United States Industrial Environmental Research EPA-600/7-79-065 Environmental Protection Laboratory February 1979 Agency Research Triangle Park NC 27711 Proceedings: Advances in Particle Sampling and Measurement (Asheville, NC, May 1978) Interagency Energy/Environment R&D Program Report ------- RESEARCH REPORTING SERIES Research reports of the Office of Research and Development, U.S. Environmental Protection Agency, have been grouped into nine series. These nine broad cate- gories were established to facilitate further development and application of en- vironmental technology. Elimination of traditional grouping was consciously planned to foster technology transfer and a maximum interface in related fields. The nine series are: 1. Environmental Health Effects Research 2. Environmental Protection Technology 3. Ecological Research 4. Environmental Monitoring 5. Socioeconomic Environmental Studies 6. Scientific and Technical Assessment Reports (STAR) 7. Interagency Energy-Environment Research and Development 8. "Special" Reports 9. Miscellaneous Reports This report has been assigned to the INTERAGENCY ENERGY-ENVIRONMENT RESEARCH AND DEVELOPMENT series. Reports in this series result from the effort funded under the 17-agency Federal Energy/Environment Research and Development Program. These studies relate to EPA's mission to protect the public health and welfare from adverse effects of pollutants associated with energy sys- tems. The goal of the Program is to assure the rapid development of domestic energy supplies in an environmentally-compatible manner by providing the nec- essary environmental data and control technology. Investigations include analy- ses of the transport of energy-related pollutants and their health and ecological effects; assessments of, and development of, control technologies for energy systems; and integrated assessments of a wide range of energy-related environ- mental issues. EPA REVIEW NOTICE This report has been reviewed by the participating Federal Agencies, and approved for publication. Approval does not signify that the contents necessarily reflect the views and policies of the Government, nor does mention of trade names or commercial products constitute endorsement or recommendation for use. This document is available to the public through the National Technical Informa- tion Service, Springfield, Virginia 22161. ------- EPA-600/7-79-065 February 1979 Proceedings: Advances in Particle Sampling and Measurement (Asheville, NC, May 1978) W.B. Smith, Compiler Southern Research Institute 2000 Ninth Avenue, South Birmingham, Alabama 35205 Contract No. 68-02-2131 Task No. 21306 Program Element No. INE623 EPA Project Officer: D. Bruce Harris Industrial Environmental Research Laboratory Office of Energy, Minerals, and Industry Research Triangle Park, NC 27711 Prepared for U.S. ENVIRONMENTAL PROTECTION AGENCY Office of Research and Development Washington, DC 20460 ------- PREFACE The Symposium on Advances in Particle Sampling and Measure- ment held in Asheville, NC, May 15-17, 1978, was sponsored by the Process Measurement Branch, Industrial Environmental Research Laboratory, U.S. Environmental Protection Agency. D. Bruce Harris, EPA, served as symposium chairman. Session chairmen were A.R. MacFarland, Texas ASM University; Dale Lundgren, Uni- versity of Florida; W.B. Kuykendal, EPA; T.T. Mercer, University of Rochester; and G.B. Nichols, Southern Research Institute. A list of reports on the research supported by the Process Measurements Branch can be obtained from Mrs. Judy Ford, MD-62, Process Measurements Branch, Industrial Environmental Research Laboratory, U.S. Environmental Protection Agency, Research Triangle Park, NC 27711, 111 ------- ABSTRACT The proceedings consist of 17 papers on improved instruments and techniques for sampling and measurement of particulate emis- sions and aerosols. Cascade impactors are described with low- pressure stages that extend the useful range of these sampling devices down to 0.02 ym? their use in measuring particle size distribution of fly ash from coal-fired boilers and in testing a smoke suppressant in a gas turbine is described. A new empiri- cal equation simplifies calibration of cyclone collectors used for sampling aerosols. Diffusion battery-nuclei counter com- binations can be used for automatic monitoring of particle-size distribution and number concentration of ambient aerosols. Trans- missometers and instruments for measuring scattered light were compared over a one-year period for continuous monitoring of stack emissions at a secondary lead smelter. Instruments for measuring electrical charge transfer and beta radiation attenua- tion were less reliable in this use. A laser light back-scattering instrument was compared in pulp and paper mills against a trans- missometer in continuous monitoring of emissions from a wood- waste fired power boiler, a kraft recovery furnace, and a lime kiln. Other papers discussed a computer-based, data reduction method for plotting curves of particle size distribution; tech- niques and equipment for generating monodisperse aerosols and their use in calibrating instruments; guidelines in selecting laboratory methods for particle sizing; minimizing weight changes in impactor collection substrates due to heat and sulfur oxides; spectroscopic methods for determination of trace elements in fly ash and their valence states; and sampling errors due to aerodynamic effects. Applications of improved sampling and measurement techniques to the evaluation of emission control devices include a wet impingement technique for measuring par- ticle sizes in wet scrubbers; the use of real-time aerosol in- struments in studying the dynamic behavior of baghouses; and the measurement of fractional collection efficiency of electro- static precipitators for particles 0.01-10 ym in diameter, en- abling the detection of transient fluctuations such as rapping reentrainment of fly ash. IV ------- CONTENTS Preface . iii Abstract iv List of Speakers and Chairmen vii Paper 1. Inertia Effects in Sampling Aerosols C.N. Davies and M. Subari 1 Paper 2. Cyclone Sampler Performance Morton Lippmann and Tai L. Chan 30 Paper 3. Research on Dust Sampling and Measurement in our Laboratory Koichi linoya 52 Paper 4. Sizing Submicron Particles With a Cascade Impactor Michael J. Pilat. 74 Paper 5. Experience in Sampling Urban Aerosols With the Sinclair Diffusion Battery and Nucleus Counter Earl O. Knutson and David Sinclair 98 Paper 6. Selecting Laboratory Methods for Particle Sizing Ronald G. Draftz 121 Paper 7. Long Term Field Evaluation of Continuous Particulate Monitors A.W. Gnyp, S.J.W. Price, C.C. St. Pierre, and D.S. Smith. . . 122 Paper 8. An In-Stack Fine Particle Size Spectrometer: A Discussion of its Design and Development Robert G. Knollenberg 169 Paper 9. Optical Measurements of Particulate Size in Stationary Source Emissions A.L. Wertheimer, M.N. Trainer, and W.H. Hart 195 Paper 10. Studies on Relating Plume Appearance to Emission Rate and Continuous Particulate Mass Emission Monitoring K.T. Hood and H.S. Oglesby. 211 v ------- Paper 11. A Data Reduction System for Cascade Impactors J.D. McCain, G. Clinard, L.G. Felix, and J. Johnson 228 Paper. 12. Aerosol Generation and Calibration of Instruments David Y.H. Pui and Benjamin Y.H. Liu . 260 Paper 13. Substrate Collectors for Impactors - An Evaluation D. Bruce Harris, G. Clinard, L.G. Felix, G. Lacey, and J.D. McCain „ . 293 Paper 14. Particle Size Measurement for the Evaluation of Wet Scrubbers Seymour Calvert, Richard Chmielewski, and Shui-Chow Yung. „ . 301 Paper 15. Evaluation of Performance and Particle Size Dependent Efficiency of Baghouses D.S. Ensor, R.Go Hooper, G. Markowski, and R.C. Carr. .... 314 Paper 16. Evaluation of the Efficiency of Electrostatic Precipitators Wallace B. Smith, John P. Gooch, Joseph D. McCain, and James E. McCormack. .......... 337 Paper 17. Some Studies of Chemical Species in Fly Ash L.D. Hulett, J.F. Emery, J.M, Dale, A.J. Weinberger, H.W. Dunn, C. Feldman, E. Ricci, and J.O. Thomson 355 Summary. Advances in Particle Sampling and Measurement William Farthing 372 Metric Conversion Factors ............ 380 VI ------- SPEAKERS AND CHAIRMEN Mr. Richard Chmielewski APT, Incorporated 4901 Morena Boulevard Suite 402 San Diego, CA 92117 Phone: 714/272-0050 Dr. C.N. Davies Department of Chemistry University of Essex Wivenhoe Park Colchester C04 3SQ ENGLAND Phone: Colchester 44144 (STD Code 020 6) Mr. R.G. Draftz IIT Research Institute 10 West 35th Street Chicago, IL 60616 Phone: 312/567-4291 Dr. David S. Ensor Meteorology Research, Inc. 464 West Woodbury Road Altadena, CA 91009 Phone: 213/791-1901 Dr. Alec Gnyp Department of Chemical Engineering University of Windsor Windsor, Ontario N9B3P4 CANADA Phone: 519/253-4232 Mr. D. Bruce Harris Environmental Protection Agency Industrial Environmental Research Laboratory Mail Stop MD-62 Research Triangle Park, NC 27711 Phone: 919/541-2557-8 Mr. Kenneth T. Hood NCASI, Engineering Experiment Station Oregon State University Corvallis, OR 97331 Phone: 503/754-2015 Dr. Lester D. Hulett Oak Ridge National Lab 4500 North E-10 Oak Ridge, TN 37830 Phone: 615/483-0155 Dr. Koichi linoya Department of Chemical Engineering Kyoto University Kyoto JAPAN Dr. Robert G- Knollenberg Particle Measurement Systems 1855 South 57th Court Boulder, CO 80301 Phone: 303/443-7100 VII ------- Dr. Earl Knutson Health & Safety Lab U.S. ERDA 376 Hudson Street New York, NY 10014 Phone: 212/620-3655 Mr. W.B. Kuykendal Environmental Protection Agency Industrial Environmental Research Laboratory Mail Stop MD-62 Research Triangle Park, NC 27711 Phone: 919/541-2557 Dr. Morton Lippmann Institute of Environmental Medicine New York University Medical Center New York, NY 10016 Phone: 212/679-3200 Dr. Dale Lundgren Environmental Engineering Department University of Florida 410 Black Hall Gainesville, FL 32611 Phone: 904/392-0846 Mr. Joseph D. McCain Southern Research Institute 2000 Ninth Avenue, South Birmingham, AL 35205 Phones 205/323-6592, extension 278 Dr. Andrew R. McFarland Civil Engineering Department Texas A&M University College Station, TX 77843 Phones 713/845-2241 Dr. Thomas T. Mercer University of Rochester Rochester, NY 14642 Phone: 716/275-3821 Mr. Grady B. Nichols Southern Research Institute 2000 Ninth Avenue, South Birmingham, AL 35205 Phone: 205/323-6592, extension 361 Dr. Michael Pilat Air Resources Engineering University of Washington Seattle, WA 98195 Phones 206/543-4789 Dr. David Pui Mechanical Engineering Department University of Minnesota Minneapolis, MN 55455 Phone: 612/323-2815 Dr. Wallace B. Smith Southern Research Institute 2000 Ninth Avenue, South Birmingham, AL 35205 Phone: 205/323-6592, extension 520 Dr. Allen Wertheimer Leeds & Northrup Company Dickerson Road North Wales, PA 19454 Phones 215/643-2000, extension 493 viii ------- PAPER 1 INERTIA EFFECTS IN SAMPLING AEROSOLS C.N. DAVIES M. SUBARI DEPARTMENT OF CHEMISTRY UNIVERSITY OF ESSEX ABSTRACT A study is made of the aspiration coefficient of orifices sampling aerosols, starting with a point sink and proceeding to a tube of finite diameter. A critical analysis is made of previous work and new experimental results are presented for sampling at 90° yaw with a sharp-edged tube. INERTIALESS PARTICLES The trajectories of particles suspended in moving air may differ from the streamlines of air flow either if their rate of fall due to gravity is appreciable, compared with the air velocity, or if the particles are sufficiently heavy to persist in their original direction to some extent when the air flow changes direction (Albrecht,1 Sell 2). Measurements of the concentration of particles, by sucking a known volume of aerosol and assessing the particles in it, are liable to error because of these gravitational and inertial effects. Consider, first, inertialess particles. These can be de- fined as having a stop-distance, ds, at the local air velocity, u, which is small compared with the distance, &, from any bound- ing solid surface. That is d = TU « l (1) s where T is the relaxation time of a particle and is equal to the mass divided by the aerodynamic drag at unit velocity. Such particles can still fall at an appreciable velocity, this being v = rg. (2) o ------- Inertialess particle systems therefore have small TU and large Jl, but the limiting size of the Stokes number of the sys- tems, Stu = TU/& « 1 (3) depends on the value of Stu, being lower for high values of vs/uf hence both Stu and vs/u need to be considered in deciding whether a particle is inertialess and, of course, since u varies from point to point in a flow field the particle may be inertialess while it is in some parts of the field but not so in others. The sampling of inertialess particles with an isolated small tube yields accurate results (Davies3). When the airflow ap- proximates to ideal flow (potential or irrotational) the par- ticles themselves trace out a potential flow pattern, the concen- tration of particles is the same at all points along a particle^ trajectory and trajectories do not intersect (Walton1*; Robinson ; Levin6) . There are two reasons why this does not mean that a sampling orifice will always take a perfect sample of inertialess par- ticles. Firstly, the velocity of the particles entering the orifice may not be the same as the air velocity, V, in the orifice. Suppose that the normal to the plane of the sampling orifice makes an angle \p with the vertical. Then the velocity with which particles enter the orifice, resolved along the normal is V + v cos ty (4) s Hence the concentration, c, calculated from the catch of par- ticles (including those stuck on the internal surface of the orifice) and the volume of air sampled, is related to the true concentration, c0, by cV = c0 (V + vg cos 4>) (5) The efficiency of sampling or the aspiration coefficient of the orifice is then, for inertialess particles, A = c/c0 = (V + vo cos 40/V (6) S Hence when 41 = 0 and the orifice faces upwards, A = 1 + vs/V and when \p = IT, with the orifice facing downwards, A = 1 - vs/V. Only when the plane of the orifice is vertical and ty = ir/2 is a true sample obtained. The other factor causing error in the sampling of inertia- less particles is the existence of dust shadows. These regions ------- free from particles exist below and downwind of objects placed in an aerosol. The effects are negligible in the case of a small tube, but a bulky sampling head creates a shadow which sometimes reduces the aspiration coefficient of its sampling orifice. The writer has described the general effects (Davies7»8'9). When the orifice in an isolated head faces upwards it always has A > 1; at low rates of suction in calm air a dust shadow exists below the head and particles settle upon the top, around the orifice, with increasing aspiration rate the shadow region climbs up over the top of the head so that particles settle only upon a decreasing area around the orifice. With an orifice in the under side of the head, in calm air, no particles enter until a certain rate of aspiration is attained; increasing above this value gradually raises the value of A until it reaches unity at an infinite rate of suction. As A increases there is no change in the deposition of particles on top of the head. In a cross wind particles enter the head at a lower suc- tion rate than is the case for calm air. The value of A remains higher than the value for calm air, as suction is increased, but the difference decreases until they become the same at a fairly high rate of suction. Dust shadows can reduce A when the orifice is not isolated, even when its plane is vertical, if it is in the lee of an ob- stacle; they may also affect the sampling of particles with inertia (Davies ). Since the concentration of inertialess particles is constant along all trajectories, the values of A which are less than unity result not from the aspiration of reduced concentrations but because some of the particle trajectories which enter the orifice originate from boundaries inside dust shadows and therefore have zero concentration at all points along their lengths. This was shown clearly by Walton1* who considered tubes of flow of inertia- less particles, particularly in elutriators. PARTICLES WITH INERTIA; POINT SINK The trajectories of particles with inertia do not form a system with a velocity potential; the concentration may vary along a trajectory and trajectories may intersect (Voloshchuk and Levin11). A true sample can still be obtained, when par- ticles exhibit unlimited inertia, if their rate of fall under gravity is negligible and if the air movement is solely due to aspiration into a point sink. The concentration builds up as the orifice is approached, due to the particles lagging behind the air flow, and the analogue of a space charge around the ori- fice is formed. Particles enter the orifice with a reduced ve- locity which compensates for the excess concentration and a true sample with A = 1 results (Davies 12). ------- If the symmetry of this "space charge" is sufficiently destroyed by wind, or by the settlement of particles under grav- ity, the aspiration coefficient of the sampling orifice is re- duced. Levin6 has shown how particles which have very limited inertia behave when approaching a point sink when they are sedimenting under gravity and there is a wind. In order to understand his paper it is best to start with the equations for inertialess particles. His equations are similar to those of Davies3 but are in polar coordinates. A great simplification of the equations was achieved by using as x-axis the direction of the vector sum of the wind velocity, W, and the sedimentation velocity of the particles, vg. This sum has magnitude u0 = (W2 + v 2 + 2Wv cos <|>)^ (7) S S where $ is the angle between W and vs. Since the particles are inertialess, the equations for the trajectories are the same as those for the streamlines of flow. The sink sucks with flow Q and creates radial velocities - Q/4Tir2 to which must be added the radial resolutes of u0. Hence the equations for radial and tangential resolutes of a trajectory are u = - Q/4irr2 + u0 cos 6 ; (8) u = - u0 sin 9 By putting H20 = Q/47TU0 (9) these are rendered dimensionless, ur/u0 = - A 02/r2 + cos 6 (10) 4 /ii . = — cinfl I The solution of these equations is (r2/2&02) sin2 6 + cos 9 = K (11) where K is constant along a streamline or an inertialess trajec- tory. The formulation of these equations is shown in Figure 1. Note the direction of the x-axis about which all trajectories ------- 1 Figure 1. The coordinate system. A sink at 0 draws a flow Q. The curve with asymptote 2 at x/£0 = -°° is a critical trajectory with stagnation point of both air flow and particle motion at S. x/C0 are symmetrical. The figure shows a meridian section and the critical trajectory through the stagnation point, S, where u = r 8 = 0 (12) It is necessary to locate the critical trajectory for the calculation of the aspiration coefficient (Davies3). The equa- tion of the critical trajectory is or /r2/2fce2J sin2 6 + cos 6 = 1 r/Jl0 = I/cos (e/2) (13) All particles with trajectories between the critical tra- jectory and the x-axis enter the orifice; none of those outside do so- The critical trajectory has the asymptote at x = -« (0 yoo/Ao = 2, (14) hence, the rate of entry of particles into the sink is TT (4fc2) c0u0 = Qc0 (15) by equation (9), so that A = 1. ------- The critical trajectory meets the x-axis at the stagnation point, S, where 6=0, y=0, r=x and x /ft0 = 1 (16) S When the particles have inertia it is necessary to consider their acceleration in order to write down the dynamic equations: m (dv /dt - VQ ae/dt) = 6TTan (-Q/4irr2 + Uo cos 9 - v ) re r m (dv /dt + v dO/dt) = Siran (- u0 sin 6 + v_) y r o where vr and VQ are the radial and tangential resolutes of par- ticle velocity. The equations are rendered dimensionless by dividing through by Girari • ua and reducing t to dimensionless t' and r to dimensionless r', so that t = t1 JU/Uo and r = r1 fi,0 Since T = m/Girar), equations (17) in dimensionless form be- come '/dt1 - v.'-ae/at1) = -i/r|2 + cos e - v ' r 6 / r (19) 1 - v^-de/dt'J = - sin 0 + VQ ' where equation (9) shows that the dimensionless scale factor, TU0/J,0 = TUO ^/4Tru0/Q = T V4TTu73/Q = k (20) By integrating these equations the particle velocity (vr, VQ) can be obtained at all points along a trajectory. Levin6 succeeded in obtaining solutions as series of rising powers of k, for small values of k, by assuming that a particle stagnation point existed at S, in the same position as the air velocity stagnation point. At S, and nowhere else, both particles and air have zero velocity. This is justifiable for small values of k, since continuity must exist between air streamlines and particle trajectories as k tends to zero. When k = 0 equation (19) reduces to equation (10) . His solutions are V = cos 6 - 1/r" + k .2 + , I2(l-r'2 cos 6) r 3(1-3 cos2 6) , 20 cos 9 _ -, . , , & \ , r • t "*" ,6 ' J 4 sin 91 , T~l+ ' • • r'6 ) v. = _ sin e - k SJJLJ. _ ka J6 sin 9 cos 6 9 .-1 3 (21) ------- When k = 0 these equations reduce to equation (10) . They include powers of 1/r ' = &0/r up to the sixth; since A0/r = 1 at the stagnation point, the trajectories are increasingly accurate for greater distances from the sink. This is important since the calculation of the aspiration coefficient, A, depends on the value of y at r = °°, 6 = IT (equations (14), (15)). In order to obtain the trajectory equations it is necessary, as in integrating equation (10) , to substitute in dr/rde = v /VQ (22) r W from equation (21) and perform the integration. It is not clear how Levin proceeded at this point but he obtained the asymptote (r = oo) of the critical trajectory by successive approximation, starting with the equation (13) for k = 0. This gave, in place of (14), the formula (yoo/S-°) = 4 - 3.2 k + 0.32 k2 (23) Hence, since then, using (9) A = 1 - 0.8 k + 0.08 k2 (24) By comparing this with the results of numerical integrations of equations (19) , Levin6 concluded that the error in A, as given by (24) was not more than 1% when k = 0.25 and not more than 2.5% when k = 0.5. It will be seen, later, that equation (24) is not valid up to such large values of k as Levin claimed. The writer (Davies12) made an analysis of the behavior of particles with inertia approaching a point sink in otherwise calm air. In the absence of appreciable rate of fall, series solutions of the dynamic equations were obtained for large and small inertia and connected by interpolation. This gave the distribution of concentration in the spherical "space charge" region near the orifice. Stepwise solutions, when the particles were also falling under gravity, showed that some particles de- scribed orbits about the sink. The calculations were made for the condition vs/V0 = 1 (25) where VQ = 1/T (QT/4TT)1/3 (26) was later defined as the dynamic sampling velocity (Davies,11* 1968) . This particular formulation arose because the dynamical equations were rendered dimensionless by measuring lengths in ------- units of the stop distance at velocity V , and times in units of the particle relaxation time, t; hence V0 = ds/T (27) In order to compare these results with those of Levin it is necessary to convert from Davies1 system to Levin's. This is easily done. Since u = vs (W = 0), we have from (26), (29) and (20) Vs/VQ = TUJQT/47I)-1/3 = (TU/fi,)2/3 = k2/3 (28) Hence the condition (25) also means that k = 1. This of course is far outside the limit for Levin's results and explains why his particles did not execute orbits around the sink. Davies found that the limiting trajectory failed to complete an orbit while trajectories outside the limiting one did not orbit at all. On this limiting trajectory the aspiration coef- ficient was estimated to be 0.37. For k = 1, Levin's series (24) gives A = 0.28; naturally, this is not the correct value, since k is too large; in fact, for slightly larger values of k the series (24) gives negative values of A. The value A = 0.37 for vs/V0 = k = 1 would be correct if all particles inside the critical trajectory entered the orifice, even after orbiting. However, it is not yet clear whether this is true. Davies found that a group of trajectories, inside the critical trajectories, completed closed orbits and then escaped from the sink. If this is correct, the value of A is reduced from 0.37 to 0.23. However, ter Kuile13 believes that all tra- jectories which execute orbits, these being inside the critical trajectory, must enter the sink. He found that in order to plot accurate trajectories, a large number of very short steps had to be taken as the sink was approached and his computer program was designed to do this. It is possible that the writer's escap- ing particles only did so because too few steps were taken along the trajectories and that they should really have been caught. To settle the point, either more trajectories need to be computed or recourse made to the theory of central orbits. Ter Kuile and the writer agree, when calculated on the nearest non-orbiting trajectory to the axis of symmetry through the sink, on the assumption that all orbiting particles enter, that for vs/V0 = k = 1, then A - 0.37. For heavy particles there is no stagnation point on the x-axis, as was assumed by Levin for k < 0.5. ------- It is important to notice that Levin's equation (24) is derived by a theory in which the effect of the inertia of the particles is dominated by their velocity of approach to the vi- cinity of the point sink; this velocity is u0. In limiting the result to low values of k, he has eliminated the influence upon the value of A of the concentration "space charge" around the sink and of particles with enough inertia to describe orbits around the sink. Because of this limitation, it will be seen that decreasing the rate of suction, Q, increases the value of k, equation (20), so that the aspiration coefficient, A, de- creases. Obviously this is because, when Q is small, more par- ticles can shoot past the sink, due to their inertia upon the wind and sedimentation velocities. This dependence of A on Q was noted by Kaslow and Emrich,21 but its significance was not realized and some confusion was created. When inertia effects are larger, inside Levin's range, those due to the aspiration velocity may preponderate and cause a re- versal of the effect on A, so that increasing Q increases the sampling error. Confusion has also been caused by a failure to realize that particles with unlimited inertia have A = 1 if the wind and sedi- mentation velocities are both negligible. Examples of error on this account are seen in the work of Kaslow and Emrich,21 Kim,22 Pickett and Sansone,17 Breslin and Stein,15 Agarwal,19 Gibson and Ogden,16 and, no doubt, others. PARTICLES WITH INERTIA; FINITE ORIFICE Levin's equation (24) applies to a point orifice. He thought that it could be used for orifices of finite diameter, D, as long as D < 2A e. (29) This means that the radius is less than the distance, OS, between the orifice and the stagnation point (16). A point sink has no orientation; on replacing it by a finite orifice the direction of the normal to the plane of the orifice introduces an additional variable. For simplicity, this will be referred to as the direction of the sampling tube, ip, as shown in Figure 2 relative to vs. An independent yaw angle, relative to W, will be considered later. Let W be the wind velocity, which is usually horizontal. V is the mean air velocity in the sampling orifice and has the direction of the sampling tube- Then V = 4Q/7TD2 (30) ------- Figure 2. The additional angle, \jj, which is necessary in proceeding from a point sink to a sampling tube of diameter D. Note that the angles >|/ and $ are not necessarily in the same plane. The angle of yaw between V and W is not shown. Stw = TW/D, Two Stokes' numbers are involved, that on the wind velocity (31) and that on the sampling velocity (32) Stv = TV/D The magnitude of the sum of the wind and sedimentation ve- locity vectors is u0 (equation 7), as before, but, from (9) and (30) *„ = (D/4) (33) and, by (20), (31), (32), (33), and (7) k = TU A = (4Tu /D) */u /V V o / " o ^ oo = 4Stw (W/V)^ {l + (vs/w)2 + 2 vg/W cos ------- = 4Stv{(w/v) 2(w/v)« (vs/v)cos ------- k. When V and W have the same or opposite directions, yaw is 0° or 180° and the concentration "space charge" is symmetrical about the sampling tube. Changing the yaw to 90° destroys this symmetry and will be accompanied by a decrease in the value of A. Some experimental results at 90° yaw are described below. When the sampling tube is large there is a possibility of the dust shadow reducing A at 180° yaw. THE DAVIES SAMPLING CRITERION The writer (Davies1 "*) proposed that accurate samples in calm air would be obtained with an isolated small tube, the words "small tube" meaning that the aspiration coefficient is inde- pendent of the orientation of the tube, provided that 5(QT/4ir)1/3 £ D/2 < 0.2{Q/irgT)J5 (41) The right hand term represents a maximum error of ±4% under the worst conditions, with the tube facing up or down (i|j = 0 or IT, equation (5)), due to sedimentation. The left hand term is derived from the excess concentration in the "space charge" region being 1.6% at a distance of 5ds from the center of the orifice (Davies12), where, by (26) and (27) = (QT/47T) 1/3 Considering the gravitational condition, use of equations (2) and (30) shows that it makes v /V < 0.04 (42) s The inertia condition reduces as follows, by (30) and (32) , 5(D2VT/16)*/3 < D/2 or 5D/2 st1/3 < D/2 (43) or stv < 0.016 When W = 0 and these values are inserted in equation (37) we obtain A = 0.9996 Hence, in absolutely calm air, the theoretical sampling error, according to Levin, is only 0.04% which is obviously too strict a criterion. However, the important effect of a low wind ve- locity needs to be looked at. Davies1 * suggested that calm air be defined as W/V < 0.2 (44) 12 ------- Note that the limited size of orifice imposed by (29) re- duces, by (33) to u0/v)2 < 0.25 (45) and that the value of u0/V defined by (42) and (44) for all values of ------- The limit of W/V to which this can be extended while still remaining within Levin's criterion (29) requires W/V < 0.5 With this value, and the factor 2.45 of (47) instead of 5, cal- culating as in (43) gives (Sty/2)1/3 = 1/2.45 or Sty = 0.136 Hence, by (35) k = 0.193 and by (24) A = 0.85 which is within Levin's other limit of 1% error at k = 0.25, (38). When the wind is not horizontal, the value of A is raised. However, the experiments described below indicate that Levin's estimate of 1% error at k = 0.25 is far too low when applied to a finite tube diameter. There are thus grounds for considering a change in the fac- tor 5 of the inertial term of the Davies criterion to 2.45 so that the new criterion is as in (47) , but lower values than this will certainly involve larger errors. (Figure 3) Several papers have been published in which the original criterion is criticized as too severe. The experimental tech- nique in some has been inadequate and in all the importance of the reaction of the wind speed and the sedimentation speed of the particles upon the inertia effect has been entirely over- looked, although it was emphasized by the writer12 and is implicit in Levin's equations (Figure 3). EXPERIMENTAL RESULTS; CALM AIR A very careful series of experimental measurements is due to Breslin and Stein1b (1975). They measured aspiration coeffi- cients with 398 < V < 5968 cm/sec and 0.04 < D < 0.4 cm, using particles of coal dust with aerodynamic diameters between 2.9 and 41 ym. By means of a Coulter counter, the dust counts were broken down into 14 size ranges so that the disadvantages of employing an aerosol of wide size distribution were overcome. Sampling was carried out with horizontal and vertical (facing upwards) tubes; in most of the latter experiments the gravita- tional error due to settlement into the orifice was small. Many experiments resulted in low values of A, down to 0.4. The extra- ordinary thing about these results is that Breslin and Stein operated with an ambient wind velocity averaging 20 cm/sec near 14 ------- ^ + (Stv/2) -1/3 Figure 3. A/[1 + (vs/V)] cos $ as a function of f(W2 + Vs^J/V2]1/2 and (Sty/2)'1/3 according to equation (37) for horizontal wind. The units on the axis of abscissae are (Stv/2)~1/3 since this is the value of the constant multiplying the inertia term of the Davies sampling criterion. The graphs enable the sampling error to be read off, for various values of (W2 + Vg2)/]/2 and vs/V, according to the value chosen for the constant, assuming that equation (37) is correct. the sampling points without realizing that this contributed very much to their values of A; in fact, they actually wrote that the spread in their results "may indicate that the inertial parameter alone is not completely adequate to characterize aero- dynamic effects at sampling inlets". Their experimental data are plotted on Figure 4, the aspira- tion coefficient, as ordinate, against (Sty/2)"1/3 . This quan- tity is chosen since it is equal to the numerical factor multiply- ing the left hand term of the Davies criterion, namely 5 in the original expression (41) and now, perhaps, reduced to 2.87 (46) or 2.45 (47). How this comes about can easily be seen from (43). In these experiments vs/V was negligibly small but W/V ranged from about 0.05 to 0.004. By inserting these values in equa- tions (37) the two curves, according to Levin, of A against 15 ------- (Stv/2)-1/3 have been plotted on Figure 4. Most of the experi- mental points fall between these curves and it is evident that the spread of the values of A as well as the low values are en- tirely due to the 20 cm/sec ambient wind. If W = vs = 0 then A = 1. In these experiments W » vs so that the reduction of A below unity was due to W. Once again, it is the effect of W and vs upon particles with appreciable inertia, which causes a reduction in A. Particle inertia alone does not affect A for isolated orifices, as long as the tube is reasonably sharp-edged and particles deposited on the inner tube wall are included in the sample. Note that Breslin and Stein use r0/ds, which is the same as (Stv/2)-1/3, and is the radius of the sampling tube divided by the stop distance of the particles from velocity V0, equations (26) and (27) . Some experiments have been performed by Gibson and Ogden; they did not attempt to measure absolute concentrations but i e i.o 0.8 0.6 0.4 — 0.05 W/V (Stv/2) -1/3 Figure 4. The experimental points of Breslin and Stein. ^ The two curves correspond to W/V = 0.004 and 0.05. They illustrate the importance of the low ambient wind velocity of 20 cm/sec when the sampling velocity was 6000 and 400 cm/sec, respectively; vs/V was very small. 16 ------- merely compared individual pairs of samples taken at differ- ing values of Sty. Sampling was carried out with \p = ------- According to equations (6) and (37) , for values of A near to unity, the aspiration coefficients can be calculated from the experimental data as follows, for comparison with the actual measured values of A. When ------- 0.8 0.6 0.4 0.2 .^^_ LEVIN'S THEORY, ADAPTED TO FINITE TUBE DIAMETER, EQUATION (51) O PATTENDEN AND WIFFEN23 DAVIES AND SUBARI, THIS PAPER .O1 0.01 0.1 -W 1 3/2 Figure 5. Experimental results for A as a function of Stv(W/V)3/2, sampling at 90° yaw angle with vs very small. the sum of those in the tube plus those on the plate, divided by the volume of air sampled. The particles inside the tube were estimated either by weighing the tube before and after de- position or by lining it with thin metal foil coated with a film of magnesium oxide. The airborne concentration was measured with a small isokinetic impactor, facing the wind, with a sharp- edged slit orifice. It is to include particles particles some solid bounce off lets of di particles incidence essential, when measuring the concentration of aerosols, particles deposited inside the sampling tube with collected on the impactor plate or filter. Liquid will usually adhere to the tube wall, on impact, but particles, especially at high rates of suction may In the experiments now described the liquid drop- -2-ethylhexyl sebacate adhered to the metal tube, but which struck the magnesium oxide layer at glancing often rebounded and reached the sampling plate. Ft is defined as the fraction of the total particles enter- ing the sampling tube which were found adhering to the wall of the tube. The experimental results are shown in Table 1. Ft could be calculated by the empirical formula Ft = 7 1 + erf Stw (W/V) 0.2 0.15 (52) 19 ------- TABLE 1. FRACTION Ft OF PARTICLES ENTERING THE SAMPLING TUBE WHICH DEPOSITS ON THE WALL OF THE TUBE Method Stw MgO 0.065 .065 .077 .077 .078 .078 .089 .089 .100 .100 .100 .100 .113 .160 .160 .160 .160 .178 .178 .178 .190 .190 .190 .190 .190 .204 .204 .220 .220 .220 w/v 0.093 .093 .110 .110 .400 .400 .400 .400 .150 .300 .400 .610 .400 .060 .120 .232 .470 .400 .400 .400 .070 .140 .270 .400 .530 .400 .400 .080 .170 .310 Ft Calculated 0 0 0.001 .001 .009 .009 .023 .023 .013 .034 .048 .077 .094 .080 .155 .260 .404 .489 .489 .489 .202 .329 .472 .560 .622 .638 .638 .365 .532 .644 Experimental 0 0 0 0 0 0 0 0 0 0 0.10 .14 0 .05 .17 .18 .25 .29 .31 .27 .36 .31 .31 .58 .64 .53 .44 .43 .58 .61 (continued) 20 ------- TABLE 1 (continued) Method St MgO 0.240 .240 .256 .278 .278 .278 .290 .290 .346 .377 .377 .397 .397 .403 .462 .630 Weighing .630 .630 .630 .722 .722 .856 .856 .895 .895 W/V 0.351 .351 .400 .200 .400 .400 .475 .475 .400 .200 .200 .400 .400 .400 .400 .400 .200 .200 .400 .200 .400 .400 .400 .400 .400 Ff Calculated 0.770 .770 .839 .798 .891 .891 .926 .926 .968 .955 .955 .987 .987 .989 .996 .999 .998 .998 .999 1.000 1.000 1.000 1.000 1.000 1.000 Experimental 0.75 .78 .81 .50 .54 .54 .92 .89 .85 .46 .57 1 1 .89 .87 1 1 1 1 1 1 1 1 1 1 and Table 1 shows that this agrees quite well with the experi- mental measurements which cover the ranges 0.068 < St^ < 0.3 and 0.05 < W/V < 0.53. Equation (52) is graphed in Figure 6 and has been extrapolated beyond the experimental values to give the curves up to W/V = 2. This was done, as an interim measure, to give warning of losses that can occur upon the tube wall. 21 ------- 0.8 0.6 0.4 0.2 T I \ I I I I I W/V 2 1 0.5|0.2 0. 0.01 Figure 6. The fraction, Ft, of particles entering the sampling tube which deposits upon the inside of the tube (experimental data in Table 1). The experimental data, for each value of A measured, are given in Table 2 and the results are plotted in Figure 5, with a separate point for each experiment. Also shown in Figure 5 are 14 points calculated from Table 2 of Pattenden and Wiffen's paper23; each is the mean of about four measurements in a wind tunnel at wind speeds between 2 and 6 m/sec, using solid particles with aerodynamic diameters from 4.5 to 25 vim. The sampling tube was vertical, in a horizontal wind, and it made no difference whether the tube pointed upwards or downwards, hence vs was negligible; the tube diameter was 1.25 cm, its end was cut off square and the wall thickness was about 0.2 cm. The mean inlet velocity was 70 cm/sec. Only their experiments with a tube without a cover are discussed here. They found that with a cylindrical rain cover over the tube there was a substan- tial increase in the aspiration coefficient; this is an example of May's stagnation point sampling, 2 |