Non-isoaxial aerosol sampling: mechanisms controlling the overall

Use of Numerical Calculations to Simulate the Sampling Efficiency Performance of a Personal Aerosol Sampler. Aaron Bird. Aerosol Science & Technology ...
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Environ. Sci. Technol. 1987, 21, 183-187

Non-Isoaxial Aerosol Sampling: Mechanisms Controlling the Overall Sampling Efficiency Ken Okazakl,? Russell W. Wiener, and Klaus Willeke* Aerosol Research Laboratory, Department of Environmental Health, University of Cincinnati, Cincinnati, Ohio 45267-0056

The dominant mechanisms that control the overall aerosol sampling efficiency are described quantitatively for non-isoaxial sampling from horizontal aerosol flows. The overall sampling efficiencies for angles of * 1 5 O , *30°, *60°, and f90° between the inlet and wind directions in the vertical plane have been systematically determined by a dynamic evaluation technique for different particle sizes, wind and inlet velocities, and inlet sizes. The inlet-size effects are represented well by Stokes number, Stk. The overall sampling efficiency has been expressed as a function of Stk X R" for angles between 30° and 90°, where R is the ratio of wind to inlet velocities. The value of n represents the relative importance of impaction on the inner wall of the inlet vs. aspiration toward the inlet. The aspiration and transmission efficiencies have been determined separately, and their contributions to the overall sampling efficiency are discussed for various angle regimes. Introduction The concentration and size distribution of an aereosol sample collected and measured by an aerosol sampling instrument should be the same as those upstream of the sampler. If changes do occur in the sampling process, they should be assessed quantitatively so that the sampling errors can be compensated for. Even when a simple thin-walled sampling inlet is used in order to avoid particle bounce at the inlet face, two important processes may still change the sample properties on the way to the sensor. One is aspiration of the particles from the air environment to the face of the inlet, and the other is transmission of the particles through the8inlet, which is generally affected by particle losses caused by gravitational deposition or impaction to the inner wall. The data and analysis for isoaxial sampling, where the sampling inlet is aligned parallel to the horizontal wind direction, are presented in a separate paper ( I ) . In that publication quantitative expressions for the prediction of sampling errors for a wide range of sampling conditions have been given. For nonisoaxial sampling from horizontal aerosol flows the data and analyses are quite different, which is presented and discussed in this paper. When the inlet is set at an angle to the wind direction, i.e., when sampling is performed under non-isoaxial conditions, the area of the inlet face projected in the wind direction is reduced by the cosine of the sampling angle (2) and particles of high Stokes number are less likely to follow the curvature of the air stream lines into the inlet. The aspiration efficiency is thus lower than that under isoaxial conditions for the same velocity ratio of wind to inlet velocity. Most of the previous studies on sampling under nonisoaxial conditions (2-10) have focused on the aspiration phenomena. Some of these studies (5, 9, 10) have dealt with the special case of 90° sampling. However, our previous studies (11,12) have shown that particle losses inside the inlet can be very significant and may be the dominant cause for reductions in the overall ~

~~

Present address: Department of Energy Engineering, Toyohashi University of Technology, Tempaku-cho, Toyohashi, 440 Japan. 0013-936X/87/0921-0183$01.50/0

sampling efficiency, which is defined as the ratio of particle concentration registered by the sensor to that in the undisturbed environment. High particle losses inside the inlet have also been noted by other investigators (2,9, I O ) for specific angles. In this paper, the dominant mechanisms that control the overall sampling efficiency under non-isoaxial conditions will be discussed for horizontal aerosol flows sampled upward or downward in the vertical plane. The effects of particle size, wind and inlet velocities, and inlet size for a wide range of angles will be quantitatively analyzed. For that purpose, many systematic experiments have been performed by use of the dynamic evaluation technique (13) in our horizontal wind tunnel system. Through analysis of our data and comparisons with other reports (2, 9), general concepts and quantitative nondimensional representations have been developed and will be discussed below. Experiments The experimental system and procedures are essentially the same as described before ( I , 12, 13). Test aerosols of oleic acid are generated by a vibrating-orifice aerosol generator and are homogeneously dispersed into the airflow. The thin-walled inlet samples aerosols from the test section of the horizontal wind tunnel and is integrated into an optical particle counter, which was modified for this purpose. For all angles of inlet to wind direction tested, the inlet face sampled aerosols at the same position on the center line of the wind tunnel (11). Thin-walled inlets are used in this study so that particle bounce at the inlet face is negligible. The overall sampling efficiency can thus be expressed as Es,R,O

= Ea,R,OEt,R,B

(1)

where E,, Ea, and E, are the overall sampling efficiency, aspiration efficiency, and transmission efficiency, respectively, and the extra subscripts refer to velocity ratio R and angle 8. The velocity ratio R is defined as R = U,/Ui (2) where U, and Vi are the wind and inlet velocities, respectively, and 8 is the angle between the undisturbed wind vector and the inlet axis. The condition R = 1and 8 = 0 corresponds to isokinetic sampling. Through application of our dynamic measurement method (13), the overall sampling efficiency, E,, is given by Es,R,# = Erel,R,&t,l,O (3) where Ere]is the relative sampling efficiency, which is measured in real time by the experimental system and is defined as the ratio of the particle concentration measured by the optical particle counter for given R and 0 to that at isokinetic condition, R = 1and 8 = 0, at the same wind velocity for the same inlet size. The transmission efficiency has been determined sepafor isokinetic sampling Et,l,O rately through fluorescence measurements with uranine dye tagged aerosols. The experimental conditions investigated in this study are shown in Table I. Here, d,,, Di, and L are the aero-

0 1987 American Chemical Society

Environ. Sci. Technol., Vol. 21, No. 2, 1987

183

Table I. Experimental Conditions d,,, Irm uw, cmts Vi, cm/s Di (id.) cm in. Dj(0.d.) cm in. L , cm 9

5-40 250, 500, 1000 125, 250, 500, 1000

0.32, 0.56, 1.03, 1.59 4/s2j

7 / s a , 'stsay 2Q/s2

0.40, 0.64, 1.11, 1.67 5 / 3 a 9 8/32,14/s21

"'/sa

20 k15O. Moo. f60°. &SOo

dynamic particle diameter (14),inlet inner diameter, and inlet length, respectively. For angles of *30°, every combination of these experimental factors has been investigated, while for the other angles several representative cases have been examined with an inlet having an inner diameter of 0.56 cm ('Is2 in). At least three measurements have been performed for each of 700 different combinations tested, and the mean value of each test sequence has been used in our data analysis. The standard deviation was less than 4% in the majority of cases except where extremely small particle count due to very low sampling efficiency at large Stokes number and sampling angle increased the deviation. Results and Discussion The overall sampling efficiencies of four inlet sizes at angles of +30° (downward sampling) and -30" (upward sampling) are shown in panels A and B of Figures 1,respectively. Upward and downward designate the direction in which the aerosol is drawn into the inlet. In this and several succeeding figures, the efficiency values are plotted as a function of nondimensional particle size, expressed through Stokes number which is defined as Stk = rU,/Di

0.02

1

0.011

0.01

'

1 1

I i r a B r l

# , , .I

1

I

I

I , I t

1 .o

0.1

10.0

Stokes Number, Stk

Flgure 1. Inlet performance for sampling at %

= f30'.

R = 1: (A)

downward sampling (+30°);(B) upward sampling (-30'). 2.0

,

I

I

,

, 1 1 8 ,

6

I

I

( T ( 1 1 ,

I

I

I

y

(4)

where r is the particle relaxation time (14) defined as

= pPd,2/(l8d

(5)

where pp is the particle density, d, is the particle diameter, and 17 is the air viscosity. As shown below, Stokes number and velocity ratio, R, are the dominant parameters controlling both aspiration to the inlet face and impaction to the inner wall of the inlet when sampling is non-isoaxial. As seen in Figure 1,all data for 9 = f30" at velocity ratio R = 1 are expressed very well as a function of Stokes number alone, including the effects of particle size, wind velocity, and inlet diameter. However, the sampling efficiences for downward sampling are higher than those for upward sampling. The regions of data cluster are within the dotted lines. For other velocity ratios of 0.5, 2, and 4, tested with all four inlet sizes, similar results have been obtained, and lines representing the mean values of the data clusters for R = 0.5-4 are shown in Figure 2 for 9 = +30°. In the Stokes number region below 0.1, the sampling efficiencies are higher for greater velocity ratios as one would expect from the aspiration effect (2). In the larger Stokes number region, the sampling efficiency is also higher for the higher velocity ratios when aerosols are sampled at 9 = +30°. If impaction of particles to the inner wall of the inlet is the dominant effect for larger Stokes number particles, one would expect a greater loss in sampling efficiency at the higher velocity ratios. The fact that the sampling efficiency is higher for the higher velocity ratios, even in the large Stokes number region, shows that the aspiration effect is able to compensate for the impaction effect for downward sampling at 30". The com184

Environ. Sci. Technol., Voi. 21, No. 2, 1987

0

'1

002-

0.5 0.01 0.0 1

I

(%,,I 0.1

I

3

I

I

,,*,I

10

I

I ,,I

10.0

Stokes Number, Stk

Figure 2. Inlet performance for sampling downward at 0 = +30° for several velocity ratios and all four inlet sizes. The curves represent the mean values of our data.

petition between aspiration and impaction effects will be discussed below for all angles studied. Since velocity ratio R separates the curves of Figure 2 in the high Stokes number region, R has been combined with Stokes number in Figure 3 for sampling at 9 = *30°. When Stk X R-1/3 is used as the abscissa for this case, the curves for all the sampling ratios from 0.5 to 4 and inlet sizes of 0.32-1.59 cm coincide in the higher inertia region of large Stokes numbers for each case of +30° and -30'. On the basis of the findings of Figure 3, we postulate that all sampling efficiency data obtained at a significant angle may be consolidated as a unique function of sampling parameter Stk X R", Le. E, = f(Stk X R") (6)

2.0

I

U,

R.05

-

I

"'I

1

,

I

I 1 1 1

500 cmls , Di = 0.56 cm

4

E

\

0.21

4

b

Ir

i I

001' 0.01

'

'

0.1

'

,

i A

, I , ,

I

1.0

10.0

Stk R-3

I

I

0.011 0.01

IIIII 0.1

Figure 3. Inlet performance as a function of sampling parameter Stk X R-'13 for 8 = *30° and R = 0.5-4 for all four inlet sizes. 2.0

I

I"II

I

-

I

I I I I I

U w 500 c m / s , D i ~ 0 . 5 6cm

u"

1.0 L

Figure 5. Sampling efficiency vs. Stk X R'15 for 8 0.5-4 (u, = 500 cm/s; D , = 0.56 cm). 2 .o

I

I I

"I

I

I

= +60° I

and R =

I I I I

Uw ' 5 0 0 cm/s , DI =0.56 cm

-

.-u

0

E.-

1 .o

Stk R i

m/

0.2-

0

a

0.01

I

I 1 1 1 1 1

0.01

0.1

,

, \ I , , , ,J

1.o

Stokes Number, Stk

Figure 4. Inlet performance for cm/s; D ,= 0.56 cm).

0 = +60° and R = 0.5-4 (U, = 500

We postulate that the numerical value of n indicates whether the aspiration or the impaction effect is dominant in controlling the overall sampling efficiency in the highinertia region. In the case of Figure 3, the value of n is -113, and this negative value indicates that the aspiration effect dominates over the impaction effect. The relative importance of the two effects is different at higher angles, as discussed below. Figure 4 shows the sampling efficiency as a function of Stokes number for sampling at 8 = +60". In this case, data taking was limited to an inlet diameter of 0.56 cm (7/32 in.). In contrast to the performance data for 8 = +30°, shown in Figure 2, all curves in Figures 4 for 8 = +60° cross each other near Stk = 0.1, and for the larger Stokes numbers, the contribution of velocity ratio R is reversed. The crossover indicates that the impaction effect has become dominant over the aspiration effect in this case. The higher Stokes number data of Figure 4 have been consolidated by plotting them as a function of sampling parameter Stk X R1I5,as shown in Figure 5 (Le., here the value of n is 115). In the case of 0 = -60°, all the data for the higher Stokes number region are also expressed uniquely as a function of Stk X R1I5, but the sampling effi-. ciency values are somewhat lower than those for 8 = +60°. We postulate that the difference in sampling efficiency values between downward (positive angle) and upward (negative angle) sampling is due to the effect of gravity on the particle impaction process on the inside wall of the inlet. When the sampling is downward, impaction occurs on the upper inside wall of the inlet and gravity pulls the

4

0.0 1 0.0 1

0 0.5

,

I

I , l l l

0.1,

1 .o

Stk R 2

Flgure 6. Sampling efficiency vs. Stk X R ' I 2 for 8 0.5-4 (U, = 500 cm/s; D , = 0.56 cm).

= *9O0

and R =

particles away from the impaction surface. When the sampling is upward, impaction occurs on the lower inside wall of the inlet and gravity pulls the particles toward the impaction surface. Therefore, gravity increases the wall loss in upward sampling but decreases the wall loss in downward sampling. Figure 6 depicts an example of inlet performance for sampling perpendicular to the wind direction at 8 = f90°. The data for all R values are represented by a single curve for all Stokes numbers, when plotted as a function of Stk X R1I2, Le., for n = 112. Furthermore, there is no longer a difference in the sampling efficiency values between downward and upward sampling, which suggests that gravity does not affect the sampling efficiency when the sampling is up or down at 90° to the horizontal airflow. The data shown in Figure 6 are for an inlet with an inner diameter of 0.56 cm (7/32 in.) sampling from an air flow of U, = 500 cm/s. Our data for the U, = 250 cm/s for that inlet, not shown here, fall onto the same curve shown in Figure 6. For relatively small angles of *15O, the mechanisms that control the overall sampling efficiency are more complicated (11). At small angles, the sampling efficiency is affected by both wind and inlet velocities, even when the velocity ratio R is fixed, and the data cannot be correlated with sampling parameter Stk X R". This indicates that a t small angles not only aspiration and impaction affect the sampling efficiency but also gravitational deposition Environ. Sci. Technol., Voi. 21, No. 2, 1987

185

.o 0 W

e

.-0

I

0

(D

0 .5

L

U

c

.-c0

Downward Sampling

In

0

t

P

a,

P

n

"

0.1

1.o

10.0

Stokes Number, Stk

-1

Figure 7. Fraction of particles deposited on inner wall of inlet for velocity ratio R = 1 (U, = 500 cm/s; D , = 0.56 cm).

inside the inlet (I). Furthermore, the difference in sampling efficiency values between downward and upward sampling with high Stokes number particles is larger a t 8 = f15' than a t 0 = f30' and *60°. The effect of gravity on particle losses in the inlet depends on the angle between the inlet and wind directions and is discussed in detail in the following paragraphs. The sharp drop offs in sampling efficiencies with increasing Stokes number in Figures 1-5 appear to be caused primarily by an increase in particle losses in the inlet as the particle size increases. The loss of particles depositing on the inner wall of the inlet may be expressed by the deposition fraction Ed Ed = 1 - E, (7) where Et is the transmission efficiency defined as the ratio of the particle concentration exiting from the inlet tube to that just past the inlet face. We have calculated the transmission efficiency from our overall sampling efficiency data through use of eq 1. The aspiration efficiencies in eq 1 were calculated from the non-isoaxial sampling expressions of Durham and Lundgren (2), which are valid for 0' < 0 < 90'. Their expression for 0 = 90' is valid only for R = 1. The deposition fractions thus obtained for various angles are shown in Figure 7 for U, = 500 cm/s, Di = 0.56 cm, and R = 1. The curve for isoaxial sampling, 19 = ,'O has been calculated through eq 7 and the following expression, which has been developed from our experimental data for transmission efficiency:

E, = e~p(-4.7KO.~~)

(8)

In this expression, we have defined a new inlet deposition parameter, K , as

K = [ ( Z X Stk)/(Re)1/2]1/2

(9)

where Z and Re are the gravitational deposition parameter (14,15) and Reynolds number (16),respectively. They are defined as = ( L / Vi) / (oi/Vs) (10) Re = pUiDi/i

Environ. Sci. Technol., Vol. 21, No. 2, 1987

Stk(Ed= 0.5, Downward) Stk (Ed=0.5. Upward)

30

60

90

Angle, 8, degree Flgure 8. Difference in gravity effect for upward vs. downward sampling ( Q ) and contribution of velocity ratio to overall sampling efficiency ( n ) for different sampling angles.

angles of 15', 30°, and 60' appears to be due to the effect of gravity on the impaction process as explained before. We have expressed this effect quantitatively through the gravity ratio Q in which Stk (Ed = 0.5, downward) represents the value of the Stokes number for 50% particle deposition when aerosols are sampled in the downward direction: Stk (Ed = 0.5, downward) (12) = log'' Stk (Ed = 0.5, upward) which is graphically presented in Figure 8. As seen, Q reaches a maximum at about 0 = 20' and becomes zero as the angle approaches 0' and 90'. Also shown in Figure 8 is the value of n for the sampling parameter in eq 6. For angles of 30' I0 5 90°, the sign of this parameter indicates which of the competing effects of aspiration and impaction dominates, and the value of n indicates the degree of dominance. For angles of 8 less than 30', the value of n cannot be uniquely defined by these two effects alone. As already seen in Figures 2 and 3 for 0 = *30°, dominance of aspiration results in a negative n value, and as seen in Figures 5 and 6, dominance of impaction results in a positive n value. Figure 8 shows that the two processes affect the overall sampling efficiency in equal amounts when sampling is at about 45', for which n = 0, and the sampling efficiency is independent of sampling ratio R. The aspiration efficiency for 0 = 90' can be calculated from the overall sampling efficiency data with eq 1 and 7, assuming that the expression for the deposition fraction, found by Davies and Subari (9),can be extrapolated up to R = 2, beyond their experimental range of 0.05 < R < 0.53. Their deposition fraction, Ed, is expressed by use of error function erf as

(11)

where V , is the gravitational settling velocity of the particle and p is the air density. It may be seen that the slope increases sharply with increasing angle and the Stokes number corresponding to 50% particle deposition in the inlet, Ed = 0.5, rapidly decreases. The dotted curve for 8 = 90' represents the data by Davis and Subari (9) and agrees well with our data. The Stokes number at Ed = 0.5 is 0.145 for our data and 0.150 for the Davies and Subari data. The difference between the solid lines (downward sampling) and the dashed lines (upward sampling) for 186

0

Q =log[

The results are shown in Figure 9 for R = 1 and 2. For R = 1,the results presented here agree with the prediction by Durham and Lundgren (2) for 0.08 < Stk < 0.17. For the higher values of Stokes number, our results have lower values of aspiration efficiency than any of the other three predictions shown in this figure. For R = 2, our results agree well with the equation of Laktionov (5)

E, = 1 - 3(Stk1/R"2)

(14)

and also with a data point (open square symbol) from

I ' "'1 -Present Results --- Laktionov OurhamaLundgren ---.-Oavies 8 Subari

s W U i

--c"

-

0

z

0.5 -

-z -2rn

-

L

D

U

0 0.01

1 .o

0.1

5.0

Stokes Number, Stk

Asplratbn efflclency vs. Stokes number for 8 = *SOo (R = 1 and 2. U. = 250 and 500 cmls) and comparison wlth other Investigations. Flgure 9.

1 .o

=5U 0.5 :

Transmission Loss

U

0

0.01

Conclusions Through this experimental study on the aerosol sampling efficiency for a thin-walled inlet sampling non-isoaxially from horizontal airflows, the following conclusions are made. (1)For angles of 30' 5 8 5 90' between the inlet and wind directions,the overall sampling efficiency is expressed well as a function of sampling parameter Stk x R". The values for exponent n are -113,115, and 112 for sampling a t 8 = *30°, *60°, and *goo, respectively. (2) Particle loss by impaction in the inlet dominates over particle loss by aspiration for angles larger than about 45O except a t 0 = 90'. (3) Downward sampling has a higher overall sampling efficiency than upward sampling because gravity pulls particles away from the upper inside wall during impaction on that wall. This difference, due to the gravity effect, is maximum a t about 8 = 20" and disappears as the angle approaches 0 or *90°. (4) By discrimination of aspiration efficiency from transmission efficiencyand quantification of their relative contributions to the overall sampling efficiency, the basic mechanisms of particle aspiration by an inlet and the removal of particles within the inlet have been clarified. Acknowledgments We thank Morris S. Ojalvo of NSF for his efforts and support. We appreciate the help of Alex Fodor in building the wind tunnel facility a t the University of Cincinnati.

0.1

1.0

5.0

Stokes Number, Stk Flgum 10. Relative magniMe of loss mechanisms that determine overall Sampllng efflclency of a thin-walled Inlet sampllng from hodzontal almows. This example 1s for R = 1 at 8 = +60° and f90'.

Durham and Lundgren (2),which was not explained by their model. At very small Stokes numbers, our results for R = 1and 2 appear to approach 0.85, which was predicted by Davies and Subari (IO). Since it is now possible to discriminate between the relative Contributions of aspiration and transmission efficiencies to the overall sampling efficiency, graphs can be made of these relative Contributions, and from them an appreciation can be gained for their magnitudes. Examples for R = 1are shown in Figure 10 for 8 = +60° and f90°. The shaded regions correspond to particle transmission losses in the inlet that are primarily due t o particle impaction on the inner wall of the inlet, especially near the inlet face. For 0 = 60°, transmission or impaction losses dominate in controlling the overall sampling efficiency, especially in the higher Stokes number region, as already discussed through Figures 4,5, and 8. For 8 = 90°, the aspiration efficiency sharply drops with the increase in Stokes number, and when plotted on a linear ordinate, the contribution of particle loss by impaction appears to he relatively small. A logarithmic scale would provide a better graphical representation of the particle reduction rate due to impaction. One should also note that one would expect the aspiration efficiency to be higher for larger values of velocity ratio, R. Figure 9 for 8 = *90° shows, however, that the aspiration efficiency is, in fact, lower for higher R values. Because the projected area of the inlet face to the wind vector is zero, 0 = *90° is a special case for sampling from airflows.

Literature Cited (1) Okazaki,K.;Wiener, R; Willeke, K. Enuiron. Sci. Technol., preceding paper in this issue. (2) Durham, M. D.; Lundgren, D. A. J . Aerosol Sei., 198O,lI, 179-188. (3) Wataon, H.H. Am. Znd. Hyg. Assoc., Q.1954,15, 21-25. (4) Raynor, G. S.Am. Ind. Hyg. Assoc. J . 1970,31,294-304. (5) Laktionov,A. B.Fir. Aerozoley, 1973,7,83 (translation from Russian, AD-760947, Foreign TechnologyDivision,Wright Patterson Air Force Base, Dayton, OH). (6) Fuchs, N. A. Atmos. Enuiron. 1975, 9, 697-707. (7) Pattenden, N.J.; Wiffen, R D. Atmos. Enuiron. 1977,11, 677481. (8) Lundgren, D.A,; Durham, M. D.; Mason, K. W. Am. Ind. Hyg. Assoc. J. 1978, 39, 640-644. (9) Davies, C. N.;Suhari, M. B. Proceedings of Aduances in Particle Sampling and Measurement; U S . Environmental Protection Agency. U S . Government Printing Office: Washington, DC, 1979;U S . EPA 600/7-79-065, pp 1-29. (10) Davies, C. N.;Suhari, M. J. Aerosol Sci. 1982, 13, 59-71. (11) Tufto,P. A.; Willeke, K. Am. Ind. Hyg. Assoc. J. 1982.43. 436-443. (12) Tuftn, P.A. Ph.D. Dissertation, University of Cincinnati, Cincinnati, OH, 1981. (13) . . Tufto. P. A,: Willeke. K. Enuiron. Sci. Technol. 1982.. 16.. 607-609. (14) Hinds, W. C. Aerosol Technology; Wiley New York, 1982; Chapter 5. (15) Schwendirnan.L. C.: Steeen. G.E.: Glissmever. J. A. Rewrt

Receiued for reuiew March 14,1986. Accepted September 19, 1986. This material is based upon work supported by the U S . National Science Foundation under Grant CPE-8213269.

Envlron. Sci. Technol.. Vol. 21.No. 2. 1987

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