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Isokinetic sampling of aerosols from tangential flow streams

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Title:
Isokinetic sampling of aerosols from tangential flow streams
Creator:
Durham, Michael Dean, 1949-
Publication Date:
Language:
English

Subjects

Subjects / Keywords:
Aerosols ( jstor )
Cyclones ( jstor )
Diameters ( jstor )
Error rates ( jstor )
Flow distribution ( jstor )
Flow velocity ( jstor )
Geometric angles ( jstor )
Nozzles ( jstor )
Pitot tubes ( jstor )
Velocity ( jstor )

Record Information

Source Institution:
University of Florida
Holding Location:
University of Florida
Rights Management:
Copyright Michael Dean Durham. Permission granted to the University of Florida to digitize, archive and distribute this item for non-profit research and educational purposes. Any reuse of this item in excess of fair use or other copyright exemptions requires permission of the copyright holder.
Resource Identifier:
4718393 ( OCLC )
0022590482 ( ALEPH )

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ISOKINETIC SAMPLING OF AEROSOLS FROM
TANGENTIAL FLOW STREAMS















By


Michael Dean Durham















A DISSERTATION PRESENTED TO THE GRADUATE COUNCIL OF
THE UNIVERSITY OF FLORIDA
IN PARTIAL FULFILLMENT OF THE REQUIREMENTS FOR THE
DEGREE OF DOCTOR OF PHILOSOPHY


UNIVERSITY OF FLORIDA 1978














ACKNOWLEDGEMENTS


This research was partially supported by a grant (Grant Number R802692-01) from the Environmental Protection Agency (EPA)-, and was monitored by EPA's Project Officer Kenneth T. Knapp. I thank them both for their financial support during my graduate work.

I wish to thank Dr. Dale Lundgren and Dr. Paul Urone for the important part that they played in my education. I am especially appreciative of Dr. Lundgren for his guidance, encouragement and confidence. He has provided me with opportunities for classroom, laboratory and field experience that were far beyond what is expected of a committee chairman.

I would like to thank Mrs. Kathy Sheridan for her assistance in preparing this manuscript.

Finally, I wish to thank my parents for their advice and encouragement, and my wife Ellie for helping me through the difficult times.

















ii















TABLE OF CONTENTS


Page


ACKNOWLEDGEMENTS ii

LIST OF TABLES ...............................................

LIST OF FIGURES ................................................ viii

LIST OF SYMBOLS ................................................ xi

ABSTRACT ....................................................... xiii

CHAPTER

I INTRODUCTION AND ISOKINETIC SAMPLING THEORY .............. 1

A. Introduction......................................... 1
B. Isokinetic Sampling Theory ........................... 2

II REVIEW OF THE PERTINENT LITERATURE ....................... 10

A. Summary of the Literature on Anisokinetic Sampling... 10
1. Sampling Bias Due to Unmatched Velocities......... 10 2. Sampling Bias Due to Nozzle Misalignment .......... 17
B. Summary of the Literature on Tangential Flow.......... 23
1. Causes and Characteristics of Tangential Flow ..... 23 2. Errors Induced by Tangential Flow................. 31
3. Errors Due to the S-Type Pitot Tube ............... 35
4. Methods Available for Measuring Velocity
Components in a Tangential Flow Field ............. 41
5. EPA Criteria for Sampling Cyclonic Flow ........... 43

III EXPERIMENTAL APPARATUS AND METHODS ....................... 48

A. Experimental Design.................................. 48
B. Aerosol Generation................................... 51
1. Spinning Disc Generator........................... 51
2. Ragweed Pollen.................................... 53
C. Velocity Determination ................................ 53
D. Selection of Sampling Locations...................... 57
E. Sampling Nozzles..................................... 57



iii












TABLE OF CONTENTS--continued


CHAPTER Page


F. Analysis Procedure..................................... 58
1. For Uranine Particles............................... 58
2. For Ragweed Pollen.................................. 58
G. Sampling Procedure..................................... 59
H. Tangential Flow Mapping................................ 60

IV RESULTS AND ANALYSIS....................................... 65

A. Aerosol Sampling Experiments........................... 65
1. Stokes Number...................................... 65
2. Sampling with Parallel Nozzles...................... 66
3. Analysis of Probe Wash .............................. 66
4. The Effect of Angle Misalignment on Sampling
Efficiencies....................................... 69
5. The Effect of Nozzle Misalignment and Anisokinetic
Sampling Velocity................................... 89
B. Tangential Flow Mapping 102

V SIMULATION OF AN EPA METHOD 5 EMISSION TEST IN A TANGENTIAL
FLOW STREAM ................................................. 117

VI SUMMARY AND RECOMMENDATIONS ................................ 129

A Summary ................................................ 129
B. Recommendations........................................ 134

REFERENCES....................................................... 135

BIOGRAPHICAL SKETCH.............................................. 139



















iv
















LIST OF TABLES


Table Page I FLOW RATE DETERMINED AT VARIOUS MEASUREMENT LOCATIONS...... 33 II CONCENTRATION AT A POINT FOR DIFFERENT SAMPLING ANGLES..... 34 III EMISSION TEST RESULTS ...................................... 36

IV SIZES AND DESCRIPTIONS OF EXPERIMENTAL AEROSOLS ............ 52

V TABLE OF OBTAINABLE VELOCITIES IN 10 cm DUCT................ 54

VI TYPICAL VELOCITY TRAVERSE IN THE EXPERIMENTAL SAMPLING
SYSTEM ..................................................... 55

VII RESULTS OF SAMPLING WITH TWO PARALLEL NOZZLES ............... 67

VIII PERCENT OF PARTICULATE MATTER COLLECTED IN THE PROBE WASH
FOR NOZZLES PARALLEL WITH THE FLOW STREAM .................. 68

IX PERCENT OF PARTICULATE MATTER COLLECTED IN THE PROBE WASH
FOR NOZZLES AT AN ANGLE OF 60 DEGREES WITH THE FLOW STREAM. 70 X ASPIRATION COEFFICIENT AS A FUNCTION OF STOKES NUMBER FOR
30 DEGREE MISALIGNMENT ..................................... 75

XI ASPIRATION COEFFICIENT AS A FUNCTION OF STOKES NUMBER FOR
60 DEGREE MISALIGNMENT ..................................... 77

XII ASPIRATION COEFFICIENT AS A FUNCTION OF STOKES NUMBER FOR
90 DEGREE MISALIGNMENT ..................................... 80

XIII COMPARISON OF SAMPLING EFFICIENCY RESULTS WITH THOSE OF
BELYAEV AND LEVIN FOR B = 0, R = 2.3 AND R = 0.5........... 92

XIV ASPIRATION COEFFICIENT AS A FUNCTION OF STOKES NUMBER FOR
R = 2, 8 = 60............................................... 94






V












LIST OF TABLES--continued


Table Page


XV ASPIRATION COEFFICIENT AS A FUNCTION OF STOKES NUMBER
FOR R = 0.5, 6 = 600....................................... 95

XVI ASPIRATION COEFFICIENT AS A FUNCTION OF STOKES NUMBER
FOR 0 = 450, R = 2.0 AND 0.5................................ 97

XVII ASPIRATION COEFFICIENT AS A FUNCTION OF STOKES NUMBER
FOR R = 2, 6 = 300.... ..................................... 98

XVIII ASPIRATION COEFFICIENT AS A FUNCTION OF STOKES NUMBER
FOR R = 2.1, 6 = 900........................................ 101

XIX LOCATION OF SAMPLING POINTS ................................ 103

XX FIVE-HOLE PITOT TUBE MEASUREMENTS MADE AT 1 DIAMETER
DOWNSTREAM OF THE CYCLONE.................................. 106

XXI FIVE-HOLE PITOT TUBE MEASUREMENTS MADE AT 2 DIAMETERS
DOWNSTREAM OF THE CYCLONE ......... .......................... 107

XXII FIVE-HOLE PITOT TUBE MEASUREMENTS MADE AT 4 DIAMETERS
DOWNSTREAM OF THE CYCLONE .................................. 108

XXIII FIVE-HOLE PITOT TUBE MEASUREMENTS MADE AT 8 DIAMETERS
DOWNSTREAM OF THE CYCLONE .................................. 109

XXIV FIVE-HOLE PITOT TUBE MEASUREMENTS MADE AT 16 DIAMETERS
DOWNSTREAM OF THE CYCLONE .................................. 110

XXV AVERAGE CROSS SECTIONAL VALUES AS A FUNCTION OF DISTANCE
DOWNSTREAM AND FLOW RATE ................................... 112

XXVI S-TYPE PITOT TUBE MEASUREMENTS MADE AT THE 8-D SAMPLING
PORT FOR THE LOW FLOW CONDITION ............................ 118

XXVII S-TYPE PITOT TUBE MEASUREMENTS MADE AT THE 8-DSAMPLING PORT
FOR THE HIGH FLOW CONDITION ................................ 119

XXVIII MIDPOINT PARTICLE DIAMETERS FOR THE 10 PERCENT INTERVALS
OF THE MASS DISTRIBUTION MMD = 3pm a. = 2.13................ 121





vi












LIST OF TABLES--continued


Table Page


XXIX ASPIRATION COEFFICIENTS CALCULATED IN THE SIMULATION
MODEL FOR THE LOW FLOW CONDITION ........................... 124

XXX ASPIRATION COEFFICIENTS CALCULATED IN THE SIMULATION
MODEL FOR THE HIGH FLOW CONDITION .......................... 125

XXXI RESULTS OF THE CYCLONE OUTLET SIMULATION MODEL FOR THREE
CONDITIONS ................................................. 127

XXXII SUMMARY OF EQUATIONS PREDICTING PARTICLE SAMPLING BIAS..... 128








































vii















LIST OF FIGURES


Figure Page


1 Isokinetic sampling...................................... 3

2 Superisokinetic sampling................................. 4

3 Subisokinetic sampling................................... 6

4 The effect of nozzle misalignment with flow stream ....... 7

5 Relationship between the concentration ratio and the
velocity ratio for several size particles ................ 11

6 Sampling efficiency as a function of Stokes number and
velocity ratio........................................... 16

7 Error due to misalignment of probe to flow stream......... 18

8 Sampling bias due to nozzle misalignment and anisokinetic
sampling velocity........................................ 21

9 Tangential flow induced by ducting....................... 25

10 Double vortex flow induced by ducting.................... 26

11 Velocity components in a swirling flow field............. 27

12 Cross sectional distribution of tangential velocity in a
swirling flow field...................................... 29

13 Cross sectional distribution of angular momentum in a
swirling flow field...................................... 30

14 S-type pitot tube with pitch and yaw angles defined ...... 38 15 Velocity error vs. yaw angle for an S-type pitot tube.... 39 16 Velocity error vs. pitch angle for an S-type pitot tube.. 40






viii












LIST OF FIGURES--continued


Figure Page


17a Conical version of a five-hole pitot tube................. 42

17b Fecheimer type three-hole pitot tube ..................... 42

18 Five-hole pitot tube sensitivity to yaw angle ............ 44

19 Fecheimer pitot tube sensitivity to yaw angle............ 45

20 Experimental set up...................................... 49

21 Sampling system.......................................... 50

22 Typical velocity profile in experimental test section.... 56 23 Experimental system for measuring cross sectional flow patterns in a swirling flow stream....................... 61

24 Cyclone used in the study to generate swirling flow...... 62 25 Photograph of the 3-dimensional pitot with its traversing unit. Insert shows the location of the pressure taps.... 63 26 Sampling efficiency vs. Stokes number at 300 misalignment for R = 1 ................................................ 72

27 Sampling efficiency vs. Stokes number at 600 misalignment for R = 1 ................................................ 73

28 Sampling efficiency vs. Stokes number at 900 misalignment for R = 1 ................................................ 74

29 Stokes number at which 95% maximum error occurs vs.
misalignment angle....................................... 83

30 J' vs. adjusted Stokes number for 30, 60 and 90 degrees.. 85 31 Aspiration coefficient vs. Stokes number model prediction and experimental data for 30, 60 and 90 degrees..... 87 32 Predicted aspiration coefficient vs. Stokes number for 15, 30, 45, 60, 75 and 90 degrees........................ 88




ix












LIST OF FIGURES--continued


Figure Page


33 Comparison of experimental data with results from Belyaev and Levin .................................................. 91

34 Sampling efficiency vs. Stokes number at 600 misalignment for R = 2.0 and 0.5 ........................................ 96

35 Sampling efficiency vs. Stokes number at 450 misalignment for R = 2.0 and R = 0.5.................................... 99

36 Sampling efficiency vs. Stokes number at 300 misalignment for R = 2.0 ................................................ 100

37 Cross sectional view of a tangential flow stream locating pitch and yaw directions, sampling points, and the negative pressure region....................................... 105

38 Decay of the average angle 6 and the core area along the axis of the duct........................................... 113

39 Decay of the tangential velocity component along the axis of the duct ................................................ 114

40 Location of the negative pressure region as a function of distance downstream from the cyclone ....................... 116

41 Particle size distributions used in the simulation model... 120























x















SYMBOLS


A. area of sampler inlet
1
A.'- projected area of sampler inlet
1
A area of stream tube approaching nozzle A ratio of measured concentration to true concentration C Cunningham correction factor C. dust concentration in inlet
1
C dust concentration in flow stream

C
r concentration ratio of aerosol generating solution Dd droplet diameter D. inlet diameter D particle diameter K inertial impaction parameter K' adjusted Stokes number

2 stopping distance L undisturbed distance upstream from nozzle n constant R ratio of free stream velocity to inlet velocity s constant V axial component of stack velocity V. velocity in inlet
1

V radial component of stack velocity
r

Vo free stream velocity



xi









V tangential component of stack velocity
t
6, 8', B" functions determining whether particles will deviate from
streamlines

p particle density

- viscosity

angle of the flow stream with respect to the stack axis

6 angle of misalignment of nozzle with respect to the flow stream T particle relaxation time Ap pressure difference






































xii















Abstract of Dissertation Presented to the Graduate Council of the University of Florida in Partial Fulfillment of the
Requirements for the Degree of Doctor of Philosophy


ISOKINETIC SAMPLING OF AEROSOLS FROM- TANGENTIAL FLOW STREAMS


By

Michael D. Durham

August, 1978


Chairman: Dale A. Lundgren
Major Department: Environmental Engineering Sciences


A comprehensive analysis of inertial effects in aerosol sampling was combined with a thorough study of swirling flow patterns in a stack following the exit of a cyclone in order to determine the errors involved in sampling particulate matter from a tangential flow stream. Two simultaneous samples, one isokinetic and the other anisokinetic,were taken from a 10 cm wind tunnel and compared to determine sampling bias as a function of Stokes number. Monodispersed uranine particles, 1 to 11 m in diameter, generated with a spinning disc aerosol generator, and mechanically dispersed 19.9 Im ragween pollen were used as experimental aerosols. The duct velocity was varied from 550 to 3600 cm/sec and two nozzle diameters of 0.465 and 0.683 cm were used to obtain values of Stokes numbers from 0.007 to 2.97. Experiments were performed at four angles, 0, 30, 60 and 90 degrees, to determine the errors encountered when sampling with an isokinetic sampling velocity but with the nozzle misaligned with the flow stream. The sampling bias approached a theoretical limit of (1-cos6) at a value of Stokes number between


xiii











1 and 6 depending on the angle of misalignment. It was discovered that the misalignment angle reduces the projected nozzle diameter and therefore effects the Stokes number; a correction factor as a function of angle was developed to adjust the Stokes number to account for this.

Using an equation empirically developed from these test results and using the equations of Belyaev and Levin describing anisokinetic sampling bias with zero misalignment, a mathematical model was developed and tested which predicts the sampling error when both nozzle misalignment and anisokinetic sampling velocities occur simultaneously. It was found that the sampling bias approached a maximum error 1l-Rcos6[ where R is the ratio of the free stream velocity to the sampling velocity. During the testing, it was discovered that as much as 60% of the particulate matter entering the nozzle remained in the nozzle and front half of the filter holder. Implications of this phenomenon with regard to particle sampling and analysis are discussed.

The causes and characteristics of tangential flow streams are described

as they relate to problems in aerosol sampling. The limitations of the S-type pitot tube when used in a swirling flow are discussed. A three dimensional or five-hole pitot tube was used to map cross sectional and axial flow patterns in a stack following the outlet of a cyclone. Angles as great as 70 degrees relative to the axis of the stack and a reverse flow core area were found in the stack.

Using information found in this study, a simulation model was developed to determine the errors involved when making a Method 5 analysis in a tangential flow stream. For an aerosol with a 3.0 pm 1\IMD (mass mean diameter)




xiv










and geometric standard deviation ( ) of 2.13, the predicted concentration was 10% less than the true concentration. For an aerosol with a 10.0 pm MMD and a a of 2.3, a 20% error was predicted. Flow rates determined by the S-type pitot tube were from 20 to 30% greater than the actual flow rate. Implications of these results are described and recommendations for modification of the Method 5 sampling train for use in a tangential flow stream are described.








































xv
















CHAPTER I
INTRODUCTION AND ISOKINETIC SAMPLING THEORY


A. Introduction


This study deals with the problems of obtaining a representative sample of particulate matter from a gas stream that does not flow parallel to the axis of the stack as in the case of swirling or tangential flow. This type of flow is commonly found in stacks and could be the source of substantial sampling error. The causes and characteristics of this particular flow pattern are described and the errors encountered in particulate concentration and emission rate determinations are thoroughly analyzed and discussed.

The analysis of sampling errors is approached from two directions in this study. One approach involves an investigation of aerosol sampling bias due to anisokinetic sampling velocities and misalignment of the nozzle with respect to the flow stream as a function of particle and flow characteristics. The second part of the study involves an accurate mapping of the flow patterns in a tangential flow system. The information obtained in the two parts of the study will be combined to simulate the errors that would be encountered when making an EPA Method 5 (1, 2) analysis in a tangential flow stream.


1






2




B. Isokinetic Sampling Theory


To obtain a representative sample of particulate matter from a moving fluid, it is necessary to sample isokinetically. Isokinetic sampling can be defined by two conditions: (3) 1) The suction or nozzle velocity, Vi, must be equal to the free stream velocity, Vo; and 2) the nozzle must be aligned parallel to the flow direction. If these conditions are satisfied the frontal area of the nozzle, A., will be equal to the area of the cross section of the flow stream entering the nozzle, Ao (see Figure 1). Thus, there will be no divergence of streamlines either away from or into the nozzle, and the particle concentration in the inlet, C., will be equal to the particle concentration in the flow stream, C .

When divergence of streamlines is produced by superisokinetic sampling, subisokinetic sampling or nozzle misalignment, there is a possibility of particle size fractionation due to the inertial properties of particles. In the case of superisokinetic sampling (see Figure 2), the sampling velocity, V., is greater than the free stream velocity, V Therefore, the area of the flow stream that is sampled, A ', will be greater than the. frontal area of the sampling nozzle, A.. All of the particles that lie in the projected area A.'
1 i
will enter into the nozzle. Particles outside this area but within A
O
will have to turn with the streamlines in order to be collected. Because of their inertia, some of the larger particles will be unable to make the turn and will not enter the sampling nozzle. Since not all of the particles in the sampled area Ao will be collected, the measured concentration will be less than the actual concentration.












33


























0 o --







II -Hi rd



0






> H IIE ,



-,-t
3 H







oo 0L





































4--4














00 el










Subisokinetic sampling defines the condition in which the sampling velocity is less than the free stream velocity (see Figure 3). In this situation the frontal area of the nozzle, A ', is greater than the sam1
pled area of the flow, Ao. The volume of air lying within the projected area, A.', but outside A will not be sampled and the streamlines will
1 o
diverge around the nozzle. However, some of the particles in this area, because of their inertia, will be unable to negotiate the turn with the streamlines and will be collected in the nozzle. Because some of the particles outside the sampled area A will be collected along with all
0
of the particles within Ao, the measured concentration will be greater than the actual particle concentration.

The bias due to misalignment of the nozzle with the flow stream

is similar to that caused by superisokinetic sampling. When the nozzle is at an angle to the flow stream (Figure 4), the projected area of the nozzle is reduced by a factor equal to the cosine of the angle. Even if the nozzle velocity is equal to the flow stream velocity, a reduced concentration will be obtained because some of the larger particles will be unable to make the turn into the nozzle with the streamlines. Therefore, whenever the nozzle is misaligned, the concentration collected will always be less than or equal to the actual concentration.

For all three conditions of anisokinetic sampling (superisokinetic, subisokinetic and nozzle misalignment), the magnitude of the measured concentration error will depend upon the size of the particles. More specifically it will depend upon particle inertia, which implies that the velocity and density of the particle are also important. Particle







6





























U














0



- A .4













v 44 C C >O






/ 4J

.













m






















j-4





I -p
00


4J ,


S)





U)


Q-H

uI N 00 I: 0


I I u










la
00 C)






o 0"





H

O 0

H
0..
a Q4










inertia affects the ability of the particle to negotiate turns with its streamline which determines the amount of error. Therefore, in all cases greater sampling errors will occur for larger particles and higher velocities.

Besides determining the direction of the sampling bias, it is

also possible to predict theoretically the minimum and maximum error for a given condition. This can be done by considering what happens when the inertia of the particles is very small (i.e., the particles can negotiate any turn that the streamlines make) and what happens when the inertia of particles is very large (i.e., the particles are unable to negotiate any turn with the streamlines). In the former case of very low inertia, it can easily be seen that since the particles are very mobile they do not leave their streamlines and therefore there will be no sampling bias. In this situation the concentration of particulate matter may be accurately obtained regardless of sampling velocity or whether the nozzle is aligned with the flow stream. Therefore, a minimum error of 0 is obtained for small inertia particles.

The maximum error that can theoretically occur in anisokinetic sampling depends on both the velocity ratio R, where R = Vo/Vi (1)


and the misalignment angle 8.

In the case of unequal velocities for very high inertia particles which are unable to negotiate any change of direction, only those particles directly in front of the projected area of the nozzle, Ai, will enter the nozzle regardless of the sampling velocity. Therefore,





9




the concentration collected by the nozzle will be equal to the number of particles entering the nozzle, AiV C divided by the volume of air sampled, A.V..
11
A.V C C V
C. 100 00 2
i A.V. V.
11 1

The ratio of the sampled concentration to the true concentration then is equal to the inverse of the velocity ratio. Therefore, the maximum sampling bias for the condition of unmatched velocities is equal to Vo/Vi or R. For example, if the sampling velocity is twice the free stream velocity, the resulting concentration will be one half the actual concentration.

For the case of a misaligned nozzle, a similar analysis is applied. For the particles with very large inertia, only those lying directly in line with the projected frontal area of the nozzle will be collected. The measured concentration would again be the number of particles collected in the nozzle, A.cosCoV o' divided by the volume of air sampled, A.V.. Therefore, the ratio of the measured to the true concentration
1 1
would be V cos9/V. or Rcos6. This represents the maximum sampling
0 1
error for anisokinetic sampling.















CHAPTER II
REVIEW OF THE PERTINENT LITERATURE


A. Summary of the Literature on Anisokinetic Sampling


1. Sampling Bias Due to Unmatched Velocities


Numerous articles have been written describing the sources and magnitude of errors when isokinetic conditions are not maintained. In one of the earlier works, Lapple and Shepherd (4) studied the trajectories of particles in a flow stream and presented a formula for estimating the order of the magnitude of errors resulting when there is a difference between the average sampling velocity and the local free stream velocity. Watson (5) examined errors in the anisokinetic sampling of spherical particles of 4 and 32 im mass mean diameter (MMD) and found the relationships shown in Figure 5. Superisokinetic sampling (sampling with nozzle velocity greater than the free stream velocity) leads to a concentration less than the actual concentration. while subisokinetic sampling has the opposite effect. Watson found that the magnitude of the error was not only a function of particle size as seen in Figure 5, but also of the velocity and the nozzle diameter. He proposed that the sampling efficiency was a function of the dimensionless particle inertial parameter K (Stokes number) defined as

TV
K = Cp V D 2/18D 0 (3) p 0op i D.


10
























0
4



u H

-,

o















u )
J
















CN O Srd
O O



H







2. 4-4





Sco ,-Pu

r.)



0 U \ Hic





12




where

D = particle diameter

C = Cunningham correction for slippage

p = particle density

T = p CD p/18 (4)
p p
p = viscosity of gas D. = nozzle diameter
1

The relaxation time is defined as T; it represents how quickly a particle can change directions. Watson concluded that to obtain a concentration correct within 10%, the velocity ratio R must lie between 0.86 and 1.13 for the 32 micron particles and between 0.5 and 2.0 for the 4 micron particles.

Data obtained by Dennis et al. (6) on a suspension of Cottrell precipitated fly ash, 14 m N ID, showed only a 10% negative error in calculated concentration for sampling velocities 60% greater than isokinetic. Tests run on an atmospheric dust of 0.5 mj m NID produced no detectable concentration changes even while sampling at a 400% variation from isokinetic flow, thus indicating that isokinetic sampling is relatively unimportant for fine particles. Hemeon and Haines (7) measured errors due to the anisokinetic sampling of particles in three size ranges (5-25, 80-100, and 400-500 pm) and in a range of nozzle to stack velocities of 0.2 to 2.0. They found that where the velocity ratio R ranges from 0.6 to 2.0 the extreme potential error was approximately 50%, and that deficient nozzle velocities resulted in greater errors than excessive nozzle velocities. In addition, they found that for the coarse particles, the velocity into the nozzle had no important





13



bearing on the quantity of dust collected. They suggested using the product of the nozzle area and the stack gas velocity approaching the nozzle as the gas sample volume, regardless of the velocity of the nozzle. By using this method for particles greater than 80 ym, it is possible to obtain small deviations even where departure from isokinetic velocity is quite large. Whiteleyand Reed (8) also observed that calculating the dust concentrations from the approach velocity instead of the actual sampling rate produced only slight errors when sampling anisokinetically for large particles.

Lundgren and Calvert (9) found the sampling bias or aspiration

coefficient A, to be a function of the inertial impaction parameter K and the velocity ratio R. They developed a chart which can be used to predict inlet anisokinetic sampling bias depending on both K and R. Badzioch's (10) equations defined the dependence of the efficiency upon particle inertia and the velocity ratio. In a slightly different terminology


A = Ci/C = 1 + (R-l) B(K) (5) where B(K) is a function of inertia given by


B(K) = [l-exp (-L/R)]/(L/Z) (6) k is the stopping distance or the distance a particle with initial velocity 1V will travel into a still fluid before coming to rest and
0
is defined by (11)

Z = TV (7)
0





14




L is the distance upstream from the nozzle where the flow is undisturbed by the downstream nozzle. It is a function of the nozzle diameter and is given by the equation:


L = nD. (8)
1

It was observed that n lies between 5.2 and 6.8 (10).

Flash illumination photographic techniques were used by Belyaev and Levin (12) to study particle aspiration. Photographic observations enabled them to verify Badzioch's claim that L, the undisturbed distance upstream of the nozzle, was between 5 to 6 times the diameter of the nozzle. They examined the data of previous studies on error due to anisokinetic sampling and concluded that the discrepancy between experimental data was due to the researchers failing to take into account three things: 1) particle deposition in the inlet channel of the sampling device; 2) rebound of particles from the front edge of the sampling nozzle and their subsequent aspiration into the nozzle; and 3) the shape and wall thickness of the nozzle. They also found that the sampling efficiency was a function of the inner diameter of the nozzle, Di, as well as K and R.

In a more recent article, Belyaev and Levin (13) examined the

dependence of the function B(K), in equation (4), on both the inertial impaction parameter, K, and the velocity ratio, R. Previous authors (10, 14) had concluded that 3(K) was a function of K alone, but Belyaev and Levin obtained experimental data demonstrating that for thin-walled nozzles, 3(K) was also a function of R. Equations were developed from the data for values of K between 0.18 and 6.0 and for values of R between











0.16 and 5.5


3(K,R) = 1 1/(1 +bK) (9) where


b = 2 + 0.617/R (10) Figure 6 shows a plot of equations (5), (9) and (10) for a range of velocity ratios and Stokes numbers. The most significant changes in the aspiration coefficient occur at values of K between 0 and 1. Beyond K = 1, the aspiration coefficient tends to assymptotically approach its theoretical limit of R. Beyond a Stokes number of about 6, it can be assumed that the aspiration coefficient equals R. This can be predicted both from equations (5), (9) and (10) and from theoretical considerations. Badzioch (10) and Belyaev and Levin (12) have shown that the streamlines start to diverge at approximately 6 diameters upstream of the nozzle. Therefore, a particle traveling at a velocity,Vo, will have to change directions in an amount of time equal to 6Di/Vo. If a particle cannot change direction in this amount of time, it will not be able to make the turn with the streamline. Since T represents the amount of time required for a particle to change directions, setting T = 6D /Vo represents the limiting size particle that will be able to make a turn with its streamline. Rearranging these terms it can be seen that this situation occurs when TV /D = 6 or at a Stokes number of 6.

Martone (15) further confirmed the importance considering free

stream velocity as well as particle diameter when sampling aerosols by








16









iI










n D Ln
CDCD In r- iN C O

(N o a 0 0
CJ


















', C4)
O.
o




C:)




Z c 0 0











C 1)
O

0, o





















(N D C)





oJ






















TJJ U .





17




analyzing concentration errors obtained while sampling submicron particles, 0.8 vm NMD and 1.28 geometric standard deviation, traveling at near sonic and supersonic velocities. He obtained sample concentrations 2-3 times greater than the true concentration when the sampling velocity was 20% of the free stream velocity (R=5).

Sehmel (16) studied the isokinetic sampling of monodisperse

particles in a 2.81 inch TDduct and found that it is possible to obtain a 20% concentration bias while sampling isokinetically with a small diameter inlet probe. Results also showed that for all anisokinetic sampling velocities, the concentration ratios were not simply correlated with Stokes number.


2. Sampling Bias Due to Nozzle Misalignment


Sampling error associated with the nozzle misalignment has not been adequately evaluated in past studies because the sampled flow field was maintained or assumed constant in velocity and parallel to the duct axis. The studies that have been performed on the effect of probe misalignment do not provide enough quantitative information to understand more than just the basic nature of the problem. Results were produced through investigations by Mayhood and Langstroth, as reported by Watson (5), on the effect of misalignment on the collection efficiency of 4, 12 and 37 vm particles (see Figure 7). In a study by Glauberman (17) on the directional dependence of air samplers, it was found that a sampler head facing into the directional air stream collected the highest concentration. Although these results coincide with






18











1.0






S0.8


E-
H



0.6
z 0




12m
z 0.4


12 p m


0.2




37 lpm

0 30 60 90 120 ANGLE OF PROBE MISALIGNMENT, degrees Figure 7. Error due to misalignment of probe to flow stream [after
Mayhood and Langstroth, in Watson (5)1.





19




theoretical predictions (i.e., measured concentration is less than or equal to actual concentration and the concentration ratios decrease as the particle size and the angle are increased), the data are of little use since two important parameters, free stream velocity and nozzle diameter, are not included in the analysis.

Raynor (18) sampled particles of 0.68, 6 and 20 im diameter at wind speeds of 100, 200, 400 and 700 cm/sec with the nozzle aligned over a range of angles from 60 to 120 degrees. He then used a trigonometric function to convert equation (5) to the form


A = 1 + B(K)[(Visin6 + V cose)/(V.cos6 + Vo sine) 1] (11)


This function only serves to invert the velocity ratio between 0 and 90 degrees and does not realistically represent the physical properties of the flow stream. In fact, equation (11) becomes unity at 45 degrees regardless of what the velocity ratio or particle size is. This cannot be true since it has been shown that the concentration ratio will be less than unity and will decrease inversely proportional to the angle and particle diameter.

A more representative function can be derived in the following

manner: Consider the sampling velocity V. to be greater than the stack
1
velocity V Let A. be the cross sectional area of the nozzle of diameter
o 1
D.. The stream tube approaching the nozzle will have a cross sectional
1
area A such that
0

A V = A. V. (12)
0 0 1 1





20




If the nozzle is at an angle e to the flow stream, the projected area perpendicular to the flow is an ellipse with a major axis D., minor axis D.cos6, and area (D i cos6)/4. The projected area of the nozzle
I i
would therefore be A.cos6 (see Figure 8). It can be seen that all the
1
particles contained in the volume V A.cose will enter the nozzle. A O 1
fraction 5'(K,R,6) of the particles in the volume (A A cosB)V will leave the stream tube because of their inertia and will not enter the nozzle. Therefore, with C defining the actual concentration of the
o
particles, the measured concentration in the nozzle would be

C A.cos6V + [1-B'(K,R,e)](A -A.cos6)Vo C
C. (13) A.V.
1 1


Using equations (1) and (12), this may be simplified to


A = Ci/C = 1 + (K,R,e) (Rcos-1l) (14)


B'(K,R,8) would be a function of both the velocity ratio R and the inertial impaction parameter K as shown by Belyaev and Levin (13). However, $' will also be a function of the angle 8 because as the angle increases, the severity of the turn that the particles must make to be collected is also increased.

It can be seen that for large values of Stokes number, 8' must approach 1 for the predicted concentration ratio in equation (14) to reach the theoretical limit of Rcos6. The maximum error should theoretically occur somewhere between a Stokes number of 1 and 6 depending on the angle

8. The upper limit of K = 6 would be for an angle of 0 degrees as described earlier in this chapter. The theoretical lower limit of K = 1







21
































CQ) <0










4J)


C)
















-C)


C)





22




would be for an angle of 90 degrees in which case the particles would be traveling perpendicular to the nozzle. Since the nozzle has zero frontal area relative to the flow stream, any particle that is collected must make a turn into the nozzle. The amount of time that a particle has to negotiate a turn is the time it takes the particle to traverse the diameter of the nozzle, or Di/V Setting this equal to T the time it takes a particle to change directions and rearranging terms, we obtain TV /D. = 1 as the limiting situation for a particle to be able to
O 1
make a turn into a nozzle positioned at a 90 degree angle to the flow stream. For angles between 0 and 90 degrees the maximum error will occur between the limits of Stokes numbers of 1 and 6 and should be proportional to the average diameter of the frontal area of the nozzle. Fuchs (19) suggests that for small angles the sampling efficiency will be of the form


A = 1 4 sin(6K/7) (15) Laktionov (20) sampled a polydisperse oil aerosol at an angle to the flow stream of 90 degrees for three subisokinetic conditions. He used a photoelectric installation to enable him to determine the aspiration coefficients for different sized particles. From data obtained over a range of Stokes numbers from 0.003 to 0.2 he developed the following empirical equation:

0.5
A = 1 3K(Vi/Vo) 0.5 (16) This equation can be used only in the range of Stokes numbers given and for a range in velocity ratios (R) from 1.25 to 6.25.






23




A few analytical studies in this area have also been published. Davies' (14) theoretical calculations of particle trajectories in a nonviscous flow into a point sink determined the sampling accuracy to be a function of the nozzle inlet orientation and diameter, the sampling flow rate and the dust particle inertia. Vitols (21) also made theoretical estimates of errors due to anisokinetic sampling. He used a procedure combining an analog and a digital computer and considered inertia as the predominant mechanism in the collection of the particulate matter. However, the results obtained by Vitols are only for high values of Stokes numbers and are of little value for this study.


B. Summary of the Literature on Tangential Flow


Although anisokinetic sampling velocity is known to cause a

particle sampling bias or error, there are also several other sampling error-causing factors such as: duct turbulence; external force fields (e.g., centrifugal, electrical, gravitational or thermal); and probe misalignment due to tangential or circulation flow. These factors are almost always present in an industrial stack gas and cannot be assumed to be negligible. Not only do these factors cause sampling error directly but in addition, they cause particulate concentration gradients and aerosol size distribution variations to exist across the stack both in the radial and angular directions.


1. Causes and Characteristics of Tangential Flow


Tangential flow is the non-random flow in a direction other than that parallel to the duct center line direction. In an air pollution





24




control device, whenever centrifugal force is used as the primary particle collecting mechanism, tangential flow will occur. Gas flowing from the outlet of a cyclone is a classic example of tangential flow and a well recognized problem area for accurate particulate sampling. Tangential flow can also be caused by flow changes induced by ducting

(22). If the duct work introduces the gas stream into the stack tangentially, a helical flow will occur (see Figure 9). Even if the flow stream enters the center of the stack, if the ducting flow rate is within an order of magnitude of the stack flow rate, a double vortex flow pattern will occur (see Figure 10).

The swirling flow in the stack combines the characteristics of vortex motion with axial motion along the stack axis. The gas stream moves in spiral or helical paths up the stack. Since this represents a developing flow field, the swirl level decays and the velocity profiles and static pressure distributions change with axial position along the stack. Swirl level is used here to represent the axial flow or transport rate of angular momentum (23). Velocity vectors in tangential or vortex flows are composed of axial, radial and tangential or circumferential velocity components (see Figure 11). The established vortex flows are generally axisymmetric but during formation of the spiraling flow the symmetry is often distorted. The relative order of magnitude of the velocity components varies across the flow field with the possibility of each one of the components becoming dominant at particular points (24).






25
























Z


CL
w I




0

-j
LL























b.







r
0








26































z


F
C)0














c~)

-C)

-C)

-C) C)
U C) 'C)



0

x

C)

0 C)

-C) C)
0
0


- 0
-I
0 C) F-






27












Vr



























Vo V Vr, t Figure 11. Velocity components in a swirling flow field.





28




The two distinctly different types of flow that are possible in

a swirling flow field are known as free vortex and forced vortex flows. When the swirling component of flow is first created in the cyclone exit, the tangential profile of the induced flow approaches that of a forced vortex. As the forced vortex flow moves along the axis of the stack, momentum transfer and losses occur at the wall which cause a reduction in the tangential velocity and dissipation of angular momentum. This loss of angular momentum is due to viscous action aided by unstable flow and fluctuating components. Simultaneously, outside the laminar sublayer at the wall where inertial forces are significant, the field develops toward a state of constant angular momentum. This type of flow field with constant angular momention is classified as free vortex flow. The angular momentum and tangential velocities of the flow decay as the gas stream flows up the stack (23).

Baker and Sayre measured axial and tangential point velocity distributions in a 14.6 cm circular duct in which swirling flow was produced by fixed vanes (23). The tangential velocity profiles and angular momentum distributions are plotted in Figures 12 and 13 from measurements taken at 9, 24 and 44 diameters downstream of the origin of tangential flow. The tangential velocity (W) is made dimensionless by dividing it by the mean spatial axial velocity (Um) at a pipe cross section. These plots indicate developing flow fields, with two definite types of flow occurring: that approaching forced vortex flow in the central region of the pipe and flow approaching free vortex flow in the outer region. Further tests showed that the free vortex field








29
























C)


cc
C





H

'H U) CC



CN If


U
C C)



-~

'p
C)


~ CC




C


C

-p

'H
p
'p
U)
-u


CC

0 'p
U C)
U) U) U)
C
p
U (2

LI) Z ("3 - C)
p







































GO











CD















0







r



*01

'0





42
C CJ C .r -











development is due primarily to viscosity at the wall and not a function of inlet conditions, whereas the profiles in the forced vortex field are very dependent on the initial conditions at the inlet. Although no reverse flow was found in these tests, other tests showed that strong swirls may produce reversed axial velocities in the central region (23).

It should be noted that although tangential velocities and angular momentum decay along the axis of the pipe, see Figures 12 and 13, even after 44 diameter the tangential velocity is still quite significant when compared to the axial velocity. Therefore, satisfying the EPA Method 5 requirement of sampling 8 stack diameters downstream of the nearest upstream disturbances will not eliminate the effect of sampling in tangential flow.

The angle of the flow relative to the axis of the stack induced by the tangential component of velocity was as high as 60 degrees at some points in the flow. This compares well with angles found when sampling the outlets of cyclones (25). Another interesting fact about the flow described in Figures 12 and 13 is that the radial positions for the tangential components W/Um = 0 show that the vortex axis is off center by as much as 0.lr/R. This indicates that the swirling fields are not exactly axisymmetrical.


2. Errors Induced by Tangential Flow


Types of errors that would be expected to be introduced by tangential flow are nozzle misalignment, concentration gradients and invalid flow measurements. The sampling error caused by nozzle misalignment has been





32




described in the previous chapter. Concentration gradients occur because the rotational flow in the stack acts somewhat as a cyclone. The centrifugal force causes the larger particles to move toward the walls of the stack, causing higher concentrations in the outer regions.

Mason (22) ran tests at the outlet of a small industrial cyclone to determine the magnitude of these three types of errors induced by cyclonic flow. Results of flow rates determined at the different locations are presented in Table I. As indicated by the data, serious errors can result in cases of tangential flow. A maximum error of 212% occurred when the pitot tube was rotated to read a maximum velocity head. Sampling parallel to the stack wall also had a large error of almost 74%. When sampling downstream of the flow straightening vanes, however, the error was reduced to 15%.

Tests performed at the same point but with different nozzle angles produced the data in Table II. Measured dust concentration was lowest when the sampling nozzle was located at an angle of 0 degrees or parallel to the stack wall. The measured dust concentration continued to increase at 30 and 60 degrees but then decreased at 90 degrees. Equation (14) shows that when sampling at an angle, under apparent isokinetic conditions (i.e., R=I), the measured concentration will be less than the true concentration by a factor directly proportional to the cose. A maximum concentration, which would be the true concentration, will occur at e = 0, which from this data should lie at an angle between 60 and 90 degrees to the axis of the stack. This can be confirmed by




















TABLE I
FLOW RATE DETERMINED AT VARIOUS MEASUREMENT LOCATIONS


Location Velocity (fps) Flow Rate (scfm) % Error


Actual Based on
Fan Performance 18 475 -Port A
(parallel) 40 826 74 Port A
(maximum Ap) 60 1,482 212 Port C
(straightened) 21 548 15





34














TABLE II
CONCENTRATION AT A POINT FOR DIFFERENT SAMPLING ANGLES Measured Concentration Nozzle Angle (grains/dscf)


0 0.243

30 0.296 60 0.332 90 0.316






35




using the data in Table I and the geometry in Figure 11 to calculate the angle #:


cos4 = Va/Vo = 13/60 (17)


This is true for = 72 degrees. Therefore, 0 = 0 when 4 = 72 degrees.

Table III gives the results of the emission tests. Sampling with the nozzle parallel to the stack wall showed an error of 53%.

Sampling at the angle of maximum velocity head reduced the error to 40%. The results cannot be compared directly to those with the parallel sampling approach because the feed rates were not the same due to equipment failure and replacement. Sampling in the straightened flow had a sampling error of 36%. It was expected that sampling at this location would give better results, but some of the particles were impacted on the straightening vanes and settled in the horizontal section of the duct, thus removing them from the flow stream.

Particle size distribution tests showed no significant effect of a concentration gradient across the traverse. This was due to the particles being too small to be affected by the centrifugal force field set up by the rotating flow.


3. Errors Due to the S-Type Pitot Tube


The errors in the measurement of velocity and subsequent calculations of flow rate in tangential flow are due primarily to the crudeness of the instruments used in source sampling. Because of the high particulate loadings that exist in source sampling, standard pitot tubes cannot be used to measure the velocity. Instead, the S-type pitot tube must be used





36
















TABLE III
EMISSION TEST RESULTS


Measured Emission Actual Emission Probe Position Rate (gr/dscf) Error %


Nozzle parallel with stack wall 0.350 0.752 53 Nozzle rotated
toward maximum Ap 0.194 0.327 40 Straightened flow 0.207 0.325 36





37



since it has large diameter pressure ports that will not plug (see Figure 14). Besides the large pressure ports it has an additional advantage of producing approximately a 20% higher differential pressure than the standard pitot tube for a given velocity. However, although the S-type pitot tube will give an accurate velocity measurement, it is somewhat insensitive to the direction of the flow (25-29). Figures 15 and 16 show the velocity errors for yaw and pitch angles. Although the S-type pitot tube is very sensitive to pitch direction, the curve for yaw angle is symmetrical and somewhat flat for an angle of 45 degrees in either direction. Because of this insensitivity to direction of flow in the yaw direction, the S-type pitot tube cannot be used in a tangential flow situation to align the nozzle to the direction of the flow, or to accurately measure the velocity in a particular direction.

The velocity in a rotational flow field can be broken up into three components in the axial, radial and tangential directions (see Figure 11). The magnitude of the radial and tangential components relative to the axial component will determine the degree of error induced by the tangential flow. Neither the radial nor the tangential components of velocity affect the flow rate through the stack, but both affect the velocity measurement made by the S-type pitot tube because it lacks directional sensitivity. If the maximum velocity head were used to calculate the stack velocity, the resultant calculated flow rates and emission levels could be off by as much as a factor of 1/cos. Aligning the probe parallel to the stack will reduce but not eliminate this error because part of the radial and tangential velocity components will still be detected by the pitot tube.









38











~











+ C)



C)
-C) U) C) C)) C-)


d


-C) C-)


C-)

H



N *1-'



C)
-z
N C) 4-) N 4~)
0 0
0
N \ H
C)
C) N
C) C) N U) 4-,








C) C) 04) r-t.








39










4 0





















-a 0





r-4 rCD *
4-u 0 C H0









) '..4 S c'












00
Cou o 0




















r,
0
T-4


































H







40















o u







t-I C7) E)



oCa


mec





























.C
U0












0U

























0
Oz
--'-D
4
3 I C
ct 1


a,














k~FU CL~C!I i








c.)





41




Therefore, the true flow rate cannot be determined by an S-type pitot tube in tangential flow because neither the radial velocity, Vr, the tangential velocity, Vt, the axial velocity, Va, nor the angle $ can be measured directly.


4. Methods Available for Measuring Velocity Components in a Tangential
Flow Field


Almost all of the reported measurements of velocity components in a tangential flow field have been based upon introduction of probes into the flow. Because of the sensitivity of vortex flows to the introduction of probes, the probe dimensions must be small with respect to the vortex core in order to accurately measure velocity.

Two common types of pressure probes capable of measuring velocity accurately are the 5-hole and 3-hole pitot tubes pictured in Figures 17a and b. The 5-hole or three dimensional directional pressure probe is used to measure yaw and pitch angles, and total and static pressure. Five pressure taps are drilled in a hemispherical or conical probe tip, one on the axis and at the pole of the tip, the other four spaced equidistant from the first and from each other at an angle of 30 to 50 degrees from the pole. The operation of the probe is based upon the surface pressure distribution around the probe tip. If the probe is placed in a flow field at an angle to the total mean velocity vector, then a pressure differential will be set up across these holes; the magnitude of which will depend upon the geometry of the probe tip, relative position of the holes and the magnitude and direction of the velocity vector. Each probe requires calibration of the pressure









42

















r-- -0



I M
































-4->
oo.
o 4
un














4 4J
00 0
(Th C 1~~~~\
'- 42o
0c









0 C)
0c


rcl)4
C)


-4
0r
c~) C)
-4
0 U 0 C




Cl.
1u
r-4

C)'C 0

C);
*j t1 )
LC.t





43




differentials between holes as a function of yaw and pitch angles. Figure 18 shows the sensitivity of a typical 5-hole pitot tube to yaw angle. Because of its sensitivity to yaw angle, it is possible to rotate the probe until the yaw pressures are equal, measure the angle of probe rotation (yaw angle) and then determine the pitch angle from the remaining pressure differentials. The probe can be used without rotation by using the complete set of calibration curves but the complexity of measurement and calculation is increased and accuracy is reduced. Velocity components can then be calculated from the measured total pressure, static pressure and yaw and pitch angle measurements.

The 3-hole pitot tube, also known as the two dimensional or Fecheimer probe, is similar to the 5-hole design except that it is unable to measure pitch angle. The probe is characterized by a central total pressure opening at the tip of the probe with two static pressure taps placed symmetrically to the side at an angle of from 20 to 50 degrees. From Figure 19 it can be seen that the probe is quite sensitive to yaw angle and can therefore be used to determine the yaw angle by rotating the probe until the pressure readings at the static taps are equal. Once this is done the total pressure is read from the central port, and the static pressure can be determined by use of a calibration chart for the particular probe. Both the 5-hole and the 3-hole pitot tubes have proven useful in determination of velocity components in tangential flow fields (25, 28, 30).


5. EPA Criteria for Sampling Cyclonic Flow


The revisions to reference methods 1-8 (2) describe a test for determination of whether cyclonic flow exists in a stack. The S-type





44













Dynamic
Pressure


0.04







0.02








-25 -20 -15 -10 -5 5 10 15 20 25 Yaw Angle, degrees



-0.02

Pressure
Differential, inches of H20


0.04









Figure 18. Five-hole pitot tube sensitivity to yaw angle.(28).






45













0.15 -0.10 Dynamic
Pressure


0.05






-30 -25 -20 -15 -10 -5 5 10 15 20 25 30 Pitch Angle, degrees
-.05




-.10
Pressure Differential, inches of H 20






Figure 19. Focheimer pitot tube sensitivity to yaw angle. (28)





46




pitot tube is used to determine the angle of the flow relative to the axis of the stack by turning the pitot tube until the pressure reading at the two pressure openings is the same. If the average angle of the flow across the cross section of the stack is greater then 10 degrees,

then an alternative method of Method 5 should be used to sample the gas stream. The alternative procedures include installation of straightening vanes, calculating the total volumetric flow rate stoichiometrically, or moving to another measurement site at which the flow is acceptable.

Straightening vanes have shown the capability of reducing swirling flows;however, there are some problems inherent in their use. One is the physical limitation of placing them in an existing stack. Another is the cost in terms of energy due to the loss of velocity pressure when eliminating the tangential and radial components of velocity. Since the vortex flows are so sensitive to downstream disturbances, it is quite possible that straightening vanes might have a drastic effect on the performance of the upstream cyclonic control device which is generating the tangential flow. Because of these reasons the use of straightening vanes is unacceptable in many situations.

Calculating the volumetric flow rate stoichiometrically might

produce accurate flow rates but the values could not be used to calculate the necessary isokinetic sampling velocities and directions.

Also, studies reported here have shown that the decay of the tangential component of velocity in circular stacks is rather slow and therefore

it would be unlikely that another measurement site would solve the problem.






47



It should be noted that EPA's approach to determining whether cyclonic flow exists in a stack is correct. Other approaches such as observing the behavior of the plume after leaving the stack could lead to improper conclusions. Hanson et al (28) found that the twin-spiraling vorticies often seen leaving stacks are the result of secondary flow effects generated by the bending of the gas stream by the prevailing crosswind and do not indicate any cyclonic flow existing in the stack.















CHAPTER III
EXPERIMENTAL APPARATUS AND METHODS


A. Experimental Design


The major components of the aerosol flow system can be seen in

Figure 20. An aerosol stream generated from a spinning disc generator was fed into a mixing chamber where it was combined with dilution air. The air stream then flowed through a 10 cm diameter PVC pipe containing straightening vanes. This was followed by a straight section of clear pipe from which samples were taken. The filter holder and nozzle used as a control sample originated in a box following the straight section. A test nozzle was inserted into the duct at an angle from outside the box. A thin-plate orifice, used to monitor flow rate, followed the sampling box. A 34000 Zpm industrial blower was used to move the air through the system. The flow rate could be controlled by changing the diameter of an orifice plate. An air by-pass between the blower and the orifice plate was used as a fine adjust for the flow.

The sampling systems (see Figure 21) consisted of stainless steel, thin-walled nozzles connected to 47 mm stainless steel Gelman filter holders. Each filter assembly was connected in series to a dry gas meter and a rotameter, and driven by an airtight pump with a by-pass valve to control flow.




48








49




Cc w

-L

F~













CCD












Q,
0 C



-- I


























C LJ LU





C





aa)








CDd







CC

2 c





--J 1---r
O3 CD CC~t 0 UJ C T a -





50

















SSO

4J
L CD








J E




JO






<5






51




B. Aerosol Generation


1. Spinning Disc Generator


A spinning disc aerosol generator (31-33) was used to generate monodisperse aerosols from 1.0 vm NMD to 11.1 um NMD (see Table IV). Droplets were generated from a mixture of 90% uranine (a fluorescent dye) and 10% methylene blue dissolved in a solution of from 90 to 100% ethanol (95% pure) and up to 10% distilled/deionized H20. Uranine was used so that the particles could be detected by fluoremetric methods. Methylene blue was added to aid in the optical sizing of the particles. The mixture of water and ethanol allowed for a uniform evaporation of the droplets. The droplets, containing dissolved solute, evaporated to yield particles whose diameters could be calculated from the equation

0.33
DP = (Cr ) DD (18)


where

D = particle diameter, um

C = ratio of solute volume to solvent volume plus solute

volume, dimensionless

DD = original droplet diameter, um

With the disc's rotational velocity, air flows and liquid feed rate held constant the size of the droplets produced were only dependent upon the ratio of the ethanol-water mixture. Since the droplets are produced from a dynamic force balance between the centrifugal force and the surface





52







TABLE IV
SIZES AND DESCRIPTIONS OF EXPERIMENTAL AEROSOLS



Number Mean
Aerosol Generation % Droplet Diameter
Description Method Ethanol Diameter, pm Particles, pm


0.0024% Spinning Disc 90 37.4 1.08 0.005% Spinning Disc 90 37.2 1.37 0.01% Spinning Disc 90 37.1 1.72 0.03% Spinning Disc 90 37.8 2.53 0.2% Spinning Disc 99 24.6 3.10 0.05% Spinning Disc 90 39.7 3.15

0.55% Spinning Disc 99 24.4 4.3

0.3% Spinning Disc 90 34.5 4.98 0.6% Spinning Disc 90 33.1 6.02 2.0% Spinning Disc 100 23.6 6.4

1.0% Spinning Disc 90 35.4 7.66

4.0% Spinning Disc 100 23.4 8.0 6.7% Spinning Disc 100 23.2 9.42

6.7% Spinning Disc 95 27.3 11.1 Ragweed Mechanical
Pollen Dispersion N.A. N.A. 19.9











tension of the drop, the surface characteristics of the liquid are quite important. The surface tensions of water and ethanol at 20 degrees C are respectively 72.8 and 22.3 dynes/cm (34). The effect of this large difference can be seen in Table IV where the droplets produced were approximately 37 im for 90% ethanol and 23 im for 100% ethanol.

Before and after each test a sample of the particles was collected on a membrane filter and sized using a light microscope to take into account any slight variation in the performance of the spinning disc.


2. Ragweed Pollen


In order to obtain large Stokes numbers, ragweed pollen was mechanically dispersed by means of a rubber squeeze bulb into the inlet of the duct. The ragweed pollen had a NMD of 19.9 im.


C. Velocity Determination


The velocity at each sampling point was measured using a standard pitot tube. The flow was maintained constant during the test by controlling the pressure drop across a thin-walled orifice placed in the system (35-37). Five orifice plates with orifices ranging in diameter from 1.8 to 7.2 cm were used to obtain a range in duct velocities of 82 to 2460 cm/sec (see Table V) in the 10 cm duct. To obtain higher velocities, a 5 cm duct was used.

A typical velocity profile across the 9.6 cm clear plastic duct is presented in Table VI and plotted in Figure 22. The profile is






54









TABLE V
TABLE OF OBTAINABLE VELOCITIES IN 10 cm DUCT



Orifice Diameter Ap Range Range in Velocity
cm cm H 0 cm/sec


1.795 5.6 21.6 82 162 2.539 5.3 21.8 162 326 3.589 4.2 22.9 304 670 5.080 4.1 22.6 582 1371 7.182 2.2 14.5 945 2460





55













TABLE VI
TYPICAL VELOCITY TRAVERSE IN THE EXPERIMENTAL SAMPLING SYSTEM (9.58 cm I.D. Duct)



Horizontal Vertical Point d/D AP, cm H 20 V, cm/sec AP, cm H20 V, cm/sec


1 0.044 1.27 1454 1.57 1618 2 0.146 1.83 1743 2.11 1871 3 0.296 2.03 1838 2.08 1859 4 0.704 2.13 1884 2.11 1871 5 0.854 1.88 1768 1.98 1813 6 0.956 1.47 1564 1.52 1591






Average Velocities (cm/sec)


From Pitot Tube Readings From Orifice AP 1740 1658







56






























0 o 0c






o u.






4-4,




o C
N














CD


CCd
oc o




0~ 0






























NJ -4 -






57





quite flat which is typical of the turbulent flow regime. The average Reynolds number for this particular case was 1.1 x 105. The velocities at traverse points 3 and 4 were used as the velocity for determination of isokinetic sampling rate and Stokes number. The difference between the average velocity determined from the pitot traverse and the orifice plate calibration is probably due to the inability of the pitot tube to accurately measure velocity near the wall at points 1 and 6.


D. Selection of Sampling Locations


Sehmel (16) observed that non-uniform particle concentrations existed across the diameter of a cylindrical duct, and that the magnitude of the concentration gradient varied with particle size. To account for these radial variations, the two sampling points were located symmetrically about the center of the duct at a distance of 2 cm from the center. Simultaneous isokinetic samples were taken at the two points and compared. Tests were repeated for different particle sizes. No concentration differences were found to exist at the two sampling points.


E. Sampling Nozzles


Two pairs of sampling nozzles were cut from stainless steel tubing of 0.465 cm and 0.683 cm I.D. The nozzles were made approximately 15 cm long to minimize the effect of the disturbance caused by the filter holders on the flow at the entrance of the nozzles. Analysis by Smith

(38) showed that a sharp-edge probe was the most efficient design;






58





therefore, the tubing was tapered on a lathe to a fine edge. Belyaev and Levin (12) observed that the rebound of particles from the tip of the nozzle into the probe was one cause of sampling error and that for tapered nozzles, the efficiency is affected by the relative wall thickness, the relative edge thickness and the angle of taper. They concluded that if the edge thickness is less than 5% of the internal diameter and the taper is less than 15 degrees, then the variation in aspiration coefficient due to particle rebound would be less than 5%. The nozzles were designed accordingly.


F. Analysis Procedure


1. For Uranine Particles


Uranine particles were collected on Gelman type A glass fiber

filters. The filters were then placed in a 250 ml beaker. One hundred milliliters of distilled water were then pipetted into the front half of the filter holder and down through the nozzle into the beaker containing the filter. The uranine leachate concentration was then diluted and analyzed by a fluorometer (39).


2. For Ragweed Pollen


The ragweed pollen was collected on membrane filters and counted under a stereo microscope. In this part of the experiment the filters and probe were analyzed separately. The filters used for collecting the particles were 5.0 Jm type SM Millipore membrane filters. In order to count the particles under a microscope a dark background was necessary;





59




therefore, each filter was dyed with ink and a grid was drawn to aid in the counting. Before being placed in the filter holders, the filters were examined under the microscope to determine if any background count existed. After each test the filters were removed and the entire area of the filter was counted.

The pollen caught in the nozzle and filter holder was analyzed

using isopropyl alcohol and 0.45 pm pore size Millipore membrane filters with black grids. The isopropyl was first filtered several times to remove background particulate matter. Once the background was low enough, the alcohol was poured into the front half of the filter holder and through the nozzles. The solution was then sucked through the membrane filters. The filters were allowed to dry and then the entire filter area was counted under the microscope.


G. Sampling Procedure


1. A desired flow rate was obtained by selecting an orifice

plate and using the by-pass as a fine adjust.

2. The velocity was measured using a standard pitot tube.

3. A solute-solvent solution was selected for a given particle

size.

4. Particles were collected on a membrane filter and sized

using a light microscope.

5. A nozzle diameter which would allow for an isokinetic

sampling rate closest to 1 cfm was selected.

6. Isokinetic sampling rates were calculated and sampling

flow rates were adjusted accordingly.






60




7. Two simultaneous isokinetic samples were taken, one

parallel to the flow (control), and one at a specified

angle. Sampling times varied from 10 to 20 minutes.


H. Tangential Flow Mapping


The system used to map the flow pattern in a tangential flow stream is shown in Figure 23. It consists of a 34000 Zpm industrial blower, a section of 15 cm PVC pipe containing straightening vanes, a small industrial cyclone collector, followed by a 6.1 meter length of 20 cm PVC pipe. The 150 cm long cyclone, shown in Figure 24 was laid on its side so that the stack was horizontal and could be conveniently traversed at several points along its length. A change in flow through this system could be produced by supplying a restriction at the inlet to the blower.

To measure the velocity in the stack a United Sensor type DA 3dimentional directional pitot tube was used. The probe, pictured with its traversing unit in Figure 25, is .32 cm in diameter and is capable of measuring yaw and pitch angles of the fluid flow as well as total and static pressures. From the blow up of the probe tip (Figure 25) it can be seen that the head consists of 5 pressure ports. Port number 1 is the centrally located total pressure tap. On each side are two lateral pressure taps 2 and 3. When the probe is rotated by the manual traverse unit until P2 = P3, the yaw angle of flow is indicated by the traverse unit scale. When the yaw angle has been determined an additional differential pressure is measured by pressure holes located perpendicularly above and below the total pressure hole 1. Pitch angle is then determined using a calibration curve for the individual probe. The yaw angle is a





61















15 cm. 1I) Straig htenin, vanes


2.4 m
Blower


i








O









6.1 m


20cm Figure 23. Experimental system for measuring
cross sectional flow patterns in
a swirling flow stream.






62
























14.7
15.2 22.9




68.6



Note: All dimensions in centimeters








68.6











Figure 24. Cyclone used in the study to generate swirling flow.







63



























5 3 1

























2 4


Figure 25. Photograph of the 3-dimensional pitot with its
traversing unit. Insert shows the location of
the pressure taps.
~~A


c\ ;<'
~A,'






5~- ~3 1 ~~~~1sj -'t;71 0.37












Figure~~~~k~jg 25. Phtgrp of.. th dmnsoalpto it t
tirwvrsn unt netsos hoaino
the presue tps






64




measure of the flow perpendicular to the axis of the stack and tangent to the stack walls. The pitch angle is a measure of the flow perpendicular to the axis of the stack and perpendicular to the stack walls. The axial component of the velocity can therefore be determined from the following equation:


Va = Vt cos@ (19)


where V = component of velocity flowing parallel to the axis of the stack.

Vt = total or maximum velocity measured by the pitot tube

-= cos [cos(pitch x cos(vawl
= cos [cos (pitch) x cos (yaw)]I
















CHAPTER IV
RESULTS AND ANALYSIS


A. Aerosol Sampling Experiments


1. Stokes Number


Experiments were set up and run with Stokes number as the independent variable. Duct velocity, nozzle diameter and particle diameter were varied in order to produce a range of Stokes numbers from 0.007 to 2.97. The Stokes number used in the analysis of data was calculated from


Cp V D
K _- p o p (20) 18D.



where

-C0.434 D /L)
C = 1 + 2.492 L/Dp + 0.84 L/D e p (11) (21)



and

L = mean free path = 0.065 lm (11) Values for density and viscosity used in the calculations were
-4
S= 1.81 x 10 g/cm-sec (40)

p = density of uranine particles = 1.375 g/cm3 (41)

p = density of ragweed pollen = 1.1 g/cm3 (18)





65






66




2. Sampling with Parallel Nozzles


In order to determine if the concentration of particles was the same at both sampling locations, simultaneous samples were taken with both nozzles aligned parallel to the duct. Table VII shows the results of tests performed over a range of Stokes numbers from 0.022 to 1.73. The average over all of the tests showed only a 0.34% difference between the two points with a 95% confidence interval of 1.2%. The data show an increase in the range of the values as the Stokes number increases. This can be expected because a small error in probe misalignment would have a greater effect at the higher Stokes number.


3. Analysis of Probe Wash


In the analysis of the tests using ragweed pollen, the filter catch and probe wash were measured separately. This method allowed for the determination of the importance of analyzing both the filter and wash. From Table VIII it can be seen that even for a solid dry particle, analysis of the probe wash is a necessity. An average of 40% of the particles entering the nozzle was collected on the walls of the nozzle-filter holder assembly. This was only for nozzles aligned parallel to the flow stream and sampling isokinetically. Therefore, the loss of particles was due to turbulent deposition and possibly bounce off the filter, and probably not inertial impaction. For tests run with the nozzle at an angle to the flow stream, it is assumed that the loss would increase as impaction of particles on the walls became








67
















0 cn 0- C0- tn



0






















0 ccc









00 c cC O ,)






68









TABLE VIII
PERCENT OF PARTICULATE MATTER COLLECTED IN THE PROBE WASH
FOR NOZZLES PARALLEL WITH THE FLOW STREAM


Probe Wash* Filter* Total* % in Wash


511 497 1008 51 196 218 414 47 161 250 411 39 366 721 1087 34 407 697 1104 37 377 669 1046 36 265 464 729 36 415 647 1062 39 351 522 873 40 220 240 460 35 442 614 1036 41


*Numbers represent the number of ragweed pollen counted.





69




important. This can be seen from the data taken at 60 degrees (see Table IX) where an average of 54% of the particles was lost on the walls.

The probe wash for eight tests using 6.7 pm uranine particles

was also analyzed separately for comparison with the results of the ragweed pollen tests. While parallel sampling, from 15 to 34% of the total mass was collected in the nozzle and front end of the filter holder. While this was somewhat less than the amount of ragweed pollen found in the nozzle, it is substantial enough to show the importance of including the nozzle wash with the filter catch. Also because of the variation of the percent collected in the nozzle during identical tests, the probe wash cannot be accounted for by a correction factor. During further testing, it was qualitatively observed that the percent in the probe wash increased with particle size and decreased with increasing nozzle diameter.


4. The Effect of Angle Misalignment on Sampling Efficiency


The aspiration coefficient was determined by comparing the amount of particulate matter captured while sampling isokinetically with a control nozzle placed parallel and a test nozzle set at an angle to the flow stream. Tests were run at three angles, 30, 60 and 90 degrees. The results showed the theoretical predictions to be quite accurate. For all three angles the aspiration coefficient approached 1 for small Stokes numbers (K), decreased as K increased and then leveled off at a minimum of cos6 for large values of Stokes number. The most significant changes occur in the range between K = 0.01 and K = 1.0.






70

















TABLE IX
PERCENT OF PARTICULATE MATTER COLLECTED IN TIlE PROBE WASH FOR NOZZLES AT AN ANGLE OF 60 DEGREES WITH THE FLOW STREAM


Probe Wash* Filter* Total* % in Wash


348 211 559 62.0 161 138 299 54.0 288 333 621 46.4


* Numbers represent the number of ragweed pollen counted.





71




Figures 26, 27 and 28 represent the sampling efficiency as a function of Stokes number for 30, 60 and 90 degrees respectively. The experimental data used in these plots are presented in Tables X, XI and XII. From these tables it can be seen that the variables of particle diameter and velocity and nozzle diameter were varied rather randomly. This was done to check the legitimacy of using Stokes number as the principle independent variable. From the shape of the curves in Figures 26-28, it can be seen that the aspiration coefficient is indeed a function primarily of Stokes number.

The curves for 30, 60 and 90 degrees are all similar in shape except for the values of Stokes number where they approach their theoretical limit. As the angle of misalignment increases, the more rapidly the aspiration coefficient reaches its maximum error. This can be accounted for as an apparent change in nozzle diameter, because it is the only parameter in the Stokes number that is affected by the nozzle angle to the flow stream. As described before, the nozzle diameter is important because it determines the amount of time available for the particle to change directions (approximately 6 D./V ). As the
1 O
nozzle is tilted at an angle to the flow stream, the projected frontal area and therefore the projected nozzle diameter are reduced proportional to the angle. Therefore, as the angle of misalignment increases, the time available for the particle to change direction decreases leading to increased sampling error for a given value of K. To normalize these curves for angle to the flow stream, it is necessary to define an "adjusted Stokes number" (K') which takes into account the change in projected









72







C) I I














0



II


0

C


C)

0 -~ C) CC 0 C




0
C)


-~
C o x ~
C) C) o 0
C) ~t
C)
-~
C C
U * -~ C)
o




C) 0 0 C)

U



C) CC
0

o ~~1


C






C) C) C) C) C) CC ~C C'] C) C)

C) C) C)
CC

Cv) ;u~OOD uor;~uusv







73






o
o










0
-rd










o 0 0 Oo



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00 cb


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de




0 F--i O i

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GC 0 0 0 0i '-b
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MU b O O 0 O0 >" 44- Cc c 00 4 -00mr m 4
ct I, 00 0 0



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CC
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CO
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82




nozzle diameter with angle. When plotted against K', the aspiration coefficients for 30, 60 and 90 degrees should approach their theoretical minima at the same place as the curves for zero misalignment angle and anisokinetic sampling velocities (see Figure 6).

To develop the adjustment factor for Stokes number, it was necessary to plot as a function of e, the value of K where the aspiration coefficient reached a value that represented 95% of the maximum error. For example the maximum theoretical error for 60 degrees is cos(60) or

0.5. Therefore the value of K of interest is where there is (.95)(0.5) = 47.5% sampling error or an aspiration coefficient of 1 .475 = .525. For zero degrees, equations (9) and (10) were solved for R = 0.5 and 6 = 0.95 to obtain a value of K = 5.9. This velocity ratio was used because its theoretical maximum sampling error is 0.5, the same as for 60 degrees. The values for 60 and 90 degrees were obtained from Figures

27 and 28 respectively. Because of the flatness of the 30 degree curve (it varies only 16% over two and a half orders of magnitude of K), it was not possible to detect exactly when the curve reached 95% of its minimum value. Therefore no value for 30 degrees was used in this analysis.

The equation for the adjusted Stokes number determined from Figure

29 is


K' = Ke 022 (22) Using this equation it can be determined that the Stokes numbers for 30, 60 and 90 degrees must be multiplied by 1.93, 3.74 and 7.24 respectively to account for the effect of nozzle angle to the flow stream on the






83


















6











o
5




4

0
c







-4












0 30 60 90

Misal ignment Angle (e) Figure 29. Stokes number at which 95% maximum error occurs
vs. misalignment angle.






84




apparent nozzle diameter. Using these correction factors it is possible to use the data to determine an expression for 8' in equation (14). Setting R = 1 and solving for 8' this equation becomes A 1
cos6


Using this expression the experimental datawere used to plot 8' as a function of the adjusted Stokes number K' (see Figure 30). From this plot, it can be observed that the data points for 30, 60 and 90 degrees all fall approximately on the same line. It should be noted that most of the scatter is due to the 30 degree data and that the amount of the scatter is somewhat deceptive. Solving equation (23) for 30 degrees, requires that the sampling bias (1-A) must be multiplied by 7.5 to normalize it with the 90 degree data. This has an effect of greatly increasing any spread in the experimental data.

To develop a model for inertial sampling bias, it was necessary

to develop an equation for the line drawn through the data in Figure 30. An equation of the form similar to that used by Belyaev and Levin was selected to fit the data.


B'(K',6) = 1 1 (24)
1 + aK'


where a and b are constants. The advantage of this equation form is that it acts similar to the theoretical expectations of the relationship (i.e., B' approaches zero for very small values of K' and approaches 1 for very large values of K').









85









I. I I











0 0*







o


U) C) C)
0

C)

-U



-U

C)

z 0 'U
0
K



K 0 -~ 0 C) K C

0

-U
U) U) C)
C U)
0 0
-p
-p
U ~0 C)
-p
C) U)


-u
C)
C)

o U)

0 C) C




<00







I -~ z

D C) D C C)


i )




Full Text
r/R
Figure 13. Cross sectional distributions of angular momentum in a swirling flow field. o


58
therefore, the tubing was tapered on a lathe to a fine edge. Belyaev
and Levin (12) observed that the rebound of particles from the tip of
the nozzle into the probe was one cause of sampling error and that for
tapered nozzles, the efficiency is affected by the relative wall thick
ness, the relative edge thickness and the angle of taper. They con
cluded that if the edge thickness is less than 5% of the internal diameter
and the taper is less than 15 degrees, then the variation in aspiration
coefficient due to particle rebound would be less than 5%. The nozzles
viere designed accordingly.
F. Analysis Procedure
1. For Uranine Particles
Uranine particles were collected on Gelman type A glass fiber
filters. The filters were then placed in a 250 ml beaker. One hundred
milliliters of distilled water were then pipetted into the front half of
the filter holder and down through the nozzle into the beaker containing
the filter. The uranine leachate concentration was then diluted and
analyzed by a fluorometer (39).
2. For Ragweed Pollen
The ragweed pollen was collected on membrane filters and counted
under a stereo microscope. In this part of the experiment the filters
and probe were analyzed separately. The filters used for collecting
the particles were 5.0 pm type SM Millipore membrane filters. In order
to count the particles under a microscope a dark background was necessary;


Adjusted Stokes Number (K')
Figure 30. 3'(K',0) vs. adjusted Stokes number for 30, 60 and 90 degrees.


TABLE VII
RESULTS OF SAMPLING WITH TWO PARALLEL NOZZLES
Velocity
cm/sec
Particle Diameter
micrometers
Nozzle Diameter
cm
Stokes Number
% Difference
1798
1.08
0 .465
0.022
-3.2
+ 0.5
+ 0.3
-0.2
+ 1.3
-1.9
+ 1.6
1798
1.39
0 .465
0.035
-0.9
+ 2.3
+ 1 .3
1798
1.094
0 .465
0.053
+ 2.6
-3.7
-0.3
1798
2.74
0 .465
0 .130
+ 0.44
-0.6
1798
4.98
0 .465
0 .420
-1.9
+ 3.2
+ 2.2
701
19.9
0 .683
1.73
+ 8.7
-0.7
-3.9
ax
'-j


Aspiration Coefficient (A)
Figure 26. Sampling efficiency vs. Stokes number at 30 misalignment for R = 1.
tsj


TABLE XX
FIVE-HOLE PITOT TUBE MEASUREMENTS
MADE AT 1 DIAMETER DOWNSTREAM OF THE CYCLONE
Point
1-D Low Flow
Total
Angles, Degrees Velocity
Pitch Yaw (j) cm/sec
Axial
Velocity
cm/sec
Tangential
Velocity
cm/sec
1
kkk
k k
kkk
kkk
kkk
kkk
2
25.5
67.9
70.1
1786
608
1655
3
17.0
77.4
78.0
1600
333
1561
4
+ + +
+ + +
+ + +
+ + +
+ + +
+ + +
5
3.0
76.0
76.0
1341
324
1301
6
21.0
60.0
62.2
1761
821
1525
7
30.0
51.0
57.0
1762
959
1369
8
32.0
48.0
55.4
1664
945
1237
1-D High Flow
Total
Axial
Tangential
Aneles. Deerees
Velocity
Velocity
Velocity
Point
Pitch
Yaw

cm/sec
cm/sec
cm/sec
1
* k
kkk
kkk
kkk
kkk
kkk
2
24.0
64.0
66.4
2782
1114
2500
3
19.0
78.5
79.1
2348
444
2301
4
+ + +
+ + +
+ + +
+ + +
+ + +
+ + +
5
3.0
74.4
74.4
1846
496
1778
6
22.0
63.8
65.8
2699
1106
2421
7
28.0
57.8
61.9
2742
1292
2320
8
31.0
54.6
60.23
2572
1277
2096
*** Point No. 1
was too
close to
the wall to
allow insertion of all five
pressure taps.
+++ Point lies inside the negative pressure section.


TO PUMPS AND GAS METERS
Figure 20.
Experimental set up.
TO BLOWER


Aspiration Coefficient (A)
1.00
0.80
0.60
0.40
0.20
0.00
O G
0.01
O
o
i u
G
Typical 95% C.I.
o
O
<&
o
o
o
o
G
J L I 1111
J I 1 I 1...1 J-l.
J 1 1111
0.
1.0
10.
Stokes Number (K)
Figure 27. Sampling efficiency vs. Stokes number at 60 misalignment for R = 1.


TABLE OF CONTENTS--continued
CHAPTER Page
F. Analysis Procedure 58
1. For Uranine Particles 58
2. For Ragweed Pollen 58
G. Sampling Procedure 59
H. Tangential Flow Mapping 60
IV RESULTS AND ANALYSIS 65
A. Aerosol Sampling Experiments 65
1. Stokes Number 65
2. Sampling with Parallel Nozzles 66
3. Analysis of Probe Wash 66
4. The Effect of Angle Misalignment on Sampling
Efficiencies 69
5. The Effect of Nozzle Misalignment and Anisokinetic
Sampling Velocity 89
B. Tangential Flow Mapping 102
V SIMULATION OF AN EPA METHOD 5 EMISSION TEST IN A TANGENTIAL
FLOW STREAM 117
VI SUMMARY AND RECOMMENDATIONS 129
A. Summary 129
B. Recommendations 134
REFERENCES 135
BIOGRAPHICAL SKETCH 139
iv


20
If the nozzle is at an angle 0 to the flow stream, the projected area
perpendicular to the flow is an ellipse with a major axis D^, minor
2
axis D^cos0, and area (D^ ttcos0)/4. The projected area of the nozzle
would therefore be A^cosG (see Figure 8). It can be seen that all the
particles contained in the volume V A.cosG will enter the nozzle. A
fraction B'(K,R,0) of the particles in the volume (A A.cos@)V will
0 10
leave the stream tube because of their inertia and will not enter the
nozzle. Therefore, with C defining the actual concentration of the
o 6
particles, the measured concentration in the nozzle would be
C A.COS0V + [1 -31(K,R,0)](A -A.cos0)V C
r 01 o L 7 J v o i J o o r,
C = (13)
A. V.
i i
Using equations (1) and (12), this may be simplified to
A = C./Co = 1 + 3'(K,R,0)(Rcose-1) (14)
B'(K,R,0) would be a function of both the velocity ratio R and the
inertial impaction parameter K as shown by Belyaev and Levin (13).
However, 3' will also be a function of the angle 0 because as the angle
increases, the severity of the turn that the particles must make to be
collected is also increased.
It can be seen that for large values of Stokes number, 6' must ap
proach 1 for the predicted concentration ratio in equation (14) to reach
the theoretical limit of Rcos0. The maximum error should theoretically
occur somewhere between a Stokes number of 1 and 6 depending on the angle
0. The upper limit of K = 6 would be for an angle of 0 degrees as des
cribed earlier in this chapter. The theoretical lower limit of K = 1


AIR FLOW
9. Tangential flow induced by ducting
FLOW PATTERN
tsJ


36
TABLE III
EMISSION TEST RESULTS
Probe Position
Measured Emission
Rate (gr/dscf)
Actual Emission
Rate (gr/dscf)
Error
Nozzle parallel
with stack wall
0.350
0.752
53
Nozzle rotated
toward maximum Ap
0.194
0.327
40
Straightened flow
0.207
0.325
36


CHAPTER IV
RESULTS AND ANALYSIS
A. Aerosol Sampling Experiments
1. Stokes Number
Experiments were set up and run with Stokes number as the independent
variable. Duct velocity, nozzle diameter and particle diameter were varied
in order to produce a range of Stokes numbers from 0.007 to 2.97. The
Stokes number used in the analysis of data was calculated from
2
18D.n
(20)
i
where
C = 1 + 2.492 L/D + 0.84 L/D e
P P
and
L = mean free path = 0.065 ym (11)
Values for density and viscosity used in the calculations were
p = 1.81 x 10 4 g/cm-sec (40)
Pp = density of uranine particles = 1.375 g/cm.0 (41)
T
p = density of ragweed pollen = 1.1 g/cm (18)
65


136
14. Davies, C. N. The Entry of Aerosols into Sampling Tubes and Heads.
Brit. J. Appl. Phys., Ser. 2, 1:921, 1970.
15. Martone, J. A. Sampling of Submicrometer Particles Suspended in Near
Sonic and Supersonic Free Jets of Air. Presented at the Annual Meeting
of the Air Pollution Control Association, Toronto, Canada, 1977.
16. Sehmel, G. Particle Sampling Bias Introduced by Anisokinetic Sampling
and Deposition within the Sampling Lines. Amer. Ind. Hyg. Assoc. J.,
31(6) : 758, 1970.
17. Glauberman, H. The Directional Dependence of Air Samplers. Amer. Ind.
Hyg. Assoc. J., 23(3):235, 1962.
18. Raynor, G. S. Variation in Entrance Efficiency of a Filter Sampler with
Air Speed, Flow Rate, Angle and Particle Size. Amer. Ind. Hyg. Assoc.
J., 31(3) :294, 1970.
19. Fuchs, N. A. Sampling of Aerosols. Atmos. Envir., 9:697, 1975.
20. Laktionov, A. G. Aspiration of an Aerosol Into a Vertical Tube from a
Flow Transverse to It. AD-760 947, Foreign Technology Division, Wright-
Patterson Air Force Base, Ohio, 1973.
21. Vitols, V. Theoretical Limits of Errors Due to Anisokinetic Sampling of
Particulate Matter. J. Air Pollut. Control Assoc., 16(2): 79, 1960.
22. Mason, K. W. Location of the Sampling Nozzle in Tangential Flow. M. S.
Thesis, University of Florida, Gainesville, Florida, 1974.
23. Baker, D. W. and C. L. Sayre. Decay of Swirling Turbulent Flow of Incom
pressible Fluids in Long Pipes. Flow: Its Measurement and Control in
Science and Industry, Volume 1, Part 1, Flow Characteristics. Instrument
Society of America, Pittsburgh, 1974, p. 301.
24. Chigier, N. A. Velocity Measurement in Vortex Flows. Flow: Its Measure
ment and Control in Science and Industry, Volume 1, Part 1, Flow Charac
teristics. Instrument Society of America, Pittsburgh, 1974, p. 399.
25. Hanson, H. A. and D. P. Saari. Effective Sampling Techniques for
Particulate Emissions from Atypical Stationary Sources. EPA-600/2-77-036,
U.S. Environmental Protection Agency, Research Triangle Park, N.C., 1977.
26. Brooks, E. F. and R. L. Williams. Process Stream Volumetric Flow Measure
ment and Gas Sample Extraction Methodology. TRW Document No. 24916-6028-
RU-00, TRW Systems Group, Redondo Beach, California, 1975.


TABLE XIV
ASPIRATION COEFFICIENT AS A FUNCTION OF STOKES NUMBER FOR R = 2, 6 = 60
Velocity
cm/sec
Particle Diameter
micrometers
Nozzle Diameter
cm
Stokes Number
Aspiration
Coefficient %
732
4.59
0.683
0.099
96.9
104.1
100.5
732
6.5
0.683
0.196
109.0
93.4
98.4
701
9.6
0.683
0.406
90.9
101.9
101.9
1402
9.6
0.683
0.812
97.6
94.0
105.0
1140
9.9
0.465
1.01
95.2
105.1
97.0


47
It should be noted that EPA's approach to determining whether
cyclonic flow exists in a stack is correct. Other approaches such
as observing the behavior of the plume after leaving the stack could
lead to improper conclusions. Hanson et al (28) found that the
twin-spiraling vorticies often seen leaving stacks are the result of
secondary flow effects generated by the bending of the gas stream by
the prevailing crosswind and do not indicate any cyclonic flow
existing in the stack.


57
quite flat which is typical of the turbulent flow regime. The average
Reynolds number for this particular case was 1.1 x lO'. The velocities
at traverse points 3 and 4 were used as the velocity for determination
of isokinetic sampling rate and Stokes number. The difference between
the average velocity determined from the pitot traverse and the orifice
plate calibration is probably due to the inability of the pitot tube to
accurately measure velocity near the wall at points 1 and 6.
D. Selection of Sampling Locations
Sehmel (16) observed that non-uniform particle concentrations
existed across the diameter of a cylindrical duct, and that the
magnitude of the concentration gradient varied with particle size.
To account for these radial variations, the two sampling points were
located symmetrically about the center of the duct at a distance of
2 cm from the center. Simultaneous isokinetic samples were taken at
the two points and compared. Tests were repeated for different
particle sizes. No concentration differences were found to exist at
the two sampling points.
E. Sampling Nozzles
Two pairs of sampling nozzles were cut from stainless steel tubing
of 0.465 cm and 0.683 cm I.D. The nozzles were made approximately 15 cm
long to minimize the effect of the disturbance caused by the filter
holders on the flow at the entrance of the nozzles. Analysis by Smith
(38) showed that a sharp-edge probe was the most efficient design;


118
TABLE XXVI
S-TYPE PITOT TUBE MEASUREMENTS
MADE AT THE 8-D SAMPLING PORT FOR THE LOW FLOW CONDITION
Point
Dynamic
Pressure
(cm H0)
.
Static
Pressure
(cm Ho0)
Ap
(cm H^O)
Ap2 ,
(cm Ho0) 2
Velocit;
(cm/sec'
8
0.96
-0.36
1.32
1.15
1229.0
7
0.99
-0.48
1.47
1.21
1298.5
6
0.66
-0.89
1.55
1.24
1331.6
5
-1.07
-0.74
0.33
0.57
614.7
4
-1.32
-1.04
-0.28
-0.53
-565.6
3
-0.41
-0.46
0.05
0.22
241.1
2
0.30
-0.17
0.47
0.69
743.2
1
0.69
-0.10
0.79
0.S9
949.3


TABLE XXIII
FIVE-HOLE PITOT TUBE MEASUREMENTS
MADE AT 8 DIAMETERS DOWNSTREAM OF THE CYCLONE
109
8-D Low Flow
Point
Angles, Degrees
Pitch Yaw cf)
Total
Velocity
cm/sec
Axial
Velocity
cm/sec
Tangential
Velocity
cm/sec
1
kkk
***
kkk
k k k
kkk
kkk
2
19.5
59.0
61.0
1414
685
1212
3
15.0
69.0
70.3
1436
484
1346
4
+ + +
+ + +
+ + +
+ + +
+ + +
+ + +
5
8.0
63.6
63.9
1396
614
1250
6
20.0
50.2
53.0
1326
798
1019
7
28.0
39.4
47.0
1289
879
818
8
29.0
38.0
46.4
1231
849
758
8-D High
Flow
Point
.Angle
Pitch
s, Degrees
Yaw cf>
Total
Velocity
cm/sec
Axial
Velocity
cm/sec
Tangential
Velocity
cm/sec
1
k k k
* *
kk-k
k kk
kkk
kkk
2
19.0
57.0
59.0
1875
966
1572
3
9.0
70.0
70.3
1881
634
1767
4
+ + +
+ + +
+ + +
+ + +
+ + +
+ + +
5
0
64.6
64.6
1743
748
1574
6
15.0
50.0
51.6
1942
1206
1488
7
21.0
43.2
47.1
1869
1272
1279
8
25.0
42.0
47.7
1795
1208
1201
*** Point No. 1 was too close to the wall to allow insertion of all five
pressure taps.
+++ Point lies inside the negative pressure section.


137
27. Grove, D. J. and W. S. Smith. Pitot Tube Errors Due to Misalignment and
Nonstreamlined Flow. Stack Sampling News, November, 1973.
28. Hanson, H. A., R. J. Davini, J. K. Morgan and A. A. Iversen. Particulate
Sampling Strategies for Large Power Plants Including Nonuniform Flow.
EPA-600/2-76-170, U. S. Environmental Protection Agency, Research Triangle
Park, N.C., 1976, 349 pp.
29. Williams, F. C. and F. R. DeJarnette. A Study on the Accuracy of Type S
Pitot Tube. EPA 600/4-77-030, U. S. Environmental Protection Agency,
Research Triangle Park, N.C., 1977.
30. Lea, J. F. and D. C. Price. Mean Velocity Measurements in Swirling Flow
in a Pipe. Flow: Its Measurement and Control in Science and Industry,
Volume 1, Part 1, Flow Characteristics. Instrument Society of America,
Pittsburgh, 1974, p. 313.
31. Green, H. L. and W. R. Lane. Particulate Clouds: Dusts, Smokes and
Mists. E. F. M. Spon. Ltd., London, 1957, p. 36.
32. Air Pollution Manual. Part II Control Equipment. Amer. Ind. Hyg.
Assoc., Detroit, 1968, p. 4.
33. Whitby, K. T., D. A. Lundgren and C. M. Peterson. Homogeneous Aerosol
Generators. J. Air and Water Poll., 9:263, 1965.
34. Perry, J. K. Chemical Engineers' Handbook, McGraw-Hill, New York, 1941.
35. Flowmeter Computation Handbook. Amer. Soc. Mech. Eng., Ne\i York, 1961.
36. Fluid Meters, Their Theory and Application. H. S. Bean, Ed., Amer. Soc.
Mech. Eng., New York, 1971.
37. Doebelin, E. 0. Measurement Systems, Application and Design. McGraw-
Hill, New York, 1975.
38. Smith, F. H. The Effects of Nozzle Design and Sampling Techniques on
Aerosol Measurements. EPA-650/2-74-070, U. S. Environmental Protection
Agency, Washington, D. C., 1974, 89 pp.
39. Manual of Fluorometric Clinical Procedures. G. K. Turner Association,
Palo Alto, California, 1971.
40. American Institute of Physics Handbook. D. E. Gray, Ed., McGraw-Hill,
New York, 1957.


Ill
checking the measurement setup, it was discovered that because of the
construction of the probe and the closeness of the first traverse
point to the opening, one of the pitch pressure points was not completely
in the flow stream. Because of this, data from traverse point number 1
are not presented with the rest of the data.
The velocity measurements at the other traverse points for both
flow rates and all five axial distances showed approximately the same
characteristics. The pitch angle increased from the core area to the
duct wall. The yaw angle and the combined angle (p decreased from the
core area to the walls. At the inlet and up to eight diameters down
stream, angles as high as 70 degrees were found near the core area of
the flow field. The total velocity, axial velocity, and the tangential
velocity all showed the same cross sectional flow pattern. The velocities
were minimum at the core, increased with radius and then slightly decreased
near the wall. These patterns are similar to those found in the swirling
flow generated with fixed vanes (23).
In order to observe the changes in the flow as a function of axial
distance from the inlet, the cross sectional averages of the angle cf>,
core area, and tangential velocity were calculated and presented in Table
XXV and plotted in Figures 38 and 39. All three parameters show a very
gradual decay of the indicators of tangential flow as was expected from
the reported tests (23). The curves have the same shape for both flow
rates.
The high core area for the measurements at 16 diameters downstream
was confirmed by repeated measurements. These values may be due to a


41
Therefore, the true flow rate cannot be determined by an S-tvpe pitot
tube in tangential flow because neither the radial velocity, V the
tangential velocity, V the axial velocity, V nor the angle cj> can
l a.
be measured directly.
4, Methods Available for Measuring Velocity Components in a Tangential
Flow Field
Almost all of the reported measurements of velocity components in
a tangential flow field have been based upon introduction of probes into
the flow. Because of the sensitivity of vortex flows to the introduction
of probes, the probe dimensions must be small with respect to the vortex
core in order to accurately measure velocity.
Two common types of pressure probes capable of measuring velocity
accurately are the 5-hole and 3-hole pitot tubes pictured in Figures 17a
and b. The 5-hole or three dimensional directional pressure probe is
used to measure yaw and pitch angles, and total and static pressure.
Five pressure taps are drilled in a hemispherical or conical probe tip,
one on the axis and at the pole of the tip, the other four spaced
equidistant from the first and from each other at an angle of 30 to 50
degrees from the pole. The operation of the probe is based upon the
surface pressure distribution around the probe tip. If the probe is
placed in a flow field at an angle to the total mean velocity vector,
then a pressure differential will be set up across these holes; the
magnitude of which will depend upon the geometry of the probe tip,
relative position of the holes and the magnitude and direction of the
velocity vector. Each probe requires calibration of the pressure


I
r/R
Figure 12. Cross sectional distribution of tangential velocity in a swirling flow field.
K)


46
pitot tube is used to determine the angle of the flow relative to the
axis of the stack by turning the pitot tube until the pressure reading
at the two pressure openings is the same. If the average angle of the
flow across the cross section of the stack is greater then 10 degrees,
then an alternative method of Method 5 should be used to sample the
gas stream. The alternative procedures include installation of
straightening vanes, calculating the total volumetric flow rate
stoichiometrically, or moving to another measurement site at which the
flow is acceptable.
Straightening vanes have shown the capability of reducing swirling
flows; however, there are some problems inherent in their use. One is
the physical limitation of placing them in an existing stack. Another
is the cost in terms of energy due to the loss of velocity pressure
when eliminating the tangential and radial components of velocity.
Since the vortex flows are so sensitive to downstream disturbances,
it is quite possible that straightening vanes might have a drastic
effect on the performance of the upstream cyclonic control device
which is generating the tangential flow. Because of these reasons the
use of straightening vanes is unacceptable in many situations.
Calculating the volumetric flow rate stoichiometrically might
produce accurate flow rates but the values could not be used to
calculate the necessary isokinetic sampling velocities and directions.
Also, studies reported here have shown that the decay of the tangential
component of velocity in circular stacks is rather slow and therefore
it would be unlikely that another measurement site would solve the problem.


I certify that I have read this study and that in ray opinion it
conforms to acceptable standards of scholarly presentation and is fully
adequate, in scope and quality, as a dissertation for the degree of
Doctor of Philosophy.
^U'nalC//U-'y\
Dale A.Lundgren, Chaijrjfsfn
Professor of Environmental
Engineering Sciences
I certify that I have read this study and that in my opinion it
conforms to acceptable standards of scholarly presentation and is fully
adequate, in scope and quality, as a dissertation for the degree of
Doctor of Philosophy.
LU.
t
Paul Urone
Professor of Environmental
Engineering Sciences
I certify that I have read this study and that in my opinion it
conforms to acceptable standards of scholarly presentation and is fully
adequate, in scope and quality, as a dissertation for the degree of
Doctor of Philosophy.
w C 1U-
\
Wayne £. Huber
Professor of Environmental
Engineering Sciences
I certify that I have read this study and that in my opinion it
conforms to acceptable standards of scholarly presentation and is fully
adequate, in scope and quality, as a dissertation for the degree of
Doctor of Philosophy.
/
L
/
<
y
[o.
/I' r . Cm
Alex E. Green
Graduate Research Professor of
Physics and Nuclear Engi
neering Sciences


TABLE XVI
ASPIRATION COEFFICIENT AS A FUNCTION OF STOKES NUMBER FOR 0 = 45, R = 2.0 and 0.5
Velocity Particle Diameter
cm/sec micrometers
Nozzle Diameter
cm
Stokes Number
Velocity
Ratio
Aspiration
Coefficient
701
9.6
0.683
0.406
0.5
67 .4
78.2
65.5
65.0
701
9.6
0.683
0.406
2.0
134.5
131.4
113.8
121 .4
to


I
Figure 8. Sampling bias due to nozzle misalignment and anisokinetic sampling velocity.


52
TABLE IV
SIZES AND DESCRIPTIONS OF EXPERIMENTAL AEROSOLS
Number Mean
Aerosol
Description
Generation
Method
O,
'O
Ethanol
Droplet
Diameter, pm
Diameter
Particles,
0.0024%
Spinning Disc
90
37.4
1.08
0.005%
Spinning Disc
90
37.2
1.37
0.01%
Spinning Disc
90
37.1
1.72
0.03%
Spinning Disc
90
37.8
2.53
0.2%
Spinning Disc
99
24.6
3.10
0.05%
Spinning Disc
90
39.7
3.15
0.55%
Spinning Disc
99
24.4
4.3
0.3%
Spinning Disc
90
34.5
4.98
0.6%
Spinning Disc
90
33.1
6.02
2.0%
Spinning Disc
100
23.6
6.4
1.0%
Spinning Disc
90
35.4
7.66
4.0%
Spinning Disc
100
23.4
8.0
6.7%
Spinning Disc
100
23.2
9.42
6.7%
Spinning Disc
95
27.3
11.1
Ragweed
Pollen
Mechanical
Dispersion
N. A.
N.A.
19.9


60
7. Two simultaneous isokinetic samples were taken, one
parallel to the flow (control), and one at a specified
angle. Sampling times varied from 10 to 20 minutes.
H. Tangential Flow Mapping
The system used to map the flow pattern in a tangential flow' stream
is shown in Figure 23. It consists of a 34000 £pm industrial blower, a
section of 15 cm PVC pipe containing straightening vanes, a small in
dustrial cyclone collector, followed by a 6.1 meter length of 20 cm PVC
pipe. The 150 cm long cyclone, shown in Figure 24 was laid on its side
so that the stack was horizontal and could be conveniently traversed at
several points along its length. A change in flow through this system
could be produced by supplying a restriction at the inlet to the blower.
To measure the velocity in the stack a United Sensor type DA 3-
dimentional directional pitot tube was used. The probe, pictured with
its traversing unit in Figure 25, is .52 cm in diameter and is capable
of measuring yaw and pitch angles of the fluid flow as well as total
and static pressures. From the blow up of the probe tip (Figure 25) it
can be seen that the head consists of 5 pressure ports. Port number 1
is the centrally located total pressure tap. On each side are two
lateral pressure taps 2 and 3. When the probe is rotated by the manual
traverse unit until P9 = P the yaw angle of flow is indicated by the
traverse unit scale. When the yaw angle has been determined an additional
differential pressure is measured by pressure holes located perpendicularly
above and below the total pressure hole 1. Pitch angle is then determined
using a calibration curve for the individual probe. The yaw angle is a


CHAPTER V
SIMULATION OF AN EPA METHOD 5 EMISSION TEST
IN A TANGENTIAL FLOW STREAM
A model has been developed and tested which describes particle
collection efficiency as a function of particle characteristics, angle
of misalignment, and velocity ratio. Together with the measurement of
velocity components in a swirling flow it is possible to analyze the
emission rate errors that would occur when performing a Method 5
analysis of the effluent stream following a cyclone.
For this simulation analysis, the volumetric flow rate and iso
kinetic sampling velocities are calculated from velocity measurements
obtained at the eight diameter sampling location using a S-type pitot
tube (see Tables XXVI and XXVII) The angle , velocity ratio, and
particle velocity are determined from velocity measurements made at
the same location using the five-hole pitot tube (see Table XXII).
The particle characteristics are obtained from particle size distribution
tests made by Mason (22) on basically the same system. From a particle
distribution with a 3.0 pm MMD and geometric standard deviation of 2.13
(see Figure 41) ten pa'rticle diameters were selected which represent
the midpoints of 10% of the mass of the aerosol (see Table XXVIII). The
density of the particles was assumed to be 2.7 g/cm The nozzle diameter
was selected using the standard criteria to be 0.635 cm (1/4 inch). In
the model it was assumed that the nozzle would be aligned parallel with
the axis of the stack, and therefore, 0 = tj).
117


Percent Less Than
99.9
Figure 41. Particle size distributions used in the simulation model.
120


7
130
The two aspects of this study, anisokinetic sampling errors and
flow measurements, were combined in a simulation model to determine the
magnitude of errors when an EPA Method 5 emission test is performed at
the exit of a cyclone.
A summary of the important results determined from this study is
as follows:
A. The flow patterns found in a stack following the exit of a
small industrial cyclone are of such a nature that it makes it extremely
difficult to obtain a representative sample with the present EPA recom
mended equipment. Angles in excess of 70 degrees relative to the stack
axis are found in some parts of the flow. Since large scale turbulence,
such as swirling flow, is inherently self-preserving in round ducts, it
decays very slowly as it moves up the stack and therefore sampling at
any location downstream of the cyclone will involve the same problems.
B. The yaw characteristics of the S-type pitot tube lead to several
types of errors when used in a tangential flow stream. Wien the angle
of yaw is less than 45 degrees, the measured velocity is greater than or
equal to the actual velocity with the maximum error being approximately
5%. Beyond 45 degrees the measured velocity drops off quite rapidly and
at an angle of 70 degrees the measured velocity is less than half the
true velocity. Because of its yaw characteristics, the S-type pitot tube
is not suitable for distinguishing the axial component of flow from the
total flow which includes the tangential component. Volumetric flow
calculations based on S-type pitot tube measurements in a swirling flow
were found to be in excess of the actual flow by as much as 309.


Aspiration Coefficient (Al
i
Stokes Number (K)
Figure 32. Predicted aspiration coefficient vs. Stokes number for 15, 30, 45, 60, 75 and 90 degrees
CO
CO


122
Using these parameters the average aspiration coefficients are
determined at each traverse point using the ten particle diameters and
equations (33) (39).
A., (1*2 ,(f>2 j K9)
A3(r3^3,K3)
1A r + 1A .+ .1A co + ..
Dp5-s Dplb-6 Dp25-6
' + 1ADp95%
(53)
1A _0 + 1A _0 + 1A_ O[ro +
Dp5% Dpl5% Dp25%
" + '1ADp95%
(34)
.
(35)
(36)
(37)
AgiRg^g^g) 1ADp5?6 + -1ADpl5% + 1ADp25;
+ 1A
Dp95%
(38)
(39)
Where A^ = total aspiration coefficient for traverse point i.
= (total velocity at i)/(sampling velocity at i).
cj> = angle of flow at point i relative to the axis of the stack.
K.,= Stokes number based on the nozzle diameter, total velocity
lk
at i, and particle diameter Dp. 0 .
K' Dp, 0= Midpoint particle diameters each representing 10% of the
total mass.
Since the sampling velocity will determine the volume of air sampled at
each traverse point, the total aspiration coefficient for each flow rate
is determined by taking an average weighted according to sampling velocity.
V.A + V.A_
10 0
iz
V.nA^ + V.-A, + V._A_ + V.nA
i5 5
i6 6
i7 7
i8 8
V. + V., + V._ + V., + V._ + V
i2 10 i5 16 i7 18
(40)
Where (Y ) = inlet velocity at traverse point j.
Because of the missing data at point. 1 and negative pressure section at
point 4, these two traverse points were not used in the analysis.


REFERENCES
1. Standards of Performance for New Stationary Sources. Federal Register,
36(247) :24876, 1971.
2. Revision to Reference Method 1-8. Federal Register, 42(160):41754, 1977
3. Wilcox, J. D. Isokinetic Flow and Sampling of Airborne Particulates.
Artificial Stimulation of Rain. Pergamon Press, New York, 1957, p. 177.
4. Lapple, C. E. and C. G. Shepherd. Calculation of Particle Trajectories.
Ind. Eng. Chem., 32(5):605, 1940.
5. Watson, H. H. Errors Due to Anisokinetic Sampling of Aerosols. Amer.
Ind. Hyg. Assoc. Quart., 15(1): 21, 1954.
6. Dennis, R., W. R. Samples, D. M. Anderson and L. Silverman. Isokinetic
Sampling Probes. Ind. Eng. Chem., 49(2) :294, 1957.
7. Hemeon, W. C. L. and G. F. Haines, Jr. The Magnitude of Errors in
Stack Dust Sampling. Air Repair, 4(3):159, 1954.
8. Whiteley, A. B. and L. E. Reed. The Effect of Probe Shape on the
Accuracy of Sampling Flue Gases for Dust Content. J. Inst. Fuel,
32:316, 1959.
9. Lundgren, D. A. and S. Calvert. Aerosol Sampling with a Side Port
Probe. Amer. Ind. Hyg. Assoc. J., 28(3) :208, 1967.
10. Badzioch, S. Collection of Gas-Borne Dust Particles by Means of an
Aspirated Sampling Nozzle. Brit. J. Appl. Phys., 10:26, 1959.
11. Fuchs, N. A. The Mechanics of Aerosols. The Macmillan Co., New York,
1964, p. 73.
12. Belyaev, S. P. and L. M. Levin. Investigation of Aerosol Aspiration
by Photographing Particle Tracks Under Flash Illumination. J. Aerosol
Sci., 3:127, 1972.
13. Belyaev, S. P. and L. M. Levin. Techniques for Collection of Representa
tive Aerosol Samples. J. Aerosol Sci., 5:325, 1974.
135


TABLE OF CONTENTS
Page
ACKNOWLEDGEMENTS
LIST OF TABLES v
LIST OF FIGURES vi'ii
LIST OF SYMBOLS xi
ABSTRACT xiii
CHAPTER
I INTRODUCTION AND ISOKINETIC SAMPLING THEORY 1
A. Introduction 1
B. Isokinetic Sampling Theory 2
II REVIEW OF THE PERTINENT LITERATURE 10
A. Summary of the Literature on Anisokinetic Sampling... 10
1. Sampling Bias Due to Unmatched Velocities 10
2. Sampling Bias Due to Nozzle Misalignment 17
B. Summary of the Literature on Tangential Flow 23
1. Causes and Characteristics of Tangential Flow 23
2. Errors Induced by Tangential Flow 31
3. Errors Due to the S-Type Pitot Tube 35
4. Methods Available for Measuring Velocity
Components in a Tangential Flow Field 41
5. EPA Criteria for Sampling Cyclonic Flow 43
III EXPERIMENTAL APPARATUS AND METHODS 48
A. Experimental Design 48
B. Aerosol Generation 51
1. Spinning Disc Generator 51
2. Ragweed Pollen 53
C. Velocity Determination 53
D. Selection of Sampling Locations 57
E. Sampling Nozzles 57
iii


SYMBOLS
- area of sampler inlet
'- projected area of sampler inlet
Aq area of stream tube approaching nozzle
A ratio of measured concentration to true concentration
C Cunningham correction factor
C. dust concentration in inlet
i
C dust concentration in flow stream
o
C
r concentration ratio of aerosol generating solution
- droplet diameter
D. inlet diameter
i
D particle diameter
P
K inertial impaction parameter
K' adjusted Stokes number
i stopping distance
L undisturbed distance upstream from nozzle
n constant
R ratio of free stream velocity to inlet velocity
s constant
Va axial component of stack velocity
V. velocity in inlet
- radial component of stack velocity
V free stream velocity
xi


104
with the rotation of the probe. Inside the core area it was not possible
to determine the direction of flow because there was no point in the 360
degree rotation of the probe where the pressures at point 2 and 3 were
the same. The location of the core area was measured at each location
along the duct axis and recorded. During the velocity measurements, it
was observed that the flow was very sensitive to downstream disturbances.
A crosswind at the end of the pipe produced large fluctuations in the
pressure measurements.
Figure 37 shows the graphical interpretation of the pitch and yaw
components of velocity. The two radii r^ and r9 represent the distance
from the center of the duct to the outer boundary of the core region.
The area in the core region was approximated by the following equation:
A
core
2
Tr(r1
~~~2
+ r.
(32)
Tables XX-XXIV show the calculated results of the velocity measure
ments at the five axial positions. The low flow was the flow measured
when a restriction was placed at the inlet of the blower. The restriction
induced approximately a 40% decrease in the flow rate. The high flow rate
represented a volumetric flow rate of 15,500 liters per minute, and the
low flow rate was 11,260 liters per minute. The Reynolds number of the
system calculated on a basis of the average axial flow rate were 80,000
and 111,000 for the low and high flow rates respectively.
After the data were broken down, it appeared that data from point
number 1 did not agree well with the rest of the traverse points. Upon


o
Misalignment Angle (6)
Figuie 29. Stokes number at which 95% maximum error occurs
vs. misalignment angle.


TABLE XIX
LOCATION OF SAMPLING POINTS
Point % of Diameter Distance from Wall, cm
1 3.3 0.65
2 10.5 2.07
3 19.4 3.83
4 32.3 6.38
5 67.7 13.36
6 80.6 15.91
7 89.5 17.67
8 96.7 19.09
Duct Diameter = 19.74 cm


43
differentials between holes as a function of yaw and pitch angles.
Figure 18 shows the sensitivity of a typical 5-hole pitot tube to yaw
angle. Because of its sensitivity to yaw angle, it is possible to rotate
the probe until the yaw pressures are equal, measure the angle of probe
rotation (yaw angle) and then determine the pitch angle from the re
maining pressure differentials. The probe can be used without rotation
by using the complete set of calibration curves but the complexity of
measurement and calculation is increased and accuracy is reduced. Vel
ocity components can then be calculated from the measured total pressure,
static pressure and yaw and pitch angle measurements.
The 3-hole pitot tube, also known as the two dimensional or
Fecheimer probe, is similar to the 5-hole design except that it is
unable to measure pitch angle. The probe is characterized by a central
total pressure opening at the tip of the probe with two static pressure
taps placed symmetrically to the side at an angle of from 20 to 50
degrees. From Figure 19 it can be seen that the probe is quite sensitive
to yaw angle and can therefore be used to determine the yaw angle by
rotating the probe until the pressure readings at the static taps are .
equal. Once this is done the total pressure is read from the central
port, and the static pressure can be determined by use of a calibration
chart for the particular probe. Both the 5-hole and the 3-hole pitot
tubes have proven useful in determination of velocity components in
tangential flow fields (25, 28, 30).
5. EPA Criteria for Sampling Cyclonic Flow
The revisions to reference methods 1-8 (2) describe a test for
determination of whether cyclonic flow exists in a stack. The S-type


TABLE XXXI
RESULTS OF THF. CYCLONE OUTLET SIMULATION MODEL
FOR THREE CONDITIONS
Particle Size Flow Concentration, Flow Rate3, Flow Rate'3, Emission Ratea,
Distribution Condition Measured/True Measured/True Measured/True Measured/True
MMD 3 ym
ag = 2.13
Low
0.937
1.27
1.16
1.19
MMD 3 ym
ag = 2.13
High
0.906
1.28
1.17
1 .16
MMD 10 ym
og =2.3
High
0.799
1.28
1.17
1.02
a Negative velocity is not used in the calculation of average velocity,
b Negative velocity is used in the calculation of average velocity.
Emission Rate ,
Measured/True
1.09
1.06
0.93


17
analyzing concentration errors obtained while sampling submicron
particles, 0.8 ym NMD and 1.28 geometric standard deviation, traveling
at near sonic and supersonic velocities. He obtained sample con
centrations 2-3 times greater than the true concentration when the
sampling velocity was 20% of the free stream velocity (R=5).
Sehmel (16) studied the isokinetic sampling of monodisperse
particles in a 2.81 inch ID duct and found that it is possible to obtain
a 20% concentration bias while sampling isokinetically with a small
diameter inlet probe. Results also showed that for all anisokinetic
sampling velocities, the concentration ratios were not simply cor
related with Stokes number.
2, Sampling Bias Due to Nozzle Misalignment
Sampling error associated with the nozzle misalignment has not
been adequately evaluated in past studies because the sampled flow
field was maintained or assumed constant in velocity and parallel to
the duct axis. The studies that have been performed on the effect of
probe misalignment do not provide enough quantitative information to
understand more than just the basic nature of the problem. Results
were produced through investigations by Mayhood and Langstroth, as
reported by Watson (5), on the effect of misalignment on the collection
efficiency of 4, 12 and 37 ym particles (see Figure 7). In a study by
Glauberman (17) on the directional dependence of air samplers, it was
found that a sampler head facing into the directional air stream col
lected the highest concentration. Although these results coincide with


15
0.16 and 5.5
3 (K, R) = 1 1/(1 +bK) (9)
where
b = 2 + 0.617/R (10)
Figure 6 shows a plot of equations (5), (9) and (10) for a range of
velocity ratios and Stokes numbers. The most significant changes in
the aspiration coefficient occur at values of K between 0 and 1.
Beyond K = 1, the aspiration coefficient tends to assymptotically ap
proach its theoretical limit of R. Beyond a Stokes number of about
6, it can be assumed that the aspiration coefficient equals R. This
can be predicted both from equations (5), (9) and (10) and from
theoretical considerations. Badzioch (10) and Belyaev and Levin (12)
have shown that the streamlines start to diverge at approximately 6
diameters upstream of the nozzle. Therefore, a particle traveling at
a velocity, V will have to change directions in an amount of time
equal to 6D^/Vo. If a particle cannot change direction in this amount
of time, it will not be able to make the turn with the streamline.
Since t represents the amount of time required for a particle to change
directions, setting x = 6D^/Vo represents the limiting size particle
that will be able to make a turn with its streamline. Rearranging these
terms it can be seen that this situation occurs when xV /D. = 6 or at a
o 1
Stokes number of 6.
Martone (15) further confirmed the importance considering free
stream velocity as well as particle diameter when sampling aerosols by


13
bearing on the quantity of dust collected. They suggested using the
product of the nozzle area and the stack gas velocity approaching the
nozzle as the gas sample volume, regardless of the velocity of the
nozzle. By using this method for particles greater than 80 pm, it
is possible to obtain small deviations even where departure from
isokinetic velocity is quite large. Whiteley and Reed (8) also observed
that calculating the dust concentrations from the approach velocity
instead of the actual sampling rate produced only slight errors when
sampling anisokinetically for large particles.
Lundgren and Calvert (9) found the sampling bias or aspiration
coefficient A, to be a function of the inertial impaction parameter K
and the velocity ratio R. They developed a chart which can be used
to predict inlet anisokinetic sampling bias depending on both K and R.
Badzioch's (10) equations defined the dependence of the efficiency upon
particle inertia and the velocity ratio. In a slightly different
terminology
A = C./Co = 1 + (R-l) 3(10 (5)
where f3(K) is a function of inertia given by
BOO [1-exp (-L/£)]/(L/£) (6)
£ is the stopping distance or the distance a particle with initial
velocity V will travel into a still fluid before coming to rest and
is defined by (11)
£ = tVo (7)


and geometric standard deviation (a ) of 2.13, the predicted concentration
was 10% less than the true concentration. For an aerosol with a 10.0 pm HMD
and a a of 2.3, a 20% error was predicted. Flow rates determined by the
§
S-type pitot tube were from 20 to 30% greater than the actual flow rate.
Implications of these results are described and recommendations for modifica
tion of the Method 5 sampling train for use in a tangential flow stream are
described.
xv


TABLE XXIV
FIVE-HOLE PITOT TUBE MEASUREMENTS
MADE AT 16 DIAMETERSDOWNSTREAM OF THE CYCLONE
16-D Low Flow
Point
Angles, Degrees
Pitch Yaw (J>
Total
Velocity
cm/sec
Axial
Velocity
cm/sec
Tangential
Velocity
cm/sec
1
* k *
kkk
k k k
k k k
kkk
kkk
2
27.0
34.0
42.4
1073
729
600
3
19.0
41.0
44.5
1169
834
767
4
9.0
58.6
59.0
1014
522
865
5
+ + +
+ + +
+ + +
+ + +
+ + +
+ + +
6
13.0
63.0
63.7
929
412
828
7
17.0
50.4
52.3
1205
735
928
8
18.0
47.6
50.11
1190
763
979
16-D
High Flow
Point
Ang
Pitch
les, Degrees
Yaw (f>
Total
Velocity
cm/sec
Axial
Velocity
cm/sec
Tangential
Velocity
cm/sec
1
k k k
kk k
k k k
k k k
k k k
kkk
2
22.5
36.4
42.0
1553
1154
921
3
21.0
44.0
47.8
1653
1110
1148
4
9.0
66.0
66.3
1513
608
1382
5
+ + +
+ + +
+ + +
+ + +
+ + +
+ + +
6
12.0
61.2
61.9
1675
789
1468
7
20.0
53.4
55.9
1753
983
1407
8
19.0
49.0
51.7
1739
1078
1312
*** Point No. 1 was too close to the wall to allow insertion of all five
pressure taps.
+++ Point lies inside the negative pressure section.


TABLE XV
ASPIRATION COEFFICIENT AS A FUNCTION OF STOKES NUMBER FOR R = 0.5, 0 = 60
Velocity
cm/sec
Particle Diameter
micrometers
Nozzle Diameter
cm
Stokes Number
Aspiration
Coefficient %
732
4,
,59
0.
,683
0.
,099
77
.7
80
.7
88
.8
732
6.
,5
0,
.683
0.
.196
79
.8
72
.2
72,
. 5
701
9.
,6
0,
.683
0.
.406
68
.4
58
. 6
62
.6
1463
7.
.8
0,
.465
0,
.8 25
47
.3
49
.2
47
.8
1585
9.
,6
0,
.465
1.
.35
34
.8
39.5
42.4
Cn


TABLE XII
ASPIRATION COEFFICIENT AS A FUNCTION OF STOKES NUMBER FOR 90 DEGREE MISALIGNMENT
Velocity Particle Diameter Nozzle Diameter Aspiration
cm/sec micrometers cm Stokes Number Coefficient %
549
1.372
0.683
0.0071
95.8
96.2
93.7
98.5
97.3
1798
1.08
0.465
0.002
95.0
93.5
97.4
1798
1.37
0.465
0.034
92.9
94.5
94.0
1798
1.72
0.465
0.053
87.6
1326
2.53
0.683
0.056
88.3
86.7
83.5
83.9
1326
3.23
0.683
0.090
73.7
74.7
75.3
1676
2.87
0.465
0.132
65.0
57.0
58.6
CO
o


Sampling
points
Figure 37. Cross sectional view of a tangential flow' stream locating pitch and yaw directions,
sampling points, and the negative pressure region.
105


134
B. Recommendations
EPA recommends that if the average angle of the flow relative to
the axis of the stack is greater than 10 degrees, then EPA Method 5
should not be performed. Since the maximum error in particle sampling
has been found to be (1 Rcos0), the 10 degree requirement is unduly
restrictive and a 20 degree limitation would be more appropriate. For
a 20 degree angle, the velocity measured by the S-type pitot tube would
be approximately the same as the true velocity (i.e., R = 1). Therefore,
the maximum error would be (1 cos 20) or 6% for a very large aerosol.
When cyclonic flow does not exist in a stack, EPA recommends
either straightening the flow or moving to another location. Because
of the physical limitations of these suggestions, a better approach
would be to modify Method 5 so that it could be used in a tangential
flow stream. By replacing the S-type pitot tube with a three-hole
pitot tube, the direction of the flow could be accurately determined
for aligning the nozzle, and the velocity components could be measured
for a correct calculation of volumetric flow rate. In addition to the
three-hole pitot tube, the modification would have to include a pro
tractor to measure the flow angle, an extra manometer, and a method of
rotating the probe without rotating the entire impinger box.


CHAPTER I
INTRODUCTION AND ISOKINETIC SAMPLING THEORY
A. Introduction
This study deals with the problems of obtaining a representative
sample of particulate matter from a gas stream that does not flow
parallel to the axis of the stack as in the case of swirling or
tangential flow. This type of flow is commonly found in stacks and
could be the source of substantial sampling error. The causes and
characteristics of this particular flow pattern are described and
the errors encountered in particulate concentration and emission
rate determinations are thoroughly analyzed and discussed.
The analysis of sampling errors is approached from two directions
in this study. One approach involves an investigation of aerosol
sampling bias due to anisokinetic sampling velocities and misalignment
of the nozzle with respect to the flow stream as a function of particle
and flow characteristics. The second part of the study involves an
accurate mapping of the flow patterns in a tangential flow system.
The information obtained in the two parts of the study will be combined
to simulate the errors that would be encountered when making an EPA
Method 5 (1, 2) analysis in a tangential flow stream.
1


59
therefore, each filter was dyed with ink and a grid was drawn to aid
in the counting. Before being placed in the filter holders, the filters
were examined under the microscope to determine if any background count
existed. After each test the filters were removed and the entire area
of the filter was counted.
The pollen caught in the nozzle and filter holder was analyzed
using isopropyl alcohol and 0.45 ym pore size Millipore membrane filters
with black grids. The isopropyl was first filtered several times to
remove background particulate matter. Once the background was low enough,
the alcohol was poured into the front half of the filter holder and
through the nozzles. The solution was then sucked through the membrane
filters. The filters were allowed to dry and then the entire filter
area was counted under the microscope.
G. Sampling Procedure
1. A desired flow rate was obtained by selecting an orifice
plate and using the by-pass as a fine adjust.
2. The velocity was measured using a standard pitot tube.
3. A solute-solvent solution was selected for a given particle
size.
4. Particles were collected on a membrane filter and sized
using a light microscope.
5. A nozzle diameter which would allow for an isokinetic
sampling rate closest to 1 cfm was selected.
6. Isokinetic sampling rates were calculated and sampling
flow rates were adjusted accordingly.


8
inertia affects the ability of the particle to negotiate turns with
its streamline which determines the amount of error. Therefore, in
all cases greater sampling errors will occur for larger particles and
higher velocities.
Besides determining the direction of the sampling bias, it is
also possible to predict theoretically the minimum and maximum error
for a given condition. This can be done by considering what happens
when the inertia of the particles is very small (i.e., the particles
can negotiate any turn that the streamlines make) and what happens
when the inertia of particles is very large (i.e., the particles are
unable to negotiate any turn with the streamlines). In the former
case of very low inertia, it can easily be seen that since the particles
are very mobile they do not leave their streamlines and therefore there
will be no sampling bias. In this situation the concentration of
particulate matter may be accurately obtained regardless of sampling
velocity or whether the nozzle is aligned with the flow stream. There
fore, a minimum error of 0 is obtained for small inertia particles.
The maximum error that can theoretically occur in anisokinetic
sampling depends on both the velocity ratio R, where
R = V /V. (1)
0 1
and the misalignment angle 0.
In the case of unequal velocities for very high inertia particles
which are unable to negotiate any change of direction, only those
particles directly in front of the projected area of the nozzle, A^,
will enter the nozzle regardless of the sampling velocity. Therefore,


LIST OF FIGURES
Figure Page
1 Isokinetic sampling 3
2 Superisokinetic sampling 4
3 Subisokinetic sampling 6
4 The effect of nozzle misalignment with flow stream 7
5 Relationship between the concentration ratio and the
velocity ratio for several size particles.... 11
6 Sampling efficiency as a function of Stokes number and
velocity ratio 16
7 Error due to misalignment of probe to flow stream 18
8 Sampling bias due to nozzle misalignment and anisokinetic
sampling velocity 21
9 Tangential flow induced by ducting 25
10 Double vortex flow induced by ducting 26
11 Velocity components in a swirling flow field 27
12 Cross sectional distribution of tangential velocity in a
swirling flow field 29
13 Cross sectional distribution of angular momentum in a
swirling flow field 30
14 S-type pitot tube with pitch and yaw angles defined 38
15 Velocity error vs. yaw angle for an S-type pitot tube.... 39
16 Velocity error vs. pitch angle for an S-type pitot tube.. 40
viii


CHAPTER II
REVIEW OF THE PERTINENT LITERATURE
A. Summary of the Literature on Anisokinetic Sampling
1. Sampling Bias Due to Unmatched Velocities
Numerous articles have been written describing the sources and
magnitude of errors when isokinetic conditions are not maintained.
In one of the earlier works, Lapple and Shepherd (4) studied the
trajectories of particles in a flow stream and presented a formula
for estimating the order of the magnitude of errors resulting when
there is a difference between the average sampling velocity and the
local free stream velocity. Watson (5) examined errors in the aniso
kinetic sampling of spherical particles of 4 and 32 pm mass mean
diameter (MMD) and found the relationships shown in Figure 5. Super-
isokinetic sampling (sampling with nozzle velocity greater than the
free stream velocity) leads to a concentration less than the actual
concentration, while subisokinetic sampling has the opposite effect.
Watson found that the magnitude of the error was not only a function
of particle size as seen in Figure 5, but also of the velocity and the
nozzle diameter. He proposed that the sampling efficiency was a function
of the dimensionless particle inertial parameter K (Stokes number)
defined as
? tV
K = Cp V D VlSnD. = 2- m
pop i 'J
10


MANOMETER
FILTER
ooo
GAS
METER
J
Figure 21
BY PASS
Sampling system.
cn
O


2
B. Isokinetic Sampling Theory
To obtain a representative sample of particulate matter from a
moving fluid, it is necessary to sample isokinetically. Isokinetic
sampling can be defined by two conditions: [3) 1) The suction or
nozzle velocity, must be equal to the free stream velocity, Vq;
and 2) the nozzle must be aligned parallel to the flow direction.
If these conditions are satisfied the frontal area of the nozzle, A.,
i
will be equal to the area of the cross section of the flow stream
entering the nozzle, Aq (see Figure 1). Thus, there will be no
divergence of streamlines either away from or into the nozzle, and
the particle concentration in the inlet, C., will be equal to the
particle concentration in the flow stream, C .
o
When divergence of streamlines is produced by superisokinetic
sampling, subisokinetic sampling or nozzle misalignment, there is a
possibility of particle size fractionation due to the inertial
properties of particles. In the case of superisokinetic sampling
(see Figure 2), the sampling velocity, V., is greater than the free
stream velocity, V Therefore, the area of the flow stream that is
o
sampled, A will be greater than the. frontal area of the sampling
nozzle, A^. All of the particles that lie in the projected area A^'
will enter into the nozzle. Particles outside this area but within A
o
will have to turn with the streamlines in order to be collected. Be
cause of their inertia, some of the larger particles will be unable to
make the turn and will not enter the sampling nozzle. Since not all of
the particles in the sampled area Aq will be collected, the measured
concentration will be less than the actual concentration.


Aspiration Coefficient (A)
1.00
0.80
0.60
0.4 0
0.20
0.00
0.01
O
O
o
o
o
|j>4-Typ
ical 95% C.I
G
O
o
J I I I L
G
I I 1 1 -L l l ti QL
0. L
1.0
l I I I l I
10.0
Stokes Number (K)
Figure 28. Sampling efficiency vs. Stokes number at 90 misalignment for R = 1.


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PAGE 1

ISOKINETIC SAMPLING OF AEROSOLS FROM TANGENTIAL FLOW STREAMS By Michael Dean Durham A DISSERTATION PRESENTED TO THE GRADUATE COUNCIL OF THE UNIVERSITY OF FLORIDA IN PARTIAL FULFILLMENT OF THE 'REQUIRE^ENTS FOR THE DEGREE OF DOCTOR OF PHILOSOPHY UNIVERSITY OF FLORIDA 1978

PAGE 2

ACKNOWLEDGEMENTS This research was partially supported by a grant (Grant Number R802692-01) from the Environmental Protection Agency (EPA)-, and was monitored by EPA's Project Officer Kenneth T. Knapp. I thank them both for their financial support during my graduate work. I wish to thank Dr. Dale Lundgren and Dr. Paul Urone for the important part that they played in my education. I am especially appreciative of Dr. Lundgren for his guidance, encouragement and confidence. He has provided me witli opportunities for classroom, laboratory and field experience that were far beyond what is expected of a committee chairman. 1 would like to thank Mrs. Kathy Sheridan for her assistance in preparing this manuscript. Finally, I wish to thank my parents for their advice and encouragement, and my wife Ellie for helping me through the difficult times. 11

PAGE 3

TABLE OF CONTENTS Page ACKNOWLEDGEMENTS ii LIST OF TABLES v LIST OF FIGURES viii LIST OF SYMBOLS xi ABSTRACT xiii CHAPTER I INTRODUCTION AND ISOKINETIC SAMPLING THEORY 1 A. Introduction 1 B. Isokinetic Sampling Theory 2 II REVIEW OF THE PERTINENT LITERATURE 10 A. Summary of the Literature on Anisokinetic Sampling. 10 1. Sampling Bias Due to Unmatched Velocities 10 2. Sampling Bias Due to Nozzle Misalignment 17 B. Summary of the Literature on Tangential Flow 23 1. Causes and Characteristics of Tangential Flow 23 2 Errors Induced by Tangential Flow 31 3. Errors Due to the S-Type Pitot Tube 35 4. Methods Available for Measuring Velocity Components in a Tangential Flow Field 41 5. EPA Criteria for Sampling Cyclonic Flow 43 in EXPERIMENTAL APPARATUS AND METHODS 48 A. Experimental Design 48 B. Aerosol Generation 51 1 Spinning Disc Generator 51 2. Ragweed Pollen 53 C. Velocity Determination 53 D. Selection of Sampling Locations 57 E. Sampling Nozzles 57 111

PAGE 4

TABLE OF CONTENTS --continued CHAPTER Page F. Analysis Procedure 58 1 For Uranine Particles 58 2. For Ragweed Pollen 58 G. Sampling Procedure 59 H. Tangential Flow Mapping 60 IV RESULTS AND ANALYSIS 65 A. Aerosol Sampling Experiments 65 1 Stokes Number 65 2. Sampling with Parallel Nozzles 66 3. Analysis of Probe Wash 66 4. The Effect of Angle Misalignment on Sampling Efficiencies 69 5. The Effect of Nozzle Misalignment and Anisokinetic Sampling Velocity 89 B. Tangential Flow Mapping 102 V SIMULATION OF AN EPA METHOD 5 EMISSION TEST IN A TANGENTIAL FLOW STREAjM 117 VI SUMMARY AND RECOMMENDATIONS 129 A. Summary 129 B. Recommendations 134 REFERENCES 135 BIOGRAPHICAL SKETCH 139 IV

PAGE 5

LIST OF Ty\BLES Table Page I FLOW RATE DETERMINED AT VARIOUS MEASUREMENT LOCATIONS 33 II CONCENTRATION AT A POINT FOR DIFFERENT SAMPLING ANGLES 34 III EMISSION TEST RESULTS 36 IV SIZES AND DESCRIPTIONS OF EXPERIMENTAL AEROSOLS 52 V TABLE OF OBTAINABLE VELOCITIES IN 10 cm DUCT. 54 VI TYPICAL VELOCITY TRAVERSE IN THE EXPERIMENTAL SAJ-IPLING SYSTEM 55 VII RESULTS OF SAMPLING WITH TWO PARALLEL NOZZLES 67 VIII PERCENT OF PARTICULATE MATTER COLLECTED IN THE PROBE WASH FOR NOZZLES PARALLEL WITH THE FLOW STREAM 68 IX PERCENT OF PARTICULATE MATTER COLLECTED IN THE PROBE WASH FOR NOZZLES AT AN ANGLE OF 60 DEGREES WITH THE FLOW STREAiM. 70 X ASPIRATION COEFFICIENT AS A FUNCTION OF STOKES NUMBER FOR 30 DEGREE MISALIGNMENT 75 XI ASPIRATION COEFFICIENT AS A FUNCTION OF STOKES NUMBER FOR 60 DEGREE MISALIGNMENT 77 XII ASPIRATION COEFFICIENT AS A FUNCTION OF STOKES NUMBER FOR 90 DEGREE MISALIGNMENT 80 XIII COMPARISON OF SAMPLING EFFICIENCY RESULTS WITH THOSE OF BELYAEV AND LEVIN FOR 6 = R = 2 3 AND R = 0.5 92 XIV ASPIRATION COEFFICIENT AS A FUNCTION OF STOKES NUMBER FOR R = 2, = 60 94

PAGE 6

LIST OF TABLES-continued Table Pape XV ASPIRATION COEFFICIENT AS A FUNCTION OF STOKES NUMBER FOR R = 0.5, 6 = 60 95 XVI ASPIR./\TION COEFFICIENT AS A FUNCTION OF STOKES NUMBER FOR e = 45, R = 2.0 AND 0.5 97 XVII ASPIRATION COEFFICIENT AS A FUNCTION OF STOKES NUMBER FOR R = 2, 6 = 30 98 XVIII ASPIRATION COEFFICIENT AS A FUNCTION OF STOKES NUMBER FOR R = 2.1, e = 90 101 XIX LOCATION OF SAMPLING POINTS 105 XX FIVE-HOLE PITOT TUBE MEASUREMENTS MADE AT 1 DIAMETER DOWNSTREAM OF THE CYCLONE 106 XXI FIVE-HOLE PITOT TUBE MEASUREMENTS MADE AT 2 DIAMETERS DOWNSTREAM OF THE CYCLONE 107 XXII FIVE-HOLE PITOT TUBE MEASURENffiNTS MADE AT 4 DIAMETERS DOWNSTREAM OF THE CYCLONE 108 XXIII FIVE-HOLE PITOT TUBE MEASUREMENTS MADE AT 8 DIAMETERS DOWNSTREAI'l OF THE CYCLONE 109 XXIV FIVE -HOLE PITOT TUBE MEASUREMENTS MADE AT 16 DIAMETERS DOIVNSTREAM OF THE CYCLONE 110 XXV AVERAGE CROSS SECTIONAL VALUES AS A FUNCTION OF DISTANCE DOWNSTREAM AND FLOW RATE 112 XXVI S-TYPE PITOT TUBE MEASUREMENTS MADE AT THE 8-D SAiMPLING PORT FOR THE LOW FLOW CONDITION 118 XXVII S-TYPE PITOT TUBE MEASUREMENTS MADE AT THE 8-D S.-UIPLING PORT FOR THE HIGH FLOW CONDITION 119 XXVIII MIDPOINT PARTICLE DIAMETERS FOR THE 10 PERCENT INTERVALS OF THE MASS DISTRIBUTION MMD = 3ym a = 2.13 121 VI .-S'^l•^=^^S^ ...MS^L ^

PAGE 7

LIST OF TABLES--continued Table Page XXIX ASPIRATION COEFFICIENTS CALCULATED IN THE SIMULATION MODEL FOR THE LOW FLOW CONDITION 124 XXX ASPIRATION COEFFICIENTS CALCULATED IN THE SIMULATION MODEL FOR THE HIGH FLOW CONDITION 125 XXXI RESULTS OF THE CYCLONE OUTLET SIMULATION MODEL FOR THREE CONDITIONS 127 XXXII SUMMARY OF EQUATIONS PREDICTING PARTICLE SA^1PLING BIAS 128 VI 1

PAGE 8

LIST OF FIGURES Figure Page 1 Isokinetic sampling 3 2 Superisokinetic sampling 4 3 Subisokinetic sampling 6 4 The effect of nozzle misalignment with flow stream 7 5 Relationship between the concentration ratio and the velocity ratio for several size particles 11 6 Sampling efficiency as a function of Stokes number and velocity ratio 16 7 Error due to misalignment of probe to flow stream IS 8 Sampling bias due to nozzle misalignment and anisokinetic sampling velocity 21 9 Tangential flow induced by ducting 25 10 Double vortex flow induced by ducting 26 11 Velocity components in a swirling flow field 27 12 Cross sectional distribution of tangential velocity in a swirling flow field 29 13 Cross sectional distribution of angular momentum in a swirling flow field 30 14 S-type pitot tube with pitch and yaw angles defined 38 15 Velocity error vs. yaw angle for an S-type pitot tube.... 39 16 Velocity error vs. pitch angle for an S-type pitot tube.. 40 Vlll

PAGE 9

LIST OF FIGURES--continued Figure Page 17a Conical version of a five-hole pitot tube 42 17b Fecheimer type three-hole pitot tube 42 18 Five-hole pitot tube sensitivity to yaw angle 44 19 Fecheimer pitot tube sensitivity to yaw angle 45 20 Experimental set up 49 21 Sampling system 50 22 Typical velocity profile in experimental test section.... 56 23 Experimental system for measuring cross sectional flow patterns in a swirling flow stream 61 24 Cyclone used in the study to generate swirling flow 62 25 Photograph of the 3-dimensional pitot with its traversing unit. Insert shows the location of the pressure taps.... 63 26 Sampling efficiency vs. Stokes number at 30 misalignment for R = 1 72 27 Sampling efficiency vs. Stokes number at 60 misalignment for R = 1 73 28 Sampling efficiency vs. Stokes number at 90 misalignment for R = 1 74 29 Stokes number at which 95% maximum error occurs vs. misalignment angle 83 30 6' vs. adjusted Stokes number for 30, 60 and 90 degrees.. 85 31 Aspiration coefficient vs. Stokes number model prediction and experimental data for 30, 60 and 90 degrees 87 32 Predicted aspiration coefficient vs. Stokes number for 15, 30, 45, 60, 75 and 90 degrees 88 IX

PAGE 10

LIST OF FIGURES--continued Figure Page 33 Comparison of experimental data with results from Belyaev and Levin 91 34 Sampling efficiency vs. Stokes number at 60 misalignment for R = 2.0 and 0.5 96 35 Sampling efficiency vs, Stokes number at 45 misalignment for I^ = 2.0 and R = 0.5 99 36 Sampling efficiency vs. Stokes number at 30 misalignment for U = 2.0 100 37 Cross sectional view of a tangential flow stream locating pitch and yaw directions, sampling points, and the negative pressure region 105 38 Decay of the average angle 9 and the core area along the axis of the duct 113 39 Decay of the tangential velocity component along the axis of the duct 114 40 Location of the negative pressure region as a function of distance downstream from the cyclone 116 41 Particle size distributions used in the simulation model... 120 ^! W^ ^t^rTJ^U^^*"*— T'^-t-*.'** i."* '^ i *'"'*-i**I-Vt'*'*

PAGE 11

SYMBOLS A. area of sampler inlet A 'projected area of sampler inlet A^ area of stream tube approaching nozzle A ratio of measured concentration to true concentration C Cunningham correction factor C. dust concentration in inlet Cq dust concentration in flow stream C r concentration ratio of aerosol generating solution D, droplet diameter D. inlet diameter 'S 1 D particle diameter K inertial impaction parameter K' adjusted Stokes number i stopping distance L undisturbed distance upstream from nozzle n constant R ratio of free stream velocity to inlet velocity s constant V axial component of stack velocity V velocity in inlet ^r ~ radial component of stack velocity V^ free stream velocity XI

PAGE 12

V^ tangential component of stack velocity &, 3', 6" functions determining whether particles will deviate from streamlines P particle density n viscosity ^ angle of the flow stream with respect to the stack axis e angle of misalignment of nozzle with respect to the flow stream T particle relaxation time Ap pressure difference Xll

PAGE 13

Abstract of Dissertation Presented to the Graduate Council of the University of Florida in Partial Fulfillment of the Requirements for the Degree of Doctor of Philosophy ISOKINETIC SAMPLING OF AEROSOLS FROM TANGENTIAL FLOW STREAMS By Michael D. Durham August, 1978 Chairman: Dale A. Lundgren Major Department: Environmental Engineering Sciences A comprehensive analysis of inertial effects in aerosol sampling was combined with a thorough study of swirling flow patterns in a stack following the exit of a cyclone in order to determine the errors involved in sampling particulate matter from a tangential flow stream. Two simultaneous samples, one isokinetic and the other anisokinetic were taken from a 10 cm wind tunnel and compared to determine sam.pl ing bias as a function of Stokes number. Monodispersed uranine particles, 1 to 11 pm in diameter, generated with a spinning disc aerosol generator, and mechanically dispersed 19.9 pm ragween pollen were used as experimental aerosols. The duct velocity was varied from 550 to 3600 cm/sec and two nozzle diameters of 0.465 and 0.6S3 cm were used to obtain values of Stokes numbers from 0.007 to 2.97. Experiments were performed at four angles, 0, 30, 60 and 90 degrees, to determine the errors encountered when sampling with an isokinetic sampling velocity but with the nozzle misaligned with the flow stream. The sampling bias approached a theoretical limit of (l-cosG) at a value of Stokes number between Xlll •(4=*— M *=-<^ti-:-a Wi

PAGE 14

1 and 6 depending on the angle of misalignment. It was discovered that the misalignment angle reduces the projected nozzle diameter and therefore effects the Stokes number; a correction factor as a function of angle was developed to adjust the Stokes number to account for this. Using an equation empirically developed from these test results and using the equations of Belyaev and Levin describing anisokinetic sampling bias with zero misalignment, a mathematical model was developed and tested which predicts the sampling error when both nozzle misalignment and anisokinetic sampling velocities occur simultaneously. It was found that the sampling bias approached a maximum error |l-Rcos0| where R is the ratio of the free stream velocity to the sampling velocity. During the testing, it was discovered that as much as 60% of the particulate matter entering the nozzle remained in the nozzle and front half of the filter holder. Implications of this phenomenon with regard to particle sampling and analysis are discussed The causes and characteristics of tangential flow streams are described as they relate to problems in aerosol sampling. The limitations of the S-type pitot tube when used in a swirling flow are discussed. A three dimensional or five-hole pitot tube was used to map cross sectional and axial flow patterns in a stack following the outlet of a cyclone. Angles as great as 70 degrees relative to the axis of the stack and a reverse flow core area were found in the stack. Using information found in this study, a simulation model was developed to determine the errors involved when making a Method 5 analysis in a tangential flow stream. For an aerosol with a 3.0 ym MMD (mass mean diameter) XIV

PAGE 15

and geometric standard deviation (o ) of 2.13, the predicted concentration was 10-5 less than the true concentration. For an aerosol with a 10.0 ym ^C^1D and a a of 2.3, a 20% error was predicted. Flow rates determined by the S-type pitot tube were from 20 to 30-5 greater than the actual flow rate. Implications of these results are described and recommendations for modification of the Method 5 sampling train for use in a tangential flow stream are described. XV • •is^m^'-'itix^i^

PAGE 16

CHAPTER I INTRODUCTION AND ISOKINETIC SAMPLING THEORY A. Introduction This study deals with the problems of obtaining a representative sample of particulate matter from a gas stream that does not flow parallel to the axis of the stack as in the case of swirling or tangential flow. This type of flow is commonly found in stacks and could be the source of substantial sampling error. The causes and characteristics of this particular flow pattern are described and the errors encountered in particulate concentration and emission rate determinations are thoroughly analyzed and discussed. The analysis of sampling errors is approached from two directions in this study. One approach involves an investigation of aerosol sampling bias due to anisokinetic sampling velocities and misalignment of the nozzle with respect to the flow stream as a function of particle and flow characteristics. The second part of the study involves an accurate mapping of the flow patterns in a tangential flow system. The information obtained in the two parts of the study will be combined to simulate the errors that would be encountered when making an EPA Method 5 (1, 2) analysis in a tangential flow stream. fc-,i^.MfinH'jt-^'r

PAGE 17

B. isokinetic S ampling Theory To obtain a representative sample of particulate matter from a moving fluid, it is necessary to sample isokinetically Isokinetic sampling can be defined by two conditions: [3} 1) The suction or nozzle velocity, V., must be equal to the free stream velocity, V ; 1 o and 2) the nozzle must be aligned parallel to the flow direction. If these conditions are satisfied the frontal area of the nozzle, A 1 will be equal to the area of the cross section of the flow stream entering the nozzle, A^ (see Figure 1). Thus, there will be no divergence of streamlines either away from or into the nozzle, and the particle concentration in the inlet, C, will be equal to the particle concentration in the flow stream, C o When divergence of streamlines is produced by superisokinetic sampling, subisokinetic sampling or nozzle misalignment, there is a possibility of particle size fractionation due to the inertial properties of particles. In the case of superisokinetic sampling [see Figure 2), the sampling velocity, V., is greater than the free stream velocity, V^ Therefore, the area of the flow stream that is sampled, A^ will be greater than the, frontal area of the sampling nozzle, A All of the particles that lie in the projected area A.' will enter into the nozzle. Particles outside this area but within A o will have to turn with the streamlines in order to be collected. Because of their inertia, some of the larger particles will be unable to make the turn and will not enter the sampling nozzle. Since not all of the particles in the sampled area A will be collected, the measured concentration will be less than the actual concentration.

PAGE 18

u u II •r > > -H > H Cu B rd M u -H -U OJ c o H 0) tn •H Em

PAGE 19

t > o u vl •H u V > > •H 1/; o H 3 W IN 3 •H. -~^S>*^0 -i-, Jfc-r 1 J— >, |fc*->fcd| |( *-p^l^J

PAGE 20

Subisokinetic sampling defines the condition in which the sampling velocity is less than the free stream velocity (see Figure 5) In this situation the frontal area of the nozzle. A.', is greater than the sampled area of the flow, A^ The volume of air lying within the projected area, A^ but outside A will not be sampled and the streamlines will diverge around the nozzle. However, some of the particles in this area, because of their inertia, will be unable to negotiate the turn with the streamlines and will be collected in the nozzle. Because some of the particles outside the sampled area A will be collected along with all o '^ of the particles within A the measured concentration will be greater than the actual particle concentration. The bias due to misalignment of the nozzle with the flow stream is similar to that caused by superisokinetic sampling. When the nozzle is at an angle to the flow stream (Figure 4), the projected area of the nozzle is reduced by a factor equal to the cosine of the angle. Even if the nozzle velocity is equal to the flow stream velocity, a reduced concentration will be obtained because some of the larger particles will be unable to make the turn into the nozzle with the streamlines. Therefore, whenever the nozzle is misaligned, the concentration collected will always be less than or equal to the actual concentration. For all three conditions of anisokinetic sampling (superisokinetic, subisokinetic and nozzle misalignment] the magnitude of the measured concentration error will depend upon the size of the particles. More specifically it will depend upon particle inertia, which implies that the velocity and density of the particle are also important. Particle ^^i'k4-nnicnTJkl'*.~M>t'WlatirCiaF^f:UlII' t

PAGE 21

u u o > V > c •H rH i u r-( M P! •H O H to

PAGE 22

5-1 y o -H :5 -U c d) g c t7> •H rH N N O a 4-1 p u E^ CD U &> •H a,

PAGE 23

inertia affects the ability of the particle to negotiate turns with its streamline which determines the amount of error. Therefore, in all cases greater sampling errors will occur for larger particles and higher velocities. Besides determining the direction of the sampling bias, it is also possible to predict theoretically the minimum and maximum error for a given condition. This can be done by considering what happens when the inertia of the particles is very small (i.e., the particles can negotiate any turn that the streamlines make] and what happens when the inertia of particles is very large (i.e., the particles are unable to negotiate any turn with the streamlines) In the former case of very low inertia, it can easily be seen that since the particles are very mobile they do not leave their streamlines and therefore there will be no sampling bias. In this situation the concentration of particulate matter may be accurately obtained regardless of sampling velocity or whether the nozzle is aligned with the flow stream. Therefore, a minimum error of is obtained for small inertia particles. The maximum error that can theoretically occur in anisokinetic sampling depends on both the velocity ratio R, where f^ = \/\ CD and the misalignment angle 9. In the case of unequal velocities for very high inertia particles which are unable to negotiate any change of direction, only those particles directly in front of the projected area of the nozzle, A i' will enter the nozzle regardless of the sampling velocity. Therefore,

PAGE 24

the concentration collected by the nozzle will be equal to the number of particles entering the nozzle, A.V C divided bv the volume of 1 o o air sampled, A.V. 1 1 A.V C C V r10 o o ^i = -icvr = T(2) 11 1 The ratio of the sampled concentration to the true concentration then is equal to the inverse of the velocity ratio. Therefore, the maximum sampling bias for the condition of unmatched velocities is equal to V^/V^ or R. For example, if the sampling velocity is twice the free stream velocity, the resulting concentration will be one half the actual concentration. For the case of a misaligned nozzle, a similar analysis is applied. For the particles with very large inertia, only those lying directly in line with the projected frontal area of the nozzle will be collected. The measured concentration would again be the number of particles collected in the nozzle, A^cosBC^V^, divided by the volume of air sampled, A^V^. Therefore, the ratio of the measured to the true concentration would be V^cose/V^ or RcosB. This represents the maximum sampling error for anisokinetic sampling.

PAGE 25

CHAPTER II REVIEW OF THE PERTINENT LITERATURE A^__Summa£)^^f^^ on Anisokinet ic Sampling j^. Sampling Bia s Due to Unmatched Velocities Numerous articles have been written describing the sources and magnitude of errors when isokinetic conditions are not maintained. In one of the earlier works, Lapple and Shepherd (4) studied the trajectories of particles in a flow stream and presented a formula for estimating the order of the magnitude of errors resulting when there is a difference between the average sampling velocity and the local free stream velocity. Watson (5) examined errors in the anisokinetic sampling of spherical particles of 4 and 32 ym mass mean diameter (MMD) and found the relationships shown in Figure 5. Superisokinetic sampling (sampling with nozzle velocity greater than the free stream velocity) leads to a concentration less than the actual concentration, while subisokinetic sampling has the opposite effect. Watson found that the magnitude of the error was not only a function of particle size as seen in Figure 5, but also of the velocity and the nozzle diameter. He proposed that the sampling efficiency was a function of the dimensionless particle inertial parameter K (Stokes number) defined as tV K = Cp V D -^/ISpD. = — ^ ,,, P o p 1 D. C3) 10

PAGE 26

11 H o H >^ t^ H U o > s C) u H \ H •H j' u R 23 W o n H 2: R O u Cm c o w (D -P 4-1 S: -0 B C O m !-l 4-1 O '— r-( -P m rJ (U H -P 4J W rO fd ^^ CL -P C 0) QJ N o 0) x: -p m 5^ O c 0) -p y-i 0) X3 o -H •H rd x; J-j W C >, O -P H -H -P U rd O -H H CD dJ P^ > tn •H P4

PAGE 27

12 where D = particle diameter C Cunningham correction for slippage p = particle density T = p CD -/18n P P ^ C4} P = viscosity of gas D^ = nozzle diameter The relaxation time is defined as r; it represents how quickly a particle can change directions. Watson concluded that to obtain a concentration correct within 10%. the velocity ratio R must lie between 0.86 and 1.13 for the 32 micron particles and between 0.5 and 2.0 for the 4 micron particles. Data obtained by Dennis et al (6] on a suspension of Cottrell precipitated fly ash. 14 |^i MMD, showed only a 10% negative error in calculated concentration for sampling velocities 60% greater than isc kinetic. Tests run on an atmospheric dust of 0.5 ym MMD produced no detectable concentration changes even while sampling at a 400% variatic from isokinetic flow, thus indicating that isokinetic sampling is relatively unimportant for fine particles. Hemeon and Haines (7) measured errors due to the anisokinetic sampling of particles in three size ranges (5-25, 80-100, and 400-500 ym) and in a range of nozzle to stack velocities of 0.2 to 2.0. They found that where the velocity ratio R ranges from 0.6 to 2.0 the extreme potential error was approximately 50%, and that deficient nozzle velocities resulted m greater errors than excessive nozzle velocities. In addition, they found that for the coarse particles, the velocity into the nozzle had no important 30Lon

PAGE 28

bearing on the quantity of dust collected. They suggested using the product of the nozzle area and the stack gas velocity approaching the nozzle as the gas sample volume, regardless of the velocity of the nozzle. By using this method for particles greater than 80 ym, it is possible to obtain small deviations even where departure from isokinetic velocity is quite large. HTHteleyand Reed (8) also observed that calculating the dust concentrations from the approach velocity instead of the actual sampling rate produced only slight errors when sampling anisokinetically for large particles. Lundgren and Calvert (9) found the sampling bias or aspiration coefficient A, to be a function of the inertial impaction parameter K and the velocity ratio R. They developed a chart which can be used to predict inlet anisokinetic sampling bias depending on both K and R. Badzioch's CIO) equations defined the dependence of the efficiency upon particle inertia and the velocity ratio. In a slightly different terminology C5) (6} A = C./C^ = 1 (R-i) g^K) where g(K) is a function of inertia given by 3CK) = [1-exp C-L/£)]/(L/£) Z is the stopping distance or the distance a particle with initial velocity V^ will travel into a still fluid before coming to rest and is defined by [11] £ = TV .7. o (7)

PAGE 29

14 L is the distance upstream from the nozzle where the flow is undisturbed by the do^stream nozzle. It is a function of the nozzle diameter and is given by the equation: L = nD. ^g^ It was observed that n lies between 5.2 and 6.8 (10). Flash illumination photographic techniques were used by Belyaev and Levin (12) to study particle aspiration. Photographic observations enabled them to verify Badzioch's claim that L, the undisturbed distance upstream of the nozzle, was between 5 to 6 times the diameter of the nozzle. They examined the data of previous studies on error due to anisokinetic sampling and concluded that the discrepancy between experimental data was due to the researchers failing to take into account three things: 1) particle deposition in the inlet channel of the sampling device; 2) rebound of particles from the front edge of the sampling nozzle and their subsequent aspiration into the nozzle.; and 3) the shape and wall thickness of the nozzle. They also found that the sampling efficiency was a function of the inner diameter of the nozzle, D., as well as K and R. In a more recent article, Belyaev and Levin (13) examined the dependence of the function 6CK), in equation (4), on both the inertial impaction parameter. K, and the velocity ratio, R. Previous authors (10, 14) had concluded that 6(K) was a function of K alone, but Belyaev and Levin obtained experimental data demonstrating that for thin-walled nozzles, B(K) was also a function of R. Equations were developed from the data for values of K between O.IS and 6.0 and for values of R betv tween

PAGE 30

15 0.16 and 5.5 3(K,R) = 1 1/(1 +bK3 (9) where b = 2 + 0.617/R (10) Figure 6 shows a plot of equations (5) (9) and (10] for a range of velocity ratios and Stokes numbers. The most significant changes in the aspiration coefficient occur at values of K between and 1. Beyond K = 1, the aspiration coefficient tends to assymptotically approach its theoretical limit of R. Beyond a Stokes number of about 6, it can be assumed that the aspiration coefficient equals R. This can be predicted both from equations (5) (9) and (10) and from theoretical considerations. Badzioch (10) and Belyaev and Levin (12) have shown that the streamlines start to diverge at approximately 6 diameters upstream of the nozzle. Therefore, a particle traveling at a velocity, V will have to change directions in an amount of time equal to 6D-/V If a particle cannot change direction in this amount of time, it will not be able to make the turn with the streamline. Since T represents the amount of time required for a particle to change directions, setting t = 6D./V represents the limiting size particle 10^ c 1 that will be able to make a turn with its streamline. Rearranging these o o terms it can be seen that this situation occurs when tV /D. = 6 or at a o 1 Stokes number of 6. Martone (15) further confirmed the importance considering free stream velocity as well as particle diameter when sampling aerosols by

PAGE 31

16 H o o o o LO o o n o o

PAGE 32

17 analyzing concentration errors obtained while sampling submicron particles, 0.8 m NMD and 1.28 geometric standard deviation, travel.-n. at near sonic and supersonic velocities. He obtained sample concentrations 2-3 times greater than the true concentration when the sampling velocity was 205„ of the free stream velocity CR=5) Sehmel (16) studied the isokinetic sampling of monodisperse particles in a 2.81 inch IDduct and found that it is possible to obtain a 20% concentration bias while sampling isokinetically with a small diameter inlet probe. Results also showed that for all anisokinetic sampling velocities, the concentration ratios were not simply correlated with Stokes number. ^-^— ^^^^^2liilg_Ji^.lJHie toN Misali gnment Sampling error associated with the nozzle misalignment has not been adequately evaluated in past studies because the sampled flow field was maintained or assumed constant in velocity and parallel to the duct axis. The studies that have been performed on the effect of probe misalignment do not provide enough quantitative information to understand more than just the basi.c nature of the problem. Results were produced through investigations by Mayhood and Langstroth, as reported by IVatson (5), on the effect of misalignment on the collectxor efficiency of 4, 12 and 37 ym particles (see Figure 7). In a study by Glauberman (17) on the directional dependence of air samplers, it was found that a sampler head facing xnto the directional air stream collected the highest concentration. Although these results coincide with

PAGE 33

*ru < IX o u 12 ym 30 60 90 120 ANGLE OF PROBE MISALIGNMENT, degrees Figure 7. Error due to misalignment of probe to flow stream faft Mayhood and Langstroth, in Watson (5]]. er

PAGE 34

19 theoretical predictions [i.e., measured concentration is less than or equal to actual concentration and the concentration ratios decrease as the particle size and the angle are increased), the data are of little use since two important parameters, free stream velocity and nozzle diameter, are not included in the analysis. Raynor (18) sampled particles of 0.68, 6 and 20 ym diameter at wind speeds of 100, 200, 400 and 700 cm/sec with the nozzle aligned over a range of angles from 60 to 120 degrees. He then used a trigonometric function to convert equation (5) to the form A = 1 + BCK)[(V.sin0 + V cos0)/ (V. cos0 + V sinG) 1] (11) This function only serves to invert the velocity ratio between and 90 degrees and does not realistically represent the physical properties of the flow stream. In fact, equation (11) becomes unity at 45 degrees regardless of what the velocity ratio or particle size is. This cannot be true since it has been shown that the concentration ratio will be less than unity and will decrease inversely proportional to the angle and particle diameter. A more representative function can be derived in the following manner: Consider the sampling velocity V. to be greater than the stack velocity V^. Let A^ be the cross sectional area of the nozzle of diameter D^. The stream tube approaching the nozzle will have a cross sectional area A such that o A V = A. V. (^7^ 11 '-^^J i-(l,_*l i'"rliil^l.t.ll-

PAGE 35

20 If the nozzle is at an angle 9 to the flow streaip,, the projected area perpendicular to the flow is an ellipse with a major axis D., minor axis D.COS0, and area (D. "^cose)/4 The projected area of the nozzle would therefore be A.cos0 (see Figure 8). It can be seen that all the particles contained in the volume V^A.cosG will enter the nozzle. A fraction 8'CK,R,9} of the particles in the volume (A A.cosGlV will o 1 ^ o leave the stream tube because of their inertia and will not enter the nozzle. Therefore, with C^ defining the actual concentration of the particles, the measured concentration in the nozzle would be C A coseV + [l-3'(K,R,e3](A -A.cos0)V C C. = -5-i .JL— 1 o o ,^^_ 1 ~ — — (1^) A.V. 1 1 Using equations (1) and (12), this may be simplified to A = C^/C^ = 1 + 3'(K,R,e)(Rcos0-l) (14) 6'(K,R,0) would be a function of both the velocity ratio R and the inertial impaction parameter K as shown by Belyaev and Levin (13). However, 3' will also be a function of the angle because as the angle increases, the severity of the turn that the particles must make to be collected is also increased. It can be seen that for large values of Stokes number, 6' must approach 1 for the predicted concentration ratio in equation (14) to reach the theoretical limit of RcosO. The maximum error should theoretically occur somewhere between a Stokes number of 1 and 6 depending on the angle a. The upper limit of K 6 would be for an angle of degrees as described earlier in this chapter. The theoretical lower limit of K = 1 1 1 miatim^ m^ nt^czmaai^uUii:.^^^^

PAGE 36

21 >s o o > Pi m +-> 0) c r-< O •H c nj •n (=; • H 1— I cd i/i •H e CD I— I N N O c •H CO 0)

PAGE 37

22 would be for an angle o£ 90 degrees in which case the particles would be traveling perpendicular to the nozzle. Since the nozzle has zero frontal area relative to the flow stream, any particle that is collected must make a turn into the nozzle. The amount of time that a particle has to negotiate a turn is the time it takes the particle to traverse the diameter of the nozzle, or D^/V Setting this equal to T the time it takes a particle to change directions and rearranging terms, we obtain tV^/D^ = 1 as the limiting situation for a particle to be able to make a turn into a nozzle positioned at a 90 degree angle to the flow stream. For angles between and 90 degrees the maximum error will occur between the limits of Stokes numbers of 1 and 6 and should be proportional to the average diameter of the frontal area of the nozzle. Fuchs [19) suggests that for small angles the sampling efficiency will be of the form A = 1 4 sinCGK/TT) (15) Laktionov (20) sampled a polydisperse oil aerosol at an angle to the flow stream of 90 degrees for three subisokinetic conditions. He used a photoelectric installation to enable him to determine the aspiration coefficients for different sized particles. From data obtained over a range of Stokes numbers from 0.003 to 0.2 he developed the following empirical equation: ^ .,.[v./v )'^ A = 1 jK^ i' 0-' (16) This equation can be used only in the range of Stokes numbers given and for a range in velocity ratios (R) from 1.25 to 6.25.

PAGE 38

23 A few analytical studies in this area have also been published. Davies' (14) theoretical calculations of particle trajectories in a nonviscous flow into a point sink determined the sampling accuracy to be a function of the nozzle inlet orientation and diameter, the sampling flow rate and the dust particle inertia. Vitols (21) also made theoretical estimates of errors due to anisokinetic sampling. He used a procedure combining an analog and a digital computer and considered inertia as the predominant mechanism in the collection of the particulate matter. However, the results obtained by Vitols are only for high values of Stokes numbers and are of little value for this study. B. Summary of the Literature on Tangential Fl ow Although anisokinetic sampling velocity is known to cause a particle sampling bias or error, there are also several other sampling error-causing factors such as: duct turbulence; external force fields (e.g., centrifugal, electrical, gravitational or thermal); and probe misalignment due to tangential or circulation flow. These factors are almost always present in an industrial stack gas and cannot be assumed to be negligible. Not only do these factors cause sampling error directly but in addition, they cause particulate concentration gradients and aerosol size distribution variations to exist across the stack both in the radial and angular directions. 1. Causes and Characteristics_ of Tangential Fl oiv an Tangential flow is the non-random flow in a direction other th that parallel to the duct center line direction. In an air pollution

PAGE 39

24 control device, whenever centrifugal force is used as the primary particle collecting mechanism, tangential flow will occur. Gas flowing from the outlet of a cyclone is a classic example of tangential flow and a well recognized problem area for accurate particulate sampling. Tangential flow can also be caused by flow changes induced by ducting (22). If the duct work introduces the gas stream into the stack tangentially, a helical flow will occur (see Figure 9). Even if the flow stream enters the center of the stack, if the ducting flow rate is within an order of magnitude of the stack flow rate, a double vortex flow pattern will occur (see Figure 10) The swirling flow in the stack combines the characteristics of vortex motion with axial motion along the stack axis. The gas stream moves in spiral or helical paths up the stack. Since this represents a developing flow field, the swirl level decays and the velocity profiles and static pressure distributions change with axial position along the stack. Swirl level is used here to represent the axial flow or transport rate of angular momentum (23) Velocity vectors in tangential or vortex flows are composed of axial, radial and tangential or circumferential velocity components (see Figure 11). The established vortex flows are generally axisymmetric but during formation of the spiraling flow the symmetry is often distorted. The relative order of magnitude of the velocity components varies across the flow field with the possibLlity of each one of the components becoming dominant at particular points (24) -^Wii^^diir^

PAGE 40

25 < a. o c •H +J o U 3 C >H s o i-i H +J faO C CD H

PAGE 41

26 m < I tc +-> o 3 T3 X o c •H o X u o > 3 a o M M 3 •H

PAGE 42

27 Figure 11. Velocity components in a swirling flow field.

PAGE 43

28 The two distinctly different types of flow that are possible in a swirling flow field are knovm as free vortex and forced vortex flows. When the swirling component of flow is first created in the cyclone exit, the tangential profile of the induced flow approaches that of a forced vortex. As the forced vortex flow moves along the axis of the stack, momentum transfer and losses occur at the wall which cause a reduction in the tangential velocity and dissipation of angular momentum. This loss of angular momentum is due to viscous action aided by unstable flow and fluctuating components. Simultaneously, outside the laminar sublayer at the wall where inertial forces are significant, the field develops toward a state of constant angular momentum. This type of flow field with constant angular momention is classified as free vortex flow. The angular momentum and tangential velocities of the flow decay as the gas stream flows up the stack (23) Baker and Sayre measured axial and tangential point velocity distributions in a 14.6 cm circular duct in which swirling flow was produced by fixed vanes (23) The tangential velocity profiles and angular momentum distributions are plotted in Figures 12 and 13 from measurements taken at 9, 24 and 44 diameters downstream of the origin of tangential flow. The tangential velocity (W) is made dimensionless by dividing it by the mean spatial axial velocity (U^) at a pipe cross section. These plots indicate developing flow fields, with two definite types of flow occurring: that approaching forced vortex flow in the central region of the pipe and flow approaching free vortex flow in the outer region. Further tests showed that the free vortex field

PAGE 44

29 rH CD •H Mh a o .-( m O o > • H )-> c M C c P o PJ o H' U P •rt 13 R O •H +J O d) U3 tn o u So H

PAGE 45

30 1 i 1 1 1 r— 1 f 1 \ -1\ r-i \ II • / 11 X X \ \ \ \ -' \\ \ \ ^ \ \ \ \ \ \ — \ 1 1 : 1 1 ( 1 I 1 / i O LT; o H 3: o I— I G 'A B •H I P i E P O o !-> 3 ,o •H •p • H PI o •H +J u m m m O U a ci. 5j

PAGE 46

development is due primarily to viscosity at the wall and not a function of inlet conditions, whereas the profiles in the forced vortex field are very dependent on the initial conditions at the inlet. Although no reverse flow was found in these tests, other tests showed that strong swirls may produce reversed axial velocities in the central region (25) It should be noted that although tangential velocities and angular momentum decay along the axis of the pipe, see Figures 12 and 13, even after 44 diameter the tangential velocity is still quite significant when compared to the axial velocity. Therefore, satisfying the EPA Method 5 requirement of sampling 8 stack diameters downstream of the nearest upstream disturbances will not eliminate the effect of sampling in tangential flow. The angle of the flow relative to the axis of the stack induced by the tangential component of velocity was as high as 60 degrees at some points in the flow. This compares well with angles found when sampling the outlets of cyclones (25) Another interesting fact about the flow described in Figures 12 and 13 is that the radial positions for the tangential components W/U = show that the vortex axis is off center by as much as O.lr/R. This indicates that the swirling fields are not exactly axis^-mmetrical 2. Errors Induced by Tangential Flow Types of errors that would be expected to be introduced by tangential flow are nozzle misalignment, concentration gradients and invalid flow measurements. The sampling error caused by nozzle misalignment lias been

PAGE 47

32 described in the previous chapter. Concentration gradients occur because the rotational flow in the stack acts somewhat as a cyclone. The centrifugal force causes the larger particles to move toward the walls of the stack, causing higher concentrations in the outer regions. Mason (22] ran tests at the outlet of a small industrial cyclone to determine the magnitude of these three types of errors induced by cyclonic flow. Results of flow rates determined at the different locations are presented in Table I. As indicated by the data, serious errors can result in cases of tangential flow. A maximum error of 212', occurred when the pitot tube was rotated to read a maximum velocity head. Sampling parallel to the stack wall also had a large error of almost 74-6. When sampling downstream of the flow straightening vanes, however, the error was reduced to 15%. Tests performed at the same point but with different nozzle angles produced the data in Table 11. Measured dust concentration was lowest when the sampling nozzle was located at an angle of degrees or parallel to the stack wall. The measured dust concentration continued to increase at 30 and 60 degrees but then decreased at 90 degrees. Equation (14) shoivs that when sampling at an angle, under apparent isokinetic conditions (i.e., R=l) the measured concentration will be less than the true concentration by a factor directly proportional to the cos9. A maximum concentration, which would be the true concentration, will occur at = 0, which from this data should lie at an angle between 60 and 90 degrees to the axis of the stack. This can be confirmed by vsss>"i^S^L^i^^fi^^s^ 2i''\'i.*.^r>^.^

PAGE 48

TABLE I FLOW RATE DETERMINED AT VARIOUS MEASURENENT LOCATIONS Location VelocjLty_j;fp_sJ__ Flow Rate (scfm) % Error Actual Based on Fan Performance Port A (parallel) Port A (maximum Ap) Port C (straightened) 18 40 60 21 475 826 1,482 548 74 212 15

PAGE 49

34 TABLE II CONCENTRATION AT A POINT FOR DIFFERENT SAMPLING ANGLES Nozzle Angle 30 60 90 easured Concentration (grains/dscf) 243 296 332 316 n ,..44
PAGE 50

35 using the data in Table I and the geometry in Figure 11 to calculate the angle cj): cos(|) = V /V = 18/60 (17) This is true for ^ 12 degrees. Therefore, 9 = when (}) = 72 degrees. :| Table III gives the results of the emission tests. Sampling with I il the nozzle parallel to the stack wall showed an error of 53%. I j Sampling at the angle of maximum velocity head reduced the error to 40-<;. The results cannot be compared directly to those with the parallel sampling approach because the feed rates were not the same due to equipment failure and replacement. Sampling in the straightened flow had a sampling error of 36%. It was expected that sampling at this location would give better results, but some of the particles were impacted on the straightening vanes and settled in the horizontal section of the duct, thus removing them from the flow stream. Particle size distribution tests showed no significant effect of a concentration gradient across the traverse. This was due to the particles being too small to be affected by the centrifugal force field set up by the rotating flow. 5. Errors Due to t he S-Type Pitot Tube The errors in the measurement of velocity and subsequent calculations of flow rate in tangential flow are due primarily to the crudenoss of the instruments used in source sampling. Because of the high particulate loadings that exist in source sampling, standard pitot tubes cannot be used to measure the velocity. Instead, the S-type pitot tube must be used

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TABLE III EMISSION TEST RESULTS Probe Position Measured Emission Rate (gr/dscf) Actual Emission Rate (gr/dscf) Error % Nozzle parallel with stack wall Nozzle rotated toward maximum Ap Straightened flow 0.350 0.194 0.207 0.752 53 0.327 40 0.325 36

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37 since it has large diameter pressure ports that will not plug (see Figure 14) Besides the large pressure ports it has an additional advantage of producing approximately a 20% higher differential pressure than the standard pitot tube for a given velocity. However, although the S-type pitot tube will give an accurate velocity measurement, it is somewhat insensitive to the direction of the flow (25-29) Figures 15 and 16 show the velocity errors for yaw and pitch angles. Although the S-type pitot tube is very sensitive to pitch direction, the curve for yaw angle is symmetrical and somewhat flat for an angle of 45 degrees in either direction. Because of this insensitivity to direction of flow in the yaw direction, the S-type pitot tube cannot be used in a tangential flow situation to align the nozzle to the direction of the flow, or to accurately measure the velocity in a particular direction. The velocity in a rotational flow field can be broken up into three components in the axial, radial and tangential directions (see Figure 11). The magnitude of the radial and tangential components relative to the axial component will determine the degree of error induced by the tangential flow. Neither the radial nor the tangential components of velocity affect the flow rate through the stack, but both affect the velocity measurement made by the S-type pitot tube because it lacks directional sensitivity. If the maximum velocity head were used to calculate the stack velocity, the resultant calculated flow rates and emission levels could be off by as much as a factor of l/cos(J). Aligning the probe parallel to the stack will reduce but not eliminate this error because part of the radial and tangential velocity components will still be detected by the pitot tube.

PAGE 53

38 •i-r 4-i in I — f c p o o 1:1I

PAGE 54

39 00 o D •H Cc o 1*^ c £ > o u H U o a; > U no

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40 a u CD '71 E E o 1 — I to O) o O > P <-J =>,= c •H o CD () (N CJ o 1 fH OJ CU o o (M • 3 o ID C w c c3 c a u +-> •w > O U u o X .—J u o o KO 3

PAGE 56

41 L Therefore, the true flow rate cannot be determined by an S-type pitot tube in tangential flow because neither the radial velocitv, V the tangential velocity, V the axial velocity, V nor the angle c^ can be measured directly. ii-JMlH^^^A^i^ilable^Jo^^ in a Tangential Flow Field ~^"" "~ ~ — -^_ ^^ — Almost all of the reported measurements of velocity components in a tangential flow field have been based upon introduction of probes into the flow. Because of the sensitivity of vortex flows to the introduction of probes, the probe dimensions must be small with respect to the vortex core in order to accurately measure velocity. Two common types of pressure probes capable of measuring velocity accurately are the 5-hole and 5-holc pitot tubes pictured in Figures 17a and b. The 5-hole or three dimensional directional pressure probe is used to measure yaw and pitch angles, and total and static pressure. Five pressure taps are drilled in a hemispherical or conical probe tip, one on the axis and at the pole of the tip, the other four spaced equidistant from the first and from each other at an angle of 30 to 50 degrees from the pole. The operation of the probe is based upon the surface pressure distribution around the probe tip. If the probe is placed in a flow field at an angle to the total mean velocity vector, then a pressure differential will be set up across these holes; the magnitude of which will depend upon the geometry of the probe tip, relative position of the holes and the magnitude and direction of the velocity vector. Each probe requires calibration of the pressure

PAGE 57

42 _J o O CD > O e o H m > (J H c o u u M ^•^^-Tl**-
PAGE 58

45 differentials betvveen holes as a function of yaw and pitch angles. Figure IS shows the sensitivity of a typical 5-hole pitot tube to yaw angle. Because of its sensitivity to yaw angle, it is possible to rotate the probe until the yaw pressures are equal, measure the angle of probe rotation (yaw angle) and then determine the pitch angle from the remaining pressure differentials. The probe can be used without rotation by using the complete set of calibration curves but the complexity of measurement and calculation is increased and accuracy is reduced. Velocity components can then be calculated from the measured total pressure, static pressure and yaw and pitch angle measurements. The 3-hole pitot tube, also known as the two dimensional or Fecheimer probe, is similar to the 5-hole design except that it is unable to measure pitch angle. The probe is characterized by a central total pressure opening at the tip of the probe with two static pressure taps placed s>imiietrically to the side at an angle of from 20 to 50 degrees. From Figure 19 it can be seen that the probe is quite sensitive to yaw angle and can therefore be used to determine the yaw angle by rotating the probe until the pressure readings at the static taps are equal. Once this is done the total pressure is read from the central port, and the static pressure can be determined by use of a calibration chart for the particular probe. Both the 5-hole and the 3-hole pitot tubes have proven useful in determination of velocity components in tangential flow fields (25, 28, 30). 5. EPA Criteria for Sampling _Cyc lonic Fl ow The revisions to reference methods 1-8 (2) describe a test for determination of whether cyclonic flow exists in a stack. The S-type sMitim**r-,mf.i

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44 Figure 18. ('ive-holc pi pitot tube sensitivity to yaw angle. (281

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45 30 -25 -20 -15 -10 -5 5 10 15 20 25 30 Pitch Angle, degrees .05 .10 Pressure Differential inches of f!^0 -.15 Figure 19. Fcchcimcr pitot tube sensitivity to yaw angle. (28) S*M $ (. •*" v^,i)r"*^*.-'s.i-*>*t*"i-r'**. i| > i I—— ,mi,-t.^—t

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46 pitot tube is used to determine the angle of the flow relative to the axis of the stack by turning the pitot tube until the pressure reading at the two pressure openings is the same. If the average angle of the flow across the cross section of the stack is greater then 10 degrees, then an alternative method of Method 5 should be used to sample the gas stream. The alternative procedures include installation of straightening vanes, calculating the total volumetric flow rate stoichiometrically, or moving to another measurement site at which the flow is acceptable. Straightening vanes have shown the capability of reducing swirling flows; however, there are some problems inherent in their use. One is the physical limitation of placing them in an existing stack. Another is the cost in terms of energy due to the loss of velocity pressure when eliminating the tangential and radial components of velocity. Since the vortex flows are so sensitive to downstream disturbances, it is quite possible that straightening vanes might have a drastic effect on the performance of the upstream cyclonic control device which is generating the tangential flow. Because of these reasons the use of straightening vanes is unacceptable in many situations. Calculating the volumetric flow rate stoichiometrically might produce accurate flow rates but the values could not be used to calculate the necessary isokinetic sampling velocities and directions. Also, studies reported here have shown that the decay of the tangential component of velocity in circular stacks is rather slow and therefore it would be unlikely that another measurement site would solve the problem.

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47 It should be noted that EPA's approach to determining whctlier cyclonic flow exists in a stack is correct. Other approaches such as observing the behavior of the plume after leaving the stack could lead to improper conclusions. Hanson et al (28} found that the twin-spiraling vorticies often seen leaving stacks are the result of secondary flow effects generated by the bending of the gas stream by the prevailing crosswind and do not indicate any cyclonic flow existing in the stack.

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CHAPTER III EXPERIMENTAL APPARATUS AND METHODS A. Experimental Design The major components of the aerosol flow system can be seen in Figure 20. An aerosol stream generated from a spinning disc generator was fed into a mixing chamber where it was combined with dilution air. The air stream then flowed through a 10 cm diameter PVC pipe containing straightening vanes. This was followed by a straight section of clear pipe from which samples were taken. The filter holder and nozzle used as a control sample originated in a box following the straight section. A test nozzle was inserted into the duct at an angle from outside the box. A thin-plate orifice, used to monitor flow rate, followed the sampling box. A 34000 £pm industrial blower was used to move the air through the system. The flow rate could be controlled by changing the diameter of an orifice plate. An air by-pass between the blower and the orifice plate was used as a fine adjust for the flow. The sampling systems (see Figure 21] consisted of stainless steel, thin-walled nozzles connected to 47 mm stainless steel Gelman filter holders. Each filter assembly was connected in series to a dry gas meter and a rotameter, and driven by an airtight pump with a by-pass valve to control flow. 48

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49 CO en LU Q_ CD or: CD 1 t— CD LU Qi ^i: LU LlJ
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50 , d •H H g 0) 3 •rH &4

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:e 51 B^ Aeroso l Generation 1_^ Sj^in ning Disc Generator A spinning disc aerosol generator (51-33) was used to generate monodisperse aerosols from 1.0 ym NMD to 11.1 ym NMD [see Table IV). Droplets were generated from a mixture of 90% uranine (a fluorescent dye) and 10?6 methylene blue dissolved in a solution of from 90 to 100% ethanol (95% pure) and up to 10% distil led/deionized H^O. Uranine was used so that the particles could be detected by fluoremetric methods. Methylene blue was added to aid in the optical sizing of the particles. The mixture of water and ethanol allowed for a uniform evaporation of the droplets. The droplets, containing dissolved solute, evaporated to yield particles whose diameters could be calculated from the equation % = ^^'-''^ % (IB) where D = particle diameter, ym C^ = ratio of solute volume to solvent volume plus solute volume, dimensionless Dp = original droplet diameter, ym With the disc's rotational velocity, air flows and liquid feed rate held constant the size of the droplets produced were only dependent upon the ratio of the ethanol -water mixture. Since the droplets are produced from a dynamic force balance between the centrifugal force and the surface

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52 TABLE IV SIZES AND DESCRIPTIONS OF EXPERIMENTAL AEROSOLS Aerosol Description Generation Method % Ethan 0.0024% Spinning Disc 90 0.005% Spinning Disc 90 0.01% Spinning Disc 90 0.03% Spinning Disc 90 0.2% Spinning Disc 99 0.05% Spinning Disc 90 0.55% Spinning Disc 99 0.3% Spinning Disc 90 0.6% Spinning Disc 90 2.0% Spinning Disc 100 1.0% Spinning Disc 90 4.0% Spinning Disc 100 6.7% Spinning Disc 100 6.7% Spinning Disc 95 lagweed Pollen Mechanical Dispersion N.A. Number Mean Droplet Diameter Ethanol Diameter, pm Particles, 37 .4 37 .2 37 .1 37 .8 24 .6 39 .7 24 .4 34. ,5 33. ,1 23. 6 35. 4 23. 4 23. 2 27. 3 pm 1 .08 1 .37 1, .72 2. ,53 3. 10 3. 15 4.98 6.02 6.4 7.66 8.0 9.42 11.1 N.A. 19.9

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55 tension of the drop, the surface characteristics of the liquid are quite important. The surface tensions of water and ethanol at 20 degrees C are respectively 72.8 and 22.3 dynes/cm (34). The effect of this large difference can be seen in Table IV where the droplets produced were approximately 37 ym for 90% ethanol and 23 ym for 100% ethanol Before and after each test a sample of the particles was collected on a membrane filter and sized using a light microscope to take into account any slight variation in the performance of the spinning disc. 2. Ragweed Pollen In order to obtain large Stokes numbers, ragweed pollen was mechanically dispersed by means of a rubber squeeze bulb into the inlet of the duct. The ragweed pollen had a NMD of 19.9 ym. C. Velocity Determination The velocity at each sampling point was measured using a standard pitot tube. The flow was maintained constant during the test by controlling the pressure drop across a thin-walled orifice placed in the system (35-37). Five orifice plates with orifices ranging in diameter from 1.8 to 7.2 cm were used to obtain a range in duct velocities of 82 to 2460 cm/sec (see Table V) in the 10 cm duct. To obtain higher velocities, a 5 cm duct was used. A typical velocity profile across the 9 6 cm clear plastic duct is presented in Table VI and plotted in Figure 22. The profile is (m'-: lllllir"-.ill*"**= w^ *-"^.M

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54 TABLE V TABLE OF OBTAINABLE VELOCITIES IN 10 cm DUCT Orii -ice Diameter Ap Range Ran ge in Velocity cm cm H^b 5.6 21.6 cm/ sec 1 795 82 162 2.539 5.3 21.8 162 326 5.5 89 4.2 22.9 304 670 5.080 4.1 22.6 582 1371 7.182 2.2 14.5 945 2460

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55 TABLE VI TYPICAL VELOCITY TRAVERSE IN THE EXPERIMENTAL SMIPLING SYSTEM (9.58 cm I.D. Duct) Point d/D AP Hor cm 11^ izontal V, cm/sec AP, cm Vert ical V cm/ sec 1 0.044 1.27 1454 1.57 161S 2 146 1.83 1743 2.11 1871 3 0.296 2.03 1S3S 2. OS 1859 4 0.704 2.13 1884 2.11 1871 5 854 1.88 1768 1.98 1813 6 0.956 1.47 1564 1.52 1591 Average Velocities [cm/sec) From Pitot Tube Readings From Orifice AP 1740 1658

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56 O ID •H CD M-< r— 1 O •H ^-1 t+J p o J-l p— J CL, rt p rH c ri o o N l-J +-> f-l u o (D iz: > O Q m \o 3 CO c o •H p u 0) 'Jl 'O •l-l 'Jl o 0) c e •H a X •H 4-^ o • t-l •H a o T— t > rt o • H ^4 (D 3 •H tl. o o c o o rj (N r—4

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57 quite flat which is typical of the turbulent flow regime. The average Reynolds number for this particular case was 1.1 x 10 The velocities at traverse points 3 and 4 were used as the velocity for determination of isokinetic sampling rate and Stokes number. The difference between the average velocity determined from the pitot traverse and the orifice plate calibration is probably due to the inability of the pitot tube to accurately measure velocity near the wall at points 1 and 6. D. Selection of Sampling Locations Sehmel (16) observed that non-uniform particle concentrations existed across the diameter of a cylindrical duct, and that the magnitude of the concentration gradient varied with particle size. To account for these radial variations, the two sampling points were located symmetrically about the center of the duct at a distance of 2 cm from the center. Simultaneous isokinetic samples were taken at the two points and compared. Tests were repeated for different particle sizes. No concentration differences were found to exist at the two sampling points. E. Sampling Nozzles Two pairs of sampling nozzles were cut from stainless steel tubing of 0.465 cm and 0.683 cm l.D. The nozzles were made approximately 15 cm long to minimize the effect of the disturbance caused by the filter holders on the flow at the entrance of the nozzles. Analysis by Smith (38) showed that a sharp-edge probe was the most efficient design; it!:*A4-.*^it*— iC-ii^-t -NS-Ui i.rr:;w

PAGE 73

58 therefore, the tubing was tapered on a lathe to a fine edge. Belyaev and Levin (12) observed that the rebound of particles from the tip of the nozzle into the probe was one cause of sampling error and that for tapered nozzles, the efficiency is affected by the relative wall thickness, the relative edge thickness and the angle of taper. They concluded that if the edge thickness is less than 5% of the internal diameter and the taper is less than 15 degrees, then the variation in aspiration coefficient due to particle rebound would be less than 5%. The nozzles were designed accordingly. F. Analysis Procedu re 1. For Uranine Particles Uranine particles were collected on Gelman type A glass fiber filters. The filters were then placed in a 250 ml beaker. One hundred milliliters of distilled water were then pipetted into the front half of the filter holder and down through the nozzle into the beaker containing the filter. The uranine leachate concentration was then diluted and analyzed by a fluorometer (39) 2. For Ragweed Pollen The ragweed pollen was collected on membrane filters and counted under a stereo microscope. In this part of the experiment the filters and probe were analyzed separately. The filters used for collecting the particles were 5.0 pm type SM Millipore membrane filters. In order to count the particles under a microscope a dark background was necessary; M-**^. Vf lDliM'1Ui-t>|c<''^kMM

PAGE 74

59 therefore, each filter was dyed with ink and a grid was drawn to aid in the counting. Before being placed in the filter holders, the filters were examined under the microscope to determine if any background count existed. After each test the filters were removed and the entire area of the filter was counted. The pollen caught in the nozzle and filter holder was analyzed using isopropyl alcohol and 0.45 ym pore size Millipore membrane filters with black grids. The isopropyl was first filtered several times to remove background particulate matter. Once the background was low enough, the alcohol was poured into the front half of the filter holder and through the nozzles. The solution was then sucked through the membrane filters. The filters were allowed to dry and then the entire filter area was counted under the microscope. G. Sampling Proc edure 1. A desired flow rate was obtained by selecting an orifice plate and using the by-pass as a fine adjust. 2. The velocity was measured using a standard pitot tube. 3. A solute-solvent solution was selected for a given particle size. 4. Particles were collected on a membrane filter and sized using a light microscope. 5. A nozzle diameter which would allow for an isokinetic sampling rate closest to 1 cfm was selected. 6. Isokinetic sampling rates were calculated and sampling flow rates were adjusted accordincrly "•-id WrTTi ;>•(•.-• • I

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60 7. Two simultaneous isokinetic samples were taken, one parallel to the flow (control), and one at a specified angle. Sampling times i^aried from 10 to 20 minutes. H. Tangential Flow Mapping The system used to map the flow pattern in a tangential flow stream is shown in Figure 25. It consists of a 54000 £pm industrial blower, a section of 15 cm PVC pipe containing straightening vanes, a small industrial cyclone collector, followed by a 6.1 meter length of 20 cm PVC pipe. The 150 cm long cyclone, shown in Figure 24 was laid on its side so that the stack was horizontal and could be conveniently traversed at several points along its length. A change in flow through this system could be produced by supplying a restriction at the inlet to the blower. To measure the velocity in the stack a United Sensor type DA 5dimentional directional pitot tube was used. The probe, pictured with its traversing unit in Figure 25, is .32 cm in diameter and is capable of measuring yaw and pitch angles of the fluid flow as well as total and static pressures. From the blow up of the probe tip (Figure 25) it can be seen that the head consists of 5 pressure ports. Port number 1 is the centrally located total pressure tap. On each side are two lateral pressure taps 2 and 3. When the probe is rotated by the manual traverse unit until P., = P,, the yaw angle of flow is indicated by the traverse unit scale. When the yaw angle has been determined an additional differential pressure is measured by pressure holes located perpendicularly above and below the total pressure hole 1. Pitch angle is then determined using a calibration curve for the individual probe. The yaw angle is a

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61 ]5 cm. ID Straightening van cs .4 m — Slower 6.1 m Figure 23. Experimental system for measuring cro.^s sectional flow patterns in a swirling flow stream. 3 V) re o -> !Ocm I Ti^i^s-**-?' n*w-

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62 k-22.f 0— > 1 T T Note: All dimensions in centimeters lI_j^J 17.1 14.7 Figure 24. Cyclone used in the study to generate swirling fl ow.

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63 3 1 2 4 Figure 25. Photograph of the 5-dimcns Lonal pitot with its traversing unit. Insert shows the location of the pressure taps.

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64 measure o£ the flow perpendicular to the axis of the stack and tangent to the stack walls. The pitch angle is a measure of the flow perpendicular to the axis of the stack and perpendicular to the stack walls. The axial component of the velocity can therefore be determined from the following equation: V^ = V^ coscj) (19) where V = component of velocity flowing parallel to tlie axis of the stack, a V = total or maximum velocity measured by the pitot tube (j) = cos [cos (pitch) X cos (yaw)]

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CHAPTER IV RESULTS AND ANALYSIS A. Ae rosol Sampling Experiments 1. Stokes Number Experiments were set up and run with Stokes number as the independent variable. Duct velocity, nozzle diameter and particle diameter were varied in order to produce a range of Stokes numbers from 0.007 to 2.97. The Stokes number used in the analysis of data was calculated from Cp V D 1 where -fn 4^4 n /LI C = 1 + 2.492 L/D + 0.84 L/D e p' ^ (11) (21) p p and L = mean free path = 0.065 pm (11) Values for density and viscosity used in the calculations were n = 1.81 X 10""^ g/cm-sec (40) p = density of uranine particles = 1.375 g/cm." (41) p = density of ragweed pollen = 1.1 g/cm (18) 65

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66 2 Sampl J^ng with Parallel N ozzles In order to determine if the concentration of particles was the same at both sampling locations, simultaneous samples were taken with both nozzles aligned parallel to the duct. Table VII shows the results of tests performed over a range of Stokes numbers from 0.022 to 1.75. The average over all of the tests showed only a 0.34% difference between the two points with a 95% confidence interval of 1.2%. The data show an increase in the range of the values as the Stokes number increases. This can be expected because a small error in probe misalignment would have a greater effect at the higher Stokes number. 5. Analysis of Probe Wa sh In the analysis of the tests using ragweed pollen, the filter catch and probe wash were measured separately. This method allowed for the determination of the importance of analyzing both the filter and wash. From Table VIII it can be seen that even for a solid dry particle, analysis of the probe wash is a necessity. An average of 40% of the particles entering the nozzle was collected on the walls of the nozzle-filter holder assembly. This was only for nozzles aligned parallel to the flow stream and sampling isokinetically Therefore, the loss of particles was due to turbulent deposition and possibly bounce off the filter, and probably not inertial impaction. For tests run with the nozzle at an angle to the flow stream, it is assumed that the loss would increase as impaction of particles on the walls became

PAGE 82

67 o o c CM Lo t^ cni K) en vO vo t-~lyi vio CTi CM CNJ K) C C O r— I ^M r-H I + + I + I + O CxJ r^ O! K) O O O rH K^, CM CO C to 1 + + + 1 1 + 1 1 + + + 1 1 w I CD '^ o PI V31 o LO tn o f) LO M o o fo > ^ hJ I — I < +-> 0) N N O 2 LTl Ln LT, LTl Ln CO o vD ^ \D CO "^ •^ ^ •5t ^o O H to
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TABLE VIII PERCENT OF PARTICULATE MATTER COLLECTED IN THE PROBE WASH FOR NOZZLES PARALLEL WITH THE FLOW STREAM 68 Probe W ash* 511 196 161 366 407 377 265 415 351 220 442 Filter" Totar 497 1008 218 414 250 411 721 1087 697 1104 669 1046 464 729 647 1062 522 873 240 460 614 1036 -6 in Wash 51 47 39 34 37 36: 36 39 40 15 41 ''Numbers represent the number of ragweed pollen counted.

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69 important. This can be seen from the data taken at 60 degrees (see Table IX) where an average of 54% of the particles was lost on the walls The probe wash for eight tests using 6.7 ym uranine particles was also analyzed separately for comparison with the results of the ragweed pollen tests. While parallel sampling, from 15 to 34% of the total mass was collected in the nozzle and front end of the filter holder. While this was somewhat less than the amount of ragweed pollen found in the nozzle, it is substantial enough to show the importance of including the nozzle wash with the filter catch. Also because of the variation of the percent collected in the nozzle during identical tests, the probe wash cannot be accounted for by a correction factor. During further testing, it was qualitatively observed that the percent in the probe wash increased with particle size and decreased with increasing nozzle diameter. 4. The Effect of Angle Misalignmen t on Sampli ng Efficiency The aspiration coefficient was determined by comparing the amount of particulate matter captured while sampling isokinetically with a control nozzle placed parallel and a test nozzle set at an angle to the flow stream. Tests were run at three angles, .30, 60 and 90 degrees. The results showed the theoretical predictions to be quite accurate. For all three angles the aspiration coefficient approached 1 for small Stokes numbers (K) decreased as K increased and then leveled off at a minimum of cos8 for large values of Stokes number. The most significant changes occur in the range between K = 0.01 and K = 1.0.

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70 TABLE IX PERCENT OF PARTICULATE MATTER COLLECTED IN THE PROBE WASH FOR NOZZLES AT AN ANGLE OF 60 DEGREES WITH THE FLOW STRE/\iM Probe Wash* Filter* Total* % in Wash 348 211 559 62.0 161 138 299 54.0 288 333 621 46.4 Numbers represent the number of ragweed pollen counted.

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71 Figures 26, 27 and 28 represent the sampling efficiency as a function of Stokes number for 30, 60 and 90 degrees respectively. The experimental data used in these plots are presented in Tables X, XI and XII. From these tables it can be seen that the variables of particle diameter and velocity and nozzle diameter were varied rather randomly. This was done to check the legitimacy of using Stokes number as the principle independent variable. From the shape of the curves in Figures 26-28, it can be seen that the aspiration coefficient is indeed a function primarily of Stokes number. The curves for 30, 60 and 90 degrees are all similar in shape except for the values of Stokes number where they approach their theoretical limit. As the angle of misalignment increases, the more rapidly the aspiration coefficient reaches its maximum error. This can be accounted for as an apparent change in nozzle diameter, because it is the only parameter in the Stokes number that is affected by the nozzle angle to the flow stream. As described before, the nozzle diameter is important because it determines the amount of time available for the particle to change directions (approximately 6 D./V ). As the nozzle is tilted at an angle to the flow stream, the projected frontal area and therefore the projected nozzle diameter are reduced proportional to the angle. Therefore, as the angle of misalignment increases, the time available for the particle to change direction decreases leading to increased sampling error for a given value of K. To normalize these curves for angle to the flow stream, it is necessary to define an "adjusted Stokes number" (K') which takes into account the change in projected

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76 c +-> o c •H o; \D rt O o tn c ^ -^ G^i LT, CTl 00 00 i-H LO +J -H rt a t'"/ cn o vC r-r-g vC t^j ^C rj r-i I-^ \0 ^D CM f-< -H C^. CO c cn M cn cc c-. CC CTl C-, cc CO CO CTl •H — Ci E -vD ^JD CO \D o ^ ^ O ^ X CD m i-H N O O o O iJ N ca O < IZ. H ^ cu +-> o; m f=: r~t c^ (J •H •p CD a.} '-' CD c t-H P o CJ H 1 — : P ^ fn rt a. fo o CO cn M CJ H CD 1 > /) rj ^^ 1 — < ^ a) CJ > vD O tn c-M

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77 o •H o t-n r-U~; O-j O -=3^ CO o tn uo r^ 1 — 1 CM LO CJ LO ^'^ C r-. c C^J Z~^ +J H J2t rt U I — [ •^ O CO LT) CTl ^ ^ m ^o r\i o 1 — 1 rj a~i CO 1 — 1 Ol O .-H bO to [•T] rH •H o CT; C7~* Cn CT) CTl a-. CTl a-, CTl C7-. en CD G^* OO CO CO CO en C-, CO 00 gr •ri 4-1 (-H IS Ph M-J C3 w (D M < C ^' u < CO l-H 's:' 'd*' •W m Pi fn 5J3 O w o o g o £ r\) o o CN) O so (/i O o o o I— 1 1— 1 Di a; • O ^ o o o o o d fe o 4-1 w W tu fn t-J M CD X C P H CD K en e c^i CS [t •H IjO LO Kl < o Q E vD \D 00 to ^ '^ o s O o ^H o o c — 1 ISI H Nl u o S z. D' IX < to <; r^ H 0) 2 +J •w. CD ;/) i-( ^ rH o 5 G t— 1 •H P p^ o to ft c: o N^ LO w CD 5 t o T—^ ^ 1 — ( r— 1 (M u U •H CJ H ,2 +-1 c: O 'H M cd H Cl. < ..Di 1— 1 O. W < X M CJ H CD CJ C/l O ^^ CD > u on CO Vi2 LO m \0 vO ^ -* CO LO I— I I-O CO C7) 00 CM to t-O o 00 t^ en '•O r--

PAGE 93

78 o r-' •r-l cu +-> -r-1 re Cj f-i •H H U^ p_ ^ m a) < o u O ^ CO G-i LjO CT-, ^J I-^ r-. CO cc 00 r-K) o t-o -* CM CTi 0~. t-t-~ ^ vO U~i C\ \o ^ to — I 1-H CO r-rt^ r-. CO LO ^H to vD r-Lo o r^ vo (^ rLo cc rj uo o-i T^f f-o ro ^ 'O fe X! 6 D z; to 00 Ol (D -i< o o p w /— ^ t3 OJ 3 C H fH •t-i 0) P +-> O 0) o t: ^.^ re •H LO 1— 1 Q ;^ VO X
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79 t^ \0 K"y C^ t^; CO C t-i-j cr> ro o o -vD OJ O fn -H •n q-l 'X) CD < O Ki C cri O O LO r-xf K^ U-1 LT, Ln vD OO CN Ul LTl LT, c. oo r^ ^H ^ LT; -^ LO o CO tn LT, -=3LT, u CD O w CN o t) A N ca t^ < O 2 CO to -p •H 4-> f Q OJ QJ O o o •H -H P s CO OJ Oi CN CTi P-^ +J CJ H OJ U (/I O --^^ 1 — ^ I0) o > o m LTl 1^ o to 04 (EM to

PAGE 95

so H z I — I < CO dP c +-> C) r-* H m M •H ci o U •rH H '-H P^t+^l to CD < O u CO Ol t^ LT! fO uo vo to oc r-^ Ci C C, CTi o~j LO ^o r^ oi cri CTi C7i U-: C' oi -^ -^ fo r-^ LO CT) o o o CO CO \o fl t^ CO CO CO CO Ki ^ Ln r^ t-t-m r^ CO \D LTl ui a o c u O o o IN ch f^ o I— ( 2 a CO Jh cu CJ l-( fc/i ^J M o C) X H E CO rt t^ p_] •H CO kJ tu c ^ o C3 C 5 < Cj o H :2 r— H o M 1 — 1 M H O u 2 g p< CO < H )-J z 0) i/i w E fH UJ ^H rH o o CJ CJ H •H 4-J f-^ 2: fn o c-i tO' tn LO t'-. ^ so SO CO ^ 'S•^ viD to LO CO SD \0 00, to to CM 00 Di I — I D, CO < X 4-' o •H a U !/; O ~-~^ 1 — 1 H (!) '.) > cn so 00 CO vD en C7-. G-. 1>J r~ r^ r-~ i-n \a so Cvl rs to \o •"^li 'tevft*^t#'' > '.J—v-jMt*"*J-

PAGE 96

81 c +-1 () C / — \ "TJ P PI •H U P>o vO oc \C OO "* vO \D fCD +-1 aj t/) 6 ^ra (D •rH 4-1 l'^. C) CD o f-H ^ o o •H r-: +-> e u k! n. CC 00 o OO •SiO OO >^ +J t) H Gj (J (/; O ^-^ — [ E CD CJ ^ 00 ^ vO t— I r-cr-, Ol t^ o o ftn o f-.

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nozzle diameter with angle. Wien plotted against K', the aspiration coefficients for 30, 60 and 90 degrees should approach their tlieoretical minima at the same place as the curves for zero misalignment angle and anisokinetic sampling velocities (see Figure 6) To develop the adjustment factor for Stokes number, it was necessary to plot as a function of 0, the value of K where the aspiration coefficient reached a value that represented 95% of the maximum error. For example the maximum theoretical error for 60 degrees is cos (60) or 0.5. Therefore the value of K of interest is where there is (.95) (0.5) = 47.5% sampling error or an aspiration coefficient of 1 .475 = .525. For zero degrees, equations (9) and (10) were solved for R = 0.5 and 6 = 0.95 to obtain a value of K = 5.9. This velocity ratio was used because its theoretical maximum sampling error is 0.5, the same as for 60 degrees. The values for 60 and 90 degrees were obtained from Figures 27 and 28 respectively. Because of the flatness of the 30 degree curve (it varies only 16% over two and a half orders of magnitude of K) it was not possible to detect exactly when the curve reached 95% of its minimum value. Therefore no value for 30 degrees was used in this analysis. The equation for the adjusted Stokes number determined from Figure 29 is ,. 0.0226 K' = Ke (22) Using this equation it can be determined that the Stokes numbers for 30, 60 and 90 degrees must be multiplied by 1.93, 3.74 and 7.24 respectively to account for the effect of nozzle angle to the flow stream on the

PAGE 98

83 X o lT, r> O a. o 00 4 I— 30 60 Misalignment Anemic (6) 90 Figure 29. Stokes number at which 95% maximum error occurs vs. misalignment angle.

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84 apparent nozzle diameter. Using these correction factors it is possible to use the data to determine an expression for 3' in equation (14). Setting R = 1 and solving for B' this equation becomes 6'(K'3=4q^ (25) Using this expression the experimental data were used to plot B' as a function of the adjusted Stokes number K' (see Figure 30) From this plot, it can be observed that the data points for 30, 60 and 90 degrees all fall approximately on the same line. It should be noted that most of the scatter is due to the 30 degree data and that the amount of the scatter is somewhat deceptive. Solving equation (23) for 30 degrees, requires that the sampling bias (1-A) must be multiplied by 7.5 to normalize it with the 90 degree data. This has an effect of greatly increasing any spread in the experimental data. To develop a model for inertial sampling bias, it was necessary to develop an equation for the line drawn through the data in Figure 30. An equation of the form similar to that used by Belyaev and Levin was selected to fit the data. 3'(K',0) = 1 ^—^ (24) 1 + aK' where a and b are constants. The advantage of this equation form is that it acts similar to the theoretical expectations of the relationship (i.e., 3' approaches zero for very small values of K' and approaches 1 for very large values of K').

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85 c o •H u H O: o •s. c t-J 'JO o t/5 O cn C o o to o /3 l/l CD c 'a •r—i >
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86 While attempting to determine the constants a and b, it was found that the form of the equation had to be altered somewhat to allow g' to approach 1 at a faster rate for values of K' greater than 4.0. The following is tlic final form of the equation selected. B'(K',e) = 1 ---i— ^ C25) 1 + ak' e The constants were determined through trial and error to be 0.55 and 0.25 for a and b respectively. Therefore, the final equation to describe the sampling efficiency due to nozzle misalignment as a function of Stokes number becomes for R = 1: A = 1 + (cose 1) 3' CK',e) [26) where CK',e) = 1 _„_i._^_^ (27) 1 + 0..S5 K'e and „ 0.0226 K' = Ke (22) Thc;5c equations are solved for 30, 60 and 90 degrees and plotted against Stokes number in Figure 31. It can be seen from the graph that the equations fit the data within experimental accuracy. Figure 32 is a plot of the sampling efficiency for angles between and 90 degrees in 15 degree increments

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87 'J) o c •M in +-> a) CD •P U 'd o •H O '+H CTl o c p: o o o 03 O •H CI, fn t/1 O < M^ E (V) luOTOijjooj uoiieafdsv

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88 0. E 3 O at) o t3 C cS m o o to ui U o ^^ u o t/5 o CO > c 4) •ri U H ,MH W
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89 5_^__Th_e_jffect of Nozzle Misalignme nt ar idJ\m^£okJ£iayx__Sa^^ Velocity To complete the analysis of anisokinetic sampling, it is necessary to know what is the combined effect of both a nozzle misalignment and a sampling velocity differing from the free stream velocity. The theoretical model predicts that the sampling efficiency will be in the form A = 1 + (Rcose 133" (28) where 3"= f[3(K,R) 3'[K',e}] (29) Since the reduction of projected nozzle diameter due to nozzle misalignment will effect the time available for a particle to change directions when sampling at an anisokinetic velocity, the adjusted Stokes number K' should also be used in the equation for 3 as well as 3'. Another modification that must be made in the model involves correcting for the fact that 3(K',R) does not equal 1 when R = 1. B(K',R=l) = l-^-^43j^^ C30) To account for this 3'(K',e) must be divided by 3(K',R = 1) so that equations (28) £).nd (29) are valid at R = 1. The model to be tested now becomes A = 1 + (RcosO 1) 3(K',R) |11^1^51__ (31) At first there appears to be an obvious flaw in the model in that the aspiration coefficient equals 1 whenever R = l/cos0 regardless of the :£%(A.i._ak

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90 Stokes number. An example of this is when R = 2 and = 60 degrees. This phenomenum can be explained as follows. Since the projected frontal area of the nozzle is one half the actual area when 9 = 60 degrees, in order to sample isokinetically such that there is no divergence of streamlines into the nozzle, the sample velocitymust be one half of the free stream velocity or R = 2. Therefore, the condition of R = l/cos6 defines the condition for obtaining a representative sample when the nozzle is misaligned with the flow stream. Since the sampling methodologies used to determine 3(K,R) and 3'CK,9) were substantially different [photographic observation vs. comparative sampling), it was necessary to see if the two methods gave comparable results before the model could be tested. Four sets of tests were run with two parallel nozzles; the control nozzle sampled isokinetically and the test nozzle sampled anisokinetically Tests were performed at two Stokes numbers (K = 0.154 and K = 0.70) and at t\TO velocity ratios (R = 2.3 and R ^ 0.51). The aspiration coefficients obtained by comparing the two measured concentrations are presented in Figure 33 and Table XIII. The data obtained lie within the experimental bounds of the lines produced from Belyaev and Levin's data [Equations (5), (9) and (10)]. Since the two methods give comparable results, experiments were run to test the model. A control nozzle was placed parallel to the flow stream and the sampling velocity was set to be isokinetic. The test nozzle was inserted at an angle from outside the duct and the sampling velocity was set to be either one half or two times the free

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91 >• Qj -^ T3 R rt > (U tt) X. 1 — 1 P3 ^ e o f^ J-* t+H o 0", E +-1 D t — "^r. ^J CO (/) cu o r-f ^ o rrj o > (-^ LJ C) r; 'J T n ••"! n "vJJ 1 — < o c rr, ^-1 r( (JH, c > o t/; o fr o C-; r^ ^ >^ fp-H — ^ G rt i) d o C CO O o f Vj luo 1 jjooj uo I iLM I dsv M C •H q; K CD O C o o to 6=0

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92 i?o o ci oi vo rvo t^ r-. CO oi a-, CO bn t-n to a n~i -^ u~! [> \o -^ ^ CD a a-: CO en r~s > rv X i — t 1 — I 1 — 1 1 — 1 1 — ^ r-H — 1 o c o o o o o > m P > < w S3 O OJ • LO O o X II H Q l-H KH 12: HH 2: < f — I X W to H • PJ J rM i-J Ha CTj II < U^ irIX P^ u o 2: m II 1— 1 U CD M (X o z w o o w h-l a: < T3 0) CO P f= U O •H -H -a +-> CD cvi pj -— D E ^ O ^— •H o U -r-i O 4-> I -H Cj 1/) f^ N C) M O n 2 u o o o CO CM to d o LO LO O O •* ^ \a vO r^ t--. o --0 lO o -It LO ao p ,— re 'M -i

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stream velocity. Tests were run for a range of Stokes numbers from 0.1 to 1. This range was selected because this was expected to be the area where the greatest change in aspiration coefficient occurred. The data obtained for R = 2 and R =0.5 for a 60 degree misalignment are presented in Tables XIV and XV. Thesedata are plotted and compared with the model's prediction in Figure 34. The aspiration coefficient does indeed appear to be unity when R = l/cos6 as in the case of R = 2 and 6 = 60 degrees. The data for R = 0.5, 9 = 60 degrees appear to approach tlieir theoretical limit of Rcose [0.25) at approximately a value of Stokes number of 2 to 5. This is near the location that the aspiration coefficient for 9 = 60 degrees, R = 1 approaches its theoretical limit. This further confirms the necessity of using an adjusted Stokes number when the probe is misaligned with the flow stream. To further test the model, experiments were run at 45 degrees (R = 2.0 and R = 0.5} and at 30 degrees (R = 2.0). Thesedata presented in Tables XVI and XVII are plotted in Figures 35 and 36 also show good agreement with the prediction model When tests were run at 9 = 90 degrees, R = 2.1 and K = 0.195 (see Table XVIII), an average aspiration coefficient of only 1.5-6 was obtained. The value predicted for equation (31) for these conditions is 49%. It appears that the model falls apart at 90 degrees for R ^ 1. This is due to the fact that when 6 = 90 degrees there is zero projected frontal area of the nozzle. This means that subisokinetic sampling could in no way produce an increase in concentration as it does when particles lie in front of the projected nozzle area. Because of this it is necessary to put the condition 9 < 90 degrees on equation (31)

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o II CD c,\= p= +-> o c •H CD P H TO U 'h H H '4^ Pi<+h] t/1 aj < o (_i 94 o-^^ cric~iG-i >-0oc rsj^o ^ •^ o CT) to 00 o ^ oc o O O^ C-) C7^ O r^ ^ LT) CTl C^ C LO cr, LO [^ O CTt CM P O (J) O C CM I— I 00 o en EU i^ O > w I— i o tu < c (D o E •H c N M O 2: NO OO 00 CO to o u < < u 0) M OJ 1/1 E ^ TO (l> r-1 p /— > 0) E O t — 1 ^ u u H •H +-> e IH CTl m LO vD vjD CTl ^ ^ cr: m C?i X p u •H a) u IT! o "-^^ 1 — 1 E (U o > to c G O

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95 O a\ c +-1 o c • H aj M •H oj o fn •H H (4-J PH'4-i[ t/1 CI; < O u CO oi U-, •=:t ^ 'j:> CO (N CO CO LO '^ I--CCO cnojr\] ooccr-j r--crir-^ctio-j O o II O w O P CTl ^ %o 1-0 Ol Oi o CN LO o I— 1 'vj00 K5 CO m N:; o 'h > H X W m tu g J c 03 t-O to M LO U1 ca •H CO c6 00 kO \o < :z Q E >.c vD \o ^ ^ H G (J • 1— i CD o o Q' o. o t1 — 1 U N g NI O n. 2 < C/3 < E-H ^ ^ tii OJ l-i •P U
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o o 96 3 3 h^ >4 U m O o c o [V3 luaiorjjsoD uo laBatdsv o o EN O § e •H E o Q SO a) P o +-> w in > o •H o H :^ j^ — — — "w^v*-i h ^ ". i pg-

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97 m o II o CD O PS o\=' c -P o P •H o +-> H nj U ^H •H •H <+^ P.<4-1 'J^ Cj < o u X p o •H H u l-J o Clj 1 — 1 e: 0) 1 > 1 E O •^ CN UO O LO -Nf CO r^ CC UO LO T:t rH M r-l O o CN o ^3 O X u: c fi tu H o hJ CO +-> cc a; < tL. H C ra f': • H CO 2 G E -o O o 1—1 0) o EO N Z tsl 3 o & 2 < w <: f-i t; o 2 +-> w Qj U1 n E f-: u R O h-J -H +-> Ur~>. OJ o n. E PJ o o CI o T ( !^ u o u H •H •z. 4-> E o !h 1 — cc H o. < Ci M a. CO < ^- +J O H cu .— u w o o ^->^ r-rH e CD u CO o 1 1 -twr^HA •(n-w-*Mi. I

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o\ 98 o p •H 5 •P •H CTl LO r-^ CTi o f^ H CO "* .— ( •H tP ca CO t^ Pi,<+J 1 — i 1 — f 1 — 1 W Oj O' < o tn u II 03 n CM ^^ It PS E cc S: t-o o Bh to p X Po E w ri in hJ 2: •H •o CQ o a E •=3< n o H H (D o U r-H N fc O 2: <• W < g. ra ^H 1— 1 CD u p l-H ^ p o H (U U LO o ^^^ — 1 E > u 1-0

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99 ^^ o LO r. fH CTl i-i r^. o 1 C ^ O o • r-. -a f-^ o -^ O -ii. >, i^ o to & o o fN o o 00 C3 rH O O LO o II OS c o CN II PJ Fh O ^H +J e m H ^^ (A c w O p > o •H (J •H C to LO •H .-..^llfil-,^ .^.., i=r-w(li^|(^

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100 i^ o V) o (V) TUOIOTJJOOQ UOiq-B'JlTdsV O II Pi h o +J B, (D S P! s o H B a; o CO > o G as •H o •r-( a) W3 fi i-t i-t \0 r-i

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101 c -M o n •H CD P -H Ct O f-< -r-J •H q-i Ph4^ W o < o a> u f-i CN CD 11 6 p LO ce: :s Cr-, t — 1 cs t/1 o QJ o ;x o OS' p w 00 ^ 3 •z V) w l-H :^ u i-< o CD n H P > W QJ X E fi Clj LO K o H \D h4 Q E ^ cQ 2: u < o O o H i-< 1 — 1 H N u N 2 O r> 2 fc < to •< fe tij 4-J h1 t/1 O g !h .(— ( rt o u. H p ft. Q o .ca E LT; o QJ o u 1 — I fn NO O O ;z; •H •H o P g h-< !h Cl a, m < p o J •H CD (J y) 1 o • r-H CD O i *—.!#. M^l -^

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102 Although the experimental data for 90 degrees do not agree well with the prediction model, they do compare favorably with the emperical equation of Laktionov (20) [equation (16)]. For the conditions of K = 0.195 and R = 2.1, his equation predicts as aspiration coefficient of 3.9%. This comparison is closer than would be expected considering the fact that two completely different sampling schemes were used, and Laktinov did not analyze the amount of particles collected in the probe. It should be pointed out that the term for B'(K',6} does not equal 1 when 9=0. This means that equation (31) will not be equal to Belyaev and Levin's predicting equations (5), (9) and (10) and therefore, equation (31) should not be used for 6=0. B. Tangential Flow Mapping Eight traverse points for the velocity measurements were selected according to EPA Method 1 (1) (see Table XIX) Measurements were made using the 5-hole pitot tube at five axial distances from the inlet -ID, 2D, 4D, 8D and 16D, where D is the inner diameter of the duct. At each point in the traverse, the pitot tube was rotated until the pressure differential between pressure taps 2 and 3 (see Figure 25) was zero. This angle was recorded as the yaw angle and the pressure readings from all five pressure taps were recorded for later calculation of total and static pressure, and pitch angle. During the initial velocity traverse, a core area was discovered in the center of the duct where the direction of the flow could not be determined with the pitot tube. The core area was characterized by negative readings at all five pressure taps which did not vary much

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TABLE XIX LOCATION OF SAI^IPLING POINTS 103 Point 1 2 3 4 5 -6 of Diameter 3 .3 10 .5 19 .4 32 3 67 7 80. 6 89. 5 96. 7 Distanc e from Wall, cm .65 2 .07 3 .S3 6 38 13 36 15 91 17. 67 19. 09 Duct Diameter = 19.74 cm

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104 with the rotation of the probe. Inside the core area it was not possible to determine the direction o£ flow because there was no point in the 360 degree rotation of the probe where the pressures at point 2 and 3 were the same. The location of the core area was measured at each location along the duct axis and recorded. During the velocity measurements, it was observed that the flow was very sensitive to domistream disturbances. A crosswind at the end of the pipe produced large fluctuations in the pressure measurements. Figure 37 shows the graphical interpretation of the pitch and yaw components of velocity. The two radii r. and r represent the distance from the center of the duct to the outer boundary of the core region. The area in the core region was approximated by the following equation: c 2 2Tr(r + r^ ) A = —^ ^^~ r391 core 2 ^^-^ Tables XX-XXIY show the calculated results of the velocity measurements at the five axial positions. The low flow was the flow measured when a restriction was placed at the inlet of the blower. The restriction induced approximately a 40% decrease in the flow rate. The high flow rate represented a volumetric flow rate of 15,500 liters per minute, and the low flow rate was 11,260 liters per minute. The Revnolds number of the system calculated on a basis of the average axial flow rate were 80,000 and 111,000 for the low and high flow rates respectively. After the data were broken dov.Ti, it appeared that data from point number 1 did not agree well with the rest of the traverse points. Upon • ^j^-a. i^-c^t -| -i ^ i |INMea ^ >t

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105 o o CD U nt <^ '^ (— ni X. o +-> H a M C •H M CIj t; o rH c C o CD H M fH CD P M t/1 0) > ^H o 1^ 1 — 1 m <+i !/) 4-J y; n cv, t/. -rCJ-, o ^r CJ u O P a; r-* > (!> H ba M c a rt M +-> a) CTl 0) 4-1 X o -M a •t) CD C •H m > •V 1 — I in cH 4-> C r— O •H •H n M Ph CJ (L) Da to p H t/l 1 — 1 t/> o O p: P crt u 10 f-tm o U 3 W) IX

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106 TABLE XX FIVE-HOLE PITOT TUBE MEASUREMENTS MADE AT 1 DIAMETER DOlVNSTRE.AiM OF THE CYCLONE 1-0 Low Flow Total Axial Tans^ential Anglos, Degrees Velocity Velocity Velocity ££iBl lAlSk I^ i _ciii/sec cm/sec' cm/sec' 2 25.5 67.9 70.1 1786 608 1655 3 n.o 77.4 78.0 1600 333 1561 4 +++ + + + +++ +++ + + + + + + 5 3.0 76.0 76.0 1341 324 1301 6 21.0 60.0 62.2 1761 821 1525 7 50.0 51.0 57.0 1762 959 1369 8 32.0 48.0 55.4 1664 945 1237 1-D High Flow Total Axial Tangential ^ Angles, Degrees Velocity Velocity Velocity ^21I}1 lllSlL 1^ i cm/sec cm/sec cm/sec 2 24.0 64.0 66.4 2782 1114 2500 3 19.0 78.5 79.1 2348 444 2301 4 +++ + + + +++ + + + +++ +++ 5 3.0 74.4 74.4 1846 496 1778 6 22.0 63.8 65.8 2699 1106 2421 7 28. 57.8 61.9 2742 1292 2320 8 31.0 54.6 60.23 2572 1277 2096 Point No. 1 was too close to the wall to allow insertion of all five pressure taps. +++ Point lies inside the negative pressure section. niVoiVbr. *an*V'l'}ir%

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lo: Point 1 2 3 4 S 6 7 8 TABLE XXI FIVE -HOLE PITOT TUBE MEASUREMENTS MADE AT 2 DIAMETERS DOIVNSTRE.AM OF THE CYCLONE 2-D Low Flow Angles^ Degrees Pitch Yaw cf) ** + + + + •!+ k -x -k 24.0 60.6 17.0 73.0 ++ + 17.0 64.0 25.5 54.4 30.5 50.4 65.2 58.5 57.0 Total Velocity cm/sec +++ +++ 1746 1761 1672 Axial Velocity cm/sec 732 925 910 Tangential Velocity cm/ sec 63.3 1754 788 1528 73.8 1601 447 1531 1569 1432 1288 2-D High Flow Angles, Degrees Point Pitch ^ Yaw A Total Velocity cm/sec Axial Velocity cm/sec Tangential Velocity cm/sec 2 3 4 5 6 7 21.0 14.0 + + + 37.0" 16.0 27.0 32.0 60.4 72.8 + + + 76.0 64.0 56.6 53.6 62.5 73. 3 + + + 78.9 65.1 60.6 59.8 2597 2276 +++ 2057 2676 2646 2621 1199 654 +++ 396 1127 1199 1318 2258 2174 ++ + 1996 2405 2209 2110 *** Point No. 1 was too close to the wall to allow insertion of all five pressure taps. +++ Point lies inside the negative pressure section. a This high valve can probably be attributed to one of the pitch pressure taps extending into the negative pressure area,

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TABLE XXII FIVE -HOLE PITOT TUBE MEASUREfENTS MADE AT 4 DIAMETEPSDOV/NSTREAM OF THE CYCLONE 4-D Low Flow 108 3int Angl Pitch *** es, De Yaw grees i *** Total Velocity cm/sec "k "k -k Axial Velocity cm/ sec *** Tangential Velocity cm/sec 1 *** 2 26.0 49.0 53.9 1484 874 1120 3 15.0 58.0 59.2 1524 780 1292 4 4.0 78.0 78.0 1144 238 1119 5 +++ +++ + + + +++ + + + ++ + 6 13.0 66.8 67.4 1548 595 1423 7 20.0 57.2 59.4 1592 810 1338 8 24.5 54.4 58.0 1559 826 1268 4-D High Flow Point Angl Pitch *** es, Degrees Yaw (f) Total Velocity cm/sec *** Axial Velocity cm/sec *** Tangential Velocity cm/sec 1 *** 2 25.0 48.0 52.7 2293 1389 1704 3 16.5 58.6 60.3 2286 1133 1951 4 3.0 82.6 82.6 1651 212.6 1637 S ++ + +++ +++ +++ +++ +++ 6 15.0 68.6 69.2 2266 804 2110 7 20.0 59.4 61.4 2425 1161 2087 8 27.0 56.0 60.1 2314 1153 1918 Point No. 1 was too close to the wall to allow insertion of all five pressure taps. +++ Point lies inside the negative pressure section. •fr*Mfci-<> -*a^^.-^rtw^^

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109 TABLE XXIII FIVE -HOLE PITOT TUBE MEASUREMENTS MADE AT 8 DIMETERS DOMSTREAM OF THE CYCLONE 8-D Low Flow Total Axial Tangential Angles, Degrees Velocity Velocity Velocity l2illl Pitch Yaw ^ cm/sec cm/sec' cm/sec 2 19.5 59.0 61.0 1414 685 1212 3 15.0 69.0 70.3 1436 484 1346 4 +++ + + + + + + +++ +++ + + + 5 8.0 63.6 63.9 1396 614 1250 6 20.0 50.2 53.0 1326 798 1019 7 28.0 39.4 47.0 1289 879 818 8 29.0 38. 46.4 1231 849 758 8-D High Flow Total Axial Tangential Mglcs, Degrees Velocity Velocity Velocity Point Pitch Yaw ^ cm/sec cm/sec cm/sec 2 19.0 57.0 59.0 1875 966 1572 3 9.0 70.0 70.3 1881 634 1767 4 +++ ++ + ++ + + + + +++ +++ S 64.6 64.6 1743 748 1574 6 15.0 50.0 51.6 1942 1206 1488 7 21.0 43.2 47.1 1869 1272 1279 S 25.0 42.0 47.7 1795 1208 1201 *** Point No. 1 was too close to the wall to allow insertion of all five pressure taps. +++ Point lies inside the negative pressure section.

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no TABLE XXIV FIVE-HOLE PITOT TUBE MEASUREMENTS MADE AT 16 DIAMETERSDO'A'NSTREA.M OF THE CYCLONE 16-D Low Flow Total Axial Tangential Angles, Degrees Velocity Velocity Velocity Point Pitch Yaw cm/sec cm/sec cm/sec 2 27.0 34.0 42.4 1073 729 600 3 19.0 41.0 44.5 1169 834 767 4 9.0 58.6 59.0 1014 522 865 5 + + + +++ + + + + + + +++ + + + 6 13.0 63.0 63.7 929 412 828 7 17.0 50.4 52.3 1205 735 928 8 18.0 47.6 50.11 1190 763 979 16-D High Flow Total Axial Tangential Angles, Degrees Velocity Velocity Velocity Point P-il^Jl 1^ i. cm/sec cm/sec_ cm/sec -r *** *** *** *** *** *** 2 22.5 36.4 42.0 1553 1154 921 3 21.0 44.0 47.8 1653 1110 1148 4 9.0 66.0 66.3 1513 608 1382 5 + + + +++ ++ + +++ +++ + + + 6 12.0 61.2 61.9 1675 789 1468 7 20.0 53.4 55.9 1755 983 1407 8 19.0 49.0 51.7 1739 1078 1312 *** Point No. 1 was too close to the wall to allow insertion of all five pressure taps. +++ Point lies inside the negative pressure section.

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Ill checking the measurement setup, it was discovered that because of the construction of the probe and the closeness of the first traverse point to the opening, one of the pitch pressure points was not completely in the flow stream. Because of this, data from traverse point number 1 c'lrenot presented with the rest of the data. The velocity measurements at the other traverse points for both flow rates and all five axial distances showed approximately the same characteristics. The pitch angle increased from the core area to the duct wall. The yaw angle and the combined angle 4) decreased from the core area to the walls. At the inlet and up to eight diameters downstream, angles as high as 70 degrees were found near the core area of the flow field. The total velocity, axial velocity, and the tangential velocity all showed the same cross sectional flow pattern. The velocities were minimum at the core, increased with radius and then slightly decreased near the wall. These patterns are similar to those found in the swirling flow generated with fixed vanes (23) In order to observe the changes in the flow as a function of axial distance from the inlet, the cross sectional averages of the angle c(), core area, and tangential velocity were calculated and presented in Table XXV and plotted in Figures 38 and 39. All three parameters show a very gradual decay of the indicators of tangential flow as was expected from the reported tests (23). The curves have the same shape for both flow rates The high core area for the measurements at 16 diameters downstream was confirmed by repeated measurements. These values may be due to a

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u: TABLE XXV AVERAGE CROSS SECTIONAL VALUES AS A FUNCTION OF DISTANCE DOWNSTREAM AND FLOW RATF Average Values for High Fl ow Diameters
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(]orc Area 113 'J E J O oi^iiv p o •p '4-1 O (/) •H X tlO C o I — 1 (= re o o ^ ^-1 p C o o o cc ir, o '/~-i f— p p SJ 4) > (D o >. cS O OS to H 3 W) •H ft

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114 o M m P o in •H cd CD c O P P CD o i^ o u o o o CM c o ri [oob'/uiDj a4_iooi:oa lorauoSuL'i != Cti P O o Q a-, 3

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115 disturbance effect of the end of the duct which was only a few diameters downstream of the sampling point. The increase in average tangential velocity at 2 diameters from the inlet can be attributed to the fact that two of the traverse points were within the core area. It can be seen from the other profiles that the inner points had lower velocity values, and therefore the exclusion of the inner points would lead to a higher velocity average. Plotted in Figure 40 is the location of the core area with respect to the duct center. It can be seen that the swirling flow is indeed not axisymmetric and the location of the core area changes location with axial distance. Only one drawing is used to represent the situation for both high and low flow rate because the location for both conditions was almost identical.

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116 o C3 4-1 to O 0) u 4-' c o •i-l ,.i^ =,^ ** i.-j. -•*

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CHAPTER V SIMULATION OF AN EPA METHOD 5 EMISSION TEST IN A Ty\NGENTIAL FLOW STREMI A model has been developed and tested which describes particle collection efficiency as a function of particle characteristics, angle of misalignment, and velocity ratio. Together with the measurement of velocity components in a swirling flow it is possible to analyze the emission rate errors that would occur when performing a Method 5 analysis of the effluent stream following a cyclone. For this simulation analysis, the volumetric flow rate and isokinetic sampling velocities are calculated from velocity measurements obtained at the eight diameter sampling location using a S-ty|5e pitot tube (see Tables XXVI and XXVII). The angle cf), velocity ratio, and particle velocity are determined from velocity measurements made at the same location using the five-hole pitot tube (see Tabic XXII). The particle characteristics are obtained from particle size distribution tests made by Mason (22) on basically the same system. From a particle distribution with a 3.0 ym MMD and geometric standard deviation of 2.13 (see Figure 41), ten particle diameters were selected which represent the midpoints of 10% of the mass of the aerosol (see Table XXVIII). The density of the particles was assumed to be 2.7 g/cm-^. The nozzle diameter was selected using the standard criteria to be 0.635 cm (1/4 inch). In the model it was assumed that the nozzle would be aligned parallel with the axis of the stack, and therefore, G = (J) 117

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118 TABLE XXVI S-TYPE PITOT TUBE MEASUREMENTS MADE AT THE S-D SAMPLING PORT FOR THE LOW FLOW CONDITION Point Dynamic Pressure (cm H^O) Static Pressure (cm H^O) Ap (cm H^O) (cm H^O) Velocity (cm/sec) 8 0.96 -0 36 1.32 1.15 1229.0 7 0.99 -0.48 1.47 1.21 1298.5 6 0.66 -0.89 1.55 1.24 1331.6 5 -1.07 -0.74 0.33 0.57 614.7 4 -1.32 -1.04 -0.2S -0.53 -565.6 3 -0.41 -0.46 0.05 0.22 241.1 2 0.30 -0.17 0.47 0.69 743.2 1 0.69 -0.10 0.79 0.89 949.3

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119 TABLE XXVII S-TYPE PITOT TUBE MEASUREMENTS MADE AT THE 8-D SAMPLING PORT FOR THE HIGH FLOW CONDITION Point Dynamic Pressure (cm H^O) Static Pressure (cm H^O) Ap (cm H^O) (cm H^O] Velocity (cm/sec] 8 2.03 -0.66 2.69 1.64 1755.4 7 1.83 -1.57 3.40 1.84 1974.7 6 1.17 -2.23 3.40 1.84 19 74.7 5 -2.26 -2.79 0.53 0.73 781.3 4 -1.83 -1.32 -0.51 -0.71 -762.5 3 -0.89 -1.02 0.13 0.36 381.2 2 0.61 -0.43 1.04 1.02 1091.7 1 0.91 -0.10 1.02 1.01 1078.3 |l^-T:T*^l•*'?1vl.|rfEfl,:;^.^f^•*p•*> •ipl*^i^— •

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120 O E P O H P 03 I/) 0) U1 O P CD M H to O •H P (X P M ) urqj, s-so'i auo.iaod

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TABLE XXVIII MIDPOINT PARTICLE DIAMETERS FOR THE 10 PERCENT INTERVALS OF THE MASS DISTRIBUTION MMD = jym a = 2. 13 121 Range 10 10 20 20 30 30 40 40 50 50 60 60 70 70 80 SO 90 90 100 Midpoint 5 15 25 35 45 55 65 75 85 95 ^mici (]} meters) 7 Dp-C 0.84 0.84 1.32 1.96 1.75 3.35 2.20 5.20 2.70 7.73 3.25 11.09 4.00 16.65 4.90 24.80 6.60 44.63 10.40 109.84

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122 Using these parameters the average aspiration coefficients are determined at each traverse point using the ten particle dianeters and equations (33) (39) A,(R,.*,,K,) = .lA„p3.^* -IVls, -I'V,, ^3f3-*3'^3) = -'V* -''Vis?, -IVS'. + iVs% (53) '^'^Dp95% (34) • (35) • (56) • (37) • (38) -'Vs-o (39) A (R (f) K ) = .lA^ ^, + .1A„ ,,„ + .lA + o b S 8 Dp5% DplS'o Dp25; Where A^ = total aspiration coefficient for traverse point i. R^ = (total velocity at i)/(sampling velocity at i) = angle of flow at point i relative to the axis of the stack. K.j^= Stokes number based on the nozzle diameter, total velocity at i, and particle diameter Dp,,,,. K'ci Dpj^„,= Midpoint particle diameters each representing 10% of the total mass. Since the sampling velocity will determine the volume of air sampled at each traverse point, the total aspiration coefficient for each flow rate is determined by taking an average weighted according to sampling velocity. A = — ^^ ^-^ -'' 'j-5 5 i ^_A__iZlX_JiO. ^ v.„ + \' TTYT^TV. + v"~T^ ^^ ^40) i2 lo i5 i6 17 18 Where (^'.);= inlet velocity at traverse point j. Because of the missing data at point 1 and negative pressure section at point 4, these tw^o traverse points were not used in the analysis.

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12: The total aspiration coefficients calculated in this raanner for the low and high flow rates were 0.937 and 0.906 respectivelv (see Table XXIX and XXX). There are two reasons for the relative low amounts of concentration error found in this analysis. One reason is that the two mechanisms causing sampling error, nozzle misalignment and anisokinetic sampling velocities, cause errors in the opposite direction. The S-type pitot tube detected a velocity less than or equal to the actual velocity which would lead to subisokinetic sam.pl ing producing an increased concentration. The nozzle misalignment when sampling parallel to the stack wall would produce a decreased concentration. So each of these errors has a tendency of reducing the other error. Another reason for the small errors was the small size of the aerosol. The Stokes numbers for over 50% of the particles were less than 0.2 and 0.3 for the low and high flow rates respectively. These values lead to small sampling errors, even when isokinetic sampling conditions are not maintained. Mason experimentally determined that the collection efficiency should be on the order of 50% (22) Since the flow rate used by Mason was approxim.ately midway between the high and low flow rate in this study, the flow patterns should be approximately the same. The discrepancy between Mason's experimental values and the values predicted by the simulation probably can be accounted for as experimental error by Mason. It would be nearly impossible to obtain a 50% sampling error for an aerosol as small as the one used without extreme anisokinetic sampling conditions. Mason also found a 40% error when sampling at the angle associated with

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TABLE XXIX ASPIRATION COEFFICIENTS CALCULATED IN THE SIMULATION MODEL FOR THE LOW FLOW CONDITION 124 Point Sampling Velocity True Velocity from S-Type Pitot from 5 -Hole Pitot cp JTube (cm/sec) Tube (cm/ sec] Degrees Ci/Co % 1 2 3 4 5 6 7 8 949.3 743.2 241.1 ++ + 614.7 1351,6 1298.5 1229.0 1414 1436 + + + 1396 1326 1289 1231 61.0 1.9 97.0 70.3 6.0 142.0 63.9 2.3 100.5 53.0 1.0 86.5 47.0 0.99 90.1 46.4 1.0 90.7 Weighted Average 93.7

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125 TABLE XXX ASPIRATION COEFFICIENTS CALCULATED IN THE SIMULATION MODEL FOR THE HIGH FLOW CONDITION Sampling Velocity True Velocity from S-Type Pitot from 5-Hole Pitot (^ Point Tube (cm/sec) Tube (cm/sec) Degrees R Ci/Co% 1875 ISSl 1743 64.6 2.20 97.60 1974.7 1942 51.6 0.98 84.10 1974.7 1869 47.1 0.95 86.30 1755.4 1795 47.7 1.02 88.50 1 1078.3 2 1091.7 3 381.2 4 +++ 5 7SI.3 59.0 1.72 95.06 70.3 4.90 131.85 Weighted Average = 90.6

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126 the maximum Ap. From Figure 15 it is apparent that by splitting the difference between the angles where the velocity pressure drops off rapidly, it should be possible to get within 20 degrees of the zero yaw angle. This means that the sample velocity measured by the S-type pitot tube will be approximately the same as the true total velocity and therefore, the sampling error should be no greater than the cosine of 20 degrees or 0.94. This would represent the maximum error for a very large aerosol and would be much less for the aerosol used in the study. Since Mason's sampling error is almost ten times as high as the theoretical maximum, it must be attributed to some flaw in the experi.mental setup. In order to see how much greater the error would be for larger particles, a similar analysis was performed using a distribution with a 10 ym mass mean diameter and 2.5 geometric standard deviation (see Figure 411. This was the distribution obtained at the outlet of a cyclone in a hot-mix asphalt plant (45). Because of the larger diameter particles the sampling efficiency was reduced to 0.799 for the high flow condition. The volumetric flow rates determined from the S-type pitot tube measurements are compared with the flow rates calculated from five-hole pitot tube measurements in Table XXXI. The axial flow rates using the five-hole pitot tube data are cal culated by multiplying the average axial velocity by the inner duct area minus the core area. The flow rates using the S-type pitot tube data were determined using two different methods varying in how the negative velocity at port four is handled. iw-... • >Saiei. ^--

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128 In the first method, the negative velocity is not used to determine the average axial velocity. The volumetric flow rate is calculated by multiplying the average axial velocity by 7/8th of inner cross sectional area. In the second method, the negative value is used in the determination of the average velocity and the entire inner duct area is used to determine the flow rate. The results presented in Table XXX, show that the insensitivity of the S-type pitot tube to yaw angle produces a higher calculated flow rate by approximately 28%. By incorporating the negative velocity in the average velocity determination, this error is reduced to 17%. It should be noted that the S-type pitot tube data fit very well what would be expected from looking at the sensitivity of the pitot tube to yaw angle [Figure 15). When the traverse point had a yaw angle less than approximately 45 degrees, the S-type pitot tube readings were very close to the total velocity. However, beyond angles of 45 degrees the pitot tube readings drop off quite rapidly and at 70 degrees, the nitot tube was reading a value of less than one fifth of the true value. The errors for both sampling efficiency and flow rate determination are presented in Table XXXI for the three simulated conditions. The sampling errors and flow rate errors are in opposite direction so that when the two values are combined to determine emission rate, the overall effect is reduced.

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CHAPTER VI SUNMARY AND RECOf-MENDATIONS A. Suiiimarv Results o£ experiments in this study liave led to a better understanding of the types and magnitude of errors that are involved when attempting to obtain a representative sample of particulate matter from gas streams with complex flow patterns. The errors induced by tangential flow were analyzed from two separate approaches. The first involved analysis of particle sampling error as a function of particle characteristics, sampling velocity relative to the flow stream velocity, and angle of the nozzle relative to the direction of flow. The second involved analysis of swirling flow patterns and their subsequent effect on flow measurements made by the S-type pitot tube. Particle sampling errors as a function of velocity ratio and angle of misalignment were studied by taking comparative anisokinetic and isokinetic samples from a straight section of duct. By analyzing the problem in this method the data obtained are more useful and have many more applications beyond this study. They provide fundamental information for a better understanding of the inertial effects in aerosol sampling. The flow measurement errors were analyzed by mapping the exact flow pattern at the exit of a cyclone using a five-hole pitot tube. Cross sectional profiles were measured at five axial distances along the stack to determine how the flow pattern changes as it moves up the stack. S-type pitot tube measurements were taken and compared to the results of the five-hole pitot tube measurements. 129

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150 The two aspects of this study, anisokinetic sampling errors and flow measurements, were combined in a simulation model to determine the magnitude of errors when an EPA Method 5 emission test is performed at the exit of a cyclone. A summary of the important results determined from this study is as follows: A. The flow patterns found in a stack following the exit of a small industrial cyclone are of such a nature that it makes it extremely difficult to obtain a representative sample with the present EPA recommended equipm.ent. Angles in excess of 70 degrees relative to the stack axis are found in some parts of the flow. Since large scale turbulence, such as swirling flow, is inherently self-preserving in round ducts, it decays very slowly as it moves up the stack and therefore sampling at any location downstream of the cyclone will involve the same problems. B. The yaw characteristics of the S-type pitot tube lead to several types of errors when used in a tangential flow stream. When the angle of yaw is less than 45 degrees, the measured velocity is greater than or equal to the actual velocity with the maximum error being approximately 5%. Beyond 45 degrees the measured velocity drops off quite rapidly and at an angle of 70 degrees the measured velocity is less than half the true velocity. Because of its yaw characteristics, the S-type pitot tube is not suitable for distinguishing the axial component of flow from the total flow which includes the tangential component. Volumetric flow calculations based on S-type pitot tube measurements in a swirling flow were found to be in excess of the actual flow by as m.uch as 50„.

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131 C. Pitot tubes based on the five-hole and three-hole designs are useful tools in determining the velocity components in a tangential flow field. The five-hole pitot tube has the advantage of giving pitch information as well as the yaw angle. However, in a cyclonic flow stream, the yaw angle is of m.uch greater magnitude than the pitch angle and therefore, the pitch angle can be ignored with small error. In the situation modeled, if pitch angle were ignored, the calculated flow rate would be in error by less than 6%. D. The particle sampling errors due to anisokinetic sampling velocity and nozzle misalignment were analyzed and a model was developed to describe the sampling efficiency as a function of velocity ratio (R) misalignment angle [6], particle diameter, particle velocity, and nozzle diameter. It was found that the maximum error for R = 1, approached (1 cose). When both a nozzle misalignment and anisokinetic sampling velocities are involved then the maximum error approaches \l Rcos9|. The equations and their limiting conditions for predicting the aspiration coefficient are summarized in Table XXXII. E. The Stokes number adequately describes the inertial characteristics of particle sampling. However, when the nozzle is misaligned to the flow stream, there is an apparent change in the inertial properties which is due to a reduced projected nozzle diameter. A correction factor was developed to adjust the Stokes number to take this into account. F. When the probe wash was analyzed separately from the filter, it was found that as much as 60% of the total particulate matter enterin-

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152 M C < to ^: r-j lO LT) t^/ ^' C^I LO CM V ^ o O o o V Si; ^ V C-, O) V 1 a-. ^ II c: — Ci II -H vl i^ r—i DC V i^ V CD V n3 V CD M CD — 1 V 1 CD 1 — i to — 1 o 1 — 1 c L/V ci vl rt f-H LT. V rt c CN o o c: (3 c ^' 1:^ I — I 'O + X l-i X b~ X u < fc a. O v-i IX, O >: $ m o •H II < CD PC :!; lea CQ II < o CM ^^ — 1 Lrt I CQ CD o CD — '^ h — V m 1 — 1 O ci o t O o d; c; u; — — "^ — i>0 11 ci ca .CD o II s II ^l II a: LT) LO II

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15: the nozzle was collected on the nozzle walls. This has implications not only on the importance of using the probe wash in the analysis, but more importantly it implies that there may be possible problems in obtaining accurate particle size data using a device such as an impactor. If the collection of particles in the nozzle is particle size dependent, then losses in the probe could lead to particle sizing errors. G. A simulation model was developed which incorporates the information obtained in this study on particle sampling errors and the flow mapping data. The particle sampling efficiency in a tangential flow stream was, as expected, a function of particle size. For a particle distribution with a mass mean diameter [MMD) of 3.0 ym and a geometric standard deviation of 2.15, the sampling errors predicted were less than 10%. For a larger distribution with a mass mean diameter of 10.0 ym and geometric standard deviation of 2.3, a 20% sampling error was predicted. One of the reasons that the sampling errors were as small as these were, is that the two mechanisms inducing sampling bias produce errors in opposite directions. The misalignment of the nozzle caused by the tangential velocity component leads to a reduction of sample concentration. The reduced sampling velocity, calculated from S-type pitot tube measurements, leads to subisokinetic sampling and an increased sample concentration. When these two mechanism.s are combined, the total error is reduced somewhat depending upon the magnitude of the two errors.

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134 B. Recomm endatio ns EPA recommends that if the average angle of the flow relative to the axis of the stack is greater than 10 degrees, then EPA Method 5 should not be performed. Since the maximum error in particle sampling has been found to be (1 RcosO) the 10 degree requirement is unduly restrictive and a 20 degree limitation would be more appropriate. For a 20 degree angle, the velocity measured by the S-type pitot tube would be approximately the same as the true velocity (i.e., R = 1] Therefore, the maximum error would be (1 cos 20) or 6% for a very large aerosol. When cyclonic flow does not exist in a stack, EPA recommends either straightening the flow or moving to another location. Because of the physical limitations of these suggestions, a better approach would be to modify Method 5 so that it could be used in a tangential flow stream. By replacing the S-type pitot tube with a three-hole pitot tube, the direction of the flow could be accurately determined for aligning the nozzle, and the velocity components could be measured for a correct calculation of volumetric flow rate. In addition to the three-hole pitot tube, the modification would have to include a protractor to measure the flow angle, an extra manometer, and a method of rotating the probe without rotating the entire impinger box.

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REFERENCES 1. Standards o£ Performance for New Stationary Sources. Federal Register, 36(247} :24876, 1971. 2. Revision to Reference Method 1-8. Federal Register, 42(160) :41754 1977. 3. Wilcox, J. D. Isokinetic Flow and Sampling of Airborne Particulates. Artificial Stimulation of Rain. Pergamon Press, New York, 1957, p. 177. 4. Lapple, C. E. and C. G. Shepherd. Calculation of Particle Trajectories. Ind. Eng. Chem. 32(5) :605, 1940. 5. Watson, 11. H. Errors Due to Anisokinetic Sampling of Aerosols. Amer. Ind. Hyg. Assoc. Quart., 15(1) :21, 1954. 6. Dennis, R. W. R. Samples, D. M. Anderson and L. Silverman. Isokinetic Sampling Probes. Ind. Eng. Chem., 49(21:294, 1957. 7. Hemeon, W. C. L. and G. F. Haines, Jr. The Magnitude of Errors in Stack Dust Sampling. Air Repair, 4(3):159, 1954. 8. Whiteley, A. B. and L. E. Reed. The Effect of Probe Shape on the Accuracy of Sampling Flue Gases for Dust Content. J. Inst. Fuel, 32:316, 1959. 9. Lundgren, D. A. and S. Calvert. Aerosol Sampling with a Side Port Probe. Amer. Ind. Hyg. Assoc. J., 28(3) :208, 1967. 10. Badzioch, 8. Collection of Gas-Borne Dust Particles by Means of an Aspirated Sampling Nozzle. Brit. J. Appl. Phys 10:26, 1959. 11. Fuchs, N. A. The Mechanics of Aerosols. The Macmillan Co., New York, 1964, p. 73. 12. Belyaev, S. P. and L. M. Levin. Investigation of Aerosol Aspiration by Photographing Particle Tracks Under Flash Illumination. J. Aerosol Sci., 5:127, 1972. 13. Belyaev, S. P. and L. M. Levin. Techniques for Collection of Representative Aerosol Samples. J. Aerosol Sci., 5:325, 1974. 135

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156 14. Davies, C. N. The Entry of Aerosols into Sampling Tubes and Heads. Brit. J. Appl. Phys., Ser. 2, 1:921, 1970. 15. Martone, J. A. Sampling of Submicrometer Particles Suspended in Near Sonic and Supersonic Free Jets of Air. Presented at the Annual Meeting of the Air Pollution Control Association, Toronto, Canada, 1977. 16. Sehmel, G. Particle Sampling Bias Introduced by Anisokinetic Sampling and Deposition within the Sampling Lines. Amer. Ind. Hyg. Assoc. J., 31(6) :758, 1970. 17. Glauberman, II. The Directional Dependence of Air Samplers. Amer. Ind. Hyg. Assoc. J., 25(3). -235, 1962. 18. Raynor, G. S. Variation in Entrance Efficiency of a Filter Sampler with Air Speed, Flow Rate, Angle and Particle Size. ,Amer. Ind. Hyg. Assoc. J., 31(5) :294, 1970. 19. Fuchs, N. A. Sampling of Aerosols. Atmos Envir., 9:697, 1975. 20. Laktionov, A. G. Aspiration of an Aerosol into a Vertical Tube from a Flow Transverse to It. AD-760 947, Foreign Technology Division, WrightPatterson Air Force Base, Ohio, 1973. 21. Vitols, V. Theoretical Limits of Errors Due to Anisokinetic Sampling of Particulate Matter. J. Air Pollut. Control Assoc, 16(2) :79, 1960. 22. Mason, K. W. Location of the Sampling Nozzle in Tangential Flow. M. S. Thesis, University of Florida, Gainesville, Florida, 1974. 23. Baker, D. W. and C. L. Sayre. Decay of Swirling Turbulent Flow of Incompressible Fluids in Long Pipes. Flow: Its Measurement and Control in Science and Industry, Volume 1, Part 1, Flow Characteristics. Instrument Society of America, Pittsburgh, 1974, p. 301. 24. Chigier, N. A. Velocity Measurement in Vortex Flows. Flow: Its Measurement and Control in Science and Industry, Volume 1, Part I, Flow Characteristics. Instrument Society of America, Pittsburgh, 1974, p. 399. 25. Hanson, H. A. and D. P. Saari. Effective Sampling Techniques for Particulate Emissions from Atypical Stationary Sources. EPA-600/2-77-056 U.S. Environmental Protection Agency, Research Triangle Park, N.C., 1977. 26. Brooks, E. F. and R. L. Williams. Process Stream Volumetric Flow Measurement and Gas Sample Extraction Methodology. TRW Document No. 24916-602SRU-00, TRW Systems Group, Redondo Beach, California, 1975. W|4"-^ >— .^^^l^iHl •-

PAGE 152

137 27. Grove, D. J. and W. S. Smith. Pitot Tube Errors Due to Misalignment and Nonstreamlined Flow. Stack Sampling News, November, 1973. 28. Hanson, H. A., R. J. Davini, J. K. Morgan and A. A. Iversen. Particulate Sampling Strategies for Large Power Plants Including Nonuniform Flow. EPA-600/2-75-170, U. S. Environmental Protection Agency, Research Triangle Park, N.C. 1976, 349 pp. 29. Williams, F. C. and F. R. DeJarnette. A Study on the Accuracy of Type S Pitot Tube. EPA 600/4-77-030, U. S. Environmental Protection Agency, Research Triangle Park, N.C, 1977. 30. Lea, J. F. and D. C. Price. Mean Velocity Measurements in Swirling Flow in a Pipe. Flow: Its Measurement and Control in Science and Industry, Volume 1, Part 1, Flow Characteristics. Instrument Society of America, Pittsburgh, 1974, p. 313. 31. Green, H. L. and W. R. Lane. Particulate Clouds: Dusts, Smokes and Mists. E. F. M. Spon. Ltd., London, 1957, p. 36. 32. Air Pollution Manual. Part II Control Equipment. Amer. Ind. Hyg. Assoc, Detroit, 1968, p. 4. 33. IVhitby, K. T., D. A. Lundgren and C. M. Peterson. Homogeneous Aerosol Generators. J. Air and Water Poll., 9:263, 1965. 34. Perry, J. K. Chemical Engineers' Handbook, McGraw-Hill, New York, 1941. 35. Flowmeter Computation Handbook. Amer. Soc. Mech. Eng., New York, 1961. 36. Fluid Meters, Their Theory and Application. H. S. Bean, Ed., y\mer. Soc. Mech. Eng., New York, 1971. 37. Doebelin, E. 0. Measurement Systems, Application and Design. McGrawHill, New York, 1975. 38. Smith, F. H. The Effects of Nozzle Design and Sampling Techniques on Aerosol Measurements. EPA-650/2-74-070 U. S. Environmental Protection Agency, Washington, D. C. 1974, 89 pp. 39. Manual of Fluorometric Clinical Procedures. G. K. Turner Association, Palo Alto, California, 1971. 40. American Institute of Physics Handbook. D. E. Gray, Ed., McGraw-Hill, New York, 1957.

PAGE 153

15S 41. Sehmel, G. A. The Density of Uranine Particles Produced by a Spinning Disc Aerosol Generator. Amer. Ind. Hyg. Assoc. J., 28C5):491, 1967. 42. Source Sampling Workbook. Control Programs Development Division, Air Pollution Training Institute, Research Triangle Park, N. C., 1975. 43. Danielson, J. A. Air Pollution Engineering Manual, Environmental Protection Agency, OAQPS AP40, l^esearch Triangle Park, N. C., 1973.

PAGE 154

BIOGRAPHICAL SKETCH Michael Durham v\(as born on December 11, 1949, in Key West, Florida. Being a member of a Navy family, he was constantly on the move and attended eight different grade schools and two high schools in Hawaii, Virginia, California and Kentucky. He studied two years at Texas Af,M University and tlien two at the Pennsylvania State University where he received a B.S. in Aerospace Engineering in 1971. His next three years were spent working with tlie National Academy of Science and the American Psychological Association in Washington, D.C. In September 1974 l:e began his graduate education in Environmental Engineering Sciences at the University of Florida. After receiving a Master of Engineering in August of 1975, he stayed on at the university as a graduate research assistant in pursuit of a Ph.D. for three years, the result of which is this dissertation. 139

PAGE 155

I certify that I have read this study and that in my opinion it conforms to acceptable standards of scholarly presentation and is fully adequate, in scope and quality, as a dissertation for the degree of Doctor of Philosophy. ^yU-neig^yU -^ Dale A. Lundgren, Chairrnrm Professor of Environmental Engineering Sciences I certify that I have read this study and that in my opinion it conforms to acceptable standards of scholarly presentation and is fully adequate, in scope and quality, as a dissertation for the degree of Doctor of Philosophy. '^'7 (^.(^ -c^C„ Paul Urone Professor of Environmental Engineering Sciences I certify that I have read this study and that in my opinion it conforms to acceptable standards of scholarly presentation and is fully adequate, in scope and quality, as a dissertation for the degree of Doctor of Philosophy. '^-V^ ^1 L \ Wayne /C. Huber Professor of Environmental Engineering Sciences I certify that I have read this study and that in my opinion it conforms to acceptable standards of scholarly presentation and is fully adequate, in scope and quality, as a dissertation for the degree of Doctor of Philosophy. ') /i-ry oicc.;. Alex E. Green Graduate Research Professor of Physics and Nuclear Engineering Sciences

PAGE 156

This dissertation was submitted to the Graduate Faculty of the College of Engineering and to the Graduate Council, and was accepted as partial fulfillment of the requirements for the degree of Doctor of Philosophy. Auaust, 197{ lUua. /f. -.&, Dean^ College of Engineering Dean, Graduate School


TABLE VI
TYPICAL VELOCITY TRAVERSE IN THE EXPERIMENTAL SAMPLING SYSTEM
(9.58 cm I.D. Duct)
Horizontal Vertical
Point
d/D
AP, cm Ho0
V, cm/sec
AP, cm H-O
<
o
3^
1
0.044
1.27
1454
1.57
1618
2
0.146
1.83
1743
2.11
1871
3
0.296
2.03
1S38
2.08
1859
4
0.704
2.13
1884
2.11
1871
5
0.854
1.88
1768
1.98
1813
6
0.956
1.47
1564
1.52
1591
Average Velocities (cm/sec)
From Pitot Tube Readings From Orifice AP
1740
1658


34
CONCENTRATION AT /
TABLE II
V POINT FOR DIFFERENT SAMPLING ANGLES
Nozzle Angle
Measured Concentration
(grains/dscf)
0
0.243
30
0.296
60
0.332
90
0.316


LIST OF TABLES--continued
Table Page
XXIX ASPIRATION COEFFICIENTS CALCULATED IN THE SIMULATION
MODEL FOR THE LOW FLOW CONDITION 124
XXX ASPIRATION COEFFICIENTS CALCULATED IN THE SIMULATION
MODEL FOR THE HIGH FLOW CONDITION 125
XXXI RESULTS OF THE CYCLONE OUTLET SIMULATION MODEL FOR THREE
CONDITIONS 127
XXXII SUMMARY OF EQUATIONS PREDICTING PARTICLE SAMPLING BIAS 128
vii


Abstract of Dissertation Presented to the Graduate Council
of the University of Florida in Partial Fulfillment of the
Requirements for the Degree of Doctor of Philosophy
ISOKINETIC SAMPLING OF AEROSOLS FROM TANGENTIAL FLOW STREAMS
By
Michael D. Durham
August, 1978
Chairman: Dale A. Lundgren
Major Department: Environmental Engineering Sciences
A comprehensive analysis of inertial effects in aerosol sampling was
combined with a thorough study of swirling flow patterns in a stack fol
lowing the exit of a cyclone in order to determine the errors involved in
sampling particulate matter from a tangential flow stream. Two simultaneous
samples, one isokinetic and the other anisokinetic, were taken from a 10 cm
wind tunnel and compared to determine sampling bias as a function of Stokes
number. Monodispersed uranine particles, 1 to 11 ym in diameter, generated
with a spinning disc aerosol generator, and mechanically dispersed 19.9 ym
ragween pollen were used as experimental aerosols. The duct velocity was
varied from 550 to 3600 cm/sec and two nozzle diameters of 0.465 and 0.683
cm were used to obtain values of Stokes numbers from 0.007 to 2.97. Experi
ments were performed at four angles, 0, 30, 60 and 90 degrees, to determine
the errors encountered when sampling with an isokinetic sampling velocity
but with the nozzle misaligned with the flow stream. The sampling bias ap
proached a theoretical limit of (l-cos0) at a value of Stokes number between
xiii


37
since it has large diameter pressure ports that will not plug (see
Figure 14). Besides the large pressure ports it has an additional
advantage of producing approximately a 20% higher differential pressure
than the standard pitot tube for a given velocity. However, although
the S-type pitot tube will give an accurate velocity measurement, it is
somewhat insensitive to the direction of the flow (25-29) Figures 15
and 16 show the velocity errors for yaw and pitch angles. Although the
S-type pitot tube is very sensitive to pitch direction, the curve for
yaw angle is symmetrical and somewhat flat for an angle of 45 degrees
in either direction. Because of this insensitivity to direction of flow
in the yaw direction, the S-type pitot tube cannot be used in a tangential
flow situation to align the nozzle to the direction of the flow, or to
accurately measure the velocity in a particular direction.
The velocity in a rotational flow field can be broken up into three
components in the axial, radial and tangential directions (see Figure 11).
The magnitude of the radial and tangential components relative to the
axial component will determine the degree of error induced by the tangential
flow. Neither the radial nor the tangential components of velocity affect
the flow rate through the stack, but both affect the velocity measurement
made by the S-type pitot tube because it lacks directional sensitivity.
If the maximum velocity head were used to calculate the stack velocity,
the resultant calculated flow rates and emission levels could be off by
as much as a factor of l/cos will reduce but not eliminate this error because part of the radial and
tangential velocity components will still be detected by the pitot tube.


71
Figures 26, 27 and 28 represent the sampling efficiency as a
function of Stokes number for 30, 60 and 90 degrees respectively.
The experimental data used in these plots are presented in Tables X,
XI and XII. From these tables it can be seen that the variables of
particle diameter and velocity and nozzle diameter were varied rather
randomly. This was done to check the legitimacy of using Stokes number
as the principle independent variable. From the shape of the curves in
Figures 26-28, it can be seen that the aspiration coefficient is indeed
a function primarily of Stokes number.
The curves for 30, 60 and 90 degrees are all similar in shape
except for the values of Stokes number where they approach their
theoretical limit. As the angle of misalignment increases, the more
rapidly the aspiration coefficient reaches its maximum error. This
can be accounted for as an apparent change in nozzle diameter, because
it is the only parameter in the Stokes number that is affected by the
nozzle angle to the flow stream. As described before, the nozzle
diameter is important because it determines the amount of time available
for the particle to change directions (approximately 6 D^/V ). As the
nozzle is tilted at an angle to the flow stream, the projected frontal
area and therefore the projected nozzle diameter are reduced proportional
to the angle. Therefore, as the angle of misalignment increases, the
time available for the particle to change direction decreases leading to
increased sampling error for a given value of K. To normalize these
curves for angle to the flow stream, it is necessary to define an "adjusted
Stokes number" (K'j which takes into account the change in projected


LIST OF FIGURES--continued
Figure Page
17a Conical version of a five-hole pitot tube 42
17b Fecheimer type three-hole pitot tube 42
18 Five-hole pitot tube sensitivity to yaw angle 44
19 Fecheimer pitot tube sensitivity to yaw angle 45
20 Experimental set up 49
21 Sampling system 50
22 Typical velocity profile in experimental test section.... 56
23 Experimental system for measuring cross sectional flow
patterns in a swirling flow stream 61
24 Cyclone used in the study to generate swirling flow 62
25 Photograph of the 3-dimensional pitot with its traversing
unit. Insert shows the location of the pressure taps.... 63
26 Sampling efficiency vs. Stokes number at 30 misalignment
for R = 1 72
27 Sampling efficiency vs. Stokes number at 60 misalignment
for R = 1 73
28 Sampling efficiency vs. Stokes number at 90 misalignment
for R ="l 74
29 Stokes number at which 95% maximum error occurs vs.
misalignment angle 83
30 B' vs. adjusted Stokes number for 30, 60 and 90 degrees.. 85
31 Aspiration coefficient vs. Stokes number model predic
tion and experimental data for 30, 60 and 90 degrees 87
32 Predicted aspiration coefficient vs. Stokes number for
15, 30, 45, 60, 75 and 90 degrees 88
lx


Aspiration Coefficient (A)
Figure 31. Aspiration coefficient vs. Stokes number model prediction and experimental data
for 30, 60 and 90 degrees.


Figure 5 Relationship between the concentration ratio and the
velocity ratio for several size particles [from Watson (5)] .


ISOKINETIC SAMPLING OF AEROSOLS FROM
TANGENTIAL FLOW STREAMS
By
Michael Dean Durham
A DISSERTATION PRESENTED TO THE GRADUATE COUNCIL OF
THE UNIVERSITY OF FLORIDA
IN PARTIAL FULFILLMENT OF THE REQUIREMENTS FOR THE
DEGREE OF DOCTOR OF PHILOSOPHY
UNIVERSITY OF FLORIDA

ACKNOWLEDGEMENTS
This research was partially supported by a grant (Grant Number
R802692-01) from the Environmental Protection Agency (EPA)-, and was
monitored by EPA's Project Officer Kenneth T. Knapp. I thank them
both for their financial support during my graduate work.
I wish to thank Dr. Dale Lundgren and Dr. Paul Urone for the
important part that they played in my education. I am especially
appreciative of Dr. Lundgren for his guidance, encouragement and
confidence. He has provided me with opportunities for classroom,
laboratory and field experience that were far beyond what is expected
of a committee chairman.
I would like to thank Mrs. Kathy Sheridan for her assistance in
preparing this manuscript.
Finally, I wish to thank my parents for their advice and encourage
ment, and my wife Ellie for helping me through the difficult times.
11

TABLE OF CONTENTS
Page
ACKNOWLEDGEMENTS
LIST OF TABLES v
LIST OF FIGURES vi'ii
LIST OF SYMBOLS xi
ABSTRACT xiii
CHAPTER
I INTRODUCTION AND ISOKINETIC SAMPLING THEORY 1
A. Introduction 1
B. Isokinetic Sampling Theory 2
II REVIEW OF THE PERTINENT LITERATURE 10
A. Summary of the Literature on Anisokinetic Sampling... 10
1. Sampling Bias Due to Unmatched Velocities 10
2. Sampling Bias Due to Nozzle Misalignment 17
B. Summary of the Literature on Tangential Flow 23
1. Causes and Characteristics of Tangential Flow 23
2. Errors Induced by Tangential Flow 31
3. Errors Due to the S-Type Pitot Tube 35
4. Methods Available for Measuring Velocity
Components in a Tangential Flow Field 41
5. EPA Criteria for Sampling Cyclonic Flow 43
III EXPERIMENTAL APPARATUS AND METHODS 48
A. Experimental Design 48
B. Aerosol Generation 51
1. Spinning Disc Generator 51
2. Ragweed Pollen 53
C. Velocity Determination 53
D. Selection of Sampling Locations 57
E. Sampling Nozzles 57
iii

TABLE OF CONTENTS--continued
CHAPTER Page
F. Analysis Procedure 58
1. For Uranine Particles 58
2. For Ragweed Pollen 58
G. Sampling Procedure 59
H. Tangential Flow Mapping 60
IV RESULTS AND ANALYSIS 65
A. Aerosol Sampling Experiments 65
1. Stokes Number 65
2. Sampling with Parallel Nozzles 66
3. Analysis of Probe Wash 66
4. The Effect of Angle Misalignment on Sampling
Efficiencies 69
5. The Effect of Nozzle Misalignment and Anisokinetic
Sampling Velocity 89
B. Tangential Flow Mapping 102
V SIMULATION OF AN EPA METHOD 5 EMISSION TEST IN A TANGENTIAL
FLOW STREAM 117
VI SUMMARY AND RECOMMENDATIONS 129
A. Summary 129
B. Recommendations 134
REFERENCES 135
BIOGRAPHICAL SKETCH 139
iv

LIST OF TABLES
Table Page
I FLOW RATE DETERMINED AT VARIOUS MEASUREMENT LOCATIONS 33
II CONCENTRATION AT A POINT FOR DIFFERENT SAMPLING ANGLES 34
III EMISSION TEST RESULTS 36
IV SIZES AND DESCRIPTIONS OF EXPERIMENTAL AEROSOLS 52
V TABLE OF OBTAINABLE VELOCITIES IN 10 cm DUCT... 54
VI TYPICAL VELOCITY TRAVERSE IN THE EXPERIMENTAL SAMPLING
SYSTEM 55
VII RESULTS OF SAMPLING WITH TWO PARALLEL NOZZLES 67
VIII PERCENT OF PARTICULATE MATTER COLLECTED IN THE PROBE WASH
FOR NOZZLES PARALLEL WITH THE FLOW STREAM 68
IX PERCENT OF PARTICULATE MATTER COLLECTED IN THE PROBE WASH
FOR NOZZLES AT AN ANGLE OF 60 DEGREES WITH THE FLOW STREAM. 70
X ASPIRATION COEFFICIENT AS A FUNCTION OF STOKES NUMBER FOR
30 DEGREE MISALIGNMENT 75
XI ASPIRATION COEFFICIENT AS A FUNCTION OF STOKES NUMBER FOR
60 DEGREE MISALIGNMENT 77
XII ASPIRATION COEFFICIENT AS A FUNCTION OF STOKES NUMBER FOR
90 DEGREE MISALIGNMENT 80
XIII COMPARISON OF SAMPLING EFFICIENCY RESULTS WITH THOSE OF
BELYAEV AND LEVIN FOR 0 = 0, R = 2.3 AND R = 0.5 92
XIV ASPIRATION COEFFICIENT AS A FUNCTION OF STOKES NUMBER FOR
R = 2, 6 = 60 94
v

LIST OF TABLES--continued
Table Page
XV ASPIRATION COEFFICIENT AS A FUNCTION OF STOKES NUMBER
FOR R = 0.5, 0 = 60 95
XVI ASPIRATION COEFFICIENT AS A FUNCTION OF STOKES NUMBER
FOR 6 = 45, R = 2.0 AND 0.5 97
XVII ASPIRATION COEFFICIENT AS A FUNCTION OF STOKES NUMBER
FOR R = 2, 0 30 98
XVIII ASPIRATION COEFFICIENT AS A FUNCTION OF STOKES NUMBER
FOR R = 2.1, 0 = 90 101
XIX LOCATION OF SAMPLING POINTS 103
XX FIVE-HOLE PITOT TUBE MEASUREMENTS MADE AT 1 DIAMETER
DOWNSTREAM OF THE CYCLONE 106
XXI FIVE-HOLE PITOT TUBE MEASUREMENTS MADE AT 2 DIAMETERS
DOWNSTREAM OF THE CYCLONE 107
XXII FIVE-HOLE PITOT TUBE MEASUREMENTS FADE AT 4 DIAMETERS
DOWNSTREAM OF THE CYCLONE 108
XXIII FIVE-HOLE PITOT TUBE MEASUREMENTS NADE AT 8 DIAMETERS
DOWNSTREAM OF THE CYCLONE 109
XXIV FIVE-HOLE PITOT TUBE MEASUREMENTS MADE AT 16 DIAMETERS
DOWNSTREAM OF THE CYCLONE 110
XXV AVERAGE CROSS SECTIONAL VALUES AS A FUNCTION OF DISTANCE
DOWNSTREAM AND FLOW RATE 112
XXVI S-TYPE PITOT TUBE MEASUREMENTS NADE AT THE 8-D SAMPLING
PORT FOR THE LOW FLOW CONDITION 118
XXVII S-TYPE PITOT TUBE MEASUREMENTS NADE AT THE 8-DSAMPLING PORT
FOR THE HIGH FLOW CONDITION 119
XXVIII MIDPOINT PARTICLE DIAMETERS FOR THE 10 PERCENT INTERVALS
OF THE MASS DISTRIBUTION MMD = 3pm a =2.13 121
cr
o
VI

LIST OF TABLES--continued
Table Page
XXIX ASPIRATION COEFFICIENTS CALCULATED IN THE SIMULATION
MODEL FOR THE LOW FLOW CONDITION 124
XXX ASPIRATION COEFFICIENTS CALCULATED IN THE SIMULATION
MODEL FOR THE HIGH FLOW CONDITION 125
XXXI RESULTS OF THE CYCLONE OUTLET SIMULATION MODEL FOR THREE
CONDITIONS 127
XXXII SUMMARY OF EQUATIONS PREDICTING PARTICLE SAMPLING BIAS 128
vii

LIST OF FIGURES
Figure Page
1 Isokinetic sampling 3
2 Superisokinetic sampling 4
3 Subisokinetic sampling 6
4 The effect of nozzle misalignment with flow stream 7
5 Relationship between the concentration ratio and the
velocity ratio for several size particles.... 11
6 Sampling efficiency as a function of Stokes number and
velocity ratio 16
7 Error due to misalignment of probe to flow stream 18
8 Sampling bias due to nozzle misalignment and anisokinetic
sampling velocity 21
9 Tangential flow induced by ducting 25
10 Double vortex flow induced by ducting 26
11 Velocity components in a swirling flow field 27
12 Cross sectional distribution of tangential velocity in a
swirling flow field 29
13 Cross sectional distribution of angular momentum in a
swirling flow field 30
14 S-type pitot tube with pitch and yaw angles defined 38
15 Velocity error vs. yaw angle for an S-type pitot tube.... 39
16 Velocity error vs. pitch angle for an S-type pitot tube.. 40
viii

LIST OF FIGURES--continued
Figure Page
17a Conical version of a five-hole pitot tube 42
17b Fecheimer type three-hole pitot tube 42
18 Five-hole pitot tube sensitivity to yaw angle 44
19 Fecheimer pitot tube sensitivity to yaw angle 45
20 Experimental set up 49
21 Sampling system 50
22 Typical velocity profile in experimental test section.... 56
23 Experimental system for measuring cross sectional flow
patterns in a swirling flow stream 61
24 Cyclone used in the study to generate swirling flow 62
25 Photograph of the 3-dimensional pitot with its traversing
unit. Insert shows the location of the pressure taps.... 63
26 Sampling efficiency vs. Stokes number at 30 misalignment
for R = 1 72
27 Sampling efficiency vs. Stokes number at 60 misalignment
for R = 1 73
28 Sampling efficiency vs. Stokes number at 90 misalignment
for R ="l 74
29 Stokes number at which 95% maximum error occurs vs.
misalignment angle 83
30 B' vs. adjusted Stokes number for 30, 60 and 90 degrees.. 85
31 Aspiration coefficient vs. Stokes number model predic
tion and experimental data for 30, 60 and 90 degrees 87
32 Predicted aspiration coefficient vs. Stokes number for
15, 30, 45, 60, 75 and 90 degrees 88
lx

LIST OF FIGURES--continued
Figure Page
33 Comparison of experimental data with results from Belyaev
and Levin 91
34 Sampling efficiency vs. Stokes number at 60 misalignment
for R = 2.0 and 0.5 96
35 Sampling efficiency vs. Stokes number at 45 misalignment
for R = 2.0 and R = 0.5 99
36 Sampling efficiency vs. Stokes number at 30 misalignment
for R = 2.0 100
37 Cross sectional view of a tangential flow stream locating
pitch and yaw directions, sampling points, and the nega
tive pressure region 105
38 Decay of the average angle 8 and the core area along the
axis of the duct 113
39 Decay of the tangential velocity component along the axis
of the duct 114
40 Location of the negative pressure region as a function of
distance downstream from the cyclone 116
41 Particle size distributions used in the simulation model... 120
x

SYMBOLS
- area of sampler inlet
'- projected area of sampler inlet
Aq area of stream tube approaching nozzle
A ratio of measured concentration to true concentration
C Cunningham correction factor
C. dust concentration in inlet
i
C dust concentration in flow stream
o
C
r concentration ratio of aerosol generating solution
- droplet diameter
D. inlet diameter
i
D particle diameter
P
K inertial impaction parameter
K' adjusted Stokes number
i stopping distance
L undisturbed distance upstream from nozzle
n constant
R ratio of free stream velocity to inlet velocity
s constant
Va axial component of stack velocity
V. velocity in inlet
- radial component of stack velocity
V free stream velocity
xi

V tangential component of stack velocity
3, 3', 3" functions determining whether particles will deviate from
streamlines
- particle density
D viscosity
angle of the flow stream with respect to the stack axis
6 angle of misalignment of nozzle with respect to the flow stream
T particle relaxation time
Ap pressure difference
XU

Abstract of Dissertation Presented to the Graduate Council
of the University of Florida in Partial Fulfillment of the
Requirements for the Degree of Doctor of Philosophy
ISOKINETIC SAMPLING OF AEROSOLS FROM TANGENTIAL FLOW STREAMS
By
Michael D. Durham
August, 1978
Chairman: Dale A. Lundgren
Major Department: Environmental Engineering Sciences
A comprehensive analysis of inertial effects in aerosol sampling was
combined with a thorough study of swirling flow patterns in a stack fol
lowing the exit of a cyclone in order to determine the errors involved in
sampling particulate matter from a tangential flow stream. Two simultaneous
samples, one isokinetic and the other anisokinetic, were taken from a 10 cm
wind tunnel and compared to determine sampling bias as a function of Stokes
number. Monodispersed uranine particles, 1 to 11 ym in diameter, generated
with a spinning disc aerosol generator, and mechanically dispersed 19.9 ym
ragween pollen were used as experimental aerosols. The duct velocity was
varied from 550 to 3600 cm/sec and two nozzle diameters of 0.465 and 0.683
cm were used to obtain values of Stokes numbers from 0.007 to 2.97. Experi
ments were performed at four angles, 0, 30, 60 and 90 degrees, to determine
the errors encountered when sampling with an isokinetic sampling velocity
but with the nozzle misaligned with the flow stream. The sampling bias ap
proached a theoretical limit of (l-cos0) at a value of Stokes number between
xiii

1 and 6 depending on the angle of misalignment. It was discovered that the
misalignment angle reduces the projected nozzle diameter and therefore ef
fects the Stokes number; a correction factor as a function of angle was
developed to adjust the Stokes number to account for this.
Using an equation empirically developed from these test results and
using the equations of Belyaev and Levin describing anisokinetic sampling
bias with zero misalignment, a mathematical model was developed and tested
which predicts the sampling error when both nozzle misalignment and aniso
kinetic sampling velocities occur simultaneously. It was found that the
sampling bias approached a maximum error |l-Rcos0¡ where R is the ratio of
the free stream velocity to the sampling velocity. During the testing, it
was discovered that as much as 60% of the particulate matter entering the
nozzle remained in the nozzle and front half of the filter holder. Implica
tions of this phenomenon with regard to particle sampling and analysis are
discussed.
The causes and characteristics of tangential flow streams are described
as they relate to problems in aerosol sampling. The limitations of the S-type
pitot tube when used in a swirling flow are discussed. A three dimensional or
five-hole pitot tube was used to map cross sectional and axial flow patterns
in a stack following the outlet of a cyclone. Angles as great as 70 degrees
relative to the axis of the stack and a reverse flow core area were found in
the stack.
Using information found in this study, a simulation model was developed
to determine the errors involved when making a Method 5 analysis in a tan
gential flow stream. For an aerosol with a 3.0 pm MMD (mass mean diameter)
xiv

and geometric standard deviation (a ) of 2.13, the predicted concentration
was 10% less than the true concentration. For an aerosol with a 10.0 pm HMD
and a a of 2.3, a 20% error was predicted. Flow rates determined by the
§
S-type pitot tube were from 20 to 30% greater than the actual flow rate.
Implications of these results are described and recommendations for modifica
tion of the Method 5 sampling train for use in a tangential flow stream are
described.
xv

CHAPTER I
INTRODUCTION AND ISOKINETIC SAMPLING THEORY
A. Introduction
This study deals with the problems of obtaining a representative
sample of particulate matter from a gas stream that does not flow
parallel to the axis of the stack as in the case of swirling or
tangential flow. This type of flow is commonly found in stacks and
could be the source of substantial sampling error. The causes and
characteristics of this particular flow pattern are described and
the errors encountered in particulate concentration and emission
rate determinations are thoroughly analyzed and discussed.
The analysis of sampling errors is approached from two directions
in this study. One approach involves an investigation of aerosol
sampling bias due to anisokinetic sampling velocities and misalignment
of the nozzle with respect to the flow stream as a function of particle
and flow characteristics. The second part of the study involves an
accurate mapping of the flow patterns in a tangential flow system.
The information obtained in the two parts of the study will be combined
to simulate the errors that would be encountered when making an EPA
Method 5 (1, 2) analysis in a tangential flow stream.
1

2
B. Isokinetic Sampling Theory
To obtain a representative sample of particulate matter from a
moving fluid, it is necessary to sample isokinetically. Isokinetic
sampling can be defined by two conditions: [3) 1) The suction or
nozzle velocity, must be equal to the free stream velocity, Vq;
and 2) the nozzle must be aligned parallel to the flow direction.
If these conditions are satisfied the frontal area of the nozzle, A.,
i
will be equal to the area of the cross section of the flow stream
entering the nozzle, Aq (see Figure 1). Thus, there will be no
divergence of streamlines either away from or into the nozzle, and
the particle concentration in the inlet, C., will be equal to the
particle concentration in the flow stream, C .
o
When divergence of streamlines is produced by superisokinetic
sampling, subisokinetic sampling or nozzle misalignment, there is a
possibility of particle size fractionation due to the inertial
properties of particles. In the case of superisokinetic sampling
(see Figure 2), the sampling velocity, V., is greater than the free
stream velocity, V Therefore, the area of the flow stream that is
o
sampled, A will be greater than the. frontal area of the sampling
nozzle, A^. All of the particles that lie in the projected area A^'
will enter into the nozzle. Particles outside this area but within A
o
will have to turn with the streamlines in order to be collected. Be
cause of their inertia, some of the larger particles will be unable to
make the turn and will not enter the sampling nozzle. Since not all of
the particles in the sampled area Aq will be collected, the measured
concentration will be less than the actual concentration.

V. = V A. = A
X O 1 o
Figure 1.
Isokinetic sampling .
C. = C
i o
04

1
o
Figure 2. Superisokinetic sampling.

5
Subisokinetic sampling defines the condition in which the sampling
velocity is less than the free stream velocity (see Figure 3). In this
situation the frontal area of the nozzle, ', is greater than the sam
pled area of the flow, A The volume of air lying within the projected
area, A^', but outside Aq will not be sampled and the streamlines will
diverge around the nozzle. However, some of the particles in this area,
because of their inertia, will be unable to negotiate the turn with the
streamlines and will be collected in the nozzle. Because some of the
particles outside the sampled area Aq will be collected along with all
of the particles within A the measured concentration will be greater
than the actual particle concentration.
The bias due to misalignment of the nozzle with the flow stream
is similar to that caused by superisokinetic sampling. When the nozzle
is at an angle to the flow stream (Figure 4), the projected area of the
nozzle is reduced by a factor equal to the cosine of the angle. Even
if the nozzle velocity is equal to the flow stream velocity, a reduced
concentration will be obtained because some of the larger particles
will be unable to make the turn into the nozzle with the streamlines.
Therefore, whenever the nozzle is misaligned, the concentration col
lected will always be less than or equal to the actual concentration.
For all three conditions of anisokinetic sampling (superisokinetic,
subisokinetic and nozzle misalignment), the magnitude of the measured
concentration error will depend upon the size of the particles. More
specifically it will depend upon particle inertia, which implies that
the velocity and density of the particle are also important. Particle


DIRECTION OF FLOW
Figure 4.
The effect of nozzle misalignment with flow stream.

8
inertia affects the ability of the particle to negotiate turns with
its streamline which determines the amount of error. Therefore, in
all cases greater sampling errors will occur for larger particles and
higher velocities.
Besides determining the direction of the sampling bias, it is
also possible to predict theoretically the minimum and maximum error
for a given condition. This can be done by considering what happens
when the inertia of the particles is very small (i.e., the particles
can negotiate any turn that the streamlines make) and what happens
when the inertia of particles is very large (i.e., the particles are
unable to negotiate any turn with the streamlines). In the former
case of very low inertia, it can easily be seen that since the particles
are very mobile they do not leave their streamlines and therefore there
will be no sampling bias. In this situation the concentration of
particulate matter may be accurately obtained regardless of sampling
velocity or whether the nozzle is aligned with the flow stream. There
fore, a minimum error of 0 is obtained for small inertia particles.
The maximum error that can theoretically occur in anisokinetic
sampling depends on both the velocity ratio R, where
R = V /V. (1)
0 1
and the misalignment angle 0.
In the case of unequal velocities for very high inertia particles
which are unable to negotiate any change of direction, only those
particles directly in front of the projected area of the nozzle, A^,
will enter the nozzle regardless of the sampling velocity. Therefore,

9
the concentration collected by the nozzle will be equal to the number
of particles entering the nozzle, A.V C divided by the volume of
10 0
air sampled, A^V^.
A.V C C V
p ioo_ oo
i A.V. = V.
(2)
li i
The ratio of the sampled concentration to the true concentration then
is equal to the inverse of the velocity ratio. Therefore, the maximum
sampling bias for the condition of unmatched velocities is equal to
V /V or R. For example, if the sampling velocity is twice the free
stream velocity, the resulting concentration will be one half the actual
concentration.
For the case of a misaligned nozzle, a similar analysis is applied.
For the particles with very large inertia, only those lying directly in
line with the projected frontal area of the nozzle will be collected.
The measured concentration would again be the number of particles col-
o i
lected in the nozzle, A^cos0CqV divided by the volume of air sampled,
A.V.. Therefore, the ratio of the measured to the true concentration
i i
would be Vqcos0/\V or Rcos6. This represents the maximum sampling
error for anisokinetic sampling.

CHAPTER II
REVIEW OF THE PERTINENT LITERATURE
A. Summary of the Literature on Anisokinetic Sampling
1. Sampling Bias Due to Unmatched Velocities
Numerous articles have been written describing the sources and
magnitude of errors when isokinetic conditions are not maintained.
In one of the earlier works, Lapple and Shepherd (4) studied the
trajectories of particles in a flow stream and presented a formula
for estimating the order of the magnitude of errors resulting when
there is a difference between the average sampling velocity and the
local free stream velocity. Watson (5) examined errors in the aniso
kinetic sampling of spherical particles of 4 and 32 pm mass mean
diameter (MMD) and found the relationships shown in Figure 5. Super-
isokinetic sampling (sampling with nozzle velocity greater than the
free stream velocity) leads to a concentration less than the actual
concentration, while subisokinetic sampling has the opposite effect.
Watson found that the magnitude of the error was not only a function
of particle size as seen in Figure 5, but also of the velocity and the
nozzle diameter. He proposed that the sampling efficiency was a function
of the dimensionless particle inertial parameter K (Stokes number)
defined as
? tV
K = Cp V D VlSnD. = 2- m
pop i 'J
10

Figure 5 Relationship between the concentration ratio and the
velocity ratio for several size particles [from Watson (5)] .

12
where
0^ = particle diameter
C = Cunningham correction for slippage
pp = particle density
T = p CD 2/18n [4)
p p
p = viscosity of gas
D. = nozzle diameter
i
The relaxation time is defined as x; it represents how quickly a particle
can change directions. Watson concluded that to obtain a concentration
correct within 10%, the velocity ratio R must lie between 0.86 and 1.13
for the 32 micron particles and between 0.5 and 2.0 for the 4 micron
particles.
Data obtained by Dennis et al. (6) on a suspension of Cottrell
precipitated fly ash, 14 pm MMD, showed only a 10% negative error in
calculated concentration for sampling velocities 60% greater than iso
kinetic. Tests run on an atmospheric dust of 0.5 pm MMD produced no
detectable concentration changes even while sampling at a 400% variation
from isokinetic flow, thus indicating that isokinetic sampling is
relatively unimportant for fine particles. Hemeon and Haines (7)
measured errors due to the anisokinetic sampling of particles in three
size ranges (5-25, 80-100, and 400-500 pm) and in a range of nozzle to
stack velocities of 0.2 to 2.0. They found that where the velocity
ratio R ranges from 0.6 to 2.0 the extreme potential error was ap
proximately 50%, and that deficient nozzle velocities resulted in greater
errors than excessive nozzle velocities. In addition, they found that
for the coarse particles, the velocity into the nozzle had no important

13
bearing on the quantity of dust collected. They suggested using the
product of the nozzle area and the stack gas velocity approaching the
nozzle as the gas sample volume, regardless of the velocity of the
nozzle. By using this method for particles greater than 80 pm, it
is possible to obtain small deviations even where departure from
isokinetic velocity is quite large. Whiteley and Reed (8) also observed
that calculating the dust concentrations from the approach velocity
instead of the actual sampling rate produced only slight errors when
sampling anisokinetically for large particles.
Lundgren and Calvert (9) found the sampling bias or aspiration
coefficient A, to be a function of the inertial impaction parameter K
and the velocity ratio R. They developed a chart which can be used
to predict inlet anisokinetic sampling bias depending on both K and R.
Badzioch's (10) equations defined the dependence of the efficiency upon
particle inertia and the velocity ratio. In a slightly different
terminology
A = C./Co = 1 + (R-l) 3(10 (5)
where f3(K) is a function of inertia given by
BOO [1-exp (-L/£)]/(L/£) (6)
£ is the stopping distance or the distance a particle with initial
velocity V will travel into a still fluid before coming to rest and
is defined by (11)
£ = tVo (7)

14
L is the distance upstream from the nozzle where the flow is undisturbed
by the downstream nozzle. It is a function of the nozzle diameter and
is given by the equation:
L = nDi (8)
It was observed that n lies between 5.2 and 6.8 (10).
Flash illumination photographic techniques were used by Belyaev and
Levin (12) to study particle aspiration. Photographic observations
enabled them to verify Badzioch's claim that L, the undisturbed distance
upstream of the nozzle, was between 5 to 6 times the diameter of the
nozzle. They examined the data of previous studies on error due to
anisokinetic sampling and concluded that the discrepancy between experi
mental data was due to the researchers failing to take into account
three things: 1) particle deposition in the inlet channel of the sampling
device; 2) rebound of particles from the front edge of the sampling noz
zle and their subsequent aspiration into the nozzle; and 3) the shape and
wall thickness of the nozzle. They also found that the sampling efficiency
was a function of the inner diameter of the nozzle, D., as well as K and R.
i
In a more recent article, Belyaev and Levin (13) examined the
dependence of the function B(K), in equation (4), on both the inertial
impaction parameter, K, and the velocity ratio, R. Previous authors (10,
14) had concluded that B(K) was a function of K alone, but Belyaev and
Levin obtained experimental data demonstrating that for thin-walled
nozzles, 3(K) was also a function of R. Equations were developed from
the data for values of K between 0.18 and 6.0 and for values of R between

15
0.16 and 5.5
3 (K, R) = 1 1/(1 +bK) (9)
where
b = 2 + 0.617/R (10)
Figure 6 shows a plot of equations (5), (9) and (10) for a range of
velocity ratios and Stokes numbers. The most significant changes in
the aspiration coefficient occur at values of K between 0 and 1.
Beyond K = 1, the aspiration coefficient tends to assymptotically ap
proach its theoretical limit of R. Beyond a Stokes number of about
6, it can be assumed that the aspiration coefficient equals R. This
can be predicted both from equations (5), (9) and (10) and from
theoretical considerations. Badzioch (10) and Belyaev and Levin (12)
have shown that the streamlines start to diverge at approximately 6
diameters upstream of the nozzle. Therefore, a particle traveling at
a velocity, V will have to change directions in an amount of time
equal to 6D^/Vo. If a particle cannot change direction in this amount
of time, it will not be able to make the turn with the streamline.
Since t represents the amount of time required for a particle to change
directions, setting x = 6D^/Vo represents the limiting size particle
that will be able to make a turn with its streamline. Rearranging these
terms it can be seen that this situation occurs when xV /D. = 6 or at a
o 1
Stokes number of 6.
Martone (15) further confirmed the importance considering free
stream velocity as well as particle diameter when sampling aerosols by

Sampling Efficiency
i

17
analyzing concentration errors obtained while sampling submicron
particles, 0.8 ym NMD and 1.28 geometric standard deviation, traveling
at near sonic and supersonic velocities. He obtained sample con
centrations 2-3 times greater than the true concentration when the
sampling velocity was 20% of the free stream velocity (R=5).
Sehmel (16) studied the isokinetic sampling of monodisperse
particles in a 2.81 inch ID duct and found that it is possible to obtain
a 20% concentration bias while sampling isokinetically with a small
diameter inlet probe. Results also showed that for all anisokinetic
sampling velocities, the concentration ratios were not simply cor
related with Stokes number.
2, Sampling Bias Due to Nozzle Misalignment
Sampling error associated with the nozzle misalignment has not
been adequately evaluated in past studies because the sampled flow
field was maintained or assumed constant in velocity and parallel to
the duct axis. The studies that have been performed on the effect of
probe misalignment do not provide enough quantitative information to
understand more than just the basic nature of the problem. Results
were produced through investigations by Mayhood and Langstroth, as
reported by Watson (5), on the effect of misalignment on the collection
efficiency of 4, 12 and 37 ym particles (see Figure 7). In a study by
Glauberman (17) on the directional dependence of air samplers, it was
found that a sampler head facing into the directional air stream col
lected the highest concentration. Although these results coincide with

CONCENTRATION RATIO: C./C
18
ANGLE OF PROBE MISALIGNMENT, degrees
Figure 7. Error due to misalignment of probe to flow stream ¡'after
Mayhood and Langstroth, in Watson (5)].

19
theoretical predictions (i.e., measured concentration is less than or
equal to actual concentration and the concentration ratios decrease as
the particle size and the angle are increased), the data are of little
use since two important parameters, free stream velocity and nozzle
diameter, are not included in the analysis.
Raynor (18) sampled particles of 0.68, 6 and 20 ym diameter at
wind speeds of 100, 200, 400 and 700 cm/sec with the nozzle aligned
over a range of angles from 60 to 120 degrees. He then used a trigono
metric function to convert equation (5) to the form
A = 1 + B(K)[(V.sinG + V cosG)/(V.cosG + V sinG) 1]
i o i o
(11)
This function only serves to invert the velocity ratio between 0 and
90 degrees and does not realistically represent the physical properties
of the flow stream. In fact, equation (11) becomes unity at 45 degrees
regardless of what the velocity ratio or particle size is. This cannot
be true since it has been shown that the concentration ratio will be less
than unity and will decrease inversely proportional to the angle and
particle diameter.
A more representative function can be derived in the following
manner: Consider the sampling velocity to be greater than the stack
velocity V Let A. be the cross sectional area of the nozzle of diameter
o 1
D.. The stream tube approaching the nozzle will have a cross sectional
area A such that
o
A V = A. V.
(12)
0 0 11

20
If the nozzle is at an angle 0 to the flow stream, the projected area
perpendicular to the flow is an ellipse with a major axis D^, minor
2
axis D^cos0, and area (D^ ttcos0)/4. The projected area of the nozzle
would therefore be A^cosG (see Figure 8). It can be seen that all the
particles contained in the volume V A.cosG will enter the nozzle. A
fraction B'(K,R,0) of the particles in the volume (A A.cos@)V will
0 10
leave the stream tube because of their inertia and will not enter the
nozzle. Therefore, with C defining the actual concentration of the
o 6
particles, the measured concentration in the nozzle would be
C A.COS0V + [1 -31(K,R,0)](A -A.cos0)V C
r 01 o L 7 J v o i J o o r,
C = (13)
A. V.
i i
Using equations (1) and (12), this may be simplified to
A = C./Co = 1 + 3'(K,R,0)(Rcose-1) (14)
B'(K,R,0) would be a function of both the velocity ratio R and the
inertial impaction parameter K as shown by Belyaev and Levin (13).
However, 3' will also be a function of the angle 0 because as the angle
increases, the severity of the turn that the particles must make to be
collected is also increased.
It can be seen that for large values of Stokes number, 6' must ap
proach 1 for the predicted concentration ratio in equation (14) to reach
the theoretical limit of Rcos0. The maximum error should theoretically
occur somewhere between a Stokes number of 1 and 6 depending on the angle
0. The upper limit of K = 6 would be for an angle of 0 degrees as des
cribed earlier in this chapter. The theoretical lower limit of K = 1

I
Figure 8. Sampling bias due to nozzle misalignment and anisokinetic sampling velocity.

22
would be for an angle of 90 degrees in which case the particles would
be traveling perpendicular to the nozzle. Since the nozzle has zero
frontal area relative to the flow stream, any particle that is collected
must make a turn into the nozzle. The amount of time that a particle
has to negotiate a turn is the time it takes the particle to traverse
the diameter of the nozzle, or D^/V Setting this equal to r the time
it takes a particle to change directions and rearranging terms, we ob
tain tV^/D^ = 1 as the limiting situation for a particle to be able to
make a turn into a nozzle positioned at a 90 degree angle to the flow
stream. For angles between 0 and 90 degrees the maximum error will
occur between the limits of Stokes numbers of 1 and 6 and should be
proportional to the average diameter of the frontal area of the nozzle.
Fuchs (19) suggests that for small angles the sampling efficiency will
be of the form
A = 1 4 sin(0K/7T) (15)
Laktionov (20) sampled a polydisperse oil aerosol at an angle to
the flow stream of 90 degrees for three subisokinetic conditions. He
used a photoelectric installation to enable him to determine the aspira
tion coefficients for different sized particles. From data obtained
over a range of Stokes numbers from 0.003 to 0.2 he developed the fol
lowing empirical equation:
A = 1
3K 0.5
(16)
This equation can be used only in the range of Stokes numbers given and
for a range in velocity ratios (R) from 1.25 to 6.25.

23
A few analytical studies in this area have also been published.
Davies' (14) theoretical calculations of particle trajectories in a
nonviscous flow into a point sink determined the sampling accuracy
to be a function of the nozzle inlet orientation and diameter, the
sampling flow rate and the dust particle inertia. Vitols (21) also
made theoretical estimates of errors due to anisokinetic sampling.
He used a procedure combining an analog and a digital computer and
considered inertia as the predominant mechanism in the collection of
the particulate matter. However, the results obtained by Vitols are
only for high values of Stokes numbers and are of little value for
this study.
B. Summary of the Literature on Tangential Flow
Although anisokinetic sampling velocity is known to cause a
particle sampling bias or error, there are also several other sampling
error-causing factors such as: duct turbulence; external force fields
(e.g., centrifugal, electrical, gravitational or thermal); and probe
misalignment due to tangential or circulation flow. These factors are
almost always present in an industrial stack gas and cannot be assumed
to be negligible. Not only do these factors cause sampling error
directly but in addition, they cause particulate concentration gradients
and aerosol size distribution variations to exist across the stack -
both in the radial and angular directions.
1. Causes and Characteristics of Tangential Flow
Tangential flow is the non-random flow in a direction other than
that parallel to the duct center line direction. In an air pollution

24
control device, whenever centrifugal force is used as the primary
particle collecting mechanism, tangential flow will occur. Gas
flowing from the outlet of a cyclone is a classic example of tangential
flow and a well recognized problem area for accurate particulate sampling.
Tangential flow can also be caused by flow changes induced by ducting
(22). If the duct work introduces the gas stream into the stack
tangentially, a helical flow will occur (see Figure 9). Even if the
flow stream enters the center of the stack, if the ducting flow rate is
within an order of magnitude of the stack flow rate, a double vortex
flow pattern will occur (see Figure 10).
The swirling flow in the stack combines the characteristics of
vortex motion with axial motion along the stack axis. The gas stream
moves in spiral or helical paths up the stack. Since this represents
a developing flow field, the swirl level decays and the velocity pro
files and static pressure distributions change with axial position
along the stack. Swirl level is used here to represent the axial flow
or transport rate of angular momentum (23). Velocity vectors in
tangential or vortex flows are composed of axial, radial and tangential
or circumferential velocity components (see Figure 11). The established
vortex flows are generally axisymmetric but during formation of the
spiraling flow the symmetry is often distorted. The relative order of
magnitude of the velocity components varies across the flow field with
the possibility of each one of the components becoming dominant at
particular points (24).

AIR FLOW
9. Tangential flow induced by ducting
FLOW PATTERN
tsJ

AIR FLOW-
Figure 10. Double vortex flow induced by ducting.
FLOW PATTERN
ro
O'

Figure 11. Velocity components in a swirling flow field.

28
The two distinctly different types of flow that are possible in
a swirling flow field are known as free vortex and forced vortex flows.
When the swirling component of flow is first created in the cyclone
exit, the tangential profile of the induced flow approaches that of a
forced vortex. As the forced vortex flow moves along the axis of the
stack, momentum transfer and losses occur at the wall which cause a
reduction in the tangential velocity and dissipation of angular
momentum. This loss of angular momentum is due to viscous action
aided by unstable flow and fluctuating components. Simultaneously,
outside the laminar sublayer at the wall where inertial forces are
significant, the field develops toward a state of constant angular
momentum. This type of flow field with constant angular momention
is classified as free vortex flow. The angular momentum and tangential
velocities of the flow decay as the gas stream flows up the stack (23).
Baker and Sayre measured axial and tangential point velocity
distributions in a 14.6 cm circular duct in which swirling flow was
produced by fixed vanes (23) The tangential velocity profiles and
angular momentum distributions are plotted in Figures 12 and 13 from
measurements taken at 9, 24 and 44 diameters downstream of the origin
of tangential flow. The tangential velocity (W) is made dimensionless
by dividing it by the mean spatial axial velocity (U ) at a pipe cross
section. These plots indicate developing flow fields, with two definite
types of flow occurring: that approaching forced vortex flow in the
central region of the pipe and flow approaching free vortex flow in
the outer region. Further tests showed that the free vortex field

I
r/R
Figure 12. Cross sectional distribution of tangential velocity in a swirling flow field.
K)

r/R
Figure 13. Cross sectional distributions of angular momentum in a swirling flow field. o

51
development is due primarily to viscosity at the wall and not a function
of inlet conditions, whereas the profiles in the forced vortex field are
very dependent on the initial conditions at the inlet. Although no re
verse flow was found in these tests, other tests showed that strong
swirls may produce reversed axial velocities in the central region (23).
It should be noted that although tangential velocities and angular
momentum decay along the axis of the pipe, see Figures 12 and 13, even
after 44 diameter the tangential velocity is still quite significant
when compared to the axial velocity. Therefore, satisfying the EPA
Method 5 requirement of sampling 8 stack diameters downstream of the
nearest upstream disturbances will not eliminate the effect of sampling
in tangential flow.
The angle of the flow relative to the axis of the stack induced by
the tangential component of velocity was as high as 60 degrees at some
points in the flow. This compares well with angles found when sampling
the outlets of cyclones (25) Another interesting fact about the flow
described in Figures 12 and 13 is that the radial positions for the
tangential components W/U = 0 show that the vortex axis is off center
by as much as 0.1r/R. This indicates that the swirling fields are not
exactly axisymmetrical.
2. Errors Induced by Tangential Flow
Types of errors that would be expected to be introduced by tangential
flow are nozzle misalignment, concentration gradients and invalid flow
measurements. The sampling error caused by nozzle misalignment has been

32
described in the previous chapter. Concentration gradients occur
because the rotational flow in the stack acts somewhat as a cyclone.
The centrifugal force causes the larger particles to move toward the
walls of the stack, causing higher concentrations in the outer regions.
Mason (22) ran tests at the outlet of a small industrial cyclone
to determine the magnitude of these three types of errors induced by
cyclonic flow. Results of flow rates determined at the different
locations are presented in Table I. As indicated by the data, serious
errors can result in cases of tangential flow. A maximum error of 212%
occurred when the pitot tube was rotated to read a maximum velocity
head. Sampling parallel to the stack wall also had a large error of
almost 74%. When sampling downstream of the flow straightening vanes,
however, the error was reduced to 15%.
Tests performed at the same point but with different nozzle
angles produced the data in Table II. Measured dust concentration
was lowest when the sampling nozzle was located at an angle of 0 degrees
or parallel to the stack wall. The measured dust concentration con
tinued to increase at 30 and 60 degrees but then decreased at 90 degrees.
Equation (14) shows that when sampling at an angle, under apparent iso
kinetic conditions (i.e., R=l), the measured concentration will be less
than the true concentration by a factor directly proportional to the
cos0. A maximum concentration, which would be the true concentration,
will occur at 0 = 0, which from this data should lie at an angle between
60 and 90 degrees to the axis of the stack. This can be confirmed by

TABLE I
FLOW RATE DETERMINED AT VARIOUS MEASUREMENT LOCATIONS
Location
Velocity (fps)
Flow Rate (scfm)
% Error
Actual Based on
Fan Performance
18
475
Port A
(parallel)
40
826
74
Port A
(maximum Ap)
60
1,482
212
Port C
(straightened)
21
548
15

34
CONCENTRATION AT /
TABLE II
V POINT FOR DIFFERENT SAMPLING ANGLES
Nozzle Angle
Measured Concentration
(grains/dscf)
0
0.243
30
0.296
60
0.332
90
0.316

using the data in Table I and the geometry in Figure 11 to calculate
the angle cf>:
coscf) Vfl/V = 13/60 (17)
This is true for = 72 degrees.
Table III gives the results of the emission tests. Sampling with
the nozzle parallel to the stack wall showed an error of 53%.
Sampling at the angle of maximum velocity head reduced the error
to 40%. The results cannot be compared directly to those with the
parallel sampling approach because the feed rates were not the same
due to equipment failure and replacement. Sampling in the straightened
flow had a sampling error of 36%. It was expected that sampling at this
location would give better results, but some of the particles were im
pacted on the straightening vanes and settled in the horizontal section
of the duct, thus removing them from the flow stream.
Particle size distribution tests showed no significant effect of
a concentration gradient across the traverse. This was due to the
particles being too small to be affected by the centrifugal force field
set up by the rotating flow.
3. Errors Due to the S-Type Pitot Tube
The errors in the measurement of velocity and subsequent calculations
of flow rate in tangential flow are due primarily to the crudeness of the
instruments used in source sampling. Because of the high particulate
loadings that exist in source sampling, standard pitot tubes cannot be
used to measure the velocity. Instead, the S-type pitot tube must be used

36
TABLE III
EMISSION TEST RESULTS
Probe Position
Measured Emission
Rate (gr/dscf)
Actual Emission
Rate (gr/dscf)
Error
Nozzle parallel
with stack wall
0.350
0.752
53
Nozzle rotated
toward maximum Ap
0.194
0.327
40
Straightened flow
0.207
0.325
36

37
since it has large diameter pressure ports that will not plug (see
Figure 14). Besides the large pressure ports it has an additional
advantage of producing approximately a 20% higher differential pressure
than the standard pitot tube for a given velocity. However, although
the S-type pitot tube will give an accurate velocity measurement, it is
somewhat insensitive to the direction of the flow (25-29) Figures 15
and 16 show the velocity errors for yaw and pitch angles. Although the
S-type pitot tube is very sensitive to pitch direction, the curve for
yaw angle is symmetrical and somewhat flat for an angle of 45 degrees
in either direction. Because of this insensitivity to direction of flow
in the yaw direction, the S-type pitot tube cannot be used in a tangential
flow situation to align the nozzle to the direction of the flow, or to
accurately measure the velocity in a particular direction.
The velocity in a rotational flow field can be broken up into three
components in the axial, radial and tangential directions (see Figure 11).
The magnitude of the radial and tangential components relative to the
axial component will determine the degree of error induced by the tangential
flow. Neither the radial nor the tangential components of velocity affect
the flow rate through the stack, but both affect the velocity measurement
made by the S-type pitot tube because it lacks directional sensitivity.
If the maximum velocity head were used to calculate the stack velocity,
the resultant calculated flow rates and emission levels could be off by
as much as a factor of l/cos will reduce but not eliminate this error because part of the radial and
tangential velocity components will still be detected by the pitot tube.

Figure 14. S-type pitot tube with pitch and yaw angles defined.
04
CO

Figure 15. Velocity error vs. yaw angle for an S-type pitot tubeT

Figure 16. Velocity error vs. pitch angle for an S-type pitot tube.
28

41
Therefore, the true flow rate cannot be determined by an S-tvpe pitot
tube in tangential flow because neither the radial velocity, V the
tangential velocity, V the axial velocity, V nor the angle cj> can
l a.
be measured directly.
4, Methods Available for Measuring Velocity Components in a Tangential
Flow Field
Almost all of the reported measurements of velocity components in
a tangential flow field have been based upon introduction of probes into
the flow. Because of the sensitivity of vortex flows to the introduction
of probes, the probe dimensions must be small with respect to the vortex
core in order to accurately measure velocity.
Two common types of pressure probes capable of measuring velocity
accurately are the 5-hole and 3-hole pitot tubes pictured in Figures 17a
and b. The 5-hole or three dimensional directional pressure probe is
used to measure yaw and pitch angles, and total and static pressure.
Five pressure taps are drilled in a hemispherical or conical probe tip,
one on the axis and at the pole of the tip, the other four spaced
equidistant from the first and from each other at an angle of 30 to 50
degrees from the pole. The operation of the probe is based upon the
surface pressure distribution around the probe tip. If the probe is
placed in a flow field at an angle to the total mean velocity vector,
then a pressure differential will be set up across these holes; the
magnitude of which will depend upon the geometry of the probe tip,
relative position of the holes and the magnitude and direction of the
velocity vector. Each probe requires calibration of the pressure

Pitch
I
~~1
Yaw
Pressure
Taps
Figure 17a. Conical version of a five-hole pitot tube.
Figure 17b. Fecheimer type three-hole pitot tube.
4^
hO

43
differentials between holes as a function of yaw and pitch angles.
Figure 18 shows the sensitivity of a typical 5-hole pitot tube to yaw
angle. Because of its sensitivity to yaw angle, it is possible to rotate
the probe until the yaw pressures are equal, measure the angle of probe
rotation (yaw angle) and then determine the pitch angle from the re
maining pressure differentials. The probe can be used without rotation
by using the complete set of calibration curves but the complexity of
measurement and calculation is increased and accuracy is reduced. Vel
ocity components can then be calculated from the measured total pressure,
static pressure and yaw and pitch angle measurements.
The 3-hole pitot tube, also known as the two dimensional or
Fecheimer probe, is similar to the 5-hole design except that it is
unable to measure pitch angle. The probe is characterized by a central
total pressure opening at the tip of the probe with two static pressure
taps placed symmetrically to the side at an angle of from 20 to 50
degrees. From Figure 19 it can be seen that the probe is quite sensitive
to yaw angle and can therefore be used to determine the yaw angle by
rotating the probe until the pressure readings at the static taps are .
equal. Once this is done the total pressure is read from the central
port, and the static pressure can be determined by use of a calibration
chart for the particular probe. Both the 5-hole and the 3-hole pitot
tubes have proven useful in determination of velocity components in
tangential flow fields (25, 28, 30).
5. EPA Criteria for Sampling Cyclonic Flow
The revisions to reference methods 1-8 (2) describe a test for
determination of whether cyclonic flow exists in a stack. The S-type

44
Figure 18. Five-hole pitot tube sensitivity to yaw angle. (28).

45
Figure 19. Fecheimer pitot tube sensitivity to yaw angle. (28)

46
pitot tube is used to determine the angle of the flow relative to the
axis of the stack by turning the pitot tube until the pressure reading
at the two pressure openings is the same. If the average angle of the
flow across the cross section of the stack is greater then 10 degrees,
then an alternative method of Method 5 should be used to sample the
gas stream. The alternative procedures include installation of
straightening vanes, calculating the total volumetric flow rate
stoichiometrically, or moving to another measurement site at which the
flow is acceptable.
Straightening vanes have shown the capability of reducing swirling
flows; however, there are some problems inherent in their use. One is
the physical limitation of placing them in an existing stack. Another
is the cost in terms of energy due to the loss of velocity pressure
when eliminating the tangential and radial components of velocity.
Since the vortex flows are so sensitive to downstream disturbances,
it is quite possible that straightening vanes might have a drastic
effect on the performance of the upstream cyclonic control device
which is generating the tangential flow. Because of these reasons the
use of straightening vanes is unacceptable in many situations.
Calculating the volumetric flow rate stoichiometrically might
produce accurate flow rates but the values could not be used to
calculate the necessary isokinetic sampling velocities and directions.
Also, studies reported here have shown that the decay of the tangential
component of velocity in circular stacks is rather slow and therefore
it would be unlikely that another measurement site would solve the problem.

47
It should be noted that EPA's approach to determining whether
cyclonic flow exists in a stack is correct. Other approaches such
as observing the behavior of the plume after leaving the stack could
lead to improper conclusions. Hanson et al (28) found that the
twin-spiraling vorticies often seen leaving stacks are the result of
secondary flow effects generated by the bending of the gas stream by
the prevailing crosswind and do not indicate any cyclonic flow
existing in the stack.

CHAPTER III
EXPERIMENTAL APPARATUS AND METHODS
A. Experimental Design
The major components of the aerosol flow system can be seen in
Figure 20. An aerosol stream generated from a spinning disc generator
was fed into a mixing chamber where it was combined with dilution air.
The air stream then flowed through a 10 cm diameter PVC pipe containing
straightening vanes. This was followed by a straight section of clear
pipe from which samples were taken. The filter holder and nozzle used
as a control sample originated in a box following the straight section.
A test nozzle was inserted into the duct at an angle from outside the
box. A thin-plate orifice, used to monitor flow rate, followed the
sampling box. A 34000 pm industrial blower was used to move the air
through the system. The flow rate could be controlled by changing the
diameter of an orifice plate. An air by-pass between the blower and
the orifice plate was used as a fine adjust for the flow.
The sampling systems (see Figure 21] consisted of stainless steel,
thin-walled nozzles connected to 47 mm stainless steel Gelman filter
holders. Each filter assembly was connected in series to a dry gas
meter and a rotameter, and driven by an airtight pump with a by-pass
valve to control flow.
48

TO PUMPS AND GAS METERS
Figure 20.
Experimental set up.
TO BLOWER

MANOMETER
FILTER
ooo
GAS
METER
J
Figure 21
BY PASS
Sampling system.
cn
O

51
B. Aerosol Generation
1. Spinning Disc Generator
A spinning disc aerosol generator (31-33) was used to generate
monodisperse aerosols from 1.0 pm NMD to 11.1 pm NMD (see Table IV).
Droplets were generated from a mixture of 90% uranine (a fluorescent
dye) and 10% methylene blue dissolved in a solution of from 90 to 100%
ethanol (95% pure) and up to 10% distilled/deionized H?0. Uranine was
used so that the particles could be detected by fluoremetric methods.
Methylene blue was added to aid in the optical sizing of the particles.
The mixture of water and ethanol allowed for a uniform evaporation of the
droplets. The droplets, containing dissolved solute, evaporated to yield
particles whose diameters could be calculated from the equation
D
P
CCr0'33) D
(18)
where
D
P
C
r
= particle diameter, pm
= ratio of solute volume to solvent volume plus solute
volume, dimensionless
= original droplet diameter, pm
With the disc's rotational velocity, air flows and liquid feed rate held
constant the size of the droplets produced were only dependent upon the
ratio of the ethanol-water mixture. Since the droplets are produced from
a dynamic force balance between the centrifugal force and the surface

52
TABLE IV
SIZES AND DESCRIPTIONS OF EXPERIMENTAL AEROSOLS
Number Mean
Aerosol
Description
Generation
Method
O,
'O
Ethanol
Droplet
Diameter, pm
Diameter
Particles,
0.0024%
Spinning Disc
90
37.4
1.08
0.005%
Spinning Disc
90
37.2
1.37
0.01%
Spinning Disc
90
37.1
1.72
0.03%
Spinning Disc
90
37.8
2.53
0.2%
Spinning Disc
99
24.6
3.10
0.05%
Spinning Disc
90
39.7
3.15
0.55%
Spinning Disc
99
24.4
4.3
0.3%
Spinning Disc
90
34.5
4.98
0.6%
Spinning Disc
90
33.1
6.02
2.0%
Spinning Disc
100
23.6
6.4
1.0%
Spinning Disc
90
35.4
7.66
4.0%
Spinning Disc
100
23.4
8.0
6.7%
Spinning Disc
100
23.2
9.42
6.7%
Spinning Disc
95
27.3
11.1
Ragweed
Pollen
Mechanical
Dispersion
N. A.
N.A.
19.9

55
tension of the drop, the surface characteristics of the liquid are
quite important. The surface tensions of water and ethanol at 20
degrees C are respectively 72.8 and 22.3 dynes/cm (34). The effect
of this large difference can be seen in Table IV where the droplets
produced were approximately 37 ym for 90% ethanol and 23 ym for 100%
ethanol.
Before and after each test a sample of the particles was collected
on a membrane filter and sized using a light microscope to take into
account any slight variation in the performance of the spinning disc.
2. Ragweed Pollen
In order to obtain large Stokes numbers, ragweed pollen was
mechanically dispersed by means of a rubber squeeze bulb into the
inlet of the duct. The ragweed pollen had a NMD of 19.9 ym.
C. Velocity Determination
The velocity at each sampling point was measured using a standard
pitot tube. The flow was maintained constant during the test by con
trolling the pressure drop across a thin-walled orifice placed in the
system (35-37). Five orifice plates with orifices ranging in diameter
from 1.8 to 7.2 cm were used to obtain a range in duct velocities of
82 to 2460 cm/sec (see Table V) in the 10 cm duct. To obtain higher
velocities, a 5 cm duct was used.
A typical velocity profile across the 9.6 cm clear plastic duct
is presented in Table VI and plotted in Figure 22. The profile is

TABLE V
TABLE OF OBTAINABLE VELOCITIES IN 10 cm DUCT
Orifice Diameter
cm
Ap Range
cm H?0
Range in Velocity
cm/sec
1.795
5.6
- 21.6
82
- 162
2.539
5.3
- 21.8
162
- 326
3.5S9
4.2
- 22.9
304
- 670
5.080
4.1
- 22.6
582
- 1371
7.182
2.2
- 14.5
945
- 2460

TABLE VI
TYPICAL VELOCITY TRAVERSE IN THE EXPERIMENTAL SAMPLING SYSTEM
(9.58 cm I.D. Duct)
Horizontal Vertical
Point
d/D
AP, cm Ho0
V, cm/sec
AP, cm H-O
<
o
3^
1
0.044
1.27
1454
1.57
1618
2
0.146
1.83
1743
2.11
1871
3
0.296
2.03
1S38
2.08
1859
4
0.704
2.13
1884
2.11
1871
5
0.854
1.88
1768
1.98
1813
6
0.956
1.47
1564
1.52
1591
Average Velocities (cm/sec)
From Pitot Tube Readings From Orifice AP
1740
1658

2000
0
0.2
0.4
0.6
0.8
1 .
d/D
Figure 22. Typical velocity profile in experimental test section (9.58 ID duct).

57
quite flat which is typical of the turbulent flow regime. The average
Reynolds number for this particular case was 1.1 x lO'. The velocities
at traverse points 3 and 4 were used as the velocity for determination
of isokinetic sampling rate and Stokes number. The difference between
the average velocity determined from the pitot traverse and the orifice
plate calibration is probably due to the inability of the pitot tube to
accurately measure velocity near the wall at points 1 and 6.
D. Selection of Sampling Locations
Sehmel (16) observed that non-uniform particle concentrations
existed across the diameter of a cylindrical duct, and that the
magnitude of the concentration gradient varied with particle size.
To account for these radial variations, the two sampling points were
located symmetrically about the center of the duct at a distance of
2 cm from the center. Simultaneous isokinetic samples were taken at
the two points and compared. Tests were repeated for different
particle sizes. No concentration differences were found to exist at
the two sampling points.
E. Sampling Nozzles
Two pairs of sampling nozzles were cut from stainless steel tubing
of 0.465 cm and 0.683 cm I.D. The nozzles were made approximately 15 cm
long to minimize the effect of the disturbance caused by the filter
holders on the flow at the entrance of the nozzles. Analysis by Smith
(38) showed that a sharp-edge probe was the most efficient design;

58
therefore, the tubing was tapered on a lathe to a fine edge. Belyaev
and Levin (12) observed that the rebound of particles from the tip of
the nozzle into the probe was one cause of sampling error and that for
tapered nozzles, the efficiency is affected by the relative wall thick
ness, the relative edge thickness and the angle of taper. They con
cluded that if the edge thickness is less than 5% of the internal diameter
and the taper is less than 15 degrees, then the variation in aspiration
coefficient due to particle rebound would be less than 5%. The nozzles
viere designed accordingly.
F. Analysis Procedure
1. For Uranine Particles
Uranine particles were collected on Gelman type A glass fiber
filters. The filters were then placed in a 250 ml beaker. One hundred
milliliters of distilled water were then pipetted into the front half of
the filter holder and down through the nozzle into the beaker containing
the filter. The uranine leachate concentration was then diluted and
analyzed by a fluorometer (39).
2. For Ragweed Pollen
The ragweed pollen was collected on membrane filters and counted
under a stereo microscope. In this part of the experiment the filters
and probe were analyzed separately. The filters used for collecting
the particles were 5.0 pm type SM Millipore membrane filters. In order
to count the particles under a microscope a dark background was necessary;

59
therefore, each filter was dyed with ink and a grid was drawn to aid
in the counting. Before being placed in the filter holders, the filters
were examined under the microscope to determine if any background count
existed. After each test the filters were removed and the entire area
of the filter was counted.
The pollen caught in the nozzle and filter holder was analyzed
using isopropyl alcohol and 0.45 ym pore size Millipore membrane filters
with black grids. The isopropyl was first filtered several times to
remove background particulate matter. Once the background was low enough,
the alcohol was poured into the front half of the filter holder and
through the nozzles. The solution was then sucked through the membrane
filters. The filters were allowed to dry and then the entire filter
area was counted under the microscope.
G. Sampling Procedure
1. A desired flow rate was obtained by selecting an orifice
plate and using the by-pass as a fine adjust.
2. The velocity was measured using a standard pitot tube.
3. A solute-solvent solution was selected for a given particle
size.
4. Particles were collected on a membrane filter and sized
using a light microscope.
5. A nozzle diameter which would allow for an isokinetic
sampling rate closest to 1 cfm was selected.
6. Isokinetic sampling rates were calculated and sampling
flow rates were adjusted accordingly.

60
7. Two simultaneous isokinetic samples were taken, one
parallel to the flow (control), and one at a specified
angle. Sampling times varied from 10 to 20 minutes.
H. Tangential Flow Mapping
The system used to map the flow pattern in a tangential flow' stream
is shown in Figure 23. It consists of a 34000 £pm industrial blower, a
section of 15 cm PVC pipe containing straightening vanes, a small in
dustrial cyclone collector, followed by a 6.1 meter length of 20 cm PVC
pipe. The 150 cm long cyclone, shown in Figure 24 was laid on its side
so that the stack was horizontal and could be conveniently traversed at
several points along its length. A change in flow through this system
could be produced by supplying a restriction at the inlet to the blower.
To measure the velocity in the stack a United Sensor type DA 3-
dimentional directional pitot tube was used. The probe, pictured with
its traversing unit in Figure 25, is .52 cm in diameter and is capable
of measuring yaw and pitch angles of the fluid flow as well as total
and static pressures. From the blow up of the probe tip (Figure 25) it
can be seen that the head consists of 5 pressure ports. Port number 1
is the centrally located total pressure tap. On each side are two
lateral pressure taps 2 and 3. When the probe is rotated by the manual
traverse unit until P9 = P the yaw angle of flow is indicated by the
traverse unit scale. When the yaw angle has been determined an additional
differential pressure is measured by pressure holes located perpendicularly
above and below the total pressure hole 1. Pitch angle is then determined
using a calibration curve for the individual probe. The yaw angle is a

61

62
Figure 24.
Cyclone used in the study to generate swirling flow.

63
Figure 25. Photograph of the 3-dimensional pitot with its
traversing unit. Insert shows the location of
the pressure taps.

64
measure of the flow perpendicular to the axis of the stack and tangent
to the stack walls. The pitch angle is a measure of the flow perpendic
ular to the axis of the stack and perpendicular to the stack walls. The
axial component of the velocity can therefore be determined from the
following equation:
V = V. coscb
a t r
(19)
where V
a
V
t
component of velocity flowing parallel to the axis of the stack,
total or maximum velocity measured by the pitot tube
cos ^ [cos(pitch) x cos(yaw)]

CHAPTER IV
RESULTS AND ANALYSIS
A. Aerosol Sampling Experiments
1. Stokes Number
Experiments were set up and run with Stokes number as the independent
variable. Duct velocity, nozzle diameter and particle diameter were varied
in order to produce a range of Stokes numbers from 0.007 to 2.97. The
Stokes number used in the analysis of data was calculated from
2
18D.n
(20)
i
where
C = 1 + 2.492 L/D + 0.84 L/D e
P P
and
L = mean free path = 0.065 ym (11)
Values for density and viscosity used in the calculations were
p = 1.81 x 10 4 g/cm-sec (40)
Pp = density of uranine particles = 1.375 g/cm.0 (41)
T
p = density of ragweed pollen = 1.1 g/cm (18)
65

66
2. Sampling with Parallel Nozzles
In order to determine if the concentration of particles was the
same at both sampling locations, simultaneous samples were taken with
both nozzles aligned parallel to the duct. Table VII shows the results
of tests performed over a range of Stokes numbers from 0.022 to 1.73.
The average over all of the tests showed only a 0.34% difference between
the two points with a 95% confidence interval of 1.2%. The data show
an increase in the range of the values as the Stokes number increases.
This can be expected because a small error in probe misalignment would
have a greater effect at the higher Stokes number.
3, Analysis of Probe Wash
In the analysis of the tests using ragweed pollen, the filter
catch and probe wash were measured separately. This method allowed
for the determination of the importance of analyzing both the filter
and wash. From Table VIII it can be seen that even for a solid dry
particle, analysis of the probe wash is a necessity. An average of
40% of the particles entering the nozzle was collected on the walls of
the nozzle-filter holder assembly. This was only for nozzles aligned
parallel to the flow stream and sampling isokinetically. Therefore,
the loss of particles was due to turbulent deposition and possibly
bounce off the filter, and probably not inertial impaction. For tests
run with the nozzle at an angle to the flow stream, it is assumed that
the loss would increase as impaction of particles on the walls became

TABLE VII
RESULTS OF SAMPLING WITH TWO PARALLEL NOZZLES
Velocity
cm/sec
Particle Diameter
micrometers
Nozzle Diameter
cm
Stokes Number
% Difference
1798
1.08
0 .465
0.022
-3.2
+ 0.5
+ 0.3
-0.2
+ 1.3
-1.9
+ 1.6
1798
1.39
0 .465
0.035
-0.9
+ 2.3
+ 1 .3
1798
1.094
0 .465
0.053
+ 2.6
-3.7
-0.3
1798
2.74
0 .465
0 .130
+ 0.44
-0.6
1798
4.98
0 .465
0 .420
-1.9
+ 3.2
+ 2.2
701
19.9
0 .683
1.73
+ 8.7
-0.7
-3.9
ax
'-j

68
TABLE VIII
PERCENT OF PARTICULATE MATTER COLLECTED IN THE PROBE WASH
FOR NOZZLES PARALLEL WITH THE FLOW STREAM
Probe Wash*
Filter-
Total*
% in Wash
511
497
196
218
161
250
366
721
407
697
377
669
265
464
415
647
351
522
220
240
442
614
1008
51
414
47
411
39
10S7
34
1104
37
1046
36
729
36
1062
39
873
40
460
35
1036
41
*Numbers represent the number of ragweed pollen counted.

69
important. This can be seen from the data taken at 60 degrees (see
Table IX) where an average of 54% of the particles was lost on the
walls.
The probe wash for eight tests using 6.7 ym uranine particles
was also analyzed separately for comparison with the results of the
ragweed pollen tests. While parallel sampling, from 15 to 34% of the
total mass was collected in the nozzle and front end of the filter
holder. While this was somewhat less than the amount of ragweed pol
len found in the nozzle, it is substantial enough to show the importance
of including the nozzle wash with the filter catch. Also because of the
variation of the percent collected in the nozzle during identical tests,
the probe wash cannot be accounted for by a correction factor. During
further testing, it was qualitatively observed that the percent in the
probe wash increased with particle size and decreased with increasing
nozzle diameter.
4. The Effect of Angle Misalignment on Sampling Efficiency
The aspiration coefficient was determined by comparing the amount
of particulate matter captured while sampling isokinetically with a
control nozzle placed parallel and a test nozzle set at an angle to the
flow stream. Tests were run at three angles, 30, 60 and 90 degrees.
The results showed the theoretical predictions to be quite accurate.
For all three angles the aspiration coefficient approached 1 for small
Stokes numbers (K), decreased as K increased and then leveled off at a
minimum of cos0 for large values of Stokes number. The most significant
changes occur in the range between K = 0.01 and K = 1.0.

70
TABLE IX
PERCENT OF PARTICULATE MATTER COLLECTED IN THE PROBE WASH
FOR NOZZLES AT AN ANGLE OF 60 DEGREES WITH THE FLOW STREAM
Probe Wash*
Filter*
Total *
% in Wash
348
211
559
62.0
161
138
299
54.0
288
333
621
46.4
* Numbers represent the number of ragweed pollen counted.

71
Figures 26, 27 and 28 represent the sampling efficiency as a
function of Stokes number for 30, 60 and 90 degrees respectively.
The experimental data used in these plots are presented in Tables X,
XI and XII. From these tables it can be seen that the variables of
particle diameter and velocity and nozzle diameter were varied rather
randomly. This was done to check the legitimacy of using Stokes number
as the principle independent variable. From the shape of the curves in
Figures 26-28, it can be seen that the aspiration coefficient is indeed
a function primarily of Stokes number.
The curves for 30, 60 and 90 degrees are all similar in shape
except for the values of Stokes number where they approach their
theoretical limit. As the angle of misalignment increases, the more
rapidly the aspiration coefficient reaches its maximum error. This
can be accounted for as an apparent change in nozzle diameter, because
it is the only parameter in the Stokes number that is affected by the
nozzle angle to the flow stream. As described before, the nozzle
diameter is important because it determines the amount of time available
for the particle to change directions (approximately 6 D^/V ). As the
nozzle is tilted at an angle to the flow stream, the projected frontal
area and therefore the projected nozzle diameter are reduced proportional
to the angle. Therefore, as the angle of misalignment increases, the
time available for the particle to change direction decreases leading to
increased sampling error for a given value of K. To normalize these
curves for angle to the flow stream, it is necessary to define an "adjusted
Stokes number" (K'j which takes into account the change in projected

Aspiration Coefficient (A)
Figure 26. Sampling efficiency vs. Stokes number at 30 misalignment for R = 1.
tsj

Aspiration Coefficient (A)
1.00
0.80
0.60
0.40
0.20
0.00
O G
0.01
O
o
i u
G
Typical 95% C.I.
o
O
<&
o
o
o
o
G
J L I 1111
J I 1 I 1...1 J-l.
J 1 1111
0.
1.0
10.
Stokes Number (K)
Figure 27. Sampling efficiency vs. Stokes number at 60 misalignment for R = 1.

Aspiration Coefficient (A)
1.00
0.80
0.60
0.4 0
0.20
0.00
0.01
O
O
o
o
o
|j>4-Typ
ical 95% C.I
G
O
o
J I I I L
G
I I 1 1 -L l l ti QL
0. L
1.0
l I I I l I
10.0
Stokes Number (K)
Figure 28. Sampling efficiency vs. Stokes number at 90 misalignment for R = 1.

TABLE X
ASPIRATION COEFFICIENT AS A FUNCTION OF STOKES NUMBER FOR 30 DEGREE MISALIGNMENT
Velocity
cm/sec
Particle Diameter
micrometers
Nozzle Diameter
cm
Stokes Number
Aspiration
Coefficient
1798
1.08
0.465
0.022
103.8
97.3
101.8
1326
2.53
0.683
0.056
99.4
101.6
99.7
100.2
1326
3.23
0.683
0.090
97.9
96.7
98.1
1676
2.87
0.465
0.132
95.8
88.8
93.4
1798
3.15
0.465
0.170
97.7
94.6
94.0
98.1
96.9
91.7
1676
4.08
0.465
0.263
88.9
90.2
94.9
Cn

TABLE X [continued)
Velocity
cm/sec
Particle Diameter Nozzle Diameter
micrometers cm
1676
6.35 0 .465
1140
9.81 0.465
2347
11.1 0.683
3627
9.4
0 .465
Stokes Number
Aspiration
Coefficient %
0 .63
93.6
89.1
100.0
1.01
96.6
S7.5
92.0
1.81
86.4
93.4
86.9
2.97
92.5
91.9
83.8
86.8
86.1
92.5
OS

TABLE XI
ASPIRATION COEFFICIENT AS A FUNCTION OF STOKES NUMBER FOR 60 DEGREE MISALIGNMENT
Velocity
cm/sec
Particle Diameter
micrometers
Nozzle Diameter
cm
Stokes Number
Aspiration
Coefficient
1798
1.08
0.465
0.022
101.3
94.7
96.5
1798
1.37
0.465
0.034
98.9
95.0
99.4
1326
2.53
0.683
0.056
94.4
94.8
95.0
93.5
1326
3.23
0.683
0.090
92.5
90.7
91.1
92.2
1676
2.87
0.465
0.132
89.5
88.2
81.5
1798
3.15
0.465
0.170
89.3
90.0
91.7
85.0
83.2

TABLD XI (continued)
Velocity Particle Diameter Nozzle Diameter Aspiration
cm/sec micrometer cm Stokes Number Coefficient %
1676
3
.81
0
.465
0
.23
75.
.0
89.
.1
81,
.8
81,
.9
1676
4,
.54
0
.465
0,
.325
74,
.7
72.
.3
69.
.0
69.
.3
1798
4.
.98
0,
.465
0
.42
73,
.5
71,
.9
71,
.6
78.
.4
1798
6.
,02
0.
.465
0,
.61
76,
.8
67.
.5
75.
1
70.
.3
1676
6.
,35
0.
.465
0
.63
75.
.7
68,
.2
72.
,0
1676
8.
0
0.
.4 65
0.
.99
65.
.8
62.7
64.2
co

TABLE XT (continued)
Velocity Particle Diameter Nozzle Diameter
cm/sec micrometers cm
1140
9.87
0.465
1551
9.42
0.465
1707
9.42
0.465
2347 11.1
0.683
3627
9.42
0.465
Stokes Number
Aspiration
Coefficient %
1.01
63.3
60.6
59.3
1.27
57.2
54.3
53.8
1.40
56.0
58.3
52.9
1.81
49.7
58.0
47.0
51.0
2.97
50.6
48.2
53.0
LO

TABLE XII
ASPIRATION COEFFICIENT AS A FUNCTION OF STOKES NUMBER FOR 90 DEGREE MISALIGNMENT
Velocity Particle Diameter Nozzle Diameter Aspiration
cm/sec micrometers cm Stokes Number Coefficient %
549
1.372
0.683
0.0071
95.8
96.2
93.7
98.5
97.3
1798
1.08
0.465
0.002
95.0
93.5
97.4
1798
1.37
0.465
0.034
92.9
94.5
94.0
1798
1.72
0.465
0.053
87.6
1326
2.53
0.683
0.056
88.3
86.7
83.5
83.9
1326
3.23
0.683
0.090
73.7
74.7
75.3
1676
2.87
0.465
0.132
65.0
57.0
58.6
CO
o

TABLE XIT (continued)
Velocity Particle Diameter
cm/sec micrometers
1494
3.84
1676
4.08
1798
4.98
1326
7.66
1676
8.0
Nozzle Diameter
cm
0.4 65
0.465
0.465
0.683
0.465
701
19.9
0.683
Stokes Number
Aspiration
Coefficient %
0.21
38.2
44.6
49.3
49.8
0.26
28.7
24.4
33.7
0.42
27.5
22.1
20.3
0.49
17.0
13.0
12.1
0.99
1.2
1.1
1.3
I .73
0
0
oo

nozzle diameter with angle. When plotted against K!, the aspiration
coefficients for 30, 60 and 90 degrees should approach their theoretical
minima at the same place as the curves for zero misalignment angle and
anisokinetic sampling velocities (see Figure 6).
To develop the adjustment factor for Stokes number, it was neces
sary to plot as a function of 0, the value of K where the aspiration
coefficient reached a value that represented 95% of the maximum error.
For example the maximum theoretical error for 60 degrees is cos(60) or
0.5. Therefore the value of K of interest is where there is (.95) (0.5) =
47.5% sampling error or an aspiration coefficient of 1 .475 = .525.
For zero degrees, equations (9) and (10) were solved for R = 0.5 and
3 = 0.95 to obtain a value of K = 5.9. This velocity ratio was used
because its theoretical maximum sampling error is 0.5, the same as for
60 degrees. The values for 60 and 90 degrees were obtained from Figures
27 and 28 respectively. Because of the flatness of the 30 degree curve
(it varies only 16% over two and a half orders of magnitude of K), it was
not possible to detect exactly when the curve reached 95% of its minimum
value. Therefore no value for 30 degrees was used in this analysis.
The equation for the adjusted Stokes number determined from Figure
29 is
K
,, 0.0226
Ke
(22)
Using this equation it can be determined that the Stokes numbers for 30,
60 and 90 degrees must be multiplied by 1.93, 3.74 and 7.24 respectively
to account for the effect of nozzle angle to the flow stream on the

o
Misalignment Angle (6)
Figuie 29. Stokes number at which 95% maximum error occurs
vs. misalignment angle.

84
apparent nozzle diameter. Using these correction factors it is possible
to use the data to determine an expression for g' in equation (14). Set
ting R = 1 and solving for g' this equation becomes
B'(K')
A 1
COS0-1
(23)
Using this expression the experimental data were used to plot g' as a
function of the adjusted Stokes number K' (see Figure 30). From this
plot, it can be observed that the data points for 30, 60 and 90 degrees
all fall approximately on the same line. It should be noted that most
of the scatter is due to the 30 degree data and that the amount of the
scatter is somewhat deceptive. Solving equation (23) for 30 degrees,
requires that the sampling bias (1-A) must be multiplied by 7.5 to
normalize it with the 90 degree data. This has an effect of greatly
increasing any spread in the experimental data.
To develop a model for inertial sampling bias, it was necessary
to develop an equation for the line drawn through the data in Figure 30.
An equation of the form similar to that used by Belyaev and Levin was
selected to fit the data.
g(K',0) = 1 r- (24)
1 + aK'
where a and b are constants. The advantage of this equation form is
that it acts similar to the theoretical expectations of the relationship
(i.e., 0' approaches zero for very small values of K' and approaches 1
for very large values of K').

Adjusted Stokes Number (K')
Figure 30. 3'(K',0) vs. adjusted Stokes number for 30, 60 and 90 degrees.

86
While attempting to determine the constants a and b, it was found
that the form of the equation had to be altered somewhat to allow 3' to
approach 1 at a faster rate for values of K' greater than 4.0. The fol
lowing is the final form of the equation selected.
S'CK',9) = 1 qmrr (25)
1 + aK'e
The constants were determined through trial and error to be 0.55 and 0.25
for a and b respectively. Therefore, the final equation to describe the
sampling efficiency due to nozzle misalignment as a function of Stokes
number becomes for R = 1:
A = 1 + (cose 1) 3'(K',0) (26)
where
31 (K',0)
1
1 + 0.55 K'e
0.2 5 K'
(27)
and
K- = Ke0-0220
(22)
These equations are solved for 30, 60 and 90 degrees and plotted against
Stokes number in Figure 31. It can be seen from the graph that the equations
fit the data within experimental accuracy. Figure 32 is a plot of the
sampling efficiency for angles between 0 and 90 degrees in 15 degree
increments.

Aspiration Coefficient (A)
Figure 31. Aspiration coefficient vs. Stokes number model prediction and experimental data
for 30, 60 and 90 degrees.

Aspiration Coefficient (Al
i
Stokes Number (K)
Figure 32. Predicted aspiration coefficient vs. Stokes number for 15, 30, 45, 60, 75 and 90 degrees
CO
CO

89
5. The Effect of Nozzle Misalignment and Anisokinetic Sampling Velocity
To complete the analysis of anisokinetic sampling, it is necessary
to know what is the combined effect of both a nozzle misalignment and a
sampling velocity differing from the free stream velocity. The theoreti
cal model predicts that the sampling efficiency will be in the form
A = 1 + (Rcos0 1)3 (28)
where
3" = f[3(K,R) 3' (K',0)]
(29)
Since the reduction of projected nozzle diameter due to nozzle misalign
ment will effect the time available for a particle to change directions
when sampling at an anisokinetic velocity, the adjusted Stokes number K'
should also be used in the equation for 3 as well as 3'- Another modifi
cation that must be made in the model involves correcting for the fact
that 3(K',R) does not equal 1 when R = 1.
3(K', R = 1) = 1 -
1
1 + 2.617 K
(30)
To account for this 3'(K',0) must be divided by 3(K',R = 1) so that
equations (28) and (29) are valid at R = 1. The model to be tested now
becomes
A =
+ (Rcos0 1) 3(K',R)
3(K',0)
3(K\R 1)
(31)
At first there appears to be an obvious flaw in the model in that the
aspiration coefficient equals 1 whenever R = l/cos0 regardless of the

90
Stokes number. An example of this is when R = 2 and 0 = 60 degrees.
This phenomenum can be explained as follows. Since the projected
frontal area of the nozzle is one half the actual area when 0 = 60
degrees, in order to sample isokinetically such that there
is no divergence of streamlines into the nozzle, the sample velocity
must be one half of the free stream velocity or R = 2. Therefore,
the condition of R = l/cos0 defines the condition for obtaining a
representative sample when the nozzle is misaligned with the flow
stream.
Since the sampling methodologies used to determine 0(K,R) and
B'(K,0) were substantially different (photographic observation vs.
comparative sampling), it was necessary to see if the two methods
gave comparable results before the model could be tested. Four sets
of tests were run with two parallel nozzles; the control nozzle
sampled isokinetically and the test nozzle sampled anisokinetically.
Tests were performed at two Stokes numbers (K = 0.154 and K = 0.70)
and at two velocity ratios (R = 2.3 and R = 0.51). The aspiration
coefficients obtained by comparing the two measured concentrations are
presented in Figure 33 and Table XIII. The data obtained lie within
the experimental bounds of the lines produced from Belyaev and Levin's
data [Equations (5), (9) and (10)].
Since the two methods give comparable results, experiments were
run to test the model. A control nozzle was placed parallel to the
flow stream and the sampling velocity was set to be isokinetic. The
test nozzle was inserted at an angle from outside the duct and the
sampling velocity was set to be either one half or two times the free

Aspiration Coefficient (A)
Stokes Number (K)
Figure 33. Comparison of experimental data with results from Belyaev and Levin (12).

I
TABLE XIII
COMPARISON OF SAMPLING EFFICIENCY RESULTS WITH THOSE OF BELYAEV AND LEVIN (13)
FOR 0 = 0, R = 2.3 AND R = 0.5
Particle
Diameter Velocity
(pm) (cm/sec)
Nozzle
Diameter Stokes
(cm) Number
Value Predicted
Velocity from Equations Experimental
Ratio (5), (9) and (10) Value
6.7
1676
0.465
0.70
2.3
3.1
1676
0.465
0.154
2.3
6.7
1676
0.465
0.70
0.51
3.1
1676
0.465
0.154
0.51
1.8 1.69
1.79
1.76
1.87
1.34 1.32
1.39
1.38
0.67 0.70
0.63
0.66
0.65
0.84 0.80
0.90
0.79
ID
to

95
stream velocity. Tests were run for a range of Stokes numbers from 0.1
to 1. This range was selected because this was expected to be the area
where the greatest change in aspiration coefficient occurred. The data
obtained for R = 2 and R =0.5 for a 60 degree misalignment are presented
in Tables XIV and XV. Thesedata are plotted and compared with the model's
prediction in Figure 34. The aspiration coefficient does indeed appear
to be unity when R = l/cos0 as in the case of R = 2 and 0 = 60 degrees.
The data for R = 0.5, 0 = 60 degrees appear to approach their theoretical
limit of Rcos0 CO.25) at approximately a value of Stokes number of 2 to 5
This is near the location that the aspiration coefficient for 0 = 60
degrees, R = 1 approaches its theoretical limit. This further confirms
the necessity of using an adjusted Stokes number when the probe is mis
aligned with the flow stream.
To further test the model, experiments were run at 45 degrees
(R = 2.0 and R = 0.5) and at 50 degrees (R = 2.0). Thesedata presented
in Tables XVI and XVII are plotted in Figures 35 and 36 also show good
agreement with the prediction model.
When tests were run at 0 = 90 degrees, R = 2.1 and K = 0.195 (see
Table XVIII), an average aspiration coefficient of only 1.5% was obtained
The value predicted for equation (31) for these conditions is 49%. It
appears that the model falls apart at 90 degrees for R f 1. This is due
to the fact that when 0 = 90 degrees there is zero projected frontal area
of the nozzle. This means that subisokinetic sampling could in no way
produce an increase in concentration as it does when particles lie in
front of the projected nozzle area. Because of this it is necessary to
put the condition 0 < 90 degrees on equation (31).

TABLE XIV
ASPIRATION COEFFICIENT AS A FUNCTION OF STOKES NUMBER FOR R = 2, 6 = 60
Velocity
cm/sec
Particle Diameter
micrometers
Nozzle Diameter
cm
Stokes Number
Aspiration
Coefficient %
732
4.59
0.683
0.099
96.9
104.1
100.5
732
6.5
0.683
0.196
109.0
93.4
98.4
701
9.6
0.683
0.406
90.9
101.9
101.9
1402
9.6
0.683
0.812
97.6
94.0
105.0
1140
9.9
0.465
1.01
95.2
105.1
97.0

TABLE XV
ASPIRATION COEFFICIENT AS A FUNCTION OF STOKES NUMBER FOR R = 0.5, 0 = 60
Velocity
cm/sec
Particle Diameter
micrometers
Nozzle Diameter
cm
Stokes Number
Aspiration
Coefficient %
732
4,
,59
0.
,683
0.
,099
77
.7
80
.7
88
.8
732
6.
,5
0,
.683
0.
.196
79
.8
72
.2
72,
. 5
701
9.
,6
0,
.683
0.
.406
68
.4
58
. 6
62
.6
1463
7.
.8
0,
.465
0,
.8 25
47
.3
49
.2
47
.8
1585
9.
,6
0,
.465
1.
.35
34
.8
39.5
42.4
Cn

Aspiration Coefficient (A)
Stokes Number (K)
Figure 34. Sampling efficiency vs. Stokes number at 60 misalignment for R = 2.0 and 0.5.
CA

TABLE XVI
ASPIRATION COEFFICIENT AS A FUNCTION OF STOKES NUMBER FOR 0 = 45, R = 2.0 and 0.5
Velocity Particle Diameter
cm/sec micrometers
Nozzle Diameter
cm
Stokes Number
Velocity
Ratio
Aspiration
Coefficient
701
9.6
0.683
0.406
0.5
67 .4
78.2
65.5
65.0
701
9.6
0.683
0.406
2.0
134.5
131.4
113.8
121 .4
to

TABLE XVII
ASPIRATION COEFFICIENT AS A FUNCTION OF STOKES NUMBER FOR R = 2, 0 = 30
Velocity
cm/sec
Particle Diameter
micrometers
Nozzle Diameter
cm
Stokes Number
Aspiration
Coefficient %
3627
9.42
0.465
2.97
188.9
184.5
171.7
to
Co

Aspiration Coefficient [A]
Stokes Number (K)
Figure 35.
Sampling efficiency vs. Stokes number at 45 misalignment for R = 2.0 and R = 0.5.

Aspiration Coefficient (A)
2.00
1.60
1.20
0.80
0 '1 0 -
0.00
0.01
Figure 36.
J L
I I I I 1
0.1
1 I I 1
1.0
Stokes Number (K)
10.0
Sampling efficiency vs. Stokes number at 30 misalignment for R = 2.0.
100

TABLE XVIII
ASPIRATION COEFFICIENT AS A FUNCTION OF STOKES NUMBER FOR R = 2.1, 0 = 90
Velocity
Particle Diameter
Nozzle Diameter
Aspiration
cm/sec
micrometers
cm
Stokes Number
Coefficient %
1676
3.5
0.465
0.195
1.8
1.5
1.3
o

102
Although the experimental data for 90 degrees do not agree well
with the prediction model, they do compare favorably with the emperical
equation of Laktionov(20) [equation (16)]. For the conditions of K =
0.195 and R = 2.1, his equation predicts as aspiration coefficient of
3.9%. This comparison is closer than would be expected considering the
fact that two completely different sampling schemes were used, and
Laktinov did not analyze the amount of particles collected in the probe.
It should be pointed out that the term for B'(K',0) does not equal
1 when 0=0. This means that equation (31) will not be equal to Belyaev
and Levin's predicting equations (5), (9) and (10) and therefore, equation
(31) should not be used for 0=0.
B. Tangential Flow Mapping
Eight traverse points for the velocity measurements were selected
according to EPA Method 1 (1) (see Table XIX). Measurements were made
using the 5-hole pitot tube at five axial distances from the inlet --
ID, 2D, 4D, 8D and 16D, where D is the inner diameter of the duct. At
each point in the traverse, the pitot tube was rotated until the pres
sure differential between pressure taps 2 and 3 (see Figure 25) was
zero. This angle was recorded as the yaw angle and the pressure readings
from all five pressure taps were recorded for later calculation of total
and static pressure, and pitch angle.
During the initial velocity traverse, a core area was discovered
in the center of the duct where the direction of the flow could not be
determined with the pitot tube. The core area was characterized by
negative readings at all five pressure taps which did not vary much

TABLE XIX
LOCATION OF SAMPLING POINTS
Point % of Diameter Distance from Wall, cm
1 3.3 0.65
2 10.5 2.07
3 19.4 3.83
4 32.3 6.38
5 67.7 13.36
6 80.6 15.91
7 89.5 17.67
8 96.7 19.09
Duct Diameter = 19.74 cm

104
with the rotation of the probe. Inside the core area it was not possible
to determine the direction of flow because there was no point in the 360
degree rotation of the probe where the pressures at point 2 and 3 were
the same. The location of the core area was measured at each location
along the duct axis and recorded. During the velocity measurements, it
was observed that the flow was very sensitive to downstream disturbances.
A crosswind at the end of the pipe produced large fluctuations in the
pressure measurements.
Figure 37 shows the graphical interpretation of the pitch and yaw
components of velocity. The two radii r^ and r9 represent the distance
from the center of the duct to the outer boundary of the core region.
The area in the core region was approximated by the following equation:
A
core
2
Tr(r1
~~~2
+ r.
(32)
Tables XX-XXIV show the calculated results of the velocity measure
ments at the five axial positions. The low flow was the flow measured
when a restriction was placed at the inlet of the blower. The restriction
induced approximately a 40% decrease in the flow rate. The high flow rate
represented a volumetric flow rate of 15,500 liters per minute, and the
low flow rate was 11,260 liters per minute. The Reynolds number of the
system calculated on a basis of the average axial flow rate were 80,000
and 111,000 for the low and high flow rates respectively.
After the data were broken down, it appeared that data from point
number 1 did not agree well with the rest of the traverse points. Upon

Sampling
points
Figure 37. Cross sectional view of a tangential flow' stream locating pitch and yaw directions,
sampling points, and the negative pressure region.
105

TABLE XX
FIVE-HOLE PITOT TUBE MEASUREMENTS
MADE AT 1 DIAMETER DOWNSTREAM OF THE CYCLONE
Point
1-D Low Flow
Total
Angles, Degrees Velocity
Pitch Yaw (j) cm/sec
Axial
Velocity
cm/sec
Tangential
Velocity
cm/sec
1
kkk
k k
kkk
kkk
kkk
kkk
2
25.5
67.9
70.1
1786
608
1655
3
17.0
77.4
78.0
1600
333
1561
4
+ + +
+ + +
+ + +
+ + +
+ + +
+ + +
5
3.0
76.0
76.0
1341
324
1301
6
21.0
60.0
62.2
1761
821
1525
7
30.0
51.0
57.0
1762
959
1369
8
32.0
48.0
55.4
1664
945
1237
1-D High Flow
Total
Axial
Tangential
Aneles. Deerees
Velocity
Velocity
Velocity
Point
Pitch
Yaw

cm/sec
cm/sec
cm/sec
1
* k
kkk
kkk
kkk
kkk
kkk
2
24.0
64.0
66.4
2782
1114
2500
3
19.0
78.5
79.1
2348
444
2301
4
+ + +
+ + +
+ + +
+ + +
+ + +
+ + +
5
3.0
74.4
74.4
1846
496
1778
6
22.0
63.8
65.8
2699
1106
2421
7
28.0
57.8
61.9
2742
1292
2320
8
31.0
54.6
60.23
2572
1277
2096
*** Point No. 1
was too
close to
the wall to
allow insertion of all five
pressure taps.
+++ Point lies inside the negative pressure section.

107
TABLE XXI
Point
MADE
An,
Pitch
FIVE-HOLE PITOT TUBE MEASUREMENTS
AT 2 DIAMETERS DOWNSTREAM OF THE CYCLONE
2-D Low Flow
Total Axial
gles, Degrees Velocity Velocity
Yaw cj> cm/sec cm/sec
Tangential
Velocity
cm/sec
1
k k k
k k *
kkk
kkk
kkk
kkk
2
24.0
60.6
63.3
1754
788
1528
3
17.0
73.0
73.8
1601
447
1531
4
+ + +
+ + +
+ + +
+ + +
+ + +
+ + +
5
+ + +
+ + +
+ + +
+ + +
+ + +
+ + +
6
17.0
64.0
65.2
1746
732
1569
7
25.5
54.4
58.3
1761
925
1432
8
30.5
50.4
57.0
1672
910
1288
2-D High Flow
Total
Axial
Tangential
Angles, Degrees
Velocity
Velocity
Velocity
Point
Pitch
Yaw
cm/sec
cm/sec
cm/sec
1
kkk
kkk
k k k
kkk
kkk
kkk
2
21.0
60.4
62.5
2597
1199
2258
3
14.0
72.8
73.3
2276
654
2174
4
+ + +
+ + +
+ + +
+ + +
+ + +
+ + +
5
37.0a
76.0
78.9
2057
396
1996
6
16.0
64.0
65.1
2676
1127
2405
-7
/
27.0
56.6
60.6
2646
1199
2209
8
32.0
53.6
59.8
2621
1518
2110
*** Point No. 1 was too close to the wall to allow insertion of all five
pressure taps.
+++ Point lies inside the negative pressure section.
a This high valve can probably be attributed to one of the pitch pressure
taps extending into the negative pressure area.

108
TABLE XXII
FIVE-HOLE PITOT TUBE MEASUREMENTS
MADE AT 4 DIAMETERS DOWNSTREAM OF THE CYCLONE
Point
4-D Low Flow
Total
Angles, Degrees Velocity
Pitch Yaw (j) cm/sec
Axial
Velocity
cm/sec
Tangential
Velocity
cm/sec
1
kkk
* kk
***
k k k
kkk
kkk
2
26.0
49.0
53.9
1484
874
1120
3
15.0
58.0
59.2
1524
780
1292
4
4.0
78.0
78.0
1144
238
1119
5
+ + +
+ + +
+ + +
+ + +
+ + +
+ + +
6
13.0
66.8
67.4
1548
595
1423
7
20.0
57.2
59.4
1592
810
1338
8
24.5
54.4
58.0
1559
826
1268
4-D High Flow
Total
Axial
Tangential
Ang
les, Degrees
Velocity
Velocity
Velocity
Point
Pitch
Yaw
cm/sec
cm/sec
cm/sec
1
kkk
* k k
kkk
k k k
kkk
k k k
2
25.0
48.0
52.7
2293
1389
1704
3
16.5
58.6
60.3
2286
1133
1951
4
3.0
82.6
82.6
1651
212.6
1637
5
+ + +
+ + +
+ + +
+ + +
+ + +
+ + +
6
15.0
68.6
69.2
2266
804
2110
7
20.0
59.4
61.4
2425
1161
2087
8
27.0
56.0
60.1
2314
1153
1918
*** Point No. 1
was too close to
the wall to
allow insert
ion of all fiv
pressure taps.
+++ Point lies inside the negative pressure section.

TABLE XXIII
FIVE-HOLE PITOT TUBE MEASUREMENTS
MADE AT 8 DIAMETERS DOWNSTREAM OF THE CYCLONE
109
8-D Low Flow
Point
Angles, Degrees
Pitch Yaw cf)
Total
Velocity
cm/sec
Axial
Velocity
cm/sec
Tangential
Velocity
cm/sec
1
kkk
***
kkk
k k k
kkk
kkk
2
19.5
59.0
61.0
1414
685
1212
3
15.0
69.0
70.3
1436
484
1346
4
+ + +
+ + +
+ + +
+ + +
+ + +
+ + +
5
8.0
63.6
63.9
1396
614
1250
6
20.0
50.2
53.0
1326
798
1019
7
28.0
39.4
47.0
1289
879
818
8
29.0
38.0
46.4
1231
849
758
8-D High
Flow
Point
.Angle
Pitch
s, Degrees
Yaw cf>
Total
Velocity
cm/sec
Axial
Velocity
cm/sec
Tangential
Velocity
cm/sec
1
k k k
* *
kk-k
k kk
kkk
kkk
2
19.0
57.0
59.0
1875
966
1572
3
9.0
70.0
70.3
1881
634
1767
4
+ + +
+ + +
+ + +
+ + +
+ + +
+ + +
5
0
64.6
64.6
1743
748
1574
6
15.0
50.0
51.6
1942
1206
1488
7
21.0
43.2
47.1
1869
1272
1279
8
25.0
42.0
47.7
1795
1208
1201
*** Point No. 1 was too close to the wall to allow insertion of all five
pressure taps.
+++ Point lies inside the negative pressure section.

TABLE XXIV
FIVE-HOLE PITOT TUBE MEASUREMENTS
MADE AT 16 DIAMETERSDOWNSTREAM OF THE CYCLONE
16-D Low Flow
Point
Angles, Degrees
Pitch Yaw (J>
Total
Velocity
cm/sec
Axial
Velocity
cm/sec
Tangential
Velocity
cm/sec
1
* k *
kkk
k k k
k k k
kkk
kkk
2
27.0
34.0
42.4
1073
729
600
3
19.0
41.0
44.5
1169
834
767
4
9.0
58.6
59.0
1014
522
865
5
+ + +
+ + +
+ + +
+ + +
+ + +
+ + +
6
13.0
63.0
63.7
929
412
828
7
17.0
50.4
52.3
1205
735
928
8
18.0
47.6
50.11
1190
763
979
16-D
High Flow
Point
Ang
Pitch
les, Degrees
Yaw (f>
Total
Velocity
cm/sec
Axial
Velocity
cm/sec
Tangential
Velocity
cm/sec
1
k k k
kk k
k k k
k k k
k k k
kkk
2
22.5
36.4
42.0
1553
1154
921
3
21.0
44.0
47.8
1653
1110
1148
4
9.0
66.0
66.3
1513
608
1382
5
+ + +
+ + +
+ + +
+ + +
+ + +
+ + +
6
12.0
61.2
61.9
1675
789
1468
7
20.0
53.4
55.9
1753
983
1407
8
19.0
49.0
51.7
1739
1078
1312
*** Point No. 1 was too close to the wall to allow insertion of all five
pressure taps.
+++ Point lies inside the negative pressure section.

Ill
checking the measurement setup, it was discovered that because of the
construction of the probe and the closeness of the first traverse
point to the opening, one of the pitch pressure points was not completely
in the flow stream. Because of this, data from traverse point number 1
are not presented with the rest of the data.
The velocity measurements at the other traverse points for both
flow rates and all five axial distances showed approximately the same
characteristics. The pitch angle increased from the core area to the
duct wall. The yaw angle and the combined angle (p decreased from the
core area to the walls. At the inlet and up to eight diameters down
stream, angles as high as 70 degrees were found near the core area of
the flow field. The total velocity, axial velocity, and the tangential
velocity all showed the same cross sectional flow pattern. The velocities
were minimum at the core, increased with radius and then slightly decreased
near the wall. These patterns are similar to those found in the swirling
flow generated with fixed vanes (23).
In order to observe the changes in the flow as a function of axial
distance from the inlet, the cross sectional averages of the angle cf>,
core area, and tangential velocity were calculated and presented in Table
XXV and plotted in Figures 38 and 39. All three parameters show a very
gradual decay of the indicators of tangential flow as was expected from
the reported tests (23). The curves have the same shape for both flow
rates.
The high core area for the measurements at 16 diameters downstream
was confirmed by repeated measurements. These values may be due to a

112
TABLE XXV
AVERAGE CROSS SECTIONAL VALUES
AS A FUNCTION OF DISTANCE DOWNSTREAM AND FLOW RATE
Average Values for High Flow
Diameters
4)
Location of*
Tangential Velocity
Core Area
Downstream
[degrees)
Core Area (cm)
(cm/sec)
(cm2)
1
68.0
5.40 13.04
2223
47.23
2
66.7
5.78 13.22
2190
43.94
4
64.3
6.79 13.93
1901
40.78
8
56.7
5.58 12.51
1480
38.26
16
54.3
7.43 14.62
1273
44.78
Average
: Values for Low
Flow
-
Diameters
Location of*
Tangential Velocity
Core Area
Downstream
(degrees)
Core Area (cm)
(cm/sec)
(cm2)
1
66.45
5.42 12.87
1441
45.16
2
63.5
5.85 13.07
1469
41.39
4
62.7
7.05 13.93
1260
38.45
8
56.9
5.63 12.23
1067
37.03
16
52.0
7.99 14.69
811
42.13
* Center of the duct is at 9.87 cm.

Angle U>)
Figure 38. Decay of the average angle 0 and the core area along the axis of the duct
uojy 3-1:)

Tangential Velocity (cm/sec)
Hiametoys downstream
Figure 39. Decay of the tangential velocity component along the axis of the duct.
114

115
disturbance effect of the end of the duct which was only a few diameters
downstream of the sampling point. The increase in average tangential
velocity at 2 diameters from the inlet can be attributed to the fact
that two of the traverse points were within the core area. It can be
seen from the other profiles that the inner points had lower velocity
values, and therefore the exclusion of the inner points would lead to a
higher velocity average.
Plotted in Figure 40 is the location of the core area with respect
to the duct center. It can be seen that the swirling flow is indeed not
axisymmetric and the location of the core area changes location with
axial distance. Only one drawing is used to represent the situation for
both high and low flow rate because the location for both conditions was
almost identical.

1
6 8 10
Diameters downstream
14
16
Figure 40. Location of the negative pressure region as a function of distance downstream from the
cyclone.
O'

CHAPTER V
SIMULATION OF AN EPA METHOD 5 EMISSION TEST
IN A TANGENTIAL FLOW STREAM
A model has been developed and tested which describes particle
collection efficiency as a function of particle characteristics, angle
of misalignment, and velocity ratio. Together with the measurement of
velocity components in a swirling flow it is possible to analyze the
emission rate errors that would occur when performing a Method 5
analysis of the effluent stream following a cyclone.
For this simulation analysis, the volumetric flow rate and iso
kinetic sampling velocities are calculated from velocity measurements
obtained at the eight diameter sampling location using a S-type pitot
tube (see Tables XXVI and XXVII) The angle , velocity ratio, and
particle velocity are determined from velocity measurements made at
the same location using the five-hole pitot tube (see Table XXII).
The particle characteristics are obtained from particle size distribution
tests made by Mason (22) on basically the same system. From a particle
distribution with a 3.0 pm MMD and geometric standard deviation of 2.13
(see Figure 41) ten pa'rticle diameters were selected which represent
the midpoints of 10% of the mass of the aerosol (see Table XXVIII). The
density of the particles was assumed to be 2.7 g/cm The nozzle diameter
was selected using the standard criteria to be 0.635 cm (1/4 inch). In
the model it was assumed that the nozzle would be aligned parallel with
the axis of the stack, and therefore, 0 = tj).
117

118
TABLE XXVI
S-TYPE PITOT TUBE MEASUREMENTS
MADE AT THE 8-D SAMPLING PORT FOR THE LOW FLOW CONDITION
Point
Dynamic
Pressure
(cm H0)
.
Static
Pressure
(cm Ho0)
Ap
(cm H^O)
Ap2 ,
(cm Ho0) 2
Velocit;
(cm/sec'
8
0.96
-0.36
1.32
1.15
1229.0
7
0.99
-0.48
1.47
1.21
1298.5
6
0.66
-0.89
1.55
1.24
1331.6
5
-1.07
-0.74
0.33
0.57
614.7
4
-1.32
-1.04
-0.28
-0.53
-565.6
3
-0.41
-0.46
0.05
0.22
241.1
2
0.30
-0.17
0.47
0.69
743.2
1
0.69
-0.10
0.79
0.S9
949.3

119
TABLE XXVII
S-TYPE PITOT TUBE MEASUREMENTS
MADE AT THE 8-D SAMPLING PORT FOR THE HIGH FLOW CONDITION
Point
Dynamic
Pressure
(cm Ho0)
Static
Pressure
(cm Ho0)
8
2.03
-0.66
7
1.83
-1.57
6
1.17
-2.23
5
-2.26
-2.79
4
-1.83
-1.32
3
-0.89
-1.02
2
0.61
-0.43
1
0.91
o
11
o
1
Ap
(cm Ho0)
Ap2 j,
(cm Ho0) 2
Velocity
(cm/sec)
2.69
1.64
1755.4
3.40
1.84
1974.7
3.40
1.84
1974.7
0.55
0.73
781.3
-0.51
-0.71
-762.5
0.13
0.36
381.2
1.04
1.02
1091.7
1.02
1.01
1078.3

Percent Less Than
99.9
Figure 41. Particle size distributions used in the simulation model.
120

121
TABLE XXVIII
MIDPOINT PARTICLE DIAMETERS
FOR THE 10 PERCENT INTERVALS OF THE MASS DISTRIBUTION
MMD = 3ym a = 2.13
o
^mid
Range
Midpoint
(y meters)
Dp"C
0 10
5
0.84
0.84
10 20
15
1.32
1.96
20 30
25
1.75
3.35
30 40
35
2.20
5.20
40 50
45
2.70
7.73
50 60
55
3.25
11.09
60 70
65
4.00
16.65
70 80
75
4.90
24.80
SO 90
85
6.60
- 44.63
90 100
95
10.40
109.84

122
Using these parameters the average aspiration coefficients are
determined at each traverse point using the ten particle diameters and
equations (33) (39).
A., (1*2 ,(f>2 j K9)
A3(r3^3,K3)
1A r + 1A .+ .1A co + ..
Dp5-s Dplb-6 Dp25-6
' + 1ADp95%
(53)
1A _0 + 1A _0 + 1A_ O[ro +
Dp5% Dpl5% Dp25%
" + '1ADp95%
(34)
.
(35)
(36)
(37)
AgiRg^g^g) 1ADp5?6 + -1ADpl5% + 1ADp25;
+ 1A
Dp95%
(38)
(39)
Where A^ = total aspiration coefficient for traverse point i.
= (total velocity at i)/(sampling velocity at i).
cj> = angle of flow at point i relative to the axis of the stack.
K.,= Stokes number based on the nozzle diameter, total velocity
lk
at i, and particle diameter Dp. 0 .
K' Dp, 0= Midpoint particle diameters each representing 10% of the
total mass.
Since the sampling velocity will determine the volume of air sampled at
each traverse point, the total aspiration coefficient for each flow rate
is determined by taking an average weighted according to sampling velocity.
V.A + V.A_
10 0
iz
V.nA^ + V.-A, + V._A_ + V.nA
i5 5
i6 6
i7 7
i8 8
V. + V., + V._ + V., + V._ + V
i2 10 i5 16 i7 18
(40)
Where (Y ) = inlet velocity at traverse point j.
Because of the missing data at point. 1 and negative pressure section at
point 4, these two traverse points were not used in the analysis.

123
The total aspiration coefficients calculated in this manner for
the low and high flow rates were 0.937 and 0.906 respectively (see
Table XXIX and XXX). There are two reasons for the relative low amounts
of concentration error found in this analysis. One reason is that the
two mechanisms causing sampling error, nozzle misalignment and aniso-
kinetic sampling velocities, cause errors in the opposite direction.
The S-type pitot tube detected a velocity less than or equal to the
actual velocity which would lead to subisokinetic sampling producing
an increased concentration. The nozzle misalignment when sampling
parallel to the stack wall would produce a decreased concentration. So
each of these errors has a tendency of reducing the other error.
Another reason for the small errors was the small size of the
aerosol. The Stokes numbers for over 50% of the particles were less
than 0.2 and 0.3 for the low and high flow rates respectively. These
values lead to small sampling errors, even when isokinetic sampling
conditions are not maintained.
Mason experimentally determined that the collection efficiency should
be on the order of 50% (22). Since the flow rate used by Mason was ap
proximately midway between the high and low flow rate in this study, the
flow patterns should be approximately the same. The discrepancy between
Mason's experimental values and the values predicted by the simulation
probably can be accounted for as experimental error by Mason. It would
be nearly impossible to obtain a 50% sampling error for an aerosol as
small as the one used without extreme anisokinetic sampling conditions.
Mason also found a 40% error when sampling at the angle associated with

124
TABLE XXIX
ASPIRATION COEFFICIENTS
CALCULATED IN THE SIMULATION MODEL FOR THE LOW FLOW CONDITION
Sampling Velocity True Velocity
from S-Type Pitot from 5.-Hole Pitot Point
Tube (cm/sec]
Tube (cm/sec')
Degrees
R
Ci/Co
1
949.3
* *
* *
* *
* **
2
743.2
1414
61.0
1.9
97.0
3
241.1
1456
70.3
6.0
142.0
4
+ + +
+ + +
+ + +
+ + +
+ + +
5
614.7
1396
63.9
2.3
100.5
6
1351.6
1326
53.0
1.0
86.5
7
1298.5
1289
47.0
0.99
90.1
8
1229.0
1231
46.4
1.0
90.7
Weighted Average = 93.7

125
TABLE XXX
ASPIRATION COEFFICIENTS
CALCULATED IN THE SIMULATION MODEL FOR THE HIGH FLOW CONDITION
Point
Sampling Velocity
from S-Type Pitot
Tube (cm/sec)
True Velocity
from 5-Hole Pitot
Tube (cm/sec)
Degrees
R
Ci/Co%
1
1078.3
k k k
* k k
k k k
kkk
2
1091.7
1875
59.0
1.72
95.06
3
381.2
1881
70.3
4.90
131.85
4
+ + +
+ + +
+ + +
+ + +
+ + +
5
781.3
1743
64.6
2.20
97.60
6
1974.7
1942
51.6
0.98
84.10
7
1974.7
1869
47.1
0.95
86.30
8
1755.4
1795
47.7
1.02
88.30
Weighted Average
=
90.6

126
the maximum Ap. From Figure 15 it is apparent that by splitting the
difference between the angles where the velocity pressure drops off
rapidly, it should be possible to get within 20 degrees of the zero
yaw angle. This means that the sample velocity measured by the S-type
pitot tube will be approximately the same as the true total velocity
and therefore, the sampling error should be no greater than the cosine
of 20 degrees or 0.94. This would represent the maximum error for a
very large aerosol and would be much less for the aerosol used in the
study. Since Mason's sampling error is almost ten times as high as
the theoretical maximum, it must be attributed to some flaw in the
experimental setup.
In order to see how much greater the error would be for larger
particles, a similar analysis was performed using a distribution with
a 10 pm mass mean diameter and 2.3 geometric standard deviation (see
Figure 41). This was the distribution obtained at the outlet of a
cyclone in a hot-mix asphalt plant (43) Because of the larger diameter
particles the sampling efficiency was reduced to 0.799 for the high flow
condition.
The volumetric flow rates determined from the S-type pitot tube
measurements are compared with the flow rates calculated from five-hole
pitot tube measurements in Table XXXI. The axial flow rates using the
five-hole pitot tube data are calculated by multiplying the average axial
velocity by the inner duct area minus the core area. The flow rates
using the S-type pitot tube data were determined using two different
methods varying in how the negative velocity at port four is handled.

TABLE XXXI
RESULTS OF THF. CYCLONE OUTLET SIMULATION MODEL
FOR THREE CONDITIONS
Particle Size Flow Concentration, Flow Rate3, Flow Rate'3, Emission Ratea,
Distribution Condition Measured/True Measured/True Measured/True Measured/True
MMD 3 ym
ag = 2.13
Low
0.937
1.27
1.16
1.19
MMD 3 ym
ag = 2.13
High
0.906
1.28
1.17
1 .16
MMD 10 ym
og =2.3
High
0.799
1.28
1.17
1.02
a Negative velocity is not used in the calculation of average velocity,
b Negative velocity is used in the calculation of average velocity.
Emission Rate ,
Measured/True
1.09
1.06
0.93

r
128
In the first method, the negative velocity is not used to determine
the average axial velocity. The volumetric flow rate is calculated by
multiplying the average axial velocity by 7/8th of inner cross sectional
area. In the second method, the negative value is used in the determi
nation of the average velocity and the entire inner duct area is used to
determine the flow rate.
The results presented in Table XXX, show that the insensitivity of
the S-type pitot tube to yaw angle produces a higher calculated flow
rate by approximately 28%. By incorporating the negative velocity in
the average velocity determination, this error is reduced to 17%.
It should be noted that the S-type pitot tube data fit very well
what would be expected from looking at the sensitivity of the pitot
tube to yaw angle (Figure 15). When the traverse point had a yaw angle
less than approximately 45 degrees, the S-type pitot tube readings were
very close to the total velocity. However, beyond angles of 45 degrees
the pitot tube readings drop off quite rapidly and at 70 degrees, the pitot
tube was reading a value of less than one fifth of the true value.
The errors for both sampling efficiency and flow rate determination
are presented in Table XXXI for the three simulated conditions. The
sampling errors and flow rate errors are in opposite direction so that
when the two values are combined to determine emission rate, the overall
effect is reduced.

7
CHAPTER VI
SUMMARY AND RECOMMENDATIONS
A. Summary
Results of experiments in this study have led to a better understanding
of the types and magnitude of errors that are involved when attempting to
obtain a representative sample of particulate matter from gas streams with
complex flow patterns. The errors induced by tangential flow were analyzed
from two separate approaches. The first involved analysis of particle sam
pling error as a function of particle characteristics, sampling velocity
relative to the flow stream velocity, and angle of the nozzle relative to the
direction of flow. The second involved analysis of swirling flow patterns and
their subsequent effect on flow measurements made by the S-type pitot tube.
Particle sampling errors as a function of velocity ratio and angle of
misalignment were studied by taking comparative anisokinetic and isokinetic
samples from a straight section of duct. By analyzing the problem in this
method the data obtained are more useful and have many more applications
beyond this study. They provide fundamental information for a better under
standing of the inertial effects in aerosol sampling.
The flow measurement errors were analyzed by mapping the exact flow
pattern at the exit of a cyclone using a five-hole pitot tube. Cross sec
tional profiles were measured at five axial distances along the stack to
determine how the flow pattern changes as it moves up the stack. S-type
pitot tube measurements were taken and compared to the results of the
five-hole pitot tube measurements.
129

7
130
The two aspects of this study, anisokinetic sampling errors and
flow measurements, were combined in a simulation model to determine the
magnitude of errors when an EPA Method 5 emission test is performed at
the exit of a cyclone.
A summary of the important results determined from this study is
as follows:
A. The flow patterns found in a stack following the exit of a
small industrial cyclone are of such a nature that it makes it extremely
difficult to obtain a representative sample with the present EPA recom
mended equipment. Angles in excess of 70 degrees relative to the stack
axis are found in some parts of the flow. Since large scale turbulence,
such as swirling flow, is inherently self-preserving in round ducts, it
decays very slowly as it moves up the stack and therefore sampling at
any location downstream of the cyclone will involve the same problems.
B. The yaw characteristics of the S-type pitot tube lead to several
types of errors when used in a tangential flow stream. Wien the angle
of yaw is less than 45 degrees, the measured velocity is greater than or
equal to the actual velocity with the maximum error being approximately
5%. Beyond 45 degrees the measured velocity drops off quite rapidly and
at an angle of 70 degrees the measured velocity is less than half the
true velocity. Because of its yaw characteristics, the S-type pitot tube
is not suitable for distinguishing the axial component of flow from the
total flow which includes the tangential component. Volumetric flow
calculations based on S-type pitot tube measurements in a swirling flow
were found to be in excess of the actual flow by as much as 309.

131
C. Pitot tubes based on the five-hole and three-hole designs are
useful tools in determining the velocity components in a tangential
flow field. The five-hole pitot tube has the advantage of giving pitch
information as well as the yaw angle. However, in a cyclonic flow
stream, the yaw angle is of much greater magnitude than the pitch angle
and therefore, the pitch angle can be ignored with small error. In the
situation modeled, if pitch angle were ignored, the calculated flow rate
would be in error by less than 6%.
D. The particle sampling errors due to anisokinetic sampling
velocity and nozzle misalignment were analyzed and a model was developed
to describe the sampling efficiency as a function of velocity ratio (R),
misalignment angle (0), particle diameter, particle velocity, and nozzle
diameter. It was found that the maximum error for R = 1, approached
(1 cos0). When both a nozzle misalignment and anisokinetic sampling
velocities are involved then the maximum error approaches ¡1 Rcos@|.
The equations and their limiting conditions for predicting the aspiration
coefficient are summarized in Table XXXII.
E. The Stokes number adequately describes the inertial character
istics of particle sampling. However, when the nozzle is misaligned to
the flow stream, there is an apparent change in the inertial properties
which is due to a reduced projected nozzle diameter. A correction factor
was developed to adjust the Stokes number to take this into account.
F.When the probe wash was analyzed separately from the filter,
it was found that as much as 60% of the total particulate matter entering

A = 1
A = 1
A = 1
A = 1
where
TABLE XXXII
SUMMARY OF EQUATIONS PREDICTING PARTICLE SAMPLING BIAS
Equation
(cosO 1) B'(K',0)
(R-l) 3(K,R) (13)
R = 1
0 <_ 0 < 90
all K
0 = 0
0.16 < R < 5.5
all K
(RcosB
B(K1, R) B'(K^9)
J bO^Tr = 1)
0.5 <_ R < 2.3
0 < 0 < 90
all K
3K
(R)
0.5
(20)
0.003 < K < 0.2
1.25 < R < 6.25
0 = 90
C./C
i o
3(K,R) = 1 1/[1 + (2 + 0.617/R) K]
, ,, 0.0220
= ke
B(k3r = i)
1/(1 + 2.617K)
= V /V.
o 1
' (K' ,0) = 1 1/(1 + 55K'e'251(1)
132

135
the nozzle was collected on the nozzle walls. This has implications
not only on the importance of using the probe wash in the analysis,
but more importantly it implies that there may be possible problems
in obtaining accurate particle size data using a device such as an
impactor. If the collection of particles in the nozzle is particle
size dependent, then losses in the probe could lead to particle
sizing errors.
G. A simulation model was developed which incorporates the
information obtained in this study on particle sampling errors and
the flow mapping data. The particle sampling efficiency in a
tangential flow stream was, as expected, a function of particle size.
For a particle distribution with a mass mean diameter (MMD) of 3.0
pm and a geometric standard deviation of 2.13, the sampling errors
predicted were less than 10%. For a larger distribution with a mass
mean diameter of 10.0 pm and geometric standard deviation of 2.3, a
20% sampling error was predicted. One of the reasons that the sampling
errors were as small as these were, is that the two mechanisms inducing
sampling bias produce errors in opposite directions. The misalignment
of the nozzle caused by the tangential velocity component leads to a
reduction of sample concentration. The reduced sampling velocity,
calculated from S-type pitot tube measurements, leads to subisokinetic
sampling and an increased sample concentration. When these two mechanisms
are combined, the total error is reduced somewhat depending upon the
magnitude of the two errors.

134
B. Recommendations
EPA recommends that if the average angle of the flow relative to
the axis of the stack is greater than 10 degrees, then EPA Method 5
should not be performed. Since the maximum error in particle sampling
has been found to be (1 Rcos0), the 10 degree requirement is unduly
restrictive and a 20 degree limitation would be more appropriate. For
a 20 degree angle, the velocity measured by the S-type pitot tube would
be approximately the same as the true velocity (i.e., R = 1). Therefore,
the maximum error would be (1 cos 20) or 6% for a very large aerosol.
When cyclonic flow does not exist in a stack, EPA recommends
either straightening the flow or moving to another location. Because
of the physical limitations of these suggestions, a better approach
would be to modify Method 5 so that it could be used in a tangential
flow stream. By replacing the S-type pitot tube with a three-hole
pitot tube, the direction of the flow could be accurately determined
for aligning the nozzle, and the velocity components could be measured
for a correct calculation of volumetric flow rate. In addition to the
three-hole pitot tube, the modification would have to include a pro
tractor to measure the flow angle, an extra manometer, and a method of
rotating the probe without rotating the entire impinger box.

REFERENCES
1. Standards of Performance for New Stationary Sources. Federal Register,
36(247) :24876, 1971.
2. Revision to Reference Method 1-8. Federal Register, 42(160):41754, 1977
3. Wilcox, J. D. Isokinetic Flow and Sampling of Airborne Particulates.
Artificial Stimulation of Rain. Pergamon Press, New York, 1957, p. 177.
4. Lapple, C. E. and C. G. Shepherd. Calculation of Particle Trajectories.
Ind. Eng. Chem., 32(5):605, 1940.
5. Watson, H. H. Errors Due to Anisokinetic Sampling of Aerosols. Amer.
Ind. Hyg. Assoc. Quart., 15(1): 21, 1954.
6. Dennis, R., W. R. Samples, D. M. Anderson and L. Silverman. Isokinetic
Sampling Probes. Ind. Eng. Chem., 49(2) :294, 1957.
7. Hemeon, W. C. L. and G. F. Haines, Jr. The Magnitude of Errors in
Stack Dust Sampling. Air Repair, 4(3):159, 1954.
8. Whiteley, A. B. and L. E. Reed. The Effect of Probe Shape on the
Accuracy of Sampling Flue Gases for Dust Content. J. Inst. Fuel,
32:316, 1959.
9. Lundgren, D. A. and S. Calvert. Aerosol Sampling with a Side Port
Probe. Amer. Ind. Hyg. Assoc. J., 28(3) :208, 1967.
10. Badzioch, S. Collection of Gas-Borne Dust Particles by Means of an
Aspirated Sampling Nozzle. Brit. J. Appl. Phys., 10:26, 1959.
11. Fuchs, N. A. The Mechanics of Aerosols. The Macmillan Co., New York,
1964, p. 73.
12. Belyaev, S. P. and L. M. Levin. Investigation of Aerosol Aspiration
by Photographing Particle Tracks Under Flash Illumination. J. Aerosol
Sci., 3:127, 1972.
13. Belyaev, S. P. and L. M. Levin. Techniques for Collection of Representa
tive Aerosol Samples. J. Aerosol Sci., 5:325, 1974.
135

136
14. Davies, C. N. The Entry of Aerosols into Sampling Tubes and Heads.
Brit. J. Appl. Phys., Ser. 2, 1:921, 1970.
15. Martone, J. A. Sampling of Submicrometer Particles Suspended in Near
Sonic and Supersonic Free Jets of Air. Presented at the Annual Meeting
of the Air Pollution Control Association, Toronto, Canada, 1977.
16. Sehmel, G. Particle Sampling Bias Introduced by Anisokinetic Sampling
and Deposition within the Sampling Lines. Amer. Ind. Hyg. Assoc. J.,
31(6) : 758, 1970.
17. Glauberman, H. The Directional Dependence of Air Samplers. Amer. Ind.
Hyg. Assoc. J., 23(3):235, 1962.
18. Raynor, G. S. Variation in Entrance Efficiency of a Filter Sampler with
Air Speed, Flow Rate, Angle and Particle Size. Amer. Ind. Hyg. Assoc.
J., 31(3) :294, 1970.
19. Fuchs, N. A. Sampling of Aerosols. Atmos. Envir., 9:697, 1975.
20. Laktionov, A. G. Aspiration of an Aerosol Into a Vertical Tube from a
Flow Transverse to It. AD-760 947, Foreign Technology Division, Wright-
Patterson Air Force Base, Ohio, 1973.
21. Vitols, V. Theoretical Limits of Errors Due to Anisokinetic Sampling of
Particulate Matter. J. Air Pollut. Control Assoc., 16(2): 79, 1960.
22. Mason, K. W. Location of the Sampling Nozzle in Tangential Flow. M. S.
Thesis, University of Florida, Gainesville, Florida, 1974.
23. Baker, D. W. and C. L. Sayre. Decay of Swirling Turbulent Flow of Incom
pressible Fluids in Long Pipes. Flow: Its Measurement and Control in
Science and Industry, Volume 1, Part 1, Flow Characteristics. Instrument
Society of America, Pittsburgh, 1974, p. 301.
24. Chigier, N. A. Velocity Measurement in Vortex Flows. Flow: Its Measure
ment and Control in Science and Industry, Volume 1, Part 1, Flow Charac
teristics. Instrument Society of America, Pittsburgh, 1974, p. 399.
25. Hanson, H. A. and D. P. Saari. Effective Sampling Techniques for
Particulate Emissions from Atypical Stationary Sources. EPA-600/2-77-036,
U.S. Environmental Protection Agency, Research Triangle Park, N.C., 1977.
26. Brooks, E. F. and R. L. Williams. Process Stream Volumetric Flow Measure
ment and Gas Sample Extraction Methodology. TRW Document No. 24916-6028-
RU-00, TRW Systems Group, Redondo Beach, California, 1975.

137
27. Grove, D. J. and W. S. Smith. Pitot Tube Errors Due to Misalignment and
Nonstreamlined Flow. Stack Sampling News, November, 1973.
28. Hanson, H. A., R. J. Davini, J. K. Morgan and A. A. Iversen. Particulate
Sampling Strategies for Large Power Plants Including Nonuniform Flow.
EPA-600/2-76-170, U. S. Environmental Protection Agency, Research Triangle
Park, N.C., 1976, 349 pp.
29. Williams, F. C. and F. R. DeJarnette. A Study on the Accuracy of Type S
Pitot Tube. EPA 600/4-77-030, U. S. Environmental Protection Agency,
Research Triangle Park, N.C., 1977.
30. Lea, J. F. and D. C. Price. Mean Velocity Measurements in Swirling Flow
in a Pipe. Flow: Its Measurement and Control in Science and Industry,
Volume 1, Part 1, Flow Characteristics. Instrument Society of America,
Pittsburgh, 1974, p. 313.
31. Green, H. L. and W. R. Lane. Particulate Clouds: Dusts, Smokes and
Mists. E. F. M. Spon. Ltd., London, 1957, p. 36.
32. Air Pollution Manual. Part II Control Equipment. Amer. Ind. Hyg.
Assoc., Detroit, 1968, p. 4.
33. Whitby, K. T., D. A. Lundgren and C. M. Peterson. Homogeneous Aerosol
Generators. J. Air and Water Poll., 9:263, 1965.
34. Perry, J. K. Chemical Engineers' Handbook, McGraw-Hill, New York, 1941.
35. Flowmeter Computation Handbook. Amer. Soc. Mech. Eng., Ne\i York, 1961.
36. Fluid Meters, Their Theory and Application. H. S. Bean, Ed., Amer. Soc.
Mech. Eng., New York, 1971.
37. Doebelin, E. 0. Measurement Systems, Application and Design. McGraw-
Hill, New York, 1975.
38. Smith, F. H. The Effects of Nozzle Design and Sampling Techniques on
Aerosol Measurements. EPA-650/2-74-070, U. S. Environmental Protection
Agency, Washington, D. C., 1974, 89 pp.
39. Manual of Fluorometric Clinical Procedures. G. K. Turner Association,
Palo Alto, California, 1971.
40. American Institute of Physics Handbook. D. E. Gray, Ed., McGraw-Hill,
New York, 1957.

138
41. Sehmel, G. A. The Density of Uranine Particles Produced by a Spinning
Disc Aerosol Generator. Amer. Ind. Hyg. Assoc. J., 28(5) :491 1967.
42. Source Sampling Workbook. Control Programs Development Division, Air
Pollution Training Institute, Research Triangle Park, N. C., 1975.
43. Danielson, J. A. Air Pollution Engineering Manual, Environmental Pro
tection Agency, OAQPS, AP40, Research Triangle Park, N. C., 1973.

BIOGRAPHICAL SKETCH
Michael Durham was born on December 11, 1949, in Key West, Florida.
Being a member of a Navy family, he was constantly on the move and
attended eight different grade schools and two high schools in Hawaii,
Virginia, California and Kentucky. He studied two years at Texas A§M
University and then two at the Pennsylvania State University where he
received a B.S. in Aerospace Engineering in 1971. His next three years
were spent working with the National Academy of Science and the American
Psychological Association in Washington, D.C. In September 1974 he began
his graduate education in Environmental Engineering Sciences at the
University of Florida. After receiving a Master of Engineering in
August of 1975, he stayed on at the university as a graduate research
assistant in pursuit of a Ph.D. for three years, the result of which is
this dissertation.
139

I certify that I have read this study and that in ray opinion it
conforms to acceptable standards of scholarly presentation and is fully
adequate, in scope and quality, as a dissertation for the degree of
Doctor of Philosophy.
^U'nalC//U-'y\
Dale A.Lundgren, Chaijrjfsfn
Professor of Environmental
Engineering Sciences
I certify that I have read this study and that in my opinion it
conforms to acceptable standards of scholarly presentation and is fully
adequate, in scope and quality, as a dissertation for the degree of
Doctor of Philosophy.
LU.
t
Paul Urone
Professor of Environmental
Engineering Sciences
I certify that I have read this study and that in my opinion it
conforms to acceptable standards of scholarly presentation and is fully
adequate, in scope and quality, as a dissertation for the degree of
Doctor of Philosophy.
w C 1U-
\
Wayne £. Huber
Professor of Environmental
Engineering Sciences
I certify that I have read this study and that in my opinion it
conforms to acceptable standards of scholarly presentation and is fully
adequate, in scope and quality, as a dissertation for the degree of
Doctor of Philosophy.
/
L
/
<
y
[o.
/I' r . Cm
Alex E. Green
Graduate Research Professor of
Physics and Nuclear Engi
neering Sciences

This dissertation was submitted to the Graduate Faculty of the College
of Engineering and to the Graduate Council, and was accepted as partia
fulfillment of the requirements for the degree of Doctor of Philosophy
August, 1978
iLJht 0..
Dean, College of Engineering
Dean, Graduate School



23
A few analytical studies in this area have also been published.
Davies' (14) theoretical calculations of particle trajectories in a
nonviscous flow into a point sink determined the sampling accuracy
to be a function of the nozzle inlet orientation and diameter, the
sampling flow rate and the dust particle inertia. Vitols (21) also
made theoretical estimates of errors due to anisokinetic sampling.
He used a procedure combining an analog and a digital computer and
considered inertia as the predominant mechanism in the collection of
the particulate matter. However, the results obtained by Vitols are
only for high values of Stokes numbers and are of little value for
this study.
B. Summary of the Literature on Tangential Flow
Although anisokinetic sampling velocity is known to cause a
particle sampling bias or error, there are also several other sampling
error-causing factors such as: duct turbulence; external force fields
(e.g., centrifugal, electrical, gravitational or thermal); and probe
misalignment due to tangential or circulation flow. These factors are
almost always present in an industrial stack gas and cannot be assumed
to be negligible. Not only do these factors cause sampling error
directly but in addition, they cause particulate concentration gradients
and aerosol size distribution variations to exist across the stack -
both in the radial and angular directions.
1. Causes and Characteristics of Tangential Flow
Tangential flow is the non-random flow in a direction other than
that parallel to the duct center line direction. In an air pollution


64
measure of the flow perpendicular to the axis of the stack and tangent
to the stack walls. The pitch angle is a measure of the flow perpendic
ular to the axis of the stack and perpendicular to the stack walls. The
axial component of the velocity can therefore be determined from the
following equation:
V = V. coscb
a t r
(19)
where V
a
V
t
component of velocity flowing parallel to the axis of the stack,
total or maximum velocity measured by the pitot tube
cos ^ [cos(pitch) x cos(yaw)]


This dissertation was submitted to the Graduate Faculty of the College
of Engineering and to the Graduate Council, and was accepted as partia
fulfillment of the requirements for the degree of Doctor of Philosophy
August, 1978
iLJht 0..
Dean, College of Engineering
Dean, Graduate School


62
Figure 24.
Cyclone used in the study to generate swirling flow.


131
C. Pitot tubes based on the five-hole and three-hole designs are
useful tools in determining the velocity components in a tangential
flow field. The five-hole pitot tube has the advantage of giving pitch
information as well as the yaw angle. However, in a cyclonic flow
stream, the yaw angle is of much greater magnitude than the pitch angle
and therefore, the pitch angle can be ignored with small error. In the
situation modeled, if pitch angle were ignored, the calculated flow rate
would be in error by less than 6%.
D. The particle sampling errors due to anisokinetic sampling
velocity and nozzle misalignment were analyzed and a model was developed
to describe the sampling efficiency as a function of velocity ratio (R),
misalignment angle (0), particle diameter, particle velocity, and nozzle
diameter. It was found that the maximum error for R = 1, approached
(1 cos0). When both a nozzle misalignment and anisokinetic sampling
velocities are involved then the maximum error approaches ¡1 Rcos@|.
The equations and their limiting conditions for predicting the aspiration
coefficient are summarized in Table XXXII.
E. The Stokes number adequately describes the inertial character
istics of particle sampling. However, when the nozzle is misaligned to
the flow stream, there is an apparent change in the inertial properties
which is due to a reduced projected nozzle diameter. A correction factor
was developed to adjust the Stokes number to take this into account.
F.When the probe wash was analyzed separately from the filter,
it was found that as much as 60% of the total particulate matter entering


1 and 6 depending on the angle of misalignment. It was discovered that the
misalignment angle reduces the projected nozzle diameter and therefore ef
fects the Stokes number; a correction factor as a function of angle was
developed to adjust the Stokes number to account for this.
Using an equation empirically developed from these test results and
using the equations of Belyaev and Levin describing anisokinetic sampling
bias with zero misalignment, a mathematical model was developed and tested
which predicts the sampling error when both nozzle misalignment and aniso
kinetic sampling velocities occur simultaneously. It was found that the
sampling bias approached a maximum error |l-Rcos0¡ where R is the ratio of
the free stream velocity to the sampling velocity. During the testing, it
was discovered that as much as 60% of the particulate matter entering the
nozzle remained in the nozzle and front half of the filter holder. Implica
tions of this phenomenon with regard to particle sampling and analysis are
discussed.
The causes and characteristics of tangential flow streams are described
as they relate to problems in aerosol sampling. The limitations of the S-type
pitot tube when used in a swirling flow are discussed. A three dimensional or
five-hole pitot tube was used to map cross sectional and axial flow patterns
in a stack following the outlet of a cyclone. Angles as great as 70 degrees
relative to the axis of the stack and a reverse flow core area were found in
the stack.
Using information found in this study, a simulation model was developed
to determine the errors involved when making a Method 5 analysis in a tan
gential flow stream. For an aerosol with a 3.0 pm MMD (mass mean diameter)
xiv


Angle U>)
Figure 38. Decay of the average angle 0 and the core area along the axis of the duct
uojy 3-1:)


LIST OF TABLES--continued
Table Page
XV ASPIRATION COEFFICIENT AS A FUNCTION OF STOKES NUMBER
FOR R = 0.5, 0 = 60 95
XVI ASPIRATION COEFFICIENT AS A FUNCTION OF STOKES NUMBER
FOR 6 = 45, R = 2.0 AND 0.5 97
XVII ASPIRATION COEFFICIENT AS A FUNCTION OF STOKES NUMBER
FOR R = 2, 0 30 98
XVIII ASPIRATION COEFFICIENT AS A FUNCTION OF STOKES NUMBER
FOR R = 2.1, 0 = 90 101
XIX LOCATION OF SAMPLING POINTS 103
XX FIVE-HOLE PITOT TUBE MEASUREMENTS MADE AT 1 DIAMETER
DOWNSTREAM OF THE CYCLONE 106
XXI FIVE-HOLE PITOT TUBE MEASUREMENTS MADE AT 2 DIAMETERS
DOWNSTREAM OF THE CYCLONE 107
XXII FIVE-HOLE PITOT TUBE MEASUREMENTS FADE AT 4 DIAMETERS
DOWNSTREAM OF THE CYCLONE 108
XXIII FIVE-HOLE PITOT TUBE MEASUREMENTS NADE AT 8 DIAMETERS
DOWNSTREAM OF THE CYCLONE 109
XXIV FIVE-HOLE PITOT TUBE MEASUREMENTS MADE AT 16 DIAMETERS
DOWNSTREAM OF THE CYCLONE 110
XXV AVERAGE CROSS SECTIONAL VALUES AS A FUNCTION OF DISTANCE
DOWNSTREAM AND FLOW RATE 112
XXVI S-TYPE PITOT TUBE MEASUREMENTS NADE AT THE 8-D SAMPLING
PORT FOR THE LOW FLOW CONDITION 118
XXVII S-TYPE PITOT TUBE MEASUREMENTS NADE AT THE 8-DSAMPLING PORT
FOR THE HIGH FLOW CONDITION 119
XXVIII MIDPOINT PARTICLE DIAMETERS FOR THE 10 PERCENT INTERVALS
OF THE MASS DISTRIBUTION MMD = 3pm a =2.13 121
cr
o
VI


61


55
tension of the drop, the surface characteristics of the liquid are
quite important. The surface tensions of water and ethanol at 20
degrees C are respectively 72.8 and 22.3 dynes/cm (34). The effect
of this large difference can be seen in Table IV where the droplets
produced were approximately 37 ym for 90% ethanol and 23 ym for 100%
ethanol.
Before and after each test a sample of the particles was collected
on a membrane filter and sized using a light microscope to take into
account any slight variation in the performance of the spinning disc.
2. Ragweed Pollen
In order to obtain large Stokes numbers, ragweed pollen was
mechanically dispersed by means of a rubber squeeze bulb into the
inlet of the duct. The ragweed pollen had a NMD of 19.9 ym.
C. Velocity Determination
The velocity at each sampling point was measured using a standard
pitot tube. The flow was maintained constant during the test by con
trolling the pressure drop across a thin-walled orifice placed in the
system (35-37). Five orifice plates with orifices ranging in diameter
from 1.8 to 7.2 cm were used to obtain a range in duct velocities of
82 to 2460 cm/sec (see Table V) in the 10 cm duct. To obtain higher
velocities, a 5 cm duct was used.
A typical velocity profile across the 9.6 cm clear plastic duct
is presented in Table VI and plotted in Figure 22. The profile is


108
TABLE XXII
FIVE-HOLE PITOT TUBE MEASUREMENTS
MADE AT 4 DIAMETERS DOWNSTREAM OF THE CYCLONE
Point
4-D Low Flow
Total
Angles, Degrees Velocity
Pitch Yaw (j) cm/sec
Axial
Velocity
cm/sec
Tangential
Velocity
cm/sec
1
kkk
* kk
***
k k k
kkk
kkk
2
26.0
49.0
53.9
1484
874
1120
3
15.0
58.0
59.2
1524
780
1292
4
4.0
78.0
78.0
1144
238
1119
5
+ + +
+ + +
+ + +
+ + +
+ + +
+ + +
6
13.0
66.8
67.4
1548
595
1423
7
20.0
57.2
59.4
1592
810
1338
8
24.5
54.4
58.0
1559
826
1268
4-D High Flow
Total
Axial
Tangential
Ang
les, Degrees
Velocity
Velocity
Velocity
Point
Pitch
Yaw
cm/sec
cm/sec
cm/sec
1
kkk
* k k
kkk
k k k
kkk
k k k
2
25.0
48.0
52.7
2293
1389
1704
3
16.5
58.6
60.3
2286
1133
1951
4
3.0
82.6
82.6
1651
212.6
1637
5
+ + +
+ + +
+ + +
+ + +
+ + +
+ + +
6
15.0
68.6
69.2
2266
804
2110
7
20.0
59.4
61.4
2425
1161
2087
8
27.0
56.0
60.1
2314
1153
1918
*** Point No. 1
was too close to
the wall to
allow insert
ion of all fiv
pressure taps.
+++ Point lies inside the negative pressure section.


TABLE XI
ASPIRATION COEFFICIENT AS A FUNCTION OF STOKES NUMBER FOR 60 DEGREE MISALIGNMENT
Velocity
cm/sec
Particle Diameter
micrometers
Nozzle Diameter
cm
Stokes Number
Aspiration
Coefficient
1798
1.08
0.465
0.022
101.3
94.7
96.5
1798
1.37
0.465
0.034
98.9
95.0
99.4
1326
2.53
0.683
0.056
94.4
94.8
95.0
93.5
1326
3.23
0.683
0.090
92.5
90.7
91.1
92.2
1676
2.87
0.465
0.132
89.5
88.2
81.5
1798
3.15
0.465
0.170
89.3
90.0
91.7
85.0
83.2


32
described in the previous chapter. Concentration gradients occur
because the rotational flow in the stack acts somewhat as a cyclone.
The centrifugal force causes the larger particles to move toward the
walls of the stack, causing higher concentrations in the outer regions.
Mason (22) ran tests at the outlet of a small industrial cyclone
to determine the magnitude of these three types of errors induced by
cyclonic flow. Results of flow rates determined at the different
locations are presented in Table I. As indicated by the data, serious
errors can result in cases of tangential flow. A maximum error of 212%
occurred when the pitot tube was rotated to read a maximum velocity
head. Sampling parallel to the stack wall also had a large error of
almost 74%. When sampling downstream of the flow straightening vanes,
however, the error was reduced to 15%.
Tests performed at the same point but with different nozzle
angles produced the data in Table II. Measured dust concentration
was lowest when the sampling nozzle was located at an angle of 0 degrees
or parallel to the stack wall. The measured dust concentration con
tinued to increase at 30 and 60 degrees but then decreased at 90 degrees.
Equation (14) shows that when sampling at an angle, under apparent iso
kinetic conditions (i.e., R=l), the measured concentration will be less
than the true concentration by a factor directly proportional to the
cos0. A maximum concentration, which would be the true concentration,
will occur at 0 = 0, which from this data should lie at an angle between
60 and 90 degrees to the axis of the stack. This can be confirmed by


using the data in Table I and the geometry in Figure 11 to calculate
the angle cf>:
coscf) Vfl/V = 13/60 (17)
This is true for = 72 degrees.
Table III gives the results of the emission tests. Sampling with
the nozzle parallel to the stack wall showed an error of 53%.
Sampling at the angle of maximum velocity head reduced the error
to 40%. The results cannot be compared directly to those with the
parallel sampling approach because the feed rates were not the same
due to equipment failure and replacement. Sampling in the straightened
flow had a sampling error of 36%. It was expected that sampling at this
location would give better results, but some of the particles were im
pacted on the straightening vanes and settled in the horizontal section
of the duct, thus removing them from the flow stream.
Particle size distribution tests showed no significant effect of
a concentration gradient across the traverse. This was due to the
particles being too small to be affected by the centrifugal force field
set up by the rotating flow.
3. Errors Due to the S-Type Pitot Tube
The errors in the measurement of velocity and subsequent calculations
of flow rate in tangential flow are due primarily to the crudeness of the
instruments used in source sampling. Because of the high particulate
loadings that exist in source sampling, standard pitot tubes cannot be
used to measure the velocity. Instead, the S-type pitot tube must be used


LIST OF FIGURES--continued
Figure Page
33 Comparison of experimental data with results from Belyaev
and Levin 91
34 Sampling efficiency vs. Stokes number at 60 misalignment
for R = 2.0 and 0.5 96
35 Sampling efficiency vs. Stokes number at 45 misalignment
for R = 2.0 and R = 0.5 99
36 Sampling efficiency vs. Stokes number at 30 misalignment
for R = 2.0 100
37 Cross sectional view of a tangential flow stream locating
pitch and yaw directions, sampling points, and the nega
tive pressure region 105
38 Decay of the average angle 8 and the core area along the
axis of the duct 113
39 Decay of the tangential velocity component along the axis
of the duct 114
40 Location of the negative pressure region as a function of
distance downstream from the cyclone 116
41 Particle size distributions used in the simulation model... 120
x


51
development is due primarily to viscosity at the wall and not a function
of inlet conditions, whereas the profiles in the forced vortex field are
very dependent on the initial conditions at the inlet. Although no re
verse flow was found in these tests, other tests showed that strong
swirls may produce reversed axial velocities in the central region (23).
It should be noted that although tangential velocities and angular
momentum decay along the axis of the pipe, see Figures 12 and 13, even
after 44 diameter the tangential velocity is still quite significant
when compared to the axial velocity. Therefore, satisfying the EPA
Method 5 requirement of sampling 8 stack diameters downstream of the
nearest upstream disturbances will not eliminate the effect of sampling
in tangential flow.
The angle of the flow relative to the axis of the stack induced by
the tangential component of velocity was as high as 60 degrees at some
points in the flow. This compares well with angles found when sampling
the outlets of cyclones (25) Another interesting fact about the flow
described in Figures 12 and 13 is that the radial positions for the
tangential components W/U = 0 show that the vortex axis is off center
by as much as 0.1r/R. This indicates that the swirling fields are not
exactly axisymmetrical.
2. Errors Induced by Tangential Flow
Types of errors that would be expected to be introduced by tangential
flow are nozzle misalignment, concentration gradients and invalid flow
measurements. The sampling error caused by nozzle misalignment has been


89
5. The Effect of Nozzle Misalignment and Anisokinetic Sampling Velocity
To complete the analysis of anisokinetic sampling, it is necessary
to know what is the combined effect of both a nozzle misalignment and a
sampling velocity differing from the free stream velocity. The theoreti
cal model predicts that the sampling efficiency will be in the form
A = 1 + (Rcos0 1)3 (28)
where
3" = f[3(K,R) 3' (K',0)]
(29)
Since the reduction of projected nozzle diameter due to nozzle misalign
ment will effect the time available for a particle to change directions
when sampling at an anisokinetic velocity, the adjusted Stokes number K'
should also be used in the equation for 3 as well as 3'- Another modifi
cation that must be made in the model involves correcting for the fact
that 3(K',R) does not equal 1 when R = 1.
3(K', R = 1) = 1 -
1
1 + 2.617 K
(30)
To account for this 3'(K',0) must be divided by 3(K',R = 1) so that
equations (28) and (29) are valid at R = 1. The model to be tested now
becomes
A =
+ (Rcos0 1) 3(K',R)
3(K',0)
3(K\R 1)
(31)
At first there appears to be an obvious flaw in the model in that the
aspiration coefficient equals 1 whenever R = l/cos0 regardless of the


90
Stokes number. An example of this is when R = 2 and 0 = 60 degrees.
This phenomenum can be explained as follows. Since the projected
frontal area of the nozzle is one half the actual area when 0 = 60
degrees, in order to sample isokinetically such that there
is no divergence of streamlines into the nozzle, the sample velocity
must be one half of the free stream velocity or R = 2. Therefore,
the condition of R = l/cos0 defines the condition for obtaining a
representative sample when the nozzle is misaligned with the flow
stream.
Since the sampling methodologies used to determine 0(K,R) and
B'(K,0) were substantially different (photographic observation vs.
comparative sampling), it was necessary to see if the two methods
gave comparable results before the model could be tested. Four sets
of tests were run with two parallel nozzles; the control nozzle
sampled isokinetically and the test nozzle sampled anisokinetically.
Tests were performed at two Stokes numbers (K = 0.154 and K = 0.70)
and at two velocity ratios (R = 2.3 and R = 0.51). The aspiration
coefficients obtained by comparing the two measured concentrations are
presented in Figure 33 and Table XIII. The data obtained lie within
the experimental bounds of the lines produced from Belyaev and Levin's
data [Equations (5), (9) and (10)].
Since the two methods give comparable results, experiments were
run to test the model. A control nozzle was placed parallel to the
flow stream and the sampling velocity was set to be isokinetic. The
test nozzle was inserted at an angle from outside the duct and the
sampling velocity was set to be either one half or two times the free


ISOKINETIC SAMPLING OF AEROSOLS FROM
TANGENTIAL FLOW STREAMS
By
Michael Dean Durham
A DISSERTATION PRESENTED TO THE GRADUATE COUNCIL OF
THE UNIVERSITY OF FLORIDA
IN PARTIAL FULFILLMENT OF THE REQUIREMENTS FOR THE
DEGREE OF DOCTOR OF PHILOSOPHY
UNIVERSITY OF FLORIDA


19
theoretical predictions (i.e., measured concentration is less than or
equal to actual concentration and the concentration ratios decrease as
the particle size and the angle are increased), the data are of little
use since two important parameters, free stream velocity and nozzle
diameter, are not included in the analysis.
Raynor (18) sampled particles of 0.68, 6 and 20 ym diameter at
wind speeds of 100, 200, 400 and 700 cm/sec with the nozzle aligned
over a range of angles from 60 to 120 degrees. He then used a trigono
metric function to convert equation (5) to the form
A = 1 + B(K)[(V.sinG + V cosG)/(V.cosG + V sinG) 1]
i o i o
(11)
This function only serves to invert the velocity ratio between 0 and
90 degrees and does not realistically represent the physical properties
of the flow stream. In fact, equation (11) becomes unity at 45 degrees
regardless of what the velocity ratio or particle size is. This cannot
be true since it has been shown that the concentration ratio will be less
than unity and will decrease inversely proportional to the angle and
particle diameter.
A more representative function can be derived in the following
manner: Consider the sampling velocity to be greater than the stack
velocity V Let A. be the cross sectional area of the nozzle of diameter
o 1
D.. The stream tube approaching the nozzle will have a cross sectional
area A such that
o
A V = A. V.
(12)
0 0 11


22
would be for an angle of 90 degrees in which case the particles would
be traveling perpendicular to the nozzle. Since the nozzle has zero
frontal area relative to the flow stream, any particle that is collected
must make a turn into the nozzle. The amount of time that a particle
has to negotiate a turn is the time it takes the particle to traverse
the diameter of the nozzle, or D^/V Setting this equal to r the time
it takes a particle to change directions and rearranging terms, we ob
tain tV^/D^ = 1 as the limiting situation for a particle to be able to
make a turn into a nozzle positioned at a 90 degree angle to the flow
stream. For angles between 0 and 90 degrees the maximum error will
occur between the limits of Stokes numbers of 1 and 6 and should be
proportional to the average diameter of the frontal area of the nozzle.
Fuchs (19) suggests that for small angles the sampling efficiency will
be of the form
A = 1 4 sin(0K/7T) (15)
Laktionov (20) sampled a polydisperse oil aerosol at an angle to
the flow stream of 90 degrees for three subisokinetic conditions. He
used a photoelectric installation to enable him to determine the aspira
tion coefficients for different sized particles. From data obtained
over a range of Stokes numbers from 0.003 to 0.2 he developed the fol
lowing empirical equation:
A = 1
3K 0.5
(16)
This equation can be used only in the range of Stokes numbers given and
for a range in velocity ratios (R) from 1.25 to 6.25.


r
128
In the first method, the negative velocity is not used to determine
the average axial velocity. The volumetric flow rate is calculated by
multiplying the average axial velocity by 7/8th of inner cross sectional
area. In the second method, the negative value is used in the determi
nation of the average velocity and the entire inner duct area is used to
determine the flow rate.
The results presented in Table XXX, show that the insensitivity of
the S-type pitot tube to yaw angle produces a higher calculated flow
rate by approximately 28%. By incorporating the negative velocity in
the average velocity determination, this error is reduced to 17%.
It should be noted that the S-type pitot tube data fit very well
what would be expected from looking at the sensitivity of the pitot
tube to yaw angle (Figure 15). When the traverse point had a yaw angle
less than approximately 45 degrees, the S-type pitot tube readings were
very close to the total velocity. However, beyond angles of 45 degrees
the pitot tube readings drop off quite rapidly and at 70 degrees, the pitot
tube was reading a value of less than one fifth of the true value.
The errors for both sampling efficiency and flow rate determination
are presented in Table XXXI for the three simulated conditions. The
sampling errors and flow rate errors are in opposite direction so that
when the two values are combined to determine emission rate, the overall
effect is reduced.


69
important. This can be seen from the data taken at 60 degrees (see
Table IX) where an average of 54% of the particles was lost on the
walls.
The probe wash for eight tests using 6.7 ym uranine particles
was also analyzed separately for comparison with the results of the
ragweed pollen tests. While parallel sampling, from 15 to 34% of the
total mass was collected in the nozzle and front end of the filter
holder. While this was somewhat less than the amount of ragweed pol
len found in the nozzle, it is substantial enough to show the importance
of including the nozzle wash with the filter catch. Also because of the
variation of the percent collected in the nozzle during identical tests,
the probe wash cannot be accounted for by a correction factor. During
further testing, it was qualitatively observed that the percent in the
probe wash increased with particle size and decreased with increasing
nozzle diameter.
4. The Effect of Angle Misalignment on Sampling Efficiency
The aspiration coefficient was determined by comparing the amount
of particulate matter captured while sampling isokinetically with a
control nozzle placed parallel and a test nozzle set at an angle to the
flow stream. Tests were run at three angles, 30, 60 and 90 degrees.
The results showed the theoretical predictions to be quite accurate.
For all three angles the aspiration coefficient approached 1 for small
Stokes numbers (K), decreased as K increased and then leveled off at a
minimum of cos0 for large values of Stokes number. The most significant
changes occur in the range between K = 0.01 and K = 1.0.


CHAPTER III
EXPERIMENTAL APPARATUS AND METHODS
A. Experimental Design
The major components of the aerosol flow system can be seen in
Figure 20. An aerosol stream generated from a spinning disc generator
was fed into a mixing chamber where it was combined with dilution air.
The air stream then flowed through a 10 cm diameter PVC pipe containing
straightening vanes. This was followed by a straight section of clear
pipe from which samples were taken. The filter holder and nozzle used
as a control sample originated in a box following the straight section.
A test nozzle was inserted into the duct at an angle from outside the
box. A thin-plate orifice, used to monitor flow rate, followed the
sampling box. A 34000 pm industrial blower was used to move the air
through the system. The flow rate could be controlled by changing the
diameter of an orifice plate. An air by-pass between the blower and
the orifice plate was used as a fine adjust for the flow.
The sampling systems (see Figure 21] consisted of stainless steel,
thin-walled nozzles connected to 47 mm stainless steel Gelman filter
holders. Each filter assembly was connected in series to a dry gas
meter and a rotameter, and driven by an airtight pump with a by-pass
valve to control flow.
48


Pitch
I
~~1
Yaw
Pressure
Taps
Figure 17a. Conical version of a five-hole pitot tube.
Figure 17b. Fecheimer type three-hole pitot tube.
4^
hO


Figure 14. S-type pitot tube with pitch and yaw angles defined.
04
CO


138
41. Sehmel, G. A. The Density of Uranine Particles Produced by a Spinning
Disc Aerosol Generator. Amer. Ind. Hyg. Assoc. J., 28(5) :491 1967.
42. Source Sampling Workbook. Control Programs Development Division, Air
Pollution Training Institute, Research Triangle Park, N. C., 1975.
43. Danielson, J. A. Air Pollution Engineering Manual, Environmental Pro
tection Agency, OAQPS, AP40, Research Triangle Park, N. C., 1973.


107
TABLE XXI
Point
MADE
An,
Pitch
FIVE-HOLE PITOT TUBE MEASUREMENTS
AT 2 DIAMETERS DOWNSTREAM OF THE CYCLONE
2-D Low Flow
Total Axial
gles, Degrees Velocity Velocity
Yaw cj> cm/sec cm/sec
Tangential
Velocity
cm/sec
1
k k k
k k *
kkk
kkk
kkk
kkk
2
24.0
60.6
63.3
1754
788
1528
3
17.0
73.0
73.8
1601
447
1531
4
+ + +
+ + +
+ + +
+ + +
+ + +
+ + +
5
+ + +
+ + +
+ + +
+ + +
+ + +
+ + +
6
17.0
64.0
65.2
1746
732
1569
7
25.5
54.4
58.3
1761
925
1432
8
30.5
50.4
57.0
1672
910
1288
2-D High Flow
Total
Axial
Tangential
Angles, Degrees
Velocity
Velocity
Velocity
Point
Pitch
Yaw
cm/sec
cm/sec
cm/sec
1
kkk
kkk
k k k
kkk
kkk
kkk
2
21.0
60.4
62.5
2597
1199
2258
3
14.0
72.8
73.3
2276
654
2174
4
+ + +
+ + +
+ + +
+ + +
+ + +
+ + +
5
37.0a
76.0
78.9
2057
396
1996
6
16.0
64.0
65.1
2676
1127
2405
-7
/
27.0
56.6
60.6
2646
1199
2209
8
32.0
53.6
59.8
2621
1518
2110
*** Point No. 1 was too close to the wall to allow insertion of all five
pressure taps.
+++ Point lies inside the negative pressure section.
a This high valve can probably be attributed to one of the pitch pressure
taps extending into the negative pressure area.


Figure 15. Velocity error vs. yaw angle for an S-type pitot tubeT


68
TABLE VIII
PERCENT OF PARTICULATE MATTER COLLECTED IN THE PROBE WASH
FOR NOZZLES PARALLEL WITH THE FLOW STREAM
Probe Wash*
Filter-
Total*
% in Wash
511
497
196
218
161
250
366
721
407
697
377
669
265
464
415
647
351
522
220
240
442
614
1008
51
414
47
411
39
10S7
34
1104
37
1046
36
729
36
1062
39
873
40
460
35
1036
41
*Numbers represent the number of ragweed pollen counted.


ACKNOWLEDGEMENTS
This research was partially supported by a grant (Grant Number
R802692-01) from the Environmental Protection Agency (EPA)-, and was
monitored by EPA's Project Officer Kenneth T. Knapp. I thank them
both for their financial support during my graduate work.
I wish to thank Dr. Dale Lundgren and Dr. Paul Urone for the
important part that they played in my education. I am especially
appreciative of Dr. Lundgren for his guidance, encouragement and
confidence. He has provided me with opportunities for classroom,
laboratory and field experience that were far beyond what is expected
of a committee chairman.
I would like to thank Mrs. Kathy Sheridan for her assistance in
preparing this manuscript.
Finally, I wish to thank my parents for their advice and encourage
ment, and my wife Ellie for helping me through the difficult times.
11


24
control device, whenever centrifugal force is used as the primary
particle collecting mechanism, tangential flow will occur. Gas
flowing from the outlet of a cyclone is a classic example of tangential
flow and a well recognized problem area for accurate particulate sampling.
Tangential flow can also be caused by flow changes induced by ducting
(22). If the duct work introduces the gas stream into the stack
tangentially, a helical flow will occur (see Figure 9). Even if the
flow stream enters the center of the stack, if the ducting flow rate is
within an order of magnitude of the stack flow rate, a double vortex
flow pattern will occur (see Figure 10).
The swirling flow in the stack combines the characteristics of
vortex motion with axial motion along the stack axis. The gas stream
moves in spiral or helical paths up the stack. Since this represents
a developing flow field, the swirl level decays and the velocity pro
files and static pressure distributions change with axial position
along the stack. Swirl level is used here to represent the axial flow
or transport rate of angular momentum (23). Velocity vectors in
tangential or vortex flows are composed of axial, radial and tangential
or circumferential velocity components (see Figure 11). The established
vortex flows are generally axisymmetric but during formation of the
spiraling flow the symmetry is often distorted. The relative order of
magnitude of the velocity components varies across the flow field with
the possibility of each one of the components becoming dominant at
particular points (24).


Aspiration Coefficient (A)
2.00
1.60
1.20
0.80
0 '1 0 -
0.00
0.01
Figure 36.
J L
I I I I 1
0.1
1 I I 1
1.0
Stokes Number (K)
10.0
Sampling efficiency vs. Stokes number at 30 misalignment for R = 2.0.
100


12
where
0^ = particle diameter
C = Cunningham correction for slippage
pp = particle density
T = p CD 2/18n [4)
p p
p = viscosity of gas
D. = nozzle diameter
i
The relaxation time is defined as x; it represents how quickly a particle
can change directions. Watson concluded that to obtain a concentration
correct within 10%, the velocity ratio R must lie between 0.86 and 1.13
for the 32 micron particles and between 0.5 and 2.0 for the 4 micron
particles.
Data obtained by Dennis et al. (6) on a suspension of Cottrell
precipitated fly ash, 14 pm MMD, showed only a 10% negative error in
calculated concentration for sampling velocities 60% greater than iso
kinetic. Tests run on an atmospheric dust of 0.5 pm MMD produced no
detectable concentration changes even while sampling at a 400% variation
from isokinetic flow, thus indicating that isokinetic sampling is
relatively unimportant for fine particles. Hemeon and Haines (7)
measured errors due to the anisokinetic sampling of particles in three
size ranges (5-25, 80-100, and 400-500 pm) and in a range of nozzle to
stack velocities of 0.2 to 2.0. They found that where the velocity
ratio R ranges from 0.6 to 2.0 the extreme potential error was ap
proximately 50%, and that deficient nozzle velocities resulted in greater
errors than excessive nozzle velocities. In addition, they found that
for the coarse particles, the velocity into the nozzle had no important


9
the concentration collected by the nozzle will be equal to the number
of particles entering the nozzle, A.V C divided by the volume of
10 0
air sampled, A^V^.
A.V C C V
p ioo_ oo
i A.V. = V.
(2)
li i
The ratio of the sampled concentration to the true concentration then
is equal to the inverse of the velocity ratio. Therefore, the maximum
sampling bias for the condition of unmatched velocities is equal to
V /V or R. For example, if the sampling velocity is twice the free
stream velocity, the resulting concentration will be one half the actual
concentration.
For the case of a misaligned nozzle, a similar analysis is applied.
For the particles with very large inertia, only those lying directly in
line with the projected frontal area of the nozzle will be collected.
The measured concentration would again be the number of particles col-
o i
lected in the nozzle, A^cos0CqV divided by the volume of air sampled,
A.V.. Therefore, the ratio of the measured to the true concentration
i i
would be Vqcos0/\V or Rcos6. This represents the maximum sampling
error for anisokinetic sampling.


14
L is the distance upstream from the nozzle where the flow is undisturbed
by the downstream nozzle. It is a function of the nozzle diameter and
is given by the equation:
L = nDi (8)
It was observed that n lies between 5.2 and 6.8 (10).
Flash illumination photographic techniques were used by Belyaev and
Levin (12) to study particle aspiration. Photographic observations
enabled them to verify Badzioch's claim that L, the undisturbed distance
upstream of the nozzle, was between 5 to 6 times the diameter of the
nozzle. They examined the data of previous studies on error due to
anisokinetic sampling and concluded that the discrepancy between experi
mental data was due to the researchers failing to take into account
three things: 1) particle deposition in the inlet channel of the sampling
device; 2) rebound of particles from the front edge of the sampling noz
zle and their subsequent aspiration into the nozzle; and 3) the shape and
wall thickness of the nozzle. They also found that the sampling efficiency
was a function of the inner diameter of the nozzle, D., as well as K and R.
i
In a more recent article, Belyaev and Levin (13) examined the
dependence of the function B(K), in equation (4), on both the inertial
impaction parameter, K, and the velocity ratio, R. Previous authors (10,
14) had concluded that B(K) was a function of K alone, but Belyaev and
Levin obtained experimental data demonstrating that for thin-walled
nozzles, 3(K) was also a function of R. Equations were developed from
the data for values of K between 0.18 and 6.0 and for values of R between


CONCENTRATION RATIO: C./C
18
ANGLE OF PROBE MISALIGNMENT, degrees
Figure 7. Error due to misalignment of probe to flow stream ¡'after
Mayhood and Langstroth, in Watson (5)].


Sampling Efficiency
i


51
B. Aerosol Generation
1. Spinning Disc Generator
A spinning disc aerosol generator (31-33) was used to generate
monodisperse aerosols from 1.0 pm NMD to 11.1 pm NMD (see Table IV).
Droplets were generated from a mixture of 90% uranine (a fluorescent
dye) and 10% methylene blue dissolved in a solution of from 90 to 100%
ethanol (95% pure) and up to 10% distilled/deionized H?0. Uranine was
used so that the particles could be detected by fluoremetric methods.
Methylene blue was added to aid in the optical sizing of the particles.
The mixture of water and ethanol allowed for a uniform evaporation of the
droplets. The droplets, containing dissolved solute, evaporated to yield
particles whose diameters could be calculated from the equation
D
P
CCr0'33) D
(18)
where
D
P
C
r
= particle diameter, pm
= ratio of solute volume to solvent volume plus solute
volume, dimensionless
= original droplet diameter, pm
With the disc's rotational velocity, air flows and liquid feed rate held
constant the size of the droplets produced were only dependent upon the
ratio of the ethanol-water mixture. Since the droplets are produced from
a dynamic force balance between the centrifugal force and the surface


Aspiration Coefficient (A)
Stokes Number (K)
Figure 33. Comparison of experimental data with results from Belyaev and Levin (12).


86
While attempting to determine the constants a and b, it was found
that the form of the equation had to be altered somewhat to allow 3' to
approach 1 at a faster rate for values of K' greater than 4.0. The fol
lowing is the final form of the equation selected.
S'CK',9) = 1 qmrr (25)
1 + aK'e
The constants were determined through trial and error to be 0.55 and 0.25
for a and b respectively. Therefore, the final equation to describe the
sampling efficiency due to nozzle misalignment as a function of Stokes
number becomes for R = 1:
A = 1 + (cose 1) 3'(K',0) (26)
where
31 (K',0)
1
1 + 0.55 K'e
0.2 5 K'
(27)
and
K- = Ke0-0220
(22)
These equations are solved for 30, 60 and 90 degrees and plotted against
Stokes number in Figure 31. It can be seen from the graph that the equations
fit the data within experimental accuracy. Figure 32 is a plot of the
sampling efficiency for angles between 0 and 90 degrees in 15 degree
increments.


Aspiration Coefficient (A)
Stokes Number (K)
Figure 34. Sampling efficiency vs. Stokes number at 60 misalignment for R = 2.0 and 0.5.
CA


7
CHAPTER VI
SUMMARY AND RECOMMENDATIONS
A. Summary
Results of experiments in this study have led to a better understanding
of the types and magnitude of errors that are involved when attempting to
obtain a representative sample of particulate matter from gas streams with
complex flow patterns. The errors induced by tangential flow were analyzed
from two separate approaches. The first involved analysis of particle sam
pling error as a function of particle characteristics, sampling velocity
relative to the flow stream velocity, and angle of the nozzle relative to the
direction of flow. The second involved analysis of swirling flow patterns and
their subsequent effect on flow measurements made by the S-type pitot tube.
Particle sampling errors as a function of velocity ratio and angle of
misalignment were studied by taking comparative anisokinetic and isokinetic
samples from a straight section of duct. By analyzing the problem in this
method the data obtained are more useful and have many more applications
beyond this study. They provide fundamental information for a better under
standing of the inertial effects in aerosol sampling.
The flow measurement errors were analyzed by mapping the exact flow
pattern at the exit of a cyclone using a five-hole pitot tube. Cross sec
tional profiles were measured at five axial distances along the stack to
determine how the flow pattern changes as it moves up the stack. S-type
pitot tube measurements were taken and compared to the results of the
five-hole pitot tube measurements.
129


63
Figure 25. Photograph of the 3-dimensional pitot with its
traversing unit. Insert shows the location of
the pressure taps.


I
TABLE XIII
COMPARISON OF SAMPLING EFFICIENCY RESULTS WITH THOSE OF BELYAEV AND LEVIN (13)
FOR 0 = 0, R = 2.3 AND R = 0.5
Particle
Diameter Velocity
(pm) (cm/sec)
Nozzle
Diameter Stokes
(cm) Number
Value Predicted
Velocity from Equations Experimental
Ratio (5), (9) and (10) Value
6.7
1676
0.465
0.70
2.3
3.1
1676
0.465
0.154
2.3
6.7
1676
0.465
0.70
0.51
3.1
1676
0.465
0.154
0.51
1.8 1.69
1.79
1.76
1.87
1.34 1.32
1.39
1.38
0.67 0.70
0.63
0.66
0.65
0.84 0.80
0.90
0.79
ID
to


V tangential component of stack velocity
3, 3', 3" functions determining whether particles will deviate from
streamlines
- particle density
D viscosity
angle of the flow stream with respect to the stack axis
6 angle of misalignment of nozzle with respect to the flow stream
T particle relaxation time
Ap pressure difference
XU


TABLE I
FLOW RATE DETERMINED AT VARIOUS MEASUREMENT LOCATIONS
Location
Velocity (fps)
Flow Rate (scfm)
% Error
Actual Based on
Fan Performance
18
475
Port A
(parallel)
40
826
74
Port A
(maximum Ap)
60
1,482
212
Port C
(straightened)
21
548
15


DIRECTION OF FLOW
Figure 4.
The effect of nozzle misalignment with flow stream.


A = 1
A = 1
A = 1
A = 1
where
TABLE XXXII
SUMMARY OF EQUATIONS PREDICTING PARTICLE SAMPLING BIAS
Equation
(cosO 1) B'(K',0)
(R-l) 3(K,R) (13)
R = 1
0 <_ 0 < 90
all K
0 = 0
0.16 < R < 5.5
all K
(RcosB
B(K1, R) B'(K^9)
J bO^Tr = 1)
0.5 <_ R < 2.3
0 < 0 < 90
all K
3K
(R)
0.5
(20)
0.003 < K < 0.2
1.25 < R < 6.25
0 = 90
C./C
i o
3(K,R) = 1 1/[1 + (2 + 0.617/R) K]
, ,, 0.0220
= ke
B(k3r = i)
1/(1 + 2.617K)
= V /V.
o 1
' (K' ,0) = 1 1/(1 + 55K'e'251(1)
132


125
TABLE XXX
ASPIRATION COEFFICIENTS
CALCULATED IN THE SIMULATION MODEL FOR THE HIGH FLOW CONDITION
Point
Sampling Velocity
from S-Type Pitot
Tube (cm/sec)
True Velocity
from 5-Hole Pitot
Tube (cm/sec)
Degrees
R
Ci/Co%
1
1078.3
k k k
* k k
k k k
kkk
2
1091.7
1875
59.0
1.72
95.06
3
381.2
1881
70.3
4.90
131.85
4
+ + +
+ + +
+ + +
+ + +
+ + +
5
781.3
1743
64.6
2.20
97.60
6
1974.7
1942
51.6
0.98
84.10
7
1974.7
1869
47.1
0.95
86.30
8
1755.4
1795
47.7
1.02
88.30
Weighted Average
=
90.6


84
apparent nozzle diameter. Using these correction factors it is possible
to use the data to determine an expression for g' in equation (14). Set
ting R = 1 and solving for g' this equation becomes
B'(K')
A 1
COS0-1
(23)
Using this expression the experimental data were used to plot g' as a
function of the adjusted Stokes number K' (see Figure 30). From this
plot, it can be observed that the data points for 30, 60 and 90 degrees
all fall approximately on the same line. It should be noted that most
of the scatter is due to the 30 degree data and that the amount of the
scatter is somewhat deceptive. Solving equation (23) for 30 degrees,
requires that the sampling bias (1-A) must be multiplied by 7.5 to
normalize it with the 90 degree data. This has an effect of greatly
increasing any spread in the experimental data.
To develop a model for inertial sampling bias, it was necessary
to develop an equation for the line drawn through the data in Figure 30.
An equation of the form similar to that used by Belyaev and Levin was
selected to fit the data.
g(K',0) = 1 r- (24)
1 + aK'
where a and b are constants. The advantage of this equation form is
that it acts similar to the theoretical expectations of the relationship
(i.e., 0' approaches zero for very small values of K' and approaches 1
for very large values of K').


135
the nozzle was collected on the nozzle walls. This has implications
not only on the importance of using the probe wash in the analysis,
but more importantly it implies that there may be possible problems
in obtaining accurate particle size data using a device such as an
impactor. If the collection of particles in the nozzle is particle
size dependent, then losses in the probe could lead to particle
sizing errors.
G. A simulation model was developed which incorporates the
information obtained in this study on particle sampling errors and
the flow mapping data. The particle sampling efficiency in a
tangential flow stream was, as expected, a function of particle size.
For a particle distribution with a mass mean diameter (MMD) of 3.0
pm and a geometric standard deviation of 2.13, the sampling errors
predicted were less than 10%. For a larger distribution with a mass
mean diameter of 10.0 pm and geometric standard deviation of 2.3, a
20% sampling error was predicted. One of the reasons that the sampling
errors were as small as these were, is that the two mechanisms inducing
sampling bias produce errors in opposite directions. The misalignment
of the nozzle caused by the tangential velocity component leads to a
reduction of sample concentration. The reduced sampling velocity,
calculated from S-type pitot tube measurements, leads to subisokinetic
sampling and an increased sample concentration. When these two mechanisms
are combined, the total error is reduced somewhat depending upon the
magnitude of the two errors.


95
stream velocity. Tests were run for a range of Stokes numbers from 0.1
to 1. This range was selected because this was expected to be the area
where the greatest change in aspiration coefficient occurred. The data
obtained for R = 2 and R =0.5 for a 60 degree misalignment are presented
in Tables XIV and XV. Thesedata are plotted and compared with the model's
prediction in Figure 34. The aspiration coefficient does indeed appear
to be unity when R = l/cos0 as in the case of R = 2 and 0 = 60 degrees.
The data for R = 0.5, 0 = 60 degrees appear to approach their theoretical
limit of Rcos0 CO.25) at approximately a value of Stokes number of 2 to 5
This is near the location that the aspiration coefficient for 0 = 60
degrees, R = 1 approaches its theoretical limit. This further confirms
the necessity of using an adjusted Stokes number when the probe is mis
aligned with the flow stream.
To further test the model, experiments were run at 45 degrees
(R = 2.0 and R = 0.5) and at 50 degrees (R = 2.0). Thesedata presented
in Tables XVI and XVII are plotted in Figures 35 and 36 also show good
agreement with the prediction model.
When tests were run at 0 = 90 degrees, R = 2.1 and K = 0.195 (see
Table XVIII), an average aspiration coefficient of only 1.5% was obtained
The value predicted for equation (31) for these conditions is 49%. It
appears that the model falls apart at 90 degrees for R f 1. This is due
to the fact that when 0 = 90 degrees there is zero projected frontal area
of the nozzle. This means that subisokinetic sampling could in no way
produce an increase in concentration as it does when particles lie in
front of the projected nozzle area. Because of this it is necessary to
put the condition 0 < 90 degrees on equation (31).


121
TABLE XXVIII
MIDPOINT PARTICLE DIAMETERS
FOR THE 10 PERCENT INTERVALS OF THE MASS DISTRIBUTION
MMD = 3ym a = 2.13
o
^mid
Range
Midpoint
(y meters)
Dp"C
0 10
5
0.84
0.84
10 20
15
1.32
1.96
20 30
25
1.75
3.35
30 40
35
2.20
5.20
40 50
45
2.70
7.73
50 60
55
3.25
11.09
60 70
65
4.00
16.65
70 80
75
4.90
24.80
SO 90
85
6.60
- 44.63
90 100
95
10.40
109.84


126
the maximum Ap. From Figure 15 it is apparent that by splitting the
difference between the angles where the velocity pressure drops off
rapidly, it should be possible to get within 20 degrees of the zero
yaw angle. This means that the sample velocity measured by the S-type
pitot tube will be approximately the same as the true total velocity
and therefore, the sampling error should be no greater than the cosine
of 20 degrees or 0.94. This would represent the maximum error for a
very large aerosol and would be much less for the aerosol used in the
study. Since Mason's sampling error is almost ten times as high as
the theoretical maximum, it must be attributed to some flaw in the
experimental setup.
In order to see how much greater the error would be for larger
particles, a similar analysis was performed using a distribution with
a 10 pm mass mean diameter and 2.3 geometric standard deviation (see
Figure 41). This was the distribution obtained at the outlet of a
cyclone in a hot-mix asphalt plant (43) Because of the larger diameter
particles the sampling efficiency was reduced to 0.799 for the high flow
condition.
The volumetric flow rates determined from the S-type pitot tube
measurements are compared with the flow rates calculated from five-hole
pitot tube measurements in Table XXXI. The axial flow rates using the
five-hole pitot tube data are calculated by multiplying the average axial
velocity by the inner duct area minus the core area. The flow rates
using the S-type pitot tube data were determined using two different
methods varying in how the negative velocity at port four is handled.


66
2. Sampling with Parallel Nozzles
In order to determine if the concentration of particles was the
same at both sampling locations, simultaneous samples were taken with
both nozzles aligned parallel to the duct. Table VII shows the results
of tests performed over a range of Stokes numbers from 0.022 to 1.73.
The average over all of the tests showed only a 0.34% difference between
the two points with a 95% confidence interval of 1.2%. The data show
an increase in the range of the values as the Stokes number increases.
This can be expected because a small error in probe misalignment would
have a greater effect at the higher Stokes number.
3, Analysis of Probe Wash
In the analysis of the tests using ragweed pollen, the filter
catch and probe wash were measured separately. This method allowed
for the determination of the importance of analyzing both the filter
and wash. From Table VIII it can be seen that even for a solid dry
particle, analysis of the probe wash is a necessity. An average of
40% of the particles entering the nozzle was collected on the walls of
the nozzle-filter holder assembly. This was only for nozzles aligned
parallel to the flow stream and sampling isokinetically. Therefore,
the loss of particles was due to turbulent deposition and possibly
bounce off the filter, and probably not inertial impaction. For tests
run with the nozzle at an angle to the flow stream, it is assumed that
the loss would increase as impaction of particles on the walls became


TABLE XVIII
ASPIRATION COEFFICIENT AS A FUNCTION OF STOKES NUMBER FOR R = 2.1, 0 = 90
Velocity
Particle Diameter
Nozzle Diameter
Aspiration
cm/sec
micrometers
cm
Stokes Number
Coefficient %
1676
3.5
0.465
0.195
1.8
1.5
1.3
o


TABLE V
TABLE OF OBTAINABLE VELOCITIES IN 10 cm DUCT
Orifice Diameter
cm
Ap Range
cm H?0
Range in Velocity
cm/sec
1.795
5.6
- 21.6
82
- 162
2.539
5.3
- 21.8
162
- 326
3.5S9
4.2
- 22.9
304
- 670
5.080
4.1
- 22.6
582
- 1371
7.182
2.2
- 14.5
945
- 2460


V. = V A. = A
X O 1 o
Figure 1.
Isokinetic sampling .
C. = C
i o
04


TABLE X [continued)
Velocity
cm/sec
Particle Diameter Nozzle Diameter
micrometers cm
1676
6.35 0 .465
1140
9.81 0.465
2347
11.1 0.683
3627
9.4
0 .465
Stokes Number
Aspiration
Coefficient %
0 .63
93.6
89.1
100.0
1.01
96.6
S7.5
92.0
1.81
86.4
93.4
86.9
2.97
92.5
91.9
83.8
86.8
86.1
92.5
OS


TABLE X
ASPIRATION COEFFICIENT AS A FUNCTION OF STOKES NUMBER FOR 30 DEGREE MISALIGNMENT
Velocity
cm/sec
Particle Diameter
micrometers
Nozzle Diameter
cm
Stokes Number
Aspiration
Coefficient
1798
1.08
0.465
0.022
103.8
97.3
101.8
1326
2.53
0.683
0.056
99.4
101.6
99.7
100.2
1326
3.23
0.683
0.090
97.9
96.7
98.1
1676
2.87
0.465
0.132
95.8
88.8
93.4
1798
3.15
0.465
0.170
97.7
94.6
94.0
98.1
96.9
91.7
1676
4.08
0.465
0.263
88.9
90.2
94.9
Cn


112
TABLE XXV
AVERAGE CROSS SECTIONAL VALUES
AS A FUNCTION OF DISTANCE DOWNSTREAM AND FLOW RATE
Average Values for High Flow
Diameters
4)
Location of*
Tangential Velocity
Core Area
Downstream
[degrees)
Core Area (cm)
(cm/sec)
(cm2)
1
68.0
5.40 13.04
2223
47.23
2
66.7
5.78 13.22
2190
43.94
4
64.3
6.79 13.93
1901
40.78
8
56.7
5.58 12.51
1480
38.26
16
54.3
7.43 14.62
1273
44.78
Average
: Values for Low
Flow
-
Diameters
Location of*
Tangential Velocity
Core Area
Downstream
(degrees)
Core Area (cm)
(cm/sec)
(cm2)
1
66.45
5.42 12.87
1441
45.16
2
63.5
5.85 13.07
1469
41.39
4
62.7
7.05 13.93
1260
38.45
8
56.9
5.63 12.23
1067
37.03
16
52.0
7.99 14.69
811
42.13
* Center of the duct is at 9.87 cm.


102
Although the experimental data for 90 degrees do not agree well
with the prediction model, they do compare favorably with the emperical
equation of Laktionov(20) [equation (16)]. For the conditions of K =
0.195 and R = 2.1, his equation predicts as aspiration coefficient of
3.9%. This comparison is closer than would be expected considering the
fact that two completely different sampling schemes were used, and
Laktinov did not analyze the amount of particles collected in the probe.
It should be pointed out that the term for B'(K',0) does not equal
1 when 0=0. This means that equation (31) will not be equal to Belyaev
and Levin's predicting equations (5), (9) and (10) and therefore, equation
(31) should not be used for 0=0.
B. Tangential Flow Mapping
Eight traverse points for the velocity measurements were selected
according to EPA Method 1 (1) (see Table XIX). Measurements were made
using the 5-hole pitot tube at five axial distances from the inlet --
ID, 2D, 4D, 8D and 16D, where D is the inner diameter of the duct. At
each point in the traverse, the pitot tube was rotated until the pres
sure differential between pressure taps 2 and 3 (see Figure 25) was
zero. This angle was recorded as the yaw angle and the pressure readings
from all five pressure taps were recorded for later calculation of total
and static pressure, and pitch angle.
During the initial velocity traverse, a core area was discovered
in the center of the duct where the direction of the flow could not be
determined with the pitot tube. The core area was characterized by
negative readings at all five pressure taps which did not vary much


nozzle diameter with angle. When plotted against K!, the aspiration
coefficients for 30, 60 and 90 degrees should approach their theoretical
minima at the same place as the curves for zero misalignment angle and
anisokinetic sampling velocities (see Figure 6).
To develop the adjustment factor for Stokes number, it was neces
sary to plot as a function of 0, the value of K where the aspiration
coefficient reached a value that represented 95% of the maximum error.
For example the maximum theoretical error for 60 degrees is cos(60) or
0.5. Therefore the value of K of interest is where there is (.95) (0.5) =
47.5% sampling error or an aspiration coefficient of 1 .475 = .525.
For zero degrees, equations (9) and (10) were solved for R = 0.5 and
3 = 0.95 to obtain a value of K = 5.9. This velocity ratio was used
because its theoretical maximum sampling error is 0.5, the same as for
60 degrees. The values for 60 and 90 degrees were obtained from Figures
27 and 28 respectively. Because of the flatness of the 30 degree curve
(it varies only 16% over two and a half orders of magnitude of K), it was
not possible to detect exactly when the curve reached 95% of its minimum
value. Therefore no value for 30 degrees was used in this analysis.
The equation for the adjusted Stokes number determined from Figure
29 is
K
,, 0.0226
Ke
(22)
Using this equation it can be determined that the Stokes numbers for 30,
60 and 90 degrees must be multiplied by 1.93, 3.74 and 7.24 respectively
to account for the effect of nozzle angle to the flow stream on the


TABLE XVII
ASPIRATION COEFFICIENT AS A FUNCTION OF STOKES NUMBER FOR R = 2, 0 = 30
Velocity
cm/sec
Particle Diameter
micrometers
Nozzle Diameter
cm
Stokes Number
Aspiration
Coefficient %
3627
9.42
0.465
2.97
188.9
184.5
171.7
to
Co


LIST OF TABLES
Table Page
I FLOW RATE DETERMINED AT VARIOUS MEASUREMENT LOCATIONS 33
II CONCENTRATION AT A POINT FOR DIFFERENT SAMPLING ANGLES 34
III EMISSION TEST RESULTS 36
IV SIZES AND DESCRIPTIONS OF EXPERIMENTAL AEROSOLS 52
V TABLE OF OBTAINABLE VELOCITIES IN 10 cm DUCT... 54
VI TYPICAL VELOCITY TRAVERSE IN THE EXPERIMENTAL SAMPLING
SYSTEM 55
VII RESULTS OF SAMPLING WITH TWO PARALLEL NOZZLES 67
VIII PERCENT OF PARTICULATE MATTER COLLECTED IN THE PROBE WASH
FOR NOZZLES PARALLEL WITH THE FLOW STREAM 68
IX PERCENT OF PARTICULATE MATTER COLLECTED IN THE PROBE WASH
FOR NOZZLES AT AN ANGLE OF 60 DEGREES WITH THE FLOW STREAM. 70
X ASPIRATION COEFFICIENT AS A FUNCTION OF STOKES NUMBER FOR
30 DEGREE MISALIGNMENT 75
XI ASPIRATION COEFFICIENT AS A FUNCTION OF STOKES NUMBER FOR
60 DEGREE MISALIGNMENT 77
XII ASPIRATION COEFFICIENT AS A FUNCTION OF STOKES NUMBER FOR
90 DEGREE MISALIGNMENT 80
XIII COMPARISON OF SAMPLING EFFICIENCY RESULTS WITH THOSE OF
BELYAEV AND LEVIN FOR 0 = 0, R = 2.3 AND R = 0.5 92
XIV ASPIRATION COEFFICIENT AS A FUNCTION OF STOKES NUMBER FOR
R = 2, 6 = 60 94
v


TABLE XIT (continued)
Velocity Particle Diameter
cm/sec micrometers
1494
3.84
1676
4.08
1798
4.98
1326
7.66
1676
8.0
Nozzle Diameter
cm
0.4 65
0.465
0.465
0.683
0.465
701
19.9
0.683
Stokes Number
Aspiration
Coefficient %
0.21
38.2
44.6
49.3
49.8
0.26
28.7
24.4
33.7
0.42
27.5
22.1
20.3
0.49
17.0
13.0
12.1
0.99
1.2
1.1
1.3
I .73
0
0
oo


5
Subisokinetic sampling defines the condition in which the sampling
velocity is less than the free stream velocity (see Figure 3). In this
situation the frontal area of the nozzle, ', is greater than the sam
pled area of the flow, A The volume of air lying within the projected
area, A^', but outside Aq will not be sampled and the streamlines will
diverge around the nozzle. However, some of the particles in this area,
because of their inertia, will be unable to negotiate the turn with the
streamlines and will be collected in the nozzle. Because some of the
particles outside the sampled area Aq will be collected along with all
of the particles within A the measured concentration will be greater
than the actual particle concentration.
The bias due to misalignment of the nozzle with the flow stream
is similar to that caused by superisokinetic sampling. When the nozzle
is at an angle to the flow stream (Figure 4), the projected area of the
nozzle is reduced by a factor equal to the cosine of the angle. Even
if the nozzle velocity is equal to the flow stream velocity, a reduced
concentration will be obtained because some of the larger particles
will be unable to make the turn into the nozzle with the streamlines.
Therefore, whenever the nozzle is misaligned, the concentration col
lected will always be less than or equal to the actual concentration.
For all three conditions of anisokinetic sampling (superisokinetic,
subisokinetic and nozzle misalignment), the magnitude of the measured
concentration error will depend upon the size of the particles. More
specifically it will depend upon particle inertia, which implies that
the velocity and density of the particle are also important. Particle


BIOGRAPHICAL SKETCH
Michael Durham was born on December 11, 1949, in Key West, Florida.
Being a member of a Navy family, he was constantly on the move and
attended eight different grade schools and two high schools in Hawaii,
Virginia, California and Kentucky. He studied two years at Texas A§M
University and then two at the Pennsylvania State University where he
received a B.S. in Aerospace Engineering in 1971. His next three years
were spent working with the National Academy of Science and the American
Psychological Association in Washington, D.C. In September 1974 he began
his graduate education in Environmental Engineering Sciences at the
University of Florida. After receiving a Master of Engineering in
August of 1975, he stayed on at the university as a graduate research
assistant in pursuit of a Ph.D. for three years, the result of which is
this dissertation.
139


Aspiration Coefficient [A]
Stokes Number (K)
Figure 35.
Sampling efficiency vs. Stokes number at 45 misalignment for R = 2.0 and R = 0.5.


115
disturbance effect of the end of the duct which was only a few diameters
downstream of the sampling point. The increase in average tangential
velocity at 2 diameters from the inlet can be attributed to the fact
that two of the traverse points were within the core area. It can be
seen from the other profiles that the inner points had lower velocity
values, and therefore the exclusion of the inner points would lead to a
higher velocity average.
Plotted in Figure 40 is the location of the core area with respect
to the duct center. It can be seen that the swirling flow is indeed not
axisymmetric and the location of the core area changes location with
axial distance. Only one drawing is used to represent the situation for
both high and low flow rate because the location for both conditions was
almost identical.


Tangential Velocity (cm/sec)
Hiametoys downstream
Figure 39. Decay of the tangential velocity component along the axis of the duct.
114


28
The two distinctly different types of flow that are possible in
a swirling flow field are known as free vortex and forced vortex flows.
When the swirling component of flow is first created in the cyclone
exit, the tangential profile of the induced flow approaches that of a
forced vortex. As the forced vortex flow moves along the axis of the
stack, momentum transfer and losses occur at the wall which cause a
reduction in the tangential velocity and dissipation of angular
momentum. This loss of angular momentum is due to viscous action
aided by unstable flow and fluctuating components. Simultaneously,
outside the laminar sublayer at the wall where inertial forces are
significant, the field develops toward a state of constant angular
momentum. This type of flow field with constant angular momention
is classified as free vortex flow. The angular momentum and tangential
velocities of the flow decay as the gas stream flows up the stack (23).
Baker and Sayre measured axial and tangential point velocity
distributions in a 14.6 cm circular duct in which swirling flow was
produced by fixed vanes (23) The tangential velocity profiles and
angular momentum distributions are plotted in Figures 12 and 13 from
measurements taken at 9, 24 and 44 diameters downstream of the origin
of tangential flow. The tangential velocity (W) is made dimensionless
by dividing it by the mean spatial axial velocity (U ) at a pipe cross
section. These plots indicate developing flow fields, with two definite
types of flow occurring: that approaching forced vortex flow in the
central region of the pipe and flow approaching free vortex flow in
the outer region. Further tests showed that the free vortex field


45
Figure 19. Fecheimer pitot tube sensitivity to yaw angle. (28)


2000
0
0.2
0.4
0.6
0.8
1 .
d/D
Figure 22. Typical velocity profile in experimental test section (9.58 ID duct).


AIR FLOW-
Figure 10. Double vortex flow induced by ducting.
FLOW PATTERN
ro
O'


TABLD XI (continued)
Velocity Particle Diameter Nozzle Diameter Aspiration
cm/sec micrometer cm Stokes Number Coefficient %
1676
3
.81
0
.465
0
.23
75.
.0
89.
.1
81,
.8
81,
.9
1676
4,
.54
0
.465
0,
.325
74,
.7
72.
.3
69.
.0
69.
.3
1798
4.
.98
0,
.465
0
.42
73,
.5
71,
.9
71,
.6
78.
.4
1798
6.
,02
0.
.465
0,
.61
76,
.8
67.
.5
75.
1
70.
.3
1676
6.
,35
0.
.465
0
.63
75.
.7
68,
.2
72.
,0
1676
8.
0
0.
.4 65
0.
.99
65.
.8
62.7
64.2
co


1
6 8 10
Diameters downstream
14
16
Figure 40. Location of the negative pressure region as a function of distance downstream from the
cyclone.
O'


123
The total aspiration coefficients calculated in this manner for
the low and high flow rates were 0.937 and 0.906 respectively (see
Table XXIX and XXX). There are two reasons for the relative low amounts
of concentration error found in this analysis. One reason is that the
two mechanisms causing sampling error, nozzle misalignment and aniso-
kinetic sampling velocities, cause errors in the opposite direction.
The S-type pitot tube detected a velocity less than or equal to the
actual velocity which would lead to subisokinetic sampling producing
an increased concentration. The nozzle misalignment when sampling
parallel to the stack wall would produce a decreased concentration. So
each of these errors has a tendency of reducing the other error.
Another reason for the small errors was the small size of the
aerosol. The Stokes numbers for over 50% of the particles were less
than 0.2 and 0.3 for the low and high flow rates respectively. These
values lead to small sampling errors, even when isokinetic sampling
conditions are not maintained.
Mason experimentally determined that the collection efficiency should
be on the order of 50% (22). Since the flow rate used by Mason was ap
proximately midway between the high and low flow rate in this study, the
flow patterns should be approximately the same. The discrepancy between
Mason's experimental values and the values predicted by the simulation
probably can be accounted for as experimental error by Mason. It would
be nearly impossible to obtain a 50% sampling error for an aerosol as
small as the one used without extreme anisokinetic sampling conditions.
Mason also found a 40% error when sampling at the angle associated with




TABLE XT (continued)
Velocity Particle Diameter Nozzle Diameter
cm/sec micrometers cm
1140
9.87
0.465
1551
9.42
0.465
1707
9.42
0.465
2347 11.1
0.683
3627
9.42
0.465
Stokes Number
Aspiration
Coefficient %
1.01
63.3
60.6
59.3
1.27
57.2
54.3
53.8
1.40
56.0
58.3
52.9
1.81
49.7
58.0
47.0
51.0
2.97
50.6
48.2
53.0
LO


Figure 16. Velocity error vs. pitch angle for an S-type pitot tube.
28


Figure 11. Velocity components in a swirling flow field.


1
o
Figure 2. Superisokinetic sampling.


119
TABLE XXVII
S-TYPE PITOT TUBE MEASUREMENTS
MADE AT THE 8-D SAMPLING PORT FOR THE HIGH FLOW CONDITION
Point
Dynamic
Pressure
(cm Ho0)
Static
Pressure
(cm Ho0)
8
2.03
-0.66
7
1.83
-1.57
6
1.17
-2.23
5
-2.26
-2.79
4
-1.83
-1.32
3
-0.89
-1.02
2
0.61
-0.43
1
0.91
o
11
o
1
Ap
(cm Ho0)
Ap2 j,
(cm Ho0) 2
Velocity
(cm/sec)
2.69
1.64
1755.4
3.40
1.84
1974.7
3.40
1.84
1974.7
0.55
0.73
781.3
-0.51
-0.71
-762.5
0.13
0.36
381.2
1.04
1.02
1091.7
1.02
1.01
1078.3


44
Figure 18. Five-hole pitot tube sensitivity to yaw angle. (28).


70
TABLE IX
PERCENT OF PARTICULATE MATTER COLLECTED IN THE PROBE WASH
FOR NOZZLES AT AN ANGLE OF 60 DEGREES WITH THE FLOW STREAM
Probe Wash*
Filter*
Total *
% in Wash
348
211
559
62.0
161
138
299
54.0
288
333
621
46.4
* Numbers represent the number of ragweed pollen counted.


124
TABLE XXIX
ASPIRATION COEFFICIENTS
CALCULATED IN THE SIMULATION MODEL FOR THE LOW FLOW CONDITION
Sampling Velocity True Velocity
from S-Type Pitot from 5.-Hole Pitot Point
Tube (cm/sec]
Tube (cm/sec')
Degrees
R
Ci/Co
1
949.3
* *
* *
* *
* **
2
743.2
1414
61.0
1.9
97.0
3
241.1
1456
70.3
6.0
142.0
4
+ + +
+ + +
+ + +
+ + +
+ + +
5
614.7
1396
63.9
2.3
100.5
6
1351.6
1326
53.0
1.0
86.5
7
1298.5
1289
47.0
0.99
90.1
8
1229.0
1231
46.4
1.0
90.7
Weighted Average = 93.7