1. Designing Filters for Optimum Performance
T.J. Ptak and Chrystal Gillilan
Presented at
National Air Filtration Association, TECH 2011

2. Filter performance criteria
Scope
Introduction
Filter performance criteria
Is it possible to select filter based several performance characteristics?
Filter pressure drop
Impact of filter media area on filter performance
Validation of filter performance
Conclusions

3. Filter selection and optimization
Consumers and filter designer
Traditional selection process of filters:
Consumer
Performance
Perceive value
Cost
Filter designer
Based on experience
Lacks an objective basis for decision making process

4. Development of rational and objective basis
Filter Selection
Development of rational and objective basis
Single criterion
Deduced from filter performance characteristics
Example - CADR
Benefits of single criterion
Comparison and selection
More filtration parameters included
Design tool

5. Filter Performance Characteristics
Pressure drop
Filtration efficiency
Gravimetric (arrestance)
Fractional efficiency
Capacity (filter life)
Dust holding capacity
Filter durability tests
Flammability tests
Compliance to environmental regulations
Cost

6. Filter Performance – Quality Factor
Is it possible to combine filter performance characteristics into one criterion?
Greater value of the criterion equal to “better” filter
Traditional quality factor (figure of merit):
E – filter efficiency and ΔPo – filter pressure drop
Potential issues:
Different ΔPo units
Results at different flow rate

7. Filter Performance - Criteria
Example 1: E1 = 80% and ΔPo = 0.40” H2O
α1 = - ln (1 – 0.8)/ 0.40 = 1.609/0.40 = 4.02
Example 2: E1 = 80% and ΔPo = 0.30” H2O
α2 = - ln (1 – 0.8)/ 0.30 = 1.609/0.30 = 5.36
Example 3: E1 = 85% and ΔPo = 0.40” H2O
α2 = - ln (1 – 0.85)/ 0.40 = 1.897/0.40 = 4.74

8. Filter Performance – Multi-Criteria
Process of simultaneously optimizing two or more objectives
Single aggregate objective function (AOF)
Weighting method, linear AOF:
MAX
E – filter efficiency; ΔPo – filter pressure drop
C – filter cost; DHC – filter dust holding capacity
λ – weighting factors; ∑ λi = λ1 + λ2 + λ3 + λ4 =1
λ – weighting factors are assigned based on priority - subjective

9. Filter Performance – Multi-Criteria
Residential filters – Home Depot
FPR (Filter Performance Rating) – AOF
FPR = λ1 (Efficiency Large Particles) +
λ2 (Efficiency Small Particles) +
λ3 DHC
λ1 + λ2 + λ3 = =1
Different weighting factors = different values of FPR
Example – DHC priority
λ1 + λ2 + λ3 = =1

10. Filter Performance – Multi - Criteria
Combination of objectives:
Other objectives: Cost, Energy
Nonlinear criteria
Mathematically more complicated
Criteria as designer tool
Optimum filter design can be obtained from given AOF criterion if functions describing filter characteristics are known
There is no single solution but a set of Pareto points

11. Filter performance criteria Filter pressure drop
Scope
Introduction
Filter performance criteria
Filter pressure drop
Does filter pressure drop follow Darcy’s law?

12. Filter Pressure Drop - Basic Concept
Filtration theory – filtration models
Efficiency
Single fiber efficiency
Filter efficiency
Pressure drop
Darcy law
Fiber drag

13. Filter Pressure Drop - Scope of Filtration
Model Characteristics
pressure drop, efficiency,
filter life, cost, durability
basis weight, thickness,
permeability, pore size
fiber or granule diameter

14. Filter Pressure Drop – Filtration Models
Capillary model
Kozeny - Carman
Fiber models
Single fiber
Cell model (Happel, Kuwabara)
Fan model (Stechkina)
Cylinder array

15. Filter Pressure Drop – Darcy’s Law
Experimental flow of water through bed of sand
DP = Uo L / k
k - Darcy law constant, permeability coefficient
Uo- velocity;  - viscosity; L - media thickness

16. Filter Pressure Drop – Kozeny - Carman
Need to correlate permeability coefficient with parameters of porous media (1927):
Model = pores are represented by bundle of capillary tubes
Poiseuille’s equation for laminar flow in tube
ΔP = Uo µ L / k
where: k = ε3/5So5(1 – ε)2
ε – porosity; So – specific surface of particles
Limitations
Deviation from spherical shape
Shapes of pores in real media

17. Filter Pressure Drop – Fibrous Media
Flow through fibrous media:
Modification of Kozeny equation
Davies (1952) – experimental correlation
ΔP = Uo µ L /k
where:
k = D2/ 64 (1- ε)1.5{1 + 56(1 – ε)3}
ε – porosity; D – fiber diameter
Limitations
0.6 < ε < 1
Reynolds number, Re = ρ U D / µ < 1

18. Filter Pressure Drop – Fibrous Media
Theoretical calculations:
Single fiber theory – widely used in calculations
Cell models – include porosity of media
ΔP = 16Uo µ L(1- ε) / D2ξ
ξ - hydrodynamic factor:
Lamb - ln Re
Kuwabara ln (1-ε)
Happel ln (1-ε)
ε – porosity; D – fiber diameter; Re – Reynolds number
Linear relationship between ΔP, U, L and µ

19. Filter Pressure Drop – Filter Media and Filters
Filter media – Fibers + Binders:
Glass fiber media pleatable - fiber diameter 3-7 µm
wire backed – fiber diameter 1- 4 µm
Synthetic media coarse – fiber diameter µm
fine – fiber diameter µm

20. Filter Pressure Drop – Filter Media and Filters
Experiment:
Filters:
Dimensions x 20 in.
Depth 1; 2 and 4 in.
Type minipleats with 4; 6; 9 and 12 PPI
wire back with 18 to 45 pleats
Testing
Initial pressure drop and efficiency
Dust holding capacity

21. Filter Pressure Drop – Filter Media
Experimental results for various media
High velocity application, MERV 7- 8
Linear function of velocity ΔP = AV

22. Filter Pressure Drop – Filter Media
Experimental results for various media
Low velocity application, MERV 10-14
Linear function of velocity ΔP = AV

23. Filter Pressure Drop – Filters
Pressure drop for 20 x 20 in. wire backed filters
Filter media – coarse synthetic fibers
Polynomial curve ΔP = BV + CV2

24. Filter Pressure Drop – Filters
Pressure drop for 20 x 20 in. minipleat filters
Filter media – glass and synthetic fine fibers
Polynomial curve ΔP = BV + CV2

25. Filter Pressure Drop – Filters and Filter Media
Pressure drop for filters and flat sheet media
Filters with 55 ft2 of media area; minipleat
Filter media – glass and synthetic fine fibers
ΔPFILTER/ ΔPMEDIA ~ 1.6 – 4 at 25 fpm

26. Filter Pressure Drop – Filters and Filter Media
Pressure drop for filters and flat sheet media
Filters with 36 ft2 of media area; minipleat
Filter media – glass and synthetic fine fibers
ΔPFILTER/ ΔPMEDIA = 1.3 – 2.2 at 25 fpm

27. Filter Pressure Drop – Filters and Filter Media
Pressure drop for filters and flat sheet media
Filters with 16.2 ft2 of media area; wire backed
Filter media – synthetic coarse fibers
ΔPFILTER/ ΔPMEDIA = 4 – 5 at 75 fpm

28. Filter Pressure Drop – Filters
Correlation between flat sheet media and filters
Flat filter media
ΔP = AV
Flow is perpendicular o the media
Filters
ΔP = BV + CV2
Filter media reduced due to pleat deformation and glue beads resulting in higher media velocity
Impact of frame on media area and flow pattern
Inertial loses due to change of flow direction
Flow through media not perpendicular

29. Filter Pressure Drop – Filters and Filter Media
Flow pattern through pleats is not perpendicular to the filter medium
Real flow pattern Assumed perpendicular flow

30. Filter Pressure Drop – Filters and Filter Media
Pleat collapsing and pleat deformation
Collapsing Deformation

31. Filter performance criteria Filter pressure drop
Scope
Introduction
Filter performance criteria
Filter pressure drop
Impact of filter media area on filter performance
Is filter media fully utilized?

32. Is filter with more media area a “better” filter? YES and NO
Filter Media Area
Is filter with more media area a “better” filter?
YES and NO
Impact of pleat density
Impact of type of filter media
Impact of filter design
Media utilization factor, UF
UF = Dust Capacity / Media Area
Comparison of filters with similar efficiency

33. Filter Media Area - Impact on Pressure Drop
Tested filters MERV x 20 x 2” wire backed
Pressure drop and initial E3 efficiency

34. Filter Media Area - Impact on Pressure Drop
Tested filters 20 x 20 x 2” – glass and synthetic minipleat
Pressure drop at 492 fpm

35. Filter Media Area - Impact on Dust Holding Capacity
Tested filters MERV x 20 x 2” minipleat
Terminal ΔP = 1” and ΔP = 1.4” H2O
Glass media with similar thickness and stiffness

36. Filter Media Area - Media Utilization
Tested filters MERV x 20 x 2” minipleat
Media area = 109 ft Media area = 55 ft2

37. Filter Media Area - Media Utilization
Tested filters MERV x 20 x 2” minipleat
Media area = 109 ft Media area = 55 ft2

38. Filter Media Area - Impact of Filter Depth
Tested filters MERV 7 – 8 wire backed with N = 18
Filter 1 in. 2 in. 4 in.
DHC at ΔP = 1 in. H2O
Media utilization, UF

39. Filter Media Area - Impact of Filter Depth
Tested filters MERV 7 – 8 wire backed with N = 18
4 in. filter, UF = in. filter, UF = 3.27

40. Filter Media Area - Media Area Utilization
Pleat collapsing – limited flow and dust collection
Collapsing

41. Filter Media Area - Optimum Design
Tested filters MERV x 20 x 2” minipleat
Pressure drop, Dust capacity, E1 and UF

42. Filter Media Area - Optimum Design
Tested filters MERV x 20 x 2” minipleat
Optimum pleat density (media area)
Is it minimum ΔP or maximum DHC?
Cost?
Impact of other design parameters such as media type
Complicated issue

43. Filter Media Area - Impact of Type of Filter Media
Tested filters MERV x 20 x 2” minipleat
Filter media Media area DHC E1 UF
Glass fiber ft
Duo layer synthetic 55 ft

44. Filter Media Area - Impact of Type of Filter
Comparison of different filters – 24 x 24”
Filter MERV Media Area DHC UF
V- cell (3V) Glass 140 ft g
V- cell (3V) Synthetic 80 ft g
V- cell (2V) Glass 100 ft2
Pocket – 26” Synthetic 69 ft g
Pocket – 19” Synthetic 51 ft g
Rigid – 12” Synthetic 61 ft g
4” Minipleat Synthetic 70 ft g

45. Filter performance criteria Filter pressure drop
Scope
Introduction
Filter performance criteria
Filter pressure drop
Impact of filter media area on filter performance
Validation of filter performance
What is variability of test results?

46. Purpose of filter testing Filter selection
Filter comparison
Filter must be tested in strict accordance to an acceptable test method
Rating
Prediction real life performance
Filter characteristics must reflect main filter goal

47. Measurement of Typical Physical Quantities
Flow rate
Flow sensor – orifice, nozzle, laminar flow element
Temperature (density, viscosity)
Differential pressure
Pressure sensor
Mass of filter, membrane
Particle concentration
Optical particle counter

48. HVAC Filters – Performance Characteristics
Test standard – ASHRAE 52.2
Differential pressure
Fractional efficiency for particle size range 0.3 – 10 µm
Initial and intermediate
Dust holding capacity at specified terminal ΔP
Reporting
PSE curve after each step of dust loading
Develop a composite minimum efficiency curve
Report average E1 0.3 – 1.0 µm
E – 3.0 µm
E µm
MERV - Minimum Efficiency Reporting Value

49. Round Robin Test sponsored by ASHRAE*
ASHRAE Variability
Round Robin Test sponsored by ASHRAE*
Participating labs 8
Selected filters 4
Type 1 – 24 x 24 x 12” glass (MERV 10-11)
Type 2 – 24 x 24 x 4” electret (MERV 8-11)
Type 3 – 24 x 24 x 4” cotton/PET (MERV 5-7)
Type 4 – 24 x 24 x 12” electret (MERV 15-16)
Filters were pre-tested at independent lab
Statistical methodology
Repeatability – precision of the method within a given lab
Sr – repeatability standard deviation
Reproducibility - precision of the method when comparing labs
SR – reproducibility standard deviation
NOTE: * from ASHRAE 1088-RP

50. Round Robin Test results
ASHRAE Variability
Round Robin Test results
Precision statistics for pressure drop measurement
Repeatability CV 1.8 – 6.7%
Reproducibility CV 5.3 – 6.8%
Precision statistics for weight gain
Repeatability CV 7.5 – 26.5%
Reproducibility CV 8.1 – 26.5%
MERV summary
Type 2 MERV 8 (9); MERV 10 (1); MERV11 (2)
Type 3 MERV 5 (1); MERV 6 (10); MERV 7 (1)
Type 4 MERV 14 (4); MERV 15 (8)

51. Round Robin Test results
ASHRAE Variability
Round Robin Test results
Precision statistics for Type 4 filters
Repeatability Sr E1 – 1.71; E2 – 0.50; E3 – 0.0 Reproducibility SR E1 – 2.63; E2 – 0.93; E3 – 0.41
Precision statistics for Type 3 filters
Repeatability Sr E1 – 1.91; E2 – 2.42; E3 – 3.94 Reproducibility SR E1 – 2.61; E2 – 3.88; E3 – 4.98
Precision statistics for Type 2 filters
Repeatability Sr E1 – 2.86; E2 – 4.99; E3 – 2.45 Reproducibility SR E1 – 5.00; E2 – 6.05; E3 – 3.04
Calculated 95% confidence interval for individual results
“2 Sr “ = 1.96 Sr
“2 SR ” = 1.96 SR

52. What does it mean for you?
ASHRAE Variability
What does it mean for you?
Pressure drop
Filter Type 2 Type 3 Type 4
Average ΔP, [in. H2O]
95% Confidence, 2 SR ± ± ±0.11
95% Confidence range – – – 0.87
Dust holding capacity
Filter Type 2 Type 3 Type 4
Average DHC, [gram]
95% Confidence, 2 SR ±32 ±44 ±72
95% Confidence range 165 – – – 210

53. What does it mean for you?
ASHRAE Variability
What does it mean for you?
Efficiency – statistics at indicated level of filtration
Filter 20% 50% 80%
95% Confidence, 2 SR
95% Confidence range 12 – – – 87
Is it as bad as Interlaboratory Testing indicate?
Report was published in 2005
Progress was made due to awareness
Significant variability still exist

54. Environmental testing
Other Tests
Environmental testing
Impact of environmental conditions on real life operation, integrity and safety (extreme temperature and humidity)
To reveal potential problems area in the filter
Durability and mechanical strength
ARI – Standard 850 Performance and Rating of Commercial and Industrial Air Filter Equipment
Breaching Test – at resistance 50% above the maximum rated
Laboratory tests
Exposure to high temperature (T = 160oF)
Exposure to low temperature (T = 0o F)
Exposure to high relative humidity (RH = 85 – 90%)
Breaching test at resistance above 400% above rated

55. Environmental requirements
Other Tests
Environmental requirements
RoHS Directive 2002/95/EC
Restriction of the use of certain Hazardous Substances
Heavy metals such as: lead, chromium, mercury and cadmium
Polybrominated biphenyls and diphenyl ethers
Proposition 65 Safe Harbor Levels (known as CA Prop 65)
List of chemicals known to State to cause cancer or reproductive toxicity
REACH – Regulation for Registration, Evaluation, Authorization and Restriction of Chemicals
Manufacturers must identify and manage risks linked to substances they manufacture and market

56. Pressure drop of filters does not follow Darcy’s law
Conclusions
Aggregate objective functions (AOF) can be used as filter selection criteria
Pressure drop of filters does not follow Darcy’s law
Optimal utilization of filter media should be a main goal of filter designers
Higher media area does not always result in a “better” filter
Current test methods need modifications to address variability issue and filter durability