NOVEL PACKAGING DESIGNS FOR IMPROVEMENTS
IN AIR FILTER PERFORMANCE
Except where reference is made to the work of others, the work described in this
dissertation is my own or was done in collaboration with my advisory committee.
This dissertation does not include proprietary or classified information.
_____________________________________
Ryan Anthony Sothen
Certificate of Approval:
W. Robert Ashurst Bruce J. Tatarchuk, Chair
Assistant Professor Professor
Chemical Engineering Chemical Engineering
Mario R. Eden Daniel Harris
Associate Professor Associate Professor
Chemical Engineering Mechanical Engineering
George T. Flowers
Dean
Graduate School
ii
NOVEL PACKAGING DESIGNS FOR IMPROVEMENTS
IN AIR FILTRATION PERFORMANCE
Ryan Anthony Sothen
A Dissertation
Submitted to
the Graduate Faculty of
Auburn University
in Partial Fulfillment of the
Requirements for the
Degree of
Doctor of Philosophy
Auburn, Alabama
August 10th, 2009
iii
NOVEL PACKAGING DESIGNS FOR IMPROVEMENTS
IN AIR FILTRATION PERFORMANCE
Ryan Anthony Sothen
Permission is granted to Auburn University to make copies of this dissertation at its
discretion, upon request of individuals or institutions and at their expense.
The author reserves all publication rights.
______________________________
Signature of Author
______________________________
Date of Graduation
iv
VITA
Ryan A. Sothen was born and raised by James E. and Lois R. Sothen in
Charleston, West Virginia. He began his collegiate studies in the Department of
Chemical Engineering at Virginia Polytechnic Institute & State University (Virginia
Tech). During his time at Virginia Tech, he worked outside the classroom as an
analytical chemist for Dominion Semiconductor and performed undergraduate research
on polymeric materials for Dr. Donald Baird. Ryan completed his Bachelor of Science in
the Spring of 2004, and subsequently enrolled in the Chemical Engineering Graduate
Program at Auburn University during the Fall of 2004.
v
DISSERTATION ABSTRACT
NOVEL PACKAGING DESIGNS FOR IMPROVEMENTS
IN AIR FILTRATION PERFORMANCE
Ryan Anthony Sothen
Doctor of Philosophy, August 10, 2009
(B.S., Virginia Polytechnic Institute & State University, 2004)
234 Typed Pages
Directed by Bruce J. Tatarchuk
Adsorbent entrapped media, such as microfibrous materials engineered at Auburn
University, provide a novel method to effectively remove harmful airborne contaminants
such as volatile organic compounds and particulate matter from polluted indoor air.
These dual-functioning materials are limited in their use as air filters due to their high
pressure drops and relatively small loading of adsorbent material. Utilization of a pleated
filter design is a common approach in the air filtration industrial to increase the available
media and reduce the pressure drop of a media. A second technique was developed to
greatly increase the capacity and further reduce the pressure drop by employing
numerous pleated filters into a single filter unit known as a Multi-Element Structured
Array (MESA).
vi
A comprehensive pressure drop model was constructed to understand the working
parameter space within these filter designs. The model was formulated on fundamental
fluid dynamics equations such as Bernoulli?s Equation and empirical data obtained on
custom-made filter units. The working models were shown to be successful in replicating
over 1500 data points spanning 20 pleated filters and 32 MESA units.
Several niche filtration designs were envisioned during the development of the
model. These designs were subsequently tested to demonstrate their performance
advantage over standard HVAC pleated designs based on dirt holding and power
consumption. It was determined that MESA architectures can be utilized to provided
equal or superior particulate removal efficiency while operating at only 20% of the power
of a traditional pleated filter.
vii
ACKNOWLEDGMENTS
The author would like to express his sincere gratitude to Dr. Bruce J. Tatarchuk for
his guidance throughout the course of my graduate studies. I would like to acknowledge the
US Army (TARDEC) for funding the research presented in this dissertation. I would also like
to thank my committee members Dr. Mario Eden, Dr. W. Robert Ashurst, Dr. Daniel Harris,
and Dr. Christopher Roy for their time and efforts to ensure the compilation of this work.
Special thanks are in order for all of my past and present CM3 colleagues. In
particular, I would like to acknowledge the members of the filtration group. My upmost
appreciations are in order to Mr. Ron Putt and Mr. Amogh Karwa for their assistance in
helping me with laboratory and theoretical issues as well as Mrs. Yanli ?Joyce? Chen for her
assistance with laboratory experimentation over the last six months. I would like to thank the
following members of the Faculty and Staff who have helped me greatly during my time at
Auburn: Mrs. Sue Ellen Abner, Mr. Dwight Cahela, Mrs. Karen Cochran, Mrs. Jennifer
Harris, Dr. Lewis Payton, Dr. Christopher Roberts, Mrs. Megan Schumacher, and Mr. Brian
Scweiker. Lastly, I would like to thank Dr. Donald Baird and Dr. Y. A. Liu for supporting
and encouraging me to continue my education career after complication of my Bachelor of
Science at Virginia Tech.
viii
Style manual or journal used: HVAC & R Research
Computer software used: Microsoft Word
ix
TABLE OF CONTENTS
LIST OF FIGURES ......................................................................................................... xiii
LIST OF TABLES.......................................................................................................... xxii
Chapter I: Introduction to Air Filtration ..............................................................................1
I.1 Motivation ..........................................................................................................1
I.2. Microfibrous Media...........................................................................................3
I.3. Influence of Pressure Drop within a HVAC System.........................................5
Chapter II: Background & Experimental for Modeling Initial Pressure Drop ....................8
II.1. Previous Pleated Filter Models ........................................................................8
II.1.1. Chen et al...........................................................................................8
II.1.2. Rivers & Murphy ............................................................................10
II.1.3. Del Fabbro et al...............................................................................10
II.1.4. Caeser and Schroth..........................................................................11
II.1.5. Tronville and Sala ...........................................................................12
II.1.6. Raber ...............................................................................................13
II.2. Objectives of Current Modeling Efforts.........................................................14
II.3 Theory .............................................................................................................15
II.3.1. Forchheimer-extended Darcy?s Law...............................................16
II.3.2. Mechanical Energy Balance / Bernoulli?s Equation .......................17
II.3.3. Equation of Continuity....................................................................21
II.3.4. Momentum Balance ........................................................................22
x
II.4. Experimental Setups.......................................................................................22
II.4.1. Media Test Rig................................................................................22
II.4.2. Filtration Test Rig ...........................................................................24
II.5. Data Acquisition.............................................................................................30
II.5.1. Media Pressure Drop Curves...........................................................30
II.5.2. Filter Pressure Drop Curves ............................................................30
II.5.3. Media Thickness .............................................................................34
Chapter III: Initial Pressure Drop Modeling of Pleated Filters..........................................35
III.1 Introduction....................................................................................................35
III.1.1. Pleated Filter Schematics...............................................................35
III.1.2. Parameters......................................................................................38
III.1.3 Proposed Flow through a Pleated Filter......................................................39
III.1.4 Modeling a Pleated Filter............................................................................40
III. 2. Identifying the Constants .............................................................................43
III. 2.1. Media Constants & Thickness ......................................................43
III. 2.2. Grating Coefficient of Friction (KG).............................................46
III. 2.3. Pleat Tip Assumption....................................................................50
III. 2.4. Pleat Coefficient of Friction (KP) .................................................51
III. 2.5. Reevaluate the Pleat Tip Contraction and Expansion...................58
III.3. Utilization and Discussion of the Model ......................................................60
III. 3.1. Pleating Curve...............................................................................60
III. 3.2. Location of the Optimal Pleat Count ............................................63
III. 3.3. Influence of Design Parameters ....................................................64
xi
III. 3.4. Limitations of the Model ..............................................................77
Chapter IV. Initial Pressure Drop of Multi-Element Structured Arrays............................78
IV.1. Introduction...................................................................................................78
IV.1.1. Multi-Element Structured Arrays Schematic.................................78
IV.1.2. Parameters......................................................................................80
IV.1. 3. Proposed Flow through a MESA..................................................82
IV.1. 4. Modeling a Multi-Element Structured Arrays..............................84
IV.2. Multi-Filter Bank Experimental ...................................................................85
IV.2. 1. Entrance Coefficient of Friction (KCB).........................................86
IV.2. 2. Exit Coefficient of Friction (KEB).................................................89
IV.2.3. Slot Coefficient of Friction (KS)....................................................91
IV.3. Discussion Utilizing the Model ....................................................................98
IV.3.1. Achievement of Objectives............................................................98
IV.3.2. The Pleating Curve of a MESA.....................................................99
IV.3.3. Locating the Optimal Pleat Count ...........................................................102
IV.3.4. Influence of Design Parameters...............................................................102
Chapter V: Theory & Experimental for Air Filtration Performance ...............................117
V.1. Introduction..................................................................................................117
V.2. Theory ..........................................................................................................117
V.2.1. Previous Research concerning Dirt Loading of Air Filters...........117
V.2.2. Particulate Removal Efficiency by Fibrous Media.......................119
V.3. Experimental ................................................................................................122
V.3.1. Test Rig and Equipment................................................................122
xii
V.3.2. Experimental Data Acquisition.....................................................130
V.3.2.1. Volumetric Flow ............................................................130
V.3.2.2. Pressure Drop across Filtration Section.........................134
V.3.2.3. Particle Count.................................................................134
V.3.3. Testing Procedures........................................................................136
V.3.3.1. Initial Pressure Drop ......................................................136
V.3.3.2 Testing Procedure for Dirt Loading................................138
V.3.3.3. Removal Efficiency Testing..........................................141
Chapter VI: Filtration Performance of Novel, Single Element Designs..........................143
VI.1. Introduction.................................................................................................143
VI.2. Materials and Methods ...............................................................................143
VI.3. Results and Discussion ...............................................................................144
VI.3.1. Initial Resistance..........................................................................144
VI.3.2. Dirt Loading.................................................................................147
VI.3.3. Estimations of Useful Lifetime and Power Consumption ...........160
Chapter VII: Filtration performance of Multi-Element Structured Arrays......................165
VII.1. Introduction ...............................................................................................165
VII.2. Particulate Removal Efficiency of a MEPFB............................................165
VII.2.1. Materials.....................................................................................166
VII.2.2. Results and Discussion...............................................................166
VII.3. Dirt Loading of MESA?s...........................................................................170
VII.3.1. Materials.....................................................................................170
VII.3.2. Results and Discussion...............................................................170
xiii
VII.3.2.1. Influence of Pleat Count within an MESA..................170
VII.3.2.2. Influence of Element Count ........................................173
VII.3.2.3. Power Consumption Analysis .....................................176
VII.4. Preferential Element Alignment within a MESA......................................177
VII.4.1. Materials and Methods ...............................................................177
VII.4.2. Results and Discussion...............................................................179
VII.4.2.1. Initial Pressure Drop....................................................179
VII.4.2.2. Dirt Loading ................................................................181
Chapter VIII: Conclusions and Future Work...................................................................192
VIII.1. Conclusions..............................................................................................192
VIII.2. Future Work .............................................................................................193
V.III.1. Utilization of Fairings .................................................................194
V.III.2. Media Compression versus Permeability....................................194
V.III.3 Pyramid Filter ..............................................................................195
References........................................................................................................................196
Appendix A......................................................................................................................197
A.1 Rotameter Calibration...................................................................................199
A.2 Calibration of Pressure Transducers .............................................................202
A.3 Construction of Filter Holder........................................................................204
A.4 Construction of MESA Unit .........................................................................204
A.5 Weight Increase of ASHRAE Dust under Atmospheric Conditions ............206
A.6 Observed Flow Channeling due to Pleat Tip Blockage ................................207
A.7 Determination of Ramping Rate ...................................................................208
xiv
Appendix B: Nomenclature .............................................................................................211
B.1 Arabic Symbols.............................................................................................211
B.2 Greek Symbols ..............................................................................................212
B.3. Subscripts .....................................................................................................212
xv
LIST OF FIGURES
Figure 1.1: Typical ?U? Pleating Curve ..............................................................................7
Figure 2.1: Sudden Contraction Diagram ..........................................................................19
Figure 2.2: Sudden Expansion Diagram ............................................................................19
Figure 2.3: Gradually Contraction Diagram ......................................................................20
Figure 2.4: Grating Diagram..............................................................................................20
Figure 2.5: Duct Diagrams.................................................................................................21
Figure 2.6: General Schematic of Media Test Rig ............................................................23
Figure 2.7: Control Pressure Drop Curve for Media Test Rig...........................................24
Figure 2.8: General Schematic of Blower Test Rig...........................................................25
Figure 2.9: Flow Distribution at 40 Hz Before (A) and After (B).....................................26
Figure 2.10: Coefficient of Variance .................................................................................28
Figure 2.11: Control Pressure Drop Curve for Filter Test Rig ..........................................29
Figure 2.12: Measurement Path for the Vane Anemometer .............................................31
Figure 2.13: Velocity Measurement Comparison..............................................................33
Figure 2.14: Pressure Measurement Comparison ..............................................................34
Figure 3.1: Pleated Filter Illustration.................................................................................36
Figure 3.2: Illustration of Pleat Dimensions......................................................................37
Figure 3.3: Pleat Tip Illustration........................................................................................38
Figure 3.4: Flow Pattern ....................................................................................................40
xvi
Figure 3.5: Control Volume of a Downstream Pleat .........................................................41
Figure 3.6: Media Resistance Curves ................................................................................44
Figure 3.7: Darcy?s Law Analysis of Media Resistance....................................................46
Figure 3.8: Illustration of Grating Schemes.......................................................................47
Figure 3.9: Pressure Drop Curves for Various Frontal Blockages ....................................47
Figure 3.10: Computed Grating Resistances .....................................................................48
Figure 3.11: Effects of Front Grating Modification...........................................................49
Figure 3.12: Effects of Back Grating Modification...........................................................50
Figure 3.13: Pressure Drop Curves for a 20?x20?x1? FM1 Filter with 42 Pleats.............52
Figure 3.14: Pleat Coefficient Graph for a 20?x20?x1? FM1 Filter with 42 Pleats ..........53
Figure 3.15: Pleat Coefficient Plots for 20?x20?x1? Filters..............................................54
Figure 3.16: Pleat Coefficient Graph .................................................................................56
Figure 3.17: A Linear Pleat Coefficient Plot .....................................................................57
Figure 3.18: Correlation Plot between Empirical and Modeled Pleat Coefficients...........58
Figure 3.19: Modified Correlation Plot .............................................................................59
Figure 3.20: Pleating Curve and Individual Resistances ...................................................61
Figure 3.21: Optimal Pleat Count Location.......................................................................64
Figure 3.22: Effects of Face Velocity on Pleating Curve ..................................................67
Figure 3.23: Effects of Media Thickness on Pleating Curve .............................................68
Figure 3.24: Effects of Media Thickness on Model?s Derivatives ....................................70
Figure 3.25: Modeled Pleat Tip Contribution to Total Resistance 20?x20?x1? Filters.....71
Figure 3.26: Modeled Effects of Filter Depth on Pleating Curve......................................72
Figure 3.27: Effects of Filter Depth on Model Derivatives...............................................73
xvii
Figure 3.28: Effects of Filter Depth on Performance Curve..............................................74
Figure 3.29: Effects of Media Resistance on Pleating Curve ............................................75
Figure 3.30: Effects of Media Resistance on Model?s Derivatives ...................................76
Figure 4.1: General Schematic of a Multi-Element Structured Array...............................79
Figure 4.2: Array Configurations (A) ?W? (B) ?WV? Configuration (C) ?WW? ............80
Figure 4.3: General Diagram of Multi-Filter Array...........................................................82
Figure 4.4: Proposed Flow Profile.....................................................................................83
Figure 4.5: Illustration and Schematic of Flow within a Normal (A)
and Contraction Modified Array (B) ..............................................................87
Figure 4.6: Measured Pressure Drop for a Normal and Modified Array...........................88
Figure 4.7: Observed and Modeled Pressure Drop Differences ........................................89
Figure 4.8: Illustration and Schematic of Flow within a Normal (A) and Expansion
Modified Array (B)..........................................................................................90
Figure 4.9: Measured Pressure Drop for a Normal and Modified Array...........................90
Figure 4.10: Observed and Modeled Pressure Drop Differences ......................................91
Figure 4.11: Pressure Drop Curves for a WV Array of 1? Filters .....................................92
Figure 4.12: Slot Coefficient Graph for a WV Array of 1? Filters....................................93
Figure 4.13: Slot Coefficient Plots for Various Configurations ........................................95
Figure 4.14: Slot Coefficient Graph...................................................................................97
Figure 4.15: Observed versus Modeled Slot Coefficient...................................................98
Figure 4.16: Correlation Plot between Observed and Modeled Data ................................99
Figure 4.17: Multi-element structured array Pleating Curve ...........................................100
Figure 4.18: Percentage Contribution of (A) Single Filter and (B) ?W? Array ..............101
Figure 4.19: Effects of Element Count on MESA Pleating Curve ..................................104
xviii
Figure 4.20: Effect of Element Count on Contribution of the pressure drop ..................105
Figure 4.21: Effects of Element Count on MESA Performance Curve...........................106
Figure 4.22: Effects of Element Width on MESA Performance Curve...........................108
Figure 4.23: Effect of Element Width on Contribution ...................................................109
Figure 4.24: Effects of Element Depth on MESA Performance Curve...........................110
Figure 4.25: Effect of Element Depth on Contribution ...................................................111
Figure 4.26: Effects of Media Constants on MESA Pleating Curve ...............................112
Figure 4.27: Effects of Media Thickness on MESA Pleating Curve...............................114
Figure 4.28: Effects of Velocity on MESA Pleating Curve.............................................115
Figure 5.1: General Trend in Filter Loading....................................................................119
Figure 5.2: Impaction Mechanism for Particulate Capture..............................................121
Figure 5.3: interception Mechanism for Particulate Capture...........................................121
Figure 5.4: Particulate Capture by Brownian Motion......................................................122
Figure 5.5: Schematic of Full Scale Test Rig ..................................................................123
Figure 5.6: upstream Picture of the Test Rig ...................................................................123
Figure 5.7: Downstream Picture of the Test Rig .............................................................124
Figure 5.8: Removal Efficiency of Upstream Filters.......................................................125
Figure 5.9: TSI 8108 Large Particle Generator Schematic..............................................128
Figure 5.10: Schematic and Picture of Sealing System ...................................................130
Figure 5.11: Blower and Tap Configuration....................................................................133
Figure 5.12 Face Velocity Calibration Curve for Test Rig?s Orifice Plate .....................134
Figure 5.13: Comparison of Upstream and Downstream Counting Probes.....................136
Figure 5.14: Alignment and Clamping System................................................................137
xix
Figure 5.15: Loading Tray with leveling Tool.................................................................140
Figure 6.1: Pleating Curve for 24?x24?x1? Filters at 500 fpm: Filters composed
of 411 SF media.............................................................................................145
Figure 6.2: Pleating Curve for 24?x24?x2? Filters at 500 fpm: Filters composed
of 411 SF media ............................................................................................146
Figure 6.3: Pleating Curve for 24?x24?x4? Filters at 500 fpm Filters composed
of 411 SF media.............................................................................................146
Figure 6.4: Dirt Loading for 24?x24?x1? Filters.............................................................148
Figure 6.5: Normalized Loading Profiles of 24?x24?x1? Filters ...................................149
Figure 6.6: Depth Filtration Regime for 20 and 28 Pleat Filter......................................150
Figure 6.7: Schematic of Preferential Loading. (A) Low and (B) High Beta Angle.......151
Figure 6.8: Normalized Loading Profiles of Select 24?x24?x1? 411SF Filters
with Transition Lines ....................................................................................152
Figure 6.9: Normalized Loading Profiles of 24?x24?x1? Filters composed
of 355H Filter Media ....................................................................................153
Figure 6.10: Dirt Loading for 24?x24?x2? Filters...........................................................154
Figure 6.11: Normalized Dirt Loading for 24?x24?x2? Filters .......................................155
Figure 6.12: Dirt Loading for 24?x24?x4? Filters...........................................................156
Figure 6.13: Normalized Dirt Loading for 24?x24?x2? Filters .......................................157
Figure 6.14: Relationship between Pleating Angle and Transition Point........................158
Figure 6.15: Average Power Consumption of 24?x24?x1? Filters..................................161
Figure 6.16: Average Power Consumption of 24?x24?x1? Filters..................................162
Figure 6.17: Average Power Consumption of 24?x24?x1? Filters..................................163
Figure 7.1: Removal Efficiency of a Single Filter and MESA........................................167
Figure 7.2: Removal Efficiency of a Single Element during Loading Conditions..........168
xx
Figure 7.3: Removal Efficiency of a MESA during Loading Conditions .......................168
Figure 7.4: Quality Factor Analysis.................................................................................169
Figure 7.5: Total Dirt Holding Capacity of V MESA with Various Pleat Counts ..........171
Figure 7.6: Normalized Dirt Holding Capacity of V MESA with Various Pleat
Counts ............................................................................................................172
Figure 7.7: Total Dirt Loading of Various Element Count Systems ...............................173
Figure 7.8: Normalized Loading Profile of a Various Element Count Systems with
emphasis placed on the Depth Loading Regime............................................174
Figure 7.9: Normalized Loading Profile of a Various Element Count Systems with
emphasis placed on the Cake Loading Regime .............................................176
Figure 7.10: Power Consumption of MESAs? and Single Filter .....................................177
Figure 7.11: Horizontally-Oriented (Left) & Vertically-Oriented (Right) Banks ...........178
Figure 7.12: Clean Resistance of DP 4-40 Elements Loaded Vertically and
Horizontally into a V MESA Configuration................................................180
Figure 7.13: Clean Resistance of DP 95 Elements Loaded Vertically and
Horizontally into a W MESA Configuration...............................................180
Figure 7.14: Dirt Loading of DP 4-40 Elements Loaded Vertically and
Horizontally into a V MESA Configuration................................................182
Figure 7.15: Dirt Loading of DP 95 Elements Loaded Vertically and
Horizontally into a W MESA Configuration...............................................182
Figure 7.16: Schematic of Pleat Nomenclature ...............................................................184
Figure 7.17: View of Inline Loaded pleats ......................................................................185
Figure 7.18: View of Shielded Loaded pleats..................................................................185
Figure 7.19: Air Permeability of Sample Obtained from Vertical MESA ......................186
Figure 7.20: Air Permeability of Sample Obtained from Horizontal MESA ..................187
Figure 7.21: Adhesive Squares and Removed Dirt from top and bottom Pleat
Sides of a Horizontally Oriented MESA after Dirt Loading .......................189
xxi
Figure 7.22: Adhesive Squares and Removed Dirt from inline Side of Vertically
Oriented MESA after Dirt Loading .............................................................190
Figure 7.23: Adhesive Squares and Removed Dirt from Shielded Side of Vertically
Oriented MESA after Dirt Loading .............................................................190
Figure 7.24: Weighed Pulled per Layer of Adhesive Backing .......................................191
Figure A1: Rotameter Calibration Set-Up .......................................................................200
Figure A2: Rotameter Calibration Curve.........................................................................201
Figure A.3: Calibration Tube...........................................................................................202
Figure A4: Calibration Curve for Pressure Transducer #1 ..............................................203
Figure A5: Calibration Curve for Pressure Transducer #2 ..............................................203
Figure A6: 24?x24?x2? Filter Holder ..............................................................................204
Figure A7: MESA Housing Schematic............................................................................205
Figure A.8: ASHRAE Dust Water Uptake over Time.....................................................207
Figure A.9: Upstream Pleat Tip after Dust Loading........................................................208
Figure A.10: Downstream Pleat Tip after Dust Loading.................................................208
Figure A.11: Variation in Pressure Measurements due to Incrementing Rate ................210
xxii
LIST OF TABLES
Table 1.1: Minimum Efficiency Removal Value and Typical Filtration Platform..............2
Table 3.1: Summary of Media Constants and Thickness ..................................................45
Table 3.2: Summary of Filters Employed..........................................................................53
Table 3.3: Summary of Pleat Coefficients.........................................................................55
Table 4.1: Blockage (FB) Tabulations................................................................................82
Table 4.2: Alpha Tabulations (in radians) .........................................................................82
Table 4.3: Summary of Elements used in Slot Coefficient Study .....................................94
Table 4.4: Summary of Observed Slot Coefficients and R2 Fit.........................................96
Table 4.5: MESA vs. Single Filter Comparison ..............................................................106
Table 4.6: Summary of Design Parameters and Effects due to their Increase.................116
Table 5.1: ASHRAE Dust Size Distribution....................................................................127
Table 5.2: Average Velocity and Coefficient of Variation within Test Rig....................128
Table 6.1: Critical Parameters of Filters Utilized ............................................................144
Table 6.2: Interval Loading Rate for 24?x24?x2? 411SF Filter with 15 Pleats ..............159
Table 6.3: Interval Loading Rate for 24?x24?x2? 411SF Filter with 20 Pleats ..............159
Table 6.4: Interval Loading Rate for 24?x24?x2? 411SF Filter with 40 Pleats ..............159
Table 6.5: Estimated Lifetime Costs for 24?x24?x1? Filters ..........................................161
Table 6.6: Estimated Lifetime Costs for 24?x24?x2? Filters ..........................................162
Table 6.7: Estimated Lifetime Costs for 24?x24?x4? Filters ..........................................163
Table 7.1: Transition Point of V MESA and Single Elements ........................................172
Table 7.2: Associated Costs.............................................................................................177
Table A1: Experimental Data ..........................................................................................201
1
CHAPTER I: INTRODUCTION TO AIR FILTRATION
I.1 Motivation
Adverse health effects stemming from poor indoor air quality (IAQ) has become a
prominent concern since the implementation of energy efficiency buildings in response to
the energy crisis of the 1970s (Kay et al. 1991, Moffat 1997). The decreased exchange
between inside and outside air due to thicker insulation and improved passageway seals
has created an environment were indoor air pollutants can reach levels that are ten times
greater than ambient outdoor conditions (Meckler 1991). The decline in IAQ has been
linked to increases in asthma, allergies, lung/respiratory cancer, and other pulmonary
diseases (Godish 2001). Poor IAQ is also a primary cause for personal discomforts such
as headaches; fatigue; dizziness; nausea; and irritation of skin, eyes, throat, and lungs that
affects the quality of life and worker performance (Moffat 1997). The foremost indoor air
pollutants are volatile organic compounds (VOC?s), ozone, nitrogen oxides, carbon
monoxide, and particulate matter less than 10 microns in diameter (Liu and Lipt?k 2000).
Since the average American spends an estimated 90% of their time indoor (EPA 2009),
effective air filtration is needed to eliminate these harmful contaminants from human
living environments.
Traditionally, home filters have consisted of a panel units composed of loose
fitting fiberglass fibers. The purpose of these filters was the removal of particles before
they damaged the working machinery of the air handler. Also, the filter prevented the
cooling coils from becoming clogged with dirt which decreases the efficiency of the heat
2
exchangers (Robinson and Ouellet 1999, Waring and Siegel 2008). Panel filters,
however, offer little in terms of removing the serious health affecting particles that are
below 10 micron. Table 1; obtain from the American Society of Heating, Refrigeration,
and Air-conditioning Engineers (ASHRAE) Standard 52.2; highlights some of the
common air filters and their ability to remove particulate matter.
Table 1: Minimum Efficiency Removal Value (MERV) and Typical Filtration Platform
MERV
Rating
0.3 to 1.0
Micron
1.0 to 3.0
Micron
3.0 to 10.0
Micron Filter Type
1 n/a n/a < 20% Panel
2 n/a n/a < 20% Panel
3 n/a n/a < 20% Panel
4 n/a n/a < 20% Panel
5 n/a n/a 20 - 35 % Cartridge Filter
6 n/a n/a 35 - 50% Cartridge Filter
7 n/a n/a 50 - 70% Cartridge Filter
8 n/a n/a > 70% Pleated Filter
9 n/a < 50 % > 85% Pleated Filter
10 n/a 50 - 60 % > 85% Pleated Filter
11 n/a 65 - 80 % > 85% Box Filter
12 n/a > 80% > 90% Box Filter
13 <75% > 90% > 90% Bag Filter
14 75 - 85% > 90% > 90% Bag Filter
15 85 - 95% > 90% > 90% Bag Filter
16 > 95% > 95% > 95% Bag Filter
Although higher MERV rated filters excel at removing particulate matter, they
can not remove VOC?s and other airborne molecular contaminants. A second filtration
system, such as a packed bed or monolith, must be employed in order to successfully
remove the non-particulate contaminants. A third option is the utilization of microfibrous
media which has been previously shown to remove many of the airborne molecular
contaminants listed above. Kalluri (2008) demonstrated the ability of microfibrous media
to remove ozone from a polluted air stream. Kennedy (2007) and Queen (2005)
3
employed microfibrous materials in cathode air filters and fire masks for the successfully
removal of VOC?s. Catalyic oxidation of carbon monoxide to the more benign carbon
dioxide has also been achieved through the use of microfibrous media (Karanjjikar 2005).
I.2. Microfibrous Media
Microfibrous Media (MfM) was developed in 1987 for use in chemical and
electrochemical applications by Auburn University?s Department of Chemical
Engineering and the Space Power Institute. The media is a sinter-locked matrix of fibers
with diameters typically ranging between two and twenty microns. Matrices can be
constructed with metal, ceramic, or polymer fibers through a traditional wet-laid paper
manufacturing process. (Tatarchuk et al. 1992, 1994). As the technology developed, the
microfibrous frameworks were used to entrap particles below 300 microns for use in
catalytic and adsorptive applications. The resulting composite structures were known as
Microfibrous Sorbent-Supported Media (MSSM) (Harris et al. 2001).
The ability to be wet-laid and entrap microscopic particles bestows several key
attributes to the media that enhances its utility in sorbent and catalytic processes. The
decreased particle size allows molecules to diffuse into a sorbent?s innermost structure at
a higher rate leading to higher utilization, smaller mass transfer zones, and shorter critical
bed depths compared to packed beds and monoliths (Harris et al. 2001, Kalluri 2008). In
turn, lower amount of costly catalytic material is needed to achieve the same
performance. The wet-lay process creates a homogeneous material that reduces
channeling effects typically associated with the use of sub-millimeter particulate supports
(Kalluri 2008). This assists with preventing the premature breakthrough of the pollutant
4
through the system. The wet-laid process also allows for customizable void volumes
ranging between 30% to 98% (Marrion et al. 1994).
Although MSSM possesses a high contacting efficiency, the drawback to its
utilization as a filtration media is a large pressure drop and relatively low loading
capacity of adsorbent material. The large resistance of the media is due to the
combinational effects of flow through the porous structure and drag forces present on the
embedded particles. The matrix must be composed of micron diameter fibers in order to
entrap the desired range of micro-sized adsorbent particles. The pressure drop of the
media has an inverse quadratic relationship with both fiber radius and particle diameter;
thus, the resistance quickly rises as smaller particles and fibers are employed (Cahela and
Tatarchuk 2001). Capacity of the media remains low due to the thinness of the material
and low concentration of support within matrix. The thickness and support concentration
parameters can be adjusted to increase capacity, but each will cause the pressure drop of
the media to increase in a linear fashion as describe by Darcy?s Law.
Darcy?s Law states that the force required to move a fluid through a porous media
is directly proportional to the media thickness (L), the superficial velocity through the
media (VS), and the permeability constant of the media (Km).
S
m
VKLghP ?? =+?? )( (1.1)
The forces acting on the fluid are pressure (P) and a potential force created on a height of
fluid (h) by the acceleration of gravity (g). The viscosity and density of the fluid flowing
through the media is denoted by ? and ? respectively. With no elevation change through
the media, the equation can be reduced and rearranged to give the following linear form:
5
S
m
VKLP ?=? (1.2)
The term ?L/Km is known as the Darcy?s constant. Darcy?s Law is generally considered
valid only in the regime of creeping flow (Reynolds Numbers < 1) (Perry and Green
1997). An increase in media thickness or decrease in permeability created by an increase
support concentration will lead to a higher pressure drop of the MSSM material.
I.3. Influence of Pressure Drop within a HVAC System
Proper design of flow resistance is of particular importance in air filtration
applications where a large pressure drop can overload the air handler unit and reduce or
prevent air flow. More importantly, pressure drop is directly related to the energy
consumption of the system. The pressure-volume work of the system can be computed
by (Rudnick 2008):
E = ?PQt ?B -1 (1.3)
The simple calculation states that the energy (E) required to move the air is the product of
the volumetric flow rate (Q) of air moved, the resistance (?P), time of operation (t), and
the efficiency of the air handler (?B). The energy consumption to move the air accounts
for 81% of the total expense in an HVAC system with procurement and additional
operational costs such as labor accounting for the remaining 19% (Arnold et al. 2005). A
significant pressure drop will render a MSSM filtration media impractical due to
substantial operational costs or unfeasible because of the mechanical limitations of the air
handler.
Pleated filters are a platform for improved pressure drop performance and
enhanced capacity of microfibrous materials. The performance enhancements result from
6
transforming the flat material into a three-dimensional, corrugated structure to increase
the available media area. The additional area extends the capacity of a filter as well as
lowers the pressure drop by slowing down the velocity through the porous material. The
addition of each pleat, however, introduces an new source of resistance due to increased
surface-fluid friction. The reduction in pressure drop through the media is steadily
counteracted by a rise in the flow resistance because of increased friction in the pleat.
Due to the exchange of media-induced flow resistance loss for pleat-induced pressure
losses, a pleated filter will experience a minimal resistance corresponding to an optimal
pleat count and media area.
Previous research by Chen et al. (1996), Del Fabbro et al. (2002), Caesar and
Schroth (2002), and Tronville and Sala (2003) each presented plots of pressure drop
versus pleat count that demonstrated this tradeoff behavior (Figure 1.1). Chen labeled the
lower pleat count region to the left of the optimal number as the media-dominated
regime. A filter was listed in the viscosity-dominated regime when it possessed more
than the optimal number of pleats. Although the previous research identified that an
optimal pleat count existed, a detailed understanding of the influential design parameters
and the impact of their variation was not well established.
7
Figure 1.1: Typical ?U? Pleating Curve
A need exists for an accurate pressure drop model to assist in designing more
efficient pleated filters. A thorough understanding of the design parameters and their
influence on the overall pressure drop would lead to better predictions regarding the
minimum initial pressure drop or maximum filtration area while maintaining an
acceptable initial resistance that a filter could obtain. A model could be further used to
establish preferred media properties with respect to permeability versus thickness; thus, it
could serve as a design tool for media construction as well. The end benefits to a
filtration design are an increase in dirt holding capacity, improvement in removal
efficiency, and reduction of operational energy costs.
8
CHAPTER II: BACKGROUND AND EXPERIEMTNAL
FOR MODELING INITIAL PRESSURE DROP
II.1. Previous Pleated Filter Models
Various models have been published that calculate the flow resistance
encountered within a pleated filter. Chen et al., Rivers & Murphy, Tronville & Sala,
Caeser & Schroth, Del Fabbro et al., and Raber have each suggested that a pleated filter
can be modeled by the general formula:
?Pf = KGEOV2F + KMVM (2.1)
The equation states that the total pressure drop across the filter (?Pf) is a second order
polynomial composed of a geometric and media term. The geometric term is equal to the
squared face velocity into the filter (VF) multiplied by a geometry coefficient (KGEO).
The media term is composed of the media velocity (VM) times the media coefficient
(KM). The media velocity is calculated by dividing the face volumetric flow by the
available filtration area. The following sections briefly discuss each researcher?s work
and their methods to model a pleated filter.
II.1.1. Chen et al.
Chen et al. (1995) calculated the pressure drop of a rectangular pleated filter
through the use of a nine-node finite numerical method. The flow resistance upstream
and downstream was computed by the Navier-Stokes equation. The pressure loss
9
through the media was estimated by Darcy-Lapwood-Brinkman equation with the media
constant (K) experimentally determined.
C
o
th
MCMf VP
MPVKPPP ??
???
?
???
? ?+=?+?=?
2 ? (2.2)
The research proposed that the optimal pleat count existed when the resistance of
the media equaled that of the viscous effects. This computation is displayed by Equation
2.3 and is rearranged into a general correlation as shown. Once the correlation
coefficient (C) is calculated, the optimal pleat count can be computed for a given media.
???
?
???
?
?+=?
?+=
?
?
3
2
) ?(
811
to
h
M
C
M
fo
MP
P
KCP
P
P
P (2.3)
Besides experimentally determining the media coefficient (K), all work presented
in the first study was theoretical. When Chen et al. (1996) subsequently investigated the
flow resistance through a triangular pleated filter, the research concluded that the face
velocity explored in the first study [<100 feet per minute (fpm)] was not a reasonable
operational value. The use of Darcy-Lapwood-Brinkman equation was found to be
invalid in the new operational velocity range. The researcher replaced the equation with
a semi-empirical model:
2
o
2
o
1 ?P
2
?P
21
???
?
???
?
?+???
?
???
?
?+=?
?
MMM
f
PMPMP
P (2.4)
The last term in Equation 2.4 is proposed to account for viscous effects that stem
from the directional flow change inside the pleat. Chen concludes that the angle of
change is influenced by the media?s resistance; therefore, M2 must be empirically solved
for each media type used.
10
II.1.2. Rivers & Murphy
Rivers and Murphy (2000) proposed a modified version of Equation 2.1 that
could be used to model the total pressure drop through any air filter.
?Pf = KGVNf + f(Vm, ?, ?SM, ?, Mt, Rf, Kn, M) (2.5)
The work primarily focused on estimating the media?s resistance. In particular, the
research investigated how the compression of an HVAC media led to non-linear rises in
resistance as face velocity was increased. The model provides great detail into predicting
media performance based on the media design parameters of media velocity, viscosity,
volumetric solid fraction, media non-uniformity, media thickness, fiber radius, Knudsen
number, and dust load (denoted in order as Vm, ?, ?SM, ?, Mt, Rf, Kn, M). To account for
the influence of geometric factors, the model relies on two non-transferable factors
lumped into a bulk term (KGVNf) that must be empirically fit for each filter. The process
first determined ?Pf versus face velocity for a filter, and then Equation 2.5 was
rearranged into a linear form to solve the constants N and KG. Reported N values varied
from 1.15 to 3.74 while the KG values were not discussed. The model can not be use in a
predictive capacity since the factors must be empirically determined for each filter.
II.1.3. Del Fabbro et al.
Del Fabbro et al. (2002) focused on modeling pressure loss created within a
pleated filter composed of HEPA and low efficiency filter medium. The research initially
attempted to compare experimental data to a computational fluid dynamic (CFD) model.
The CFD model was ultimately deemed too computational expensive and difficult for the
accuracy of results it provided. The study turned to a semi-empirical, dimensionless
model that identified and utilized the following eight critical design parameters: pressure
11
drop, filtration velocity, media resistance, media thickness, density, viscosity, pleat
height, and pleat opening.
The model could theoretically predict pressure drop through a pleated filter if the
critical parameters are known or specified; however, the model was shown to be
incapable of accurately predicting the experimental data presented by Del Fabbro. The
results displayed significant positive and negative deviations between experimental and
modeled data with divergences as large as 100 Pa (0.4? H2O) and 500 Pa (2? H2O).
Beyond the strong deviations, the flow conditions studied were far below a normal filter?s
operating range. The maximum, modeled face velocity of 15 cm/s (30 fpm) was an
order of magnitude below standard operational conditions. The study also failed to
account for the pressure drop associated with the filter?s housing.
II.1.4. Caeser and Schroth
Caeser and Schroth (2002) created a three termed model for predicting pressure
drop in deep-pleated (4 to 12 inches) filters. The three resistances were the influence of
airflow in and out of the pleats, through the pleats, and through the media. The airflow in
and out of the pleats was modeled by a coefficient of friction. A reduced Navier-Stokes
equation was used to compute pressure drop through the pleats. The media?s resistance
was calculated by Darcy?s Law. The total resistance of a filter was the summation of the
three terms.
Although the methodology employed by Caeser and Schroth was unique, the
research overall had several deficiencies. The coefficient of friction listed in the research
resembles a sudden contraction modified by a second parameter. The second parameter
was listed as a function of entry and exit edge sharpness, yet a means to calculate the
12
second parameter was not presented. The study focused on deep-pleated HEPA and
ULPA that are commonly built with metal spacers/combs to keep the pleats from
collapsing, yet the model lacks a method to account for the influence of these additional
structures. Several assumptions are postulated to reduce the Navier-Stokes equation into
a more computationally simple form. The validity of these assumptions was never
proven against experimental data.
II.1.5. Tronville and Sala
Tronville and Sala (2003) expanded on Equation 2.1 by proposing two new
formulas to calculate the coefficients. Following the research of Rivers and Murphy, the
pressure drop for flow through the media (1/Kc) was modeled by the Carmen-Kozeny
equation with the solid mass fraction (?) described by the Natanson ? Pich function. The
parameter Dc is the pore hydraulic diameter and ?z is the thickness of the filter. The
geometric resistance coefficient (1/Kair) was based on the pleat count per unit length (?)
raised to an empirically determined power N multiplied by the face velocity. Equation
2.6 is the end result of substituting the new coefficients into Equation 2.1. The two
unknowns (N and Dc) can be solved by plotting a second-degree polynomial to
experimental data obtained for a filter.
D
C
N
DD UzD
fUU
KcKairz
P ?
?
???
???
?
???
?
?+=??
??
?
? +=
?
??
2
)(211 (2.6)
The research only empirically determined the coefficients for a single filter. The
authors assume that determining the parameter N at one pleat configuration would allow
them to assess geometry resistance effects at all pleat arrangements. The minipleat style
filter in this study possessed 304 pleats per meter, yet the model makes predictions for
13
pleat counts upwards of 1000 pleats per meter. With no supplementary experimental data
to back this claim, the assumption that the model is capable of making this prediction
becomes questionable. Furthermore, the model makes no concessions to account for
filter housing or variations in filter depth.
II.1.6. Raber
Raber (1982) attempted to establish the effects of dirt loading on the flow
resistance within a pleated filter. The media?s resistance was experimentally identified
by testing a small media sample to determine the impact of dust loading on the pressure
drop. The term was found to be a second order polynomial that increased as the sample
was loaded with dirt. The geometric resistances were numerically calculated from the
momentum balance based on a characteristic half-pleat control volume. The half pleat
was divided into five elements, and the total resistance across the half-pleat was
calculated by sequentially solving the momentum balance with the conservation of mass
equation and the media influence polynomial.
To assess the validity of the calculations, Raber built four 24?x24?x12? (HxWxD)
prototype filters that possessed 16 pleats. The filters were tested at a face velocity of 500
fpm and loaded with dust until a final resistance of 1? H2O was reached. The prototypes
were not accurately modeled by the calculation. The initial deviations were
approximately 0.05? H2O to 0.1? H2O and grew beyond 0.2?H2O as the filters were
loaded.
A probable source of error is the elimination of the friction term from the
momentum balance. The research dismisses the friction losses due to the relatively
moderate velocities encountered within the pleat. The moderate velocities, however, are
14
the product of employing 128 square feet of media to reduce the face velocity from 500
fpm to 3.9 fpm. The assumption?s dismissal becomes increasingly debatable when
attempting to model shallower filters with substantially higher pleat velocities.
Although Raber does not incorporate friction losses into his model, he does
outline seven areas that would be associated with friction loss. This outline, described in
Section 3.I.C, serves as the basis for the flow pattern used in this research.
II.2. Objectives of Current Modeling Efforts
The overarching goal of this work is the formulation of a model that meets the
key objectives described below. The study was deemed necessary since the prior models
often fail to achieve two or more of these requirements. The sixth objective is unique to
this research, and no previous work regarding this subject was found.
1. Predictive
The model should be capable of predicting total pressure drop based solely on
geometric design and media properties. The use of non-transferable factors should not be
utilized. In particular, a model should not need empirical pressure drop versus face
velocity data from a fully-constructed filter in order to make predictions.
2. Full Accounting of Design Parameters
The model should meticulously account for all previously identified contributing
design parameters. The inability to properly assess the design parameters results in
misattributed resistances and erroneous predictions. The most commonly ignored design
parameters are the contribution of pleat tips to the overall resistance and the effect of
structural elements within the filter.
15
3. Accurate
The ability to accurately predict a desired behavior is the primary objective of any
modeling endeavor. A model should be able to predict the initial pressure drop of a filter
to within ?10% for a given operational velocity.
4. Experimentally Verified
An empirical model should be based upon observed data covering a wide range of
all design variables. A theoretical model needs to be tested against a similarly diverse
field of design variables.
5. Computationally Benign
The model allows for quick calculations to improve the utility of the model. Long
computation times and exceeding complex mathematics can hinder the usefulness of a
predictive model.
6. Adaptable
The model should be able to make predictions for a single pleated filter as well as
a Multi-Element Structured Arrays (MESA?s). Multi-Element Structured Arrays are a
novel filtration platform that incorporates numerous filter elements together to further
reduce the pressure drop and drastically increase the available media area. The model
should fulfill requirements 1 through 5 for both types of filtration systems.
II.3. Theory
The following equations are used in the research and modeling efforts:
Forchheimer-extended Darcy?s Law, Bernoulli?s Equation, the Equation of Continuity,
and the Momentum Balance. Several previously published coefficients of friction are
employed in conjunction with Bernoulli?s equation.
16
II.3.1. Forchheimer-extended Darcy?s Law
The high operational velocities associated with a particulate air filter often result
in non-linear deviations from Darcy?s Law for flow through the media (Rivers & Murphy
2000, Chen et al. 1996). Rivers & Murphy concluded that the deviations were the
product of media compression due to the air?s inertial force being sufficient to compress
the fibers together. Although Darcy?s Constant should be slightly decreased due to the
overall reduction in length of the porous media, the compression changes the internal
void volume and tortuosity of the media leading to higher superficial velocities,
decreased permeability, and an overall increase in Darcy?s Cconstant.
A practical method to account for the non-Darcian behavior is the addition of a
second-order term to Darcy?s Law (Scheidegger 1974). Equation 2.7 is known as a
Forchheimer-extended Darcy?s law. The ?A? term is equivalent to the Darcy?s Law
constant (?L/Km). The ?B? constant accounts for the non-linear deviation due to inertial
effects.
?P = AVM + BVM2 (2.7)
Numerous theoretical equations exist that attempt to relate the physical
significance of the second media constant, but these theories require extensive knowledge
of the media?s fiber dimensions and packing densities (Rivers & Murphy 2000). The
research presented by Rivers and Murphy demonstrates the complexity and difficulty in
accurately modeling media performance with these theories. Since the primary objective
of the research is to identify and determine the resistances created by the geometric
design parameters and not the media formulation, it is preferable to model the media
constants by a quick, empirical approach that will not introduce as much theoretical error.
17
The second order term also allows the model to account for the presence of particle
matter embedded within the fibrous framework.
II.3.2. Mechanical Energy Balance / Bernoulli?s Equation
The mechanical energy balance is a summation of kinetic, potential, mechanical,
compressive, and viscous energy terms. Bernoulli?s Equation is a specialized case of the
mechanical energy balance. Bernoulli?s Equation assumes incompressible, steady-state
flow while maintaining a control volume with stationary, solid boundaries (Perry and
Green 1997). Bernoulli?s Equation is:
P1/? + ?VV12/2 + gZ1 + ?Ws = P1/? + ?VV22/2 + gZ2 + Lv (2.8)
Rearranging similar terms:
?(P/? + ??V2 + gZ) = ?Ws ? Lv (2.9)
Equation 2.5 states the change in pressure, kinetic energy, and potential energy is
equal to the mechanical energy (?Ws) added to the system minus the viscous losses (Lv).
The term alpha (?V) is the ratio of velocity cubed over the average velocity cubed. Alpha
assumes a value of unity for turbulent flow. Bernoulli?s Equation can be further
simplified by eliminating elevation change within the control volume and removing all
mechanical work. The following equation results when applied between two points:
?P = P1 ? P2 = ?? (V22 ? V12) + Lv (2.10)
The viscous loss term (Lv) accounts for the change of mechanical energy into
heat due to viscous forces. The term is also referred to as the minor or miscellaneous
losses. Denoting the viscous losses as minor or miscellaneous is misleading because they
are frequently the primary resistance forces within a system (Perry and Green 1997).
There are two methods to account for the losses: equivalent length or velocity head. The
18
later will be used in this dissertation. The Lv term can be reported in equivalent number
of velocity heads.
Lv = ?? KV2 (2.11)
The K value is referred to as either the velocity head loss coefficient or the
coefficient of friction. Although the viscous losses can be theoretically computed by
simultaneously solving both the mechanical energy balance and momentum balance for
the given control volume, they are most often determined through experimental
measurements (Bird et al. 2001, Perry and Green 1997). The coefficient is required to be
a dimensionless function of either geometry, Reynolds number, or both. The importance
of the Reynolds number increases in laminar flow due to the rise in friction at the
boundaries (Bird et al. 2001). The V term is an arbitrary, reference velocity on which the
coefficient is based.
The present research makes use of the following five previously researched
friction coefficients: sudden contractions, sudden expansions, gradually contractions,
flow across a perforated plate, and flow through a duct. Each coefficient?s formula,
general control volume schematic, and reference velocities are presented below.
19
1. Coefficient of Friction for a Sudden Contraction
Idelchik (1994)
Figure 2.1: Sudden Contraction Diagram
0.75
1? ??
?
?
???
? ?=
LARGE
SMALL
C A
AK (2.12)
(Based on downstream velocity)
2. Coefficient of Friction for a Sudden Expansion
Idelchik (1994)
Figure 2.2: Sudden Expansion Diagram
2
1 ??
?
?
???
? ?=
LARGE
SMALL
E A
AK (2.13)
(Based on upstream velocity)
20
3. Coefficient of Friction for a Gradually Contraction
Fried and Idelchik (1989)
Figure 2.3: Gradually Contraction Diagram
KGC = [(-0.0125N4 + 0.0224N3 ? 0.00723N2 + 0.00444N - 0.00745)(A3 - 2?A2 ? 10A)]
(2.14)
A = 0.01745? (where ? is in radians)
N = A2 / A1
(Based on upstream velocity)
4. Coefficient of Friction for Flow Across a Perforated Plate
Idelchik (1994)
Figure 2.4: Grating Diagram
2
707.1
?
???
?
???
?
???
?
???
? ?=
TOTAL
FREE
TOTAL
FREE
G A
A
A
AK (2.15)
(Based on downstream velocity)
21
5. Darcy-Weisbach Equation: Flow in a Duct with Smooth Walls
Idelchik (1994)
Figure 2.5: Duct Diagrams
???
?
?
???
?=
h
T D
LK (2.16)
(Based on flow velocity)
l = 64/Re Re < 2000 (Laminar Regime)
( ) ??
?
??
?
??= 264.1log(Re)8.1
1? Re > 4000 (Turbulent Regime)
?
hVD=Re (2.17)
Tabular data is available in the Handbook of Hydraulic Resistance (Idelchik
1994) for computing ? in the transitional regime defined by Reynolds number between
2000 and 4000.
II.3.3. Equation of Continuity
The equation of continuity is based on the conservation of mass (Perry and Green
1997). The equation denotes that mass flow entering and leaving a control volume is
equal. When constant density is assumed, the equation can be written as:
V1 A1 = V2 A2 (2.18)
22
II.3.4. Momentum Balance
Although not extensively used in the study, the momentum balance is:
mgFuAPuAPuAVuAVdtd S ++?+?=? 2221112222211211 ?? (2.19)
The balance asserts that the change of momentum is the difference between the amount
of momentum carried into the system by the fluid and the pressure acting on the fluid
versus the momentum carried out by the fluid and the pressure acting on the outlet fluid
(Bird et al. 2001). Addition factors such as the force of gravity on the fluid?s mass and
the force of system?s surfaces on the fluid (Fs) are factored into the balance.
II.4. Experimental Setups
Two separate test rigs were constructed and used to measure pressure drop
performance across a media sample and a filtration system. A general description of the
test rigs, control runs, and equipment verification are provided in this section.
II.4.1. Media Test Rig
The media constants were determined using a 1-inch circular diameter duct
powered by house air at 100 psig (Figure 2.6). The duct length to diameter ratio was
sufficiently long (48-to-1) to ensure no entrance effects. A media sample was held in
place by two plates tightened together by four nut and bolt assemblies. A twelve inch
outlet section was located downstream of the media sample to prevent additional pressure
loss due to a sudden expansion out of the tube.
23
Figure 2.6: General Schematic of Media Test Rig
Airflow to the rig was controlled by two rotameters. The rotameters were
connected in series to produce a stable, controllable volumetric flow between 0 and 160
SCFH. This correlated to a maximum superficial velocity of 488.9 fpm within the one
inch test rig. The rotameters were calibrated by a volumetric displacement test (See
appendix for calibration procedure and results). Resistance measurements were obtained
with an Omega Model PX154?010DI differential pressure transmitter connected to a
pressure tap located two inches upstream and five inches downstream of the media
sample. The taps had a one-eighth inch diameter and were drilled flush with the inner
tube diameter to prevent increased friction. The pressure transmitter had a range of -1.0
to 10? H2O with a resolution of 0.001? H2O.
A control test performed on the media test rig resulted in 0.003? H2O of pressure
drop at the maximum volumetric flow. The measured resistance follows the Darcy-
Weisbach Equation (Eq. 2.16) for flow in a circular pipe with a smooth interior. The
measured and calculated values are shown in Figure 2.7. The step-shaped appearance of
24
the measured data was the product of the differential pressure transmitter?s resolution of
0.001? H2O. The slope shifts in the calculated plot were due to the transition from
laminar to turbulent flow.
0
0.001
0.002
0.003
0.004
0.005
0 100 200 300 400 500 600
Face Velocity (fpm)
Pre
ssu
re
Dr
op
("
H
2O
)
Measured Data
Darcy-Weisbach Calculation
Figure 2.7: Control Pressure Drop Curve for Media Test Rig
II.4.2. Filtration Test Rig
A general schematic of the filtration test rig is depicted by Figure 2.8. The test rig
was composed of the following eight subunits: (1) blower, (2) blower sleeve, (3) three-
way transition, (4) baffles, (5) air straighteners, (6) main duct, (7) filter box, and (8)
outlet duct. The primary building material was 5/8? thick particle board. The subunits
were fastened by nut and bolt fixtures. All joints were sealed with a polymer glue gun.
The edge of each section was fitted with ?? foam weather-stripping. After tightening the
bolts to compress the weather-stripping, the resulting seal produced no noticeable leaks.
25
Figure 2.8: General Schematic of Blower Test Rig
The air handler used was a Dayton System with a 15? impellor powered by a 3 Hp
Hitachi motor. The motor was controlled by a Hitachi frequency drive with a range of
zero to sixty hertz at 0.1 Hz increments. The outlet port dimensions for the blower were
16? x 11.5?.
A sleeve served as a connecting segment between the blower and the three-way
transition. The sleeve was attached to the blower?s outlet port. A pressure tap, located
on the sleeve, coupled with a pressure transducer monitored resistance across the blower.
Once inside the three-way transition, the cross-sectional dimensions expanded from 16? x
11.5? to 19.5? x 19.5? (H x W). The three-way transition then connected to the baffles.
The baffles were composed of 4 vertical planks followed by 4 horizontal planks.
This created an outlet composed of twenty-five squares. The allowable flow to each
square was controlled by the position of the vertical and horizontal planks. The baffles
were followed by the flow straighteners. The first straightener was a perforated metal
plate that blocked fifty percent of the cross-sectional area. The second straightener was a
heavy mesh screen. The airflow passed from the straighteners into the main duct. The
main duct was composed of three extensions. It had a length of twelve feet with internal
dimensions of 19.5? x 19.5? (H x W).
26
The baffles, flow straighteners, and main duct served to delivery a uniformly-
distributed airflow into the filter box. The baffles directed large quantities of air to the
desired segments of the duct. The straighteners assisted with leveling the flow by
introducing a considerable resistance into the system. The length of the main duct
allowed the air to evenly disperse. The before-and-after effects of adding these subunits
are highlighted below. The figure was created by measuring velocity at each point
depicted by the 7x7 grid with a hot-wire anemometer (Extech Model # 407123). Without
any duct modifications, the blower delivered a heavily concentrated volumetric flow to
the left-hand side of the ductwork. The distribution system eliminated this ?hot spot? and
reduced the variation between the maximum and minimum localized velocity by an order
of magnitude.
Figure 2.9: Flow Distribution at 40 Hz Before (A) and After (B)
Once it had traveled through the main duct, the air entered into the filter box. The
filter box could be loaded with a single filter or a multi-element pleated filter array. The
filter box had the following dimensions: 19.5?x19.5?x 24? (HxWxL). The top of the
filter box contained a window in order to observe that the pleat?s integrity remained intact
27
throughout the experiments. The filter box was followed by the outlet section. The 24?
long outlet section prevented an increase in pressure drop due to sudden expansion out
into the room.
A metal strip was positioned four inches from the front of the filter box to secure
a single filter into position. The strip had a height of 1/8? that allowed it to fit behind the
filter?s housing without interfering with the pressure measurements. For array tests, the
filters were held together and sealed into place using duct tape. No additional support
was needed to keep the filter array in position due to the tight fit of the filter box.
Pressure drop across the filtration section was monitored by a Dywer Mark II
monometer and an Invensys Foxboro IDP10 differential pressure transmitter. The
equipment was connected upstream into the duct by three pressure taps located ten inches
before the filter test box. A 1/8? pressure tap located in the center of the duct was
connected to the manometer. The manometer?s second connection was left open to the
room?s atmosphere. The other two pressure taps were evenly spaced across the top of the
duct. The taps had a 1/4? opening within the duct that reduced to a 1/8? tube fitting. All
taps were drilled flush to the ducts interior wall to prevent additional friction. The two
taps were connected together via a ?T? junction. The line was then ran to the differential
pressure transmitter. The transmitter?s outlet was connected to a second ?T? junction.
The ?T? split lines were connected downstream to pressure taps located six inches before
the duct outlet. The dual tap configuration was a method to average the pressure drop
readings.
Air to the blower was drawn from the room. All tests were performed in an
environment of approximately 20?C (68 ?F) and elevation of 215 meters (705 ft) above
28
sea level; therefore, the density of air was assumed to possess a constant valve of 1.16
kg/m3 (0.0725 lb/ft3) throughout the experiments.
The ASHRAE 52.2 Standard provided an outline for certifying an acceptable flow
distribution and pressure drop across an empty test section. The flow distribution test,
outlined in Section 5.2, consisted of a nine-point test at three volumetric flow rates (472,
1970, and 2990 cfm) (ASHRAE 2007). A nine square grid was bracketed off at the
outlet of the duct with a thin metal wire. The average velocity was taken at the center of
each grid square for one minute. The test was repeated three times at each square. The
square?s velocity value was composed of the average from the three tests. The
coefficient of variance was computed between all nine squares at a given volumetric flow
rate. The coefficient of variance was defined as the standard deviation between the nine
points divided by the mean. The coefficient of variance must be less than ten percent to
pass. Data and the coefficients of variance for the ductwork utilized in this study were
presented in Figure 2.10. The velocities units were listed in meter per second (m/s).
Figure 2.10: Coefficient of Variance
Section 5.16.2 of ASHRAE Standard 52.2 states that the pressure drop across the
test section at 1970 cfm (500 fpm in a 2?x2? duct) shall be less than 0.03? H2O (ASHRAE
29
1999). The test rig?s recorded pressure drop was approximately 0.001? H2O at the
volumetric flow of 1970 cfm.
As with the media test rig, the pressure drop between the pressure taps was
adequately calculated by the Darcy-Weisbach equation. The results of the control run
and the calculated values were presented in Figure 2.11. The step-like distribution of the
measured values was due to the pressure transmitter?s resolution of 0.001? H2O. The
transition from laminar to turbulent flow was not observed in the control plot because it
occurred at 24 fpm. Since the flow was primarily turbulent in the ductwork, the alpha
term in Bernoulli?s Equation equaled unity.
0
0.001
0.002
0.003
0.004
0.005
0 200 400 600 800 1000 1200Face Velocity (fpm)
Pre
ssu
re
Dr
op
("
H
2O
)
Measured Data
Darcy-Weisbach Calculation
Figure 2.11: Control Pressure Drop Curve for Filter Test Rig
30
II.5. Data Acquisition
II.5.1. Media Pressure Drop Curves
Three pressure drop runs were performed on each media sample. The first run
consisted of 35 data points, the second run 12 data points, and the third run 11 data
points. A data point consisted of setting the rotameter to a flow rate and recording the
corresponding pressure drop. Each run used a different strategy for incrementing the
rotameters to randomize the data collection.
II.5.2. Filter Pressure Drop Curves
All data collected during a single filter experiment followed the manner described
below unless stated otherwise. The blower frequency was first set at 5 hertz, and the flow
was allowed to equilibrate. The pressure drop across the blower was measured by the
pressure transducer. The pressure drop across the filtration section was measured by the
differential pressure transmitter and manometer. An average velocity was measured with
an Extech Model 451104 vane-anemometer over a thirty second period by uniformly
moving the meter over the path indicated below at the outlet of the test rig. This
measurement technique was based on the ASHRAE 52.2 velocity uniformity test.
31
Figure 2.12: Measurement Path for the Vane Anemometer
The measurements were repeated at the following frequencies in the order listed:
10, 15, 20, 25, 30, 35, 40, 37.5, 32.5, 27.5, 22.5, 17.5, 12.5, and 7.5 hertz. The test was
repeated up to three times on certain filters, but multiple runs were ultimately abandoned
due to time constraints. Frequencies above forty hertz were not measured during single
filter tests because they corresponded to velocities greater than 1000 fpm. Frequencies
below five hertz were not measured in either filter arrangement because the blower was
not able to overcome the initial flow resistance created by the test rig; therefore, there
was no flow in the ductwork.
For the multi-element test, data was collected in the same manner up until 35
hertz. Frequencies larger than 35 hertz corresponded to face velocities greater than 1000
fpm. The frequency was then decreased in a following manner: 33.7, 32.5, 31.3, 28.7,
27.5, 26.3, 23.7, 22.5, 21.3, 18.7, 17.5, 16.3, 13.7, 12.5, 11.3, 8.7, 7.5, and 6. 3 hertz.
Only the pressure drop measurements were recorded as the frequency was decreased.
32
This was done to save time on data recording since the velocity could be accurately
calculated from the blower curve based on pressure drop data (Figure 2.13).
Once the data was collected for a filter or array, a pressure drop curve was created
by plotting pressure drop versus face velocity. A regression line was fitted to each
pressure drop curve for use in data analysis. The fitted line helped alleviate individual
data discrepancies. The Darcy-Weisbach equation was used to remove the background
noise from the measurements.
As stated, the velocity values were computed from the blower curve in multi-filter
tests. The volumetric flow could be calculated based on the pressure drop across the
blower and frequency setting by the following series of equations:
i) RPM = 37.75 x Setting (Hz) Rate per Minute
ii) k = RPM / 2265 (Hz) k Factor
iii) ?P60Hz = ?Pblower / k2 Pressure Drop at 60 Hz
iv) V60 Hz = -25.32?P60Hz2 ? 389.08?P60Hz + 5185.5 Volumetric Flow at 60 Hz
v) V = kV60 Hz Volumetric Flow at Setting
Once the volumetric flow was known, the face velocity was calculated by dividing the
volumetric flow by allowable flow area. Figure 2.13 was a comparison of 189 velocities
measured by the vane-anemometer and the resulting calculations from the blower curve.
33
y = 0.9816x
R2 = 0.9914
0
100
200
300
400
500
600
700
800
900
1000
0 200 400 600 800 1000
Velocity Computed by Vane Anemometer (fpm)
Ve
loc
ity
C
om
pu
ted
by
B
low
er
Cu
rve
(f
pm
)
Figure 2.13: Velocity Measurement Comparison
The measurement comparison between the differential pressure transmitter and
the manometer was shown in Figure 2.14. The meters showed a one-to-one
correspondence. The figure developed a plateau-shaped distribution as pressure drop
increased. This was due to the gradual decrease in manometer resolution at readings
above 0.1? H2O.
34
y = 1.0098x
R2 = 0.9978
0
0.2
0.4
0.6
0.8
1
1.2
0 0.2 0.4 0.6 0.8 1 1.2
Differential Pressure Transmitter Measurement (" H2O)
Ma
nom
ete
r M
eas
ure
me
nt
("
H2O
)
Figure 2.14: Pressure Measurement Comparison between Manometer and Transmitter
II.5.3. Media Thickness
The media thickness was determined with a micrometer. A given media was
layered twenty times, and the thickness was measured. The test was repeated twice, and
the average thickness of a single layer was calculated from the three tests.
35
CHAPTER III: INITIAL PRESSURE DROP MODELING
OF PLEATED FILTERS
III.1. Introduction
III.1.1. Pleated Filter Schematics
The following schematics (Figure 3.1, 3.2, & 3.3) are provided to familiarize the
reader with the dimensions and nomenclature used throughout the research to describe a
pleated filter. Figure 3.1 is an illustration of a filter with nine pleats. The symbols FD,
FH, and FW stand for filter depth, filter height, and filter width. A filter will often be
referred to as an ?X? inch filter. This size dimension denotes the filter depth. The face
dimensions (FH and FW) remain constant throughout the research involving a single
pleated filter. In the orthogonal view, the top of the filter is shown as partially removed
to expose the pleat?s geometry.
36
Figure 3.1: Pleated Filter Illustration
A more detailed view of the pleat structure is presented in Figure 3.2. Because of
the technique use to construct a pleated filter, the pleat length (PL) is the same dimension
as the filter depth. The pleat depth (PD) is therefore shorter than the overall depth of the
filter. The allowable flow area into the pleat is slightly less than the pleat opening (PO)
due to the fractional blockage created by the pleat tip (PT). The pleat pitch, also called
pleat angle, is denoted by the Greek letter Beta. The pleat height, which is not shown,
runs the span of the pleat tip and is equivalent to the filter height.
37
Figure 3.2: Illustration of Pleat Dimensions
Figure 3.3 is an illustration of a pleat tip formation from a flat sheet of media. A
pleat tip is modeled as a rounded peak created by folding the media around a pinch point.
The pinch point is indicated by the square box. The label MT represents the media?s
thickness. The effective flow area blocked by the tip is indicated by label AT (Area of
Pleat Tip). The label ME is the approximate length of material used in the creation of the
pleat tip. The angle ? is solely used in calculations.
38
Figure 3.3: Pleat Tip Illustration
III.1.2. Parameters
Most of the filter?s parameters are defined by the ductwork employed or the end
user. The remaining parameters are dependent on the defined parameters.
Filter Parameters
Filter Height (FH): Dictated by the Duct Height
Pleat Height (PH): Dictated by the Duct Height
Filter Width (FW): Dictated by the Duct Width
Filter Depth (FD): Specified by the User
Pleat Length (PL): Specified by the User (Equivalent to Filter Depth)
Pleat Count: Specified by the User
Grating Blockage: Specified by the User
Media Thickness (MT): Specified by the User (Property of Media)
Permeability: Specified by the User (Property of Media)
39
Pleat Parameters
Pleat Tip = 2sin(?)Media Thickness
Pleat Opening = Filter Width / Pleat Count
Pleat Pitch [?] = sin-1(? Pleat Opening / Pleat Length)
Gamma [?] = ?/2 ? Pleat Pitch
Media Loss (AT) = 2(Media Thickness) x Gamma
III.1.3. Proposed Flow through a Pleated Filter
The modeling efforts began by defining a pathway for air to flow through a filter.
The pathway chosen, first proposed by Raber (1982), consisted of air traveling through
seven regions of varying cross-sectional area to pass through a pleated filter. A uniform
flow profile is assumed to exist in the upstream duct before the filter. A typical pleated
filter employs a grating that increases the structure integrity of the filter and the pleats.
The flow is contracted by the grating resulting in an increased velocity. The air expands
back out after the grating, yet it is quickly contracted as it is channeled around the pleat
tips and into the pleats.
Once in the filter?s pleats, the air begins to split and change directions to allow
entrance into the media at an angle perpendicular to the media?s surface. The air expands
out onto the media?s surface area after the directional change. The proposed flow pattern
through the filter?s pleats is very similar to the flow in a converging or diverging wye.
The fourth region is the media?s accessible surface area. The area does not
include the small portion of the media that will be pinched shut in the pleat tips. The air
flow then follows a similar, albeit reversed, path out of the filter system into the
downstream duct after flowing through the media.
40
Figure 3.4: Flow Pattern
Area Calculations:
i) Area 1 (Area 7): Duct Width x Duct Height
ii) Area 2 (Area 6): (Filter Width x Filter Height) x (1 - % Blocked)
iii) Area 3 (Area 5): (Filter Width x Filter Height) ? Pleat Count x Pleat Tip x Pleat Height
iv) Area 4: (Pleat Count x Pleat Height) x (2 Pleat Length ? Media Loss)
III.1.4. Modeling a Pleated Filter
The total pressure drop through a pleated filter was modeled as a summation of
individual resistances. The individual resistances were formulated by applying
Bernoulli?s Equation or Forchheimer-extended Darcy?s Law to the seven proposed flow
areas. The singular parts were summed together in the same way that electronic
resistances can be added in series. This method was previously used by Idelchik (1994)
to model an electrostatic filter and is similar in nature to the three-tiered modeled
proposed by Caeser and Schroth (2002).
41
i) Across Front Grating: ?P1 = ? ?[(V22 ? V12) + KGV22 ]
ii) Flow from Grating to Pleat Inlet: ?P2 = ? ?[(V32 ? V22) + KCV32 ]
iii) Flow from Pleat Inlet to Media Surface: ?P3 = ? ?[(V42 ? V32) + KP1V32 ]
iv) Flow through Media: ?P4 = AV4 + BV42
v) Flow from Media Surface to Pleat Outlet: ?P5 = ? ?[(V52 ? V42) + KP2V52 ]
vi) Expansion from Pleat Outlet into Grating: ?P6 = ? ?[(V62 ? V52) + KEV52 ]
vii) Across Back Grating: ?P7 = ? ?[(V72 ? V62) + KGV62 ]
?PT = ??Pi = ?P1 + ?P2 + ?P3 + ?P4 + ?P5 + ?P6 + ?P7 (3.1)
KC, KE, and KG were modeled as previous published coefficients of friction
computed by Equations 2.12, 2.13, and 2.15. KP1 and KP2 are unique friction coefficients
for flow in the upstream and downstream pleats for which no previous formula could be
found; thus, a new formula had to be developed. A coefficient?s formula can be
identified by simultaneously solving the mechanical energy balance and the momentum
balance. Figure 3.5 is a pleat control volume for the downstream pleat.
Figure 3.5: Control Volume of a Downstream Pleat
42
Momentum Balance
d?/dt = [V4W4 + P4 A4] Ui ?[V5W5 + P5 A5]Ui + Fs->f + mg
Force of Fluid on the Solid
Forces in y-Direction
Fy = ? (V4W4 + P4 A4)cos(?) + ? (V4W4 + P4 A4) cos(-?) - 0 = 0
Forces in x-Direction
Fx = (V4W4 + P4A4)sin(?) ? (V5W5 + P5A5)
Fx = ?V42A4(A5/ A4) + P4 A4(A5/ A4) ? ?V52A5- P5 A5
Fx = ?(V42 ? V52)A5 - (P5 ? P4)A5
Ff->s = (Fx2 + Fy2)? Assuming Ff->s is zero
0 = ?(V42 ? V52)A5 - (P5 ? P4)A5
(P5 ? P4) = ?(V42 ? V52)
Mechanical Energy Balance
? (V52 ? V42) + (1/?)(P5 ? P4) + Lv = 0
Lv = ? (V42 ? V52) ? (1/?)(P5 ? P4)
Substituting in Momentum Balance Solution
Lv = ? (V42 ? V52) ? (1/?)[ ?(V42 ? V52)]
Lv = ? (V52 ? V42) V42 = (V5A5/ A4)2
Lv = ? V52 (1-(A5/A4))
k ? [1 - (A4/ A5)2] ? [1 - (1/?)2] where the reference velocity is V4
The solution indicates that the coefficient is a function of the pleat pitch (?). As
will be shown in Section 3.II.D, the solution does not directly correspond to the observed
data. Possible sources of error can be found in two simplifying assumptions. First, the
force of the fluid on the surface (Ff->s) can not be readily neglected as proposed. Second,
assuming air will enter and exit the media at a strictly perpendicular angle is
questionable.
The pleat coefficients were determined in an empirical manner since the two
balances could not be simultaneously solved. Experimentally, the individual
contributions of KP1 and KP2 could not be separated and analyzed due to the upstream and
downstream pleat symmetry. The two coefficients were therefore combined into a single
43
coefficient (KP) since they share identical geometries and experience the same velocities.
The newly formed pleat coefficient was then substituted in their place.
With the equation of continuity assumed valid, the series can be simplified by
replacing all downstream velocities with their reciprocal upstream velocities. The seven
terms can be summed and rearranged into the following model:
?PF = ? ? [(2KG)V22 + (KC + KE + KP)V32] + AV4 + BV42 (3.2)
The first four terms represent the geometric contribution and the last two terms denote the
media influence; thus, the equation can be rewritten to resemble Equation 2.1.
III.2. Identifying the Constants
The objective of the experimental program was to verify the validity of utilizing
previously published coefficients to model particular aspects of the filter design as well
as to empirically determine a new coefficient for friction encountered in the pleat. Since
the media constants will be unique and vary with the media used in the filter, the
approach began by measuring the media constants (A & B) and thickness of the materials
utilized in the research. The previous published coefficients (KG, KC, and KE) were then
shown to be applicable. The pleat coefficient for a single filter was empirically
determined from empirical ?PT versus face velocity data. This technique was based on
Rivers and Murphy?s approach to identify the constants N and KG from their model. A
more universal coefficient was developed by determining KP for a multitude of filter
designs.
III.2.1. Media Constants & Thickness
The research utilized five types of media. For future identification purposes, the
media types will be referred to in this dissertation by FM1, FM2, FM3, FM4, or FM5.
44
Figure 3.6 presents the flow resistance versus face velocity results obtained from flat
media sheets. The points on the graph represent the experimentally collected data. The
lines are second-order polynomials fitted by Excel by applying a least-square regression
line.
0
0.2
0.4
0.6
0.8
1
1.2
1.4
1.6
1.8
2
0 100 200 300 400 500
Media Velocity (fpm)
Pre
ssu
re
Dr
op
("
H
2O
)
Media 1 (FM1)
Media 2 (FM2)
Media 3 (FM3)
Media 4 (FM4)
Media 5 (FM5)
Figure 3.6: Media Resistance Curves
The media constants were determined from the polynomial fits. A table of each
media parameters and degree of fit is shown below. As previously observed by Chen et
al. (1996), the second order coefficient B is sufficiently smaller than the first order
coefficient. The average thickness of each media type is also listed in Table 3.1.
45
Table 3.1: Summary of Media Constants and Thickness
Media Thickness A x 10-4 B x 10-7 R2
(-) (in) / [mm] (" H2O * min / ft) ("H2O * min2 / ft2) (-)
FM1 0.0193 / [0.5 mm] 4.09 x 10-4 8.94 x 10-7 0.9990
FM2 0.0194 / [0.5mm] 4.87 x 10-4 11.59 x 10-7 0.9988
FM3 0.0625 / [1.6 mm] 9.73 x 10-4 17.28 x 10-7 0.9983
FM4 0.0398 / [1 mm] 15.89 x 10-4 19.18 x 10-7 0.9989
FM5 0.0417 / [1.1 mm] 32.88 x 10-4 29.25 x 10-7 0.9990
Figure 3.7 shows how the utilization of Darcy?s Law to describe the media
resistance at the typical operational velocities will result in modeling errors. Darcy?s
Law remains valid at low velocities as seen in Graph A, but deviations begin to arise
between observed and predicated values when face velocities extended beyond
approximately 150 fpm. It is commonplace for the media velocity to be above 150 fpm
since HVAC filters often operate at 500 fpm face velocity. A pleating factor greater than
3.33 would be needed in order to lower the face velocity of a 20?x20? filter below 150
fpm. Graph B is an attempt to fit the linear Darcy?s Law to the entire velocity range for
FM1 and FM5 media. Both attempts show an R-square value below the average value of
0.999 observed in Figure 3.6 when utilizing Forchheimer?s Equation.
46
Figure 3.7: Darcy?s Law Analysis of Media Resistance
III.2.2. Grating Coefficient of Friction (KG)
The Handbook of Hydraulic Resistance computes the coefficient of friction for
fluid flowing through a shaped, perforated plate by Equation 2.14. In order to verify that
the filter housing could be modeled by the same formula, the frame was mechanistically
altered and the corresponding measured pressure deviation was compared to the
calculated deviation.
The filter utilized in the grating experiments consisted of a FM2 media with 22
pleats per filter and nominal dimensions of 20?x20?x1?. The filter?s standard housing
was composed of a diamond grid that blocks 34.5% of the flow area. Additional grating
was uniformly added to the filter?s front to increase the blocked flow area from 34.5% to
59.4%. Subsequently, the filter?s grating was removed resulting in only 16.0% of the
flow area blocked. The appearance of the different grating schemes is visible below.
47
Figure 3.8: Illustration of Grating Schemes
(A) Normal Filter (B) High Blockage Filter (C) Low Blockage Filter
A pressure drop versus face velocity curve was experimentally observed for each
grating configuration. The curves were plotted in Figure 3.9. The markers represented
the observed data and the solid lines were Excel-fitted regression lines.
0
0.2
0.4
0.6
0.8
1
0 150 300 450 600 750 900
Face Velocity (fpm)
Pre
ssu
re
Dr
op
("
H
2O
)
Normal Filter (34.5% Blocked)
Plated Filter (59.4% Blocked)
Bare Filter (16.0% Blocked)
Figure 3.9: Pressure Drop Curves for Various Frontal Blockages
The validity of using Equation 2.14 was proven by comparing the increase in
resistance of the observed system (Figure 3.9) to the increase in resistance of the
48
computed system (Figure 3.10). Figure 3.10 was constructed by using Equation 2.11
with the following Kg values to estimate the resistance created by the grating by itself:
For Normal Blockage: KG = (1.707 ? 0.655)/(0.655)-2 = 2.50
For Low Blockage: KG = (1.707 ? 0.840)/(0.840)-2 = 1.23
For High Blockage: KG = (1.707 ? 0.406)/(0.406)-2 = 7.89
0.00
0.10
0.20
0.30
0.40
0.50
0.60
0.70
0 200 400 600 800 1000
Face Velocity (fpm)
Pre
ssu
re
Dr
op
("
H
2O
)
Low Blockage (16.0 % Blocked)
Normal Blockage (34.5 % Blocked)
High Blockage (59.4% Blocked)
Figure 3.10: Computed Grating Resistances
The observed pressure increase between the curves in Figure 3.9 was generated
solely by the grating modification since the same filter was utilized in all three tests. The
magnitude of the increase was quantified by using the Low Blockage curve as a
reference. Likewise, the resistance increase in Figure 3.10 was the product of an equal
percentage blockage increase. The extent of the increase was gauged using the Low
Blockage as a baseline. If Equation 2.14 adequately described the resistance created by
the grating, then the resistance rise in both systems would be identical. As portrayed in
Figure 3.11, the overlap of the observed and computed pressure drop rises indicated that
49
Equation 2.11 in conjunction with Equation 2.14 properly predicted the resistance
behavior of the grating.
0
0.1
0.2
0.3
0.4
0.5
0.6
0 200 400 600 800 1000
Face Velocity (fpm)
Pre
ssu
re
Dr
op
("
H
2O
)
Observed Difference Between Normal and Stripped Blockage
Observed Difference Between Plated and Stripped Blockage
Calculated Difference Between Normal and Stripped Blockage
Calculated Difference Between Plated and Stripped Blockage
Figure 3.11: Effects of Front Grating Modification
A similar test was performed by modifying the grating on the back of a filter. The
results from the back modification test are shown in Figure 3.12. The markers again
designated the observed pressure difference while the solid line denoted the calculated
predictions. As shown, modification of the housing at the back of the filter produced a
nearly identical result.
50
0
0.1
0.2
0.3
0.4
0.5
0.6
0 200 400 600 800 1000
Face Velocity (fpm)
Pre
ssu
re
Dr
op
("
H
2O
)
Observed Difference Between Normal and Stripped Blockage
Observed Difference Between Plated and Stripped Blockage
Calculated Difference Between Normal and Stripped Blockage
Calculated Difference Between Plated and Stripped Blockage
Figure 3.12: Effects of Back Grating Modification
III.2.3. Pleat Tip Assumption
The contraction and expansion into and out of the pleats is assumed to be
accurately modeled by Equation 2.11 using friction coefficients computed by Equations
2.12 and 2.13. It is exceedingly difficult to experimentally alter a pleat tip and analyze
the resulting contribution to flow resistance without inadvertently affecting other
resistances. The assumption that a pleat tip acts as a non-porous wall is based on Darcy?s
Law. When a media is pleated, the porous material is folded on top of itself creating a
pleat tip of increased thickness and/or decreased permeability. Either an increase in
media thickness or a decrease in permeability will result in a path of greater flow
resistance according to Darcy?s constant. Air flow through the pleat tip is therefore
assumed to be blocked due to this heightened resistance and will be channeled around the
51
tips and into the pleats. This assumption was previously incorporated into the research of
Caesar and Schroth (2002) and stated by Raber (1982).
III.2.4. Pleat Coefficient of Friction (KP)
The pleat coefficient for a specific filter was determined by obtaining ?PT versus
face velocity data over a range of velocities. The model was rearranged into the
following linear form:
?PT - ? ? [(2KG)V22 + (KC + KE)V32] + BV4 + AV42 = ? ?KPV32 (3.3)
Vi values were computed from the face velocity using the equation of continuity. The
coefficients KG, KC, KE, A, and B were calculated by methods previously discussed. The
friction created by the pleating was empirically determined by subtracting all known flow
resistances from the experimentally measured total pressure drop. The resulting
difference was then plotted verses the reference velocity term (? ?V32). The pleat
coefficient can then be inferred from the slope.
Figure 3.13 graphically showcases this methodology for a FM1 filter with 42
pleats and nominal dimensions of 20? x 20?x 1?. The dashed line is a least-squared
regression fitted to the experimentally measured pressure drop versus face velocity data.
The solid line is a model compilation of the known pressure drops due to the flow
through the media, blockage created by the filter grating, and the channeling due to pleat
tip contraction and expansion. The hyphenated line represents the observed difference
between the least-squared regression and the modeled line. It is equivalent to the left-
hand side of Equation 3.3.
52
R2 = 0.9963
0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1
0 250 500 750 1000
Face Velocity (fpm)
Pre
ssu
re
Dr
op
("
H
2O
)
Measured Data
Fitted Line
Model of Known Terms
Observed Difference
Figure 3.13: Pressure Drop Curves for a 20?x20?x1? FM1 Filter with 42 Pleats
A linear trend resulted when plotting the observed difference versus ??V32 for the
filter (Figure 3.14). A regression line forced through zero was fitted using Excel. The
slope of the line equated to the pleat coefficient of friction. The resulting coefficient is
only valid for a filter with identical design parameters. In order to acquire a more
universal coefficient for the model, the pleat coefficient needed to be determined for a
wide range of parameter space covering various pleat counts, filter depths, media
thicknesses, permeability, and face velocities. The following table itemized the twenty
filter variations used to determine the pleat coefficient. The pleat coefficient for each
filter was determined by the same method outlined above. All filters used in this study
were manufactured by Quality Filters, Inc. in Robertsdale, Alabama.
53
y = 83.206x
R2 = 0.9999
0
0.05
0.1
0.15
0.2
0.25
0.3
0.35
0.4
0.45
0 0.001 0.002 0.003 0.004 0.005
??V32 (" H2O)
Ob
se
rve
d D
iffe
ren
ce
("
H
2O
)
Figure 3.14: Pleat Coefficient Graph for a 20?x20?x1? FM1 Filter with 42 Pleats.
Table 3.2: Summary of Filters Employed
Filter Depth Width Height Pleat Count Media Type
A 0.85" (1") 19.5" (20") 19.5" (20") 22 FM2
B 1.75" (2") 19.5" (20") 19.5" (20") 16 FM2
C 0.85" (1") 19.5" (20") 19.5" (20") 14 FM1
D 0.85" (1") 19.5" (20") 19.5" (20") 19 FM1
E 0.85" (1") 19.5" (20") 19.5" (20") 23 FM1
F 0.85" (1") 19.5" (20") 19.5" (20") 28 FM1
G 0.85" (1") 19.5" (20") 19.5" (20") 32 FM1
H 0.85" (1") 19.5" (20") 19.5" (20") 37 FM1
I 0.85" (1") 19.5" (20") 19.5" (20") 42 FM1
J 0.85" (1") 19.5" (20") 19.5" (20") 47 FM1
K 0.85" (1") 19.5" (20") 19.5" (20") 55 FM1
L 1.75" (2") 19.5" (20") 19.5" (20") 19 FM1
M 1.75" (2") 19.5" (20") 19.5" (20") 34 FM1
N 3.5" (4") 19.5" (20") 19.5" (20") 19 FM1
O 0.85" (1") 19.5" (20") 19.5" (20") 19 FM3
P 0.85" (1") 19.5" (20") 19.5" (20") 32 FM3
Q 1.75" (2") 19.5" (20") 19.5" (20") 19 FM3
R 1.75" (2") 19.5" (20") 19.5" (20") 32 FM3
S 1.75" (2") 19.5" (20") 19.5" (20") 56 FM5
T 3.5" (4") 19.5" (20") 19.5" (20") 12 FM4
54
The resulting coefficient plots for all 20?x20?x1? FM1 filters with pleat counts
varying between 14 and 55 pleats per filter are graphed in Figure 3.15. The equation
listed beside each plot indicates the pleat coefficient value and the degree of fit. As
expected, the pleat coefficient?s magnitude increased as more pleats were incorporated
into a filter due to heighten friction inside the pleat. Table 3.3 presents an inventory of
the filters, geometric parameters, calculated pleat coefficients, and R-squared fit.
y = 1.79x R2 = 0.999
y = 2.50x R2 = 0.999
y = 3.33x R2 = 0.999
y = 4.10x R2 = 0.999
y = 4.96x R2 = 0.999
y = 5.57x R2 = 0.999
y = 6.44x R2 = 0.999
y = 7.80x R2 = 0.999
y = 1.32x R2 = 0.999
0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0 0.02 0.04 0.06 0.08 0.1 0.12
??V42 (" H2O)
Ob
ser
ve
d D
iff
ere
nc
e (
" H
2O
)
Filter Type C
Filter Type D
Filter Type E
Filter Type F
Filter Type G
Filter Type H
Filter Type I
Filter Type J
Filter Type K
Figure 3.15: Pleat Coefficient Plots for 20?x20?x1? Filters
55
Table 3.3: Summary of Pleat Coefficients
Filter Pleats PO PD PL PH Beta Kp R2
(-) (-) (ft) (ft) (ft) (ft) (rad) (-) (-)
A 22 0.074 0.061 0.071 1.625 0.521 2.083 0.9761
B 16 0.102 0.137 0.146 1.625 0.348 1.893 0.9498
C 14 0.116 0.042 0.071 1.625 0.819 1.329 0.9991
D 19 0.086 0.057 0.071 1.625 0.604 1.791 0.9998
E 23 0.071 0.062 0.071 1.625 0.499 2.501 0.9998
F 28 0.058 0.065 0.071 1.625 0.410 3.335 0.9995
G 32 0.051 0.067 0.071 1.625 0.358 4.104 0.9998
H 37 0.044 0.068 0.071 1.625 0.310 4.960 0.9997
I 42 0.039 0.068 0.071 1.625 0.273 5.573 0.9999
J 47 0.035 0.069 0.071 1.625 0.244 6.442 0.9998
K 55 0.030 0.070 0.071 1.625 0.209 7.802 0.9997
L 19 0.086 0.140 0.146 1.625 0.293 2.311 0.9794
M 34 0.048 0.144 0.146 1.625 0.164 5.867 0.9974
N 19 0.086 0.289 0.292 1.625 0.147 3.506 0.9992
O 19 0.086 0.059 0.071 1.625 0.604 1.837 0.9932
P 32 0.051 0.067 0.071 1.625 0.358 3.938 0.9737
Q 19 0.086 0.140 0.146 1.625 0.293 2.466 0.9612
R 32 0.051 0.144 0.146 1.625 0.174 5.116 0.9979
S 56 0.029 0.145 0.146 1.625 0.099 10.066 0.9906
T 12 0.135 0.284 0.292 1.625 0.232 1.881 0.9850
Based on this data, an empirical coefficient of friction for flow through a pleat
was formulated. Coefficients of friction are functions of Reynolds number,
dimensionless geometric ratios, or both. Reynolds number has a prominent effect on the
coefficient only when laminar flow is present. The flow was almost always turbulent for
the test conditions encountered; therefore, the Kp coefficient was based solely on
geometric configuration.
From the partial solution to the momentum and mechanical energy balanced
provided earlier, the pleat coefficient should be related to the function (1/?)2. Figure 3.16
is a plot of each experimentally-determined coefficient versus the function. The function
does not have a direct correlation to the observed coefficients. In particular, three distinct
56
trends were observed indicating an additional factor must be included. This discrepancy
is to be expected due to simplifying assumptions that were made in order to
simultaneously solve the mechanical and momentum balances. A general power law
trend was visualized between the function and the pleat coefficients. The dashed lines
were functions possessing the generic formula y=mx0.67.
0
2
4
6
8
10
0 10 20 30 40 50
(1/?)2 (-)
Em
pir
ica
lly
-D
ete
rm
ine
d K
p (
-)
Figure 3.16: Pleat Coefficient Graph
The formula was reduced to contain only the 1/? term in order to simplify the
modeled coefficient. The scaling component Z was chosen to be 4/3 (x2 * x0.67 ? x4/3) to
eliminate the power law fit. For future reference, the function (1/?)4/3 will be referred to
by the Greek letter ?. The plotted data was further refined by indicating the data points
that corresponded to 1?, 2?, and 4? deep filters. Figure 3.17 was the resulting graph.
57
y = 1.1076x
R2 = 0.9953
y = 0.5539x
R2 = 0.997
y = 0.3107x
R2 = 0.9971
0
2
4
6
8
10
0 5 10 15 20
(1/?)1.26 (-)
Em
pir
ica
lly
-D
ete
rm
ine
d K
p (
-)
1" Filters
2" Filters
4" Filters
Figure 3.17: A Linear Pleat Coefficient Plot
Figure 3.17 indicates that the depth of the filter is an influential factor in
determining the pleat coefficient. Unlike the one inch filters, the pleat coefficients for the
two and four inch are greatly overestimated by ? alone. It is hypothesized that ?
corresponds to the resistance created by the turn and separation of air in the pleat, but it
does not fully account for the area available to make this maneuver. Due to the
increased spacing within the two and four inch filters, the air flow is allowed to gradually
slow and expand which reduces friction. This in turn leads to a lower pleat coefficient.
The pleat coefficient is accurately modeled by adding a dimensionless coefficient ? to
account for the available area for the pleats to occupy.
Kp = ?? (3.4)
? = (1/?)4/3 (3.5)
? = 0.11(FHD/FD) (3.6)
FHD = (2FHFD) / (FH + FD) (3.7)
58
y = 0.996x
R2 = 0.9956
0
2
4
6
8
10
12
0 2 4 6 8 10 12
?? (-)
Em
pir
ica
lly
-D
ete
rm
ine
d K
p (
-)
Figure 3.18: Correlation Plot between Empirical and Modeled Pleat Coefficients
III.2.5. Reevaluate the Pleat Tip Contraction and Expansion
The model assumed the contraction and expansion created by the pleat tip was
adequately modeled by Equation 2.12 & 2.13. The model and experimental data were
reanalyzed while ignoring the pleat tip contribution. Returning to the proposed model
(Equation 3.2), exclusion of the pleat tips removes the coefficients KC and KE as well as
the velocities into the pleats (V3) and out of the pleats (V5). The reformulated model can
be written as:
?PT = ? ? [(2KG + KP)V22 ] + AV3+ BV32 (3.8)
Using same method as described in Section D, the model was rearranged into a
linear form and the pleat coefficient of friction was empirically-determined for a given
filter based on experimental resistance data. The most accurate coefficient of friction
formula was determined to be:
59
Kp = 0.07903(FHD/FD)( 1/?)1.29 (3.9)
The following graph shows the results between the empirically-determined and modeled
pleat coefficients.
y = x
R2 = 0.9164
0
2
4
6
8
10
12
14
16
18
0 2 4 6 8 10 12 14 16 18
0.079(FH/FD)0.935(1/?)1.29 (-)
Em
pir
ica
lly
-D
ete
rm
ine
d K
p (
-)
Figure 3.19: Modified Correlation Plot
The pleat coefficient could not be properly fitted after the pleat tips were
excluded. A telling aspect was found in the three points denoted with an ?X?. These
three markers showed the largest deviation from the model. These markers correspond to
filters type P, R, and S (going left to right on the graph). These filters possessed the
largest pleat tip blockage. Filters P and R were built with the thicker FM3 media and had
a pleat count of 32. Filter S used the 1 mm thick FM5 media with 56 pleats. Since the
effects of the pleat tip were being adsorbed into the pleat coefficient, it was natural to
observe a higher than average pleat coefficients in filters with a larger pleat tip blockage.
60
This result furthered strengthened the assumption that pleat tips play an active role in the
pressure drop.
During the subsequent research presented in Chapter V through VII, the channel
of particulate matter around the pleat tip can be visualized when a filter is subjected to
dust loading. This indicates that the air flow is diverging around the material and not
passing through the tip. The Appendix showcases the occurrence of the channeling
through a series of photographs.
III.3. Utilization and Discussion of the Model
III.3.1. Pleating Curve
A conventional pleating ?U? curve was generated by modeling the 20?x20?x1?
filters with FM1 media constants. The graph, Figure 3.20, was calculated by holding
velocity constant at 500 fpm and varying the pleat count from twelve to sixty pleats per
filter. The model predictions were plotted as lines while the circles represent the
observed total pressure drop for filter types C through K. The modeled resistances due to
the pleat contraction and expansion were left off the graph for clarity because their
contribution was very small (< 0.002? H2O). The observed pressure losses were fitted
with error bars signaling plus or minus five percent of their value. The total modeled
resistance fell within the error bars of the experimental data.
61
0
0.05
0.1
0.15
0.2
0.25
0.3
0.35
0.4
0.45
0.5
10 15 20 25 30 35 40 45 50 55 60
Pleat Count (Pleats / Filter)
Pr
es
su
re
Dr
op
("
H
2O
)
Measured Filter Resistance
Housing Losses
Media Losses
Pleat Losses
Modeled Filter Resistance
Figure 3.20: Pleating Curve and Individual Resistances
The modeling results of Figure 3.20 confirm previously published general trends
regarding pleated filters. The resistance versus pleat count graph clearly indicates a
lowest obtainable resistance (LOR) corresponds to an optimal pleat count. The LOR
occurred due to the tradeoff of media resistances for viscous resistances as the pleat count
was increased. The graph also partly corroborated with Chen?s assertion that pleat tip
blockage could be ignored; however, FM1 was a thin media (~ 0.5mm) and the same
claim can not be made for all media types.
A novel feature of the model is the inclusion of a distinct term for the housing
losses. Previous research usually ignores the housing effects or their influence is masked
because they are simply combined in with the geometric losses. This has a two-fold
disadvantage from a filter design perspective. First, the housing resistance is wrongfully
attributed to other geometric design parameters such as pleat height or pleat pitch. This
62
artificially augments the actually influence of these geometric parameters leading to
errors in design estimates. Second, the nature of the housing resistance acts in a different
manner than the other geometric losses. The structural pressure drop serves as a fixed
resistance and does not change with pleat count. All other geometric resistances increase
with pleat count. A small increase due to the incorporation of the grating losses into the
geometric resistances becomes further skewed as pleat count rises. By identifying and
separating the grating contribution, the model provides a better understanding of the
individual resistances allowing enhanced analysis, improved design, and increased
performance.
The model also identifies various design strategies that could minimize material
costs, minimize energy consumption, or maximize a filter?s useful life while maintaining
an acceptable initial pressure drop. Figure 3.20 indicates the presence of a semi-flat
valley between 27 and 47 pleats where these design goals can be exploited. The initial
pressure drop hovers around the acceptable starting resistance of 0.25? H2O in this valley.
At the low pleat count end, a filter with 27 pleats can be constructed that will perform at
an adequate pressure drop without incurring a higher production cost due to increased
material costs. This is the traditional design point of most filter manufacturers. A more
energy efficient filter can be constructed by increasing pleat count to the LOR of 36
pleats. By increasing the pleat count further, the high end count of the valley offers the
largest filtration area that can be incorporated into the filter without sufficiently
increasing the initial pressure drop. The ability to locate and work within this valley
demonstrates the utility of an accurate pressure drop model to a filter designer.
63
III.3.2. Location of the Optimal Pleat Count
Although it can be used as a general heuristic, the optimal pleat count does not
simply exist where the media and geometric resistances are equal. The optimal pleat
count in Figure 3.20 is 36 pleats, yet the media and pleat resistances are equal at 38
pleats. The lowest obtainable resistance and the optimal pleat count occur when the total
pressure drop?s rate of change with respect to pleat count is zero. Since Equation 3.2 is
composed of polynomials, the model can be broken down into individual terms and the
first derivative with respect to pleat count can be readily computed.
1st Derivative:
( ) ( ) ( ) ( ) ( ) ( )
CCC
P
C
E
C
C
C
G
C
F
P
BV
P
AV
P
VK
P
VK
P
VK
P
VK
P
P
?
?+
?
?+
?
?+
?
?+
?
?+
?
?=
?
?? 24423212321232121 ????
(3.10)
654321 TermTermTermTermTermTermPP
C
T +++++=
?
??
The grating contribution?s (Term 1) first derivative is zero because it is not a
function of pleat count. The first derivative of the viscous/geometric effects (Terms 2, 3,
and 4) are always positive while the media resistances (Terms 5 and 6) have continuously
negative first derivatives with respect to pleat count. Since the left hand side of Equation
3.10 equals zero at the optimal pleat count, it can be rearranged to give Equation 3.11.
Equation 3.11 and Figure 3.21 clearly indicates the balance between viscous and media-
dominated resistances.
( ) ( )
CC
PEC
P
BVAV
P
VKVKVK
?
+?=?
?
?
??
?
?
++?? 244232323
21
?? (3.11)
64
-0.04
-0.035
-0.03
-0.025
-0.02
-0.015
-0.01
-0.005
0
0.005
0.01
0 10 20 30 40 50 60 70 80
Pleat Count (Pleats / Filter)
Ra
te
of
Ch
an
ge
("
H2
O
/ P
lea
t)
Geometric Derivatives
Media Derivatives
Total Pressure Derivative
Figure 3.21: Optimal Pleat Count Location
III.3.3. Influence of Design Parameters
The model has established the ability to accurately portray the cause and effect
relationship of adding more pleats to a filter design. It can also be used to calculate the
optimal pleat count and determine the magnitude of the viscous and media derivatives.
Pleat count, however, is just one of the many design factors that can be manipulated in a
filter. Previous models identified the following design variables within a pleated filter:
pleat count, face velocity, filter height, filter width, filter depth, fluid density, fluid
viscosity, solid volume fraction, media thickness, fiber radius, Knudsen number, media
permeability, and dirt loading. In this section, the model will be employed to investigate
the influence of face velocity, filter depth, media thickness, and media constants. The
remaining variables were not directly examined due to reasons described below.
65
Solid volume fraction, fiber radius, Knudsen number, and media permeability
were lumped together as general media constants in this research. The individual effects
of each variable can be related to the empirical constants through theoretical equations
such as the Carmen-Kozeny (Rivers and Murphy 2000) or the porous media permeability
(PMP) equation (Cahela and Tatarchuk 2001). By studying the response of the generic
media constants, one can deduce the effects these parameters would have on the overall
performance.
The influence of density and viscosity can also be readily factored in, but their
effects were not analyzed in this study. A change in these fluid properties has an
identical influence on both the viscous and media terms, and thus shifts the whole ?U?
curve up or down. Furthermore, it would be more beneficial to study the effect of
temperature on performance since density and viscosity are dependent on the temperature
of the fluid. Although this was not explored either, a general assessment would be a rise
in temperature will result in a decrease in air density and as thus a decrease in the overall
flow resistance of a filtration system. This observation was previously made in Filters
and Filtration Handbook (Dickenson 1992). The model could also theoretically be
utilized to study pleated filters in other filtration projects with different fluids such as
water or oils. Last, the effect of dirt loading will discussed in Chapters 5 through 7.
1. Effects of Face Velocity
Face velocity universally influences both the viscous and media terms much like
air density and viscosity. Unlike the fluid properties, face velocity is an operational
condition that is more readily controlled by the system user. HVAC systems primarily
run at a set velocity of 300 fpm for residential homes or 500 fpm for commercial
66
buildings, but other applications that utilize pleated filter operate at different ranges.
Cathode air filters, for example, typically run at 0 to 200 fpm depending on the fuel cell
power output. It is intuitive from Equation 2.1 that increasing the face velocity will result
in a higher resistance; however, the general impacts of face velocity on the pleating curve
have not previously been reported.
The effects of face velocity were study by modeling a 20?x20?x1? FM1 media
filter as air speeds rose from 100 fpm up to 700 fpm. At low face velocities, the curve
resembles more of a line than the traditional ?U? shape. The curve gains its distinctive
profile by increasing face velocity that in turn heightens both viscous and media effects.
The optimal pleat count is shifted to a lower pleat count because the viscous terms are
second order functions of velocity; thus, they are able to overtake the media effects in a
lower pleat count regime.
67
0
0.15
0.3
0.45
0.6
0.75
10 20 30 40 50 60
Pleat Count (Pleats / Filter)
Pre
ssu
re
Dr
op
("
H
2O
)
100 fpm 200 fpm
300 fpm 400 fpm
500 fpm 600 fpm
700 fpm
Figure 3.22: Effects of Face Velocity on Pleating Curve
Common blowers typically operate at set face velocity, but energy efficient
variable air volume (VAV) HVAC systems will cycle between 100 and 700 fpm
throughout the course of the day. In a similar fashion, compressors on fuel cells will
ramp up and down based on the required power load. Since the optimal pleat count varys
with face velocity, the model can be used as a design tool to construct a filter with a pleat
count corresponding to the lowest energy cost over the course of the operation.
2. Effects of Media Thickness
To examine the effects of various media thicknesses on the pressure drop
behavior of a pleated filter, individual pleating curves were generated for various
thicknesses between 0.5 and 3.5 mm while holding the other design parameters constants.
The model makes predictions based on a set flow rate (500 fpm), pleat length (2?
68
nominal), and fixed resistance through the media. A fixed resistance means the overall
resistance for flow across the media is constant. Idealistically, this occurs when an
increase in thickness is counteracted by increase in permeability to maintain a set
pressure drop across the media according to Darcy?s Law. A fixed resistance can simply
be modeled by keeping the media constants steady (A=10x10-4 and B=17.5x10-7) since
Darcy?s Law is not utilized. Modeling a fixed resistance system allows the individual
effect of media thickness to be discerned without observing additional phenomena. The
??? marks the optimal pleat count for each plot.
0
0.2
0.4
0.6
0.8
1
0 10 20 30 40 50 60
Pleat Count (Pleats / Filter)
Pre
ssur
e D
rop
("
H2O
)
0.5 mm
1.5 mm
2.5 mm
3.5 mm
Figure 3.23: Effects of Media Thickness on Pleating Curve
An increased media thickness steepens the viscous-regime and raises the overall
resistance of the U curve due to a two-prong effect. The obvious reason for the shift is a
thicker media creates a larger pleat tip blockages and higher resistances. The more
69
influential effect, however, is a heightened rate of closure for the pleat opening. A
thicker media occupies more space within a filter and allows fewer pleats to be placed
into a filter before the pleat openings become constrained. The synergy of these two
influences sizably increases the magnitude of the geometric terms leading to the sharp
rise in the viscous-dominated region. This causes the optimal pleat count to occur at a
much lower available media. Since optimal pleating occurs at a lower count, the filter
can not amass a sufficient filtration area to decrease the media velocity. The
corresponding heighten pressure drop through the media causes the overall resistance to
remain high.
The leftward shift of the optimal pleat count and the overall increase in the lowest
obtainable pressure drop can be visualized by studying the derivatives of Figure 3.23.
Figure 3.24 shows the sizable increase of the viscous derivatives as thicker media is
employed. Only one media derivative is presented because media thickness barely
affects the media terms. A slightly change in the media terms does occur from the
increased media area consumed to make the thicker pleat tips, but this negligible effect
can be seen by the convergence of each plot?s media-dominated section in Figure 3.23.
70
-0.04
-0.02
0
0.02
0.04
5 15 25 35 45 55
Pleat Count (Pleats / Filter)
Ra
te
of
Ch
an
ge
("
H
2O
/ P
lea
t)
Media Derivative
0.5mm Viscous Derivative
1.5mm Viscous Derivative
2.5mm Viscous Derivative
3.5mm Viscous Derivative
Figure 3.24: Effects of Media Thickness on Model?s Derivatives
Several of the previous published studies neglect the effects of pleat tip blockage
into and out of the pleats. Chen et al. (1996) states that the flow resistance due to the
media tips can be ignored in triangular pleat systems. This assumption holds
approximately true for a thin media. The pleat tip blockage for a 0.5 mm thick media
never accounts for more than two-thirds of a percent of the total pressure loss (Figure
3.25). The same can not be said for a thicker media. A filter composed of 3.5 mm thick
media will accrue roughly ten percent of its total pressure drop from entering and exiting
the pleat tips. Figure 3.25 is compiled from data generated while modeling Figure 3.23.
71
0
1
2
3
4
5
6
7
8
9
10
5 15 25 35 45 55 65
Pleat Count (Pleats / Filter)
Co
ntr
ibu
tio
n t
o T
ota
l R
es
ist
an
ce
(%
) 0.5 mm
1.5 mm
2.5 mm
3.5 mm
Figure 3.25: Modeled Pleat Tip Contribution to Total Resistance
20?x20?x1? Filters at 500 fpm
3. Effects of Filter Depth
The model was employed to study the effects created by varying the filter depth
while holding constant the flow rate (500 fpm), media constants (A = 10x10-4; B =
17.5x10-7), and media thickness (0.5 mm). Increasing filter depths directly translates to
increasing pleat length. The results presented in Figure 3.26 indicate that increasing filter
depth decreases the optimal pleat count and lowest obtainable resistance. This
observation was previously made in Chen?s research.
72
0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1
0 10 20 30 40 50 60
Pleat Count (Pleats / Filter)
Pre
ssu
re
Dr
op
("
H
2O
)
1" Filter Depth
2" Filter Depth
4" Filter Depth
Figure 3.26: Modeled Effects of Filter Depth on Pleating Curve
A variation of filter depth impacts both the media and the viscosity terms. The
additional pleat length increases the available filtration area and quickly removes the
influence of the media term at a low pleat count. This leads to a decreased LOR because
the viscous terms? magnitudes are relatively small at the low pleat counts. As pleat count
rises, the growth of pleat resistance in deeper filters outpaces the shallower filters due to
heighten friction. This contributes to the steeper pressure rise in the viscosity-dominated
region.
73
-0.03
-0.025
-0.02
-0.015
-0.01
-0.005
0
0.005
0.01
0 10 20 30 40 50 60 70
Pleat Count (Pleats / Filter)
Ra
te
of
Ch
an
ge
("
H
2O
/ P
lea
t)
1" Media Derivative
1" Viscous Derivative
2" Media Derivative
2" Viscous Derivative
4" Media Derivative
4" Viscous Derivative
Figure 3.27: Effects of Filter Depth on Model Derivatives
Although the influences of filter design variables on total pressure drop are
conventionally plotted versus pleat count, it is beneficial to compare resistances versus
available filtration area when dealing with variations in filter depth. The real design issue
centers not on the number of pleats that can be incorporated into a filter but on the
available filtration area of the filter. Pleat count usually directly translated to available
filtration area, but this is not true in filters of different depths. The same pleat count in a
4? deep filter translates to four times the area of its 1? counterpart.
74
0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1
0 10 20 30 40 50 60
Filtration Area (sq. ft)
Pre
ssu
re
Dr
op
("
H
2O
)
1" Filter Depth
2" Filter Depth
4" Filter Depth
Figure 3.28: Effects of Filter Depth on Performance Curve
As seen in Figure 3.28, increasing filter depth reduces total pressure drop while
greatly increasing the available filtration area. The previous plot is misleading in the fact
that it appears that a 1? and 2? filter, given the right number of pleats, can operates at a
lower resistance than a 4? filter. The 4? filter is clearly able to operate at a lower
pressure drop over the entire range of available media area.
4. Effects of Media Constants
Figure 3.29 was generated by varying the media constants at a fixed flow rate
(500 fpm), media thickness (0.0032 ft [1 mm]), and pleat length (1.75 inches nominal)
while increasing pleat count. The ??? marks the optimal pleat count.
75
0
0.25
0.5
0.75
1
1.25
1.5
0 15 30 45 60 75
Pleat Count (Pleats / Filter)
Pre
ssu
re
Dr
op
("
H
2O
)
A = 1 x 10^-4; B = 1 x 10^-7
A = 5 x 10^-4; B = 5 x 10^-7
A = 10 x 10^-4; B = 10 x 10^-7
A = 20 x 10^-4; B = 20 x 10^-7
A = 30 x 10^-4; B = 30 x 10^-7
Figure 3.29: Effects of Media Resistance on Pleating Curve
Figure 3.29 indicates that an increase in the media constants results in a higher
optimal pleat count and higher optimal resistance. A change in the media resistance
solely influences the media term and has no bearing on the filter?s viscous terms unlike
media thickness, face velocity, and pleat length. The media term?s derivative is therefore
greatly increased while the viscous term remains the same (Figure 3.30). The optimal
pleating arrangement must be shifted right to allow room for the magnitude of the
viscosity?s derivative to counteract the increase in the media derivative. Even though this
shift increases the available filtration space, it still does not provide sufficient area to
reduce the media velocity and the overall media resistance. The result is an increase in
optimal resistance. It should be noted that the plots begin to converge in the viscosity-
76
dominated region. This is expected because the media term eventually approaches zero
as pleat count increases; thus, eliminating the effects of media resistance from the plots.
-0.05
-0.04
-0.03
-0.02
-0.01
0
0.01
0.02
0 15 30 45 60 75
Pleat Count (Pleats/Filter)
Ra
te
of
Ch
an
ge
("
H
2O
/Pl
eat
)
Geometric Derivative
Media Derivative (A = 1 x 10-4; B = 1x10-7)
Media Derivative (A = 5 x 10-4; B = 5x10-7)
Media Derivative (A = 10 x 10-4; B = 10x10-7)
Media Derivative (A = 20 x 10-4; B = 20 x10-7)
Media Derivative (A = 30 x 10-4; B = 30x10-7)
Figure 3.30: Effects of Media Resistance on Model?s Derivatives
An interesting media design paradox occurs between media permeability and
media thickness. A decrease in media thickness leads to a smaller LOR as shown in the
media thickness section. In order to create a thinner media, the material must be
compressed. Compression leads to a decrease in media permeability and an increase in
the media constants. An increase in media constants results in a rise in the LOR. Thus, it
is uncertain if compressing the media will lead to an overall reduction or increase in the
lowest obtainable resistance. Future research will be performed to study the impact of
media compression on media constants.
77
III.3.4. Limitations of the Model
Although constructed over a wide range of parameter space, it should be noted
that there are limitations to the accuracy of the model as a design tool. The pleat
coefficient is based on experimental data obtained for 20? x 20? face dimensions. The
model, in theory, should be applicable to other filter dimensions but additional research
needs to be conducted. Filter with depths greater than four inches were not studied. Only
general estimations of viscous effects created by filters with depths greater than four
inches can be made based on observed trends. The same statement can be said about
pleat counts above 60 per filter and media thickness above 2 mm. The experimental data
upon which the research was based did not explore face velocities above 1000 fpm, yet
HVAC filters do not typically operate above 500 fpm so this is only a minor limitation.
78
CHAPTER IV: INITITAL PRESSURE DROP OF
MULTI-ELEMENT STRUCTURED ARRAYS
IV.1. Introduction
Multi-Element Structured Arrays (MESA?s) are a novel platform that integrates
multiple pleated filter elements into a single filtration system. The MESA?s concept is an
extension of the pleated filter design. A pleated filter extends the media area and reduces
the resistance by transforming a flat material into a three dimensional filter. The MESA
takes a flat, pleated filter and turns it into a three dimensional array of filters to further
extend the filtration area and reduce the pressure drop. The idea is a derivation of the
common V-Bank filtration systems utilized to house mini-pleat filtration media. Unlike
V-Banks, MESA?s use off-the-shelf filter element that can be inserted into the array?s
framework.
IV.1.1. Multi-Element Structured Array Schematic
Figure 4.1 showcases the major dimensions and parameters of a Multi-Element
Structured Array. All parameters associated with a single filter remain unchanged. A
triangular ?slot? is created when the filters are angled into place. The slot?s dimensions
depend on the number of elements used. A general schematic of a two element array is
shown below, but the same nomenclature can be applied to arrays with additional
elements. Included in Figure 4.1 is a photograph of two elements loaded into a clear,
polycarbonate filter box.
79
Figure 4.1: General Schematic of a Multi-Element Structured Array
The schematic above depicts a filter box loaded with two 20?x20?x2? filter
elements. An array constructed with two filters will be referred to as possessing a ?V?
configuration. Three additional array configurations were utilized in this chapter. For
future reference, arrays configurations will be designated based on their appearance as
illustrated in Figure 4.2.
80
Figure 4.2: Array Configurations (A) ?W? (B) ?WV? Configuration (C) ?WW?
IV.1.2. Parameters
The system parameters of a Multi-Element Structured Array are specified by the
user?s needs or dictated by the ductwork. The pleat parameters are calculated in the same
manner outlined in Chapter 3. The slot parameters are functions of the system
parameters and can be solved by a system of equations.
System Parameters
Filter Height (FH): Dictated by the Duct Height
Pleat Height (PH): Dictated by the Duct Height
Filter Width (FW): Dictated by the User
Slot Height (SH): Dictated by the User (equal to Filter Width)
Filter Depth (FD): Specified by the User
Pleat Length (PL): Specified by the User (equal to Filter Depth)
Pleat Count: Specified by the User
Grating Blockage: Specified by the User
Media Thickness (MT): Specified by the User (Property of Media)
Permeability (A & B): Specified by the User (Property of Media)
Element Count (EC) Specified by the User
81
Slot Parameters
Edge Blockage (FB) Solved by System of Equation
Slot Pitch [?] Solved by System of Equation
Slot Opening (SO) = Duct Width / # Filters ? 2 x Edge Blockage
Slot Depth (SD) = sin-1(?Slot Opening / Filter Width)
Blockage System of Equations
Figure 4.3 is a general V array schematic used to solve the system of equations.
The element count, the duct?s dimension, and the depth of each filter element are known.
The remaining dimensions of the array can be simultaneously solved by the following set
of equations.
Known: Duct Width (DW)
Element Count (EC)
Filter Depth (FD)
Filter?s Width (FW)
Computed: Opening (BO) = Duct Width / # Filters
Unknown: Slot Pitch (? )
Element Blockage (FB)
Space Variable (FE)
Three equations: (I) cos(?) = FB / FD
(II) cos( ?? - ?) = FB / FE
(III) sin (?) = ? BO / (FW + FE)
82
Figure 4.3: General Diagram of Multi-Filter Array
Table 4.1: Blockage (FB) Tabulations
Element Width Element Depth V Array W Array WV Array WW Array
19.5" 1" 0.0628' 0.0693' 0.0703' 0.0706'
19.5" 2" 0.1324' 0.1439' 0.1454' n/a
19.5" 4" 0.2753' 0.2909' n/a n/a
14.5" 1" 0.0552' 0.0680' 0.0698' 0.0704'
9.5" 1" n/a 0.0639' 0.0685' 0.0698'
Table 4.2: Alpha Tabulations (in radians)
Element Width Element Depth V Array W Array WV Array WW Array
19.5" 1" 0.479 0.209 0.124 0.082
19.5" 2" 0.447 0.259 0.169 n/a
19.5" 4" 0.337 0.073 n/a n/a
14.5" 1" 0.677 0.284 0.167 0.110
9.5" 1" n/a 0.432 0.162 0.078
IV.1.3. Proposed Flow through a Multi-element structured array
In order to develop the model, a pathway for airflow through the array had to be
proposed. The path consisted of eleven areas of varying accessibility for air to flow
through a MESA (Figure 4.4). The upstream flow in the duct is assumed uniform. The
air velocity increases at the front of the array due to the contraction created by the
83
element?s edges. The air is channeled around the edges and into the array?s slot(s). In
the slot, the air diverges and expands as it reaches the face of each filter element.
While in the filter element, the air is assumed to flow in an identical path outlined
in the single filter flow profile (Chapter III.1.3). The air is contracted due to the filter
housing and pleat tip blockage. It then travels down the filter?s pleats before entering the
media. The air passes through the media and out of the filter element in a reverse
manner. The air converges as it exits the elements and enters into the downstream slot.
The exit from the array causes a further increase in area and velocity decrease. The air
finally uniformly redistributes in the downstream duct.
Figure 4.4: Proposed Flow Profile
84
Area Calculations:
Area 1 (Area 11):
Duct Width x Duct Height
Area 2 (Area 10):
(Duct Width x Duct Height) ? (Edge Blockage x Element Height x # Element)
Area 3 (Area 9):
Element Width x Element Height x #Element
Area 4 (Area 8):
[Element Width x Element Height x (1 -% Blockage)] x #Element
Area 5 (Area 7):
[(Element Wid. x Element Ht.) ? # Pleat x Pleat Tip x Pleat Height] x # Element
Area 6:
[(Pleat Count x Pleat Height) x (2 Pleat Length ? Media Loss)] x # Element
IV.1.4. Modeling a Multi-Element Structured Array
The MESA model was developed as an extension of the single pleated filter
model. The total flow resistance through a Multi-Element Structured Array was
compiled as a summation of eleven discrete resistances. The individualistic resistances
were formulated by applying Bernoulli?s equation or Forchheimer-extended Darcy?s Law
to each of the eleven flow sections.
Flow into Slot: ?P1 = ? ?[(V22 ? V12) + KCBV22 ]
Flow from Slot Inlet to Filter Face: ?P2 = ? ?[(V32 ? V22) + KS1V32 ]
Across Front Grating: ?P3 = ? ?[(V42 ? V32) + KGV32 ]
Flow from Grating to Pleat Inlet: ?P4 = ? ?[(V52 ? V42) + KCPV52 ]
Flow from Pleat Inlet to Media Surface: ?P5 = ? ?[(V62 ? V52) + KP1V52 ]
Flow through Media: ?P6 = AV6 + BV62
Flow from Media Surface to Pleat Outlet: ?P7 = ? ?[(V72 ? V62) + KP2V72 ]
Expansion from Pleat Outlet into Grating: ?P8 = ? ?[(V82 ? V72) + KEPV72 ]
Across Back Grating: ?P9 = ? ?[(V92 ? V82) + KGV92 ]
Flow from Filter Face to Slot Outlet: ?P10 = ? ?[(V102 ? V92) + KS2V102 ]
Flow out of Slot: ?P11 = ? ?[(V112 ? V102) + KEBV112 ]
?PT = ??Pi = ?P1 + ?P2 + ?P3 + ?P4 + ?P5 + ?P6 + ?P7 + ?P8 + ?P9 + ?P10 + ?P11
(4.1)
85
Terms ?P3 through ?P9 were previously identified and verified in the single filter
section. (Of note: the nomenclature for coefficients KC and KE were changed to KCP and
KEP to indicate the sudden contraction or expansion due to the pleat tips). KCB and KEB
also referred to a sudden contraction and expansion, but these coefficients referenced the
flow change in and out of the array.
The new coefficients KS1 and KS2 accounted for friction encountered in the slot(s)
upstream and downstream of the filters. The slot(s) can be thought of as macro-pleats
due to their similar geometry; therefore, it is not surprising that the momentum and
mechanical energy balance could not be simultaneously solved for the slot(s) geometry
either. The partial solution to the balances indicated the coefficient should be a function
of slot pitch (?).
An empirical approach was taken to distinguish the coefficients due to the
inability to theoretically solve for them. The two constants were merged into one
coefficient (KS) since the individual influences of KS1 and KS2 could not be separated and
discerned. After making the appropriate substitutions and utilizing the
upstream/downstream symmetry, the series of equations were reduced and re-written into
the following Multi-Element Structured Array model:
?PT = ? ?[(KCB + KEB )V22 + (2KG+ KS)V32 + (KCP + KEP + KP)V52] + AV6 + BV62
(4.2)
IV.2. MESA Experimental
The experimental objective was to verify the use of the nine parameters that
comprise the Multi-Element Structured Array model. A, B, KG, KCP, KEP, and KP were
proven valid or empirical determined by the research presented in the previous chapter.
The present objective was to establish the model?s remaining three terms: KCB, KEB, and
86
KS. The coefficients KCB and KEB were proven to be accurately model by a sudden
contraction or a sudden expansion coefficient by mechanistically altering an array?s
blockage and measuring the responding deviation in pressure. The slot coefficient (KS)
was empirically developed by an analogous methodology used to formulate the pleat
coefficient. The process examined 32 arrays employing assorted media types, element
depths, element widths, pleat counts, and element counts to devise a robust coefficient.
IV.2.1. Entrance Coefficient of Friction (KCB)
The added resistance for entering the array can accurately be calculated by
Equation 2.11 using a friction coefficient computed by Equation 2.12. This assessment
was authenticated by modifying the blockage created by the front edge of the elements
and comparing the corresponding resistance to the computational predications. Unlike the
experimental approach used to verify the filter grating, the contraction created by the
array?s edge could not be modified by adding extra blockage. Several modifications to
increase the flow blockage were envisioned, yet each modification had secondary
influences that skewed other resistances or geometries. Instead of trying to increase the
blockage and monitor the responding pressure increase, the effects of the blockage were
removed and the decrease in resistance was observed.
The array?s entrance blockage was eliminated by adding a long, gradual
contraction to the front of the array. The gradual slope of the contraction removed the air
friction normally encountered when reducing the allowable flow area. Thus, the sudden
contraction and the resistance of the contraction were removed from the total pressure
drop. The overall drop in resistance was then compared to the expected resistance
87
computed by the sudden contraction coefficient (Equation 2.12) with the ratio
AFREE/ATOTAL equal to A2/A1.
Figure 4.5 illustrates a normal array configuration and the modified design. The
transition was created by adding a 19.5? (H) by 23? (W) board to each front edge. The
boards are highlighted below in blue. The boards were taped to the duct walls and the
element?s front edge to eliminate additional friction due to uneven surfaces. The filter
array had to be slightly positioned into the outlet section of the test rig to accommodate
the additional length of the front transitional boards, yet all elements of the system
remained between the pressure taps.
Figure 4.5: Illustration and Schematic of Flow
within a Normal (A) and Contraction Modified Array (B)
The experimental procedure was similar in manner to the one used in the grating
coefficient tests. A pressure drop curve was first recorded for the normal array geometry,
and then a second pressure drop curve was measured for the modified array entrance.
The test was conducted on a ?V? configuration array using elements with depths of two
and four inches. Figure 4.6 graphs the experimentally recorded data for a normal and
88
modified ?V? array constructed with 4? deep filter elements. The data points in the
enlarged area were outfitted with error bars of ?0.002? H2O.
Figure 4.6: Measured Pressure Drop for a Normal and Modified Array
Since the gradual contraction was of significant length and the overall decrease in
area remained small, the coefficient of friction and pressure drop of the transition were
approximately zero.
A = 0.01745(sin-1(0.275/1.625)) = 0.141
N = (1.625 - .275*2)/1.625 = 0.66
KGC = [(-0.0125N4 + 0.0224N3 ? 0.00723N2 + 0.00444N - 0.00745)(A3 - 2?A2 ? 10A)]
KGC = 5.5x10-3 ? 0
This meant that the observed decrease in resistance from Figure 4.6 could be directly
compared to the calculated resistance of the array blockage. The observed decrease due
to the modification closely correlated to the expected resistance created by a sudden
contraction (Figure 4.7); therefore, the viscous loss equation combined with the friction
coefficient for a sudden contraction accurately modeled the pressure drop created by the
elements edge walls.
89
0
0.002
0.004
0.006
0.008
0.01
0.012
0.014
0.016
0.018
0.02
0 150 300 450 600 750 900 1050
Face Velocity (fpm)
Pre
ssu
re
Di
ffe
ren
tia
l ("
H
2O
)
Computed Resistance [2" Deep Elements]
Computed Resistance [4" Deep Elements]
Observed Decrease [2" Deep Elements]
Observed Decrease [4" Deep Elements]
Figure 4.7: Observed and Modeled Pressure Drop Differences
IV.2.2. Exit Coefficient of Friction (KEB)
An analogous test was preformed to verify the use of a sudden contraction
(Equation 2.11) to model the pressure loss when air exits from the filter array. A normal
pressure drop curve was measured followed by a second pressure drop curve for a
modified design. The modified outlet design changed the sudden expansion into a
gradually transition. Since the same array is used in both experiments, the observed
difference between the two configurations can be compared to the calculated pressure
drop expected by a sudden expansion. The array was modified by adding a tail fin
composed of two 19.5? (H) by 23? (W) boards to the back of the filter?s edges. Figure
4.8 provides a general set-up for the experiment while Figure 4.9 presents the results.
90
Figure 4.8: Illustration and Schematic of Flow
within a Normal (A) and Expansion Modified Array (B)
Figure 4.9: Measured Pressure Drop for a Normal and Modified Array
The experiment was performed on a ?V? array loaded with 4 inch filters. Figure
4.10 indicates that the expansion out of the array can accurately be modeled by a sudden
expansion coefficient due to the good correlation between the computed and observed
pressure differences.
91
0.000
0.003
0.006
0.009
0.012
0.015
0 200 400 600 800 1000
Face Velocity (fpm)
Pre
ssu
re
Dr
op
("
H
2O
)
Observed Decrease
Computed Resistance
Figure 4.10: Observed and Modeled Pressure Drop Differences
IV.2.3. Slot Coefficient of Friction (KS)
The slot friction coefficient was formulated through the use of empirical data
spanning 32 MESA systems. Equation 4.2 was reorganized into the following form:
{?PT - ? ? [(KC1 + KE2)V22 + (2KG)V32 + (KC2 + KE1 + KP)V52] + BV6 + AV62} = KS
(??V32) (4.3)
Data relating ?PT versus face velocity data was acquired for a specific array. All
velocities in the above equation were calculated from the face velocity using the equation
of continuity. The friction coefficients were calculated based on known geometric
dimensions, and the media constants were experimentally determined. The slot
coefficient for a particular array was solved by plotting the calculated values on the left-
92
hand side versus the reference velocity term (??V32). The process was repeated for
various element types to improve the versatility of the coefficient.
The following graph demonstrated the procedure for a filtration array loaded with
six, 20?x20?x1? elements. Each element contained 32 pleats and was constructed with
FM1 media (Filter Type G). The black circles marked experimentally measured pressure
drop versus velocity data. The dashed line was a least-squared fit to the experimentally
measured data. The solid, black line was the modeled pressure loss due to known
coefficients. The hyphenated line represented the unaccounted pressure drop. It was
created by subtracting the solid line from the dashed line.
0
0.05
0.1
0.15
0.2
0.25
0.3
0.35
0.4
0 200 400 600 800 1000
Face Velocity (fpm)
Pre
ssu
re
Dr
op
("
H
2O
)
Measured Data
Regression Line
Model of Known Terms
Obserrved Difference
Figure 4.11: Pressure Drop Curves for a WV Array of 1? Filters
The hyphenated line was plotted versus ??V32 in Figure 4.12 below. A linear
line forced through the origin was fitted by Excel. The slot coefficient was calculated as
93
172.2 from the plot?s slope. This particular slot coefficient is only valid for a ?WV? array
configuration employing 20?x20?x1? elements.
y = 172.24x
R2 = 0.9995
0
0.05
0.1
0.15
0.2
0.25
0.3
0 0.0003 0.0006 0.0009 0.0012 0.0015 0.0018
??V32 (" H2O)
Ob
ser
ve
d D
iff
ere
nc
e (
" H
2O
)
Figure 4.12: Slot Coefficient Graph for a WV Array of 1? Filters
Thirty-two filtration arrays were utilized to investigate the effects of design
variation on the slot coefficient. The following table compiled the element types and
configurations used. All filter elements were modeled as single, pleated filters in the
previous chapter expect for Type X and Y. Type X and Y possessed widths less than
19.5? and were unable to be loaded as a single filter.
94
Table 4.3: Summary of Elements used in Slot Coefficient Study
Filter Depth Width Height
Pleat
Count
Media
Type Combinations
D 0.85" (1") 19.5" (20") 19.5" (20") 19 FM1 2x , 4x, 6x, & 8x
G 0.85" (1") 19.5" (20") 19.5" (20") 32 FM1 2x , 4x, 6x, & 8x
J 0.85" (1") 19.5" (20") 19.5" (20") 47 FM1 2x , 4x, 6x, & 8x
B 1.75" (2") 19.5" (20") 19.5" (20") 16 FM2 2x , 4x, & 6x
L 1.75" (2") 19.5" (20") 19.5" (20") 19 FM1 2x , 4x, & 6x
S 1.75" (2") 19.5" (20") 19.5" (20") 56 FM5 2x , 4x, & 6x
N 3.5" (4") 19.5" (20") 19.5" (20") 19 FM1 2x & 4x
T 3.5" (4") 19.5" (20") 19.5" (20") 12 FM4 2x & 4x
X 0.85" (1") 9.5" (10") 19.5" (20") 17 FM1 4x, 6x, & 8x
Y 0.85" (1") 14.5" (10") 19.5" (20") 17 FM1 2x , 4x, 6x, & 8x
The slot coefficient results obtained by loading a filter box with two, four, six and
eight Type J filters is plotted in Figure 4.13. Each line was a least-square regression line
forced through zero. The slope and degree of fit is presented to the right of each line. As
expected, the coefficient rose as more filters were added into the array owing to an
increase in friction. This frictional increase occurred because an identical volumetric
quantity of air was attempting to flow through a reduced area. The slot of the
20?x20?x1? V array, for example, has approximately 1.3 times the open volume of the a
20?x20?x1? WW array?s slot. The reduced flow area increases the average velocity in
the slot as well as heightened fluid-fluid interaction within the slot. Friction is increased
by forcing the air to make a sharper turn before entering into the individual elements in
higher count arrays. Table 4.4 listed all computed slot coefficients and their degree of fit.
95
y = 175.09x
R2 = 0.9997
y = 56.229x
R2 = 0.9989 y = 8.1489x
R2 = 0.9953
y = 444.65x
R2 = 0.9996
0
0.05
0.1
0.15
0.2
0.25
0.3
0.35
0.4
0.45
0 0.002 0.004 0.006 0.008 0.01 0.012 0.014 0.016
??V32 (" H2O)
Di
ffe
ren
ce
("
H
2O
)
Two Type J Filters
Four Type J Filters
Six TypeJ Filters
Eight Type J Filters
Figure 4.13: Slot Coefficient Plots for Various Configurations
96
Table 4.4: Summary of Observed Slot Coefficients and R2 Fit
System
Element
Count
Slot
Opening
Slot
Length
Slot
Depth Alpha Ks R2
(-) (ft) (ft) (ft) (rad) (-) (-)
D - V 2 1.499 1.625 1.442 0.479 7.658 0.9980
D - W 4 0.674 1.625 1.590 0.209 49.620 0.9998
D - WV 6 0.401 1.625 1.613 0.124 153.890 0.9975
D - WW 8 0.265 1.625 1.620 0.082 399.590 0.9982
G -V 2 1.499 1.625 1.442 0.479 8.435 0.9996
G - W 4 0.674 1.625 1.590 0.209 56.966 0.9990
G - WV 6 0.401 1.625 1.613 0.124 172.190 0.9995
G - WW 8 0.265 1.625 1.620 0.082 408.040 0.9977
J - V 2 1.499 1.625 1.442 0.479 8.449 0.9956
J - W 4 0.674 1.625 1.590 0.209 56.529 0.9990
J - WV 6 0.401 1.625 1.613 0.124 175.400 0.9997
J - WW 8 0.265 1.625 1.620 0.082 444.960 0.9996
B - V 2 1.360 1.625 1.476 0.432 9.020 0.9901
B- W 4 0.525 1.625 1.604 0.162 93.882 0.9967
B - WV 6 0.251 1.625 1.620 0.077 388.000 0.9985
L - V 2 1.360 1.625 1.476 0.432 11.270 0.9990
L - W 4 0.525 1.625 1.604 0.162 105.760 0.9995
L - WV 6 0.251 1.625 1.620 0.077 439.850 1.0000
S - V 2 1.360 1.625 1.476 0.432 6.859 0.9999
S - W 4 0.525 1.625 1.604 0.162 80.104 0.9967
S - WV 6 0.251 1.625 1.620 0.077 386.710 0.9987
N - V 2 1.074 1.625 1.534 0.337 22.591 0.9985
N - W 4 0.231 1.625 1.621 0.071 390.700 0.9997
T - V 2 1.074 1.625 1.534 0.337 20.765 0.9893
T - W 4 0.231 1.625 1.621 0.071 344.317 0.9970
X - W 4 0.685 0.792 0.714 0.447 14.479 0.9999
X - WV 6 0.405 0.792 0.765 0.258 40.558 0.9999
X - WW 8 0.267 0.792 0.780 0.169 93.643 0.9993
Y- V 2 1.515 1.208 0.231 0.677 3.418 0.9974
Y - W 4 0.676 1.208 0.716 0.284 26.593 0.9999
Y - WV 6 0.402 1.208 0.766 0.167 89.383 0.9987
Y - WW 8 0.265 1.208 0.780 0.110 218.180 0.9987
The partial solution to the mechanical and momentum balances for a slot was
used as a starting point for modeling the slot coefficient. The solution (1/?)2 was plotted
below versus the empirically-determined coefficients.
97
y = x
R2 = 0.9865
0
100
200
300
400
500
0 100 200 300 400 500
10.26(SL/SO)2(-)
Em
pir
ica
lly
-O
bs
erv
ed
K
s (
-)
Figure 4.14: Slot Coefficient Graph
The modeled formula showed a linear relationship to the empirically-observed
coefficient. An oddity occurred involving both observed slot coefficients for array
systems consisting of four, 4? elements. Each array possessed an unusually low
coefficient. These coefficients were tagged by the solid, black diamonds. One possible
reason for the divergence was that by loading four, 4? filters into a box an abnormal flow
pattern was created due to approximately 70% of the duct being blocked by the array?s
front edges. The extreme flow pattern could have been inducing other unforeseen effects
within the system that was not able to be accounted for by the model.
The slot coefficient was reevaluated with the two abnormal values removed. The
main reason for this was the impracticality of packaging 4? filters into a ?W? array. The
average pressure loss in such a configuration at 500 fpm was 0.6? H2O. The same
amount of media could be loaded into an array utilizing 1? or 2? deep elements while
98
maintaining a total pressure drop below 0.25? H2O. It is therefore more beneficial to
possess a slot coefficient that could accurately describe the useful arrays instead of a
coefficient that attempted to model all systems with less accuracy. After the removal of
the two abnormal values, the slot coefficient was determined as:
Ks = 2.575(1/?)2 (4.4)
with V3 as the Reference Velocity
y = x
R2 = 0.9869
0
100
200
300
400
500
0 100 200 300 400 500
?? (-)
Em
pir
ica
lly
-O
bse
rve
d K
s (
-)
Figure 4.15: Observed versus Modeled Slot Coefficient
IV.3. Discussion Utilizing the Model
IV.3.1. Achievement of Objectives
The one-to-one correlation on over 1500 data points demonstrates the two
models? ability to calculate resistance as a function of face velocity. The inner dashed
lines in Figure 4.16 equal ?5% from unity and the outer dashed lines correspond to ?10%
from unity. The empirical pleat coefficient was formulated on 680 individual data points
spanning twenty design variations. The slot?s friction coefficient was devised from 750
99
data points encompassing thirty different array architectures. The models accounted for
all known pleated filter parameters and are fully capable of making predictions based
solely on empirical data pertaining to the media constants. All geometric coefficients are
based on physical design variables without the use of non-transferable factors.
Theoretical equations relating media constants to media properties such as fiber diameter
and void volume could readily be incorporated to make the model fully independent of
empirical data. The model is composed entirely of polynomials allowing for quick
analysis and estimations times.
y = 0.9982x
R2 = 0.997
0
0.25
0.5
0.75
1
1.25
0 0.25 0.5 0.75 1 1.25
Modeled Pressure Drop (" H2O)
Ob
ser
ve
d P
res
sur
e D
rop
("
H
2O
)
Figure 4.16: Correlation Plot between Observed and Modeled Data
IV.3.2. The Pleating Curve of a Multi-Element Structured Array
The array model was employed to study the effects created by increasing pleat
count within a multi-element array. Figure 4.17 displays a ?W? array configuration
loaded with 20?x20?x1? FM1 media filter elements to illustrate the resistances
100
encountered within an array. The red circles were experimentally observed values with
error bars of ?5 %. The individual plots for pleat contraction, pleat expansion, array
contraction, and array expansion were removed for clarity. Since each term by itself
contributed less than 0.003? H2O of resistance, they were summed and plotted as the
cumulative resistance entitled ?Miscellaneous.?
0
0.04
0.08
0.12
0.16
10 25 40 55 70
Pleat Count (Pleats / Filter)
Pre
ssu
re
Dr
op
("
H
2O
)
Miscellaneous Resistances
Grating Resistance
Pleat Resistance
Slot Resistance
Media Resistance
Total Resistance
Observed Resistanaces
Figure 4.17: Multi-element structured array Pleating Curve
The resistance behavior of a Multi-Element Structured Array partially mimics the
trends observed in a single filter?s pleating curve, yet the overall magnitude of the
pressure drop and the contributing factors are substantially different. Foremost, the total
flow resistance is between one-third to one-half the resistance of a single 20?x20?x1?
FM1 media filter over the same range of pleat counts. The pleat and media terms no
longer serve as the primary contributor to pressure drop. Likewise, the impact of the
101
grating has been heavily reduced. The slot resistance now accounts for the bulk of the
overall resistance. Just like the grating term, the slot term acts as a fixed resistance and is
not a function of pleat count. The contraction and expansion into and out of the MESA
also act as fixed resistances. The filtration system still trades media losses for pleat
induced resistances, and the optimal pleat count is dependent upon these terms. Below is
a graphical representation of the percentage contribution to the total resistance from each
resistance term. The chart was compiled from data obtained at the optimal pleat count in
Figures 3.20 and 4.17.
Figure 4.18: Percentage Contribution of (A) Single Filter and (B) ?W? Array
The reduction in the grating, pleat, and media term are the product of
incorporating multiple filters to reduce the face velocity into each element. Since the
grating and pleat terms are second order polynomial functions of face velocity,
decreasing the airflow into each element by one-fourth results in a 16-fold decrease in
their resistance. A one-fourth reduction in face velocity results in a 4 to 16-fold reduction
of the media term depending on the media constants. Likewise, the utilization of eight
elements would result in a 64-fold decrease in elemental resistances.
102
Slowing the face velocity into the elements grants an array a unique range of
benefits. MESA?s can serve as a platform to house high-resistance media that would be
otherwise impractical to use. Furthermore, an array can employ any media type and
operate at a vastly decreased resistance over a traditional pleated filter. With the
reduction of the element?s viscous effects, the individual filters can be pleated to a much
higher extent before reaching a limiting resistance.
IV.3.3. Locating the Optimal Pleat Count
The MESA model is simply an extension of the single filter?s model. The three
terms italicized below are new additions, but the remaining terms are all present in the
single?s filter model. The contraction into the array (KCB), expansion out of the array
(KEB), and resistance through the slot(s) (KS) are all functions of element count and not
functions of pleat count. Thus, the optimal pleat count is computed in the same manner
as presented in Chapter III.
?PT = ? ?[(KCB + KEB )V22 + KSV32 + 2KGV32 + (KCP + KEP + KP)V52] + AV6 + BV62
IV.3.4. Influence of Design Parameters
The model was employed to examine the variation of parameters and the resulting
effects on resistance in order to better understand the design space and behaviors of a
MESA. Media constants, media thickness, filter depth, and face velocity were identified
as important design parameters in the single filter section. These factors remain critical
in the MESA design as well as factors unique to MESAs such as element width and
number of elements.
103
1. Effects of Filter Element Count
The filter element count is the most important design factor in a Multi-Element
Structured Array. An array?s main resistance is created by flow through the slot as seen
in Figure 4.18B. This resistance is primarily a function of element count. The element
count also has a significant influence on the impact of other design parameters. The
incorporating of two to eight elements will reduce the face velocity into each individual
element by 50% to 87.5% respectfully. This substantial reduction in velocity allows an
array to essentially eliminate or considerably hinder any influence created by pleat count,
grating contribution, media thickness, or media constants.
The model was used to study various element counts by calculating resistance
data for 20?x20?x1? deep filter elements in five configurations. Media properties were
set at a thickness of 1.5 mm with constants A = 10x10-4 and B = 15 x 10-7. The results
were plotted in Figure 4.19.
104
0
0.15
0.3
0.45
0.6
0.75
0 25 50 75 100 125 150 175 200
Pleat Count (Pleats/ Filter)
Pre
ssu
re
Dr
op
("
H
2O
)
V Bank
W Bank
WV Bank
WW Bank
Single Filter
Figure 4.19: Effects of Element Count on MESA Pleating Curve
The pleating curves lose their distinctive ?U? shape and adopted an ?L? shape as
the total number of filter elements increased due to the reduction of the face velocity
encountered by each element. The presence of the media-dominated regime in higher
element arrays was essentially removed due to the array?s ability to incorporate a
substantial media area even at low pleat counts. The viscous-dominated regime still
existed; however, the pleating had to be taken to an unusually high count before the
viscosity-induced resistance could become relevant.
The optimal pleat count shifted right as element count increased since the
viscosity resistances were more impeded in higher element arrays. The lowest obtainable
resistance experienced a minimum and then began to rise (see Figure 4.20). This rise was
due to the incremental increase in the fixed resistances. Each additional element further
105
enhanced the friction for flow within the slots as well as increased the resistances created
by a larger expansion and contraction within the array. After the ?WV? configuration,
the minor decrease in media and pleat resistances were not able to compensate for the
subsequent increase in fixed resistances. The charts below present each term?s individual
contribution to the total pressure drop as the number of elements increased.
0.000
0.050
0.100
0.150
0.200
0.250
0.300
0.350
0.400
0.450
Single Element V Bank W Bank WV Bank WW Bank
Pr
ess
ure
D
rop
("
H
2O
)
Bank Contraction/Expansion
Slot Resistance
Grating Resistance
Pleat Resistance
Media Resistance
Total
Figure 4.20: Effect of Element Count on Contribution
Although the extra elements help to reduce the operational pressure drop, the
major advantage of the MESA designs was the vast increase in available filtration area.
The pressure drop data from Figure 4.19 was plotted below versus their corresponding
available filtration area. Table 4.5 presents the optimal pleat count of each system,
available filtration area, and lowest obtainable resistance (LOR). Each array was
compared to the available filtration area and LOR of the 20?x20?x1? filter system
106
composed of an identical media. The arrays, at the very minimum, were able to double
the available filtration area while operating at fifty percent of the pressure drop.
0
0.15
0.3
0.45
0.6
0.75
0 50 100 150 200 250 300 350Available Filtration Area (sq. ft)
Pre
ssu
re
Dr
op
("
H
2O
)
V Bank
W Bank
WV Bank
WW Bank
Single Filter
Figure 4.21: Effects of Element Count on MESA Performance Curve
Table 4.5: MESA vs. Single Filter Comparison
System Optimal Count Media Area Lowest ?P Area Increase ?P Reduction
(-) (Pleats/Filter) (sq. ft) (" H2O) (%) (%)
Single 38 8.0 0.410 n/a n/a
V 44 19.0 0.176 237.9 42.9
W 52 44.9 0.109 561.2 26.5
WV 57 73.7 0.106 921.8 25.9
WW 61 105.2 0.123 1314.4 30.1
The orange circle represents the most area that can be incorporated into a system
before going over the 0.25? H2O mark. This mark is heuristically considered the
maximum acceptable starting resistance of an HVAC filter. A single 20?x20?x1? filter
composed of this media would not be constructed due to its high pressure drop. The
107
media would be manufactured into a 2? or 4? deep filter. Employing the single filter
model for a quick computation, a 4? filter with 27 pleats could be built with the same
media and maintain a resistance of 0.25? H2O. The filter would possess slightly less than
25 square feet of available filtration area. A ?WW? array would still be able to
incorporate nine times the media and operate at the same resistance.
2. Effects of Filter Element Width
Filters with shorter widths were modeled as MESA?s to study to the impact of
shallower slots depths. Theses systems mimic the commercially available products such
as V-Banks. Arrays composed of shorter element widths provide a lower obtainable
resistance than their wider counterparts at low filtration areas, but lose their competitive
advantage at higher media areas due to increased pleat resistances. The shallower slot
depth decreased the coefficient of friction for flow within the slot and decreased the fixed
resistances of the system. The shorter-width filters were unable to handle the additional
material as pleat count and the amount of packaged media increased. The pleat openings
essentially close and the friction within the pleat rose. The filter elements with longer
widths were able to better accommodate the additional pleats leading to increased
filtration area.
The effects of element width were observed while constructing Figure 4.22.
Three widths were modeled at 500 fpm using ?WV? arrays composed of 20?x20?x1?
depth element. Each element was modeled with 1mm thick media and constants of A =
15x10-4 and B = 20 x 10-7.
108
0
0.05
0.1
0.15
0.2
0.25
0.3
0 25 50 75 100 125Available Filtration Area (sq. ft)
Pr
ess
ure
D
rop
("
H
2O
)
19.5" Filter Width
14.5" Filter Width
9.5" Filter Width
Figure 4.22: Effects of Element Width on MESA Performance Curve
The plot?s behavior for arrays composed with shorter filter widths acted as a
hybrid between single filters and 19.5? width arrays. A shallow array had more of the
traditional ?U? shape than the deeper slotted arrays. As the width of the elements
increase, the graph began to flatten out as more of the overall pressure drop was
comprised from fixed resistance instead of media and pleat pressure drops. Below was a
plot of the contribution of each terms resistance to the total pressure drop at the optimal
pleat count. The pleat and media terms were the dominate resistances in the single filter
accounting for nearly eighty percent of the total pressure drop combined. They remained
the prevalent resistances in the 9.5? width array, but as the widths were further increased
their effects were reduced to less than thirty percent of the total pressure drop in 19.5?
wide arrays.
109
0
0.05
0.1
0.15
0.2
0.25
0.3
0.35
0.4
Single Filter 9.5" Width 14.5" Width 19.5" Width
Pre
ssu
re
Dr
op
("
H
2O
)
Bank Contraction Resistance
Bank Expansion Resistance
Grating Resistance
Pleat Resistance
Slot Resistance
Media Resistance
Total Resistance
Figure 4.23: Effect of Element Width on Contribution
3. Effects of Filter Element Depth
A larger filter depth equated to a lower pressure drop and a higher available
filtration area in single filter, yet the same did not hold true for Multi-Element Structured
Arrays. Naturally, deeper elements increase the blockage resistance by creating a larger
contraction and expansion into and out of the array. More significant though is the
increase in slot resistance due to the decrease of the slot?s pitch. The slot?s pitch has to
be decreased in order to accommodate the deeper elements into the array. The synergy of
these effects leads to an increase in the fixed resistances that rendered a deeper element
array less efficient.
Figure 4.24 and 4.25 were composed to illustrate these claims by modeling a ?V?
array configuration of various elements depths at 500 fpm. Each element was modeled
with 1 mm thick media and constants of A = 15x10-4 and B = 20 x 10-7. The effects lead
110
to a 0.05? H2O increase in the fixed resistances of the 4? filter array over the 2? filter
array. This allowed the 2? element array to operate at a lower pressure drop for most of
the curve.
0.1
0.15
0.2
0.25
0.3
0.35
0.4
0.45
0.5
0.55
0.6
0 10 20 30 40 50 60 70
Media Area (sq. ft)
Pre
ssu
re
Dr
op
("
H
2O
)
4" Filter Depth
2" Filter Depth
1" Filter Depth
Figure 4.24: Effects of Element Depth on MESA Performance Curve
Figure 4.25 displays the individual contribution of each term at the lowest
obtainable resistance. Just as seen in a single filter, the media and pleat resistances
decrease as the element depth increases. The net decrease of the media and pleat,
however, can not compensate for the rise in fixed resistances of the array.
111
0
0.02
0.04
0.06
0.08
0.1
0.12
0.14
0.16
0.18
0.2
1" Elements 2" Elements 4" Elements
Pre
ssu
re
Dr
op
("
H
2O
)
Contraction/Expansion
Resistance
Grating Resistance
Pleat Resistance
Slot Resistance
Media Resistance
Total Resistance
Figure 4.25: Effect of Element Depth on Contribution
Although not the case for V MESA?s modeled above, 1? deep filter elements
typically outperform deeper-element arrays at higher element counts because they
minimize contraction/expansion resistances and possess larger slot pitches. These
geometric advantages reduce the fixed resistances that serve as the primary resistance in
higher-element count arrays. Two and four inch deep elements are only able to package
more media at a lower resistance than the 1? elements when the element count is low.
5. Effects of Media Constants
An increase in the media constants within a Multi-Element Structured Array will
heighten the resistance of the media and raise the overall pressure drop of the system, but
the magnitude of resistance rise depends heavily on the number of elements. The effects
of media constants on a MESA are similar to those seen in a single filter, but the overall
extent of their influence is diminished.
112
The lowest obtainable resistance of a 2? deep single pleated filter varied from
0.13? H2O to 0.46? H2O as the media constants changed from A=1x10-4 and B=1x10-7 to
A=30x10-4 and B=30x10-7. Figure 4.26 modeled the same filter elements (2? deep and 1
mm thick media) in a V configuration at 500 fpm. The LOR changed from 0.09? H2O at
A=1x10-4 and B=1x10-7 to 0.21? H2O at A=30x10-4 and B=30x10-7. The media-
dominated regime showed a large increase, yet an array should not be constructed in this
regime. Since the onset of pleat resistances are delayed in a MESA, the system was
ultimately able to incorporate a large quantity of pleats to reduce the high-resistance
media effects. The same outcome could have been obtained by employing an array with
more elements. This makes MESAs an appealing platform for high resistance materials
since their resistances can be eliminated by various design techniques.
0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0 10 20 30 40 50 60
Pleat Count (Pleat / Filter)
Pre
ssu
re
Dr
op
("
H
2O
)
A = 1x10^-4; B = 1x10^-7
A = 5x10^-4; B = 5x10^-7
A = 10x10^-4; B = 10x10^-7
A = 20x10^-4; B = 20x10^-7
A = 30x10^-4; B = 30x10^-7
Figure 4.26: Effects of Media Constants on MESA Pleating Curve
113
5. Effects of Media Thickness
Media thickness has a unique ability to influence the viscous-dominated region of
the pleating curve and possesses the potential to hinder the maximum available filtration
area of an array. The resistance in the viscous-dominated regime increases as additional
tip blockage is added and as the flow in the pleats becomes constrained. A thicker media
accelerates both of these factors, but the constricted flow due to a bulkier media is the
major inhibiting effect. This hastens the rate of pleat closure and limits the quantity of
pleats that can be incorporated into an array. The overall effect of a thicker media shifts
the viscous-dominated regime from a quasi-flat line into a more traditional, steep slope.
To illustrate the effects of media thickness, Figure 4.27 was composed by
modeling various media thickness within a ?W? array at a face velocity of 500 fpm. The
array housed 2? elements containing media with constants of A = 15x10-4 and B = 20 x
10-7. Similar to the results obtained for a single filter, a thicker media shifts the optimal
pleat count left and to a higher lowest obtainable resistance.
114
0.1
0.15
0.2
0.25
0.3
0.35
0.4
0 20 40 60 80 100
Pleat Count (Pleats / Filter)
Pre
ssu
re
Dr
op
("
H
2O
)
0.5 mm 1.5 mm
2.0 mm 2.5 mm
3.0 mm
Figure 4.27: Effects of Media Thickness on MESA Pleating Curve
6. Effects of Face Velocity
Increasing the velocity within a Multi-Element Structured Array raises the overall
resistance of the pleating curve. The media-dominated regime and viscous-dominated
regimes in particular have a tendency to rise at an exaggerated rate. This produces the
curling effects that give rise to a more distinct ?U? shape. The degree of curl principally
depends on the number of elements within the array being examined.
The plot below is a computation done on 2? elements loaded into a ?W? array.
The media possessed constants of A = 15x10-4 and B = 20 x 10-7 and had a thickness of 1
mm. The overall resistance grows in response to an increase in velocity. The main
difference between the effects seen below and the ones observed in the single filter
section is the lack of response in the viscous-dominated region. As stated earlier, the face
115
velocity in a ?W? array is reduced by one-fourth resulting in a one-sixteenth reduction in
the resistance of viscous terms. The media-regime may experience anywhere from a one-
fourth to a one-sixteenth reduction depending on the magnitude of A and B. Thus, a
large increase in velocity does not have the same pronounced effect on the viscous terms
in an array as it does in a single pleated filter. The face velocity?s ability to curl the
media and viscous regions would be further enhanced when fewer elements are utilized
and diminished when more filters are employed.
0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
0 15 30 45 60 75
Pleat Count (Pleats / Filter)
Pre
ssu
re
Dr
op
("
H2
O)
200 fpm 400 fpm
600 fpm 800 fpm
1000 fpm
Figure 4.28: Effects of Velocity on MESA Pleating Curve
7. Influence Summary
Table 4.6 was compiled based on data and observations made during simulations
ran with the model. The table is a general reference to indicate the net effect (?+?:
increased resistance;
116
?-?: decrease in resistance) that an increase in the design parameter will have on a
particular resistance. A single filter can be optimized with respect to pleat count by
balancing the media and viscous terms. A MESA can be optimized with respect to
element count, element width, and element depth. The optimization arises from
balancing the traditional pleat and media resistances versus the fixed resistances of the
system.
Table 4.6: Summary of Design Parameters and Effects due to their Increase
Design Variable Array Edges Slot Pleat Tip Pleat Media
Element Count + + - - -
Element Width + (minor) + - - -
Element Depth + + - - -
Media Thickness n/a n/a + + - (minor)
Media Constants n/a n/a n/a n/a +
Pleat Count n/a n/a + + -
117
CHAPTER V: THEORY AND EXPERIMENTAL
FOR AIR FILTRATION PERFORMANCE
V.1. Introduction
The previous chapters identified novel packaging designs such as higher pleat
counts and utilization of multiple elements that provided a means to increase the
available media area while maintaining or lowering the initial resistance. The aim of the
remaining chapters is to investigate these pleating and design arrangements to determine
the influence of increasing pleat count, pleat height, and element count on initial pressure
drop, aging profiles, and removal efficiency. This was accomplished by testing
commercially available and custom-order 24?x24? filters with an in-house rig modeled
after the ASHRAE 52.2 Standard (ASHRAE 2007). The filtration designs were then
analyzed for energy consumption, quality factor, and useful lifetime based on the
empirical data. The background information provide in this chapter will highlight key
terms and models of filtration theory as well as equipment and procedures to carry out the
experimentations.
V.2. Theory
V.2.1. Previous Research concerning Dirt Loading of Air Filters
The initial pressure drop of a filter only serves as the baseline for the overall
power consumption. A reduction in the initial resistance is important because it translates
into a net reduction of energy across the lifetime of the filter, yet it at times represents
118
only a fraction of the overall working pressure drop. The filter?s pressure drop increases
due to the accumulation of dirt over its operational lifetime. The capture of dirt is
referred to as aging or loading of the filter while the pressure increase per weight of dirt
catch is known as the aging or loading rate. The operational pressure drop and power
consumption will therefore be a function of the initial pressure drop and the dirt loading
[Novick et al. 1992.]
?Pfilter = ?Pinitial + ?Pload (5.1)
The rate of filter resistance increase with dirt loading has been the subject of
extensive research [Novick et al. 1992, Lebedev & Kirisch 1995, Walsh et al. 1996,
Japuntich et al. 1997, Davis and Kim 1999, B?mer and Call? 2000]. As a filter is
challenged with particulate matter, the pressure drop will undergo two distinct regions of
aging. Initially, the filter?s resistance will increase marginally with the additional of dirt.
This region is known as the depth filtration region because the dirt is being accumulated
within the depth of the fibers during this period. The dirt, at first, acts as single particles
adhered to the surface of the fibers. Subsequent particles will then begin to adhere to the
initial particles forming agglomerate chains on the surface of the fibers. These dendrite
chains act as secondary fibers capable of capturing additional dirt. Eventually, the pores
of the filter become clogged and particles no longer load within the depths of the fibrous
material [Thomas et al. 1999, Song et al. 2006].
119
Figure 5.1: General Trend in Filter Loading
At this point, the filter transitions from the depth loading to surface loading.
Surface loading is characterized by a steep increase in resistance per weight of particles
loaded. A layer, known as the cake, is formed on the surface of the filter since the dirt is
no longer able to penetrate into the filter. Subsequent particles load onto the cake causing
the thickness of the filtering media to increase. By Darcy?s Law, the resistance will
increase proportionally with the thickness of the porous media [Thomas et al.1999].
V.2.2. Particulate Removal Efficiency by Fibrous Media
A filtration system?s foremost responsibility is the removal of particulate matter
from the air stream. Medium and high efficiency filters accomplish this through a series
of mechanisms that act in conjunction to remove particles much smaller than the average
pore size of the filtration medium. These mechanisms are as followed: sieving, inertial
impaction, interception, Brownian motion, electrostatic deposition, and settling [Davis
120
1973, Brown 1993]. The probability of a particle passing through a filter of thickness (h)
composed of fibers with length (L) and radius (R) can be modeled from the single fiber
theory as:
Penetration = 100exp(-2 ? LRh) (5.2)
The collection efficiency of the fiber (?) is a summation of the individual collection
efficiency of each mechanism. Sieving and settling are only effective at removing large
particle from the air stream, and particles of this size usually settle out in the ductwork
before reaching the filter. Electrostatic deposition is of importance in filters employing a
charged surfactant coating to draw particles out of the air streams. Impaction,
interception, and Brownian motion account for the majority of particle removal; thus, the
collection efficiency can be described as (Davis1973):
? = ? DIFFUSION + ? IMPACTION + ? INTERCEPTION (5.3)
The theories behind each mechanism are quite complex and not precisely understood.
Discussion of the multitude of theories is beyond the scope of this research, yet a general
assessment of each mechanism is presented below.
Inertial impaction is used to describe particulate capture by means of physical
contact with the filtration fiber due to deviations from the streamlines. As the air flow
approaches a filter fiber, the streamlines will diverge and flow will be channel around the
fiber. Larger particle with significant momentum are not capable of making this direction
change. The particle?s inertia causes it to deviate from the streamline and collide with the
front side of the fiber. The efficiency of this mechanism increases with larger particle
size and faster approach velocities [Brown 1993]. The mechanism is sketched as:
121
Figure 5.2: Impaction Mechanism for Particulate Capture
Interception occurs when a particle is following on a streamline and that passes
close to a fiber. The particulate is captured if the streamline is within one particle radius
of the fiber. The particle will deposit on the front half of the fiber by this mechanism.
The efficiency is primarily dependent on the packing density of the fibers and diameter of
fiber [Brown 1993].
Figure 5.3: Interception Mechanism for Particulate Capture
Very small particles are carried by the air flow, but they do not strictly follow the
streamlines. As the particles randomly move through the filter due to Brownian motion,
there is a probability that they will encounter a fiber and adhere. This is referred to as
capture by Brownian motion or diffusion. The probability of capture increases with
increasing packing density of fibers, decreased diameter of fiber, and increased resident
time within the fiber mesh [Brown 1993]. Particles will be deposited on all sides of the
fiber when this mechanism is prevalent.
122
Figure 5.4: Particulate Capture by Brownian Motion
V.3. Experimental
V.3.1. Test Rig and Equipment
Performance for 24? x 24? face dimension filtration units were conducted on a
test rig modeled after the ASHRAE 52.2 Standard [ASHRAE 2007]. Modifications were
made to reduce the cost, simplify the overall design, and remain compatible with
previously purchased in-house equipment and materials. The system was engineered to
delivery 2000 cfm of specifically tailored air for evaluation of air-cleaning devices in
regards to pressure drop, particulate removal efficiency, and dirt holding capacity.
Provided below was a full schematic of the rig, a general description of the equipment,
and an overview of the test procedures used throughout the remainder of the dissertation.
123
Figure 5.5: Schematic of Full Scale Test Rig
Figure 5.6: Upstream Picture of the Test Rig
124
Figure 5.7: Downstream Picture of the Test Rig
The rig was set up in a positive displacement arrangement. Room air was
introduced into the test duct by a Dayton systems blower driven by a 3 HP motor. The
blower could deliver the required 2000 cfm correlating to a 500 fpm face velocity with up
to 4.4? H2O of static head. The motor was controlled by a Hitachi frequency drive with a
range of zero to sixty hertz at 0.1 Hz increments. The frequency drive could be
programmed to ramp up or down at a controlled rate.
The air exited the blower via a stainless steel four-way expansion that increased
the cross section area of the rig to 24? x 24?. The transition led directly to an upstream
filtration box that is capable of holding a HEPA air filter or a 36? deep pocket bag filter.
All dirt loading and efficiency tests employed the HEPA filter while initial pressure drop
tests utilized the bag filter. The HEPA filter [American Air Filter?s (AAF) Astrocel]
removed 99.97% of 0.3 micron diameter particulate matter. This particle size is
considered the most penetrating; therefore, the removal rate of all other particle sizes
would be greater than 99.97%. The high removal efficiency was needed to remove
125
background contamination and provide a uniform baseline during efficiency testing.
Figure 5.5 below demonstrates the removal efficiency of the HEPA compared to the
MERV 15 bag filter (AAF DriPak 2000).
1.E+00
1.E+01
1.E+02
1.E+03
1.E+04
1.E+05
1.E+06
0.3-0.5 0.5-0.7 0.7-1.0 1.0-2.0 2.0-3.0 3.0-5.0 5.0-7.0 7.0+
Particle Size Range (?m)
Nu
mb
er
of
Pa
rtic
les
(-)
HEPA Filter
MERV 15 Bag Filter
Background Air
Figure 5.8: Removal Efficiency of Upstream Filters
The bag, or pocket, filter was used when large volumetric flow rates were needed,
yet high purity background air was not necessary. The pocket filter allowed the system to
achieve higher face velocities because of its low pressure drop (0.45? H2O at 500 fpm).
The filter prevented background air from artificially aging the test filter while being
capable of supplying a sufficient volume of air that a HEPA filter would not allow.
The clean air passed from the filtration box into the aerosol inlet section. The rig
was capable of challenging filters with particulate matter ranging from 0.01 ?m to 100
?m. In order to create challenge particles spanning three orders of magnitude, the system
126
was equipped with a TSI 8108 Large Particle Generator and a Blue Heaven custom-built
dust loader.
The TSI 8108 system was built to output a polydispersed challenge of KCl salt
particles in the range of 0.1 to 10 ?m. The particles were created by pumping a 30% KCl
solution at1.2mL/min into a spray nozzle where it was mixed with 1 cfm of atomizing air.
The nebulized particles were dispersed into a 12? diameter by 5? high plenum where the
droplets were dried with 4 cfm of preheated air. A Kr- air ionizer neutralized any charges
present on the aerosol. Charge removal was necessary to prevent the particle from being
artificially captured by electrostatic deposition within the ductwork or the test filter. The
KCl particles exited the plenum via a 1.5? NPT pipe. The pipe delivered the particles
into the center of the ductwork facing the direction of flow. Distribution was enhanced
by introducing the particles in this manner. The manufacturer?s schematic is below.
Figure 5.9: TSI 8108 Large Particle Generator Schematic
127
The generator produced a stable concentration of 600 particle/cm3 of 1 micron
and 10 particle/cm3 of 10 micron aerosol when nebulizing the KCl solution. The unit can
also be employed to nebulized other material such as monodisperesed polystyrene latex
(PSL) spheres in the size range of 0.01 to 20 microns.
Unlike the TSI 8108, the Blue Heaven unit was designed to artificially age the test
filter with a high concentration of particulate matter. The loader was designed to meet
the ASHRAE 52.2 Standard, and the critical dimension for the unit may be found there
[ASHRAE 2007]. The loader was designed to introduce dirt into the rig by a venturi
pump. House air was sent through a desiccant bowl to dry the air to a dew point of -45?F
before being supplied to the unit at 80 PSI. The air throttling through the venturi pump
caused a vacuum to be formed on the feed tray. The belt driven feed tray brought the
challenge dirt into proximity of the vacuum at a steady linear rate of 0.5 ft/min. The
height of the challenge on the feed tray determined the particulate concentration in the
test rig.
A common artificial aging material is ASHRAE synthetic test dirt. ASHRAE dirt
is a conglomeration of ASTM ISO fines (73%), carbon black (23%), and milled cotton
linters (4%). ASTM ISO fines are a mixture of alumina oxide and silica dioxide. The
carbon black is Raven 411 and is commonly used in toner ink. Table 5.1 denotes the
manufacturer?s reported size distribution for the ISO fines. The carbon black cotton
linters both possessed dimensions larger than 10 microns.
128
Table 5.1: ASHRAE Dust Size Distribution
Particle Size Composition
micron % Less Than
1 2.5 - 3.5
2 10.5 - 12.5
3 18.5 - 22.0
4 25.5 - 29.5
5 31.0 - 36.0
7 41.0 - 46.0
10 50.0 - 54.0
20 70.0 - 74.0
40 88.0 - 91.0
80 99.5 - 100
120 100
The challenge particulates were mixed and distributed throughout the cross
section of the system by the upstream static mixer. The three-part mixer began by
contracting and concentrating the loaded air with a 12? circular opening orifice plate. To
expanded and distributed the mixed air, a 12? circular disk built from a 50% blocked
perforated stainless steel was located one foot behind the orifice plate. A 50% blocked
perforated stainless steel ring (outside diameter of 18? with inner diameter of 12?)
followed six inches behind the disk and further distributed the loaded air. The test air
reached the filtration system via two, four foot long sections designed to allow the air to
further distribute and self correct. The mixer, in conjunction with the upstream duct,
provided a uniform flow into the filtration test section. Table 5.2 shows that the
coefficient of variances (CoV) for delivered airflow to the filtration section was less than
10% as mandated by ASHRAE Standard 52.2. The CoV measurements were performed
with an Extech vane-anemometer using the method highlighted in Section II.5.1.
129
Table 5.2: Average Velocity and Coefficient of Variation within Test Rig
Setting (Hz) 15 20 30 40 50 60
Average Velocity (m/s) 1.05 1.39 2.04 2.80 3.49 4.22
Standard Deviation 0.06 0.11 0.11 0.21 0.29 0.32
Coefficient of Variance 6.18 8.03 5.52 7.53 8.32 7.60
The upstream duct also houses an isokinetic probe used during removal efficiency
testing. The probe was located 12 inches in front of the filtration unit positioned in the
center of the ductwork.
The test section was an adjustable region that can accommodate filtration units up
to 36? in depth. This was accomplished through a linear motion track created out of
80/20 aluminum extrusion on which the downstream ductwork and final filter rest. The
filtration units were custom built for each filter design. Further information concerning
their construction can be found in the Appendix.
The air passed through the test section and traveled into the downstream
ductwork. The downstream duct was an 8? long section that housed a second isokinetic
probe. The final filter, a 36? 95% efficiency pocket filter (AAF DriPak 2000), was
located at the end of the duct work to capture any challenge particulate that passed
through the tested filter.
The transitions between sections were outfitted with a clamping system to seal the
rig and prevent the loss of volumetric flow and challenge particulates. Each section
possessed a 3 inch wide flanged joining plate. Closed cell foam with a thickness of 3/8?
was added to the width of each flange. The seal between the sections was created by
compressing the foam to a minimum of 75% of its original thickness. The compression
was created by outfitting the flange with bolt assemblies and specialized tracks. The
extruded aluminum U-channel tracks doubled as a second enclosing mechanism and ran
130
the width of the flange. A schematic and picture of the sealing mechanism is shown
below.
Figure 5.10: Schematic and Picture of Sealing System
V.3.2. Experimental Data Acquisition
The rig was designed to measure pressure drop, face velocity, and
upstream/downstream particle count for a given filter unit. From these measurements,
the filter?s performance could be assessed for power consumption, dirt holding capacity,
and particle removal efficiency. The following sections detail how each individual
measurement was made as well as the general procedure for each test.
V.3.2.1.Volumetric Flow
Volumetric flow measurements were derived from the pressure drop across the
orifice plate. The resistance to flow created by the orifice can be directly related to the
face velocity by the following equation (Perry and Green 1997).
V = ((2?P / ?Cd))? (5.3)
131
The pressure drop across the orifice plate was measured by an Invsys differential
pressure transmitter. The meter has a programmable span to include differential
pressures up to 30.00? H2O. The span was set at 3.500? H2O because this was slightly
higher than the maximum achievable resistance across the orifice with the current blower
configuration. The meter transmits a 4-20 mA signal which was converted to a 1-5 V
signal via a precision resistor. The voltage drop across the resistor was monitor by a
Personal Measurement System PMS1208LS data logger. The data logger communicated
with a PC through a USB cord where the TracerDAQ software recorded the signal.
The differential pressure was measured 6 inches upstream and downstream of the
plate. To minimize error associated with flow misdistribution, a four tap configuration
was employed. Each tap was located 90 degrees apart from one another and was
stationed flush to the test rig. The lines running from each tap were connected together
via a manifold.
The positioning of the taps included the resistance created by the flow distributors
as well. This meant that previous published coefficient of discharge (Cd) could not be
used; thus, the coefficient had to be determined experimentally. Experimental
determination of the coefficient was achieved by creating a calibration curve formulated
through two methods. The first method utilized a vane-anemometer to gather face
velocity measurements at set frequencies. The coefficient was calibrated against these
measurements. For thoroughness, a second calibration method was employed based on
the manufacturer?s blower curves.
The vane anemometer method was based on the ASHRAE 52.2 Standard
technique for verifying flow distribution within a duct. The outlet to the filtration rig was
132
sectioned off into a 3x3 grid. The blower was set to the desired frequency, and the face
velocity was allowed to equilibrate. An Extech vane anemometer was positioned at one
the nine points and was allowed to reach a steady velocity. The anemometer?s recorder
was turned on, and a running average of the face velocity through that point was gathered
over a one minute period. The procedure was conducted three times for all nine points,
and an average face velocity for this technique (VT) was computed. This value can then
be used with the resistance measured at the orifice plate to compute the coefficient value
calculated by:
Cd = ? ?VT2 / ?PORIFICE (5.4)
The second method to verify the flow rate utilized the manufacturer supplied
blower curves to compute the face velocity over the range of blower frequencies. An
Omega pressure transducer measured the pressure differential at the inlet to the blower
and the immediate outlet of the blower as shown below.
133
Figure 5.11: Blower and Tap Configuration
The pressure at the blower?s outlet was measured by a four-tap configuration.
Each tap was located 90 degrees apart from each previous tap. The taps were connected
together by a manifold to get an average resistance at the exit of the blower.
The volumetric flow rates were calculated for each frequency based on the
recorded pressure drop at the blower and the blower curve equations presented in Chapter
II.5.1. The coefficient was computed using Equation 5.4 and a face velocity (VT) derived
from the blower curve equations. The graph below is the calibration curve created for the
orifice plate based on both the vane anemometer readings and the computed blower curve
values. The coefficient of discharge was determined to be 44.
134
0
1
2
3
4
5
0 10 20 30 40 50 60 70
Frequency (Hz)
Fa
ce
Ve
loc
ity
(m
/s)
Computed via Orifice Equation
Computed from Blower Curves
Measured by Vane Anemometer
Figure 5.12 Face Velocity Calibration Curve for Test Rig?s Orifice Plate
V.3.2.2. Pressure Drop across Filtration Section
The pressure drop across the filtration test section was measured with a second
Invsys differential pressure transmitter. The meter also had a programmable span to
include differential pressures up to 30.00? H2O. The span was set at 1.500? H2O because
this represented the upper working limit for most air filters. The transmitter possessed a
resolution of 0.001? H2O and transmitted to the data logger in the same manner as
discussed before. A two tap system was employed with mountings located on the right
and left walls six inches before and after the test section. The taps were fashioned
flushed with the ductwork to prevent eddies from forming at the point of measurement.
Each pair of taps was then joined by a tee junction before being connected to the pressure
transducer. The length of tubing used to connect each tap to the tee and each tee to the
135
meter were identical in length. The two tap configuration was employed to minimize
error associated with flow misdistribution. A 4-tap configuration was unneeded since
flow misdistribution should be at a minimal with a CoV for the rig being less than 10%
over all flow rates.
V.3.2.3. Particle Count
Particle Counting was conducted with a Lighthouse Solair 3100+ light scattering
optical particle counter. The system pulled a constant 1 cfm of sample air into the unit
via a vacuum pump. Based on the light scattering principle, the equipment sized and
counted the airborne particulate matter into the following eight distributions: 0.3-0.5 ?m,
0.5 ? 0.7 ?m, 0.7-1.0 ?m, 1.0 ? 2.0 ?m, 2.0-3.0 ?m, 3.0- 5.0 ?m, 5.0 -7.0 ?m, and 7.0+
?m.
Samples were pulled from the isokinetic probes located at the center line of the
ductwork 1 foot before and 4 feet behind the test section. The isokinetic probes were
connected via Bev-a-Line XX tubing to a three way valve. Bev-a-Line XX tubing was
chosen because of its low occurrence of particle adhesion in the line. The three-way
valve allows samples to be taken from the upstream and downstream probes without
moving the particle counter.
The incoming sample had to be diluted down with clean, house air before being
counted because the TSI 8108 generated an overall particle concentration (107 particle/ft3)
well beyond the counting limit of the Solair 3100+. Clean air was obtained by running
compressed air through two, inline HEPA filters and a desiccant dryer. The clean air was
mixed with the sample air from the ductwork before being connected to the particle
counter. The dilute ratio was chosen as 21 LPM clean air and 7 LPM challenge air. This
136
ratio brought the concentration within a countable domain while keeping the resident
time in the tubing to a minimal (0.75 seconds) to prevent particle from settling in the line.
In order to use upstream and downstream dual probe configuration as described
above, it had to be determined that there was no deviation in sample counts between the
two locations. Figure 5.13 below shows that the two probes show similar counts when
monitoring a baseline concentration without the present of a test filter.
1.E+00
1.E+01
1.E+02
1.E+03
1.E+04
1.E+05
1.E+06
0 5 10 15 20 25 30
Sample #
Pa
rtic
le
Co
un
t (-
)
0.3-0.5 ?m (Upstream)
2.0-3.0 ?m (Upstream)
3.0-5.0 ?m (Upstream)
7.0+ ?m (Upstream)
0.3-0.5 ?m (Downstream)
2.0-3.0 ?m (Downstream)
3.0-5.0 ?m (Downstream)
7.0+ ?m (Downstream)
Figure 5.13: Comparison of Upstream and Downstream Counting Probes
V.3.3. Testing Procedures
V.3.3.1. Initial Pressure Drop
The initial, or clean, resistance to flow for a filtration unit was achieved by
measuring the pressure drop across the orifice plate and filtration section over the entire
range of frequencies. The filtration unit, either a single filter or a multi-element
137
structured array, was first loaded into its appropriate housing unit. The housing was
secured within the test rig by bolt assemblies and quick-grip clamps. When tighten, the
bolts aligned perpendicular to the flanges. This allowed the filtration units to
reproducibly mate with the flanges in the desired, flushed position to ensure the
elimination of flow disturbances due to misalignment. The 8 quick grip clamps were
positioned equal-distance around the perimeter of the test section. Each clamp provided
300 pounds of force equating to 15.7 PSI of pressure on the foam seals.
Figure 5.14: Alignment and Clamping System
The room temperature, dew point, and atmospheric pressure were recorded with
an Extech 445815 Hygrometer and a Conex JDB1 digital barometer. Based on the dew
point, the partial pressure of water (PH2O) in the air was computed. The partial pressure
of the air (PAIR) was calculated using the computed partial pressure of water and the
barometric pressure (PATM). The air density was calculated from the ratio of the
138
components using the ideal gas law. The equations to perform these calculations are
shown below.
PH2O =(6.1078*10^((7.5*(Dew Point (K))-2048.625)/(( Dew Point (K))-35.85)))*100
PAIR = PATM - PH2O
Air Density (in kg/m3) = PAIR / (287.05*T(K)) + PH2O / (461.50*T(K))
The pressure transmitters were then turned on and zeroed. The data acquisition
software was then initiated. The software recorded a 12-bit signal from each pressure
transmitter at a rate of 5 data points per second. The blower was turned on and allowed
to automatically ramp up to 60 Hz over the course of 420 seconds. A ramp rate of 420
seconds was chosen to eliminate trailing effects due to the transmitters not being in
equilibrium at the same point in time. Further information regarding this behavior can be
found in the Appendix. Once the blower reached 60 Hz, the system was shut down and
the data-logging software was stopped.
A text data file was generated from the software that was further processed in
Excel. The transducer?s readings, which were recorded as a 1 to 5 volt signal, was
changed to the corresponding pressure drop measurements. Face velocity was
determined from the orifice plate calibration curve utilizing the current air density.
V.3.3.2. Testing Procedure for Dirt Loading
Dirt loading tests were performed to artificially age the filter at an accelerated rate
in order to evaluate filter performance. The face velocity used during dirt loading was
500 fpm (2000 cfm). This velocity was chosen because it is a one of two common set
points in the HVAC industry. It was preferred over the second set point (300 fpm)
139
because the larger particles in the ASHRAE dust tend to settle in the ductwork due to
longer resident times.
The procedure began by weighing the test filter element(s) with a DENVER
Instruments S2002 scale. The scale has a top capacity of 2000 g with a resolution of
0.01g. The filter elements were prepped for the dirt loading test in the same manner as
the initial resistance. The specially design filter encasements and clamps held and
positioned the filer element in the correct arrangement. Pressure transmitters were zeroed
and atmospheric conditions recorded. The blower was initiated and set to deliver 1985
cfm of house air into the rig.
The clean air was mixed with a known concentration of dirt introduced into the
system by the Blue Heaven dust loader. The concentration was fixed by assuring that a
uniform height of dirt was evenly distributed across the tray. This was accomplished
with a leveling tool shown below. Challenge dirt was first dried out in an oven at 110?C
(230?F) for 30 minutes to promote dispersion of the material when subjected to the
shearing forces of the venturi pump. The dirt was then loaded into the feed tray and
gradually spread out to achieve a uniform layer.
140
Figure 5.15: Loading Tray with leveling Tool
The tray was loaded to a height of 0.25? with a tray width of 4.5?. The chain feed
rate was 0.5 linear inches per minute. This equated to 0.56 in3 of challenge per minute.
When picked up and mixed with the 15 cfm of air supplied by the venturi pump and the
1985 cfm of clean air, the volumetric concentration delivered to the filter was 1.6 x10-7
ft3 dirt per ft3 air. A fully loaded tray (272.0 cm3 volumetric loading dirt) was
experimentally determined to weigh 82.9 grams. This equated to an apparent packing
density of 0.30 g / cm3 of tray volume. The mass load to the rig was computed to be 2.81
g / min equating to a delivered concentration of 1.4 x 10-3 g ASHRAE dust per ft3 air.
Data acquisition took place by turning on the pressure transmitter when the dirt
loader was turned on. There was a one minute lag between the time the dirt load started
and when the tray delivered the first amount of challenge dirt to the venturi pump. This
lag could easily be identified and removed from the gathered data.
141
Although the rig loaded the filter at a uniform rate, the blower will not continue to
output the desired volumetric flow. The blower?s volumetric output steadily dropped as
the static head in the system increased due to the filter?s loading. In order to keep the
blower set at 1985 cfm, the frequency drive was manually incremented to maintain a set
point resistance across the orifice plate. The rate at which the filter loads was quite low;
thus, it was very easy to maintain the flow within +- 20 cfm.
The filter was aged with ASHRAE dirt until a resistance of 1.0? H2O across the
filter unit was achieved. The test was stopped and the filter unit was removed and
weighed to determine the amount of dirt loaded. It was possible to periodically pull and
weigh the filter, but it was determine to be unnecessary for data processing since the
system loads at a uniform rate. Chapter VI showcases the uniformity of the loading rate
in context with other results. Periodically pulling the filter introduces errors into the data
collection due to potential disturbances of the cake formation on the filter?s surface.
Additionally, it ran the risk of dropping the filter and ruining the test.
V.3.3.3. Removal Efficiency Testing
A filtration removal efficiency test was performed to identify the ability of the
filter to remove particles based on their diameter. The test began by loading the desired
filters into their respectful filtration unit. The units were then clamped and sealed within
the ductwork in the same manner described for the initial resistance testing and loading
test. The blower was initiated and allowed to reach a face velocity of 500 fpm. The TSI
nebulizer was then started and the challenge KCl particle concentration was allowed to
equilibrate over a five minute period before data collection started.
142
Data collection was conducted with a Solair 3100+ particle counter. The process
was initialized by taking a 20 second sample count from the upstream isokinetic probe.
The three-way valve was then switched to allow a sample from the downstream
isokinetic probe to be obtained. Before the downstream sample was gathered, the counter
performed a 10 second self-purge to remove any remaining particles out of the line from
the previous sample. The counter then measured a 20 second count of the downstream
particles. The process was repeated until 50 counts were taken from the upstream and
downstream probes.
The data from the Solair 3100+ was downloaded via Lighthouse LMS Exchange
software. The data was transferred to Microsoft Excel were it was further processed.
The removal efficiency for a given size range was calculated based on the differential of
the downstream count to the average of the before and after upstream count. This is
shown in the formula below:
Penetration = [0.5(Ui-1 + Ui+1) ? Di]/ [0.5(Ui-1 + Ui+1)] 5.5
143
CHAPTER VI: FILTRATION PERFORMANCE OF NOVEL,
SINGLE FILTER DESIGNS
VI.1. Introduction
Section III.3 showed that by pleating beyond the initial acceptable resistance, a
filter could be constructed that incorporates more media while decreasing the initial
pressure drop. The capture of dust and debris by the filter increases the resistance of the
media and power consumption of the filter. Common notation would assume that an
increase in media area would result in a reduction of the rate that the filter loads and an
extension of the useful operational life of the filter. This assumption must be verified
before these novel designs can be utilized to their maximum potential. The following
chapter examines these packaging designs to determine how the additional media area
translates into enhanced energy performance.
VI.2. Materials and Methods
The filters utilized during this project were specially order from Quality Filters in
Robertsdale, AL. The elements possessed depths between 1? and 4? and employ pleating
strategies that span the media- and viscous-dominated regimes of the U curve. The
media used was Kimberly Clark Intrepid? 411SF and Type 355H. The following table
lists the filters, dimensions, and pleat counts. The filters were loaded with ASHRAE dirt
purchased from Blue Heaven Technology. Each filter was analyzed for initial resistance
and subjected to a loading test as outline before.
144
Table 6.1: Critical Parameters of Filters Utilized
Filter Depth Width Height Pleat Count Media Type
1 13/16" (1") 23.75" (24") 23.75" (24") 20 411 SF
2 13/16" (1") 23.75" (24") 23.75" (24") 28 412 SF
3 13/16" (1") 23.75" (24") 23.75" (24") 36 413 SF
4 13/16" (1") 23.75" (24") 23.75" (24") 44 414 SF
5 13/16" (1") 23.75" (24") 23.75" (24") 52 415 SF
6 13/16" (1") 23.75" (24") 23.75" (24") 60 416 SF
7 1.75" (2") 23.375" (24") 23.375" (24") 15 417 SF
8 1.75" (2") 23.375" (24") 23.375" (24") 20 418 SF
9 1.75" (2") 23.375" (24") 23.375" (24") 25 419 SF
10 1.75" (2") 23.375" (24") 23.375" (24") 30 420 SF
11 1.75" (2") 23.375" (24") 23.375" (24") 35 421 SF
12 1.75" (2") 23.375" (24") 23.375" (24") 40 422 SF
13 3.5" (4") 23.375" (24") 23.375" (24") 10 423 SF
14 3.5" (4") 23.375" (24") 23.375" (24") 16 424 SF
15 3.5" (4") 23.375" (24") 23.375" (24") 22 425 SF
16 3.5" (4") 23.375" (24") 23.375" (24") 28 426 SF
17 13/16" (1") 23.75" (24") 23.75" (24") 20 355 H
18 13/16" (1") 23.75" (24") 23.75" (24") 28 356 H
19 13/16" (1") 23.75" (24") 23.75" (24") 36 357 H
20 13/16" (1") 23.75" (24") 23.75" (24") 44 358 H
21 13/16" (1") 23.75" (24") 23.75" (24") 52 359 H
22 13/16" (1") 23.75" (24") 23.75" (24") 60 360 H
VI.3. Results and Discussion
VI.3.1. Initial Resistance of 411SF Filters
Figure 6.1 through 6.3 demonstrated the initial ?U? curves for each set of filter
depths composed of 411SF media. In additional, the model presented in Chapter III was
utilized to predict the initial resistance. The model was able to estimate the resistance
quite well without the need for modification factors. One of the limitations discussed in
Chapter IV was the potential inability to apply the model to filtration systems with face
dimensions different than 20?x20?. The figures show that this is not the case for filter
with dimensions of 24?x24?.
145
0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
10 20 30 40 50 60 70
Pleat Count (Pleats/Filter)
Pre
ssu
re
Dr
op
("
H
2O
)
Model Predictions
Observed Results
Figure 6.1: Pleating Curve for 24?x24?x1? Filters at 500 fpm
Filters composed of 411 SF media
Minor discrepancies where observed when modeling the 24?x24?x2? filters;
however, the valves for the most part fell within the ? 5% error bars. Of particular note,
the pressure drop of the 24?x24?x2? filter with 35 pleats could most certainly be
attributed to improper construction. The pleating was erratic with several of the pleats
very tightly spaced while others remained open. The deviation of the 24?x24?x4? 15
pleat filter is attributed to the variation in element housing. Quality filters constructed
this filter with a different filter housing which possessed combs and a higher degree of
blockage than the other 24?x24?x4? filters. The combs were removed prior to testing,
but the filter still had a additional housing effects that could not be removed.
146
0
0.1
0.2
0.3
0.4
0.5
0.6
5 10 15 20 25 30 35 40 45 50
Pleat Count (Pleats / Filter)
Pre
ssu
re
Dr
op
("
H
2O
)
Model Predictions
Observed Results
Figure 6.2: Pleating Curve for 24?x24?x2? Filters at 500 fpm
Filters composed of 411 SF media
0
0.1
0.2
0.3
0.4
0.5
0.6
0 5 10 15 20 25 30 35
Pleat Count (Pleats / Filter)
Pre
ssu
re
Dr
op
("
H
2O
)
Model Predictions
Observed Values
Figure 6.3: Pleating Curve for 24?x24?x4? Filters at 500 fpm
Filters composed of 411 SF media
147
VI.3.2. Dirt Loading
Figure 6.4 presents the dirt loading results obtained on the 24?x24?x1? deep
filters. It was presumed that the additional filtration media would allow an element to
hold more dirt. It can be seen that the higher pleat counts do hold more dirt than the
lower pleat counts. The 20, 28, 36, 44, 52, and 60 pleat filter were able to catch 22.8,
40.7, 52.0, 59.5, 64.0, and 58.4 grams of dirt respectfully before reaching their final
resistance of 1.0? H2O.
The ability to capture more particulate matter, however, did not have a linear
relationship with increasing available media. The effect can be seen when comparing the
52 pleat element to the 60 pleat element. The 60 pleat element not only started at a
higher resistance, but it remained at a higher resistance over the course of the filter aging.
If the dirt holding increased linearly with media, the 60 pleat should age slower and
eventually operate at a lower resistance.
148
0
0.2
0.4
0.6
0.8
1
1.2
0 15 30 45 60 75
Load (g ASHRAE Dust)
Pre
ssu
re
Dr
op
("
H
2O
)
20 Pleats
28 Pleats
36 Pleats
44 Pleats
52 Pleats
60 Pleats
Figure 6.4: Dirt Loading for 24?x24?x1? Filters
Figures 6.5 better demonstrates this behavior by plotting the nominal increase in
resistance versus the normalized loading per media area. The nominal increase in
resistance is the current resistance minus the filter starting resistance, or more simply:
?PNOMINAL = ?PFILTER ? ?PINITIAL 6.1
The nominal resistance eliminates the discrepancies created by variations in the initial
resistance and allows the data to be viewed as increase in pressure per unit of loading.
The normalized dirt loading is defined as the weight capture divide by the available
media. By plotting the data in this manner, the filter can be assessed based on the
pressure performance and utilization of the media employed.
149
0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0 1 2 3 4 5 6
Normalized Dirt Loading (g/sq.ft)
No
mi
na
l R
es
ist
an
ce
In
cre
as
e (
" H
2O
)
20 Pleats
28 Pleats
36 Pleats
44 Pleats
52 Pleats
60 Pleats
Figure 6.5: Normalized Loading Profiles of 24?x24?x1? Filters (411SF Media)
The normalized rate of loading between the various pleat counts is clearly
affected by the degree of pleating. The incorporation of extra media lowered the rate of
loading as seen by comparing the 20 pleat curve to the 28 pleat curve. This can be
explained by Darcy?s law. Previous research states that dirt loads within the filter and
then on the surface. Both of these effects will influence the media or Darcian term of the
filter?s pressure drop by decreasing the permeability and increasing the thickness. The
Darcian term is a first order function of media face velocity. The additional media area
slows the face velocity through the media; thus, the resistance induced by a thicker, lower
permeability media due to dirt clogging is reduced because of the lower media face
velocity. The net outcome is a slower normalized aging of the unit.
This hypothesis is supported by examining the slopes of the 20 and 28 pleat filters
while operating in the depth filtration regime. The slope of the 20 pleat filter, fitted by
150
Excel as shown below, was calculated at 0.1068? H2O per g/ft2 loaded. The slope of the
28 pleat filter was determined to be 0.0735? H2O per g/ft2 loaded. The normalized
loading rate was thus reduced by 30%. The face velocity through the 20 pleat filter is
calculated to be 93.3 fpm. The inclusion of extra 8 pleats into the design reduced the face
velocity to 66.6 fpm. This equated to a 29% decrease in face velocity.
y = 0.1068x
R2 = 0.9892
y = 0.0735x
R2 = 0.9953
0
0.05
0.1
0.15
0.2
0.25
0.3
0 0.5 1 1.5 2 2.5 3
Normalized Dirt Loading (g/sq.ft)
No
mi
al
Re
sis
tan
ce
Inc
rea
se
("
H2
O)
20 Pleats
28 Pleats
Figure 6.6: Depth Filtration Regime for 20 and 28 Pleat Filter
By this approach, increasing the pleat count further should result in an even
greater reduction in media face velocity and subsequently normalized aging rate of the
filter. Again, this was not observed. Counter intuitively, the normalized aging rate
begins to increase after the 28 pleat filter. Although the 36 pleat filter still possessed a
lower aging rate than the 20 pleat, all pleat counts above 36 have a faster normalized
aging rate than the 20 pleat filter.
151
The one of two hypotheses for this effect is preferential blockage of the material
brought on by an increase in the pleating angle beta (?). The media is more exposed to
the incoming dirt challenge at lower pleating angles. An increase in the angle aligns the
fibers to be more directly behind their upstream neighbor. Large particles, such as those
found in ASHRAE dirt, cannot follow the streamlines and preferentially load on the
surface fibers of the filter. This blocks the inner portions of the filter from subsequent
particles, and the filter prematurely transitions to cake formation. Figure 6.7
demonstrates this hypothesis. The green circles represent the array of fibers within the
filtration media. The black dots are large particulates that are captured by impaction or
interception. The blue line represents the flight path of the particle. As can be seen in
this simple schematic, the higher angled media eliminates the interiors of the media from
being accessed by the particles. A shell builds on the front of the fiber causing the media
to prematurely transition from depth to cake filtration.
Figure 6.7: Schematic of Preferential Loading. (A) Low Beta Angle (B) High Beta Angle
152
Figure 6.8, which only re-graphs three of the six filters for clarity, indicates a
premature transition from depth filtration to cake filtration does occur. The normalized
loading rate of the 20 pleat filter is a linear line; thus, no transition occurs over the
loading ranges explored (0 to 4.5 g/sq.ft). The 28 pleat filter shows a transition from
depth to cake filtration at approximately 4 g/sq.ft. The higher angled 60 pleat filter
transitions very quickly from depth to cake filtration at 1.75 g/sq.ft. Although difficult, it
can also be deuced from Figure 6.5 that the transitions from depth to cake for the 36, 44,
and 52 pleated filter occurs at 3.5, 3.0, and 2.75 g/ sq.ft respectfully
y = 0.075x
y = 0.1064x
0
0.1
0.2
0.3
0.4
0.5
0.6
0 1 2 3 4 5 6 7
Normalized Dirt Loading (g/sq.ft)
No
mi
na
l R
esi
sta
nc
e I
nc
rea
se
("
H2
O)
20 Pleats
28 Pleats
60 Pleats
20 Pleat Depth Loading
28 Pleat Depth Loading
28 Pleat Cake Loading
60 Pleat Cake Loading
Figure 6.8: Normalized Loading Profiles of Select 24?x24?x1?
411SF Filters with Transition Lines.
The loading results of filter composed of type 355H media were very similar to
the results obtain with filter composed of type 411SF media. High pleat count filters
153
demonstrated a decrease in the normalized loading rate in the depth regime, yet transition
to cake loading prematurely.
The second hypothesis proposes that the premature transition to cake filtration is
caused by the reduction in face velocity through the filter. The reduction allows the
uppermost fiber layers to filter the incoming air with a higher efficiency. The topmost
layers thus become clogged more rapidly.
0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0 1.5 3 4.5 6 7.5
Normialized Loading (g/ sq.ft)
No
mi
na
l R
es
ist
an
ce
In
cre
as
e (
" H
2O
)
20 Pleats
28 Pleats
36 Pleats
44 Pleats
52 Pleats
60 Pleats
Figure 6.9: Normalized Loading Profiles of 24?x24?x1? Filters (355H Media)
The results were also similar when the analysis was performed on deeper pleated
filters. In Figure 6.10, higher pleat counts display more dirt holding capacity than their
lower pleat count counterparts. The only except is the 35 pleat count filter; however, this
is most likely a result of its poor construction. The benefits of pleating into the viscous-
dominate regime can be visualized by comparing the 30 pleat count to the 40. Although
154
the 40 pleat filter has a higher initial resistance, the overall pressure drop is lower
throughout most the course of operation.
0
0.2
0.4
0.6
0.8
1
1.2
0 20 40 60 80 100 120 140 160
Dirt Loading (G ASHRAE Dirt)
Pr
ess
ure
D
rop
("
H
2O
)
15 Pleats
20 Pleats
25 Pleats
30 Pleats
35 Pleats
40 Pleats
Figure 6.10: Dirt Loading for 24?x24?x2? Filters (411SF Media)
Looking at the normalized dirt loading of the 2? filters, all higher pleated filters
show a slightly slower rate of aging in the depth filtration regime; however, all of these
filters transition to the cake regime sooner than 15 pleat filter. This observance correlates
to the discussion above. The 15, 20, 25, 30, 35, and 40 pleat filters transition out of the
depth regime respectfully at the 5.5, 4.5, 4.0, 3.75, 2.5, and 3.0 g/ sq.ft
155
0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
0 1.5 3 4.5 6 7.5 9
Normialized Dirt Loading (g / sq.ft)
No
mi
al
Re
sis
tan
ce
Inc
rea
se
("
H2
O)
15 Pleats
20 Pleats
25 Pleats
30 pleats
35 pleats
40 Pleats
Figure 6.11: Normalized Dirt Loading for 24?x24?x2? Filters (411SF Media)
Figure 6.12 and 6.13 shows that the 4 inch deep filters exhibit the same trends.
Another interesting behavior is well displayed in the normalized dirt loading of the 4 inch
filters. The slope of the aging rate is nearly identical during the depth filtration regime;
however, once the filters transition to the cake regime their slopes become much greater
at higher pleat counts. The 10 pleat filter shows a cake slope of 0.28? H2O increase per
g/sq.ft loaded. The 28 pleat filter shows an increase of 0.46? H2O per g/sq.ft. Thus, it is
very important when utilizing higher pleat counts to change the filter sooner after the
transition has occurred.
156
0
0.2
0.4
0.6
0.8
1
1.2
1.4
1.6
0 20 40 60 80 100 120 140 160
Dirt Loading (g ASHRAE DIrt)
Pre
ssu
re
Dr
op
("
H
2O
)
10 Pleats
16 Pleats
22 Pleats
28 Pleats
Figure 6.12: Dirt Loading for 24?x24?x4? Filters (411SF Media)
157
0
0.2
0.4
0.6
0.8
1
1.2
0 1 2 3 4 5 6 7 8 9
Normialized Dirt Loading (g/ sq.ft)
No
mi
al
Re
sis
tan
ce
Inc
rea
se
("
H2
O) 10 Pleats16 Pleats
22 Pleats
28 Pleats
Figure 6.13: Normalized Dirt Loading for 24?x24?x2? Filters (411SF Media)
Figure 6.14 examines all 22 filters to see if there is a relationship between the
transition point and the pleating angle. The data indicates that there is a general trend
between increasing pleat angle and delaying the onset of the transition point. The graph
also indicates that the depth of the filter plays a role with the onset of the transition point.
In general, filters with deeper pleats transition at a higher media utilization for a given
pleating angle.
158
Figure 6.14: Relationship between Pleating Angle and Transition Point
Initially, there was some concern that the observed results were actually an
artifact of the measurement process. Filters, unlike sieve trays, can not capture 100% of
the test dirt. The two media (411SF and 355H) types utilized in this experimentation are
only rated for removing >95% and >90% of ASHRAE dust. As discussed, a filter
becomes more efficient at removing dirt as it ages. Since the filters were only weighed at
the start and end of the test and believed to load at a uniform rate, in theory the majority
of dirt could have been captured in the cake regime when the filtration efficiency is at its
highest. This would artificially skew the results so that the steep increase in resistance
looks to be the caused by only a small amount of dirt.
To eliminate this possibility, the 24?x24?x2? 411SF filter were not loaded
continuously from start to finish. The filters were loaded from their initial resistance
159
until a resistance of 0.5? H2O was reached. The filters were removed, weighed, and
reinserted to be loaded again. This process was continued with stopping points of 0.75
and 1.0? H2O. The results of the loading rates for the 15, 20, and 40 pleated filters are
shown in Tables 6.2 through 6.4.
Table 6.2: Interval Loading Rate for 24?x24?x2? 411SF Filter with 15 Pleats
Time Filter Weight Loading Interval Loading Load Rate
(min) (g) (min) (g) (g/min)
0 383.52 n/a 0 n/a
11.41 411.08 11.41 27.56 2.42
20.06 435.63 8.65 24.55 2.84
26.42 452.28 6.36 16.65 2.62
Table 6.3: Interval Loading Rate for 24?x24?x2? 411SF Filter with 20 Pleats
Time Filter Weight Loading Interval Loading Load Rate
(min) (g) (min) (g) (g/min)
0 462.79 n/a 0 n/a
19.91 516.06 19.91 53.27 2.68
30.44 543.32 10.53 27.26 2.59
37.34 561.15 6.9 17.83 2.58
Table 6.4: Interval Loading Rate for 24?x24?x2? 411SF Filter with 40 Pleats
Time Filter Weight Loading Interval Loading Load Rate
(min) (g) (min) (g) (g/min)
0 701.92 n/a 0 n/a
24.99 773.16 24.99 71.24 2.85
45.37 825.25 20.38 52.09 2.56
56.69 853.52 11.32 28.27 2.50
The three filters showed that they did not age at a faster rate as they were loaded
with dirt and their efficiency increased. The average loading rate for each filter was 2.62,
2.62, and 2.63 g/min with coefficients of variance of 8.1, 2.0, and 7.2 %.
160
VI.3.3. Estimations of Useful Lifetime and Power Consumption
Based on the loading data obtained, estimations for the useful lifetime and the
average energy consumption of these filters were made. The analysis had to make
several assumptions before the values could be calculated. A filter was assigned a useful
life of 6 months or until 1? H2O pressure drop was reached. The filter was changed at
this point. The operational conditions were set at 2000 cfm with an average run time of
12 hours per day.
The total atmospheric dust concentration was estimated to be 30 ug/m3 of air with
the filter capturing a third of the dirt concentration. Total atmospheric dirt concentration
will very widely based on the environment. Remote conditions can possess less than 5
ug/m3. At the other end of the spectrum, dirt concentrations of 100 ug/m3 and above have
been recorded in urban settings (Bouchertall 1989, Kim et al. 2002). The rate of loading
is highly dependent on the composition of the incoming particle challenge, but it was
assumed that the loading rate based on the previously presented data held valid. The
national average power cost was taken from the Department of Energy?s Energy
Information Agency website as $0.11/kWh (April 2009 estimate). Energy consumption
only accounted for the pressure volume work to move air across the filter. The blower
efficiency and the losses due to power conversion were estimated at 70%. Filter costs
listed below were price paid to procure the filters from Quality Filters during the Fall of
2007. The power and energy analysis shown in Figure 6.15 through 6.17 and Tables 6.5
through 6.7 were prepared base on these assumptions.
161
0
1
2
3
4
0 30 60 90 120 150 180Time (Days)
Fil
ter
P
ow
er
Co
ns
um
pti
on
(W
)
1" with 20 Pleats 1" with 52 Pleats
2" with 15 Pleats 2" with 35 Pleats
4" with 10 Pleats 4" with 22 Pleats
Figure 6.15: Average Power Consumption of 24?x24?x1? Filters
Table 6.5: Estimated Lifetime Costs for 24?x24?x1? Filters
Filter Pleats
Filter
Cost
Energy
Usage Energy Cost Total Cost
Type (#) ($) (kWh) ($) ($)
Standard 1" Deep 20 $3.42 566 $62.33 $65.75
Premium 1" Deep 28 $4.79 508 $55.95 $60.74
Custom 1" Deep 36 $6.14 438 $48.22 $54.36
Custom 1" Deep 44 $7.52 422 $46.48 $54.00
Custom 1" Deep 52 $8.89 398 $43.84 $52.73
Custom 1" Deep 60 $10.26 436 $47.96 $58.22
The analysis demonstrated that using higher pleat counts will result in a decreased
energy usage. The energy reduction will more than offset the initial increase in
procurement costs. For example, an additional upfront cost of $5.47 to purchase a 52
pleat filter instead of a 28 filter decreased the energy requirement by 168 kWh over the
course of six months. This translated into a reduction in energy cost of $18.49.
162
0
0.5
1
1.5
2
2.5
3
3.5
4
4.5
0 30 60 90 120 150 180
Time (Days)
Fil
ter
P
ow
er
Co
ns
um
pti
on
(W
)
15 Pleats
20 Pleats
25 Pleats
30 Pleats
35 Pleats
40 Pleats
Figure 6.16: Average Power Consumption of 24?x24?x2? Filters
The power analysis preformed on the 24?x24?x2? demonstrated the benefit of
simply adding a marginal amount of additional media. The increase in media area from
15 to 20 pleats is enough to maintain the filter in the depth filter regime during the full six
months of operation. This results in a reduction of 80 kWh in energy.
Table 6.6: Estimated Lifetime Costs for 24?x24?x2? Filters
Filter Pleats
Filter
Cost Energy Usage Energy Cost Total Cost
Type (#) ($) (kWh) ($) ($)
Commercial 2" Deep 15 $4.65 468 $51.49 $56.14
Custom 2" Deep 20 $6.20 389 $42.84 $49.04
Custom 2" Deep 25 $7.44 307 $33.87 $41.31
Custom 2" Deep 30 $9.25 276 $30.44 $39.69
Custom 2" Deep 35 $10.85 264 $29.08 $39.93
Custom 2" Deep 40 $12.40 266 $29.27 $41.67
163
The employment of an even deeper-pleated filters results in a further reduction in
energy consumption. The best case energy scenario for a 1? and 2? deep filter has
estimated consumptions of 398 kWh and 264 kWh, yet a 4? filter can operate as low as
196 kWh over the same time span.
0
0.5
1
1.5
2
2.5
3
3.5
4
4.5
0 30 60 90 120 150 180
Time (Days)
Fil
ter
P
ow
er
Co
ns
um
pti
on
(W
)
15 Pleats
20 Pleats
25 Pleats
30 Pleats
35 Pleats
40 Pleats
Figure 6.17: Average Power Consumption of 24?x24?x4? Filters
Table 6.7: Estimated Lifetime Costs for 24?x24?x4? Filters
Filter Pleats
Filter
Cost
Energy
Usage Energy Cost Total Cost
Type (#) ($) (kWh) ($) ($)
Standard 4" Deep 10 $6.40 340 $37.49 $43.89
Custom 4" Deep 16 $10.24 237 $26.08 $36.32
Custom 4" Deep 22 $14.09 200 $21.96 $36.05
Custom 4" Deep 28 $17.92 196 $21.63 $39.55
The above analysis shows the effectiveness of the novel design in reducing the
energy consumption of a filtration unit. By utilizing a custom pleated 24?x24?x4? deep
filter over a standard 24?x24?x1? (Table 6.5), the energy consumption is reduced by 66%
164
resulting in an estimated energy savings of almost $40. The net upfront cost to procure
the 4? filter is a mere $11.08 more.
A 66% reduction in HVAC Pressure-Volume work would have a major impact on
the annual energy consumption of the United States. The Department of Energy
estimates that 60 million American households utilize some form of central air. These
households consume 356 billion kWh annually to power these air units (DOE 2009). Of
that 356 billion kWh, roughly 15% goes to the Pressure-Volume work required to move
air across the filter units. The deployment of a more efficiently designed filter would
reduce this consumption and could lead to a 35.7 billion kWh reduction in annual energy
consumption within the United States.
165
CHAPTER VII: FILTRATION PERFORMANCE OF MULTI-ELEMENT
STRUCTURED ARRAYS
VII.1. Introduction
Multi-Element Structured Arrays are capable of decreasing the initial pressure
drop of a filtration system by incorporating numerous filter element into a single
configuration thereby decreasing the face velocity through each element. The reduction
in resistance is often greater than 50% when compared to the precursor single elements.
As with a single filter, the initial pressure drop is just one of many criteria on which
performance can be based. The aspects of removal efficiency and dirt loading must be
assessed in order to evaluate the overall performance of a MESA. The following chapter
performs head-to-head comparison between MESA?s and the single elements that
comprise them to determine the deviations in removal efficiency and dirt holding
capacity. Modifications within the MESA design are also tested to verify enhancements
on the overall filtration performance.
VII.2. Particulate Removal Efficiency of a MEPFB
Since the removal efficiency of a filter is primarily dependent on the media design
and particulate challenge, a MESA should not suffer from any major reduction in its
ability to capture particles. There is a concern though that a MESA might decrease the
removal efficiency of the impaction mechanism due to the large reduction in media
velocity. If a MESA is not capable of removing particulate matter at the same efficiency
as the elements from which it is built, then the overall benefit of the unit will be greatly
166
decreased. This assessment depends entirely on the MESA being properly sealed into
place.
VII.2.1. Materials
A particulate removal evaluation was performed on a single 24?x24?x1? pleated
filter and on a V bank built with identical 24?x24?x1? elements. The filter elements used
were commercially available from Quality Filters. Each element possessed 28 pleats and
was composed of Kimberly Clark Intrepid? filtration media (Type 355H). A general
description of the test rig and procedure used for the experimental can be found in
Chapter V.
VII.2.2. Results and Discussion
The MESA filtration unit demonstrated a removal efficiency that was comparable
with the single filter?s removal efficiency. Figure 7.1 was the observed results for the
removal efficiency testing. The removal efficiencies of the two systems essentially
overlapped or fell within the standard deviation error bars for particulate sizes greater
than 1 micron. Of note, the removal efficiency of the MESA units in the sub-micron
regime was higher than the single filter. The primary removal mechanism for particles
of this size range is Brownian diffusion. Since the air velocity through the MESA?s
media was one-half the value of the single filter, the resident time in the filter was
increased. It was quite reasonable to expect the removal efficiency to improve in this
regime since capture by Brownian motion increased with increased resident time.
167
0
10
20
30
40
50
60
70
80
90
100
0.3-0.5 0.5-0.7 0.7-1.0 1.0-2.0 2.0-3.0 3.0-5.0 5.0-7.0 7.0+
Channel Range (?m)
Re
mo
va
l E
ffic
ien
cy
(%
)
Single Filter
MESA Filter
Figure 7.1: Removal Efficiency of a Single Filter and MESA
Figure 7.2 & 7.3 demonstrates the increase in removal efficiency with increasing
dirt loading for the single filter as well as the MESA unit. This behavior is very common
in depth loading filters and has been well reported in the literature (Japuntich et al. 1994,
Stenhouse and Trottier 1991, Podgorski and Grzybowski 2000). The removal efficiency
of a depth filter increases with loading because of the formation of dendrites within the
fibrous media. The dendrites act as additional fibrous onto which the particles are
captured. The major exception to this behavior occurs with electrostatic filter. As these
particular filters clog, the charge on the fibers neutralizes with the loaded dirt and the
removal efficiency drops.
168
0
10
20
30
40
50
60
70
80
90
100
0.3-0.5 0.5-0.7 0.7-1.0 1.0-2.0 2.0-3.0 3.0-5.0 5.0-7.0 7.0+
Channel Range (?m)
Re
mo
va
l E
ffic
ien
cy
(%
)
Clean
0.5" H2O
0.75" H2O
1.0" H2O
Figure 7.2: Removal Efficiency of a Single Element during Loading Conditions
0
10
20
30
40
50
60
70
80
90
100
0.3-0.5 0.5-0.7 0.7-1.0 1.0-2.0 2.0-3.0 3.0-5.0 5.0-7.0 7.0+
Channel Size (?m)
Re
mo
va
l E
ffic
ien
cy
(%
)
Clean
0.5" H2O
0.75 " H2O
1.0 " H2O
Figure 7.3: Removal Efficiency of a MESA during Loading Conditions
169
Both filter systems were capable of removing particles 2.0 micron and larger with
an efficiency of >90 % once loaded. The single filter, however, significantly lagged
behind the MESA?s efficiency in the lower micron regime. In particular, the single filter
was never able to successfully remove particles in the 0.3 to 0.5 micron range.
The real benefit of a MESA style unit can be seen when comparing the systems
with a performance versus costs filters metric such as the quality factor. The quality
factor is the log removal efficiency divided by the pressure drop [Brown 1993, Matteson
and Orr 1987].
QF = ln(?) / ?P 7.1
The chart below compared the MESA to a single filter based on this parameter. The
MESA?s boosted a quality factor at least double that of the single filter?s factor over the
parameter spaced explored.
0
5
10
15
20
25
30
35
40
0.3-0.5 0.5-0.7 0.7-1.0 1.0-2.0 2.0-3.0 3.0-5.0 5.0-7.0 7.0+
Channel Size (micron)
Qu
ali
ty
Fa
cto
r (
%
pe
r "
H
2O
)
Single Filter
MESA
Figure 7.4: Quality Factor Analysis
170
VII.3. Dirt Loading of MESA?s
MESA?s have been demonstrated to perform at an equal or better removal
efficiency compared to single filter element, yet they do so at a reduced initial pressure
drop while providing additional available media. Chapter VI demonstrated that an
increase in media area did not automatically translate into an increase in dirt holding
capacity. MESA comprised of various elements and pleat counts were investigated to
obtain a working knowledge of their dirt holding capacities. The results of the tests were
use to evaluated MESA for useful lifetime, power consumption, percent media
utilization, and performance enhancement over single filters.
VII.3.1. Materials
The experimentation utilized custom ordered 24?x24?x1? purchased from Quality
Filters. The filters were constructed with Kimberly Clark Intrepid? filtration media Type
355H. The filters were subjected to a loading analysis with ASHRAE synthetic dirt
procured from Blue Heaven Technologies.
VII.3.2. Results and Discussion
VII.3.1.1. Influence of Pleat Count within an MESA
V MESA units were employed to study the effect of increasing the element pleat
count while holding all other variables constant. The result (Figure 7.5 and 7.6) showed
that the general trends observed were similar in nature to the trends observed in the single
filter elements. MESA?s constructed with higher pleated element demonstrated the
capacity to hold more dirt before reaching their final resistance of 1.0? H2O.
171
0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1
0 50 100 150 200
Total Dirt Loading (g)
Pre
ssu
re
Dr
op
("
H
2O
)
V MESA - 20 Pleats
V MESA - 28 Pleats
V MESA - 36 Pleats
V MESA - 44 Pleats
V MESA - 52 Pleats
V MESA - 60 Pleats
Figure 7.5: Total Dirt Holding Capacity of V MESA with Various Pleat Counts
The additional area provided by increasing the element pleat count in a MESA did
not show a linear relationship with dirt loading. The normalized dirt loading showed that
the elements still underwent a preferred media utilization pattern with a 28 pleat count
MESA demonstrating the highest utilization. This pattern was very similar to the one
present in Chapter VI.
172
0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1
0 1.5 3 4.5 6 7.5 9
Normialized Dirt Loading (g/sq. ft)
No
mi
na
l R
es
ist
an
ce
In
cre
as
e (
" H
2O
) V MESA - 20 Pleats V MESA - 28 Pleats
V MESA - 36 Pleats
V MESA - 44 Pleats
V MESA - 52 Pleats
V MESA - 60 Pleats
Figure 7.6: Normalized Dirt Holding Capacity of V MESA with Various Pleat Counts
Table 7.1 was constructed by locating the transition point of all pleat counts of the
V Mesa and the precursor single elements that were ensemble into the MESA?s. As seen,
the lower pleat count elements of each designs showed similar utilization of the media
before transitioning out of the depth regime. This trend did not continue as the elements
are pleated higher. Higher pleated MESA showed a lower media utilization than their
single element counterparts.
Table 7.1: Transition Point of V MESA and Single Elements
Pleating Single Filter Transition V MESA Transition
Pleats / Element (g / sq. ft) (g / sq. ft)
20 3.0 3.0
28 2.8 2.8
36 2.75 2.5
44 2.5 1.75
52 2.25 1.75
60 2.0 1.5
173
VII.3.1.2. Influence of Element Count within an MESA
V and W MESAs? constructed out of 24?x24?x1? filter elements were compared
to their single filter precursor to determine the influence of increasing the element count
of a filtration system. The elements possessed 28 pleats and were made from Kimberly
Clark 355H fibrous media. Both arrays were able to operate at a lower resistance level
than the single filter when subjected to the filtration loading. Due to the decreased initial
resistance, the V MESA was able to be loaded with 42 grams of ASHRAE dust before it
even reaches the initial pressure drop of the single filter. The W MESA further
outperformed the other systems and was capable of operating below their initial pressure
drop until it captured 75 grams and 125 grams of dirt respectively. The total dirt holding
achieved by the W MESA (241.3 g) before reaching the final resistance was significantly
greater than both the single filter (53.5g) and V MESA (130.3 g).
0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1
0 50 100 150 200 250
Dirt Loading (g)
Pre
ssu
re
Dr
op
("
H
2O
)
Single Filter
V MESA
W MESA
Figure 7.7: Total Dirt Loading of Various Element Count Systems
174
The MESA did not show the same aging rate or media utilization that a single
element displays. In the depth filtration regime, the V and W MESA aged at a slower
rate (0.042? H2O per g/ft2 and 0.02? H2O per g/ft2) than the single filter (0.064? H2O per
g/ft2). This corresponded to a 34% and 69% reduction in the aging rate while in the depth
regime. The most likely explanation for the decreased loading rate was the 50% and 75%
reduction of face velocity achieved with utilizing more elements within the MESAs?.
0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1
0 2 4 6 8 10
Normialized Dirt Loading (g/sq.ft)
No
mi
na
l R
esi
sta
nc
e I
nc
rea
se
("
H2
O) Single FilterV MESA
W MESA
Single Filter Depth Loading
V MESA Depth Loading
W MESA Depth Loading
Figure 7.8: Normalized Loading Profile of a Various Element Count Systems with
emphasis placed on the Depth Loading Regime
The transition to cake filtration occurred at approximately 2.8 g/ft2 for both the
single element and the V MESA, yet the W MESA transitions sooner at 2.2 g/ft2. Based
on the hypothesis of preferential surface loading postulated for the single filter element,
this was expected since the elements are aligned more directly with the incoming
175
challenge dirt as well as subjected to a slower media velocity. This theory was backed by
the increased normalized loading rate in the cake regime of both MESA?s. In particular,
the W MESA loaded at a 67% quicker rate than the single element once it had
transitioned to cake filtration. This is important to realize because a MESA will very
quickly increase in power consumption once cake filtration is reached; thus, appropriate
change out measures must be implemented.
The shape of the transition region of the MESA was also interesting because it
occurs over a broad range. Figure 7.9 below graphed the above plot with the V MESA
removed for clarity. The single filter had two, very pronounced slopes indicating depth
and surface filtration with a sharp transition point. The MESA had a gradual,
intermediate slope between the depth close and the cake slope. The exact reason for this
broad transition is unknown.
176
0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1
0 1.5 3 4.5 6 7.5 9
Normialized Dirt Loading (g/sq.ft)
No
mi
na
l R
es
ist
an
ce
In
cre
as
e (
" H
2O
) Single Filter
W MESA
Single Filter Depth Loading
W MESA Depth Loading
Single Filter Cake Loading
W MESA Cake Loading
Figure 7.9: Normalized Loading Profile of a Various Element Count Systems with
emphasis placed on the Cake Loading Regime
VII.3.1.3. Power Consumption Analysis
A power consumption analysis similar to the one performed in Chapter VI was
reused to demonstrate the power consumption and associated cost of a MESA system
compared to a single filter. Over the six month period, both MESAs? were able to
operate significantly below the initial power consumption of the single filter. The
employment of a V MESA instead of a traditional, flat filter resulted in a 40% reduction
in energy consumption. The saving to the end user was an estimated $19.83 over the six
month period. A W MESA, with its decreased loading rate in the depth regime, barely
aged and had a power consumption that was essentially a function of its initial pressure
177
drop. The net decrease in energy consumption was almost 80% resulting in a savings of
$38.96.
0
0.5
1
1.5
2
2.5
3
3.5
4
4.5
5
0 30 60 90 120 150 180
Time (Days)
Filt
er
Po
we
r C
on
sum
pti
on
(W
)
Single Filter
V MESA
W MESA
Figure 7.10: Power Consumption of MESAs? and Single Filter
Table 7.2: Associated Costs
Filter Pleats Filter Cost Energy Usage Energy Cost Total Cost
Type (#) ($) (kWh) ($) ($)
Std. 1" Deep 28 $3.98 462 $50.81 $58.77
V MESA 28 $7.96 281 $30.98 $38.94
W MESA 28 $15.92 107 $11.85 $27.77
VII.4. Preferential Element Alignment within a MESA
Pleated filter elements can be loaded into a MESA in two manners: horizontally-
oriented pleats (left side) or vertically-oriented pleats (right side). The effect of
alignment on performance was examined since the variation could affect the pressure
drop, dirt loading capacity, and aging profile of an array.
178
Figure 7.11: Horizontally-Oriented (Left) & Vertically-Oriented (Right) Banks
VII.4.1. Materials and Methods
Two filter types employed in MESA architectures were utilized to determine if
there was a performance deviation between the different pleat alignments corresponding
to a preferred configuration. Each MESA was evaluated for initial pressure drop and
loading profile. The first MESA unit was composed of DP 4-40 air filters from Airguard.
DP 4-40 elements possessed dimensions of 24?x24?x4? (23.375?x23.375?x3.75?) and
were rated as MERV 8 filters. The filters were tested in a vertical and horizontal
alignment pattern within a V MESA housing. The second MESA unit employed
Airguard DP 95 filters. The 24?x24?x2? (23.375?x23.375?x1.75?) filters were loaded
into a W MESA. The manufacturer?s reported MERV rating for the DP 95 unit was 13.
It was necessary that all elements used in this experiment were identically made
because defects within a single element can translate into misperceived performance
variations between the pleat alignments when loaded into a bank. It was assumed that all
elements purchased from a commercial manufacturer would have similar initial
resistances and be free from defects. This assumption was verified by testing each filter
179
for initial pressure drop while oriented perpendicular to flow. Only slight variations
totally less than 5% were observed in the clean resistances and no physical defects were
seen among the filter sets.
VII.4.2. Results and Discussion
VII.4.2.1. Initial Pressure Drop
The initial pressure drop of the DP 4-40 and DP 95 MESA?s with pleats aligned
in both configurations are shown in Figure 7.12 and 7.13. Figure 7.12 demonstrates that
there were only minor variations within the initial resistance of the MESA units
composed of DP 4-40 filter. The horizontally-aligned MESA did operate at a slightly
reduced resistance above 500 fpm, but the magnitude of the decrease was small. This
also occurred in a flow rate regime in which filters traditionally do not operate. The
MESA composed of DP 95 filters displays no difference in initial resistance except for
some minor fluctuations due to noise in the measurement devices. These observances
were to be expected because air can access the same amount of media in both
configurations.
180
0
0.05
0.1
0.15
0.2
0.25
0.3
0 100 200 300 400 500 600 700 800
Face Velocity (fpm)
Pre
ssu
re
Dr
op
("
H
2O
)
Horizontally-Oriented Pleats
Vertically-Oriented Pleats
Figure 7.12: Clean Resistance of DP 4-40 Elements Loaded Vertically and Horizontally
into a V MESA Configuration
0
0.25
0.5
0.75
1
0 100 200 300 400 500 600 700 800
Face Velocity (fpm)
Pre
ssu
re
Dr
op
("
H
2O
)
Vertically Oriented pleats
Horizontally Oriented pleats
Figure 7.13: Clean Resistance of DP 95 Elements Loaded Vertically and Horizontally
into a W MESA Configuration
181
VII.4.2.2. Dirt Loading
Although the initial resistance did not indicate much benefit between the two
alignments, the MESA?s with horizontally-oriented pleats did show a slight improvement
in filtration performance over the vertically aligned under dirt loading conditions. These
results can be seen in Figures 7.14 and 7.15.
In the case of the DP 4-40 filters, the performance was roughly the same
throughout the test; however, the vertically-oriented filter transitioned from depth-to-cake
filtration regime slightly sooner than in the horizontally-oriented filter. For the DP 95
filter based MESA?s, the horizontally oriented filter units showed a slower rate of growth
across the entire loading curve. The gap between the two orientations grew as the filters
were further aged. Of note, the filters were not able to transition from depth to cake
filtration because of the high initial resistance resulting in a shorten lifetime. Further
loading of the DP 95 units could have possibly indicated a larger deviation in the units?
performance; however, the test had to be stopped because of blower limitations.
182
Figure 7.14: Aging of DP 4-40 Elements Loaded Vertically and Horizontally into a V
MESA Configuration
0
0.2
0.4
0.6
0.8
1
1.2
0 20 40 60 80 100
Dirt Loaded (g ASHRAE Dirt)
Pre
ssu
re
Dr
op
("
H
2O
)
Vertically-Oriented Pleats
Horizontally-Oriented Pleats
Figure 7.15: Dirt Loading of DP 95 Elements Loaded Vertically and Horizontally into a
W MESA Configuration
183
It was postulated that the horizontally align bank elements achieve this slight
performance advantage over the vertically align elements because of the media being
preferentially loaded. The horizontally-oriented elements have both sides of the pleats
equally exposed to the incoming dirt challenge. The vertical-oriented pleats were not
equally exposed to the challenge dirt. The front side of the pleat was more inline with the
dirt as shown in Figure 7.12. For future reference, the pleat shaded grey below will be
referred to as the ?inline side? and the blue pleats are known as the ?shielded side?.
184
7.16: Schematic of Pleat Nomenclature
Although a preferential cake formation could be visually seen, it was very
difficult to quantitatively assess its influence and presence. The cake could not be
photographed because the opacity of the carbon black in the ASHRAE dirt obscured any
distinguishing contrasts or shadows. Figure 7.17 and 7.18 below were the best
representations that could be captured with the available digital camera. The inline side
pleats were solid black indicating complete coverage of the filtration media with the
185
carbon black. The shielded side pleats were primary black indicating that challenge dirt
was reaching the media, but small portions of the filter media remained the original green
color.
Figure 7.17: View of Inline Loaded pleats
Figure 7.18: View of Shielded Loaded pleats
186
To determine the degree of loading, two techniques were attempted. The initial
approach was to obtain basis weights at various intervals. This approach proved
inadequate because the media could not be dissected without distributing the cake
formation. Although the cake layer was destroyed, an air permeability test was still
conducted on the samples cut. The air permeability was conducted using the calibration
rig discussed in the Appendix.
y = 0.0027x
R2 = 0.9958
y = 5E-07x2 + 0.0026x
R2 = 0.9974
0
0.5
1
1.5
2
2.5
3
3.5
4
4.5
5
0 200 400 600 800 1000 1200 1400 1600
Face Velocity (fpm)
Pre
ssu
re
Dr
op
("
H
2O
)
Shielded #1
Shielded #2
Inline #1
Inline #2
Figure 7.19: Air Permeability of Sample Obtained from Vertical MESA
187
y = 7E-07x2 + 0.0029x
R2 = 0.9887
y = 5E-07x2 + 0.003x
R2 = 0.9974
0
0.5
1
1.5
2
2.5
3
3.5
4
4.5
5
5.5
0 200 400 600 800 1000 1200 1400 1600
Face Velocity (fpm)
Pre
ssu
re
Dr
op
("
H
2O
)
Top #1
Top #2
Bottom #1
Bottom #2
Figure 7.20: Air Permeability of Sample Obtained from Horizontal MESA
Figure 7.19 and 7.20 were created by dissecting the DP 4-40 filters and running
two samples from each filter. Figure 7.19 demonstrates that the pleat?s inline with the
incoming dirt showed a higher resistance than the pleats that have been shielded. This
would indicate that the filter was being loading unequally on the inline side. The samples
obtained from the horizontally aligned unit show resistances that were very similar. The
Excel-fitted trendlines indicated that the top and bottom pleats aged by the same degree.
A comparison between the two plots showed that the equally loaded horizontal
pleats had a higher resistance than both the inline and shielded pleats of the vertical
MESA. This was unique because the horizontal MESA operated at a lower resistance;
however, the result is most likely due to errors in the measurement technique. It would
be expected that the shield pleats have a higher permeability than the horizontal pleats
188
because they received less loading. The inline pleat, by the same mindset, should have a
lower permeability due to additional dirt loading. This was not seen because the cake
layer present on the inline side was disturbed when the samples were cut. It was believe
the inline pleat?s permeability was much lower during operating because of the cake layer
that accumulates on the surface. Thus, this technique was not valid.
The next approach adopted was to measure the flow resistance in situ at select
location to determine the magnitude of loading without disturbing the cake layer. This
technique proved unusable because of difficulties aligning a pressure probe within the
pleats as well as obtaining a good seal for an accurate measurement. Future work should
focus on improving the viability of the technique.
The third approach, known as the peeling technique, gently dissected the filtration
media utilizing adhesive squares (Thomas et al. 1999). Each square possessed two sides
of equal adhesive material. The square was attached to a wooden backing and an initial
weight as measured using a Citizen CX265 scale. The scale had a top weight of 60 g and
a precision of 0.0001 g. The square was then situated above the desire test spot, and
then pressed down with a 10 pound-force clamp. The clamp was then loosed, and the
square was then reweighed to determine the amount of dirt removed. The process was
continued until the square began to pull the fibers from the filter. Unlike the other
techniques, the cake layer was captured and removed from the surface in a manner gentle
enough to maintain its structural integrity.
The layering technique was preformed twice for each pleat side configuration.
Figure 7.21 through 7.23 showed the resulting squares after the analysis was performed
189
on the different pleat sides. Figure 7.24 graphed the averaged removed dirt per layer of
adhesive square.
Figure 7.21: Adhesive Squares and Removed Dirt from top and bottom Pleat Sides of a
Horizontally Oriented MESA after Dirt Loading
190
Figure 7.22: Adhesive Squares and Removed Dirt from inline Side of Vertically Oriented
MESA after Dirt Loading
Figure 7.23: Adhesive Squares and Removed Dirt from Shielded Side of Vertically
Oriented MESA after Dirt Loading
As seen in the pictures and the graph, the inline pleat side preferentially loads
with dirt more readily than its shielded counterpart. The results also backs the
assumption that the filtration media within the horizontally aligned MESA were exposed
to the dirt in an equal manner since the same amount of cake was deposit on the top and
191
bottom pleats. It was odd that the degree of difference between the quantities of dirt
loaded in the two orientations translates into a rather small difference in actual filtration
performance. The cake formation of the inline pleat surface was roughly ten times greater
than the shielded counterpart and five times greater than the horizontally oriented pleat
sides. Future research needs to be performed in order to more readily identify the flow
patterns and loading profiles within the two MESA orientations.
0
0.01
0.02
0.03
0.04
0.05
0 1 2 3 4 5 6 7 8 9
Layer # (-)
W
eig
ht
Re
mo
ve
d (
g)
Vertical MESA (Inline Pleat)
Vertical MESA (Shielded Pleat)
Horizontal MESA (Top Pleat)
Horizontal MESA (Bottom Pleat)
Figure 7.24: Weighed Pulled per Layer of Adhesive Backing
192
VIII. CONCLUSIONS AND FUTURE WORK
VIII.1. Conclusions
Novel packaging designs created by incorporate more pleats, elements, or deeper
pleats demonstrated a substantial boost in energy performance over traditional filter
designs. The incremental upfront cost to procure the filters is easily offset by the
reduction of energy cost associated with operation. These design could be operated on
the same maintenance schedule and essentially show no signs of aging before they are
replaced.
The addition of more pleats and elements each showed an optimal count resulting
in the lowest energy consumption. This optimal is brought about due to a gradually
decline in media utilization as more pleats and elements are sequentially used. For single
pleated filters, this optimal setting corresponded to a pleat count slightly higher than the
optimal count needed to obtain the lowest initial resistance. Further experimentation and
modeling efforts need to be employed to verify if this is a general trend among all filters
or a coincidence within these filter sets.
The most unique aspect of the aging test was the prematurely transitioning from
depth-to-cake as more pleats and element were added to the system. This is extremely
important because most filtration research assumes that the results obtained on a flat
piece of media will directly correlate to the performance characteristics when pleated. An
example of this is Raber (1982) who was unsuccessfully in attempting to model the aging
193
evolution of filter by extending the results deduced on the loading of a flat sheet to the
loading of a pleated filer. Location of the transition point is a high priority of interest to
the engineering community because it marks the time that the filter needs to be changed.
During the depth regime, the rise in pressure drop is low thus the filter is operating at a
high quality factor. Once the filter transition to cake region, the quality factor quickly
drops and the filter needs to be replaced.
VIII.2. Future Work
The robust worldwide market and the IAQ demands driving its growth provide a
strong incentive for further exploration of multi-element structured arrays as a platform
for dual-functioning microfibrous media. The recommendation for future work centers on
continuation of the current research as well as potential areas of deployment of
microfibrous media within newly devised packaging designs.
The utilization of microfibrous media as a dual functioning media needs to be
accessed in a full scale experimentation to determine the influence of fiber diameter,
particulate size, and porosity on pressure drop, particle removal efficiency, support
retention, dirt holding capacity, breakthrough time for a given contaminant, and
degradation of breakthrough time due to dirt blinding. A few potential areas of
deployment are cathode air filters for solid oxide or PEM fuel cells; air filtration masks
for biological or fire personal protection; remove of particulate matter and chemicals due
to cigarette smoke; and utilization in clean room or semiconductor environment.
As an extension of the current work, additional experimentation is foremost
needed to determine the exact mechanism causing the premature transition of the pleated
filters and MESA?s. Further investigation should also be conducted to determine the
194
influence of increasing element count in MESA composed of deeper pleated elements.
All experimentation preformed to this point could be further investigated through the use
of CFM modeling as well as flow visualization employing fluorescent tracers
particulates.
VIII.2.1 Utilization of Fairings
MESA modifications, such as the addition of fairings to reduce eddies created by
the front edge, should be investigated to lower the initial resistance of the system and
potentially extend the useful lifetime. Chapter IV demonstrates that the addition of a
gradual contraction to the front of the bank and a gradual expansion out of the bank
should eliminate the pressure drop associated with the blockage. Figure 4.20 indicated
that the addition of the fins should reduce a WW configured MESA?s initial pressure
resistance by approximately 10%. The effect on dirt capacity and removal efficiency
should be negligible, but this needs to be assessed.
VIII.2.2 Media Compression versus Permeability
Although unconventional for a pleated filter design standpoint, a MESA unit
might be better served by compressing the media and incurring a higher media resistance.
Once beyond the media-dominated regime, the only drawback to increasing the pleat
count is the heighten resistance due to flow in tighter pleats and additional pleat tip
blockage. The utilization of a thin media reduces both of these resistance influences. A
bank can then be built with a higher pleat count leading to a low media velocity and
higher filtration areas. The heighten media resistance will be offset by the substantially
lowered media velocity given ample media area. Thus, a bank can be packaged with more
media without drastically increasing the overall pressure drop.
195
VIII.2.3 Pyramid Filter
Higher element MESAs suffer from increased fixed resistance due to front edge
blockage. The utilization of fairing might offset this resistance; however, a second
approach is to design the filter units with a pyramid shape. The pyramid design would
effectively remove all resistance created by flow blockage. In addition, it also has the
potential to load more media into a give volume of ductwork than a MESA.
196
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200
APPENDIX A
A.1. Rotameter Calibration
The rotameters used to supply air to the media test rig were calibrated by a timed,
volumetric displacement technique. A container of known volume (9.2 liters) was
submerged in a large basin of water. The rotameters were set to the desired volumetric
flow rate. The rotameters? discharge was then positioned into the submerged container,
and the time to displace the 9.2L of water from the container was record. The volumetric
flow rate could be calculated by dividing the container?s volume by the recorded time to
displace the water. Fifteen different rotameters setting were examined, and the test was
performed twice at each setting. The rotameters were showed to be properly calibrated.
Figure A1: Rotameter Calibration Set-Up
201
y = 1.0055x
R2 = 0.9974
0
20
40
60
80
100
120
140
160
180
0 20 40 60 80 100 120 140 160 180
Rotameter Setting (SCFH)
Ob
se
rve
d V
olu
me
tric
Fl
ow
(S
CF
H)
Figure A2: Rotameter Calibration Curve
Table A1: Experimental Data
R1 R2 Total Flow Time 1 Time 2 Observed Flow Deviation
(scfh) (scfh) (scfh) (s) (s) (scfh) (%)
0 0 0 0 0 0.00 0.00
15 0 15 72.14 72.05 16.22 7.54
20 0 20 55.59 55.48 21.06 5.04
25 0 25 46.07 45.95 25.42 1.66
30 0 30 38.6 38.73 30.25 0.83
35 0 35 33.41 33.3 35.07 0.19
40 0 40 30.5 30.12 38.59 3.66
0 40 40 28.63 28.03 41.29 3.11
20 40 60 18.28 18.1 64.30 6.69
40 40 80 14.2 14.16 82.48 3.01
0 80 80 14.05 14.41 82.19 2.67
20 80 100 11.15 11.16 104.85 4.63
40 80 120 9.51 9.53 122.86 2.33
0 120 120 9.68 9.63 121.14 0.94
20 120 140 8.57 8.5 137.04 2.16
40 120 160 7.5 7.5 155.95 2.60
202
A.2. Calibration of Pressure Transducers
The pressure transducers utilized in the research were verified to be accurately
working by testing their measurements against a known pressure drop. The test apparatus
consisted of a 20? long ?? internal diameter PVC tube. Using the rotameters calibrated
above, a known volumetric flow rate was delivered to the tube. The pressure drop across
the tube was measured 1? foot the air inlet and 18? downstream. The measured resistance
could then be compared to the theoretical resistance calculated by Darcy?s Weisbach
equation for flow through a tube. The results and schematic are shown below.
Figure A.3: Calibration Tube
203
0
0.25
0.5
0.75
1
1.25
1.5
1.75
0 20 40 60 80 100 120 140
Volumetric Flow Rate (cfm)
Pre
ssu
re
Dr
op
("
H
2O
)
Measured Resistance
Theortical Resistance
Figure A4: Calibration Curve for Pressure Transducer #1
0
0.5
1
1.5
2
2.5
3
3.5
4
0 20 40 60 80 100 120 140 160 180 200
Volumetric Flow Rate (cfm)
Pr
ess
ure
D
rop
("
H
2O
)
Measured Resistance
Theortical Resistance
Figure A5: Calibration Curve for Pressure Transducer #2
204
A.3.Construction of Filter Holders
Single 24?x 24? filter holders were constructed out of aluminum bars cut to
precisely fit the nominal dimensions of the filter. Three units were constructed to fit the
three filter deeps used in this dissertation. The bars where outfitted with upstream and
downstream flanges that partial blocked the filter?s grating. The flanges were equipped
with closed cell foam creating a solid seal and preventing edge leak around the filter.
Reinforcing brackets were added to prevent the flanges from deforming when subjected
to the pressure of the clamps.
Figure A6: 24?x24?x2? Filter Holder
A.4. Construction of MESA Unit
MESA units were constructed primarily out of 5/8? particle board. The boards
were obtained as 48? x 24? rectangular pieces. They were then cut down into 24?x 24?
and 28?x24? sections. The 28?x24? squares serve as the top and bottom walls for the
MESA. The 24? x24? side walls were positioned into place using 24? spacer molds, and
205
then they were fastened to the extended squares using drywall screws. L brackets were
added to all eight corner to further strength the MESA unit.
Figure A7: MESA Housing Schematic
The units were outfitted with 1.5? flanges in order to mate up with the ductwork
and form a tight seal. The flanges were reinforced with 1? wide strips of particle board.
The reinforcing brackets were necessary to prevent the flanges from failing when
subjected to the 1800 pounds of force created by the clamping system. All cracks and
joints were sealed with RTV silicone gasket sealant. The flexible RTV gasket was both
air and water impermeable.
The filter elements were held in the MESA units by a combination of
mechanisms. The front edges were created by custom cutting aluminum or plastic
206
extruded U channel. The U channel fit tightly between the top and bottom walls to serve
as an anchor for the filter element. L channel were add to the top and bottom walls to
serve as support and provided additional seals for the filters. A solid seal is created
between the L bracket and the MESA unit through the use of closed-cell foam.
A.5. Weight Increase of ASHRAE Dirt under Atmospheric Conditions
The ASHRAE dirt is dried in an oven at 110?C (230?F) for 30 minutes prior to
being placed onto the dirt loader. The dust is dried to prevent agglomerations from
forming. The dirt is composed of three materials (AL2O3, SiO2, and Carbon black )
usually associated with high surface area. This could lead to water adsorption over the
course of the test would cause the errors in the associated weight of dirt loading. The
constituents of ASHRAE dirt, however, have very low pore volume to negate this
phenomenon from occurring. The graph below demonstrates the average uptake of the
synthetic challenge dust over the course of 90 minutes. Ninety minutes was chosen
because it represents the maximum time from leaving the oven to end weighing.
207
0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0 15 30 45 60 75 90 105
Time (min)
Pe
rce
nta
ge
W
eig
ht
Ga
in
(%
)
Figure A.8: ASHRAE Dust Water Uptake over Time
A.6. Observed Flow Channeling due to Pleat Tip Blockage
The models are based on the assumption that air is channeled around the pleat tips
due to an increase in Darcy?s constant. The carbon black present in the ASHRAE dust
stains the media when it comes into contact. Figure () and () below shows that incoming
challenge dirt was channeled away from the tips. Figure () is the upstream pleat tips after
a low dust loaded. Subsequent loading will turn the tips black; however, the downstream
tips retain their original white coloration even after the filter has been fully loaded.
208
Figure A.9: Upstream Pleat Tip after Dust Loading
Figure A.10: Downstream Pleat Tip after Dust Loading
A.7. Determination of Ramping Rate
The Hitachi inverter can control the frequency of the blower as well as the
frequency?s rate of changed. This function, when coupled with the data logging
capabilities of the pressure transmitters, allows flow versus pressure drop measurements
to be collected over the entire operational frequency range instead of at certain set points.
209
The inverter?s ramping rate, however, does affect the measurement readings. A fast
ramping rate causes the data to be artificially skewed towards a lower resistance at a
given face velocity. This occurs because the resistance data being recorded by the
upstream orifice?s transmitter is not in equilibrium at same point in time with the data
signal being recorded by the downstream filter?s transmitter.
It was necessary to determine an appropriate ramp rate in order to eliminate this
data lag. First, steady state data was gathered at various increments throughout the
frequency range. This data shows the actual pressure drop versus face velocity
relationship of the filter. Figure A11 illustrates the significant lag between a ramp rate of
120 Hz/min and steady state values. The lag in equilibrium between the two pressure
meters can be clearly seen at the end of the curve. The face velocity, which is measured
via the orifice transmitter, reaches equilibrium at 60 Hz several seconds before the filter?s
transmitter reaches equilibrium. This causes the final section of the graph to resemble a
vertical line. It was determined that a rate of 8.57 Hz/min was the fastest the system
could be ramped without created deviations between the set points and a continuous
graph.
210
0
0.1
0.2
0.3
0.4
0.5
0.6
0 100 200 300 400 500 600 700 800 900
Face Velocity (fpm)
Pre
ssu
re
Dr
op
("
H
2O
)
120 Hz/min
8.57 Hz/min
Steady State Points
Figure A.11: Variation in Pressure Measurements due to Incrementing Rate
Figure A.11 was generated by performing consecutive runs on the same filter
arrangement. The 95% efficiency pre-filter ensured that the filter did not age over the
course of the experimental tests. Before and after weight on the filter confirm this
statement. The tests were conducted by setting the inverter to the desired ramping rate
and allowing the system to auto-ramp to 60 Hz while the pressure transmitters data-
logged the measurements. The following ramping rates were investigated: 120 Hz/min,
60 Hz/min, 30 Hz/min, 20 Hz/min, 15 Hz/min, 12 Hz/min, 10 Hz/min, 8.57 Hz/min, 7.5
Hz/min, and 6 Hz/min. The additional data was not plotted for clarity reasons. The set
points were gathered by setting the frequency to a desired point, and then allowing the
system to remain static over the course of 30 seconds. The data for the last tens seconds
was gathered, processed, and then plotted.
211
APPENDIX B: NOMENCLATURE
B.1. Arabic Symbols
Ai = Area at Point i, ft2
A = Media (Darcy?s) Constant, ? H2O?min/ft
AT = Pleat Tip Media Loss, ft2
B = Media Constant, ? H2O?min2/ft2
Dc = Pore Hydraulic Diameter, ft
DH = Duct Height, ft
Dh = Hydraulic Diameter, ft
Di = Downstream Particle Count at time i, -
DW = Duct Width, ft
E = Energy, W?hr
EC = Element Count, -
FB = Front Edge Blockage, ft2
FD = Filter Depth, ft
FH = Filter Height, ft
Fi, = Force in Direction i, lbf
Fs = Force of surfaces on fluid, lbf
FW = Filter Width, ft
g = Gravity, ft/min2
h = Height, ft
Ki, = Friction Coefficient, -
Kn = Knudsen number, -
L = Length, ft
Lv = Viscous Losses, W?hr
m = mass, lbm
M = Dust Load, lbm
MT = Media Thickness, ft
N = Empirical Constant,
Pi = Pressure at Point i, ? H2O
Pc = Pleat Count, -
PH = Pleat Height, ft
PL = Pleat Length, ft
?P = Pressure Drop
Q = Volumetric Flow Rate, ft3/min
QF = Quality Factor, %/?H2O
R = Fiber Radius, ft
Re = Reynolds number, -
212
SO = Slot Opening, ft
SD = Slot Depth, ft
SH = Slot Height, ft
t = Time, min
Ui = Upstream Particle Count at time i, -
ui = Vector in Direction I, -
Vi = Velocity at Point I, ft/min
W = Mass Flow Rate, lbm/s
?z = Filter Thickness, ft
B.2. Greek Symbols
? = Slot Pitch, radian
?V = Velocity Ratio, -
?SM = Solid Mass Fraction, -
? = Pleat Pitch, radian
? = Gamma Pleat Angle, radian
?Ws = Mechanical Energy Added, W?hr
? = Momentum, lbm?ft/min
? = Pleat Coefficient Term, -
?i = Efficiency of Term I, -
l = Tube Friction Coefficient, -
? = Viscosity, Pa?s
? = Density, lbm/ft3
? = Pleat Count, -
? = Pleat Coefficient Term, -
B.3. Subscripts
geo ? geometry
m ? media
f ? filter
g ? grating
e ? expansion
c ? contraction
t ? tube
p ? pleat
s ? slot
a ? array
d ? discharge
T ? technique
B ? blower