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Experimental study on the penetration efficiency of fine aerosols in thin capillaries
Journal of Aerosol Science 111 (2017) 26–35
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Experimental study on the penetration efficiency of fine aerosols in thin capillaries
MARK
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Mei Tian , Hongen Gao, Xiaoyuan Han, Yindong Wang, Ronghu Zou Northwest Institute of Nuclear Technology, P.O. Box 69-27, Xi’an 710024, Shaanxi, China
AR TI CLE I NF O
AB S T R A CT
Keywords: Aerosol Thin capillary Penetration efficiency Air leakage rate Flow velocity
Aerosol penetration efficiency is one of the most important parameters for the safety assessment of a containment shell or containers of radioactive materials. In this work, a practical procedure has been developed to study the penetration efficiency of fine aerosol particles (size < 300 nm) through capillaries with bore sizes ranging from 5 to 20 µm and lengths from 10 mm to 80 mm under pressure differences from 60 to 450 kPa. The effects of the upstream aerosol concentration, capillary dimension, and pressure difference on the aerosol penetration were investigated, and the relationships between the aerosol penetration efficiency and the air leakage rate as well as the average flow velocity in the capillary were obtained. The results showed that the penetration efficiency of aerosols through a capillary was positively related to the pressure difference as well as the air leakage rate until reaching 100%. For a given air leakage rate, the aerosol penetration efficiency fluctuated within a relatively wide range due to the influence of the pressure difference and capillary dimensions. The aerosol penetration efficiency decreased significantly with increasing capillary length but was identical for capillaries of the same length but different bore sizes. The aerosol penetration efficiency in capillaries showed a better correlation with the average flow velocity than with the air leakage rate. For flow velocities below 5 m/s, the aerosol penetration efficiency increased with the air velocity in the capillary, while for velocities above 5 m/s, a constant level of approximately 80–100% was maintained.
1. Introduction The main function of a containment structure that encloses a nuclear reactor is the retention of radioactive materials in the event of an accidental breach of the vessel. Leaks in containment vessels most likely arise at welding lines, joints and isolation valves or due to accidental ruptures in structural components. Any leaks of radioactive gas or particles might lead to serious safety issues. Moreover, an adequate pressure difference will increase the leakage of radioactive particles. The leakage rate of fluid could easily be obtained by measuring the pressure difference across the leakage paths, but it is more difficult to assess the leakage of aerosols in the absence of an operational procedure. The leakage of gas and aerosols is not synchronous, especially in a lower flow-rate leakage path. There is some experimental and theoretical evidence to support the strong retention of aerosols in leakage paths, which could even be completely plugged in some cases (Morton & Mitchell, 1995; Parozzi et al., 2005; Watanabe, Hashimoto, & Osaki, 1998). Therefore, aerosol penetration through the containment leakages may be significantly lower, even by orders of magnitude, in comparison to that associated with the air leakage rate. Aerosol penetration through leakage paths has been investigated for a long time. Leaks may occur in various forms, such as thin
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Corresponding author. E-mail address: [email protected] (M. Tian).
http://dx.doi.org/10.1016/j.jaerosci.2017.06.001 Received 1 August 2016; Received in revised form 30 May 2017; Accepted 1 June 2017 Available online 10 June 2017 0021-8502/ © 2017 Elsevier Ltd. All rights reserved.
Journal of Aerosol Science 111 (2017) 26–35
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irregular cracks, non-circular-shaped orifices, annular passages, and labyrinthine paths through mechanical packing. Therefore, it is impossible to map all the different kinds of leakage paths accurately, and an ideal leakage path model is usually applied in relevant experimental and theoretical research. Several early experimental works were carried out to study the aerosol penetration and plugging effects through capillaries with regular, well-defined geometry. Morewitz (1982) provided a detailed review of these early works, which mostly focused on the correlation between the observed leakage rates or plugging times and experimental parameters. Mitchell, Edwards, and Ball (1990) studied the penetration of aerosol particles with sizes ranging from 0.5 to 15 µm through a fine capillary varying from 20 to 80 µm in bore and from 10 to 50 mm in length. Burton, Mitchell, and Morton (1993) and Morton et al. (1995) investigated the role of pressure difference in regulating the rate at which a small capillary was plugged by deposited aerosols. They observed that aerosols mainly deposited close to the entrances of capillaries. It was also demonstrated that the driving pressure across an ultrafine leak path is of fundamental importance in determining the mass of aerosols that might penetrate the defective seal of a container. When the driving pressure is low, the leak-path appears likely to be plugged quickly. Williams (1994) discussed the theory of particle deposition and plugging in tubes and cracks, and an equation for determining the shape and formation rate of a plug was developed. A theory of the transport of aerosols through small capillaries was constructed by Clement (1995) and applied to examine the experimental results obtained by Mitchell et al. (1990) and Morton et al. (1995). The results showed that a cutoff in the aerosol penetration through capillaries was expected to occur at low laminar flow rates corresponding to air leakage rates between 10−5 and 10−4 Pa m3 s−1. Akhatov, Hoey, Swenson, and Schulz (2008) experimentally studied the aerosol flow through a converging microcapillary, which had a diameter of 100 mm and a length of 1 cm. Farzan, Sushanta, and Jason (2011) developed a simple expression for the penetration efficiency of aerosols in rectangular microchannels and cylindrical microtubes. Hinds (1982) presented a deposition efficiency formula for laminar pipe flow. Luo and Yu (2008) researched the particle deposition in a laminar pipe flow, considering thermophoresis, gravity, lift force, diffusion, and convection. A revised semi-implicit method was employed to solve the aerosol transport equation. The deposition efficiency of an aerosol in a pipe was obtained, and the concentration distribution of an aerosol at an arbitrary cross-section of the pipe was given. A simplified mechanistic model for particle penetration and plugging in tubes and cracks was developed by Mitrakos et al. (2008). Zhang, Dang, and Liu (2012) investigated the correlation between the aerosol leakage rate and gas leakage rate in capillaries. Ghaffarpasand et al. (2012) investigated the penetration efficiency of tungsten oxide and ammonium nitrate particles with diameters between 3 and 17 nm under turbulent flow conditions. When reviewing the above studies, it was found that few had experimentally investigated the aerosol penetration efficiency in ultrafine capillaries under different amounts of pressure, which is one of the most important parameters in the safety assessment of a containment shell or a container of radioactive materials. The aerosol penetration efficiency can be calculated from a comparison of the upstream and downstream aerosol concentrations, but the aerosol transport and deposition mechanisms in an ultrafine capillary are much more complicated and difficult to describe. Several main factors, such as the aerosol instability, complexity of aerosol deposition behavior in ultrafine capillaries and possibility of capillary plugging, would interfere with accurate measurements of the upstream and downstream aerosol concentrations. In this paper, a practical method was developed to investigate the aerosol penetration behavior of fine aerosols though an ultrafine capillary.
2. Experimental methodology 2.1. Experiment of aerosol penetration through a capillary A schematic diagram of the experimental apparatus is shown in Fig. 1. It consists of three parts: aerosol source, capillary subassembly and particle detector.
Fig. 1. Schematic diagram of experimental apparatus for determining the aerosol penetration efficiency in a capillary. All connection tubes are as short as possible.
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2.1.1. Aerosol source The smoke from a mosquito coil was used as the aerosol source in the experiment. The aerosol source was prepared as follows: The source container was evacuated to 2 kPa, and a quantity of mosquito coil smoke was inhaled until the pressure increased to 8–20 kPa. Then, the pressure was adjusted to a certain value between 150 kPa and 600 kPa using clean air. The aerosol source container was made of stainless steel, and the volume was approximately 33 L. 2.1.2. Capillary subassembly This included the capillary and a sample collection part. The fused silica capillaries (Polymicro Technologies Inc., USA) with bore sizes from 5 µm to 20 µm and lengths from 10 mm to 80 mm were used. The capillary was vertically fixed in the center of a partition board using epoxy resin adhesive, which was nipped in the middle of a flange. Because the gas flow rate through the capillary was too low to meet the nominal flow rate of the particle counter, clean air had to be introduced. To effectively allow the leaked particles to enter into the counter, a structure of concentric cylinders (shown in Fig. 1) was designed for sample collection. Clean air would enter into the outer shell from a high efficiency filter and flow into the inner tube at the surface of the partition board. A valve was fixed between the capillary subassembly and the source container so that no particle penetrated the capillary before the experiments. A microgroove was cut into the surface of the bottom flange in the radial direction. The groove was so small that the change of the pressure in the source container was considered to be negligible. Meanwhile, the gas flow rate in the connection tube was increased, and aerosols in the connection tube could be updated in a timely way. A capillary subassembly with a larger inner tube was used to measure the concentration of the aerosol source at higher pressure, for which a 200 µm × 10 mm capillary was employed. There was no microgroove cut into the bottom flange of this subassembly because the gas flow rate in the 200 µm × 10 mm capillary could meet the nominal flow rate of the particle counter when the pressure in the source container was higher than 150 kPa. 2.1.3. Particle detector The particle number concentration was measured using an ultrafine condensation particle counter (UCPC, TSI, Inc., Model 3776), which can be operated with sampling flow rates of 0.3 L/min and 1.5 L/min and is capable of counting particles larger than 2.5 nm in diameter. To minimize the dilution of the aerosols, the 0.3 L/min flow rate mode was employed in the experiments. The number-size distribution of the aerosol source was measured using an electrical low-pressure impactor (ELPI, TSI, Inc.), which measures the airborne particle size distribution in the size range of 0.03–10 µm with 12 channels. 2.1.4. Experimental procedure The aerosol source was prepared according to the aerosol source section and settled for 10 min so that the particles in the source container were mixed completely. Then, the number concentration of the aerosol source was measured. The aerosol concentration in the source container was usually controlled to be between 2 × 105 particle/cm3 and 3 × 105 particle/cm3 at the beginning. After that, the UCPC was switched to the target capillary, and the sampling system was cleaned completely using particle-free air; then, aerosol particles that leaked from the target capillary were counted for 2–3 min. Finally, the concentration of the aerosol source was measured once again. The penetration efficiency (P) of the aerosols through the capillary was calculated as the follows:
P=
(Cd − C0) qPd N′ N ′Pd = = N CAU La × 60 × 106 CAU La × 60 × 106
(1)
where N is the number of particles leaked from the capillary per minute without considering deposition on the channel walls and N′ is the number of particles actually leaked per minute. Cd is the average number concentration of particles leaked from the capillary, and C0 is the background concentration of the sampling and counting system (mL−1). q is the flow rate of the UCPC (300 mL/min). Pd is the capillary exit (downstream) pressure. La is the gas leakage rate (Pa m3 s−1) through the capillary. CAU is the particle number concentration in the source container, which is measured at normal pressure. The main error of the penetration efficiency calculation comes from the particle counting statistics of the UCPC. At a sampling flow rate of 300 mL/min and for 20 s measurement intervals with a particle concentration near 10 particle/cm3, there were approximately 1000 particles detected per interval, and the typical counting statistics errors were below 5%; when the particle concentration was as low as 1–2 particle/cm3, the typical counting statistics errors increased to approximately 10%. 2.2. Measurement of gas leakage The gas leakage rate through a capillary can be determined by measuring the increase in pressure of a vessel located downstream. The schematic diagram of the experimental apparatus is presented in Fig. 2. A capacitance diaphragm gauge (Inficon Inc., CDG025D) was employed to measure the vacuum pressure in the downstream vessel. The system is capable of detecting the air leakage rates of values with a standardized leakage rate (SLR) as low as 5 × 10−7 Pa m3 s−1. The flow in the capillary under the experimental conditions would nearly be in a viscous state. The gas leakage rate (La) can also be obtained by solving the following expression, which was derived from Poiseuille's law for laminar flow (Poiseuille, see Lamb, 1945):
La =
4 2 2 1 π dc (pu − pd ) (pu + pd ) QV = 2 128 2ηl
(2) 28
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Fig. 2. Schematic diagram of the experimental apparatus for determining the capillary gas leakage rate.
where Pu and Pd are the pressure of the capillary entrance (upstream) and exit (downstream), respectively. dc and lc are the diameter and length of the capillary, respectively. η is the gas viscosity (kg m−1 s−1). The air leakage rates of capillaries with bore sizes from 5 µm to 30 µm and a length of 10 mm were tested using the apparatus presented in Fig. 2. The results showed that the agreement between the measured and predicted air leakage rates was generally good (RSD ≤ 5%); thus, the air leakage rate of a capillary before aerosol exposure was calculated using Eq. (2), and the device was mainly used for examining capillaries after aerosol exposure. 3. Results and discussion 3.1. Size distribution of aerosol source and deposition The size distribution of the aerosols generated by burning the mosquito coil was measured using the ELPI, and the result is presented in Fig. 3. As shown, over 98% of the aerosol particles were smaller than 300 nm in size. The aerosol concentration in the source container will decrease gradually due to various deposition mechanisms, such as particle diffusion, settling, and inertial deposition. The change curves of the aerosol concentration in the source container at pressures of 150 kPa, 200 kPa and 300 kPa are presented in Fig. 4. As shown, the aerosol concentrations have similar changes for different amounts of source pressure. In addition, particles deposit rapidly when the concentration is higher than 1 × 105/cm3. 3.2. Measurement of the aerosol source concentration at high pressure To calculate the aerosol penetration efficiency, the aerosol concentration in the source container should be measured accurately. Because the pressure in the source container is higher than that of the UCPC, it is impossible to measure the aerosol source concentration directly. There are two practical methods for solving this problem: One is to first release the source container air until achieving normal pressure and then to measure the aerosol source concentration. The other is to directly measure the aerosol source concentration with a larger bore capillary, in which the aerosol penetration efficiency is considered to be 100%. In our experiment, a Φ200 μm × 10 mm capillary was employed. When Pd is normal pressure and Pu is higher than 150 kPa, the air flow rate in the Ф200 μm × 10 mm capillary is higher than 0.3 L/min and meets the requirement of the UCPC. The aerosol source concentrations measured in the high-pressure and normal-pressure state are listed in Table 1. As shown, almost
Fig. 3. Number-size distribution of mosquito-coil smoke aerosols.
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Fig. 4. Change curves of the aerosol concentration in the source container at pressures of 150 kPa, 200 kPa and 300 kPa.
all of the aerosol concentrations measured at high pressure were slightly lower than those measured at normal pressure, but the relative deviation (RD) was less than 5%. 3.3. Aerosol penetration efficiency in an ultrafine capillary For given aerosol particle sizes, the penetration efficiency in an ultrafine capillary is mainly affected by the capillary dimension, as well as Pu and Pd. 3.3.1. Aerosol source concentration influence on the penetration efficiency In theory, the aerosol penetration efficiency does not change notably with the source concentration, but is this true for an ultrafine capillary? The aerosol penetration efficiency in three capillaries was obtained for different source concentrations. To avoid the capillary blockage effect, a capillary tube was used only 2–3 times, and the test time was controlled at less than 3 min. The results are shown in Fig. 5. Fig. 5 shows that the aerosol penetration efficiency in a capillary underwent no significant variation when the aerosol concentration of the source was varied from 2 × 104 cm−3 to 3.2 × 105 cm−3. Furthermore, the air leakage rates of the capillaries were monitored, and no difference was found before and after aerosol exposure. This means that significant blockage in the capillaries did not occur. Note that each capillary was used only 2–3 times and that the test time was very short in our experiments. If a capillary was used many times, the aerosol deposition would gradually change the shape of the leakage path and decrease the bore volume. Under the same deposition rate, a high concentration of the aerosol source might more quickly lead to a change in the leakage path shape and subsequently produce a low aerosol penetration efficiency. 3.3.2. Influence of the pressure difference on the aerosol penetration efficiency To simulate a real situation, the normal pressure was maintained in the capillary exit, and the pressure difference across the capillary was adjusted by Pu. For a given capillary size, Pu directly determines the gas leakage rate and gas flow velocities. The aerosol penetration efficiency in capillaries with bore sizes from 5 to 20 μm and a length of 10 mm was obtained, and the results are shown in Fig. 6. It can be seen that the results have some degree of discretization, which might have resulted from the slight difference of the Table 1 Comparison of aerosol source concentrations measured at high pressure and normal pressure. Serial
Aerosol source concentrations (particle/cm3)
Pu (Pa)
Measured at high pressure A-1 A-2 A-3 B-1 B-2 B-3 C-1 C-2 C-3 D-1 D-2 D-3
1.55 1.55 1.57 2.00 2.06 2.00 3.06 3.02 2.99 5.03 5.01 5.09
× × × × × × × × × × × ×
5
10 105 105 105 105 105 105 105 105 105 105 105
1.67 1.10 1.74 5.80 1.43 2.10 1.25 4.05 7.50 4.28 6.86 2.01
× × × × × × × × × × × ×
5
10 105 105 104 105 105 105 104 104 104 104 105
RSD (%) Measured at normal pressure 1.73 1.15 1.76 6.03 1.44 2.11 1.28 4.18 7.64 4.40 6.87 2.10
30
× × × × × × × × × × × ×
105 105 105 104 105 105 105 104 104 104 104 105
−3.47 −4.35 −1.14 −3.81 −0.69 −0.47 −2.34 −3.11 −1.83 −2.73 −0.15 −4.29
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Fig. 5. Aerosol penetration efficiency in capillaries for different source concentrations.
capillary entrance and the counting error of the UCPC, as well as the uncertainty of the aerosol penetration in an ultrafine capillary. The deviation of parallel samples could reflect the range of the aerosol penetration efficiency; thus, the error bars of the data points are not shown in the figures. Fig. 6 shows that the aerosol penetration efficiency was positively correlated with Pu until reaching 100%. For the Φ5 μm × 10 mm capillary, no leaked aerosols were detected when Pu was 150 kPa, corresponding to an air leakage rate of 6.8 × 10−7 Pa m3/s; subsequently, the aerosol penetration efficiency increased with Pu, reaching 40–70% when Pu was 600 kPa, corresponding to an air leakage rate of 1.8 × 10−5 Pa m3/s. For the Φ10 μm × 10 mm capillary, the aerosol penetration efficiency was approximately 10%
Fig. 6. Penetration efficiency of aerosols through capillaries for different amounts of upstream pressure.
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Fig. 7. Correlations between the aerosol penetration efficiency and gas leakage rate through capillaries with different dimensions.
when Pu was 120 kPa, corresponding to an air leakage rate of 4.4 × 10−6 Pa m3/s; it was 80–100% when Pu was 400 kPa, corresponding to an air leakage rate of 1.0 × 10−4 Pa m3/s. The air leakage rates of the capillaries rapidly increased with the bore size for the same pressure difference, and the aerosol penetration efficiency was 80–100% for the Φ15 μm × 10 mm and the Φ20 µm × 10 mm capillary when Pu was 200 kPa and 150 kPa, corresponding to air leakage rates of 1.1 × 10−4 Pa m3/s and 1.8 × 10−4 Pa m3/s, respectively. It can be seen that aerosol particles with small sizes were quite capable of penetrating the capillaries, and for a capillary with a length of 10 mm, the aerosol penetration efficiency was 80–100% when the air leakage rates were approximately 1 × 10−4 Pa m3/s. 3.3.3. Influence of the capillary dimension on the aerosol penetration efficiency The aerosol penetration efficiency in capillaries with different bore and length was tested, and the correlations between the aerosol penetration efficiency and air leakage rate are presented in Fig. 7. It can be seen that the aerosol penetration efficiency was consistent for capillaries of the same length under the same air leakage rate, despite the different bore sizes, but it decreased significantly as the capillary length increased. For the 10 mm-long capillaries, the aerosol penetration efficiency reached 80–100% when the air leakage rate was approximately 1 × 10−4 Pa m3/s; when it was as low as 2 × 10−5 Pa m3/s, the penetration efficiency was still 40–60%. For capillaries with a length of 40 mm, the aerosol penetration efficiency reached 80–100% when the air leakage rate was 2–3 × 10−4 Pa m3/s; when it was as low as 2 × 10−5 Pa m3/s, the penetration efficiency was only approximately 10%. For capillaries with a length of 80 mm, the aerosol penetration efficiency could not reach 100% even when the air leakage rate was 4 × 10−4 Pa m3/s, and it can be inferred that the aerosol penetration efficiency would be less than 5% for the air leakage rate as low as 2 × 10−5 Pa m3/s. It is clear that the air leakage rates corresponding to 100% aerosol penetration efficiency increased when the capillary became longer. For aerosol particles with small sizes, Brownian diffusion might be the main deposition mechanism, bore size and length of the capillary would affect the deposition efficiency of aerosols. Fig. 7 showed that long capillaries are advantageous to the deposition of aerosols, but it seemed that the influence of bore size was not significant. The reason would be discussed in the Section 3.3.5. 3.3.4. Correlations between the aerosol penetration efficiency and gas leakage rate through capillary as well as the average flow velocity Although the results obtained from the aerosol penetration experiments are believed to have some uncertainties, a certain tendency was clearly evident. Fig. 7 shows that the aerosol penetration efficiency was positively correlated to the gas leakage rate through the capillary until it reached 100%, but for a given gas leakage rate, the aerosol penetration efficiency fluctuated within a wide range due to the influence of the pressure difference and capillary dimension. Clement (1995) noted that a cutoff in aerosol penetration through capillaries is expected to occur at low laminar flow rates corresponding to a small capillary radius, long capillary length, or small pressure difference, and the experiments of Mitchell et al. (1990) and Morton et al. (1995) supported the existence of this cutoff at air leakage rates between 10−5 and 10−4 Pa m3/s. Fig. 7 shows that the cutoff of penetrability occurred at air leakage rates between 10−6 and 10−4 Pa m3/s under the experimental conditions, which is basically consistent with the results of Clement (1995). The slight difference might be due to the different experimental conditions and methods. It is noted in Fig. 7 that the air leakage rate of the cutoff in aerosol penetration increased with the length of capillary. The correlation between the aerosol penetration efficiency and the average flow velocity in the capillary is shown in Fig. 8. Comparing Figs. 7 and 8, it could be found that the aerosol penetration efficiency in a capillary has a much better correlation with the average flow velocity. When the average air velocity is less than 5 m/s, the aerosol penetration efficiency in a capillary increases with the air velocity and then remains at a constant level, i.e., approximately 80–100%. 3.3.5. Discussion It is known from the experiment and general physical principles that the rate of deposition depends on the gas flow regime. Under 32
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Fig. 8. Correlation between the aerosol penetration efficiency and average flow velocity in capillaries.
the experimental conditions, the air flow in the capillary is in the laminar state, and there are three separate mechanisms of the particle deposition that need to be considered: gravitational settling, Brownian diffusion and inertial impaction. Because over 90% of the mosquito-coil-smoke particles have sizes less than 200 nm, inertial impaction may be ignored. To assess the importance of gravitational settling and Brownian diffusion for fine particles in a capillary, the effective diffusion deposition velocity (Vd) and gravitational settling velocity (Vg) of particles were calculated according to Eq. (3) (Williams, 1994) and Eq. (4) (Hinds, 1982), respectively. The results are listed in Table 2.
Vd =
2D Rc
(3)
where D is the diffusion coefficient of the particles and Rc is the radius of the capillary.
Vg =
ρg dp gCc 18η
(4)
where ρg is the density of particles, dp is the diameter of particles, g is the gravitational acceleration, η is the gas viscosity (kg m−1 s−1) and Cc is the Cunningham correction factor. Table 2 shows that Brownian diffusion is the major deposition mechanism when the particle size is smaller than 200 nm. For laminar flow in a cylindrical tube, the particle penetration efficiency (P), considering Brownian diffusion alone, can be calculated as follows (Hinds, 1982).
P P
= =
1 − 5.5μ2/3 + 3.77μ for μ < 0.007 0.819 exp( −11.5μ) + 0.0975 exp( −70.1μ) + 0.0325 exp( −179μ) for μ > 0.007
(5)
where μ, the parameter of diffusion deposition, is defined as
μ=
Dlc πRc2 U
(6)
where lc is the capillary length and U is the average flow velocity. The experimental values and calculated values of the particle penetration efficiency in 10 mm-long capillaries with different bore sizes are presented in Fig. 9. It can be seen that the calculated results are consistent with the experimental data at the lowest upstream pressure, and with the increase in upstream pressure, the experimental values gradually become higher than the calculated values, especially for capillaries with smaller bore sizes. It was indicated that particles have a stronger capability to penetrate an ultrafine capillary at higher pressure than expected. This may be explained by Bernoulli's effect. Due to the different gas velocities on the two sides of the aerosol, there is a force KB causing the aerosol to return to the axis of the capillary (see Fig. 10). This force is proportional Table 2 The effective diffusion deposition velocity and gravitational settling velocity of particles in tubes with radii ranging from 5 µm to 25 µm. Particle
Vd (mm/s)
Diameter (μm)
R = 25 µm
R = 10 µm
R = 7.5 µm
R = 5 µm
1 0.5 0.2 0.1 0.01
0.0022 0.0051 0.0182 0.0566 0.8831
0.0055 0.0126 0.0454 0.1414 2.2078
0.0073 0.0169 0.0605 0.1886 2.9437
0.0110 0.0253 0.0908 0.2829 4.4156
Vg (mm/s)
33
0.0353 0.0102 2.32 × 10−3 9.02 × 10−4 3.94 × 10−4
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Fig. 9. Comparison of the aerosol penetration efficiency in capillaries between experimental data and the predictions made by the diffusion model.
to the aerosol cross section and to the square of the difference of the gas velocities on the two sides of the aerosol. In detail one finds (Wollnik, 1976):
KB ~m4/3ν0 2r 2ρ
(7)
Here ν0 is the velocity of the gas moving on the axis of the capillary, m is the aerosol mass, ρ is the specific weight of the gas, and r is the distance of the aerosol from the capillary axis. For the derivation of Eq. (7) it was assumed that the aerosol diameter is small compared to r. The force KB increases with the velocity ν0 the average of which should not exceed 0.1 Mach (Wollnik, 1976). For an ultrafine capillary, a large pressure difference will lead to a high gas velocity, and consequently, the force KB increases and the deposition of aerosols weakens. The thinner the capillary, the greater the diffusion deposition efficiency of aerosols, and Bernoulli's effect appears relatively more notable. With the increase in capillary bore size, the difference between experimental values and modeling predictions would narrow gradually, just as shown in Fig. 9. In the case of same gas leakage rate, the gas velocity would increase with the decrease of capillary bore size, and Bernoulli's effect is enhanced, which lead to the influence of bore size on deposition of aerosols appearing not significant(see Fig. 7).
Fig. 10. The velocity distribution across a capillary for a laminar gas flow.
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4. Conclusion The penetration and deposition of aerosols in capillaries are complex and governed by the entry restriction, narrow leakage path and pressure conditions. The method developed in this study to determine the initial penetration efficiency of aerosols in an ultrafine capillary was proven to be practical. The initial penetration efficiency can show the strongest level of capillary leakage and is valuable for the conservative estimation of hazard or risk due to the penetration of a dangerous aerosol though a fine leakage path. The influence of the pressure difference, capillary bore size and length on the aerosol penetration efficiency has been investigated, and correlations between the aerosol penetration efficiency and gas leakage rate as well as the mean flow velocity were explored. This work demonstrated that the aerosol penetration efficiency is positively correlated to the air leakage rate through a capillary until reaching 100%, but for a given gas leakage rate, the aerosol penetration efficiency would change within a relatively wide range due to the influence of the pressure difference, capillary length and bore size. For the flow velocities below 5 m/s, the aerosol penetration efficiency increases with the air velocity in a capillary, while for velocities above 5 m/s, a constant level of approximately 80–100% is maintained. This proves that particles with small sizes have a strong penetration capability in ultrafine capillaries. Furthermore, fine aerosol particles have a stronger capability to penetrate an ultrafine capillary at higher pressure difference than expected due to Bernoulli's effect. One aspect that needs to be further investigated is the particle plugging process in capillaries under different amounts of pressure. Some experiments have shown that particle plugging in a fine capillary is very complex and has great uncertainties. These findings will be helpful in the treatment of aerosol leakage in a variety of nuclear or non-nuclear applications, especially with respect to the integrity of valves and fittings for the supply of particle-free gases and for the containment of particles in pressurized environments. References Akhatov, I., Hoey, J., Swenson, O., & Schulz, D. (2008). Aerosol flow through a long micro-capillary: Collimated aerosol beam. Microfluidics and Nanofluidics, 5, 215–224. Burton, A. C., Mitchell, J. P., & Morton, D. A. V. (1993). The influence of pressure on the penetration of aerosols through fine capillaries. Journal of Aerosol Science, 24(Suppl 1), S559–S650. Clement, C. F. (1995). Aerosol penetration through capillaries and leaks: Theory. Journal of Aerosol Science, 26, 369–385. Farzan, Tavakoli, Sushanta, K. Mitra, & Jason, S. Olfert (2011). Aerosol penetration in microchannels. Journal of Aerosol Science, 42, 321–328. Ghaffarpasand, O., Drewnick, F., Hosseiniebalam, F., Gallavardin, S., Fachinger, J., Hassanzadeh, S., & Borrmann, S. (2012). Penetration efficiency of nanometer-sized aerosol particles in tubes. Journal of Aerosol Science, 50, 11–25. Hinds, W. C. (1982). Aerosol technology: Properties, behavior, and measurement of airborne particle. UK: John Wiley and Sons Press. Luo, X. W., & Yu, S. Y. (2008). Deposition of aerosol in a laminar pipe flow. Science in China Series E: Technological Sciences, 51, 1242–1254. Mitchell, J. P., Edwards, R. T., & Ball, M. H. E. (1990). The penetration of aerosols through fine capillaries. Nuclear Technology, 1, 101–116 (RAMTRANS). Mitrakos, D., Chatzidakis, S., Hinis, E. P., Herranz, L. E., Parozzi, F., & Housiadas, C. (2008). A simple mechanistic model for particle penetration and plugging in tubes and cracks. Nuclear Engineering and Design, 238, 3370–3378. Morewitz, H. A. (1982). Leakage of aerosols from containment buildings. Health Physics, 42, 195–207. Morton, D. A. V., & Mitchell, J. P. (1995). Aerosol penetration through capillaries and leaks: Experimental studies on the influence of pressure. Journal of Aerosol Science, 26, 353–367. Parozzi, F., Chatzidakis, S., Gelain, T., Herranz, L. E., Hinis, E., Housiadas, C., ... Vendel, J. (2005). Investigation on aerosol transport in containment cracks. In Proceedings of the international conference on nuclear energy for New Europe. Bled, Slovenia. 5–8 September. Poiseuille, see Lamb, H. (1945). Hydrodynamics. New York: Dover Publication (Ch. 11). Watanabe, A., Hashimoto, T., & Osaki, M. (1998). Fission product aerosol trapping effects in the leakage path of containment penetration under severe accident conditions. In Proceedings of the third OECD specialist meeting on nuclear aerosols in reactor safety. Germany. Williams, M. M. R. (1994). Particle deposition and plugging in tubes and cracks (with special reference to fission product retention). Progress in Nuclear Energy, 28, 1–60. Wollnik, H. (1976). Principles behind a He-Jet system and its application for isotope separation. Nuclear Instruments and Methods, 139, 311–318. Zhang, Z. H., Dang, H. J., & Liu, L. B. (2012). Investigation on correlation of aerosol leakage rate with gas leakage rate in capillary. Atomic Energy Science and Technology, 46, 1517–1521.
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Contents lists available at ScienceDirect
Journal of Aerosol Science journal homepage: www.elsevier.com/locate/jaerosci
Experimental study on the penetration efficiency of fine aerosols in thin capillaries
MARK
⁎
Mei Tian , Hongen Gao, Xiaoyuan Han, Yindong Wang, Ronghu Zou Northwest Institute of Nuclear Technology, P.O. Box 69-27, Xi’an 710024, Shaanxi, China
AR TI CLE I NF O
AB S T R A CT
Keywords: Aerosol Thin capillary Penetration efficiency Air leakage rate Flow velocity
Aerosol penetration efficiency is one of the most important parameters for the safety assessment of a containment shell or containers of radioactive materials. In this work, a practical procedure has been developed to study the penetration efficiency of fine aerosol particles (size < 300 nm) through capillaries with bore sizes ranging from 5 to 20 µm and lengths from 10 mm to 80 mm under pressure differences from 60 to 450 kPa. The effects of the upstream aerosol concentration, capillary dimension, and pressure difference on the aerosol penetration were investigated, and the relationships between the aerosol penetration efficiency and the air leakage rate as well as the average flow velocity in the capillary were obtained. The results showed that the penetration efficiency of aerosols through a capillary was positively related to the pressure difference as well as the air leakage rate until reaching 100%. For a given air leakage rate, the aerosol penetration efficiency fluctuated within a relatively wide range due to the influence of the pressure difference and capillary dimensions. The aerosol penetration efficiency decreased significantly with increasing capillary length but was identical for capillaries of the same length but different bore sizes. The aerosol penetration efficiency in capillaries showed a better correlation with the average flow velocity than with the air leakage rate. For flow velocities below 5 m/s, the aerosol penetration efficiency increased with the air velocity in the capillary, while for velocities above 5 m/s, a constant level of approximately 80–100% was maintained.
1. Introduction The main function of a containment structure that encloses a nuclear reactor is the retention of radioactive materials in the event of an accidental breach of the vessel. Leaks in containment vessels most likely arise at welding lines, joints and isolation valves or due to accidental ruptures in structural components. Any leaks of radioactive gas or particles might lead to serious safety issues. Moreover, an adequate pressure difference will increase the leakage of radioactive particles. The leakage rate of fluid could easily be obtained by measuring the pressure difference across the leakage paths, but it is more difficult to assess the leakage of aerosols in the absence of an operational procedure. The leakage of gas and aerosols is not synchronous, especially in a lower flow-rate leakage path. There is some experimental and theoretical evidence to support the strong retention of aerosols in leakage paths, which could even be completely plugged in some cases (Morton & Mitchell, 1995; Parozzi et al., 2005; Watanabe, Hashimoto, & Osaki, 1998). Therefore, aerosol penetration through the containment leakages may be significantly lower, even by orders of magnitude, in comparison to that associated with the air leakage rate. Aerosol penetration through leakage paths has been investigated for a long time. Leaks may occur in various forms, such as thin
⁎
Corresponding author. E-mail address: [email protected] (M. Tian).
http://dx.doi.org/10.1016/j.jaerosci.2017.06.001 Received 1 August 2016; Received in revised form 30 May 2017; Accepted 1 June 2017 Available online 10 June 2017 0021-8502/ © 2017 Elsevier Ltd. All rights reserved.
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irregular cracks, non-circular-shaped orifices, annular passages, and labyrinthine paths through mechanical packing. Therefore, it is impossible to map all the different kinds of leakage paths accurately, and an ideal leakage path model is usually applied in relevant experimental and theoretical research. Several early experimental works were carried out to study the aerosol penetration and plugging effects through capillaries with regular, well-defined geometry. Morewitz (1982) provided a detailed review of these early works, which mostly focused on the correlation between the observed leakage rates or plugging times and experimental parameters. Mitchell, Edwards, and Ball (1990) studied the penetration of aerosol particles with sizes ranging from 0.5 to 15 µm through a fine capillary varying from 20 to 80 µm in bore and from 10 to 50 mm in length. Burton, Mitchell, and Morton (1993) and Morton et al. (1995) investigated the role of pressure difference in regulating the rate at which a small capillary was plugged by deposited aerosols. They observed that aerosols mainly deposited close to the entrances of capillaries. It was also demonstrated that the driving pressure across an ultrafine leak path is of fundamental importance in determining the mass of aerosols that might penetrate the defective seal of a container. When the driving pressure is low, the leak-path appears likely to be plugged quickly. Williams (1994) discussed the theory of particle deposition and plugging in tubes and cracks, and an equation for determining the shape and formation rate of a plug was developed. A theory of the transport of aerosols through small capillaries was constructed by Clement (1995) and applied to examine the experimental results obtained by Mitchell et al. (1990) and Morton et al. (1995). The results showed that a cutoff in the aerosol penetration through capillaries was expected to occur at low laminar flow rates corresponding to air leakage rates between 10−5 and 10−4 Pa m3 s−1. Akhatov, Hoey, Swenson, and Schulz (2008) experimentally studied the aerosol flow through a converging microcapillary, which had a diameter of 100 mm and a length of 1 cm. Farzan, Sushanta, and Jason (2011) developed a simple expression for the penetration efficiency of aerosols in rectangular microchannels and cylindrical microtubes. Hinds (1982) presented a deposition efficiency formula for laminar pipe flow. Luo and Yu (2008) researched the particle deposition in a laminar pipe flow, considering thermophoresis, gravity, lift force, diffusion, and convection. A revised semi-implicit method was employed to solve the aerosol transport equation. The deposition efficiency of an aerosol in a pipe was obtained, and the concentration distribution of an aerosol at an arbitrary cross-section of the pipe was given. A simplified mechanistic model for particle penetration and plugging in tubes and cracks was developed by Mitrakos et al. (2008). Zhang, Dang, and Liu (2012) investigated the correlation between the aerosol leakage rate and gas leakage rate in capillaries. Ghaffarpasand et al. (2012) investigated the penetration efficiency of tungsten oxide and ammonium nitrate particles with diameters between 3 and 17 nm under turbulent flow conditions. When reviewing the above studies, it was found that few had experimentally investigated the aerosol penetration efficiency in ultrafine capillaries under different amounts of pressure, which is one of the most important parameters in the safety assessment of a containment shell or a container of radioactive materials. The aerosol penetration efficiency can be calculated from a comparison of the upstream and downstream aerosol concentrations, but the aerosol transport and deposition mechanisms in an ultrafine capillary are much more complicated and difficult to describe. Several main factors, such as the aerosol instability, complexity of aerosol deposition behavior in ultrafine capillaries and possibility of capillary plugging, would interfere with accurate measurements of the upstream and downstream aerosol concentrations. In this paper, a practical method was developed to investigate the aerosol penetration behavior of fine aerosols though an ultrafine capillary.
2. Experimental methodology 2.1. Experiment of aerosol penetration through a capillary A schematic diagram of the experimental apparatus is shown in Fig. 1. It consists of three parts: aerosol source, capillary subassembly and particle detector.
Fig. 1. Schematic diagram of experimental apparatus for determining the aerosol penetration efficiency in a capillary. All connection tubes are as short as possible.
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2.1.1. Aerosol source The smoke from a mosquito coil was used as the aerosol source in the experiment. The aerosol source was prepared as follows: The source container was evacuated to 2 kPa, and a quantity of mosquito coil smoke was inhaled until the pressure increased to 8–20 kPa. Then, the pressure was adjusted to a certain value between 150 kPa and 600 kPa using clean air. The aerosol source container was made of stainless steel, and the volume was approximately 33 L. 2.1.2. Capillary subassembly This included the capillary and a sample collection part. The fused silica capillaries (Polymicro Technologies Inc., USA) with bore sizes from 5 µm to 20 µm and lengths from 10 mm to 80 mm were used. The capillary was vertically fixed in the center of a partition board using epoxy resin adhesive, which was nipped in the middle of a flange. Because the gas flow rate through the capillary was too low to meet the nominal flow rate of the particle counter, clean air had to be introduced. To effectively allow the leaked particles to enter into the counter, a structure of concentric cylinders (shown in Fig. 1) was designed for sample collection. Clean air would enter into the outer shell from a high efficiency filter and flow into the inner tube at the surface of the partition board. A valve was fixed between the capillary subassembly and the source container so that no particle penetrated the capillary before the experiments. A microgroove was cut into the surface of the bottom flange in the radial direction. The groove was so small that the change of the pressure in the source container was considered to be negligible. Meanwhile, the gas flow rate in the connection tube was increased, and aerosols in the connection tube could be updated in a timely way. A capillary subassembly with a larger inner tube was used to measure the concentration of the aerosol source at higher pressure, for which a 200 µm × 10 mm capillary was employed. There was no microgroove cut into the bottom flange of this subassembly because the gas flow rate in the 200 µm × 10 mm capillary could meet the nominal flow rate of the particle counter when the pressure in the source container was higher than 150 kPa. 2.1.3. Particle detector The particle number concentration was measured using an ultrafine condensation particle counter (UCPC, TSI, Inc., Model 3776), which can be operated with sampling flow rates of 0.3 L/min and 1.5 L/min and is capable of counting particles larger than 2.5 nm in diameter. To minimize the dilution of the aerosols, the 0.3 L/min flow rate mode was employed in the experiments. The number-size distribution of the aerosol source was measured using an electrical low-pressure impactor (ELPI, TSI, Inc.), which measures the airborne particle size distribution in the size range of 0.03–10 µm with 12 channels. 2.1.4. Experimental procedure The aerosol source was prepared according to the aerosol source section and settled for 10 min so that the particles in the source container were mixed completely. Then, the number concentration of the aerosol source was measured. The aerosol concentration in the source container was usually controlled to be between 2 × 105 particle/cm3 and 3 × 105 particle/cm3 at the beginning. After that, the UCPC was switched to the target capillary, and the sampling system was cleaned completely using particle-free air; then, aerosol particles that leaked from the target capillary were counted for 2–3 min. Finally, the concentration of the aerosol source was measured once again. The penetration efficiency (P) of the aerosols through the capillary was calculated as the follows:
P=
(Cd − C0) qPd N′ N ′Pd = = N CAU La × 60 × 106 CAU La × 60 × 106
(1)
where N is the number of particles leaked from the capillary per minute without considering deposition on the channel walls and N′ is the number of particles actually leaked per minute. Cd is the average number concentration of particles leaked from the capillary, and C0 is the background concentration of the sampling and counting system (mL−1). q is the flow rate of the UCPC (300 mL/min). Pd is the capillary exit (downstream) pressure. La is the gas leakage rate (Pa m3 s−1) through the capillary. CAU is the particle number concentration in the source container, which is measured at normal pressure. The main error of the penetration efficiency calculation comes from the particle counting statistics of the UCPC. At a sampling flow rate of 300 mL/min and for 20 s measurement intervals with a particle concentration near 10 particle/cm3, there were approximately 1000 particles detected per interval, and the typical counting statistics errors were below 5%; when the particle concentration was as low as 1–2 particle/cm3, the typical counting statistics errors increased to approximately 10%. 2.2. Measurement of gas leakage The gas leakage rate through a capillary can be determined by measuring the increase in pressure of a vessel located downstream. The schematic diagram of the experimental apparatus is presented in Fig. 2. A capacitance diaphragm gauge (Inficon Inc., CDG025D) was employed to measure the vacuum pressure in the downstream vessel. The system is capable of detecting the air leakage rates of values with a standardized leakage rate (SLR) as low as 5 × 10−7 Pa m3 s−1. The flow in the capillary under the experimental conditions would nearly be in a viscous state. The gas leakage rate (La) can also be obtained by solving the following expression, which was derived from Poiseuille's law for laminar flow (Poiseuille, see Lamb, 1945):
La =
4 2 2 1 π dc (pu − pd ) (pu + pd ) QV = 2 128 2ηl
(2) 28
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Fig. 2. Schematic diagram of the experimental apparatus for determining the capillary gas leakage rate.
where Pu and Pd are the pressure of the capillary entrance (upstream) and exit (downstream), respectively. dc and lc are the diameter and length of the capillary, respectively. η is the gas viscosity (kg m−1 s−1). The air leakage rates of capillaries with bore sizes from 5 µm to 30 µm and a length of 10 mm were tested using the apparatus presented in Fig. 2. The results showed that the agreement between the measured and predicted air leakage rates was generally good (RSD ≤ 5%); thus, the air leakage rate of a capillary before aerosol exposure was calculated using Eq. (2), and the device was mainly used for examining capillaries after aerosol exposure. 3. Results and discussion 3.1. Size distribution of aerosol source and deposition The size distribution of the aerosols generated by burning the mosquito coil was measured using the ELPI, and the result is presented in Fig. 3. As shown, over 98% of the aerosol particles were smaller than 300 nm in size. The aerosol concentration in the source container will decrease gradually due to various deposition mechanisms, such as particle diffusion, settling, and inertial deposition. The change curves of the aerosol concentration in the source container at pressures of 150 kPa, 200 kPa and 300 kPa are presented in Fig. 4. As shown, the aerosol concentrations have similar changes for different amounts of source pressure. In addition, particles deposit rapidly when the concentration is higher than 1 × 105/cm3. 3.2. Measurement of the aerosol source concentration at high pressure To calculate the aerosol penetration efficiency, the aerosol concentration in the source container should be measured accurately. Because the pressure in the source container is higher than that of the UCPC, it is impossible to measure the aerosol source concentration directly. There are two practical methods for solving this problem: One is to first release the source container air until achieving normal pressure and then to measure the aerosol source concentration. The other is to directly measure the aerosol source concentration with a larger bore capillary, in which the aerosol penetration efficiency is considered to be 100%. In our experiment, a Φ200 μm × 10 mm capillary was employed. When Pd is normal pressure and Pu is higher than 150 kPa, the air flow rate in the Ф200 μm × 10 mm capillary is higher than 0.3 L/min and meets the requirement of the UCPC. The aerosol source concentrations measured in the high-pressure and normal-pressure state are listed in Table 1. As shown, almost
Fig. 3. Number-size distribution of mosquito-coil smoke aerosols.
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Fig. 4. Change curves of the aerosol concentration in the source container at pressures of 150 kPa, 200 kPa and 300 kPa.
all of the aerosol concentrations measured at high pressure were slightly lower than those measured at normal pressure, but the relative deviation (RD) was less than 5%. 3.3. Aerosol penetration efficiency in an ultrafine capillary For given aerosol particle sizes, the penetration efficiency in an ultrafine capillary is mainly affected by the capillary dimension, as well as Pu and Pd. 3.3.1. Aerosol source concentration influence on the penetration efficiency In theory, the aerosol penetration efficiency does not change notably with the source concentration, but is this true for an ultrafine capillary? The aerosol penetration efficiency in three capillaries was obtained for different source concentrations. To avoid the capillary blockage effect, a capillary tube was used only 2–3 times, and the test time was controlled at less than 3 min. The results are shown in Fig. 5. Fig. 5 shows that the aerosol penetration efficiency in a capillary underwent no significant variation when the aerosol concentration of the source was varied from 2 × 104 cm−3 to 3.2 × 105 cm−3. Furthermore, the air leakage rates of the capillaries were monitored, and no difference was found before and after aerosol exposure. This means that significant blockage in the capillaries did not occur. Note that each capillary was used only 2–3 times and that the test time was very short in our experiments. If a capillary was used many times, the aerosol deposition would gradually change the shape of the leakage path and decrease the bore volume. Under the same deposition rate, a high concentration of the aerosol source might more quickly lead to a change in the leakage path shape and subsequently produce a low aerosol penetration efficiency. 3.3.2. Influence of the pressure difference on the aerosol penetration efficiency To simulate a real situation, the normal pressure was maintained in the capillary exit, and the pressure difference across the capillary was adjusted by Pu. For a given capillary size, Pu directly determines the gas leakage rate and gas flow velocities. The aerosol penetration efficiency in capillaries with bore sizes from 5 to 20 μm and a length of 10 mm was obtained, and the results are shown in Fig. 6. It can be seen that the results have some degree of discretization, which might have resulted from the slight difference of the Table 1 Comparison of aerosol source concentrations measured at high pressure and normal pressure. Serial
Aerosol source concentrations (particle/cm3)
Pu (Pa)
Measured at high pressure A-1 A-2 A-3 B-1 B-2 B-3 C-1 C-2 C-3 D-1 D-2 D-3
1.55 1.55 1.57 2.00 2.06 2.00 3.06 3.02 2.99 5.03 5.01 5.09
× × × × × × × × × × × ×
5
10 105 105 105 105 105 105 105 105 105 105 105
1.67 1.10 1.74 5.80 1.43 2.10 1.25 4.05 7.50 4.28 6.86 2.01
× × × × × × × × × × × ×
5
10 105 105 104 105 105 105 104 104 104 104 105
RSD (%) Measured at normal pressure 1.73 1.15 1.76 6.03 1.44 2.11 1.28 4.18 7.64 4.40 6.87 2.10
30
× × × × × × × × × × × ×
105 105 105 104 105 105 105 104 104 104 104 105
−3.47 −4.35 −1.14 −3.81 −0.69 −0.47 −2.34 −3.11 −1.83 −2.73 −0.15 −4.29
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Fig. 5. Aerosol penetration efficiency in capillaries for different source concentrations.
capillary entrance and the counting error of the UCPC, as well as the uncertainty of the aerosol penetration in an ultrafine capillary. The deviation of parallel samples could reflect the range of the aerosol penetration efficiency; thus, the error bars of the data points are not shown in the figures. Fig. 6 shows that the aerosol penetration efficiency was positively correlated with Pu until reaching 100%. For the Φ5 μm × 10 mm capillary, no leaked aerosols were detected when Pu was 150 kPa, corresponding to an air leakage rate of 6.8 × 10−7 Pa m3/s; subsequently, the aerosol penetration efficiency increased with Pu, reaching 40–70% when Pu was 600 kPa, corresponding to an air leakage rate of 1.8 × 10−5 Pa m3/s. For the Φ10 μm × 10 mm capillary, the aerosol penetration efficiency was approximately 10%
Fig. 6. Penetration efficiency of aerosols through capillaries for different amounts of upstream pressure.
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Fig. 7. Correlations between the aerosol penetration efficiency and gas leakage rate through capillaries with different dimensions.
when Pu was 120 kPa, corresponding to an air leakage rate of 4.4 × 10−6 Pa m3/s; it was 80–100% when Pu was 400 kPa, corresponding to an air leakage rate of 1.0 × 10−4 Pa m3/s. The air leakage rates of the capillaries rapidly increased with the bore size for the same pressure difference, and the aerosol penetration efficiency was 80–100% for the Φ15 μm × 10 mm and the Φ20 µm × 10 mm capillary when Pu was 200 kPa and 150 kPa, corresponding to air leakage rates of 1.1 × 10−4 Pa m3/s and 1.8 × 10−4 Pa m3/s, respectively. It can be seen that aerosol particles with small sizes were quite capable of penetrating the capillaries, and for a capillary with a length of 10 mm, the aerosol penetration efficiency was 80–100% when the air leakage rates were approximately 1 × 10−4 Pa m3/s. 3.3.3. Influence of the capillary dimension on the aerosol penetration efficiency The aerosol penetration efficiency in capillaries with different bore and length was tested, and the correlations between the aerosol penetration efficiency and air leakage rate are presented in Fig. 7. It can be seen that the aerosol penetration efficiency was consistent for capillaries of the same length under the same air leakage rate, despite the different bore sizes, but it decreased significantly as the capillary length increased. For the 10 mm-long capillaries, the aerosol penetration efficiency reached 80–100% when the air leakage rate was approximately 1 × 10−4 Pa m3/s; when it was as low as 2 × 10−5 Pa m3/s, the penetration efficiency was still 40–60%. For capillaries with a length of 40 mm, the aerosol penetration efficiency reached 80–100% when the air leakage rate was 2–3 × 10−4 Pa m3/s; when it was as low as 2 × 10−5 Pa m3/s, the penetration efficiency was only approximately 10%. For capillaries with a length of 80 mm, the aerosol penetration efficiency could not reach 100% even when the air leakage rate was 4 × 10−4 Pa m3/s, and it can be inferred that the aerosol penetration efficiency would be less than 5% for the air leakage rate as low as 2 × 10−5 Pa m3/s. It is clear that the air leakage rates corresponding to 100% aerosol penetration efficiency increased when the capillary became longer. For aerosol particles with small sizes, Brownian diffusion might be the main deposition mechanism, bore size and length of the capillary would affect the deposition efficiency of aerosols. Fig. 7 showed that long capillaries are advantageous to the deposition of aerosols, but it seemed that the influence of bore size was not significant. The reason would be discussed in the Section 3.3.5. 3.3.4. Correlations between the aerosol penetration efficiency and gas leakage rate through capillary as well as the average flow velocity Although the results obtained from the aerosol penetration experiments are believed to have some uncertainties, a certain tendency was clearly evident. Fig. 7 shows that the aerosol penetration efficiency was positively correlated to the gas leakage rate through the capillary until it reached 100%, but for a given gas leakage rate, the aerosol penetration efficiency fluctuated within a wide range due to the influence of the pressure difference and capillary dimension. Clement (1995) noted that a cutoff in aerosol penetration through capillaries is expected to occur at low laminar flow rates corresponding to a small capillary radius, long capillary length, or small pressure difference, and the experiments of Mitchell et al. (1990) and Morton et al. (1995) supported the existence of this cutoff at air leakage rates between 10−5 and 10−4 Pa m3/s. Fig. 7 shows that the cutoff of penetrability occurred at air leakage rates between 10−6 and 10−4 Pa m3/s under the experimental conditions, which is basically consistent with the results of Clement (1995). The slight difference might be due to the different experimental conditions and methods. It is noted in Fig. 7 that the air leakage rate of the cutoff in aerosol penetration increased with the length of capillary. The correlation between the aerosol penetration efficiency and the average flow velocity in the capillary is shown in Fig. 8. Comparing Figs. 7 and 8, it could be found that the aerosol penetration efficiency in a capillary has a much better correlation with the average flow velocity. When the average air velocity is less than 5 m/s, the aerosol penetration efficiency in a capillary increases with the air velocity and then remains at a constant level, i.e., approximately 80–100%. 3.3.5. Discussion It is known from the experiment and general physical principles that the rate of deposition depends on the gas flow regime. Under 32
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Fig. 8. Correlation between the aerosol penetration efficiency and average flow velocity in capillaries.
the experimental conditions, the air flow in the capillary is in the laminar state, and there are three separate mechanisms of the particle deposition that need to be considered: gravitational settling, Brownian diffusion and inertial impaction. Because over 90% of the mosquito-coil-smoke particles have sizes less than 200 nm, inertial impaction may be ignored. To assess the importance of gravitational settling and Brownian diffusion for fine particles in a capillary, the effective diffusion deposition velocity (Vd) and gravitational settling velocity (Vg) of particles were calculated according to Eq. (3) (Williams, 1994) and Eq. (4) (Hinds, 1982), respectively. The results are listed in Table 2.
Vd =
2D Rc
(3)
where D is the diffusion coefficient of the particles and Rc is the radius of the capillary.
Vg =
ρg dp gCc 18η
(4)
where ρg is the density of particles, dp is the diameter of particles, g is the gravitational acceleration, η is the gas viscosity (kg m−1 s−1) and Cc is the Cunningham correction factor. Table 2 shows that Brownian diffusion is the major deposition mechanism when the particle size is smaller than 200 nm. For laminar flow in a cylindrical tube, the particle penetration efficiency (P), considering Brownian diffusion alone, can be calculated as follows (Hinds, 1982).
P P
= =
1 − 5.5μ2/3 + 3.77μ for μ < 0.007 0.819 exp( −11.5μ) + 0.0975 exp( −70.1μ) + 0.0325 exp( −179μ) for μ > 0.007
(5)
where μ, the parameter of diffusion deposition, is defined as
μ=
Dlc πRc2 U
(6)
where lc is the capillary length and U is the average flow velocity. The experimental values and calculated values of the particle penetration efficiency in 10 mm-long capillaries with different bore sizes are presented in Fig. 9. It can be seen that the calculated results are consistent with the experimental data at the lowest upstream pressure, and with the increase in upstream pressure, the experimental values gradually become higher than the calculated values, especially for capillaries with smaller bore sizes. It was indicated that particles have a stronger capability to penetrate an ultrafine capillary at higher pressure than expected. This may be explained by Bernoulli's effect. Due to the different gas velocities on the two sides of the aerosol, there is a force KB causing the aerosol to return to the axis of the capillary (see Fig. 10). This force is proportional Table 2 The effective diffusion deposition velocity and gravitational settling velocity of particles in tubes with radii ranging from 5 µm to 25 µm. Particle
Vd (mm/s)
Diameter (μm)
R = 25 µm
R = 10 µm
R = 7.5 µm
R = 5 µm
1 0.5 0.2 0.1 0.01
0.0022 0.0051 0.0182 0.0566 0.8831
0.0055 0.0126 0.0454 0.1414 2.2078
0.0073 0.0169 0.0605 0.1886 2.9437
0.0110 0.0253 0.0908 0.2829 4.4156
Vg (mm/s)
33
0.0353 0.0102 2.32 × 10−3 9.02 × 10−4 3.94 × 10−4
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Fig. 9. Comparison of the aerosol penetration efficiency in capillaries between experimental data and the predictions made by the diffusion model.
to the aerosol cross section and to the square of the difference of the gas velocities on the two sides of the aerosol. In detail one finds (Wollnik, 1976):
KB ~m4/3ν0 2r 2ρ
(7)
Here ν0 is the velocity of the gas moving on the axis of the capillary, m is the aerosol mass, ρ is the specific weight of the gas, and r is the distance of the aerosol from the capillary axis. For the derivation of Eq. (7) it was assumed that the aerosol diameter is small compared to r. The force KB increases with the velocity ν0 the average of which should not exceed 0.1 Mach (Wollnik, 1976). For an ultrafine capillary, a large pressure difference will lead to a high gas velocity, and consequently, the force KB increases and the deposition of aerosols weakens. The thinner the capillary, the greater the diffusion deposition efficiency of aerosols, and Bernoulli's effect appears relatively more notable. With the increase in capillary bore size, the difference between experimental values and modeling predictions would narrow gradually, just as shown in Fig. 9. In the case of same gas leakage rate, the gas velocity would increase with the decrease of capillary bore size, and Bernoulli's effect is enhanced, which lead to the influence of bore size on deposition of aerosols appearing not significant(see Fig. 7).
Fig. 10. The velocity distribution across a capillary for a laminar gas flow.
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4. Conclusion The penetration and deposition of aerosols in capillaries are complex and governed by the entry restriction, narrow leakage path and pressure conditions. The method developed in this study to determine the initial penetration efficiency of aerosols in an ultrafine capillary was proven to be practical. The initial penetration efficiency can show the strongest level of capillary leakage and is valuable for the conservative estimation of hazard or risk due to the penetration of a dangerous aerosol though a fine leakage path. The influence of the pressure difference, capillary bore size and length on the aerosol penetration efficiency has been investigated, and correlations between the aerosol penetration efficiency and gas leakage rate as well as the mean flow velocity were explored. This work demonstrated that the aerosol penetration efficiency is positively correlated to the air leakage rate through a capillary until reaching 100%, but for a given gas leakage rate, the aerosol penetration efficiency would change within a relatively wide range due to the influence of the pressure difference, capillary length and bore size. For the flow velocities below 5 m/s, the aerosol penetration efficiency increases with the air velocity in a capillary, while for velocities above 5 m/s, a constant level of approximately 80–100% is maintained. This proves that particles with small sizes have a strong penetration capability in ultrafine capillaries. Furthermore, fine aerosol particles have a stronger capability to penetrate an ultrafine capillary at higher pressure difference than expected due to Bernoulli's effect. One aspect that needs to be further investigated is the particle plugging process in capillaries under different amounts of pressure. Some experiments have shown that particle plugging in a fine capillary is very complex and has great uncertainties. These findings will be helpful in the treatment of aerosol leakage in a variety of nuclear or non-nuclear applications, especially with respect to the integrity of valves and fittings for the supply of particle-free gases and for the containment of particles in pressurized environments. References Akhatov, I., Hoey, J., Swenson, O., & Schulz, D. (2008). Aerosol flow through a long micro-capillary: Collimated aerosol beam. Microfluidics and Nanofluidics, 5, 215–224. Burton, A. C., Mitchell, J. P., & Morton, D. A. V. (1993). The influence of pressure on the penetration of aerosols through fine capillaries. Journal of Aerosol Science, 24(Suppl 1), S559–S650. Clement, C. F. (1995). Aerosol penetration through capillaries and leaks: Theory. Journal of Aerosol Science, 26, 369–385. Farzan, Tavakoli, Sushanta, K. Mitra, & Jason, S. Olfert (2011). 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