As presented by Leffler (1966;
1968) and Brown (1993), van der Waals forces between macroscopic bodies are
expressed in terms of the Hamaker constant, A1 :
F= AJRa
6z2
0
(2.38)
where Ra is the radius of the surface asperity that is closest to the fiber, and Z0 is the
distance between the particle and the fiber. The Hamaker constant, A1 , depends on the
number of atoms participating in the force transfer and upon their polarizability. This
constant is not always easy to determine. Brown ( 1993) provides a listing of Hamaker
constants for metallic and nonmetallic materials.
Electrostatic forces are based on electrical excess charges of the adhered surfaces,
particle or fiber. As given by Brown, the force of adhesion due to an electrostatic charge
q of a particle with radius RP is:
q] 1{1+ :.)
F~=~~~~~
 16trefip8 [r + !._z_f_2Rp)Ir + !._ 1;f 2RP )]
2 '\ Z0 2 '\z0 + 8
(2.39)
where 8 is the depth at which the charge density falls to e1 of that at the surface, E0 is
the permittivity of free space, r is Euler's constant. Electrostatic adhesion charges can
initially induce increased deposition of the dust particles on the fibers, if of sufficient
magnitude and appropriate polarity (Lofller, 1966). However, experiments have shown
that maximum adhesion forces due to electrostatic charges are much weaker (by a factor
 .... .~~~ ~ ___ J_
42
of 100) than the measured total adhesion forces. Note that Equation (2.38) represents the
adhesion force due to electrostatic charges once contact has taken place and does not
represent the "collection force" induced by the electrostatic attraction mechanism
discussed in SubSection 2.3.4.
Surface tension or capillary forces act in liquid bridges between the adhered
surfaces. With sorption layers which are freely mobile, wedges of liquid can form at the
contact points between particles and fibers. An underpressure prevails in these wedges.
Figure 2. 9 shows a sphere attached to a plane by means of a liquid bridge. If the angle of
contact is zero, the force between them as expressed by Brown is:
F = 4;rrRP (2.40)
where r is the boundarysurface tension of the liquid bridge and is independent of the
particle radius. A calculation based on simple geometry yields that the force is
independent of the amount of liquid present, so long as, a complete bridge is formed
(Brown, 1993). As the area of contact decreases, the curvature increases, and the internal
pressure of the liquid bridge also increases.
_..L
43
Figure 2.9 Sphere attached to a plane by capillary forces (Brown, 1993)
2. 6. 3 Conditions Affecting Particle Retention
Experimental measurements have shown that adhesion between particles and fibers
is primarily caused by van der Waals forces (Loftier, 1966; 1968; 1971b). However, at
relative humidities greater than 80%, the mechanism of adhesion most likely to prevail is
that of capillary adhesion due to surface adsorbed water (Freshwater and Stenhouse,
1972, Brown, 1993). Adhesion forces are stronger when acting on large particles, as
shown by Figure 2.10. However, larger particles are more likely to bounce at impact and
the drag exerted on larger particles by an airflow is greater, which may allow larger
___ :  ~ ~~j._
44
particles to be detached at a lower air flow (Brown, 1993). It is also easier to detach
particles from thick fibers than from thin ones (Larsen, 1958).
90
'o:l
u
'5
iii
0 70
'o:l
~ u so u u 5 .§ 30
c.>.
"0..0
~• lOt 4 i: 3 2 u s u..
~ y ur'
Applied force (N)
Figure 2.10 Distribution of Adhesion Energies of Quartz Particles Deposited at a
Filtration Velocity of0.42 mls on Polyamide Fibers: (1) 15.1 J.lm Particles~
(2) 10.3 J.lffi Particles~ (3) 8.3 J..1n1 Particles; (4) 5.1 J.1ffi Particles (Brown, 1993).
Dahneke suggests that for maximum retention ability, filters should contain fibers
of small diameter made of material with low Young's modulus (Dahneke, 1971 ). Such a
filter would have the best ability to capture the full range of particles sizes including the
large solid dust particles. The degree of adhesion does not appear to depend on the
hardness of the particles being filtered (Brown, 1993 ). Increasing relative humidity tends
to improve particle adhesion due to slightly softer fibers and an increase in the degree of
surface contact. Dahneke suggests that the flow velocity through the filter should not be
too high, although, to catch the large particles by inertial interception, the flow velocity
cannot be too low either. Furthermore, he indicates that the decrease of fiber diameter has
two strong influences on the capture of large particles (Dahneke, 1971): lowers the
45
velocity range in which inertial interception is effective and raises the velocity at which the
onset ofbouncing occurs.
The adhesion of particles to fibers is greater for particles that have been captured
at a higher filtration velocity. These particles captured at higher velocities are slightly
tighter bound and often very difficult to remove. It has been stated by many investigators
that the air velocity needed toreentrain particles is several times the filtration velocity (up
to 10 times for 50% removal): "Particle detachment is more likely to occur at the moment
of impact, and it can be reasonably concluded that particles that do not initially bounce are
unlikely to be reentrained by the air flow from which they were captured," (Brown,
1993). Many investigators dating as far back as the 1950's have concluded similar
findings that, although bounce may occur, blowoff is unlikely to occur: "Probably the
most important point to note from these experiments is that no particles were removed
from the fibers at air flows such as are used in commercial filters ... (Larsen, 1958)."
2. 6. 4 Ptak and Jaroszczyk Adhesion Model
Although much work has been conducted on adhesion theory and adhesion
measurements, only very limited quantitative prediction methods for 17 adh are available
(Wang and Kasper, 1991; Ptak and Jaroszczyk, 1990; Brown, 1993). The only authors
known to have developed any correlation or model in predicting particle to fiber adhesion
efficiencies are Wang and Kasper (1991) and Ptak and Jaroszczyk (1990).
 ••••• .,c~~==~~~
46
The Wang and Kasper adhesion model is based on a wide range of actual empirical
data and data extrapolated down to the molecular range. For a known value of impact
velocity to critical velocity (maximum impact velocity above which bounce occurs) ratio,
an adhesion efficiency may be determined from their universal curve, independent of
particle size, specific adhesion energy, and other operating variables, assuming a
Boltzmann velocity distribution (as an alternative to the Kuwahara flow field.) However,
they stress that their curve is only valid for a particle range of 0.1 to 10.0 nm (0.01 J..lm).
Particles greater than 0. 01 J..lm have a mean impact velocity significantly below their
critical velocity; hence, most collisions are effective and 77 adh approaches 1. 0 as expected
in classic filter efficiency theory (Wang and Kasper, 1991). For larger particles, greater
than a few microns, particle bounce following impaction decreases the filter efficiencies
(Wang and Kasper, 1991). The Wang and Kasper model is best suited for membrane
filters where diffusion and interception prevail over inertial impaction.
Ptak and J aroszczyk ( 1990) recognized the importance of distinguishing the
difference between collection efficiency and collision efficiency. The difference is
associated with the momentum of solid dust particles and their adhesion to the fiber
surface. Collection efficiency refers to the amount of particles collected, adhered, and
retained by the fibers, whereas, collision efficiency refer to the amount of particles merely
making contact with a fiber. Referring back to Equation (2.5), Ptak and Jaroszczyk refer
to 77 adh as the adhesive probability factor:
7"/ s = 7"/ co/171 adh
· ______.. ...
47
By considering common variables and parameters used in calculating and predicting
adhesion forces, Ptak and Jaroszczyk concluded that they may be used to determine the
adhesion probability factor or 11 adh . Thus, the general dependence of adhesion probability
is as follows:
11adh = 11adh(Pp,Dp,uoo,D[,f..l) (2.41)
where p P is the particle density. Using dimensional analysis, they incorporated the
Reynolds number of the particle, similiar to Equation (2.4), and the Stokes number as in
Equation (2.24):
and
ReP= DpuooPp
J..l
R;ppuoo
St = 9JJRr
(2.42)
By definition, the adhesion efficiency must fall in the range 0 ~ 11 adh ~ 1.0 . Hence, Ptak
and Jaroszczyk expressed this range as:
ao
'ladh = (RePStt +co
(2.43)
where the constants may be detennined experimentally, such that, a0 = C0 and bo > 0.
The final form of the Ptak and Jaroszczyk adhesion model is given as:
190 (2.44)
'ladh = ( )0.68 RePStc +190
48
The authors obtained good correlation between experimental results and their adhesion
model, Equation (2.44), using their Interception and Inertial model of SubSection 2.5.5,
Equation (2.36), with a solidity factor.
2. 7 Pleated Air Filters
2. 7.1 Discussion
All of the filtration theories and models discussed in previous sections have been
based on a flat sheet of filtering media. However, most filters used in a variety of
industrial applications are pleated. A pleated filter is more compact and allows for more
filtration area. Increasing the filtration area allows more particles to be captured in a fixed
volume and so reduces the filtration velocity which in tum reduces the pressure drop at a
fixed volume (Brown, 1993). It is understood that the pressure drop should decrease as
the number of pleats per unit length is increased. However, eventually the restricted space
between pleats will cause the pressure drop to rise again due to the increased viscous drag
(Chen et al., 1994). Although there are limited studies on pleated filter optimization, Chen
et al. developed an analytical model which compares favorably with Yu and Goulding's
(1992) semianalytical model. Studies conclude that an optimum pleat count for minimum
pressure drop exits at a certain pleat height for a specific filter medium type (Brown,
1993; Chen et al., 1994).
I
  ~l
49
2. 7.2 Pleated Surface Area
It is common to base all filtration theories and calculations on the surface area of
the filtering media. Figure 2.6 illustrates a filter pleat geometry. The element of width x,
lengthy, and thickness h represents an elemental filter bed. The elemental surface area,
ae' is defined by simple geometry:
(
2h )
2
ae = x,/ : + y2 (2.45}
X
1
~I ~ t y
I
h
_l
_j l p
Figure 2.11 Filter Pleat Geometry (Newman. 1994)
00~~~ .··· ~·t
50
2. 7. 3 Air Velocity Inside Pleated Filters
Although recent computational fluid dynamic calculations suggest nonuniform
flow near the pleats of a filter (Cai, 1993; Tebbutt, 1995), for simplicity, it is assumed here
that the velocity is uniform. Assuming uniform velocity, the velocity near the filter pleats,
u, is obtained through simple geometry and continuity,:
u= u xy
0 ae
(2.46)
where u0 is the axial velocity upstream of the filter. The velocity u0 is easily obtained
experimentally, just upstream of a filter. Note that the velocity u as in equation (2.3) of
SubSection 2.2.2 refers to the velocity upstream of the filter media; or rather, the velocity
near the filter pleats. From Equation (2.3) the velocity within the filter media is obtained:
u
uoo = 1c
in terms of the measured upstream velocity, U0 :
u = 00 (2.47)
The air velocity inside the filter media is greater than the velocity near the filter pleats,
uiXJ > u , and the measured axial velocity upstream of the filter is greater than the air
velocity near the filter pleats, U0 > u . The filter media velocity required by all of the
filtration efficiency models implemented was obtained directly from the measured axial
velocity upstream of the filter using Equation (2.47).
_L
51
2.8 Methodology
2.8.1 Typical Properties of Automotive Air Filtration Paper
Automotive air filtration media used in paper filters is typically cellulose wood
pulp comprised of southern softwood kraft, SSK, mercerized SSK, northern and southern
or eucalyptus hardwood kraft wood pulps. As obtained from Ahlstrom Filtration, the
typical mixtures in automotive air filter paper range from a position of 80 percent
mercerized SSK, 15 percent SSK, and 5 percent hardwood (for a very high permeability
grade) to 50 percent hardwood SSK, 25 percent SSK, 25 percent hardwood (for a very
high efficiency grade). The average fiber diameters as specified by Ahlstrom Filtration are
provided in Table 2.1. Also provided by Ahlstrom Filtration is a range of typical
properties for auto air filtration media. Refer to Table 2.2.
Table 2.1
Average Fiber Diameters Used in Automotive Air Filtration Paper
Fiber Type Average Fiber Diameter I
[J.LmJ
SSK 45
Mercerized SSK 4045
I
Northern US, Southern US, 1830
Eucalyptus Hardwood Kraft Pulp I
L
52
Table 2.2
Typical Properties for Automotive Air Filtration Paper
Property Property Range
Frazier Air Permeability 60 120 [cfin]
(number of £t;3 /minute of air to pass
through one ft? of media at a
pressure drop of0.5 inches ofH20)
Basis Weight 110 165 [g/m2]
Media Thickness 450 700 [11m]
Unsaturated Paper Density 0.18 0.22 [glee]
  ·  
2.8.2 Fiber Diameter
Most filtration efficiency models are based on the assumption that all fibers in a
filter bed are of uniform diameter. With this in mind, a uniform equivalent fiber diameter
must be determined and justified. Sabnis (1993) suggested that a uniform equivalent fiber
diameter may be determined by calculating a weight averaged fiber diameter based on the
composition of high permeability grade and high efficiency grade filters obtained from
Ahlstrom filtration. Sabnis used the mean filter diameter of the diameter range presented
in Table 2.1. Sabnis obtained D f = 43.5 7 5 f.DTl for high permeability grade filters and
Dr= 39.125f.DTI, for high efficiency grade filters. Sabnis assumed that the Purolator
.o ··~· =·=~o· ·~
53
AF3 192 filter is of a very high efficiency grade, and simply used a uniform equivalent fiber
diameter of 38.0 J.l.m.
Licht (1980) provides an alternative method of determining a uniform equivalent
diameter based on the weight fraction of the composition:
n
log D} = "Lx1 log D~ (2.48)
j=l
Using this expression with the composition presented earlier gives a uniform equivalent
diameter of 43.235 J.l.m for high permeability grade and 39.910 J.1.ffi for a high efficiency
grade.
As referenced in Dorman (1966) and Licht (1980), Davies suggests that an
"effective fiber diameter" may be determined based on the pressure loss through the filter
media at a given flowrate:
pQh70c1
·
5
(1 + 52C
15
) (2.49)
Der = ,/ 
This equation is applicable for high packing densities, c > 0.02 . The effective fiber
diameter is usually greater than that measured under the microscope (Dorman, 1966;
Brown, 1993). Before an effective fiber diameter may be determined, the packing density
of the filter must be known. The packing density and how it was determined is discussed
in the following subsection. An effective fiber diameter corresponding to the calculated
packing density is given.
54
2.8.3 Packing Density
The dimensionless packing density or packing fraction, c, defined as the volume
fraction of the fibers, is related in Equation (2.1):
c = lrR}L = 1 P0
assuming the media consists of fibers with uniform radius, R1 . In order to find c, it is
necessary to determine the density ofthe fibers, Pt (Davies, 1973). Then, as in Equation
(2.1):
c =Volume ofFibers = ;:,! = 1 _ p
Volume of Filter Ah 0 (2.50)
However, the actual fiber density of a multicomponent filter is not easily measured with
high accuracy. Thus, an alternate method of determining the packing density of the filter,
c, was incorporated.
In measurements of the resistance of filters, a unique dimensionless function exists
(Davies, 1973; Brown, 1993):
.MARJ
f(c) = pQh (2.51)
This equation embodies the fundamental law of filtration theory, Darcy's Law, which
states that the pressure across a filter is proportional to the rate of fluid flow through the
filter. The quantity Qh/ A.&' is referred to as the permeability and is a unique function of
the packing density and fiber radius. Many correlations among a range of porous media
have been developed and described by Equation (2.51 ). A very extensive study was
~...,,..,.·~ ....,....~~
55
carried out by Jackson et al. (1986) in which the measurements for a variety of physical
systems, both liquids and gases, by a large number of authors were plotted together.
Figure 2.12 was taken from Brown (1993) and shows the envelope curves for f(c) based
on the data comparison by Jackson et al. The bold line is the empirical formula developed
by Davies (1973):
f(c) = J6c15(1.0 +56c3
·
0
) (2.52)
This equation gives a good description of typical results expected at very low packing
fractions, c < 0.02 . Referring to Figure 2.12, the values of packing fraction vary by four
orders of magnitude and the values of f(c) by almost six. It is clear that a strong
correlation exists between c andf(c).
In efforts to determine the packing density of the Purolator AF3192 filter, a
pressure drop of5767 Pa (23.15 in. H20) was measured at an actual flow rate of0.06 m3/s
(126.5 cfin) through a 102 mm (4.0 in.) diameter section of flat filter media. Equation
(2.51) was used to calculate a value of j(c) assuming a weight averaged uniform
equivalent fiber diameter of 39.125 J..Lm for a high efficiency grade filter, as estimated
previously. (Refer to SubSection 2.8.2 Fiber Diameter.) At a value ofj(c) = 23.303, a
packing density range of 0.2113 to 0.5623 was obtained from Figure 2.12. The midpoint
of this range corresponds to a packing density of 0.3447. A packing density of c = 0.345
was used in all work presented in this thesis.
Previous work on this project has assumed a packing density of 0.23 based on an
assumed Frazier air permeability of 150 cfm defined as the number of ft? /minute of air to
~ ~ L
56
pass through one ft? of media at a pressure drop of0.5 in. HzO (Sabnis, 1993; Newman,
1994). By conducting actual pressure measurements through the filter media, an actual
permeability value was calculated eliminating the need to assume some value of Frazier air
permeability. Consequently, it is understood here, that the determined packing density of
c = 0.345 better represents the true packing density of the filter media as compared to the
previously assumed value of c = 0.23.
With the packing density known, an effective fiber diameter may be calculated
using Equation (2.49): Der = 51.78 J..Lm. This effective fiber diameter is higher than the
average fiber diameters listed in SubSection 2.8.1. However, this value is realistic. The
effective fiber diameter is typically higher than that measured under a microscope due to
likely reasons being that in real filters the fibers are not all perpendicular to the airflow and
the real fiber structures are not uniform (Brown, 1993).
In summary, for the Purolator AF3192 filter, a packing density value of c = 0.345
and an effective fiber diameter of Der = 51.78 J..Lm were used in all work presented.
~·.1..
~
~
0.01
0.003
0.001
0.0003
O.()(X) llf< K I I I I I I I
0.0001 0.001 0.01 0.1 1.0
Packing fraction (c)
Figure 2.12 Envelope Curves for f(c) Versus Packing Fraction, c, with
Davies' (1973) Very Low Packing Fraction Empirical Formula
Line Curve, Equation (2.52), (Brown, 1993).
57
58
2.8.4 Program "EFFMODEL.FOR"
The FORTRAN program EFFMODEL.FOR was developed to incorporate models
presented in this chapter. EFFMODEL.FOR incorporates an individual efficiency
component (interception, inertial impaction, and adhesion) subroutine, EFFRIA, a single
fiber efficiency subroutine, SINGLEE, and an elemental fiber efficiency subroutine,
ELEMENT. Program EFFMODEL was developed and implemented to obtain all
computational results presented in Chapter V Filtration Efficiencies. All computations
were conducted on Microsoft Programmer's WorkBench 1.10, 1990. A complete listing
of the main program and subroutines source code is provided in Appendix B. Sample
input and output files are provided in Appendix C.
Program EFFMODEL requires the user to supply an input file of upstream filter
velocities arranged in ascending order corresponding to the 66 data point locations
specified in Figure 3.7 of Chapter ID Experimental Setup. Refer to the sample input file
provided in Appendix C. Related elemental areas are tabulated per data point.
Subroutine EFFRIA implements three efficiency models for interception, inertial
impaction, and adhesion. The interception model implemented is the semiempirical model
developed by Lee and Liu (1982b), as in Equation (2.23):
Jc 1~
TIR = Ku l+IP
The inertial impaction model implemented is the isolated fiber efficiency model developed
by Landahl and Herrmann (1949), Equation (2.28). This model was corrected using the
L
59
Ptak and Jaroszczyk (1990) solidity factor of Equation (2.6). Thus as in Equation (2.29),
the final form of the inertial impaction model is:
11J= 3 s2 Stc + 0.77 tc + 0.22
SFst:
The particle adhesion model implemented is the model developed by Ptak and Jaroszczyk,
as in Equation (2.44):
190
11adh = ( )068 ReP Stc · + 190
At large particle diameters, the interception and the inertial impaction models may
exceed unity. This is possible for large values of IP such that RP + R1 >b. For these
conditions, the particles pass outside the Kuwahara flow field zone of radius b; thus, the
filtration models are no longer applicable. It may further be noted that, although the
individual component efficiencies may exceed a value of one, the elemental fiber efficiency
defined by Equation (2.11) will never exceed unity. Nonetheless, in efforts to avoid
negative penetration values, all models implemented in subroutine EFFRIA were limited to
efficiencies of unity or lower.
Subroutine SIN GLEE implements the single fiber collection efficiency model, as in
Equation (2.5):
17 s = 17 coll17 adh
L
60
where 17 coli is the collision efficiency, and 17 adh is the retention or adhesion efficiency.
The collision efficiency is defined as in Equation (2.14) for interception and inertial
impaction:
T/coll = 1 (1 T7R)(1 T/1) (2.53)
Thus, the final form ofEquation (2.5) is as follows:
T/s =[l(I77RXI77I)]T7adh (2.54)
Single fiber efficiencies were calculated for both perfect adhesion and nonperfect
adhesion as described by the Ptak and Jaroszczyk (1990) adhesion model, Equation
(2.44).
Subroutine ELEMENT calculates the elemental fiber efficiency based on the single
fiber efficiency due to interception, inertial impaction, and perfect and non perfect particle
adhesion. This elemental fiber efficiency model is defined in Equation (2.11):
(
2c17)1 J T/e = 1 exp ;r(l c)Rf
Figure 2.13 is a plot of the individual efficiencies obtained from program
EFFMODEL for a particle diameter of 2.5 Jlm. Note that the models follow the typical
characteristics of filtration efficiencies as illustrated in Figure 2.5. Measured upstream
velocities presented within this thesis typically range from 0.0 to less than 7.0 m/s. The
interception efficiency does not vary with velocity. With increasing upstream velocities,
the inertial impaction efficiency eventually reaches unity and the adhesion efficiency
approaches zero. For larger particle diameters, the peaks and end bounds of the curves
cc~~J_
61
represented in Figure 2.5 and Figure 2.13 are achieved at lower velocities. Similarly, with
a smaller fiber diameter and a smaller packing density, as used by Sabnis, the peaks and
end bounds ofthe curves are achieved at lower velocities. Refer to Figure 2.14.
Within the main program, overall filter efficiencies are calculated assurrung a
uniform particle concentration per unit volume using Equation (2.13):
I[~aeu~]
i=l •
1] =] n ]
f I[aeu~ i
i=l
Note that a uniform particle concentration does not imply a uniform volumetric flow rate
of particles.
The user may specifY an optional SAE fine test dust, SAE coarse test dust, or a
simple particle radius input. The SAE test dust distributions refer to the two grades of
particle size distributions by percent weight listed in Table 1.1. Overall elemental
efficiencies and overall total elemental efficiencies for the specified SAE test dusts are
calculated. A total of four output files are generated: VELSTRE, EFFCO:MP,
SINGELEM, and SAEDUST (when applicable). Refer to Appendix C for sample output
files.
L
1.00 ·· . ·.....~
~ ·.... ........... .__
0.75
~
... ......................... 
·.
/
/
·. ..._
/_...
//
62
c
Q) ·a 0.50 /
:= /..,/. ..,..... ·w
0.25
0.00
0
/
.#
2
/ .·
/.·/
y
/
/
4 6 8 10 12 14 16
Upstream Velocity [m/s]
 Interception   Single Fiber
 Inertial Impaction      Elemental
 Adhesion
Figure 2.13 Efficiency Curves Obtained from Program EFFMODEL
at Rp = 1.25 J.!In, c = 0.345, Det= 51.78 J.lm.
_,o.. o.. o··~o·o··oo 0 0 •••• ···L
1.00
0.75
~ c:
~ 0.50
I; w
0.25
0.00
··. .__ ·...........
.. I __ .· I
/
0 2 4
 . .  .  ......... ....... ... ...... . ...__ ···. ;:>·/ /
/ · /
/
/
/   //
/ .
;/
;.·
/ I
6 8 10 12 14 16
Upstream Velocity [m/s]
 Interception   Single Fiber
 Inertial Impaction     · Elemental
· Adhesion
Figure 2.14 Efficiency Curves Obtained from Program EFFMODEL
with Parameters Used by Sabnis (1993), Rp = 1.25 J.1lll, c = 0.230, Dt= 38.0 Jlm.
63
··~··~.1..
CHAPTER m
EXPE~NTALSETUP
3 .1 Experimental Apparatus
64
An experimental setup was assembled to pass air flow into the SAE J726 test
housing and through the filter specimens. Laser Doppler Velocimetry, LDV, was used to
measure the velocities of the flow field at two separate upstream horizontal planes. A
schematic of the experimental apparatus is shown in Figure 3. 1. The air flow was drawn
through the test housing by a downstream centrifugal multistage exhauster (also referred
to as a blower). The centrifugal multistage exhauster has a maximum flow rate of 1000
scfin and was set to run at the SAE specified test flow rate of 125 scfm. Upstream of the
apparatus, a 6Jet atomizer (TSI Incorporated MODEL 9306) was used to generate the
0.966 J..l.m Polystyrene Latex, PSL, aerosol particles used for seeding. A separate
compressed air supply passed through the atomizer. In efforts to avoid introducing water
droplets and condensation into the flow stream, the PSL particles were heated with a fan
heater just after leaving the atomizer. A flow distributor chamber was constructed in
efforts to redirect the flow stream and avoid potential flow swirls prior to entering the
plexiglas tubing upstream of the test housing. It was found to be convenient to mount the
tube to housing flanges with four quick release clamps. A wooden sphere used to obstruct
the inlet flow, in efforts to provide a more uniformly distributed flow, was
____ j_
EJ Flow Distributor Fan Heater Atomizer
Tube to Housing J , l
Flange
Upstream
Pressure Taps
Sphere
Filter
Housing 1 1 ( I
Flange Downstream
Pressure Taps
Figure 3 .1 Experimental Apparatus
65
To Blower
66
easily mounted and suspended from the tube to housing flanges, as shown in Figure 3 .1.
The SAE test housing was constructed as specified in Figure 1.2 using quarter inch
Plexiglas. The filter specimen is centered and mounted between the top and bottom
portions of the test housing, as shown in Figure 1.2. The housing is conveniently mounted
with four easy release clamps securing both the housing and the filter specimen. The flow
leaving the test housing entered a section of PVC pipe connected to the downstream
blower. Pressure taps located both upstream and downstream of the test housing were
used to monitor the differential pressure through the filter specimen.
The test housing was mounted on a stand allowing for adjustable vertical
positioning. During actual testing, the test housing was stationary. The laser transceiver
was mounted on a three axis automated traverse table. The horizontal translations were
controlled by two stepper motors driven by a separate personal computer. Vertical
translations were perfonned manually, allowing for measurements at separate horizontal
planes.
3.2 Laser Doppler Velocimetry Diagnostics
The measurement instrument used in this experiment was a dual component laser
Doppler velocimetry system incorporating fiber optics. A schematic of the laser Doppler
velocimetry system is provided in Figure 3.2. A Coherent lnnova 70A, 4 watt, argon ion
~~~~L
Fiber
Optic
Cables
Transceiver
Fifter
Fiber
Couplers
Laser
Beam
Doppler
Burst
Signal
PC
 Laser
Steering
Mirrors
I
IPou
Photodetector
Unit I DSA
.
~ 00
Figure 3.2 Schematic of the Laser Doppler Velocimetry System.
67
68
laser was operated at a wavelength of 488 run. A Bragg cell within the system fiber drive
applies a 40 MHz frequency shift to the beam. (Note that a Bragg cell will generate
several ordered beams of multiple shifts: +80 MHz, +40MHz, OMHz, 40MHz, 80MHz.)
The frequency shifting produces a moving fringe pattern which eliminates directional
ambiguity from velocity measurements of reversing flows. The 1st order, +40 MHz
shifted, beam and the Oth order, nonshifted, beam produced by the Bragg cell are then
separately split into two blue and two green beams of wavelengths 488 run and 515 run,
respectively. This gives a total of four beams, one shifted and one unshifted beam for each
color. An Aerometrics, Inc. Doppler Signal Analyzer, DSA, processing Doppler bursts
was used and operated by a 486DX/266 MHz personal computer. For ease in managing
and organizing the DSA processed data, I developed a simple program to select and
arrange the off line DSA data series output. A source code listing of this program is
provided in Appendix D Source Code Listing ofPICKDAT A.FOR.
Within the fiber drive, the four beams are aligned by the fiber couplers and
transmitted to the fiber optic transceiver through separate fiber optic cables. The fiber
optic transceiver both focuses the four beams and collects backscattered light reflected by
the seeding particles passing through the probe volume. The transceiver has a 500 mm
focal length lens producing a probe volume 737 J.Lm in length and 66 J.Lm in diameter. The
collected light is transmitted through a fifth fiber optic cable to the photodetector unit.
The photodetector unit contains two photomultipliers one sensing the detected light from
the green beams and the other sensing the detected light from the blue beams. The two
.L
69
photomultipliers translate the detected light into an analog voltage signal and send it to the
DSA processing system. A complete listing of the DSA processing system and other
equipment used is provided in Section 3.6 Equipment Listing.
3.3 Principles ofLaser Doppler Velocimetry
The scattered light signal, called the Doppler burst signal, contains intensity
maximas and minimas. An example of a raw Doppler burst is given in Figure 3.3. The
signals are a result of the seeding particles passing through the probe volume and crossing
the brighter and darker bands of the interference fringe pattern of the beam intersections.
The low frequency component of the signal is the pedestal. The pedestal is created when
the particle passes through the Guassian intensity distribution of the laser beams, resulting
in a low frequency signal. The Doppler bursts are superimposed on the pedestals and
caused by the seeding particle passing through the interference fringe pattern of the beam
intersections, as described by Hall and Hiatt (1994). Other authors may consider the
pedestals as part of the Doppler burst.
A diagram illustrating a particle passing through a probe volume is provided in
Figure 3. 4. The fringe spacing, d , is a function of the beam crossing angle and the laser
beam wavelength. The photomultipliers translate the detected light signals to an analog
voltage signal. The LDV Doppler Signal Analyzer detects the Doppler bursts and
_,~~
70
performs a Fast Fourier Transform, FFT, of the digitized burst signal. The DSA processor
performs validation tests on the individual spectra, rejecting low quality noisy data. The
peak frequency in the spectrum resulting from the FFT may be considered to be the rate at
which the particle is crossing the interference fringes in the probe volume. With the
Doppler frequency shift, f , known and the fringe spacing, d, known from the LDV' s
optical parameters, the velocity of the particle, and hence the velocity of the air stream, is
obtained:
V=Jd (3.1)
The frequency shifting producing the moving fringe pattern eliminates directional
ambiguity from velocity measurements of reversing flows. The measurement of reversing
flows is a strong advantage in that it does not require prior knowledge of the complex
velocity flow field directions. No calibration of the LDV system is needed. Another
advantage of using an LDV system is that the flow is not disturbed. However, seeding
particles are required and caution must be used in selecting a particle and a particle size
which ensures that the particle is large enough to provide a reflecting light signal yet small
enough to follow the flow without disrupting the flow stream. The backscatter
arrangement allows the transeiver to serve as both focusing beam optics and light
collecting optics.
The disadvantages of using an LDV system include that the apparatus must allow
for light to be transmitted and reflected easily. Thus, the apparatus in which velocity
measurements are to be conducted must be constructed of transparent material with
71
uniform transparency to pass the laser beam and to receive the reflected signal.
Furthermore, for large wall angles displacement of a transmitted light beam due to
material refraction and the incidence beam angle may not only distort the probe volume
but may also displace the dual beam probe volumes to a point where the two probe
volumes no longer cross. If the probe volumes do not properly cross, the signal will be
distorted and the blue and green sampling volumes will be at different locations.
All measurements presented in this thesis were measured at two different
horizontal planes in the test housing where the wall angle is 0.0° and 18.7°. For
simplicity, it was assumed here that the effects of the displaced and distorted probe
volume were insignificant. However, preliminary calculations indicate that the 73 7 Jlm
probe volume of the dual component laser system transmitted through the SAE Test
Housing with a diffuser wall angle of 18.7° may experience a displacement of as much as
1000 Jlm. Assuming that the reflected light scatter will be counter displaced, this
displacement may not pose major bias error other than a drop in intensities of the reflected
light. However in addition to the total probe volume displacement, the two probe
volumes may be displaced from each other by as much as 100 Jlm. Preliminary
calculations of the probe volume displacements for 9.5 mm (0.375 in.) and 6.4 mm (0.25
in.) thick Plexiglas with varying housing angles are presented in Appendix E. It is
recommended here that these effects be further investigated and that such necessary offi'on
line corrections be implemented. Note that the velocity measurements presented in this
thesis which are used for the filtration efficiency models were all measured downstream of
72
the diffuser section at a wall angle of 0.0° and do not pose any bias errors due to
refraction and incidence beam angle effects.
_..i...
,
nme
Figure 3.3 An Example of a Raw Doppler Burst Signal (Hiatt, 1994).
Vop = Velocity
)
,.,I~ w
I ' d /_
l . 1+
\ }
Probe Volume
73
' /
~
LaserB~,
t:J ==
Cross Section Lens
ofProbe Volume
Figure 3.4 Diagram of a Particle Passing Through the Fringe Pattern.
74
3.4 SetUp and Parameters ofLaser Doppler Velocirnetry Measurements
The flow stream was seeded with 1 !J.Ill (0.966 J..Lm) diameter polystyrene latex
particles produced from a 250 PPM water solution by a 6Jet Atomizer with the pressure
regulator set at 60 psig. The seed particles were introduced to the flow stream through
the flow distributor as illustrated in Figure 3 .1. In efforts to avoid introducing water
droplets and condensation into the flow stream, the flow stream was heated with a fan
heater just after leaving the atomizer. The four laser beams of the LDV system were
aligned so that measurements were performed in agreement with the sign convention and
coordinate system illustrated in Figure 3.5. The axial velocity component is normal to the
plane of the filter and is positive downward through the filter. The transverse velocity
component is in the direction of the long axis of the filter and is positive towards the exit
of the flow leading to the exhaust blower.
The measurements presented in this thesis were conducted in either of the two
horizontal planes illustrated in Figure 3.6. Plane I is approximately 12.7 mm (0.5 in.)
upstream of the filter pleat peaks and Plane II is approximately 50.8 mm (2.0 in.). Any
plane between Plane I and II would be physically impossible for proper beam trransmission
due to the plexiglas interface and adhesive used to join the diffuser section with the zero
angle wall of the test housing. Furthermore, to avoid complex probe volume distortion
due to wall angles, all four beams must be entering the housing at the same wall angle.
Note that at all measurements were downstream of any sphere positioned within the test
75
housing. The measurement grid was spaced at increments of 12.7 mm (0.5 in.) across the
short axis of the filter and 19.0 mm (0.75 in.) across the long axis of the filter, as
illustrated in Figure 3. 7. Measurements were only performed in one half of the filter
region corresponding to positive Y coordinates. This allowed for measurements to be as
close to the filter as possible. The restriction is due to the lowest of the four beams
needing to clear the filter edge. At Plane II, measurements can be conducted across the
full filter region. Nonetheless, for simplicity and convenience, all measurements
conducted were limited to the positive Xcoordinates.
The nonuniform test housing flow required the DSA processing parameters to be
adjusted as the sampling probe volume was transversed to different locations in the flow
field. The different mean velocities, flow directions, and seed particle concentrations all
contributed to the need to adjust the DSA parameters accordingly. The reader is referred
to the Aerometrics Applications User's Manual (Aerometrics, 1992) for a detailed
description of the parameters and settings. These variations resulted in data rates and
validation rates that were different in different regions of the flow field.
In efforts to provide consistent velocity measurements across the flow field, all
measurements presented were obtained from the average of 500 validated samples with
coincidence on. In working with Newman (1994), we determined that for PSL particles
of 100 PPM to 300 PPM a total of 500 samples per data point would be the least number
of points that could be used and still obtain a reliable run with an uncertainty of ±2% of
the average flow velocity. At a 500 sample validation, data within the SAE test housing
76
was obtained within 30 seconds to 300 seconds, actual DSA run time per data point.
Newman achieved data just under 200 seconds with a 1000 sample validation for a reliable
run within ±1% of the average flow velocity. The difference can be attributed to the much
more uniform flow through the prototype test housing used by Newman. In the central
region of the SAE test housing, the number of validations is easily achieved within 60
seconds. In the slower, more lightly seeded flow away from the centerline, a much longer
total time is required to obtain the 500 samples. No corrections were applied here for the
velocity biases that may enter into the LDV measurements within the varied flow regions.
Bias errors include velocity bias, gradient bias, fringe bias, and filter bias errors.
Velocity bias simply means that regions of faster velocity fluid will carry more fluid (Q =
VA) through the probe volume than regions of slower velocity fluid. Assuming the fluid is
unifonnly seeded, the regions of faster velocity will be sampled more than the regions of
slower velocity in a given time interval resulting in higher mean velocity readings.
Velocity bias is corrected by using residence time weighting. It is recommended here that
such velocity bias corrections be investigated and implemented if velocity bias errors are
determined to be large. Gradient bias occurs when there is a velocity gradient across the
probe volume. It is assumed here that no velocity gradient is present within the small
region of the probe volume. Thus, no corrections were applied for gradient biases. Fringe
bias is related to the fact that the probability of a particle generating a measurable signal
depends on the direction of the particle relative to the laser beams. This bias was solved
by using a frequency shift system which creates a moving fringe pattern eliminating
Velocity
Sign
Convention
/
/ Filter
I
positive axial
direction
//
/
77
positive
transverse
direction
··
Positioning
Coordinate
System
+Y
+X
+Z
Figure 3.5 Sign Convention and Coordinate System for Velocity Measurements
~~j_
Filter
SAE Test Housing
Plane II
Slmm (2.0 in)
____ !_____ Plane I
113mm (0.5 in)
~
1 "11''1111'11'11'11'"111111111111'11'1111"'11111111'" 1 ~~
~
Figure 3.6 Velocity Measurement Planes
 ~L
........
(U! sL ·o)
tiiW 6l
• •
• •
• •
• •
• •
• •
• •
• 1 •
• f
~I I~
Ctr! sz·o)
tiiW t79
• • • •
• • • •
• • • •
• • • •
• • • •
• • •
• • •
• • •
• • •
• f '
I
Ctr! s·o) \ IJ
tiiW L"Zl
X
80
directional ambiguity from velocity measurements of reversing flows. Filter bias is related
to the filtering settings which filter out some velocity measurements. Filters were set at a
level to ensure that only low and high noise was filtered. Furthermore, histograms of
velocity measurements were viewed to ensure that a full approximate Gaussian
distribution was present indicating that no flow velocities were being filtered.
3. 5 Flow Visualizations
Flow visualization techniques are commonly used to provide a qualitative insight
of a flow field. These techniques may provide a quick and easy overall perspective of the
flow field. The insight gained from the flow visualizations, may justify the need for further
investigations and the need for quantitative measurements of the flow field, LDV
measurements. Flow visualizations help complement LDV measurements and aid in the
understanding of a flow field. It has been determined from past work that some of the
conventional flow visualization techniques do not work well for the separated and highly
turbulent flow within the SAE test housing (Sabnis, 1993). Water droplet and intermittent
smoke visualizations have been found to be an effective method of qualitatively analyzing
the flow field within a filter test housing (Newman, 1994; Sabnis, 1993). Intermittent
smoke flow visualizations using laser sheet lighting were conducted and are presented
within this thesis. The smoke generator described in Appendix F was found to be an
·~· ·.. ... · ·.=~ ... _:_c=._)..
81
effective system for smoke flow visualizations using axial and transverse laser sheets.
Smoke generating procedures are outlined and provided in a step process in Appendix F.
All flow visualizations were captured on still photography and video tape.
With the laser power controller set at a range of 0.8 Watts to over 2.0 Watts, a
sheet of laser light was produced by projecting a beam of the laser through a cylindrical
lens. The lens creates a sheet of laser light that fans out from the lens in a plane of
Gaussian distributed intensities. The laser sheet was positioned horizontally and vertically
through the test housing. A two dimensional plane or "slice" of the flow field was visible
for qualitative analysis.
3.6 Equipment Listing
PSL particles: Polystyrene Latex, PSL, Microspheres of0.966 !J.m in diameter were used
as seeding particles for the LDV system. The uniform latex microspheres were
purchased from Duke Scientific Corp. The particles are packaged in a 10% solid
to water solution. To obtain a 250 PPM solution, 2.5 cc of the 10% solution was
mixed with 1000 ml of distilled water. For best results, care should be taken to
ensure that the water droplets evaporate before reaching the test housing. For
velocity measurements within the SAE test housing, PSL particles were found to
be more reliable seeding particles than water droplets (Newman, 1994).
~~~ ____ l
82
Atomizer: A TSI Incorporated Model 9306 6Jet Atomizer was used to generate the PSL
aerosol. The atomizer was operated using all six jets at a regulated air pressure of
60 psig.
Plexiglas SAE Universal Air Filter Test Housing: The original transparent housing
constructed by Sabnis (1993) was used. In efforts to achieve a smoother clean
surface for LDV measurements the original housing was altered by replacing one
of the long axis vertical walls with a 6.4 mm (0.25 inch) thick glass. Sabnis
constructed the housing as specified in the SAE J726 Test Code. A detailed
drawing ofthe housing specifications is provided in Figure 1.2. The housing can
house any size panel air filter as specified in SAE 11141 provided that the
aluminum support is sized accordingly. For easy mounting, the flange between the
entrance tube and the housing and the flange between the top and bottom portion
of the housing are each secured using four easy release visegrip clamps.
Consistent alignments were ensured using push pins through the flanges. All other
joints are permanently glued and are periodically checked for leaks using soapy
water. The inlet plexiglas pipe has a diameter of 88.9 mm (3.5 in.) and is 889 mm
(35 in.) in length. For test purposes, the housing is mounted upside down, as
compared to the SAE J726 Test Code.
Filter Specimen: Purolator AF3192 (recently replaced by Purolator Al3192) panel air
filters were supplied by Purolator Products Inc. for all velocity measurements
presented in this thesis. The reader is referred to Appendix A for a complete
J..
83
listing of the AF3192 filter specifications. These filters are made from a resin
impregnated cellulose fiber paper mat that is first embossed and scored. An
adhesive is then applied and the paper is folded, creating the pleats. The pleats are
counted, cut, sealed at the ends, and mounted to a rubber holder or gasket. The
filter is then heated to cure the resin and secure the strength of the pleats. A
screen is then mounted on the back of the filter for additional support. This screen
helps the filter maintain its structure integrity in the event of engine backfire and
moisture.
Centrifugal Multistage Exhauster/Blower: In the past, a 1.5 hp centrifugal blower capable
of producing a maximum flow rate of 225 scfin was used for velocity
measurements of clean filters. Due to the joint efforts of me and my colleagues,
separate clean filter tests and dirty filter tests were conducted periodically. The
testing of dirty filters requires a much stronger blower to achieve a flow rate of
125 scfin through the filter due to the increase in pressure drop through the filter
(Liu et al, 1995). Consequently, it was convenient to run all experiments with the
use of a larger blower, the multistage centrifugal exhauster. The multistage
centrifugal exhauster is part of the Automotive Air Filter Test Stand. The
multistage centrifugal exhauster is powered by a 40 hp induction motor and can
achieve flow rates ranging from 25 scfin to I 000 scfin. All flow rates are easily
measured with corrections for operating temperatures and barometric pressure.
Automotive Air Filter Test Stand: The Automotive Air Filter Test Stand was designed
1..
84
and built by Facet Enterprises, Inc. in 1976 and is comprised of a multistage
centrifugal exhauster, laminar flow element, high efficiency absolute filter, elevated
test stand area, and a control panel. This test stand was designed and built for dust
loading and testing of dirty automotive air filters, both round and panel type. This
complete system is on an extended loan from Purolator Products Inc.
Mass Flow Rate Sensor: In the past, a TSI Incorporated Series 2010 Mass Flowmeter
was used to measure the flow rate through the test housing. On occasion, this
flowmeter was used to verify the settings and readings of the Automotive Air filter
Test Stand. The flow sensor has a maximum measurable flow rate of 500 SCFM
and is easily calibrated with a 76 nun ASME flow nozzle.
Laser: A Coherent 4 watt laser, lnnova 70 Model, consisting of an argon ion plasma tube
powered by an Innova 70A power supply was used. During actual testing, the
intensity of the beam ranged from 0.2 Watts to 1.2 Watts and was controlled by a
remote controller. Note that the 515 nm green beams are not visible below a
power setting of 0.4 Watts.
Bragg Cell & Driver: An IntraAction Bragg cell driver model ME40H controlled the
Bragg cell mounted inside the fiber drive. The light beam from the plasma tube
was direct by steering mirrors into the fiber drive and through the Bragg cell. The
40 MHz Bragg cell splits the beam into several beams of different multiple shifts
and one of zero shift. The +40MHz shifted beam and the nonshifted beam are
used downstream ofth~ Bragg celL
==....._.. ............................... ~~~~~iiiiiiiiiiiiii~~~~~~~~~~=~==~~~ '~ ~ ... ,., '·~~ __J,_
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Fiber Drive: An Aerometrics Model FBD.l240 fiber drive was used and consists of the
Bragg cell, laser optics, beam splitters, fiber couplers, and fiber cables. The beam
splitting prisms split the unshifted and shifted beams into two separate beams of
different wavelengths, for a total of four beams. Resulting in one unshifted and
one shifted beam for each color. Mirrors direct each of the beams into the fiber
couplers which align and focus the beams onto the fiber cables leading to the
transceiver. The fiber drive allows for easy and consistent alignment, as long as
the laser beam is aligned properly into the Bragg cell, one merely needs to adjust
the fiber couplers for maximum intensity out through the transceiver.
Transceiver: An Aerometrics model XR.V.l212 transceiver receives the four beams
through fiber optic cables. The beams are transmitted through a 500 mm lens
producing a probe volume of 737 J.lm in length and 66 J.1ffi in diameter. The
transceiver collects the backscattered light reflected from seeding particles passing
through the probe volume. The collected light is then transmitted through a fifth
fiber optic cable to the photodetector unit which distinguishes the blue and green
light scatter.
Photodetector Unit: The Aerometrics photodetector unit model ROM.2200.L contains
two photomultipliers, one for each wavelength light, blue and green. The
photomultipliers convert the optical light scatter signal into an analog voltage
signal and pass it on to the DSA.
Doppler Signal Analyzer. DSA: The raw Doppler burst signal is analyzed by the
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Aerometrics Doppler Signal Analyzer model DSA.3220, Version 4.18s DSA D,
Copyright 1989, 1991, 1992, with revisions updated April 1993 (Aeromet