Environ. Sci. Technol. 1992,26,390-394
Pergamon: Oxford, UK, 1979; p 100. Bell, A. T. In Vibrational Spectroscopy of Molecules on Surfaces, 1st ed.; Yaks, J. T., Madey, T. E., Eds.; Plenum: New York, 1987; pp 105-134. Lau, C. L.; Snyder, R. G. Spectrochim. Acta, Part A 1971, 27, 2073. Alpert, N. L., Keiser, W. E., Szymanski, H. A. IR Theory and Practice of Infrared Spectroscopy, 1st ed.; Plenum: New York, 1973. Farmer, V. C. In The Infrared Spectra of Minerals, 1st ed.; Farmer, V. C., Ed.; Mineral Society: London, 1974; pp 331-359. Soma, Y.; Soma, M. Chem. Phys. Lett. 1983,94,475.
(37) Ernstbrunner, E.; Girling, R. B.; Crossman, W. E. L.; Hester, R. E. J. Chem. SOC.,Perkin Trans. 2 1978, 177. (38) Santacesaria, E.; Gelosa, D.; Picenoni, D.; Danise, P. J. Colloid Interface Sci. 1984, 98, 467. (39) Richards, R. E.; Rees, L. V. C. Langmuir 1987, 3, 335. (40) Richards, R. E.; Rees, L. V. C. Zeolites 1988,8, 35. (41) Doner, H. E.; Mortland, M. M. Science 1969, 166, 1406. Received for review March 20,1991. Revised manuscript received July 15,1991. Accepted August 27, 1991. This work was supported, in part, by the Environics Laboratory, Air Force Engineering and Services Center, Tynall AFB, FL, under Contract FO8635-89- C-0152.
Aerosol Particle Losses in Isokinetic Sampling Probe Inletst Bijian Fan, Andrew R. McFarland," and N. K. Anand Aerosol Technology Laboratory, Department of Mechanical Engineering, Texas A&M University, College Station, Texas 77843
w Substantial losses of aerosol particles can occur in the inlet region of isokinetic sampling probes. Okazaki and Willeke developed a semiempirical model based on gravitational settling in developing boundary layers to predict these losses. However, that model predicts zero losses in vertical probes, which is contrary to experimental evidence. From first principles, we have numerically analyzed depositional losses in isokinetic probes by calculating the flow field and then determining particle trajectories. By including the Saffman force (which causes motion transverse to the free stream velocity direction) in addition to the gravitational force, we have shown good agreement with the semiempirical model of Okazaki and Willeke. The geometric standard deviation is 1.16 for our calculations relative to the Okazaki-Willeke model for a range of conditions which they tested. In comparison, the geometric standard deviation is 1.12 for the experimental data of Okazaki and Willeke relative to their semiempirical model.
Introduction I n experimental studies of isokinetic inlets, it has been noted that a substantial fraction of the aerosol can be deposited on the internal walls of the probe (1-4). For example, when an isokinetic probe was used to sample a flow rate of 170 L/min from a 14 m/s airstream, wall losses of 10-pm aerodynamic equivalent diameter (AED) aerosol particles were 40% (4). In situations involving source characterization, such as performed with the EPA method 5 sampling train ( 5 ) ,wall losses are of little importance since the analytical procedure requires that the internal walls of the probe be washed to remove the inadvertently deposited material. However, there are many instances in which it is crucial that the aerosol be effectively transported from the free stream through the inlet. As an example, continuous air monitors (CAMS) are used to detect the presence of radioactive aerosol particles in the working environment in nuclear plants. In many applications, the aerosol to be analyzed is isokinetically sampled from a flow duct and transported to a remotely located CAM. To adequately assess the capabilities of CAM samplers, it is important to have knowledge of the fraction of aerosol which will penetrate the sampling inlets and flow tubes. A semiempirical model has been developed to predict wall losses in horizontally oriented isokinetic inlets (2). +Air Quality Laboratory Publication 6441/01/04/91/BJF. 390
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This model takes into account gravitational settling in the developing laminar boundary layer. However, losses in vertically oriented tubes have also been noted (6). Recently, numerical studies of aerosol deposition in various components of aerosol transport systems have been receiving attention (7-9). In those studies, the particle deposition mechanisms are inertial impaction, gravitational settling, and thermal diffusion, the latter of which is significant only for submicrometer particles. In a study on probe sampling (9),it was noted that a discrepancy exists between the experimental data and numerical modeling, where the modeling is based on first principles. The discrepancy is believed to be mainly caused by various assumptions by different investigators about the gas flow and the forces acting on the aerosol particles. Herein, the reasons for the discrepancy will be examined. In the present study, the gas flow field in and about the probe is simulated numerically, and the resultant forces acting on the particle are analyzed and compared quantitatively. The particle trajectories are computed to predict wall losses. Results based on numerical analysis are compared with a semiempirical model developed by Okazaki and Willeke (2).
Gas Flow in a Sampling Probe Consider an aerosol sampling probe oriented horizontally and aligned parallel with the flow. Even a sharp-edged probe can be expected to disturb the flow field, so a flow analysis must extend not only to the internal flow in the probe, but also to the external flow field. To compare present results with the data base given in ref 2, we will use the same probe geometry and operational conditions. The inside diameter, D, of the probe is fixed at 5.6 mm, the angle between the tube outside wall and the free-stream velocity is taken to be loo, and the probe length, L, is fixed at 200 mm. From the standpoint of the flow field, it can be treated as an axisymmetric case, which is a two-dimensional problem in (r, z ) coordinates, where the z direction is along the probe axis and the r direction is normal to the axis. The finite element mesh used in the numerical computations is shown in Figure 1. The model equations which were employed to represent the flow are the steady-state incompressible momentum (Navier-Stokes) and continuity equations. The boundary conditions are zero velocity at all walls, zero radial stress along the center line of the flow in the tube, a uniform free-stream air velocity of U,, and
00 13-936X/92/0926-0390$03.00/0
0 1992 American Chemical Society
m,(dV/dt) = F
PROQE CENTERLINE
PROBE CEMERUNE
,'
Figure 1. Conflguration of computational domain. Due to the axisymmetric nature of the flow, only half of the field ls shown. Probe diameter 5.6 mm; probe length 200 mm.
specification of the pressure at the probe exit. The latter parameter controls the flow rate into the probe, which, in turn, is adjusted to satisfy the isokinetic condition. The isokinetic condition is defined as a velocity ratio, R, of unity, where R = Um/Uinand Vi, = &/Ain, with Q the volumetric flow rate through the probe and Ah the probe inlet area. A finite element analysis of flow field was made using a commercial code, FIDM (IO). A nine-noded Lagrangian element was used for velocity interpolation, and a fournoded bilinear element was used for pressure interpolation. FIDAP uses the Galerkin technique to solve the model equations. An example of the numerical simulation of the flow field, Figure 2, shows the velocity vectors corresponding to a free stream velocity of 5 m/s. The flow region around the entrance of the probe has been disturbed by the probe edge. As will be shown, this disturbance enhances the particle deposition in the entrance region of the probe. We wish to draw particular attention to the fact that isokinetic sampling (R = 1)does not assure a uniform flow field in the entrance region inside the probe-a phenomenon which does not comply with conventional understanding.
Mechanisms of Relative Particle Motion in a Gas
where F is the total force acting on an aerosol particle. In the following analysis, only relatively small particles (d, 5 30 pm) will be considered and it will be assumed that the disturbance of particles on the flow is negligible. Thus, particles may move freely in longitudinal ( 2 ) and transverse (r)directions under the influence of the forces considered. Henceforth in this work, the term flow disturbance will be used to describe the variation in free-stream flow caused by the presence of the probe. In previous studies (7-9),inertial and gravitational forces were taken into account; however, those two forces are not the only ones acting on particles in a nonbniform flow field although they may be dominant, particularly for large particles with horizontally oriented probes. The theory for motion of a small particle in a nonuniform flow, as opposed to a uniform flow, which is defined as an unlimited and updisturbed medium, has been formulated (11,12) with subsequent modifications and improvements (13-17'). In particular, the forces acting on a particle due to the flow were examined by those investigators. It has been pointed out (17)that the curvature of flow velocity profile, which appears only in nonuniform flow, will modify the aerodynamic drag force (Fd)on a particle in a low Reynolds number range. Here the Reynolds number is based upon the relative velocity between the particle and gas. Assuming a spherical particle with steady Stokes flow, the drag force on the particle produced by the disturbed flow around the particle is 1 Fdi = 3 r d p ( u , ( Y ( t ) , t-) vc(t))+ -prd,3(V2U,)IY(t) (2) a where p is the gas dynamic viscosity. This force is dominant and is taken as a reference when other forces are considered. Previous investigators ( I 7) comprehensively examined the motion of an aerosol particle in a nonuniform flow field and formulated the resultant force acting on a particle due to the flow as a surface integral of the fluid stress tensor:
m,(dVi/dt) = m,,gi + $uijnj ds
Flow Review of Various Forces Which Act on Aerosol Particles. Here, we consider the motion of an aerosol particle in the flow field. A particle with diameter d, and where mass mp is instantaneously centered at Y ( t )= (Yi(t)), t refers to time. The particle moves with a velocity V ( t ) = ( V i @ )in) a gas which has a velocity u ( t ) = (ui(Y(t),t)). The gas velocity is predicted by numerical simulation of the flow field. From Newton's law, the equation of motion of the particle is
(1)
(3)
where uij is the fluid stress tensor, given by uij = -pa,
+ P(dUi/dXj + dUj/dXi)
(4)
(gi) is the gravitational vector, (nj)is the outward-directed normal vector of the particle surface, p is the pressure and (aij}is Kroneker's delta. By evaluation of the fluid stress tensor acting on the particle, the equation of motion was derived as
EXPANDED VIEW OF FLOW NEAR INLET EDGE
Environ. Sci. Technol., Vol. 26, No. 2, 1992
391
1 - 3spdp{V,(t) - ui(Y,t) - 24 --d,2VZ~ily/ 40
where m, is the fluid mass displaced by the particle and u is the kinematic viscosity of the fluid. On the right side of this equation, the first term is the gravitational force, Fgi;the second term is the pressure gradient force (F,J; the third term is the added mass or associated term ( F J ; the fourth term is the Stokes law drag force (Fdi);and the fifth term is the Basset force (FBi), which is due to curvature in the velocity profile. The distinction between the two different time derivatives is that d/dt is used to denote the derivative following a moving aerosol particle, namely
and the operator D/Dt is used to denote the time derivative following a fluid element:
It represents the fluid acceleration as observed at the instantaneous center of the particle. However, in the context of the low Reynolds number approximation, the two derivatives are approximately the same. Two forces which can potentially cause aerosol particles to deposit on probe walls are not taken into account in eq 5, since that equation is based on the assumption that particles are far from boundaries. There is high shear in the gas at probe walls which may produce transverse force on a particle that, in turn, may contribute to particle deposition on the walls. These forces, the Magnus forces ( F M ) , due to particle spin, and the Saffman force (Fs),due to boundary shear, will be considered herein. The expressions for these two forces are (18-20) 1 F - -ap,dP3(V - U) X (52, - 0,) (8) M - 8 where
B,=
(a)
-
vxv
wp=(+u
and Fs = (Fs,, FSJ
(9) The parameters Fs, and Fs, are the radial and axial components of the Saffman force and are given by
where Cs is a constant (1.615) and p g is the gas density. Theoretical analyses on the effects of the Saffman force have been previously reported (21,22). That analysis and 392
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the numerical calculations presented herein show the magnitude of the transverse forces are highest in the boundary layer as contrasted with the core flow, where they are negligible in comparison with the drag and gravity forces. In the case of the inlet region of a probe, the large shear at the boundary can make the two transverse forces commensurate with other forces. It has been noted (23) that the Saffman force can produce concentration heterogeneities in the developing boundary layer of an upright channel. Equation of Motion of an Aerosol Particle. Based on above analysis, the equation of motion of an aerosol particle in a sampling inlet can be represented by d Vi m - - - Fgi + Fpi + F,i + Fdi + Fbi FMi + Fsi (IO) dt In addition, the equation for the rotational motion of an aerosol particle is
+
where I, is the moment of inertia of the particle. In the numerical calculations, an implicit time integration scheme was applied to solve the equations of motion in order to obtain the particle trajectories and thereby determine deposition upon walls. Mechanisms of Particle Deposition in the Boundary Layer. Particle deposition on a wall is caused by forces acting in the transverse direction. In the core region of the flow, the external forces which dominate particle dispersion are aerodynamic drag and gravity; however, in the boundary layer region other external transverse forces can come into effect, and the particle motion can differ considerably from that in the core region. We will consider the effect of each of the above noted forces upon particle motion. On the basis of calculations, we will then discard the negligible terms and utilize the remaining transverse terms in determining particle losses in the inlet region of a probe. First, consider the use of a dimensionless radial distance from the center line of the probe, r*, where r* = r/R and R is the tube radius. Values of 0 and unity for r* correspond to the tube center line and inside wall, respectively. Next, assume that the drag force has the largest magnitude-it will be used as a reference when other transverse forces are considered. The force ratios which will be compared are
All of these force ratios were calculated at various locations in the flow field for a range of aerosol particle sizes of 10-30-pm AED, for free-stream velocities of 1-10 m/s and for the probe characteristics specified earlier. The results show the force ratios B,, B,, and BM are negligible for the range of conditions investigated. In the boundary layer, only the Saffman force is of the same order of magnitude as the gravitational and drag forces. The magnitude of this force relative to aerodynamic drag is shown in Figure 3 for the condition of a free-stream velocity of 5 m/s and a particle size of 30-pm AED. For comparison, the value of the gravitational force ratio, B, is also shown. These calculations were made by following the trajectory of a particle which would strike the wall as that particle passed through the boundary layer. Note that, in the graph, the values of Bs and B, are shown as functions of r* only for the region near the wall. This is because ultimately the depositional losses are associated
0 25
I M
020-
u
f
0.05
-
4
~ - - - - - - - - - _ - - _ _ - -
0 00
083
0 84
0 85
0 8I= 6
097
Dimensionless Radial Distance
098
098
IO0
- O k a r a k l - l l l l e k e Model + U, = 2.5 m/s
1
.
, U
=
5.0 m/a
U,
i
IO. m/s
0 001
r*
0 010
0 100
Deposition Parameter, K
Flgure 3. Comparison of Saffman and gravitational forces with the drag force in the boundary layer region: particle size 30-pm AED; free-stream velocity U, = 5 m/s.
Flgure 4. Comparison of present numerical prediction of aerosol particle penetration with Okazaki-Willeke model. The data points represent particle sizes of lo-, 20-, and 30-pm AED at each velocity.
with the transverse motion of particles near the wall. The effects of the Saffman force are associated with shear (19), and the highest value of shear occurs in the boundary layer. There is little shear in the core flow in an aerosol sampling inlet and the Saffman force is of no consequence in that region. Other calculations have been carried out to evaluate the effects of particle size and free-stream velocity upon the Saffman force. The results of such calculations show that the force ratio, Bs, increases with both size and velocity.
the Saffman force is neglected, the agreement is poor. An estimate of the fit of our computational results to the model of Okazaki and Willeke can be obtained by considering the geometric standard deviation, sg, of the calculated points relative to the model, namely 1 ln2 sg = -C(ln Pi - In Pow)2 (14) N-1 i
Aerosol Penetration through a Sampling Probe Because gravitational settling in horizontally oriented probes is a nonaxisymmetric process, a three-dimensional version of the flow field was used in computation of the particle trajectories. To calculate particle penetration through a sampling probe, we started with an array of 20 000 particles uniformly distributed in the free-stream region of the test probe. The initial condition on particle motion is an assumption that particles travel with the free-stream velocity. From our previous analysis (9),the use of 20 000 particles was found to be statistically sufficient to calculate aerosol penetration through the probe and wall losses on the internal walls of the probe. Here, the penetration, P, is the ratio of the number of particles at the probe exit plane to the number of particles in the free stream in the projected area of the probe entrance plane. Due to the flow disturbance in the entrance region of the probe and the flow disturbance in the developing boundary layer, the transversal Saffman force together with gravitational settling and inertial effects causes some of the aerosol particles to strike the walls. The results of numerical computations for depositional losses are summarized in Figure 4,where the penetration through a probe is compared with the semiempirical model of Okazaki and Willeke (2). Here, we have used their probe deposition parameter, K , as the independent variable:
K=
4F GR Stk
(13)
where Re = pgUinD/p is the Reynolds number, Stk = Cppdp2U,/9pDis the Stokes number, G = g L / U m 2is the gravitational parameter, g is the gravitational constant (9.80 m/s2), and p p is the particle density. The computations were carried out for three free-stream velocities: 2.5, 5, and 10 m/s and for particle sizes of lo-, 20-, and 30-pm AED. The calculational results show good agreement with the model of Okazaki and Willeke. On the other hand, when
where N is the number of data points, Pi is the penetration at a given set of computational conditions, and Pow is the penetration calculated from the Okazaki-Willeke model. For the data points shown in Figure 4, sg = 1.16. By comparison, the geometric standard deviation of the experimental data of Okazaki and Willeke relative to their model is 1.12.
Discussion of Results From above analysis, it can be concluded that drag, gravity, and inertia are not the only significant forces acting on an aerosol particle in the inlet region of a probe. Inclusion of the Saffman force yields calculational results that agree favorably with the semiempirical model of Okazaki and Willeke (2). We believe that the nun-erica1 computations on the flow field with the inclusion of the Saffman force help to explain the anomalously high deposition of particulate matter in the inlet region of a sampling probe. In addition to the work reported herein, we have also conducted trial numerical runs to estimate the wall losses for vertically oriented inlets. The preliminary results show good agreement with the experimental data of Davies (6). Literature Cited (1) Durham, M. D.; Lundgren, D. A. J . Aerosol Sci. 1980,11, 179. (2) Okazaki, K.; Willeke, K. Aerosol Sci. Technol. 1987,7,275. (3) Hangal, S.; Willeke, K. Atmos. Enuiron. 1990, 24, 2379. (4) McFarland, A. R.; Ortiz, C. A.; Moore, M. E.; DeOtte, R. E., Jr.; Somasundaram, S. Enuiron. Sci. Technol. 1989,23, 1487. (5) U.S. Environmental Protection Agency. Fed. Regist. 1987, 52, 24634. (6) Jayasekera, P. N.; Davies, C. N. J . Aerosol Sci. 1980, 11, 535. (7) Balashazy, I.; Martonen, T. B. Aerosol Sci. Technol. 1989, 13, 20. (8) Tsai, C. J.; Pui, D. Y. H. Aerosol Sci. Technol. 1990, 12, 813. (9) Fan, B.; Wong, F. S.; Anand, N. K.; McFarland, A. R. Optimization of aerosol penetration through transport lines. Aerosol Technology Laboratory Report 6441/01/31 f 91/ NKA; Department of Mechanical Engineering, Texas A&M University, College Station, TX, 1990. Environ. Sci. Technol., Vol. 26, No. 2, 1992 393
Environ. Sci. Technol. 1992, 26, 394-396
FZDAP Package Manual; Revision 4.0,1st. ed. Fluid Dynamics International Inc.: Evanston, IL, 1986. Tchen, C. M. Ph.D. Thesis, Hague, Martinus Nijhoff, 1964. Corrsin, S.; Lumley, J. Appl. Sei. Res. 1956,A6, 114. Buevich, Y. A. Fluid Dynam. 1966,6, 119. Riley, J. J. Ph.D. Thesis, The Johns Hopkins University, Baltimore, MD, 1971. Soo, S.L.Phys. Fluids 1975,18, 263. Gitterman, M.; Steinberg, V. Phys. Fluids 1980,23, 2154. Maxey, M. R.; Riley, J. J. Phys. Fluids 1983,26,883. Rubinow, S.I.; Keller, J. B. J. Fluid Mech. 1961,11,447. Saffman, P. G. J. Fluid Mech. 1965,22,385. Shraiber, A. A.;Gavin, I. B.; Naumov, V. A.; Yatsenko, V. P. In Turbulent flows ingas suspensions; Dolinsky, A. A.,
Ed.; Hemisphere Publishing Co.: New York, 1990; Chapter 2,p 45. (21) Gorbis, Z. R.; Spokonyi, F. E.; Zagaynova, R. V. Znzh. Fiz. Zh.1976,30, 657. (22) Ishii, R. Phys. Fluids 1984,27,34. (23) Grinshpun, S.A.;Lipatov, G. N.; Senenyuk, T. I. J. Aerosol Sci. 1989,20, 975. Received for review May 2,1991. Revised manuscript received August 8,1991. Accepted August 21,1991. Funding was provided by the U.S. Nuclear Regulatory Commission under Contract Grants NRC-04-89-353 and NRC-04-90-115. Dr. Stephen A. McGuire is the monitor for both grants.
Polychlorinated Dibenzo-p-dioxins and Dibenzofurans Associated with Wood-Preserving Chemical Sites: Biomonitoring with Pine Needles Stephen Safe,” Kirk W. Brown, Klrby C. Donnelly, Cathy S. Anderson, and Karl V. Markiewlcz
Departments of Veterinary Physiology and Pharmacology and Soil and Crop Sciences, Texas A&M University, College Station, Texas 77843 Michael S. McLachian, Anton Reischl, and Otto Hutzinger
Chair of Ecological Chemistry and Geochemistry, University of Bayreuth, P.O. Box 101251, 8580, Bayreuth, FRG Gas chromatography-mass spectrometry (GC-MS) analysis of pine needle extracts from two pentachlorophenol wood-preserving sites detected relatively high overall concentrations of polychlorinated dibenzo-p-dioxins (PCDDs; 1798 and 935 ppt) and dibenzofurans (PCDFs; 310 and 141 ppt). The dominant congener was octachlorodibenzo-p-dioxin (Cl,DD), the CPCDDs > CPCDFs, and relatively low levels of the tetra- and pentachlorodibenzofurans (CC1,DFs and C1,DFs) were detected. This pattern was similar to that observed for the PCDD and PCDF contaminants detected in commercial pentachlorophenol and significantly different from the pattern observed for combustion-derived PCDDs and PCDFs. The levels of these compounds were significantly lower in two “pristine” areas in the Kootenai National Forest and the Glacier-Waterton International Peace Park (i.e., CPCDDs was
