A Predictive Model for Aerosol Transmission through a Shrouded

Oct 29, 1996 - The model for wall loss ratio underpredicts the experimental values by 8% (which influences the transmission ratio by about 2%), and ...
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Environ. Sci. Technol. 1996, 30, 3192-3198

A Predictive Model for Aerosol Transmission through a Shrouded Probe HONGRUI GONG, SUMIT CHANDRA, ANDREW R. MCFARLAND,* AND N. K. ANAND Aerosol Technology Laboratory, Department of Mechanical Engineering, Texas A&M University, College Station, Texas 77843

experimental data. Applications of shrouded probes involve sampling air from turbulent flows, and the model is based on conditions that simulate those encountered by shrouded probes in typical stack flows. The model takes into account turbulent, inertial, and gravitational effects. It is assumed that the shrouded probe is oriented parallel to the direction of flow and the inner probe is sufficiently small such that it only samples from the core region of the shroud.

Introduction Shrouded aerosol sampling probes utilize an aerodynamic decelerator (shroud) placed about an inner probe. A model has been developed for predicting the transmission ratio (T) of aerosol from a free stream to the exit plane of the inner probe. This expression, T ) FAsApr(1 - WL), is based on use of an existing empirical model to characterize the aspiration ratios of the shroud (As) and inner probe (Apr) and based upon new models to characterize the wall loss ratio in the inner probe (WL) and to relate the concentration in the core region of the shroud to the mean concentration predicted by the existing aspiration model through a correlation function, F. Extensive computational results provide a data base for specification of the correlation function. The need for the correlation function results from the phenomenon that particle enrichment in a subisokinetic shroud is non-uniform, with the concentration higher near the wall than in the center region. However, the concentration in the core region of the shroud, which is the aerosol that is ultimately sampled, is quite uniform, albeit at a level that is somewhat higher than the concentration in the free stream. This correlation function depends on particle Stokes number and the velocity ratio between free stream and shroud inlet. The predictive equation was verified by comparing its results with data from physical experiments conducted in aerosol wind tunnels with several sizes of shrouded probes. The standard error of experimental data of aerosol transmission about the predictive equation was 7.7%. The model was also evaluated in-depth by examining its ability to predict the overall aspiration of aerosol from the free stream to the inlet plane of the inner probe, wall loss ratio, and transmission of aerosols from the free stream to the exit plane of the inner probe. The results show that the model underestimates the aspiration by approximately 2%. The model for wall loss ratio underpredicts the experimental values by 8% (which influences the transmission ratio by about 2%), and transmission ratio prediction is within 1% of average

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Principle of Operation of a Shrouded Probe. The shrouded probe (Figure 1), was developed by McFarland et al. (1) for continuous aerosol sampling from stacks and ducts of the nuclear industry. Aerosol flow from the free stream in a stack or duct is decelerated in a shroud and then sampled by an inner probe. In a typical application, the free stream velocity is on the order of 10 m/s, and that free stream velocity is decelerated by a factor of 3 or 4 inside the shroud. Typically, the sampling flow rate of the inner probe is on the order of 50 L/min. Under such conditions, when the stream enters the shroud there is inertial enrichment of supramicrometer-sized aerosol particles at the shroud entrance plane. However, curvature of the air streamlines near the wall in the entrance region of the shroud is much more pronounced than in the core flow (2). As a consequence, inertial enrichment should be primarily concentrated in the region near the inside wall of the shroud. Because the inner probe only samples from the core flow while the flow near the inside wall of the shroud is discharged back to the stack flow stream, the aerosol concentration in the sample that enters the inner probe can be nearly representative of the concentration in the free stream. Also, because the inner probe is typically operated at a velocity that is only on the order of 1/4 that in the free stream, the diameter of the inner probe is typically about twice that of an unshrouded isokinetic probe that samples at the same flow rate. The lower inlet velocity and the larger diameter of the inner probe produce beneficial effects. The internal wall losses in the shrouded probe and anisokinetic effects are both less than those of an unshrouded probe. In addition, studies have shown that a shrouded probe essentially provides unbiased samples of 10 µm aerodynamic diameter (AD) aerosol particles at yaw angles as large as 22°, and its performance in sampling 10 µm AD particles is relatively unaffected by free stream turbulence intensity values as high as 30% (3, 4). Regulatory Considerations. With respect to the application for which the shrouded probe was originally developed, i.e., the sampling of radionuclide aerosol particles from stacks and ducts, the U.S. Environmental Protection Agency (EPA) has established a maximum dose of 10 mrem (milliroentgen equivalent man) per year that can be accrued by any member of the public as a result of emissions from a nuclear facility (5, 6). Dispersion modeling * Corresponding author fax: [email protected].

S0013-936X(95)00908-4 CCC: $12.00

(409)862-2418; e-mail address:

 1996 American Chemical Society

FIGURE 1. Shrouded probe.

of emissions from all sources is used to determine if a facility is in compliance with the dose requirement. Continuous emission sampling (CES) must be carried out on any individual source that can potentially contribute more than 0.1 mrem in a year. In determining which stacks and ducts of a facility must be monitored, no credit is given for control equipment on the source. Because the stacks and ducts that can emit radionuclide aerosol particles are typically HEPA-filtered, the CES requirement can be quite conservative under normal facility operating conditions, yet it should provide meaningful emissions data if there were to be an accidental release. In the past, the EPA required all nuclear facilities to follow a specified protocol for CES of stacks and ducts, which involved the use of EPA Method 1 (7), for selecting a sampling location along the axis of a stack, and American National Standards Institute Standard N13.1-1969 (8) for guidance in the methodology of sampling. EPA Method 1 requires that the sampling location must be at least eight duct diameters from the nearest upstream flow disturbance (elbow, etc.) and at least two duct diameters from the nearest downstream flow disturbance. ANSI N13.1-1969 recommends that sampling should be performed with sharpedged probes, which must be operated isokinetically if particles larger than 5 µm in diameter could be present. Because it is necessary to design sampling systems to operate under both normal and accident conditions (when proportionately higher concentrations of large particles could be present), it is customary to sample isokinetically. Under the ANSI standard, for large ducts it is recommended that rakes of isokinetic probes be used to span the duct cross section, ostensibly to collect representative samples. Use of EPA Method 1 protocol does not provide assurance that representative samples can be collected at a selected site (9), and the use of sharp-edged ANSI-type probes can cause substantial internal wall losses of particles. Fan et al. (10) showed that under typical stack sampling conditions, 75% of 10 µm AD aerosol particles are lost on the internal wall of an ANSI-type probe. Because of these limitations, the EPA has approved the use of Alternate Reference Methodologies (ARM) for U.S. Department of Energy facilities (11). Also, under the Clean Air Act Amendments of 1990, the U.S. Congress mandated that the EPA shall setup and promulgate rules for continuous emission monitoring of incinerators that process over 250 t/day (12). If such rules are promulgated and if they involve extractive sampling of particulate matter, we anticipate the same problems would be encountered as those by the nuclear industry and that protocol, such as that embodied in the ARM, would be needed. The ARM essentially focuses on single-point representative sampling at a location where any contaminants are well mixed with the bulk flow and where the velocity profile is relatively flat. Numerical criteria on coefficients of variation of contaminant and velocity profiles are stipulated

in the ARM for the acceptability of a location. If aerosol particles can be present in the stack or duct, a shrouded probe is to be used for extracting the sample. The shrouded probe must have an aerosol transmission ratio, T, between 0.8 and 1.3. Shrouded Probe Performance Parameters. The transmission ratio of a shrouded aerosol sampling probe, T, is defined as

T)

ce co

(1)

where ce is the aerosol concentration at the exit plane of the inner probe; co is the aerosol concentration in the undisturbed free stream at the probe location. The transmission ratio depends upon aspiration of aerosol into the shroud, As, and inner probe, Apr, and upon wall losses in the inner probe as characterized by the wall loss ratio, WL. The aspiration ratio of the shroud is represented by

As )

cs co

(2)

where cs is the aerosol concentration at the shroud entrance plane. The aerosol concentration is non-uniform across the shroud entrance, so the parameter As will be used herein to represent the spatial average aerosol concentration at the probe entrance. Because the inner probe only samples from the core region of the shroud, we will need an expression to relate the aerosol concentration in the core of the shroud, csc, to the mean concentration of aerosol at the shroud inlet plane, cs. Let

F)

csc csc/co Asc ) ) cs cs/co As

(3)

where F is the correlation function, which must be empirically evaluated; Asc is the aspiration ratio for the core region in the shroud. The aspiration ratio of the inner probe is

Apr )

cpr csc

(4)

where cpr is the aerosol concentration at the inlet plane of the inner probe. The wall loss ratio of the inner probe is

WL ) 1 -

ce cpr

(5)

Combining eqs 1-5 gives

T ) FAsApr(1 - WL)

(6)

At the present time, only two tools are available for characterizing the transmission ratio; namely, the numerical calculational approach of Gong et al. (2), which is computationally intensive, and, the wind tunnel testing methodology (1, 3), which is labor intensive. However, if each of the parameters in the right side of eq 6 could be evaluated, an estimate could be made of the transmission ratio of a shrouded probe. This would permit users and designers of sampling systems to readily evaluate the performance of a shrouded probe to determine if it meets criteria such as those of the ARM. In this paper, a correlation for the

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wall loss ratio, WL, is developed based on experimental results. The model for the prediction of overall aspiration ratio of the shrouded probe is formulated based on the numerical simulations of the shrouded probe. The transmission ratio in eq 6 can be estimated by the wall loss model and a model for the overall aspiration, A, of a shrouded probe, where the latter is defined as

A ) FAsApr

(7)

During the operation of a sampling probe, losses occur on its inner wall principally as a result of turbulent inertial deposition. In the correlation for wall loss ratio for the inner probe of a shrouded probe, turbulent inertial deposition is taken into account by a Stokes number based upon the probe inlet diameter and the probe inlet velocity. If sedimentation is of importance in wall losses, the effect is taken into account by a particle Froude number (13). In addition to these phenomena, deposition at the inlet region is also affected by streamline bending caused by anisokineticity of sampling operation. This effect is taken into account introducing the ratio of the shroud velocity (Us) to the probe velocity (Upr) in the correlation. Several models have been developed for predicting the aspiration of unshrouded probes (14-17) that allow determination of the mean aspiration ratio at the shroud inlet cross section, As, or at the inlet of the inner probe, Apr. However, there is no method by which the parameter F can be specified. One of the purposes of this study is to provide such a method.

Model Form of the Correlation Function. Davies (18) employed a relationship to account for anisokinetic effects in sampling an air stream with a probe oriented parallel to the stream. The relationship is derived from the conservation of particles approaching a probe inlet and is expressed as

A ) 1 + R(Rpr - 1)

(8)

where Rpr ) Uo/Upr; Uo is the velocity of the undisturbed free stream at the location of the probe; Upr is the mean velocity in the probe at the inlet plane. Based on available experimental data, Davies proposed that R could be expressed as a function of Stokes number, Stk, as

R)

2Stk 1 + 2Stk

(9)

where the Stokes number is represented by

Stk )

CFpDp2Uo 9µdpr

(10)

Here C is Cunningham’s slip correction (19); Fp is the particle density; Dp is the particle diameter (assuming a spherical shape); µ is the viscosity of flowing fluid (air); dpr is the sampling probe inlet diameter. Vincent et al. (16) found a better fit to experimental data could be obtained if R were represented by

R)

kStk 1 + kStk

(11)

where k ) 1.05. Liu et al. (17) obtained a value of k ) 1.2 based on curve fitting of the model to numerical predictions of the aspiration ratio. Rather than consider k as a constant,

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Belyaev and Levin (14) proposed that k should be treated as a function of the velocity ratio, Rpr, through an equation of the form

k ) Rpr + 0.31

(12)

Here, we propose to express the correlation function, F, in a form similar to the Davies relationship, viz.

F ) 1 - R(Rs - 1)

(13)

where Rs ) Uo/Us; Us is the mean velocity in the shroud at the inlet plane; R is of a more general form than that used by others; namely

R)

c1Stks 1 + βStks

(14)

Here Stks ) CFpDp2Uo/9µds; c1 is a constant; β ) c2 + c3(Rs - 1); c2 is a constant; c3 is a constant. The correlation function can then be represented by

c1Stks F ) 1 - (Rs - 1) [c2 + c3(Rs - 1)]Stks + 1

(15)

This equation predicts that F will decrease with increases in Stokes number and velocity ratio and that F tends to unity when the velocity ratio is close to 1 or when the Stokes number approaches zero. These are the desired properties of the function F for it to reflect the realistic inertial effects. If the velocity ratio is equal to 1, the shroud is sampling isokinetically. As a consequence, the concentration would be uniform at the inlet cross section of the shroud, and there would be no inertial enrichment. As the Stokes number tends to zero, particles will follow the streamlines, so the concentration will be uniform across the shroud entrance section. In both cases, the aspiration predicted by a model such as that of Vincent et al. (16) would provide the correct results for the shroud. The form of the correlation function given in eq 15 requires values for the three constants: c1, c2, and c3. In this study, numerical calculations of particle trajectories were used to obtain the spatial distribution of particle concentration within the shroud inlet plane. Curve fitting was then used to determine the coefficients. Curve Fitting To Obtain Values of Constants in the Correlation Function. The numerical method developed by Gong et al. (2) was used to calculate the aerosol profiles inside the shroud. Figure 2 shows examples of the concentration profiles at the shroud inlet for two different velocities. These calculations were carried out for a 102 mm diameter shroud; however, the form of the concentration profiles should be similar for other shroud sizes. It is evident, in Figure 2, that the concentration is much higher near the wall than in the core region, but it is almost constant in the core region. In Figure 3, the concentration profiles are shown at different locations along the axis of the shroud. Z1 and Z3 are located at the entrance of the shroud and 3 mm from the entrance of the inner probe, respectively. Z2 is midway between Z1 and Z3. It may be noted that except in the near wall region, the concentration profiles are almost constant at different locations. Because the inlet diameter of the inner probe is usually small in comparison with the shroud diameter (on the order of one-half or less), the inner probe will typically sample well within the constant concentration region. Also, the concentration from which

FIGURE 2. Numerically calculated aerosol concentration profiles at the entrance cross section of a shroud. Particle size ) 10 µm AD; shroud diameter ) 102 mm; velocity ratio, Rs ) 3.31.

FIGURE 4. Comparison of curves for the correlation function (eq 15) with numerical data that were used as the basis for establishing the coefficients in eq 15.

The mean aspiration ratios of the shroud and inner probe (As and Apr) for these two shrouded probes were calculated from the model of Vincent et al. (16). The mean aspiration ratio of the inner probe (Apr), the Stokes number, and the velocity ratio in the model of Vincent et al. (16) are based on the velocity in the core region of the shroud at the shroud entrance (Usc). By curve fitting numerical results for a shrouded probe, Usc can be determined as a function of the mean velocity in the shroud (Us) and the velocity ratio for the shroud (Rs). The results are

FIGURE 3. Concentration profiles at different locations along the axis of a shroud. Distance is measured from the inlet plane of the inner probe. Z1 corresponds to the shroud inlet plane. Particle size ) 10 µm AD; free stream velocity ) 20 m/s; velocity ratio, Rs ) 3.31.

the inner probe samples should not be significantly affected by the axial location of the inner probe, provided the inner probe is not near the shroud entrance where the velocity profile can be disturbed (1). Overall aspiration ratios, A, for shrouded probes can be calculated using the method of Gong et al. (2). In the numerical simulation of Gong et al., the flow field was calculated with a k -  turbulence model, and then particles were injected in the free stream of the simulated flow field. The particle trajectory calculations included such effects as Stokes drag, gravitation, Saffman force, and turbulence dissipation. The aspiration ratio was calculated by tracking 8000 particles in the flow field. It was found from numerical tests that if 8000 or more particles are tracked, the results are independent of the number of particles tracked in the flow field. The numerical method was used to calculate the overall aspiration ratios, A, for two shrouded probes. One of these has a 102 mm diameter shroud fitted about an inner probe that has an inlet diameter of 30 mm. Nominal sampling flow rate of the inner probe is 170 L/min (6 cfm). Numerical simulations involved free stream velocities of 5, 10, and 20 m/s. The second unit has a shroud that is 51 mm diameter, an inner probe that is 15 mm diameter, and a nominal sampling flow rate of 57 L/min (2 cfm). Numerical tests were conducted with this shrouded probe at free stream velocities of 10 and 20 m/s. Both probes were numerically tested with particles of 5, 8, 10, 13, 15, and 18 µm AD.

(

[

Usc ) Us 1 + 1.45 1 -

)]

1 + ln Rs Rs

(16)

The value of the correlation function was then determined from eq 7, and that result was used for F in eq 15. The coefficients c1, c2, and c3 were obtained by using a least squares procedure to fit the data to eq 15. The model coefficients are found to be c1 ) 0.861, c2 ) 2.34, and c3 ) 0.939, which allows the correlation function to be rewritten as

0.861Stks F ) 1 - (Rs - 1) [2.34 + 0.939(Rs - 1)]Stks + 1

(17)

A comparison of predictions from the use of eq 17 with the data from the numerical tests is shown in Figure 4. This figure shows the fit of the correlation given by eq 17 to the data points (obtained by numerical calculation) that were used to find the values of the constants c1, c2 and c3. The geometric standard deviation, sg, of the numerical data relative to the correlation function is 1.02, where sg is defined as

ln2 sg )

1

N

∑(ln F - ln F N-3 i

n,i)

2

(18)

1

Fn,i is the value of the correlation function from a numerical test and Fi is the corresponding value of the correlation function predicted from eq 17. The agreement between the correlation function and the numerical tests can also be demonstrated by a correlation coefficient, r, which is defined by

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N

∑(ln F - ln F i

r2 )

2 n,i)

1

(19)

N

∑(ln F - 〈ln F i

n,i〉)

2

1

where < > represents the average of a data set. The correlation coefficient, r, between the curves and the numerical data is 0.99. Form of the Correlation Function for Wall Loss Ratio. Following the wall loss model of Fan et al. (13), the wall loss ratio (WL) was modeled as

( )

WL ) κ 1 +

L Fr

ζ

Stkprγ

( ) Us Upr

η

(20)

where

Stkpr )

CFpDp2Upr 9µdpr FIGURE 5. Comparison of overall aspiration ratios predicted from eq 7 with experimental data.

and

Fr )

Upr2 gdpr

and L is a non-dimensional length normalized with respect to the diameter of the inner probe. Fan et al. had a Reynolds number effect embodied in their equation; however, our shrouded probe data did not show a dependency of wall losses on Reynolds number, so that parameter is not included in eq 20. Using this correlational model and carrying out regression analysis on the experimental data, the following values for κ, ζ, γ, and η were obtained: κ ) 0.496, ζ ) 0.194, γ ) 0.613, and η ) 1.191. Comparison with Experimental Results. The predictive equations for aspiration ratio, wall loss ratio, and transmission ratio of shrouded probes were verified by comparison with experimental data. Tests of the shrouded probes were conducted in an aerosol wind tunnel using apparatus and methodology described by Chandra and McFarland (3). Basically, the test procedure was to generate monodisperse aerosol particles and introduce that aerosol into the test section of a wind tunnel, where it was simultaneously sampled with a shrouded probe and two unshrouded isokinetic probes. Free stream aerosol concentration in the wind tunnel was established by measurements of the sum of aerosol that is transmitted through and deposited on the internal walls of the unshrouded isokinetic probes. Aerosol transmitted through a probe was collected on a sampling filter at the probe exit plane, and the aerosol deposited on the walls of a probe was recovered by washing the internal walls of the probe to elute an analytical tracer (sodium fluorescein). Transmission ratio of a shrouded probe was determined by dividing the aerosol concentration at the exit plane of a shrouded probe by the free stream aerosol concentration (eq 1). A filter was used to collect aerosol at the exit plane of a shrouded probe. From eqs 1-7, the overall aspiration ratio of a shrouded probe is

A)

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ce/co cpr T ) ) 1 - WL ce/cpr co

(21)

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FIGURE 6. Comparison of wall loss ratios predicted from eq 20 with experimental data.

Experimentally, the value of cpr was obtained by adding the wall losses in the inner probe to the aerosol transmitted through the shrouded probe. Aspiration ratios, predicted from eqs 7 and 17, are plotted in Figure 5 against the experimentally determined aspiration ratios. The model for aspiration ratio underpredicts the experimental values by an average of 2%. Similarly, the wall loss ratio predicted by eq 20 was plotted against experimental values (Figure 6), and the model was found to underpredict the experimental values by an average of 8%; however, this has only a 2% effect on the transmission ratio. Transmission ratio can be predicted from eq 6 using the aspiration ratio and wall loss ratio as calculated above. A comparison of transmission ratios predicted by the model with experimentally determined values is shown in Figure 7. Slope of the best fit line through origin in that plot is 0.99, so predictions by the model underestimate experimental results by about 1%. This indicates that the model

The uncertainty in measurement of aerosol particle concentrations is estimated to be 6%. This is calculated from the errors in measuring the volume of liquid solutions of analytical tracer, times, and instrument readings. The error in measuring the free stream velocity is estimated to be less than 10%, and the error in measurement of the sampling flow rate is estimated to be less than 2%. The propagated uncertainty in the experimental values of the transmission ratio is estimated to be 0.06.

List of Symbols

FIGURE 7. Comparison of transmission ratios predicted from eq 6 with experimental data.

FIGURE 8. Agreement between experimental and correlational transmission ratios for two 57 L/min shrouded probes for different free stream velocities.

estimates the experimental results without appreciable bias. A 95% confidence interval band on the prediction is also shown in Figure 7 as dotted lines. Free stream velocity is one of the important operating conditions that may vary during the operation of a sampling probe. In order to check how well the prediction tracks the transmission ratio with varying free stream velocity, experimental transmission ratios of two 57 L/min shrouded probes, which are designated as RF-2-111 and RF-2-112, were plotted against the predicted values for varying free stream velocities in Figure 8. One of the probes (RF-2-111) was designed for near-optimal performance in a free stream velocity of 4 m/s, and the other was designed for nearoptimal performance at a velocity of 12 m/s. The maximum difference between the two experimental and predicted values of transmission ratio is less than 5%. Discussion of Errors. All experimental data points are based on at least three test runs for that operating condition.

Parameters A overall aspiration ratio of a shrouded probe, dimensionless c1, c2, c3 constants in the correlation function, dimensionless c aerosol concentration, kg/m3 or particles/m3 C Cunningham’s slip correction inlet diameter of inner probe, m dpr inside diameter of a shroud, m ds particle diameter, m Dp F correlation function, dimensionless Fr Froude number, dimensionless k constant used in aspiration models, dimensionless L normalized length, dimensionless r correlation coefficient, dimensionless velocity ratio ) Uo/Upr Rpr Rs velocity ratio ) Uo/Ush, dimensionless geometric standard deviation, dimensionless sg Stk Stokes number, dimensionless T transmission ratio, dimensionless undisturbed free stream velocity at the location Uo of a probe, m/s Upr average fluid velocity at the inlet cross section of a probe, m/s Us average fluid velocity in a shroud, m/s fluid velocity in the core region of a shroud, m/s Usc WL wall loss ratio, dimensionless Z axial distance inside of a shroud, m R parameter used in characterizing aspiration, generally a function of Stk, dimensionless β, γ, κ, ζ, coefficients, dimensionless η µ fluid (air) viscosity, Pa s-1 Fp Particle density, kg/m3 General Subscripts e refers to the exit plane of a shrouded probe o refers to undisturbed free stream from which samples are withdrawn s refers to a parameter that is averaged across the inlet cross section of a shroud sc refers to the core flow in a shroud pr refers to the inner probe

Acknowledgments Funding for this research was provided by the U.S. Nuclear Regulatory Commission (NRC) under Grants NRC-04-92-

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080 and NRC-040-94-099. Dr. Stephen A. McGuire is the NRC Project Officer for both grants. This support is gratefully acknowledged. This is Aerosol Technology Laboratory Report 8838/12/95/HG.

Literature Cited (1) McFarland, A. R.; Ortiz, C. A.; Moore, M. E.; DeOtte, R. E., Jr.; Somasundaram, S. Environ. Sci. Technol. 1989, 23, 1487-1492. (2) Gong, H.; Anand, N. K.; McFarland, A. R. Aerosol Sci. Technol. 1993, 19, 294-304. (3) Chandra, S.; McFarland, A. R. Am. Ind. Hyg. Assoc. J. 1995, 56, 459-466. (4) Chandra, S.; McFarland, A. R. Shrouded probe performance: Variable flow operation and the effect of free stream turbulence; Aerosol Technology Laboratory Report 8838/10/95/SC; Department of Mechanical Engineering, Texas A&M University: College Station, TX, 1995. (5) U.S. Environmental Protection Agency. 40CFR61, Subpart H, Code of Federal Regulations; U.S. Government Printing Agency: Washington, DC, 1993. (6) U.S. Environmental Protection Agency. 40CFR61, Subpart I, Code of Federal Regulations; U.S. Government Printing Agency: Washington, DC, 1993. (7) U.S. Environmental Protection Agency. 40CFR60, Appendix A, Method 1. Code of Federal Regulations; U.S. Government Printing Agency: Washington, DC, 1993. (8) ANSI Standard N13.1-1969; American National Standards Institute: New York, New York 1969.

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(9) McFarland, A. R.; Rodgers. J. C. Single point representative sampling with shrouded probes; Report LA-12612-MS; Los Alamos National Laboratory: Los Alamos, NM, 1993. (10) Fan, B. J.; Wong, F. S.; Ortiz, C. A.; Anand, N. K.; McFarland, A. R. Proceedings of the 22nd DOE/NRC Air Cleaning Conference; NUREG /CP-0130, CONF9020823; 1993. (11) U.S. Environmental Protection Agency. Letter from M. D. Nichols, Assistant Administrator for Air and Radiation Programs, EPA, to R. F. Pelletier, Director, Office of Environmental Guidance, U.S. DOE; Nov 21, 1994. (12) U.S. Statutes at Large. Public Law 101-549.104: Part 4; U.S. Government Printing Office: Washington, DC, 1991. (13) Fan, B. J.; Wong, F. S.; McFarland, A. R.; Anand, N. K. Aerosol Sci. Technol. 1992, 17, 326-332. (14) Belyaev, S. P.; Levin. L. M. J. Aerosol Sci. 1974, 5, 325-338. (15) Davies, C. N.; Subari, M. J. Aerosol Sci. 1982, 13, 59-71. (16) Vincent, J. H.; Stevens, D. C.; Mark, D.; Marshall, M.; Smith, T. A. J. Aerosol Sci. 1986, 17, 211-224. (17) Liu, B. Y. H.; Zhang, Z. Q.; Keuhn, T. H. J. Aerosol Sci. 1989, 20, 367-380. (18) Davies, C. N. Brit. J. Appl. Phys. 1968, 1, 921-932. (19) Fuchs, N. A. The Mechanics of Aerosols; Pergamon Press: New York, 1964.

Received for review December 4, 1995. Revised manuscript received July 1, 1996. Accepted July 2, 1996.X ES9509083 X

Abstract published in Advance ACS Abstracts, October 1, 1996.