Quantifying the effects of operational parameters on ...

Journal of Aerosol Science 106 (2017) 11–23

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Quantifying the effects of operational parameters on the counting efficiency of a condensation particle counter using response surface Design of Experiments (DoE) Longfei Chen, Yuegang Ma, Yuejie Guo, Cuiqi Zhang, Zhirong Liang, Xin Zhang

MARK

⁎

School of Energy and Power Engineering, Beihang University, Beijing, China

AR TI CLE I NF O

AB S T R A CT

Keywords: Condensation particle counter (CPC) Cut-off size Design of Experiment (DoE) Response surface design (RSD)

The size-resolved counting efficiency of an in-house ultrafine condensation particle counter (IUCPC) being challenged by sodium chloride (NaCl) particles was experimentally determined with a reference electrometer TSI 3068B. The influence of several operational parameters including the saturator temperature (35 to 45 ℃), the condenser temperature (10 to 25 ℃), the capillary sample flow rate (30 to 60 mL/min) and the total flow rate (300 to 400 mL/min) on the cut-off size D50 (particle diameter with 50% counting efficiency) was investigated using response surface design of experiments (DoE). Thirty one test points with varying operational conditions including 7 replicated test points were performed to evaluate the primary effects of operational parameters and their interactive effects on the cut-off size D50 of the IUCPC. The results indicated that the saturator temperature and the condenser temperature had a greater impact on the cut-off size D50 than the capillary flow rate and the total flow rate. CFD simulation demonstrated that high capillary flow rate in the IUCPC could induce a wider diffusion zone for the core aerosol flow, making more particles enter low supersaturation area near the wall. According to the ANOVA (analysis of variance), the most influential factor for the cut-off size D50 was the condenser temperature, followed by the saturator temperature, the total flow rate and the capillary flow rate. Some interactive effects from combinations of factors on the D50 are also significant. R-squared value of 0.9176 implied that the ultimate model for the IUCPC D50 consistently fits the experimental results.

1. Introduction Condensation particle counters (CPCs) are widely used to detect atmospheric and engine exhaust nanoparticle number concentration (Biswas, Verma, Schauer & Sioutas, 2009; Hata, 2013; Sipilä et al., 2008). Nano-scale particles are enlarged in a region of supersaturated vapor to several micrometers by condensing working fluid onto particles, thus they can be detected by optical means. There are two primary types of CPCs, laminar type and mixing type, both commercially available. A laminar type CPC comprises of a saturator, a condenser and an optical particle counter (OPC). Sufficient heat input and residence time of working fluid

Abbreviations: A, represent saturator temperature in model [°C]; B, represent condenser temperature in model [°C]; C, represent capillary flow rate in model [mL/ min]; D, represent total flow rate in model [mL/min]; D0, particle diameter with 0% counting efficiency [nm]; D50, particle diameter with 50% counting efficiency [nm]; D100, particle diameter with 100% counting efficiency [nm]; Q1, capillary flow rate [mL/min]; Q2, total flow rate [mL/min]; Ts, saturator temperature [°C]; Tc, condenser temperature [°C]; ANOVA, Analysis of Variance; DoE, design of experiments; OPC, optical particle counter; IUCPC, in-house ultrafine condensation particle counter; RSD, response surface design ⁎ Corresponding author. E-mail address: [email protected] (X. Zhang). http://dx.doi.org/10.1016/j.jaerosci.2016.12.005 Received 7 June 2016; Received in revised form 27 November 2016; Accepted 19 December 2016 Available online 29 December 2016 0021-8502/ © 2016 Elsevier Ltd. All rights reserved.

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enable the saturation in the saturator and the vapor is carried by the carrier gas to the condenser, where the vapor achieves a supersaturation state because of cooling (alcohol-based CPC). In mixing type CPCs, a hot saturated flow is mixed with a cooler sample flow. The mixing type CPC can be utilized to detect sub-3 nm ultrafine particles in atmospheric studies (Mordas, Sipilä & Kulmala, 2008). Iida, Stolzenburg, and McMurry (2009) proposed a novel method of successively connecting a low vapor pressure working fluid based CPC with a butanol-based CPC to detect sub-3nm nanoparticles, and this two-stage method has been further investigated by other researchers (Jiang, Chen, Kuang, Attoui & McMurry, 2011; Kuang, Chen, McMurry & Wang, 2012; Magnusson, Anisimov & Koropchak, 2010). The counting efficiency and the detection limit (cut-off size) are consistently the most critical indicators for evaluating the CPC performance. The cut-off size D50 is essentially the diameter where 50% of sampled particles are activated and detected. A number of studies focusing on the counting efficiencies of CPCs use D50 as a key performance parameter. UN-ECE Regulation 83 for light duty vehicles also specifies that D50 is a critical parameter of the compliant CPCs, which is 23 nm under EU 6 phase. It is primarily determined by particle properties, working fluid, the CPC structure and the working conditions. The contact angle between the working fluid and tested particles is a primary cause that renders CPC to show different counting efficiency toward different type of particles. Researchers used commercial CPCs to measure the number concentration of ultrafine particles with different chemical compositions, and the counting efficiency or cut-off size for different particles varied with each other (Hakala, Manninen, Petäjä & Sipilä, 2013; Liu, Kaufman, Osmondson, Sem, Quant & Oberreit, 2006; Mamakos, Giechaskiel & Drossinos, 2013; Mordas, Manninen, Petäjä, Aalto, Hämeri & Kulmala, 2008; X. Wang, Caldow, Sem, Hama & Sakurai, 2010). Giechaskiel, Wang, Gilliland, and Drossinos (2011) theoretically investigated the effect of particle chemical composition on the counting efficiency of a commercial n-butanol CPC, and found that the dependence of the counting efficiency on particle chemical composition was pronounced at low CPC temperature differences (the temperature difference between the saturator and the condenser. Kuang et al. (2012) found that for a given particle composition and size, negatively charged particles were preferentially detected compared to positively charged particles. Counting efficiencies of different type of CPCs from the same or different manufactures differed from each other when measuring the same test aerosol simultaneously (Alofs, Lutrus, Hagen, Sem & Blesener, 1995; Giechaskiel et al., 2009). Previous researchers focused on designing in-house CPCs instead of commercial CPCs to meet required specifications or to have more control on operational parameters. Collings, Rongchai, and Symonds (2014) proposed a novel CPC which operate at high temperature to measure only solid particles from engine exhaust directly, with several diffusion pump oils being chosen as working fluids. Both simulated and experimental results reveal that this CPC was capable of detecting particles with a diameter down to 10 nm when the instrument was challenged with ambient, NaCl and diesel soot particles. Ito, Seto, Otani, and Sakurai (2011) developed an improved version of the mixing type CPC equipped with a newly designed evaporator system, facilitating the control of the saturation ratio by controlling the operational parameters such as flow rates and temperatures independently. Under various supersaturation conditions (4.65, 5.41 and 6.19), particles size resolved counting efficiencies were also presented while a calibrated TSI 3775 CPC was used as a reference instrument. The temperatures of the condenser and the saturator (or conditioner and growth tube for water-based CPC) are regarded as the key factors influencing the CPC cut-off size (Kim, Iida, Kuromiya, Seto, Higashi & Otani, 2014; Mordas, Manninen, et al., 2008; Mordas, Sipilä, et al., 2008; Petäjä, Mordas, Manninen, Aalto, Hämeri & Kulmala, 2006). Baltzer, Onel, Weiss, and Seipenbusch (2014) presented a novel construction CPC style which set the saturator vertically in line with the condenser and continuously cycle working fluid through a helical groove. D50 decreased sharply from 25 nm to 5 nm when the temperature difference increased from 19 ℃ to 29 ℃ with constant saturator temperature of 39 ℃, whilst the D50 altered little when the temperature difference further increased. A mixing type CPC proposed by Wang, McNeill, Collins, and Flagan (2002) has been further investigated by other researchers. The counting efficiency of this type CPC showed a similar behavior to laminar flow-type CPCs: D50 decreased from 8.5 nm to 6.1 nm when the temperature differences varied from 25 ℃ to 29 ℃ (Wehner, Siebert, Hermann, Ditas & Wiedensohler, 2011). Other working conditions including flow rates and pressures on the cut-off sizes were also investigated by previous researchers. D50 increased when the inlet pressure decreased (Takegawa & Sakurai, 2011). Stratmann, Herrmann, Petäjä, and Kulmala (2010) used Fluent to theoretically investigate the influencing factors of counting efficiency and found that for a polydisperse aerosol, the counting efficiency of small particles could be influenced by the number concentration of large particles due to vapor depletion. Lewis & Hering (2013) found that the concentration effects for water-based systems can be mitigated through the use of smaller tube diameters. Banse, Esfeld, Hermann, Sierau, and Wiedensohler (2001) studied the performance of a TSI 3762, the cut-off size D50 decreased from 10.5 nm to 8.4 nm when the flow rate declined from 3 L/min to 1.5 L/min with temperature difference being 20℃. The existing research has demonstrated the relationship between the responses (the cut-off size, the counting efficiency) and operational parameters (e.g. saturator temperature, condenser temperature, pressure and flow rate), yet it is time consuming and costly to thoroughly investigate the effects of all the primary parameters on the D50. The effect of individual parameter on the counting efficiency could be evaluated by varying the parameter only, however, the interactive effects between parameters on the counting efficiency have not been considered. To this end, an attempt was made to establish a quadratic model linking individual CPC operational parameter and the cut-off size D50 to systematically explore the individual effects and the interactive effects of those parameters on the D50. DoE (Design of Experiments) is a useful technique to explore the relationships between influencing factors and response value, and it has been used for a wide range of research fields (Chen, Liu, Sun & Huo, 2015; Chen, Zhang, Gong & Liang, 2015). In this study, the response surface design (RSD) DoE, which takes curvature effects into account, was adopted to build the model for predicting the D50 of an in-house ultrafine condensation particle counter (IUCPC) based on four different parameters (saturator temperature, condenser temperature, total flow rate and capillary flow rate). The combination of saturator temperature 12

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Fig. 1. Schematic diagram of experimental set-up.

and condenser temperature determines the supersaturation extent inside the condenser, whilst the total flow rate and the capillary flow rate governs the aerosol residence time and particle number inside the condenser. Monodisperse sodium chloride particles were generated by evaporation and condensation method to experimentally determine the cut-off size D50 as the response of the DoE. 2. Experiment apparatus and methodology 2.1. Experimental Fig. 1 shows the setup for calibrating the IUCPC performance. NaCl particles were generated using the evaporation-condensation method (Jiang, Chen, et al., 2011). A ceramic boat loaded with NaCl powders was placed in a high temperature ceramic tube furnace. Throughout the experiment, the tube furnace temperature was maintained at 650 ℃. NaCl rich vapor stream was produced by passing particle-free air through the furnace. Polydisperse NaCl nanoparticles were formed when particle-free cooling air was mixed with the hot vapor, and then large particles were removed by an impactor with 1 µm cut-off size to prevent accumulation and deposition inside the system. Sampled particles entered a neutralizer TSI 3087 to form particles with stationary bipolar charge distribution. The flow then passes a TSI DMA 3085, a particle size classifier, to obtain monodisperse negatively charged NaCl nanoparticles. The DMA was operated in an open-loop with the flow rate of both sheath and excess flows being 13 L/min. The selected monodisperse particles were then transported to the IUCPC and an aerosol electrometer TSI 3068B, which is regarded as a reference instrument. The IUCPC counting efficiency at a given particle size is equal to the ratio of the particle concentration measured by IUCPC to that measured by TSI 3068B. In the IUCPC, sheath gas is utilized to increase the sampling flow rate and hence reduce the particle diffusion loss, which is critical for particles in the range of 5–20 nm (Sem, 2002). The CPC comprises of three primary parts: saturator, condenser, and optical particle counter (OPC). Butanol is stored in the saturator as the working fluid while a diesel particle filter (DPF) was used which has a porous structure in the saturator to serve as a wick thus making the sheath gas fully saturated. The condenser has a 5 mm diameter and 10 cm long inner cylindrical hole, which retains a lower temperature than the saturator using a thermo-electrical device. Sheath air is saturated with butanol in the saturator, and supersaturation is achieved through cooling in the condenser. In the optical particle counter (OPC), the conjunction area of the air flow district and optical path is considered as sensitive volume. When large particle traverse this area, Mie-scattering light can be focused by lens to a photodiode, thus pulses are generated and counted. The optical particle counter (OPC) is a Huayu CLJ-E301 OPC, a sensor which is designed to detect dust particles larger than 0.3 μm. In order to achieve a higher upper limit of measurable number concentration, the inner diameter of the OPC inlet nozzle was reduced by replacing the original nozzle of the OPC with a new nozzle of smaller inner diameter so that the effective sensitivity volume was reduced to avoid coincident effects for high concentration measurements. A nozzle of 1 mm diameter is placed between the condenser and the OPC, thus constraining the particles in the center of OPC near 13

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the sensitive volume where the laser intensity remains at the highest level. During the experiments, only ‘single particle counting’ mode was adopted, thus grown particles pass the sensitive volume of the OPC individually. In terms of the inlet section, the total inlet flow with challenge particles initially flow upward through a vertical stainless pipe, then travels downward through the outer tube and filtered by a High Efficiency Particle Filter (HEPA). The filtered gas passes the saturator while only a small portion of the sample gas passes through the capillary and enters the condenser. The design of the saturator/condenser are similar to those used in the TSI 3025 CPC (Mark R. Stolzenburg & McMurry, 1991), except that the total flow rate and the sheath gas flow rate are controlled and monitored by two variable area flow meters. Three flow rates, namely, the total flow, the capillary flow, the sheath gas flow, can be adjusted by controlling two needle valves. The total flow and sheath gas flow were calibrated by a bubble flow meter (Gilibrator-2) with a resolution of 0.1 mL/min. Because the capillary is buried deeply within the plumbing, it is not easy to directly measure the pressure drop across it or the flow rate inside the capillary. The capillary flow rate was determined by taking the difference of the much larger total and sheath flows, which will inevitably impair the accuracy. Apart from the variable area flow meter, another pressure drop flow meter (SMART SENSOR AS510) with a 0.4 mm orifice was placed at the exit of the OPC to double check the total flow rate. The variable area flow meter and the pressure drop flow meter were all stable for the duration of each test point. The careful flow rate measurement for the total flow and the sheath flow would mitigate the inaccuracy of the capillary flow rate determination. The uncertainties of the counting efficiency resulted from several factors: DMA flow error, DMA sizing error, DMA resolution (the ratio of DMA classified particle mean diameter to the full width at half maximum) and the counting errors of both the electrometer and the IUCPC. The DMA flow error is smaller than 2%. The sizing error of the DMA for the working conditions (pressure, flow rate, DMA electrode voltage fluctuation) in this study corresponded to about 3%. The resolution of the DMA at the test range is about 10, which is defined as the reciprocal of the NFWHM (normalized full-width at half-maximum) (Jiang, Attoui, et al., 2011). To be more precise about the resolution, a lognormal approximation to the transfer function was adopted to calculate the mobility resolutions of the DMA, which varied from 7.17 (for particles with diameter of 3.77 nm) to 9.68 (for particles with diameter of 40 nm) (Mark R Stolzenburg & McMurry, 2008). The uncertainty of the electrometer flow is 3% for the test range, which is determined by the flow meter used (Model 4140). Thus, the uncertainty of the electrometer contributed by the flow uncertainty is also around 3%. The uncertainties of IUCPC flows were determined by the bubble flow meter (Gilibrator-2) with a resolution of 0.1 mL/min. The inlet capillary flow rate was 30–60 mL/min, and the resolution should be 0.2 mL/min because the bubble flow meter was used to calibrate the total flow and the sheath flow only. Therefore, the uncertainty of the IUCPC capillary flow is less than 1%. This analysis is valid when the variable area flow meters are constant for each test point which was the case in our study. The effects of these flow uncertainties are all included in the total uncertainty of the instruments, which turned out to be insignificant. For the electrometer, the uncertainty (6%) is the quotient of the zero drift (180#/mL) to the minimum particle concentration at the test range (3000#/mL). For the IUCPC, the uncertainty is the ratio between the maximum variation number concentration and the number concentration measured by the reference TSI 3068B electrometer, which was only several particles per mL, thus this can be ignored for all the test points with thousands of particles per mL. 2.2. Response surface design DoE Response Surface Methodology (RSM) can predict the relationship between the response and the independent variables, and is capable of optimizing the response surface function and predicting the future response (Sahu, Acharya & Meikap, 2009). In this study, the response refers to the D50 whilst the independent variables include saturator temperature, condenser temperature, total flow rate and capillary flow rate. The benefits of using DoE can be summarized as follows: firstly, DoE can not only evaluate the effect of individual parameter on the D50, also evaluate the interactive effects of two or more parameters on the D50; secondly, since all the parameters can be coded, their coefficients can directly reflect the importance of the operational parameters; thirdly, the analysis of variance (ANOVA) in DoE is a powerful tool to compare the variation of the response values within the replicated runs versus the residual (model residual) variation; fourthly, if the center points does not fit to the DoE model, a quadratic model is suggested to incorporate the curvature effects; lastly but not least, the sensitivity of the D50 to the selected operational parameters or the response characteristics of the D50 can be obtained by converting the coded equation into a sensitivity equation form, which can be used to obtain the response characteristics of the D50 by calculating the deviation from the D50 at the cubic center if one or more parameters drift from their set points. Design Expert (from Stat-Ease, Inc.) and Minitab (from Minitab Inc.), the two commonly used software packages, were utilized to conduct the response surface design DoE in this study. The results from both software turned out to be identical. Typically, response surface design DoE approach involves the following steps: firstly, designing the test points; secondly, performing the experiments according to the run order; thirdly, entering the experimental results as response values and analyzing the statistical significance and accuracy of the model and each term in the model via ANOVA (Analysis of Variance); lastly, eliminating insignificant terms and obtaining the final model with the quantification of the effects of individual and interactive parameters on the response (D50 in this case) (Vohra & Satyanarayana, 2002). The maximum temperature difference between the saturator and the condenser was set to be 35 ℃ in order to avoid homogeneous nucleation while the minimum temperature difference was set to be 10 ℃ to ensure sufficient supersaturation for activating sub30 nm particles. When the total flow rate exceeds 400 mL/min, homogeneous nucleation can occur occasionally at high temperature difference between the saturator and the condenser. Thus the maximum total flow rate was chosen at 400 mL/min. The central 14

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Table 1 Operational parameters and results for thirty one test points proposed by the DoE. CPC parameters

Point type

Tc (℃)

Ts (℃)

Q1 (mL/min)

Q2 (mL/min)

D50 (nm)

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31

1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 −1 −1 −1 −1 −1 −1 −1 −1 0 0 0 0 0 0 0

10 25 10 25 10 25 10 25 10 25 10 25 10 25 10 25 10 25 17.5 17.5 17.5 17.5 17.5 17.5 17.5 17.5 17.5 17.5 17.5 17.5 17.5

35 35 45 45 35 35 45 45 35 35 45 45 35 35 45 45 40 40 35 45 40 40 40 40 40 40 40 40 40 40 40

30 30 30 30 60 60 60 60 30 30 30 30 60 60 60 60 45 45 45 45 30 60 45 45 45 45 45 45 45 45 45

300 300 300 300 300 300 300 300 400 400 400 400 400 400 400 400 350 350 350 350 350 350 300 400 350 350 350 350 350 350 350

11.95 20.95 11.17 14.21 12.58 22.09 10.95 21.05 14.34 21.93 12.93 15.91 13.21 18.18 9.55 15.73 11.92 18.34 17.17 14.6 14.68 15.7 13.77 15 13.67 14.89 15.12 14.95 15.53 14.86 15.31

composite design is one common type of the RSD and it included corner points, axial points and a center point (corresponding to ‘1’, ‘−1’, ‘0’ in Table 1). Corner points were the combination of each operational parameter with boundary value. The inclusion of axial points allowed a model with quadratic terms to account for the curvature effect. Thirty one working conditions were pre-determined by the RSD DoE with the central point being replicated seven times to evaluate the reproducibility as shown in Table 1. Ts and Tc are the abbreviations of the saturator temperature and condenser temperature with the unit of ℃, whilst Q1 and Q2 represent the capillary flow rate and the total flow rate with the unit of mL/min. The analysis of variance (ANOVA) is a critical tool in DoE to compare the variation of the response values within the replicated runs versus the residual (model residual) variation. Furthermore, the fitness of the center points to the derived DoE model using linear and interaction terms is considered as an indication of the second degree curvature. Thus, if the center points did not fit to the DoE model, a quadratic model needed be chosen to incorporate the curvature effects (Chen, Zhang, et al., 2015). 3. Results and discussion 3.1. IUCPC D50 at different working regimes To avoid abnormal operations such as homogeneous nucleation, vapor depletion, coincident effect, preliminary tests were conducted prior to each test point using an oscilloscope and aerosol electrometer TSI 3068B. Firstly, HEPA-filtered inlet sample was used to challenge the IUCPC to rule out the possibility of homogeneous nucleation. The raw pulses from the oscilloscope were also of normal amplitude even for high aerosol flow rates, which implies the vapor amount is sufficient at all the test points to grow all the particles to optically detectable sizes. The counting efficiency derived from the electrometer can reach up to 95% for large enough particles, which further reassured that no abnormal conditions were present throughout the investigation. A fitting empirical formula adopted by (Mordas, Manninen, et al. (2008) was utilized to fit the experimental data, as follows:

η (Dp ) = 1 − e(α1− DP )/ α2 D

(1)

−D

where α1 = D0 and α2 = 50ln(2) 0 . The counting efficiency curve fitting to the experimental data was determined by using a least square error method. The D50 refers to the intersection point between the fitting curve and the horizontal line indicating 0.5 counting efficiency. An example of how to determine D50 from the experimental data (under the test condition 14) is shown in Fig. 2. The good fit suggests that our IUCPC has similar characteristics with other mature CPCs. 15

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Fig. 2. Experimental counting efficiency (square) and its fitting curve (solid) for the in-house CPC operating at condition 14 (the saturator temperature is 35 ℃, the condenser temperature is 25 ℃, the capillary flow rate is 60 mL/min, the total flow rate is 400 mL/min). The dotted dash line represents the number concentration of furnace generated NaCl particles measured by the electrometer TSI 3068B.

Experiments were conducted according to the test sequence as shown in Table 1. The experimental data of IUCPC operating at condition 14 are presented in Fig. 2, with the saturator and the condenser temperature set to 35 ℃ and 25 ℃, and the total flow rate and the sample capillary flow rate set to 400 and 60 mL/min, respectively. The counting efficiency exceeded 90% for particles larger than 30.3 nm (electrical mobility equivalent diameter) and decreased dramatically with decreasing size, reaching 50% for particles with diameter of 18.2 nm, and was below 10% for particles smaller than 13.8 nm in diameter. The number concentrations were small enough for all the test points to ensure ‘single counting’ mode of the CPC. Thus, the coincidence effect can be considered negligible. It can be noted that at small temperature difference between the saturator and the condenser (test point 2, 6, 10, 14), the D50 was much larger than other points, which is because of the low supersaturation degree. In order to evaluate the effects of the four factors on the cut-off size in a systematic way, the DoE and the associated Analysis of Variance (ANOVA) was utilized using Minitab and Design Expert. 3.2. Analysis of variance (ANOVA) of DoE 3.2.1. ANOVA of DoE DoE is capable of establishing polynomial models to explore the relationships between the factors (different operational parameters) and the response (the D50). In order to evaluate the significance and soundness of the proposed model, the analysis of variance (ANOVA) was performed using Design Experts. The ANOVA can quantitatively evaluate the significance of individual parameters and the interactive effect on the D50. A few insignificant model terms (e.g. BC, BD) with high P-values were deliberately removed to improve the significance of the DoE model. The final ANOVA results are presented in Table 2. In the AVONA table, F-value and p-value are critical indicators for assessing the significance of the DoE derived model and the Table 2 ANOVA analysis for the proposed model (A: condenser temperature in °C; B: saturator temperature in ℃; C: capillary flow rate in mL/min; D: total flow rate in mL/ min). D50

Model Linear A B C D Linear mixture AB AC AD CD Lack of fit R-Squared Adj R-Squared Adeq Precision

F value

P value

30.62 53.80 180.12 34.85 0.047 0.19 7.44 4.36 3.77 5.59 16.06 3.89 0.9176 0.8876 23.009

< 0.0001 < 0.0001 < 0.0001 < 0.0001 0.8296 0.6675 0.001 0.0486 0.0653 0.0273 0.0006 0.0508

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associated terms. These two values are originated from an F-test, in which the test statistic has an F-distribution under the null hypothesis H0. In this case, H0 states that the selected CPC operational parameter has no effect on the response value D50.The critical value 0.05 for the p value is used to determine whether the model is statistically significant or not. The p value represents the probability that the observed F-statistic or larger occurs under the H0 assumption. Basically, a small p value ( < 0.05) implies that the H0 can be rejected and the effect of the corresponding parameter is statistically significant (Zar, 2010). Even though the C and D have higher p value, some interaction terms such as AD or CD are significant terms with low p value, so C and D have to be retained in the model. The F statistic of the overall model is a ratio of two different measure of variance for the data.

F=

between−group variability within−group variability

(2)

The “between-group variability” can be calculated from Eq. 3.

∑ ni (Yi

− Y )2 /(K − 1)

(3)

Yi denotes the sample mean in the i th group, ni is the number of observations in the i th group, Y denotes the overall mean of the data, and K denotes the number of groups. The “within-group variability” can be calculated from Eq. 4.

∑ (Yij − Yi )2 /(N − K ) (4)

ij

j th

i th

Yij is the observation in the out of K groups and N is the overall sample size. The numerator is computed by measuring the variance of the means and the denominator is an average of the sample variances for each group (the variance of the seven replicated runs). If the null hypothesis H0 is true then the 2 measures will be similar and the ratio will be close to 1. If the H0 is false, then the numerator will be large relative to the denominator and the ratio will be greater than 1. Thus, a high F-value implies that the variation described by the model (Regression) is significantly larger than the variation inherent in the process (Residual). The P-value is the probability of achieving the F-value or greater (Zar, 2010). For the F value of each term, the test for the significance of a parameter dependence is to compare the decrease in the residual sum of squares (RSS) of the model incurred by adding the parameter over degrees of freedom of 1 to the variance of the replicate measurements. It can be determined from Eq. 5. F=

RSSw / o − RSSw RSSreplicate / d . f .

(5)

RSSw/ o means the RSS of the model without the specific parameter, RSSw means the RSS of the model with the specific parameter, RSSreplicate means the RSS of the replicate measurements, d . f . means the degree of freedom. High P-values ( > 0.05) for Lack of Fit imply that the model residual (residuals excluding replicate variation) was not significantly greater than the replicate error. Thus, the model had no lack of fit and is accurate enough to describe the process. Furthermore, the high R-squared values (the ratio between the model residual and the replicated variability) and high ‘Adeq. Precision’ values ( > 4) also suggest that the derived model linking the IUCPC operational parameters and the cut-off size D50 is accurate and statistically significant. Fig. 3 illustrates the effects of individual factors on the response (the D50), whilst other parameters were set to their own mean values. For example, as Tc increased and Ts decreased, the resulting D50 increased. However, the Tc exhibited a greater influence on the cut-off size than the Ts. As the temperature increases, the ratio of two adjacent saturation pressures with the same temperature difference will shrink, and thus the saturation ratio at higher temperatures is lower than that at lower temperatures even though the saturator-condenser temperature difference is identical. Both the capillary flow rate and the total flow rate had significantly less influence on the D50 than the saturator temperature and the condenser temperature. However, the interactive effect with the condenser temperature and with respect to other parameters on the D50 is illustrated in Fig. 4. Fig. 4 demonstrated the individual and interactive effects between the condenser temperature Tc, the saturator temperature Ts,

Fig. 3. D50 Main effects plots.

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Fig. 4. Interaction diagram of factors influencing the D50. (a) the interactive effects of Tc and Ts on the D50; (b) the interactive effects of Tc and Q1 on the D50; (c) the interactive effects of Tc and Q2 on the D50; (d) the interactive effects of Q1 and Q2 on the D50;.

the capillary flow rate Q1 and the total flow rate Q2 on the D50. Fig. 4(a) shows that the D50 increased dramatically with the increase of Tc, and a lower value of Ts increases the sensitivity of D50 to Tc. This is as a result of the increase in Tc thereby reducing the extent of supersaturation, hence small particles tended to escape without activation. The saturator temperature also exhibited a pronounced impact on the D50 because this determined the amount of the working liquid vapor and consequently the supersaturation extent in the condenser. The higher the value of Ts the correspondingly lower D50 was recorded. Fig. 4(b) shows that the condenser temperature has a significant impact on the D50 and the capillary flow rate Q1 has a small impact on the sensitivity of D50 to Tc. When the condenser temperature was 10 ℃, the cut-off size D50 at the capillary flow rate of 30 mL/min was larger than that of 60 mL/min. This is because at the lower capillary flow rate, the flow rate-dependent particle diffusion loss, particularly for small particles, was more severe than that at the higher capillary flow rate. Therefore, the counting efficiency for small particles was higher for 60 mL/min cases than that for 30 mL/min. However, when the condenser temperature was 25 ℃, the cut-off size D50 at the capillary flow rate of 30 mL/min was smaller than that of 60 mL/min, which is converse to the cases with Tc of 10 ℃. At the higher Tc, the widened diffusion zone of the core aerosol flow might have played a bigger role in determining the D50 than the diffusion loss in the capillary. The widened diffusion zone of the core aerosol flow means that some particles goes into the zone of low supersaturation towards the wall resulting in low counting efficiency or large D50. However, when the Tc is small enough, the diffusion loss plays a bigger role in the D50 because the supersaturation is high enough to enable activation even for wider diffusion zone of the core aerosol flow. To verify the hypothesis, a CFD simulation was conducted using FLUENT software and the results are shown in Fig. 5. For the CFD simulation, only flow in the condenser was modeled. The thickness of the capillary tube was also considered in the simulation. Except for the two inlets and the upper outlet, other boundary conditions are set to be ‘wall’. The axial velocity and the absolute value of radial velocity are presented in Fig. 5. The presence of large amount warm-toned color indicate a high axial and radial velocity. From Fig. 5, one can easily find that the capillary fluid is more likely to flow toward the condenser wall when the capillary flow rate increased from 30 mL/min to 60 mL/min with the sheath flow rate remaining at 300 mL/ min. Consequently, small particles are more likely to be carried with capillary flow toward the wall at higher capillary flow rate, in other words, the diffusion zone of the core aerosol flow become wider, which means that more particles go into the zone of low supersaturation (near the wall) resulting in low counting efficiency or large D50. However, when the Tc is small enough, the diffusion loss plays a bigger role in the D50 because the supersaturation is high enough to enable activation even for wider diffusion zone of the core aerosol flow. Another possible reason is due to the different design of the IUCPC from the commercial TSI 3025 CPC. In the IUCPC, the aerosol 18

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Fig. 5. Velocity distribution in the condenser with z from 0 to 0.02 m. (a) Axial velocity distribution for case1 (the capillary flow rate is 30 mL/min, whilst the sheath flow rate is 300 mL/min) (b) Axial velocity distribution for case2 (the capillary flow rate is 60 mL/min, whilst the sheath flow rate is 300 mL/min) (c) Radial velocity distribution for case1 (d)Radial velocity distribution for case2.

is not injected into the vapor-laden sheath flow until the very entrance into the condenser, whilst the aerosol is injected upstream prior to entering the condenser. The reason for the difference is that the cross flow momentum of the sheath gas would influence the aerosol flow if the same design was adopted as TSI 3025 CPC. Thus, less vapor might diffuse towards the core aerosol flow due to less mixing time at the point that peak supersaturation is reached. This in turn results in a lower peak supersaturation and a higher value of D50. The greater the fraction of the total flow that is the aerosol flow, the greater this effect will be. Fig. 4(c) demonstrated a clear trend between the Tc and the D50 with a slight influence caused by the total flow rate Q2 on this trend. The dependence of D50 on the Tc is consistent with the Fig. 4(a), (b). When the condenser temperature was 10 ℃, the D50 at the total flow rate of 400 mL/min was larger than that of 300 mL/min. One possible reason would be that the higher total flow rate Q2 effectively reduced the residence time of particles in the condenser, and hence inhibited particle activation process. The residence time might be critical because the activation process may take some time which is comparable to the residence time in the condenser. 19

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There is a detailed introduction of the kinetic theory for heterogeneous nucleation process elsewhere in literature (Giechaskiel et al., 2011). The theory states that the work (free energy) of formation of a critical cluster on a pre-existing particle is less than the work of formation in its absence, seed particles are activated at lower saturation ratios than required by homogeneous nucleation. The nucleation rate is governed by the activation rate constant per seed particle. Some other researchers also found that the total flow rate would influence the counting efficiency dramatically due to the change in the residence time of particles in the condenser (Banse et al., 2001; Wiedensohlet et al., 1997). Previous researchers also found that the particle growing time was 0.3 s which is comparable to the residence time (McMurry, 2000). Apart from the impact of the residence time, there is a possibility of the maximum supersaturation being pushed towards the end of the condenser. When the total flow rate Q2 increased, the supersaturation peak occurred downstream of the condenser which might influence the activation process as well. At a higher Tc (25 °C), the temperature difference between the saturator and the condenser was relatively low, and the supersaturation degree in the condenser is low. As the Q2 decreases, the velocity difference between the aerosol flow and the sheath gas flow increases, and the widened diffusion zone of the aerosol flow (as shown in Fig. 5) would become the dominant factor hampering particle condensation. It is also worth noting that the Q1 and Q2 had reverse effects on the D50 vs Tc curves. The reason is that as the total flow rate Q2 increases, the proportion of aerosol capillary flow rate Q1 in the total flow decreases hence an opposite trend was observed. Fig. 4(d) exhibited divergent trends between the D50 and the capillary flow rate Q1 with differing Q2. Overall, the changing range of the D50 caused by the interaction of Q1 and Q2 was dramatically smaller than other interactions, because the data span of the D50 in Fig. 4(d) is much smaller than Fig. 4(a–c). The individual effect of Q1 and Q2 on the D50 is also insignificant (as shown in Fig. 3). Therefore, the trend in Fig. 4(d) might not be as clear and definite as other interactions. The Q1 and Q2 would influence the D50 through the velocity difference between the core aerosol flow and the sheath gas flow, as it determines the width of the diffusion zone of the core aerosol flow. In addition, the Q1 will determine the diffusion loss in the capillary which in turns change the counting efficiency of the CPC. Fig. 6 shows the normal probability plots of the residuals for D50 for all the test points. A studentized residual is the quotient resulting from the division of a residual by an estimate of its standard deviation. The normal probability plot of residuals was used to verify the assumption that the residuals (model residuals) are normally distributed. The normal probability plot of the residuals generally follows a straight line without changing slope or points that are far away from the line, which means that the normality assumption of residuals are satisfied. The residuals versus run order plot is depicted as Fig. 7 to verify the assumption that the residuals are independent from one another, and the effects on the D50 are not influenced by the run order or other time dependent factors. Independent residuals show no trends or patterns when displayed in time order. Patterns in the points may indicate that residuals near each other may be correlated, and thus, not independent. Fig. 7 represents an ideal plot in which no trends or groupings are visible and the residuals on the plot fall randomly around the center line. 3.2.2. D50 Index model Previous ANOVA analysis demonstrated that the derived model is statistically significant and accurate in predicting the D50. Design Expert is capable of quantitatively describe the response using the operational parameters with coded units. The least value is identified as '−1' in coded units and the maximum value is normalized as '1' in coded units with other values being scaled linearly. With the coded units, the original orthogonal operational parameters become orthogonal unit vectors and the model terms can be estimated independently. The model for the IUCPC D50 as s function of four factors with coded units can be expressed as Eq. 6.

D50 = 15.23 + 3.32 × A′−1.46 × B′ + 0.054 × C′−0.11 × D′ − 0.55 × A′ × B′ + 0.51 × A′ × C′−0.62 × A′ × D′−1.05 × C′ × D′

(6)

A’, B’, C’, D’ are coded variables for the condenser temperature, the saturator temperature, the capillary flow rate and the total flow rate respectively. The low settings of the variables are identified by −1 in coded units (e.g. A’=−1 when Tc=10 °C) and the

Fig. 6. Normal probability plots of the residuals for D50.

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Fig. 7. Relationship between residuals and the run order in which the experiments were performed for D50.

high settings of the variables are identified by 1 in coded units (e.g. A’=1 when Tc=25 °C). Other values can be calculated via linear interpolation (e.g. A’=0 when Tc=17.5 °C). Coded units enables the direct comparison of the size of the coefficients (on a common scale) to determine which factor has the largest impact on the response. As a response sensitivity study, it would be convenient to convert the coded equation (Eq. 6) to the final sensitivity equation form as follows:

D50 = 15.23 + 24.9 × (A−A0 )−7.3 × (B−B0 ) + 0.81 × (C −C0 )−5.5 × (D −D0 ) − 41.25 × (A−A0 ) × (B −B0 ) + 114.75 × (A−A0 ) × (C −C0 )−465 × (A−A0 ) × (D −D0 )−157.5 × (C −C0 ) × (D −D0 )

(7)

where the subscript ‘0’ indicates a set of operating parameters at the cubic center point. The equation is expressed as a function of four factors in uncoded (or natural) units (i.e. A: condenser temperature in °C; B: saturator temperature in °C; C: capillary flow rate in mL/min; D: total flow rate in mL/min). This equation can calculate the deviation from the D50 at the cubic center if one or more parameters drift from their set points. The difference between the predicted D50 (calculated from the model) and the actual D50 (obtained from experiments) are presented in Fig. 8. According to Table 1, the minimum D50 of 9.55 nm was achieved with A, B, C, D being 10 °C, 45 °C, 60 mL/min, 400 mL/min, respectively. This test point had the largest saturator-condenser temperature difference and the largest sheath gas flow rate, which provided a high supersaturation extent for particle activation. The modeled D50 can be evaluated from the same set of the four parameters using Eq. 6, which was determined to be 9.99 nm. The minimal difference between the experimental data and the modeled result can be considered adequate. 4. Conclusion This study examined the effects of four operational parameters (including the saturator and the condenser temperature, the capillary flow rate and the total flow rate) on the cut-off size D50 (particle diameter with 50% counting efficiency) of an in-house condensation particle counter (IUCPC). Based on response surface design DoE (Design of Experiments), 31 working conditions were pre-determined including 7 replicated test points to evaluate the reproducibility. A non-linear model was fitted to the experimental results. The ANOVA analysis demonstrated that the proposed model and all the individual and interaction terms of the model were

Fig. 8. Predicted D50 versus actual D50.

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statistically significant and accurate, and there was no ‘Lack of Fit’ of the derived models. According to the ANOVA analysis and additional CFD simulation, the combination of the supersaturation distribution, the diffusion zone of the core aerosol flow, and particle residence time primarily determine the D50 response characteristics. These factors are governed by the operational parameters of the IUCPC individually or interactively with the condenser temperature being the most influential parameter. The DoE derived model is not universally applicable since the results may possibly alter in conjunction with other factors such as the CPC structure and the test range of parameters being studied. Acknowledgements This research is supported by National Natural Science Foundation of China (91641119) and is also part of the Project ‘Fundamental Investigation of Quasi-Azeotropic Hydrous Ethanol and Bio-jet Fuel Blends and their Influence on the Characteristics of Particulate Matter Emissions’ supported by National Natural Science Foundation of China (51306011). Valuable help from Professor Jiang jingjun, Dr. Runlong Cai and Dr. Xiaotong Chen at the Tsinghua University is gratefully acknowledged. References Alofs, D. J., Lutrus, C. K., Hagen, D. E., Sem, G. J., & Blesener, J. (1995). Intercomparison between commercial condensation nucleus counters and an alternating temperature gradient cloud chamber. Aerosol Science and Technology, 23(2), 239–249. Baltzer, S., Onel, S., Weiss, M., & Seipenbusch, M. (2014). Counting efficiency measurements for a new condensation particle counter. Journal of Aerosol Science, 70, 11–14. http://dx.doi.org/10.1016/j.jaerosci.2013.12.011. 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