Aerosol Science and Technology

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Particle Deposition in a Two-Dimensional Slot from a Transverse Stream

François Rémi Carrié a; Mark P. Modera b a LABORATOIRE DES SCIENCES DE L'HABITAT, ECOLE NATIONALE DES TRAVAUX PUBLICS DE L'ETAT, VAULX-EN-VELIN CEDEX, FRANCE b ENVIRONMENTAL ENERGY TECHNOLOGIES DIVISION, E. O. LAWRENCE BERKELEY NATIONAL LABORATORY, UNIVERSITY OF CALIFORNIA, BERKELEY, CA First Published on: 01 January 1998 To cite this Article: Carrié, François Rémi and Modera, Mark P. (1998) 'Particle Deposition in a Two-Dimensional Slot from a Transverse Stream', Aerosol Science and Technology, 28:3, 235 - 246 To link to this article: DOI: 10.1080/02786829808965524 URL: http://dx.doi.org/10.1080/02786829808965524

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ELSEVIER

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Particle Deposition in a Two-Dimensional Slot from a Transverse Stream Frun~oisRCmi CarriC

Mark P. Modern* B1 DG 00 ROOM 3074, ENVIRONMLNTAL EVLKGY 7 L ( HNOLO(rlL5 DIVI\ION, I: 0 LAWKFNCL U L K K f l t Y \ATIONAL LAHOKAIOKY, LNIVFRSITY O t CAL1bOKPIIA, BLKKLLtY, CA 04720

ABSTRACT. This paper addresses the problem of coarse mode particle deposition in a two-dimensional slot from a transverse flow. A dimensional analysis enables us to identify five independent dimensionless groups: the leak Reynolds number, Re, the dimensionless velocity gradient of the approaching flow, a,the Stokes number, Stk, the slot aspect-ratio, elh, and the interception parameter, dJh. A sticky aerosol (MMD 3-7 pm; GSD ;= 2-3) was injected into a 15 cm diameter duct and blown out through a rectangular opening (3 X 40 mm; e = 0.6 mm) drilled in a direction perpendicular to the flow. A video camera was set up to continuously monitor the leak behavior in time. The image then was digitized, enabling us to assess the slot-width as a function of time. I t appeared that the slot could be sealed in less than 20 minutes. These results were compared with a simplified model based on a scale analysis of the deposition velocity on the slot thickness. Agreement between predicted and measured leak-widths is very good when the pressure differential across the opening does not exceed 60 Pascals. Deposition on the upstream edge is observed 28: only when its surface is not smooth. AEROSOLSCIENCEAND TECHNOLOGY 235-246 (1998) O 1998 American Association for Aerosol Research

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NOMENCLATURE C,,, mass concentration of the aerosol [kg/ m31 resistance coefficient of the orifice [-] C, c surface corresponding to the slot (black pixels) [m2] D duct diameter [m] d( ) differential [-I dJj particle diameter [m] - --

-Author to whom correspondcn~c\hould he addrescd Aerosol Sclcncc 'ind Te~hnology28 235-246 (1908) 0 1098 Amer~canAsw~idtionfor Aerosol Rcscdr~h Publlshcd by Eltevler Sclencc 1 n ~

vclocity gradient of the approach~ng flow [s-'1 duct wall thickness [m] accelerdt~onof grav~ty[m/sz] leak-wtdth [m] slot Reynolds number p,v,h/p [-I duct Reynolds number [-I pnrtlcle Reynolds numbcl (based on tts rclat~vcvcloc~ty)[-I r a d ~ uof~ curvature of the streamhnes [llll particle-to-alr demity ratlo [-I

236 F. R. Carri2, M. P. Modera

Stk t

t, ,

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us U

v

",. VS

W

x Y Y.7

Stokes number ~v,/v,= SReIlX (~l,,/h)~

d z 1-1

time [s] residence time in the separation zone t,,, - Y J ~[sl , velocity upstream of the slot at y = y, [mls] velocity along x [mls] velocity along y [m/s] radial velocity of the particle [m/s] bulk velocity through the slot', here q l / C 2APlp, [mls] thickness of the seal [m] horizontal coordinate [mj vertical coordinate [m] height of the dividing suction Ytreamline [m]

Greek Letters dimensionless velocity gradient of the approaching flow hlv, dU1dy [-I pressure differential across the slot [Pa] deposition efficiency [-] dynamic viscosity of the fluid of intcrcst [kglm s] density [kg/m3] density of particle build-up [kg/m3] uncertainty associated with the measurement of c [m2] particle relaxation time [s]

Subscripts and Superscripts f i

o

p I

-

pertaining to the fluid of interest at 1 minutes for the beginning of the experiment at thc bcginning of the experiment pertaining to particlc dimensionless quantitie~ average value

Aerosol Science and Technology 28:3 March 1998

GSD MMD

Geometric Standard Deviation Median Mass Diameter

INTRODUCTION The practical objective of this research is to reduce duct leakage in residential air distribution systems (ADS), as earlier research proved that the energy savings potential of sealing duct leaks is on the order of 20% of the furnace or air conditioner energy use (Modera, 1993). Given that 25% to 75% of the leaks are not accessible (Robison and Lambert, 1989), conventional technologies such as using duct tape or mastic are often not satisfactory. Existing remote sealing technologies have been examined (e.g., introducing a rolling mechanical cart or unfolding a cylinder in the duct network). Althou& the application of these techniques might be of interest for some pipe networks (the cart was patented and used for gas pipes (Smith, 1983) and the unfolding cylinder is used to seal large underground pipes), the complexity of a residential duct system docs not allow straightforward application of these technologies. Our attention thus is focused on the use of aerosol sealants, the versatility of this technique allowing us to deal with bends and bifurcations without significantly affecting its performance. Understanding aerosol deposition in leaks is of paramount importance in this study. Here, we start with a theoretical approach to the problem that includes: a) a dimensional analysis, and b) the development of a simplified model to predict particle deposition. The remainder of the paper is dedicated to the description of the experimental apparatus used to determine the sealing efficiencies in a rectangular opening, the experimental results obtained, and a comparison with the model predictions.

Abbreviations ADS

'

Air-Distribution Systcm

The pleasure coctficient mryht hc drftcrcnt from that of a perfect o~lficehecause of the presence of the cross-flow Fol morc dct'uls, the redder may letcr to (Thomas and Corneliuu, 1982)

DIMENSIONAL ANALYSIS Even though many researchers have investigated the flow through orifices, very little information is available on flow suction through a slot from a transverse stream. The authors are only aware of the work per-

Aerosol Science and Technology 28:3 March 1998

Particle Deposition in a Two-Dimensional Slot 237

Dividing streamline

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X

FIGURE 1. Uniform shear flow approaching a two-dimensional slot (see Thomas and Cornelius, 1982).

formed by Thomas and Cornelius (1982) who experimentally investigated a laminar boundary-layer suction slot. Using fluorescent dye in a water channel, they have consistently observed that the dividing streamline stagnates on the downstream corner of the slot. Their observations2 lead them to assume in their analysis that the flow could be viewed as a uniform shear flow sucked into an orifice (Figure 1). Based on this assumption, the only variablesQhat should affect the deposition efficiency are dUidy, v,, h, e , d,, F , pp and p,. Application of the T-theorem (Olson, 1962) using the leakwidth (h), the bulk velocity at the leak (v,), and the particle density (p,) as repeating variables enables us to identify five dimensionless parameters that characterize the deposition process: the dimensionless velocity gradient a , the leak Reynolds number Re, the particle to transverse-slot-width ratio d,!h, the wall-thickness to transverseslot-width ratio eih, and the particle to air density ratio S . S can be rearranged with the other parameters to form the Stokes number: "ome of these experimcnts were performed at similar flow regimes as the ones tested in this paper. -'Gravitational settling is ignored. This is a reasonable assumption only if the deposition velocity is much greater than the gravitational settling velocity; according to Eq. (3) this is equivalent to saying thatg 1).

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The dimensionless parameters intervening in 77 [Eq. ( 5 ) ] are reduced to Stk and elh. This result seems reasonable considering that impaction is generally governed by Stk. Also, the disappearance of explicit intervention of d J h , a , and Re is understandable as: 1. interception is negligible, 2. the velocity gradient will have little influence in the vicinity of the slot, and 3. the viscosity effects on the flow pattern are not accounted for in this approach.

EXPERIMENTAL APPARATUS The principal objective of our experimentation is to quantify the scaling effectiveness of an aerosol sealant under varying conditions in a laboratory facility at Lawrence Berkeley Laboratory. An important aspect of the issue of particle deposition in the leaks is to understand how the particlcs are going to stick to the duct wall and eventually "build a bridge" between the boundarics. Vinyl plas-

Particle Deposition in a Two-Dimensional Slot 239

Aerosol Science and Technology 28:3 March 1998

6: Mass flow controller network

-7

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7: Video camera

To exhaust

FIGURE 3. Schematic diagram of the experimental apparatus in use to quantify aerosol sealing effectiveness in a two-dimensional slot.

tics seem appropriate to achicve this goal since they arc widely used to smooth and waterproof surfaces. However, it is critical to understand that particles need to hold their shape in order to "build a bridge." As a matter of fact, if the particles are too deformable, they will tend to spread over the duct wall, preventing any particle buildup. This is the reason why the current apparatus utilizes an aerosol generated from a liquid suspension of an acetate-acrylate vinyl polymer and then dried in order to obtain solid sticky particles. Thc present facility consists of a blower hooked to an injection chamber, which is in turn connected to a 3.75 meter duct. The apparatus, shown schematically in Figure 3, includes: (1) a desiccant drying section, (2) a vane-anemometer flow measurement device, (3) an assortment of commercially available sprayers, (4) a peristaltic pump to control and measure the liquid flow rate to the spray nozzle, (5) a Mark V (Pilat University of Washington) cascade impactor to assess aerosol size distribution, (6) a massflow controller network to ensurc isokinetic sampling4, and (7) a video camera (Sony Hi8 TR81) to continuously monitor leak-width

' It should hc noticed that sampling can not be truly isokinetic since the bulk flow is turbulent.

as a function of time. Two close-up lenses ( + I ; +2 diopter) are hooked to the camera for focusing purposes. The pressure in the duct can be adjusted with several dampers, enabling us to control the air flow rate through the apparatus as well as the pressure differential across the leaks. The data from all of the measurement devices described in Figure 3 are sent to a IBM-PC and stored in a data file. As regards the sprayers, different technologies were examined, including thc use of an ultrasonic nozzle that produces a fairly monodisperse aerosol. However, only a few commercially available aerosol generators were found to be capable of atomizing our vinyl polymer: our suspension tended to clog the devices. The best results were obtained with a SUE15B air atomizing spray setup manufactured by Spraying Systems Company, Wheaton, Ill. The use of this equipment is nevertheless nonoptimal, as the aerosol generated is polydisperse (GSD 2-3). Experiments performed in the past with a similar apparatus showed that the accumulation of particles on the walls of 3 mm round leaks as well as a 3 mm annular gaps (typically encountered at a joint between two ducts) eventually plugs the openings. Ideally, if the sticking probability of the

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240 F. R. Cnrri6, M. I? Modem

Two-dimensional slot

7

f-

Particle build up

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Duct wall

Aerosol Science and Technology 2 8 3 March 1998

FIGURE 4. Toa ~ i e wof a 3 2.77 pm; GSD = 2.09.

X

40 mm leak after 20 minutes of aerosol injection during experiment A X . MMD =

aerosol is 1, and assuming that the only geometrical parameter that varies as impaction occurs is h , the rate at which the leak-width decreases can be obtained by writing the mass balance equation of the aerosol dcposit. It is directly linkcd to the deposition efficiency: -

d2h = d (G,,,)dt

e

s(cx, Re, 2 Stk,

where d(C,,,) is the mass concentration of particles having diameters between cl, and dI, + + l ( d , ) . Thus, by monitoring the slot size as a function of timc under varying conditions, it is possible to compare our expcrimcntal data with the leak-width behavior predicted by Eq. (6) [where q is obtained with Eq. (91. For a monodisperse acrosol, or if the mean deposition efficiency ( i j ) can be evaluated over the particlc size range, Eq. (6) simplifies to:

Although it is theoretically possible to assess the deposition efficiency with Eq. (6) for each particlc size directly from the slot behavior expcrimental data, this method could not he used in our case. To do so, the aerosol needs to be monodisperse and particular attention should be given to the accuracy of the measurement of the derivatives dlz/dt. Figure 4 shows a 3 x 40 mm (e = 0.6 mm) leak 20 minutes after starting aerosol injection during experi~ncntA.15. The surface near the opening was painted in white to a) enhance the contrast and 13) neatly divide the slot itself from the walllparticles. As images can be digitized in a C I F 8-bit gray format, the numbcr of black pixels (corresponding to the leak) can be counted versus thc number of whitc pixels (duct wall or particle buildup). Grabbing images every timc step enables us to obtain average leak-width as a f~mction of time. Image analysis is per-

Aerosol Science and Technology 283 March 1998

Particle Deposition in a Two-Dimensional Slot 241

Edge of particle deposit

Slot edge (upstream)

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--\ Slot edge (downstream)

FIGURE 5. 3 x 40 mm slot after 20 minutes of aerosol injection during experiment A.15. Original image (Figure 4) is cropped and edges are detected.

formed using the pbmplus package from Jef Poskanzer (available on internet: http: //www.arc.umn.edu). As for the uncertainty of the measurement, it is mainly due to the image resolution near the edges. In fact, the abrupt transition between low- and high-intensity pixels causes the edges to be fuzzy. Therefore, the uncertainty CT (roughly half the area of the edges) is evaluated using the edge detection program pgmedge (see Figure 5). Measurements are performed on four different frames every given time step and then averaged in order to reduce or eliminate possible uncertainty (e.g., due to shaking of the camera). In turn, the size of the leak may be determined with the following equation:

RESULTS AND DISCUSSION Two series of experiments (totaling 37 experiments) were performed to check the accuracy of the predictions of the theoretical model developed herein. The experiments performed included:

1. air flow rates between 45 m3/h and 200 m3/h (7,000 < Re, < 32,000), 2. pressure differentials across the leaks of 20, 40, 60 or 80 Pascals, and 3. a mass median diameter for the aerosol between 3-7 pm. During many experiments, against all expectations, significant aerosol deposition

was observed on the upstream edge. As a matter of fact, although the slot was machined with precision, the layer of paint applied afterward apparently constituted a lip large enough to alter the flow pattern and thus cause elevated collection on the upstream edge (see Morewitz, 1982). Consequently, the slot was carefully sanded afterward and, as expected, little or no deposition occurred upstream. At first, we believed that experimental data on the downstream edge could still be exploited and compared with the model for those experiments, provided that the upstream edge deposition was corrected for (Figure 6). However, it was found that these results were not repeatable, and as a consequence they will not be discussed hereafter. Some measurement problems were also encountered with the cascade impactor during the first series of experiments. In addition, in some cases the polymer concentration was too high and thus prevented evaporation, leading to the problem quoted above regarding the formation of the seal. Consequently, only the second series of experiments (B.l through B.16) is analyzed in this paper. Regarding the bulk velocity through the slot, its knowledge is limited to the accuracy of our assessment of the coefficient of discharge. Previous studies (Thomas and Cornelius, 1982; Andrews and Sabersky, 1990) showed that this coefficient might differ significantly from that of a perfect orifice because of the presence of the transverse flow. They further affirm that little work is documented on such matters. Literature was reviewed and it ap-

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Acrosol Science and Technology 283 March 1998

Air Aow rate: 113 mA3/h;Pressure differential: 80.7 Pa Concentration: 0.85 mgll; MMD: 3.36 pm; GSD = 2.49 FIGURE 6. Accumulation of aerosol particles in a two-dimensional slot as a function of time during experiment A.3. Air flow rate: 113 mA3/h; Pressure differential: 80.7 Pa Concentration: 0.85 mgil; MMD: 3.36 pm; GSD = 2.49.

peared that, in effect, today's available information on that subject is insufficient to definitively determine the discharge coefficients. However, with a being of order unity in our case, the resistance coefficients should be relatively close to those calculated without the transverse flow (Thomas and Cornelius, 1982). As a result, these were estimated with the tables provided by Ide17Chik(1960). The slot-width for a typical experiment is plotted as a function of time in Figure 7. Eq. 5 is used to compute the deposition efficiency and the theoretical slot behavior can be derived from the integration of Eq. 6 over the particle size range (Figure 8). Experiments B.3, B.6 and B.7 were performed under similar experimental conditions and provided consistent results (Figure 9). Based upon the full series of experiments, it appears that the prediction is very close to the observed leak behavior at 20,40 and 60 Pascals (Figure 10). However, the model significantly overprcdicts the actual scaling effectiveness at 80 Pascals (Figures 11 and 12).

There are several limitations to the model developed that could explain the observed discrepancy at 80 Pa. First, as the pressure in the duct system is increased, the Reynolds number and thc Stokes number of the particles are also increascd, which implies that Stokes law and the quasistationary assumption may no Longer apply. However, rather than being due to these two effects, we believe that the discrepancy in the results is due to particle depletion before entry into the orifice, which the theory does not take into account. Indeed, particlcs tend to be entrained downstream as the Stokes number increases. Thus, the aerosol concentration in the vicinity of the deposition surface may be significantly lower than the mainstream concentration (C,,,). Finally, the reader should note that average cascade impactor results were provided as input in the theoretical model which implies that variations of the size distribution over the course of an experiment could bias the results.

Particle Deposition in a Two-Dimensional Slot 243

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Aerosol Science and Technology 28:3 March 1998

FIGURE 7. Accumulation of aerosol particles in a two-dimensional slot as a function of time during experiment B.15. Air flow rate: 45.4 mqih; Pressure differential: 59.8 Pa.

FIGURE 8. Size distribution evaluated with a Mark V cascade impactor during experiment B.15. The deposition efficiency curve displayed is computed with Eq. (5) for a 3 mm slot.

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Aerosol Science and Technology 28:3 March 1998

I

o

i

Predicted slot-width [mm]

3

FIGURE 9. Measured versus predicted slot-width for experiments B.3, B.6, B.7.

I

I

0

1

I

Predicted slot-widti [mm]

I

I

3

FIGURE 10. Measured versus predicted slot-width for experiments B.l through B.16 (experiments performed at 80 Pa are omitted).

Particle Deposition in a Two-Dimensional Slot 245

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Aerosol Science and Technology 28:3 March 1998

0

'o"

2000

Time[s]

3060

Air flow rate: 117 m3/h; Pressure differential: 78.8 Pa FIGURE 11. Accumulation of aerosol particles in a two-dimensional slot as a function of time during experiment B.12. Air flow rate: 117 myih; Pressure differential: 78.8 Pa.

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7

I

1

I

I

I

I

I

I

.5

1

5

10

20

50

Particle diameter [pm] FIGURE 12. Size distribution evaluated with a Mark V cascade impactor during experiment B.12. The deposition eficiency curve displayed is computed with Equation 5 for a 3 mm slot.

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Aerosol Science and Technology 28:3 March 1998

CONCLUSION Our experimental study of particle deposition in a two-dimensional slot from a transverse flow aroused our attention to many problems associated with the measurement of the size of the leak as a function of time as well as the uncertainty inherent to the method. It is nonetheless worthwhile to note that a simplified model based on an approximate method similar to those used in impingement instruments provides us with values of the deposition efficiency that can predict (especially well at low-pressure differentials) the slot behavior as a function of time. Another breakthrough of this research was to prove that particle deposition on the upstream edge of the slot does not occur if its surface is sufficiently smooth. This suggests that typical leaks encountered in situ will be plugged faster than expected. Further work on this subject should include: identification of spray technologies to generate a monodisperse aerosol with the vinyl polymer currently in use, validation of the model on a wider range of flow rates, and determination of the flow patterns and discharge coefficients. Finally, we believe that the use of today's available video equipment should be envisioned in many research programs as it appears particularly time efficient and informative. For instance, this study may be of interest for researchers in thc medical field for the visualization and the experimental assessment of particle deposition in airway bifurcations. . -

--.

.

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The researclz reported here wa.r ,funded in pu~tby the Californiu hstitute,for Eneigy Efficiency (CIEE), a raeurch unit ofthe Unive~sityof Crilifomia. IWdication of reseurch resu1t.s does not impply CIEE enrlo~sementof or agreement with these findings, nor that of any ClEE sponsor. Thi~swork was al,ro suppotted by !he Assistant Secretary for Conservation und Renewable Energy, Ofice of' Building Eneqy Research and Development, Building Systems Divkion of the U.S. Departmen1 of Energy under Contract No. DE-ACO3-76SFOOO98. T l ~ authors e wo~ddalso like to thank Vincent Bevutto fir hi~s vuluable advice reynrding the video equipment, David Flechetfor his sigtzlificant contribution in the development of the aperitnentul apparuhq Alild Lacsen for his ussistunce in

many upcriments discussed herein, urzd Nicole Fur& for hey inspiring suggestions.

References Andrews, K. A. and Sabcrsky, R. H. (1990). Flow Through an Orifice from a Transverse Stream, J o ~ ~ r nofa lFluids Engineering. Transaction of the ASME 112524-526. Clement, C. F. (1992). Aerosol Penetration thro~glzCapillaries and Leaks. AEA Report AEA-lnTec- I1 83, Hanvell Laboratory, Oxfordshire, U.K., Dcccmber 1992. Fuchs, N. A. (1964). The Mechunics of Aerosols, Dover Publications, New York, pp. 151-159. Hinds, W. C. (1982). Aerosol Technology: Properties, Behavior, and Measurement of Airborne Particles, John Wiley & Sons, New York, pp. 104-125. Idel'Chik, I. E. (1960). Handbook of Hydraulic Resistance-Coeficients of Local Resistance and of Friction. Translated from Russian, Israel Program for Scientific Translations, Jerusalem, p. 144. Mitchell, J. P., Marshall, I. A,, Latham, L. J., and Ball, M. H. E. (1992). The Penetration of Aerosols through Fine Orifices. Itzt. J. Radioactive Materials Transport (RAMTRANS). 3(1):5- 17. Modera, M. P. (1993). Characterizing the Performance of Residential Air-Distribution Systems. Energy and B~~ilrlings, 20(1):65-75. Morewitz, H. A. (1982). Leakage of Acrosols from Containment Buildings (Part 2). Health Physics, 42: 195-207. Olson, R. M. (1962). E.ssentia1.s of Engineering Fluid Mechunics. Second Printing. International Textbook, Scranton, pp. 144-152. Robison, D. and Lambert, L. (1989). Field Invcstigation of Residential Infiltration and Hcating Duct Leakage. ASHRAE TI-ansuctions 95(Part 2):542-550. Smith, R. B. (1983). Internal Wrapping Method and Apparatus. U.S. Patent No. 4,415,390. Thomas, A. S. W. and Cornelius, K. C. (1982). Investigation of a Laminar Boundary-Layer Suction Slot. AIAA Journal 20(6):790-796. Vaughan, E. U. (1978). Simple Model for Plugging of Ducts by Aerosol Dcposits, Trans. Am. Nucl. Soc. 28507-508. Received 25 April 1996; accepted 31 July 1997