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Simulation of three-stage operating temperature for supersaturation water-based condensational growth tube
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ScienceDirect www.elsevier.com/locate/jes
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Simulation of three-stage operating temperature for supersaturation water-based condensational growth tube Jiejie Bian 1,2, Huaqiao Gui 1,3, Zhibo Xie 3, Tongzhu Yu 1,3,**, Xiuli Wei 1,3, Wenyu Wang 1,2, Jianguo Liu 1,2,3,* 1
Key Laboratory of Environmental Optics and Technology, Anhui Institute of Optics and Fine Mechanics, Chinese Academy of Sciences, Hefei 230031, China 2 University of Science and Technology of China, Hefei 230026, China 3 CAS Center for Excellence in Regional Atmospheric Environment, Institute of Urban Environment, Chinese Academy of Sciences, Xiamen 361021, China
article info
abstract
Article history:
In order to realize accurate dynamic control of supersaturation and to study condensation
Received 27 June 2019
growth characteristics of nanoparticles through different levels of supersaturation, a series
Received in revised form
of parametric analyses and systematic comparisons between two-stage and three-stage
11 December 2019
operating temperature designs were simulated with COMSOL Multiphysics. The simula-
Accepted 12 December 2019
tion results showed that the three-stage operating temperature did not change peak su-
Available online xxx
persaturation compared with two operating temperatures, and the three-stage operating temperature was superior in decreasing the amount of water vapor and the temperature,
Keywords:
thus lowering particle loss and variation in detection and collection. The peak supersat-
Operating temperature
uration level increased by 0.3 as the flow rate increased from 0.6 to 2.0 L/min, but the
Supersaturation profile
supersaturation peak moved from 0.0027 z0 to 0.08 z0 (i.e., the growth time and the final
Flow rate
size decreased by 40%). Peak supersaturation increased as the temperature difference
Minimum activation size
increased or the temperature difference window was shifting left, and minimum activation
Temperature difference
size decreased. Shifting the 70 C temperature difference window from 9 C, 79 Ce1 C, 71 C for the condenser and initiator temperatures resulted in peak supersaturation in the centerline being above 5.8, and the activation size changed as low as 1 nm. Experiments with flow rates varying by a factor of 2.5 (from 0.6 to 1.5 L/min) resulted in a final size decrease of 43% (from 3.2 to 1.8 mm), and experimental results of outlet particle size distributions were equivalent with theoretical analysis as the operating temperature was changed. © 2019 The Research Center for Eco-Environmental Sciences, Chinese Academy of Sciences. Published by Elsevier B.V.
* Corresponding author. Key Laboratory of Environmental Optics and Technology, Anhui Institute of Optics and Fine Mechanics, Chinese Academy of Sciences, Hefei, 230031, China. ** Corresponding author. Key Laboratory of Environmental Optics and Technology, Anhui Institute of Optics and Fine Mechanics, Chinese Academy of Sciences, Hefei, 230031, China. E-mail addresses: [email protected] (J. Bian), [email protected] (T. Yu), [email protected] (J. Liu). https://doi.org/10.1016/j.jes.2019.12.007 1001-0742/© 2019 The Research Center for Eco-Environmental Sciences, Chinese Academy of Sciences. Published by Elsevier B.V. Please cite this article as: Bian, J et al., Simulation of three-stage operating temperature for supersaturation water-based condensational growth tube, Journal of Environmental Sciences, https://doi.org/10.1016/j.jes.2019.12.007
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Introduction During atmospheric pollution formation, visibility degrades sharply and is often accompanied by haze. Condensational growth is an effective manner of nanoparticle growth (Kulmala et al., 2004; Zhang et al., 2012). Particulate matter activation and hygroscopic growth as cloud condensation nuclei and droplets are important factors in haze formation (Pandis et al., 1990). Results from the tropical rainforest region show that the ultrafine particles (less than 50 nm) can be quickly activated and transformed to cloud droplets, and these can potentially contribute to the formation of cloud condensation nuclei (Fan et al., 2018). Due to the fact that ultrafine particles are small, their activation requires a high degree of supersaturation of water vapor (Andreae and Rosenfeld, 2008). Condensational growth is not only employed to enable concentration measurements for particles too small to be detected optically (Stolzenburg and McMurry, 1991; McMurry, 2000), but also has been used for the collection of particles for chemical analysis (Khlystov, 1995; Weber et al., 2001) or to permit aerodynamic focusing and concentration of ultrafine particles (Sioutas, 1999; Demokritou et al., 2002). Creating a supersaturation region is necessary for activating particle growth, as it can provide a warm and humid output flow. Hering and Stolzenburg (2005) introduced a mixing method for water-based condensational growth in laminar flow. In short, due to the high diffusivity of the water vapor, the system uses a warm, wet wall growth region to create the supersaturation necessary for particle activation and growth. The laminar flow provides welldefined saturation profiles. The system is capable of activating particles as small as 3 nm and has provided the basis for a line of water-based condensation particle counters (Hering et al., 2005; Iida et al., 2008; Kupc et al., 2013). All these condensational growth methods (herein referred to as the original approach) were employed until (Hering et al., 2014) provided a new moderator concept of condensational growth for decreasing the amounts of added heat and water vapor. The detection efficiency of condensation particle counters (CPC) is normally enhanced by increasing the temperature difference between the condenser and the initiator sections € ja € et al., 2006; Kuang (Hermann and Wiedensohler, 2001; Peta et al., 2012; Barmpounis et al., 2018). Enhancing the temperature difference increases the degree of supersaturation in the growth tube, which in turn increases the activation probability of the smaller particles (Mordas et al., 2012). For the laminar flow CPC, the supersaturation profile in the growth tube is a non-uniform spatial distribution with values ranging from 1 to the maximum determined by the temperature of the condenser and initiator sections. Temperature difference is a parameter for controlling the degree of supersaturation and the activation size, but as the relevant parametric analysis has not been done, it is difficult to find suitable parameters of ultrafine particle condensed growth conditions for a controlled design. To realize the accurate measurement of nanoparticles and to accurately control supersaturation, a series of parametric analyses and systematic comparisons of the original twostage operating temperature and newer three-stage
operating temperature designs were simulated using COMSOL. The relevant verification experiments were done as well.
1.
Theory and methods
1.1.
Activation size theory
The supersaturation S is defined as the ratio of the partial pressure of the condensing vapor, Pva (Pa) to its equilibrium vapor pressure Psat;T (Pa) at the flow temperature T (K): S ¼ Pva Psat;T
(1)
The smaller the particle is, the higher the supersaturation required to activate growth. This is due to the Kelvin effect, which associates the equilibrium vapor pressure to the diameter of a droplet composed of that condensed vapor. The equilibrium vapor pressure over a droplet is higher than over a flat surface because of the surface tension. The Kelvin effect is described asDk;va , Dk;va ¼ ð4ss Mw Þ
rl Rg TlnS
(2)
where ss (N/m), Mw (kg/mol), and rl (kg/m3) are the surface tension, molecular weight, and the liquid density of the condensing species, respectively; Rg (J/(mol*K)) is the universal gas constant, and T (K) is the absolute temperature. Dk;va is a property of the condensing species equal to the diameter of a droplet in equilibrium with its vapor at saturation ratio S and temperature T. The value is the same as the activation diameter for the case of a particle that is wetted by but insoluble in the condensing vapor. Thus, a particle composed of a material that is not wetted by the condensing vapor will have a larger activation diameter than Dk;va . For soluble particles, the equilibrium vapor pressure becomes lower due to the condensate covering the particle surface, and the critical diameter required for growth is smaller.
1.2.
Heat and mass transfer theory
The saturation profiles throughout the condensing growth tube depend on the temperature, T (K), and the vapor part pressure Pva (Pa) of the position. Fluid flow through a cylindrical growth tube is described by the energy equation of a Newtonian fluid. The heat transfer equation is described by equation (3), rCp
vT vT vq vT vT 1 v vT 1 v2 T v2 T þ vr þ þ vz ¼k r þ 2 2þ 2 vt vr r vq vz r vr vr r vq vz
þ mfv (3) q represents the angle between a projected line in the axial plane and the positive x axis in a cylindrical coordinate system and z represents the axial position. The particle flow is assumed to be an incompressible Newtonian fluid with a fully developed parabolic flow profile: r2 vz ðrÞ ¼ v0 1 2 R
(4)
v0 (m/s), r (mm), and R (mm) represent initial velocity, radial
Please cite this article as: Bian, J et al., Simulation of three-stage operating temperature for supersaturation water-based condensational growth tube, Journal of Environmental Sciences, https://doi.org/10.1016/j.jes.2019.12.007
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position, and growth tube radius respectively. Axial thermal diffusion and other second-order effects such as Stefan flow are ignored. If the above assumptions are met, then equation (3) is simplified as a one-dimensional heat transfer partial differential equation of steady laminar flow: r2 vT 1 v vT v2 T ¼ Dth r þ 2 v0 1 2 vz r vr vr vz R
(5)
R (mm) is the radius of the growth tube; Dth ¼ k=ðrCp Þ is the thermal diffusivity of the flow gas, and Cp (J/(kg*K)) represents heat capacity. In a similar way, the partial differential equation for partial vapor pressure Pva is described as r2 vPva 1 v vPva v2 Pva r ¼ Dva þ v0 1 2 2 r vr vz vr vz R
(6)
where, Dva ( cm2 =s) is the mass diffusivity of the vapor. The boundary conditions for the partial differential equation are based on the temperature setting of the growth tube: Inlet conditions of the growth tube: Tðr; 0Þ ¼ T0 , Pva ðr; 0Þ ¼ P0 ; Wall conditions of the growth tube: TðR;zÞ ¼ Tw ,Pva ðR;zÞ ¼ Pw . The inlet profiles of vapor pressure are assumed to be uniform; at the growth tube wall, the vapor is assumed to be saturated and the particle concentration equal to zero. The entering temperature profile and wall temperature are assumed to be uniform. Fluid properties evaluated at a mean temperature are treated as constants over the domain.
1.3. Two- and three-stage operating temperature principle Fig. 1b illustrates the three-stage operating temperature method using a moderated, warm-walled laminar flow water condensation growth tube. The system consists of cool-walled followed by warm-walled and cool-walled regions, the conditioner, initiator, and moderator, respectively. All regions have wetted walls. As the laminar flow passes from the cooler conditioner into the warm, wet-walled initiator section and the cool moderator section, both water vapor and heat diffuse into the flow from the walls. Because of its higher diffusivity, the water transport is more rapid, creating a region of vapor supersaturation. The particle growth occurs in the initiator and moderator regions, and the water vapor from the initiator section provides the water vapor for particle activation. The moderator section provides enough distance for growth. In other words, condensational growth continues in the cooler moderator stage, and this stage removes both water vapor and heat while maintaining supersaturated conditions. In Fig. 1a, the two-stage operating temperatures consist of a cool-walled conditioner followed by a warm-walled growth region. All regions have wetted walls.
1.4.
Evaluation method for numerical modeling
Fluid flow through the cylindrical growth tube is simplified as a 2-D axial symmetric model, where r is the radial position,
3
and z is the axial position. Temperature, humidity and vapor pressure were calculated using COMSOL Multiphysics. The cylindrical geometry is modeled in two dimensions. Physical fields such as laminar flow, heat transfer in moist air and moisture transport in the air were coupled in order to simulate the variation tendencies of saturation and temperature. The flow was assumed to be parabolic; thus, inlet flow was regarded as the Laminar flow in the COMSOL. In the calculation by COMSOL Multiphysics, heat transfer in moist air and moisture transport in the air are used instead of the equations of heat and mass transfer. In the physical field of Heat transfer in moist air, the temperature of the inlet flow is 5 C, the tube wall was treated as a temperature boundary, and the wall temperature was set for our requirement that the initial temperature of the domain equals 5 C, thus the inlet condition temperature T0 and the wall condition temperature Tw of the growth tube are constant. In the physical field of moisture transport in the air, the humidity of the inlet flow was set at 95% RH. The tube wall was treated as a humidity boundary; the wall was set at 100% RH, and the initial humidity of the tube domain was equal to 50% RH. In this way, the inlet condition water vapor P0 and the wall condition water vapor Pw of the growth tube are constant. The convection-diffusion equation was solved to calculate the temperature and supersaturation profile. At the same time, the activation diameter from the Kelvin effect was described. The calculations assumed a water vapor mass diffusivity ofDva ¼ 0:251 cm2 =s, and a thermal diffusivity ofDth ¼ 0:215 cm2 =sec.
2.
Results and discussion
2.1.
Saturation and temperature profiles
Fig. 2 shows the maximum values of the supersaturation spatial distribution for two and three operating temperatures; there is an obvious change for the three operating temperatures condition. The temperature difference between the initiator and moderator sections led to the variation in the boundary of the supersaturation profile. In Fig. 2a, the temperature difference between the initiator and moderator sections is zero; the boundary is smooth, and the maximum degree of supersaturation is 2.93. In Fig. 2b, the temperature difference between the initiator and moderator sections is 40 C; another supersaturation region appears, but the maximum value of the second supersaturation region is far below the value of 2.93, and the position of the maximum value is the same as in the two-stage operating temperature design. Thus, the operating temperature only slightly affected the saturation profile of the moderator section, and did not affect the position of the maximum value. Fig. 3 compares centerline saturation and centerline dew temperatures for the growth tubes employing two and three operating temperatures. Three operating temperatures decreased the dew temperature of the exit but maintained the maximum peak supersaturation. Therefore, the minimum activation size was constant. As shown in Fig. 3a, a 5 C, 95% RH flow is introduced into a 10 C conditioner followed by 65 C of the initiator and 65 C moderator growth region, or into a 10 C conditioner followed by 65 C of the initiator and
Please cite this article as: Bian, J et al., Simulation of three-stage operating temperature for supersaturation water-based condensational growth tube, Journal of Environmental Sciences, https://doi.org/10.1016/j.jes.2019.12.007
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Fig. 1 e Flow carries particles from the conditioner into an initiator section with a warm, wetted wall, followed by a cooler moderator section. This setup is termed the three-stage operating temperature design; the temperatures of the initiator and moderator sections are equal for the two-stage operating temperature design. The lengths of conditioner, initiator, and moderator are 154 mm, 76 mm, and 100 mm, respectively. The diameters of the two different condensation growth tubes are both 4.6 mm.
Fig. 2 e Supersaturation spatial distribution at (a) two operating temperatures (10 C and 65 C) and (b) three operating temperatures (10 C, 65 C, and 25 C) with laminar flow at 5 C, 95% RH, and 1.5 L/min flow rate entering the growth tube. moderator with wall temperatures of 10 C, 15 C, 20 C, 25 C, or 30 C. The saturation S is a function of the non-dimensional parameter z/z0, where z is the axial distance from the inlet of the initiator section, and z0 is defined as the ratio of the flow Q (L/min) to the water vapor diffusion constant Dva (cm2/sec): z0 ¼ Q=Dva
(7)
For water vapor diffusion and an inlet flow of 1.5 L/min, z0 was approximately 1 m for the cylindrical geometry. The supersaturation profile along the centerline in the tube was
not sensitive to the wall operating temperature of the downstream region. All trajectories demonstrated the same maximum value of supersaturation. Moreover, along the centerline this maximum occurs at an axial position of 0.06 z0, nearly at the initiator exit. The delay of trajectories is due to the time required for vapor to be transported from the walls to the centerline. During the flow into the moderator section, water vapor is removed by the cold wall. The downstream values of saturation for five operating temperatures were within 10%. For the same inlet and wall conditions, the dew temperature is shown in Fig. 3b. It is obvious
Please cite this article as: Bian, J et al., Simulation of three-stage operating temperature for supersaturation water-based condensational growth tube, Journal of Environmental Sciences, https://doi.org/10.1016/j.jes.2019.12.007
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5
Fig. 3 e (a) Saturation and (b) dew temperature at the centerline of a laminar flow at 5 C and 95% RH entering the growth tube with different wall temperatures.
that the dew temperature of the three-stage operating temperature system decreased by a larger margin than with the two operating temperatures. When the moderator temperature was changed from 10 C to 30 C for three operating temperatures, the dew temperature at the exit was below 35 C at all times. However, the dew temperature in the twostage operating temperature system was 52 C. Therefore, the dew temperature at the exit can be adjusted by changing the moderator temperature. Fig. 4 illustrates the variation in the saturation ratio, temperature profiles, and water vapor pressure profiles for two or three operating temperatures as a specific case. The temperature of the inlet flow is offset at 5 C, and the RH is 95%. The respective temperatures of the conditioner, initiator, and moderator sections are 10 C, 65 C, and 65 C in the two-stage operating temperature design and are 10 C, 65 C, and 25 C in the three-stage operating temperature design. Saturation, temperature, and water vapor pressure are shown along four different trajectories from the centerline (r/R0 ¼ 0) to near the edge of the tube (r/R0 ¼ 0.75, where R0 is the growth tube radius). In Fig. 4a, it is obvious that the peak saturation is uniform at all radial positions, whether for two or three operating temperatures. Both the supersaturation and the temperature followed nearly identical tracks until reaching the peak saturation. Thus, the minimum activation size of a particle and the ideal size (where the particle size is large enough to be easily detected by light scattering) were similar for two and three operating temperatures. Because of the first order, the droplet growth depends on the supersaturation; one expects similar droplet growth.
Fig. 4b, c shows that the temperature and water vapor pressure in the moderator section with three operating temperatures were lower than those with two temperatures. With two operating temperatures, the temperature along each trajectory was near the temperature of the initiator section. However, with the three-stage operating temperature design, the temperature increases to a value below the temperature of the initiator section and then slowly cools. In Fig. 4b, when the three-stage operating temperature design (here 10 C, 65 C, and 25 C) is selected, the maximum centerline temperature is about 27 C. The temperature at 0.5 R0 remains below 30 C during the entire time. In contrast, with two operating temperatures, the temperature of the flow continues to increase after reaching the peak supersaturation, with the temperature between 58 C and 62 C at the exit. As shown in Fig. 4c, the three-stage operating temperature design reduced the water vapor content in the moderator section. With the two-stage operating temperature design, the water vapor is continually added to the flow throughout the growth region. In contrast, with the three-stage operating temperature design, water is added to the flow only throughout the initiator section. Some of the water vapor is also removed in the moderator section. The water vapor content can be reduced further by setting a cooler wall temperature for the moderator section.
2.1.1.
Flow rate effect
The saturation region will move when the inlet flow rate changes. As shown in Fig. 5, as the inlet flow rate was adjusted from 0.6 to 2.0 L/min (the temperature difference was 55 C,
Please cite this article as: Bian, J et al., Simulation of three-stage operating temperature for supersaturation water-based condensational growth tube, Journal of Environmental Sciences, https://doi.org/10.1016/j.jes.2019.12.007
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Fig. 4 e Profiles of the (a) saturation, (b) temperature, and (c) water vapor content for laminar flow with 5 C, 95% RH entering two-stage operating temperature (10 C and 65 C) and three-stage operating temperature (10 C, 65 C, and 25 C) growth tubes. Dashed lines line represent two operating temperatures, and solid lines indicate three operating temperatures.
Fig. 5 e The centerline supersaturation profile with laminar flow at 5 C and 95% RH entering the growth tube calculated at three operating temperatures of 10 C, 65 C, and 25 C for different inlet flow rates.
Please cite this article as: Bian, J et al., Simulation of three-stage operating temperature for supersaturation water-based condensational growth tube, Journal of Environmental Sciences, https://doi.org/10.1016/j.jes.2019.12.007
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and the operating temperatures were 10 C, 65 C, and 25 C), the peak supersaturation moved from 0.0027 z0 to 0.08 z0, and the saturation regions were closer to the exit because of the increase in the flow rate. At the same time, the peak supersaturation increased by 0.3 as the flow rate increased from 0.6 to 2.0 L/min. However, the growth time for droplets and the final droplet size were decreased by 40%. Therefore, the increase of the inlet flow rate made the growth of droplets to a detectable size more difficult. In order to attain the ideal growth size, there should be a perfect match between inlet flow rate and the length of the growth tube when the diameter of the growth tube is kept constant.
2.1.2.
Operating temperature effect
Temperature difference is an important factor for controlling supersaturation. The greater the temperature difference, the higher the degree of supersaturation. At the same time, shifting the temperature difference window to the left also causes higher supersaturation. As seen in Fig. 6a, peak supersaturation becomes greater as the temperature difference is changed from 65 C to 90 C, and the greater the temperature difference, the more rapid the increase of peak supersaturation. In Fig. 6b, the temperature difference between the condenser and the initiator was kept constant at 90 C, the temperature difference window was varied by changing the condenser temperature from 1 C to 9 C and the initiator temperature from 91 C to 99 C. As shown, the peak supersaturation along the centerline for the five temperature
7
windows increases with the shifting of the temperature difference window to the left.
2.2.
Minimum activation size
The minimum activation size is related to the peak supersaturation level. As shown in equation (2), minimum activation size is related to the condensing vapor species, temperature, and saturation. Water vapor is selected as the condensing vapor in this calculation. Fig. 7 illustrates part of the Kelvin diameter contour map for a laminar flow with 5 C, 95% RH entering a two-stage operating temperature system (10 C, 95 C) growth tube. The temperature difference is 85 C, and the inlet flow rate is 1.5 L/min. The minimum activation size is about 1 nm near the centerline. The smaller the activation size, the nearer the position to the centerline. The aerosol flow near the centerline will contribute to the activation efficiency.
2.2.1.
Effect of flow rate
Activation size becomes smaller as the inlet flow rate increases, though the impact varies depending on the temperature difference. As shown in Fig. 8, when the flow increased from 1.0 to 3.5 L/min, the minimum activation size decreased from 1.75 to 1.45 nm for a temperature difference of 70 C. However, as the temperature difference increased, the impact on the minimum activation size became weaker. There was no impact of temperature difference at 90 C when the flow
Fig. 6 e Centerline saturation comparison of (a) different temperature differences and (b) shifting the temperature window to the left for laminar flow at 5 C, 95% RH entering two-stage operating temperature and three-stage operating temperature growth tubes. Please cite this article as: Bian, J et al., Simulation of three-stage operating temperature for supersaturation water-based condensational growth tube, Journal of Environmental Sciences, https://doi.org/10.1016/j.jes.2019.12.007
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Fig. 7 e Kelvin diameter distribution contour map for laminar flow with 5 C, 95% RH entering a two-stage operating temperature (10 C, 95 C) growth tube.
Fig. 8 e Minimum activation size as a function of inlet flow rate calculated for laminar flow at 5 C, 95% RH entering a threestage operating temperature (initiator temperature ¼ 95 C) growth tube.
rate increased. At the same time, the supersaturation spatial distribution moves closer to the exit position due to the increase in the flow rate. In addition, the growth time for droplets will be shorter, and final size will be smaller. Thus, in order to attain the ideal growth size, there should be a suitable selection between inlet flow rate and activation size (i.e., temperature difference).
2.2.2.
Effect of temperature difference
Peak supersaturation will be higher as the temperature difference becomes larger, and the activation size will be smaller. Thus, changing the temperature difference can be employed for controlling the minimum activation size. Fig. 9 shows that the minimum activation size decreases with increasing temperature difference. The impact becomes less
Fig. 9 e Minimum activation size and peak supersaturation as functions of temperature difference. The red line is the function for minimum activation size and the blue line is for the peak supersaturation. The inlet flow rate is 1.5 L/min with 95% RH. Please cite this article as: Bian, J et al., Simulation of three-stage operating temperature for supersaturation water-based condensational growth tube, Journal of Environmental Sciences, https://doi.org/10.1016/j.jes.2019.12.007
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Fig. 10 e Comparison of minimum activation size for various temperature difference windows. The temperature difference from top to bottom is constant at 50 C, 60 C, 70 C, 80 C and 90 C.
as the temperature difference increases. A temperature difference of 90 C can activate a 1 nm particle to grow to a detectable size. However, the greater the temperature difference, the lower the reduction of minimum activation size. If the requirement for detection limitation is 2 nm, a temperature difference of 90 C is not required, as a temperature difference of 55 C is sufficient. Thus, the difficulty in using a high temperature difference is circumvented. As the temperature difference increases, the peak supersaturation also increases as a convex curve. At the same time, the activation size is related to the temperature and saturation for a specific condensing vapor species. As supersaturation is temperature dependent, the selection of temperature is an important requirement.
2.2.3.
Effect of temperature difference window
The movement of the temperature difference window has a certain impact on the minimum activation size. The temperature difference also has varying degrees of effect. As seen in Fig. 10, the minimum activation size becomes smaller by shifting the temperature difference window to the left. The decrease is related to the temperature difference; the minimum activation decreased by 0.064 nm, 0.06 nm, 0.58 nm, 0.034 nm, and 0.04 nm, respectively, for temperature difference windows left-shifted to 50 C, 60 C, 70 C, 80 C, and 90 C.The effect on the decrease of minimum activation size is more apparent when the temperature difference is 70 C
(1e71 C), and the minimum activation size is smaller than for a temperature difference window of 80 C (1e81 C). The minimum activation size dropped to 1.2 nm with conditioner and initiator temperatures of 1 C and 71 C. And the activation size is better than 2.5 nm of water-base CPC (model 3788, TSI, USA).
2.3.
Experimental verification
2.3.1.
Experimental setup
The experimental setup was constructed based on a standard particle generator (Met One model 255 Gen) and an aerodynamic particle sizer (APS, model 3321 TSI, USA) as shown in Fig. 11. Standard particle generator mixes sodium chloride particles with deionized water and atomizes the mixture to obtain aerosol particles. The aerosol particles flow into the built-in charger of the generator for charging, and are then classified by the Differential Mobility Analyzers (DMA, model 3082 TSI, USA) to generate monodispersed particles of selected sizes. Two flowmeters (model 4199 TSI, USA) are necessary to control the flow rate for clean air supply and for flow removal of remaining particles. The temperature control for the conditioner and initiator are based on semiconductor refrigerating and heater units. The output droplet size distributions were measured using an aerodynamic particle sizer (APS). This was done by sampling directly into the 1.0 L/min APS aerosol sample flow rate.
Fig. 11 e Experimental setup for varying operating temperature and flow rate. Please cite this article as: Bian, J et al., Simulation of three-stage operating temperature for supersaturation water-based condensational growth tube, Journal of Environmental Sciences, https://doi.org/10.1016/j.jes.2019.12.007
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amount of water vapor available for diffusion. Once the particles have been activated, a two-temperature difference can provide the same growth environment except for water vapor content, so the larger temperature difference results in a larger droplet size than with the lower temperature difference. The movement of the temperature difference window results in an equivalent median diameter distribution, but the concentration is different. The water vapor content may also be a reason, because shifting the temperature difference window to the left will result in a larger water vapor content. When the particle concentration is large enough, the water vapor dissipation will hinder growth of the particles. Fig. 12 e Output droplet size distributions measured by an aerodynamic particle sizer for varying flow rates at the three operating temperatures of 10 C, 65 C, and 25 C.
3.
Conclusions
The present study comprises a systematic comparison of twostage and three-stage operating temperature methods for growth tubes related to decreasing the temperature and water vapor content at the exit. Some effective parameters such as flow rate and temperature difference are analyzed for obtaining the ideal activation size and final growth size. The temperature difference is defined as the difference between the condenser and initiator temperatures. The key results were as follows:
Fig. 13 e Output droplet size distributions measured by aerodynamic particle size for varying temperature differences and temperature difference windows in the three-stage operating temperature design.
2.3.2.
Flow rate effect
Fig. 12 compares the droplet sizes for different inlet flow rates using the three operating temperatures of 10 C, 65 C, and 25 C. The data show similar behavior for flow rates varying by a factor of 2.5 (from 0.6 to 1.5 L/min), with exiting droplet diameters changing by about 43% (from 3.2 to 1.8 mm). A lower flow rate provides more effective length for droplet growth, and thus promotes larger droplet growth. Both increasing the length of the growth tube and providing lower inlet flow promote larger droplet growth. This corresponds to the simulations of flow rate. A higher flow rate results in the movement of the supersaturation region toward the exit, so the particle activation will occur later, and the growth time will be less.
2.3.3.
Operating temperature effect
Fig. 13 illustrates the effect of temperature difference and temperature difference window on final droplet size. The temperature difference window is insensitive to the final droplet size, but a higher temperature difference provides a larger size. As the data show, at a constant moderator temperature of 25 C, but with the initiator operated at 70 C and 60 C, the resulting droplet size is shifted to a smaller particle size, from 2.3 to 2.0 mm median diameter. The main reason for this is that a larger temperature difference leads to a higher
(1) The parametric analysis and systematic comparison of the original two-stage operating temperature and newer three-stage operating temperature designs confirm that the three-stage operating temperature design results in a lower temperature and water vapor content at the exit but does not change the peak supersaturation level, and thus, this design is a good choice for particle detection and collection. (2) The change in the flow rate results in the movement of the supersaturation spatial distribution and a decrease in the minimum activation size. When the flow rate increased from 0.6 to 2.0 L/min, the peak supersaturation increased by 0.3, but the peak supersaturation moved from 0.0027 z0 to 0.08 z0 (i.e., the growth time and the final size both decreased by 40%). In order to attain the ideal growth size, there should be a perfect match between inlet flow rate and the length of the growth tube. (3) Enhancing the temperature difference can attain higher supersaturation and smaller activation size. Further development of shifting the temperature difference window left also contributed to the supersaturation and activation size. The effect for the decrease in the minimum activation size is greater when the temperature difference is 70 C, compared with 50 C, 60 C, 80 C, and 90 C; the minimum activation size diminishes to 1.2 nm when setting the respective conditioner and initiator temperatures to 1 C and 71 C. (4) Experiments with varying flow rates and operating temperatures for comparing the final growth size show that with flow rates varying by a factor of 2.5 (from 0.6 to 1.5 L/min), final size decreased by 43% (from 3.2 to 1.8 mm). The results were consistent with the theoretical analysis. Lower flow rate results in larger final size, and
Please cite this article as: Bian, J et al., Simulation of three-stage operating temperature for supersaturation water-based condensational growth tube, Journal of Environmental Sciences, https://doi.org/10.1016/j.jes.2019.12.007
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larger temperature difference or shifting the temperature difference to the left provide more water vapor for particle growth. This research concerning parametric analysis and systematic comparison can provide guidance for specific systems design. The next step is to construct systems and study the condensational growth characteristics of nanoparticles through condensation growth tubes for different levels of supersaturation.
Conflict of interest The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper.
Acknowledgement
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This research was supported by Natural Science Foundation of China (No. 91544218), the National Key Research and Development Program of China (No. 2016YFC0201001), the Science and Technological Fund of Anhui Province for Outstanding Youth (1808085J19), the Science and Technological Fund of Anhui Province (1908085MD114), and The CASHIPS Director's Fund, Grant NO. YZJJ2019QN1.
Appendix A. Supplementary data Supplementary data to this article can be found online at https://doi.org/10.1016/j.jes.2019.12.007.
references
Andreae, M.O., Rosenfeld, D., 2008. Aerosol-cloud-precipitation interactions. Part 1. The nature and sources of cloud-active aerosols. Earth-Sci. Rev. 89 (1e2), 13e41. Barmpounis, K., Ranjithkumar, A., Schmidt-Ott, A., Attoui, M., Biskos, G., 2018. Enhancing the detection efficiency of condensation particle counters for sub-2 nm particles. J. Aerosol Sci. 117, 44e53. Demokritou, P., Gupta, T., Koutrakis, P., 2002. A high volume apparatus for the condensational growth of ultrafine particles for inhalation toxicological studies. Aerosol Sci. Technol. 36 (11), 1061e1072. Fan, J.W., Rosenfeld, D., Zhang, Y.W., Giangrande, S.E., Li, Z.Q., Machado, L.A.T., et al., 2018. Substantial convection and
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precipitation enhancements by ultrafine aerosol particles. Science 359 (6374), 411eþ. Hering, S.V., Spielman, S.R., Lewis, G.S., 2014. Moderated, waterbased, condensational particle growth in a laminar flow. Aerosol Sci. Technol. 48 (4), 401e408. Hering, S.V., Stolzenburg, M.R., 2005. A method for particle size amplification by water condensation in a laminar, thermally diffusive flow. Aerosol Sci. Technol. 39 (5), 428e436. Hering, S.V., Stolzenburg, M.R., Quant, F.R., Oberreit, D.R., Keady, P.B., 2005. A laminar-flow, water-based condensation particle counter (wcpc). Aerosol Sci. Technol. 39 (7), 659e672. Hermann, M., Wiedensohler, A., 2001. Counting efficiency of condensation particle counters at low-pressures with illustrative data from the upper troposphere. J. Aerosol Sci. 32 (8), 975e991. Iida, K., Stolzenburg, M.R., McMurry, P.H., Smith, J.N., Quant, F.R., Oberreit, D.R., et al., 2008. An ultrafine, water-based condensation particle counter and its evaluation under field conditions. Aerosol Sci. Technol. 42 (10), 862e871. Khlystov, A.W., Wyers, G.P., Slanina, J., 1995. The steam-jet aerosol collector. Atmos. Environ. 1352e2310 (95), 2229e2234, 00180-8. Kuang, C., Chen, M., McMurry, P.H., Wang, J., 2012. Modification of laminar flow ultrafine condensation particle counters for the enhanced detection of 1 nm condensation nuclei. Aerosol Sci. Technol. 46 (3), 309e315. Kulmala, M., Laakso, L., Lehtinen, K.E.J., Riipinen, I., Dal Maso, M., Anttila, T., et al., 2004. Initial steps of aerosol growth. Atmos Chem. Phys. 4, 2553e2560. Kupc, A., Bischof, O., Tritscher, T., Beeston, M., Krinke, T., Wagner, P.E., 2013. Laboratory characterization of a new nanowater-based cpc 3788 and performance comparison to an ultrafine butanol-based cpc 3776. Aerosol Sci. Technol. 47 (2), 183e191. McMurry, P.H., 2000. The history of condensation nucleus counters. Aerosol Sci. Technol. 33 (4), 297e322. Mordas, G., Petaja, T., Ulevicius, V., 2012. Optimisation of the operation regimes for the water-based condensation particle counter. Lith J. Phys. 52 (3), 253e260. Pandis, S.N., Seinfeld, J.H., Pilinis, C., 1990. The smog-fog-smog cycle and acid deposition. J. Geophys Res-Atmos. 95 (D11), 18489e18500. € ja € , T., Mordas, G., Manninen, H., Aalto, P.P., Ha € meri, K., Peta Kulmala, M., 2006. Detection efficiency of a water-based tsi condensation particle counter 3785. Aerosol Science and Technology 40 (12), 1090e1097. Sioutas, C., Kim, S., Chang, M., 1999. Development and evaluation of a prototype ultrafine particle concentrator. J. Aerosol Sci. 30, 1001e1017. Stolzenburg, M.R., McMurry, P.H., 1991. An ultrafine aerosol condensation nucleus counter. Aerosol Sci. Technol. 14 (1), 48e65. Weber, R.J., Orsini, D., Daun, Y., Lee, Y.N., Klotz, P.J., Brechtel, F., 2001. A particle-into-liquid collector for rapid measurement of aerosol bulk chemical composition. Aerosol Sci. Technol. 35 (3), 718e727. Zhang, R.Y., Khalizov, A., Wang, L., Hu, M., Xu, W., 2012. Nucleation and growth of nanoparticles in the atmosphere. Chem. Rev. 112 (3), 1957e2011.
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ScienceDirect www.elsevier.com/locate/jes
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Simulation of three-stage operating temperature for supersaturation water-based condensational growth tube Jiejie Bian 1,2, Huaqiao Gui 1,3, Zhibo Xie 3, Tongzhu Yu 1,3,**, Xiuli Wei 1,3, Wenyu Wang 1,2, Jianguo Liu 1,2,3,* 1
Key Laboratory of Environmental Optics and Technology, Anhui Institute of Optics and Fine Mechanics, Chinese Academy of Sciences, Hefei 230031, China 2 University of Science and Technology of China, Hefei 230026, China 3 CAS Center for Excellence in Regional Atmospheric Environment, Institute of Urban Environment, Chinese Academy of Sciences, Xiamen 361021, China
article info
abstract
Article history:
In order to realize accurate dynamic control of supersaturation and to study condensation
Received 27 June 2019
growth characteristics of nanoparticles through different levels of supersaturation, a series
Received in revised form
of parametric analyses and systematic comparisons between two-stage and three-stage
11 December 2019
operating temperature designs were simulated with COMSOL Multiphysics. The simula-
Accepted 12 December 2019
tion results showed that the three-stage operating temperature did not change peak su-
Available online xxx
persaturation compared with two operating temperatures, and the three-stage operating temperature was superior in decreasing the amount of water vapor and the temperature,
Keywords:
thus lowering particle loss and variation in detection and collection. The peak supersat-
Operating temperature
uration level increased by 0.3 as the flow rate increased from 0.6 to 2.0 L/min, but the
Supersaturation profile
supersaturation peak moved from 0.0027 z0 to 0.08 z0 (i.e., the growth time and the final
Flow rate
size decreased by 40%). Peak supersaturation increased as the temperature difference
Minimum activation size
increased or the temperature difference window was shifting left, and minimum activation
Temperature difference
size decreased. Shifting the 70 C temperature difference window from 9 C, 79 Ce1 C, 71 C for the condenser and initiator temperatures resulted in peak supersaturation in the centerline being above 5.8, and the activation size changed as low as 1 nm. Experiments with flow rates varying by a factor of 2.5 (from 0.6 to 1.5 L/min) resulted in a final size decrease of 43% (from 3.2 to 1.8 mm), and experimental results of outlet particle size distributions were equivalent with theoretical analysis as the operating temperature was changed. © 2019 The Research Center for Eco-Environmental Sciences, Chinese Academy of Sciences. Published by Elsevier B.V.
* Corresponding author. Key Laboratory of Environmental Optics and Technology, Anhui Institute of Optics and Fine Mechanics, Chinese Academy of Sciences, Hefei, 230031, China. ** Corresponding author. Key Laboratory of Environmental Optics and Technology, Anhui Institute of Optics and Fine Mechanics, Chinese Academy of Sciences, Hefei, 230031, China. E-mail addresses: [email protected] (J. Bian), [email protected] (T. Yu), [email protected] (J. Liu). https://doi.org/10.1016/j.jes.2019.12.007 1001-0742/© 2019 The Research Center for Eco-Environmental Sciences, Chinese Academy of Sciences. Published by Elsevier B.V. Please cite this article as: Bian, J et al., Simulation of three-stage operating temperature for supersaturation water-based condensational growth tube, Journal of Environmental Sciences, https://doi.org/10.1016/j.jes.2019.12.007
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Introduction During atmospheric pollution formation, visibility degrades sharply and is often accompanied by haze. Condensational growth is an effective manner of nanoparticle growth (Kulmala et al., 2004; Zhang et al., 2012). Particulate matter activation and hygroscopic growth as cloud condensation nuclei and droplets are important factors in haze formation (Pandis et al., 1990). Results from the tropical rainforest region show that the ultrafine particles (less than 50 nm) can be quickly activated and transformed to cloud droplets, and these can potentially contribute to the formation of cloud condensation nuclei (Fan et al., 2018). Due to the fact that ultrafine particles are small, their activation requires a high degree of supersaturation of water vapor (Andreae and Rosenfeld, 2008). Condensational growth is not only employed to enable concentration measurements for particles too small to be detected optically (Stolzenburg and McMurry, 1991; McMurry, 2000), but also has been used for the collection of particles for chemical analysis (Khlystov, 1995; Weber et al., 2001) or to permit aerodynamic focusing and concentration of ultrafine particles (Sioutas, 1999; Demokritou et al., 2002). Creating a supersaturation region is necessary for activating particle growth, as it can provide a warm and humid output flow. Hering and Stolzenburg (2005) introduced a mixing method for water-based condensational growth in laminar flow. In short, due to the high diffusivity of the water vapor, the system uses a warm, wet wall growth region to create the supersaturation necessary for particle activation and growth. The laminar flow provides welldefined saturation profiles. The system is capable of activating particles as small as 3 nm and has provided the basis for a line of water-based condensation particle counters (Hering et al., 2005; Iida et al., 2008; Kupc et al., 2013). All these condensational growth methods (herein referred to as the original approach) were employed until (Hering et al., 2014) provided a new moderator concept of condensational growth for decreasing the amounts of added heat and water vapor. The detection efficiency of condensation particle counters (CPC) is normally enhanced by increasing the temperature difference between the condenser and the initiator sections € ja € et al., 2006; Kuang (Hermann and Wiedensohler, 2001; Peta et al., 2012; Barmpounis et al., 2018). Enhancing the temperature difference increases the degree of supersaturation in the growth tube, which in turn increases the activation probability of the smaller particles (Mordas et al., 2012). For the laminar flow CPC, the supersaturation profile in the growth tube is a non-uniform spatial distribution with values ranging from 1 to the maximum determined by the temperature of the condenser and initiator sections. Temperature difference is a parameter for controlling the degree of supersaturation and the activation size, but as the relevant parametric analysis has not been done, it is difficult to find suitable parameters of ultrafine particle condensed growth conditions for a controlled design. To realize the accurate measurement of nanoparticles and to accurately control supersaturation, a series of parametric analyses and systematic comparisons of the original twostage operating temperature and newer three-stage
operating temperature designs were simulated using COMSOL. The relevant verification experiments were done as well.
1.
Theory and methods
1.1.
Activation size theory
The supersaturation S is defined as the ratio of the partial pressure of the condensing vapor, Pva (Pa) to its equilibrium vapor pressure Psat;T (Pa) at the flow temperature T (K): S ¼ Pva Psat;T
(1)
The smaller the particle is, the higher the supersaturation required to activate growth. This is due to the Kelvin effect, which associates the equilibrium vapor pressure to the diameter of a droplet composed of that condensed vapor. The equilibrium vapor pressure over a droplet is higher than over a flat surface because of the surface tension. The Kelvin effect is described asDk;va , Dk;va ¼ ð4ss Mw Þ
rl Rg TlnS
(2)
where ss (N/m), Mw (kg/mol), and rl (kg/m3) are the surface tension, molecular weight, and the liquid density of the condensing species, respectively; Rg (J/(mol*K)) is the universal gas constant, and T (K) is the absolute temperature. Dk;va is a property of the condensing species equal to the diameter of a droplet in equilibrium with its vapor at saturation ratio S and temperature T. The value is the same as the activation diameter for the case of a particle that is wetted by but insoluble in the condensing vapor. Thus, a particle composed of a material that is not wetted by the condensing vapor will have a larger activation diameter than Dk;va . For soluble particles, the equilibrium vapor pressure becomes lower due to the condensate covering the particle surface, and the critical diameter required for growth is smaller.
1.2.
Heat and mass transfer theory
The saturation profiles throughout the condensing growth tube depend on the temperature, T (K), and the vapor part pressure Pva (Pa) of the position. Fluid flow through a cylindrical growth tube is described by the energy equation of a Newtonian fluid. The heat transfer equation is described by equation (3), rCp
vT vT vq vT vT 1 v vT 1 v2 T v2 T þ vr þ þ vz ¼k r þ 2 2þ 2 vt vr r vq vz r vr vr r vq vz
þ mfv (3) q represents the angle between a projected line in the axial plane and the positive x axis in a cylindrical coordinate system and z represents the axial position. The particle flow is assumed to be an incompressible Newtonian fluid with a fully developed parabolic flow profile: r2 vz ðrÞ ¼ v0 1 2 R
(4)
v0 (m/s), r (mm), and R (mm) represent initial velocity, radial
Please cite this article as: Bian, J et al., Simulation of three-stage operating temperature for supersaturation water-based condensational growth tube, Journal of Environmental Sciences, https://doi.org/10.1016/j.jes.2019.12.007
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position, and growth tube radius respectively. Axial thermal diffusion and other second-order effects such as Stefan flow are ignored. If the above assumptions are met, then equation (3) is simplified as a one-dimensional heat transfer partial differential equation of steady laminar flow: r2 vT 1 v vT v2 T ¼ Dth r þ 2 v0 1 2 vz r vr vr vz R
(5)
R (mm) is the radius of the growth tube; Dth ¼ k=ðrCp Þ is the thermal diffusivity of the flow gas, and Cp (J/(kg*K)) represents heat capacity. In a similar way, the partial differential equation for partial vapor pressure Pva is described as r2 vPva 1 v vPva v2 Pva r ¼ Dva þ v0 1 2 2 r vr vz vr vz R
(6)
where, Dva ( cm2 =s) is the mass diffusivity of the vapor. The boundary conditions for the partial differential equation are based on the temperature setting of the growth tube: Inlet conditions of the growth tube: Tðr; 0Þ ¼ T0 , Pva ðr; 0Þ ¼ P0 ; Wall conditions of the growth tube: TðR;zÞ ¼ Tw ,Pva ðR;zÞ ¼ Pw . The inlet profiles of vapor pressure are assumed to be uniform; at the growth tube wall, the vapor is assumed to be saturated and the particle concentration equal to zero. The entering temperature profile and wall temperature are assumed to be uniform. Fluid properties evaluated at a mean temperature are treated as constants over the domain.
1.3. Two- and three-stage operating temperature principle Fig. 1b illustrates the three-stage operating temperature method using a moderated, warm-walled laminar flow water condensation growth tube. The system consists of cool-walled followed by warm-walled and cool-walled regions, the conditioner, initiator, and moderator, respectively. All regions have wetted walls. As the laminar flow passes from the cooler conditioner into the warm, wet-walled initiator section and the cool moderator section, both water vapor and heat diffuse into the flow from the walls. Because of its higher diffusivity, the water transport is more rapid, creating a region of vapor supersaturation. The particle growth occurs in the initiator and moderator regions, and the water vapor from the initiator section provides the water vapor for particle activation. The moderator section provides enough distance for growth. In other words, condensational growth continues in the cooler moderator stage, and this stage removes both water vapor and heat while maintaining supersaturated conditions. In Fig. 1a, the two-stage operating temperatures consist of a cool-walled conditioner followed by a warm-walled growth region. All regions have wetted walls.
1.4.
Evaluation method for numerical modeling
Fluid flow through the cylindrical growth tube is simplified as a 2-D axial symmetric model, where r is the radial position,
3
and z is the axial position. Temperature, humidity and vapor pressure were calculated using COMSOL Multiphysics. The cylindrical geometry is modeled in two dimensions. Physical fields such as laminar flow, heat transfer in moist air and moisture transport in the air were coupled in order to simulate the variation tendencies of saturation and temperature. The flow was assumed to be parabolic; thus, inlet flow was regarded as the Laminar flow in the COMSOL. In the calculation by COMSOL Multiphysics, heat transfer in moist air and moisture transport in the air are used instead of the equations of heat and mass transfer. In the physical field of Heat transfer in moist air, the temperature of the inlet flow is 5 C, the tube wall was treated as a temperature boundary, and the wall temperature was set for our requirement that the initial temperature of the domain equals 5 C, thus the inlet condition temperature T0 and the wall condition temperature Tw of the growth tube are constant. In the physical field of moisture transport in the air, the humidity of the inlet flow was set at 95% RH. The tube wall was treated as a humidity boundary; the wall was set at 100% RH, and the initial humidity of the tube domain was equal to 50% RH. In this way, the inlet condition water vapor P0 and the wall condition water vapor Pw of the growth tube are constant. The convection-diffusion equation was solved to calculate the temperature and supersaturation profile. At the same time, the activation diameter from the Kelvin effect was described. The calculations assumed a water vapor mass diffusivity ofDva ¼ 0:251 cm2 =s, and a thermal diffusivity ofDth ¼ 0:215 cm2 =sec.
2.
Results and discussion
2.1.
Saturation and temperature profiles
Fig. 2 shows the maximum values of the supersaturation spatial distribution for two and three operating temperatures; there is an obvious change for the three operating temperatures condition. The temperature difference between the initiator and moderator sections led to the variation in the boundary of the supersaturation profile. In Fig. 2a, the temperature difference between the initiator and moderator sections is zero; the boundary is smooth, and the maximum degree of supersaturation is 2.93. In Fig. 2b, the temperature difference between the initiator and moderator sections is 40 C; another supersaturation region appears, but the maximum value of the second supersaturation region is far below the value of 2.93, and the position of the maximum value is the same as in the two-stage operating temperature design. Thus, the operating temperature only slightly affected the saturation profile of the moderator section, and did not affect the position of the maximum value. Fig. 3 compares centerline saturation and centerline dew temperatures for the growth tubes employing two and three operating temperatures. Three operating temperatures decreased the dew temperature of the exit but maintained the maximum peak supersaturation. Therefore, the minimum activation size was constant. As shown in Fig. 3a, a 5 C, 95% RH flow is introduced into a 10 C conditioner followed by 65 C of the initiator and 65 C moderator growth region, or into a 10 C conditioner followed by 65 C of the initiator and
Please cite this article as: Bian, J et al., Simulation of three-stage operating temperature for supersaturation water-based condensational growth tube, Journal of Environmental Sciences, https://doi.org/10.1016/j.jes.2019.12.007
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Fig. 1 e Flow carries particles from the conditioner into an initiator section with a warm, wetted wall, followed by a cooler moderator section. This setup is termed the three-stage operating temperature design; the temperatures of the initiator and moderator sections are equal for the two-stage operating temperature design. The lengths of conditioner, initiator, and moderator are 154 mm, 76 mm, and 100 mm, respectively. The diameters of the two different condensation growth tubes are both 4.6 mm.
Fig. 2 e Supersaturation spatial distribution at (a) two operating temperatures (10 C and 65 C) and (b) three operating temperatures (10 C, 65 C, and 25 C) with laminar flow at 5 C, 95% RH, and 1.5 L/min flow rate entering the growth tube. moderator with wall temperatures of 10 C, 15 C, 20 C, 25 C, or 30 C. The saturation S is a function of the non-dimensional parameter z/z0, where z is the axial distance from the inlet of the initiator section, and z0 is defined as the ratio of the flow Q (L/min) to the water vapor diffusion constant Dva (cm2/sec): z0 ¼ Q=Dva
(7)
For water vapor diffusion and an inlet flow of 1.5 L/min, z0 was approximately 1 m for the cylindrical geometry. The supersaturation profile along the centerline in the tube was
not sensitive to the wall operating temperature of the downstream region. All trajectories demonstrated the same maximum value of supersaturation. Moreover, along the centerline this maximum occurs at an axial position of 0.06 z0, nearly at the initiator exit. The delay of trajectories is due to the time required for vapor to be transported from the walls to the centerline. During the flow into the moderator section, water vapor is removed by the cold wall. The downstream values of saturation for five operating temperatures were within 10%. For the same inlet and wall conditions, the dew temperature is shown in Fig. 3b. It is obvious
Please cite this article as: Bian, J et al., Simulation of three-stage operating temperature for supersaturation water-based condensational growth tube, Journal of Environmental Sciences, https://doi.org/10.1016/j.jes.2019.12.007
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Fig. 3 e (a) Saturation and (b) dew temperature at the centerline of a laminar flow at 5 C and 95% RH entering the growth tube with different wall temperatures.
that the dew temperature of the three-stage operating temperature system decreased by a larger margin than with the two operating temperatures. When the moderator temperature was changed from 10 C to 30 C for three operating temperatures, the dew temperature at the exit was below 35 C at all times. However, the dew temperature in the twostage operating temperature system was 52 C. Therefore, the dew temperature at the exit can be adjusted by changing the moderator temperature. Fig. 4 illustrates the variation in the saturation ratio, temperature profiles, and water vapor pressure profiles for two or three operating temperatures as a specific case. The temperature of the inlet flow is offset at 5 C, and the RH is 95%. The respective temperatures of the conditioner, initiator, and moderator sections are 10 C, 65 C, and 65 C in the two-stage operating temperature design and are 10 C, 65 C, and 25 C in the three-stage operating temperature design. Saturation, temperature, and water vapor pressure are shown along four different trajectories from the centerline (r/R0 ¼ 0) to near the edge of the tube (r/R0 ¼ 0.75, where R0 is the growth tube radius). In Fig. 4a, it is obvious that the peak saturation is uniform at all radial positions, whether for two or three operating temperatures. Both the supersaturation and the temperature followed nearly identical tracks until reaching the peak saturation. Thus, the minimum activation size of a particle and the ideal size (where the particle size is large enough to be easily detected by light scattering) were similar for two and three operating temperatures. Because of the first order, the droplet growth depends on the supersaturation; one expects similar droplet growth.
Fig. 4b, c shows that the temperature and water vapor pressure in the moderator section with three operating temperatures were lower than those with two temperatures. With two operating temperatures, the temperature along each trajectory was near the temperature of the initiator section. However, with the three-stage operating temperature design, the temperature increases to a value below the temperature of the initiator section and then slowly cools. In Fig. 4b, when the three-stage operating temperature design (here 10 C, 65 C, and 25 C) is selected, the maximum centerline temperature is about 27 C. The temperature at 0.5 R0 remains below 30 C during the entire time. In contrast, with two operating temperatures, the temperature of the flow continues to increase after reaching the peak supersaturation, with the temperature between 58 C and 62 C at the exit. As shown in Fig. 4c, the three-stage operating temperature design reduced the water vapor content in the moderator section. With the two-stage operating temperature design, the water vapor is continually added to the flow throughout the growth region. In contrast, with the three-stage operating temperature design, water is added to the flow only throughout the initiator section. Some of the water vapor is also removed in the moderator section. The water vapor content can be reduced further by setting a cooler wall temperature for the moderator section.
2.1.1.
Flow rate effect
The saturation region will move when the inlet flow rate changes. As shown in Fig. 5, as the inlet flow rate was adjusted from 0.6 to 2.0 L/min (the temperature difference was 55 C,
Please cite this article as: Bian, J et al., Simulation of three-stage operating temperature for supersaturation water-based condensational growth tube, Journal of Environmental Sciences, https://doi.org/10.1016/j.jes.2019.12.007
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Fig. 4 e Profiles of the (a) saturation, (b) temperature, and (c) water vapor content for laminar flow with 5 C, 95% RH entering two-stage operating temperature (10 C and 65 C) and three-stage operating temperature (10 C, 65 C, and 25 C) growth tubes. Dashed lines line represent two operating temperatures, and solid lines indicate three operating temperatures.
Fig. 5 e The centerline supersaturation profile with laminar flow at 5 C and 95% RH entering the growth tube calculated at three operating temperatures of 10 C, 65 C, and 25 C for different inlet flow rates.
Please cite this article as: Bian, J et al., Simulation of three-stage operating temperature for supersaturation water-based condensational growth tube, Journal of Environmental Sciences, https://doi.org/10.1016/j.jes.2019.12.007
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and the operating temperatures were 10 C, 65 C, and 25 C), the peak supersaturation moved from 0.0027 z0 to 0.08 z0, and the saturation regions were closer to the exit because of the increase in the flow rate. At the same time, the peak supersaturation increased by 0.3 as the flow rate increased from 0.6 to 2.0 L/min. However, the growth time for droplets and the final droplet size were decreased by 40%. Therefore, the increase of the inlet flow rate made the growth of droplets to a detectable size more difficult. In order to attain the ideal growth size, there should be a perfect match between inlet flow rate and the length of the growth tube when the diameter of the growth tube is kept constant.
2.1.2.
Operating temperature effect
Temperature difference is an important factor for controlling supersaturation. The greater the temperature difference, the higher the degree of supersaturation. At the same time, shifting the temperature difference window to the left also causes higher supersaturation. As seen in Fig. 6a, peak supersaturation becomes greater as the temperature difference is changed from 65 C to 90 C, and the greater the temperature difference, the more rapid the increase of peak supersaturation. In Fig. 6b, the temperature difference between the condenser and the initiator was kept constant at 90 C, the temperature difference window was varied by changing the condenser temperature from 1 C to 9 C and the initiator temperature from 91 C to 99 C. As shown, the peak supersaturation along the centerline for the five temperature
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windows increases with the shifting of the temperature difference window to the left.
2.2.
Minimum activation size
The minimum activation size is related to the peak supersaturation level. As shown in equation (2), minimum activation size is related to the condensing vapor species, temperature, and saturation. Water vapor is selected as the condensing vapor in this calculation. Fig. 7 illustrates part of the Kelvin diameter contour map for a laminar flow with 5 C, 95% RH entering a two-stage operating temperature system (10 C, 95 C) growth tube. The temperature difference is 85 C, and the inlet flow rate is 1.5 L/min. The minimum activation size is about 1 nm near the centerline. The smaller the activation size, the nearer the position to the centerline. The aerosol flow near the centerline will contribute to the activation efficiency.
2.2.1.
Effect of flow rate
Activation size becomes smaller as the inlet flow rate increases, though the impact varies depending on the temperature difference. As shown in Fig. 8, when the flow increased from 1.0 to 3.5 L/min, the minimum activation size decreased from 1.75 to 1.45 nm for a temperature difference of 70 C. However, as the temperature difference increased, the impact on the minimum activation size became weaker. There was no impact of temperature difference at 90 C when the flow
Fig. 6 e Centerline saturation comparison of (a) different temperature differences and (b) shifting the temperature window to the left for laminar flow at 5 C, 95% RH entering two-stage operating temperature and three-stage operating temperature growth tubes. Please cite this article as: Bian, J et al., Simulation of three-stage operating temperature for supersaturation water-based condensational growth tube, Journal of Environmental Sciences, https://doi.org/10.1016/j.jes.2019.12.007
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Fig. 7 e Kelvin diameter distribution contour map for laminar flow with 5 C, 95% RH entering a two-stage operating temperature (10 C, 95 C) growth tube.
Fig. 8 e Minimum activation size as a function of inlet flow rate calculated for laminar flow at 5 C, 95% RH entering a threestage operating temperature (initiator temperature ¼ 95 C) growth tube.
rate increased. At the same time, the supersaturation spatial distribution moves closer to the exit position due to the increase in the flow rate. In addition, the growth time for droplets will be shorter, and final size will be smaller. Thus, in order to attain the ideal growth size, there should be a suitable selection between inlet flow rate and activation size (i.e., temperature difference).
2.2.2.
Effect of temperature difference
Peak supersaturation will be higher as the temperature difference becomes larger, and the activation size will be smaller. Thus, changing the temperature difference can be employed for controlling the minimum activation size. Fig. 9 shows that the minimum activation size decreases with increasing temperature difference. The impact becomes less
Fig. 9 e Minimum activation size and peak supersaturation as functions of temperature difference. The red line is the function for minimum activation size and the blue line is for the peak supersaturation. The inlet flow rate is 1.5 L/min with 95% RH. Please cite this article as: Bian, J et al., Simulation of three-stage operating temperature for supersaturation water-based condensational growth tube, Journal of Environmental Sciences, https://doi.org/10.1016/j.jes.2019.12.007
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Fig. 10 e Comparison of minimum activation size for various temperature difference windows. The temperature difference from top to bottom is constant at 50 C, 60 C, 70 C, 80 C and 90 C.
as the temperature difference increases. A temperature difference of 90 C can activate a 1 nm particle to grow to a detectable size. However, the greater the temperature difference, the lower the reduction of minimum activation size. If the requirement for detection limitation is 2 nm, a temperature difference of 90 C is not required, as a temperature difference of 55 C is sufficient. Thus, the difficulty in using a high temperature difference is circumvented. As the temperature difference increases, the peak supersaturation also increases as a convex curve. At the same time, the activation size is related to the temperature and saturation for a specific condensing vapor species. As supersaturation is temperature dependent, the selection of temperature is an important requirement.
2.2.3.
Effect of temperature difference window
The movement of the temperature difference window has a certain impact on the minimum activation size. The temperature difference also has varying degrees of effect. As seen in Fig. 10, the minimum activation size becomes smaller by shifting the temperature difference window to the left. The decrease is related to the temperature difference; the minimum activation decreased by 0.064 nm, 0.06 nm, 0.58 nm, 0.034 nm, and 0.04 nm, respectively, for temperature difference windows left-shifted to 50 C, 60 C, 70 C, 80 C, and 90 C.The effect on the decrease of minimum activation size is more apparent when the temperature difference is 70 C
(1e71 C), and the minimum activation size is smaller than for a temperature difference window of 80 C (1e81 C). The minimum activation size dropped to 1.2 nm with conditioner and initiator temperatures of 1 C and 71 C. And the activation size is better than 2.5 nm of water-base CPC (model 3788, TSI, USA).
2.3.
Experimental verification
2.3.1.
Experimental setup
The experimental setup was constructed based on a standard particle generator (Met One model 255 Gen) and an aerodynamic particle sizer (APS, model 3321 TSI, USA) as shown in Fig. 11. Standard particle generator mixes sodium chloride particles with deionized water and atomizes the mixture to obtain aerosol particles. The aerosol particles flow into the built-in charger of the generator for charging, and are then classified by the Differential Mobility Analyzers (DMA, model 3082 TSI, USA) to generate monodispersed particles of selected sizes. Two flowmeters (model 4199 TSI, USA) are necessary to control the flow rate for clean air supply and for flow removal of remaining particles. The temperature control for the conditioner and initiator are based on semiconductor refrigerating and heater units. The output droplet size distributions were measured using an aerodynamic particle sizer (APS). This was done by sampling directly into the 1.0 L/min APS aerosol sample flow rate.
Fig. 11 e Experimental setup for varying operating temperature and flow rate. Please cite this article as: Bian, J et al., Simulation of three-stage operating temperature for supersaturation water-based condensational growth tube, Journal of Environmental Sciences, https://doi.org/10.1016/j.jes.2019.12.007
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amount of water vapor available for diffusion. Once the particles have been activated, a two-temperature difference can provide the same growth environment except for water vapor content, so the larger temperature difference results in a larger droplet size than with the lower temperature difference. The movement of the temperature difference window results in an equivalent median diameter distribution, but the concentration is different. The water vapor content may also be a reason, because shifting the temperature difference window to the left will result in a larger water vapor content. When the particle concentration is large enough, the water vapor dissipation will hinder growth of the particles. Fig. 12 e Output droplet size distributions measured by an aerodynamic particle sizer for varying flow rates at the three operating temperatures of 10 C, 65 C, and 25 C.
3.
Conclusions
The present study comprises a systematic comparison of twostage and three-stage operating temperature methods for growth tubes related to decreasing the temperature and water vapor content at the exit. Some effective parameters such as flow rate and temperature difference are analyzed for obtaining the ideal activation size and final growth size. The temperature difference is defined as the difference between the condenser and initiator temperatures. The key results were as follows:
Fig. 13 e Output droplet size distributions measured by aerodynamic particle size for varying temperature differences and temperature difference windows in the three-stage operating temperature design.
2.3.2.
Flow rate effect
Fig. 12 compares the droplet sizes for different inlet flow rates using the three operating temperatures of 10 C, 65 C, and 25 C. The data show similar behavior for flow rates varying by a factor of 2.5 (from 0.6 to 1.5 L/min), with exiting droplet diameters changing by about 43% (from 3.2 to 1.8 mm). A lower flow rate provides more effective length for droplet growth, and thus promotes larger droplet growth. Both increasing the length of the growth tube and providing lower inlet flow promote larger droplet growth. This corresponds to the simulations of flow rate. A higher flow rate results in the movement of the supersaturation region toward the exit, so the particle activation will occur later, and the growth time will be less.
2.3.3.
Operating temperature effect
Fig. 13 illustrates the effect of temperature difference and temperature difference window on final droplet size. The temperature difference window is insensitive to the final droplet size, but a higher temperature difference provides a larger size. As the data show, at a constant moderator temperature of 25 C, but with the initiator operated at 70 C and 60 C, the resulting droplet size is shifted to a smaller particle size, from 2.3 to 2.0 mm median diameter. The main reason for this is that a larger temperature difference leads to a higher
(1) The parametric analysis and systematic comparison of the original two-stage operating temperature and newer three-stage operating temperature designs confirm that the three-stage operating temperature design results in a lower temperature and water vapor content at the exit but does not change the peak supersaturation level, and thus, this design is a good choice for particle detection and collection. (2) The change in the flow rate results in the movement of the supersaturation spatial distribution and a decrease in the minimum activation size. When the flow rate increased from 0.6 to 2.0 L/min, the peak supersaturation increased by 0.3, but the peak supersaturation moved from 0.0027 z0 to 0.08 z0 (i.e., the growth time and the final size both decreased by 40%). In order to attain the ideal growth size, there should be a perfect match between inlet flow rate and the length of the growth tube. (3) Enhancing the temperature difference can attain higher supersaturation and smaller activation size. Further development of shifting the temperature difference window left also contributed to the supersaturation and activation size. The effect for the decrease in the minimum activation size is greater when the temperature difference is 70 C, compared with 50 C, 60 C, 80 C, and 90 C; the minimum activation size diminishes to 1.2 nm when setting the respective conditioner and initiator temperatures to 1 C and 71 C. (4) Experiments with varying flow rates and operating temperatures for comparing the final growth size show that with flow rates varying by a factor of 2.5 (from 0.6 to 1.5 L/min), final size decreased by 43% (from 3.2 to 1.8 mm). The results were consistent with the theoretical analysis. Lower flow rate results in larger final size, and
Please cite this article as: Bian, J et al., Simulation of three-stage operating temperature for supersaturation water-based condensational growth tube, Journal of Environmental Sciences, https://doi.org/10.1016/j.jes.2019.12.007
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larger temperature difference or shifting the temperature difference to the left provide more water vapor for particle growth. This research concerning parametric analysis and systematic comparison can provide guidance for specific systems design. The next step is to construct systems and study the condensational growth characteristics of nanoparticles through condensation growth tubes for different levels of supersaturation.
Conflict of interest The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper.
Acknowledgement
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This research was supported by Natural Science Foundation of China (No. 91544218), the National Key Research and Development Program of China (No. 2016YFC0201001), the Science and Technological Fund of Anhui Province for Outstanding Youth (1808085J19), the Science and Technological Fund of Anhui Province (1908085MD114), and The CASHIPS Director's Fund, Grant NO. YZJJ2019QN1.
Appendix A. Supplementary data Supplementary data to this article can be found online at https://doi.org/10.1016/j.jes.2019.12.007.
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