1、954 2009 ASHRAEABSTRACTThis paper provides an improvement on the dynamic twin chamber method to measure volatile organic compound (VOC) diffusion coefficient and partition coefficient by considering the convective mass transfer resistance on the both surfaces of the building material. A formula anal
2、yzing this improvement is obtained. It is found that the diffusion coefficient is under-estimated by ignoring the convective mass transfer resistance in the traditional twin chamber method. The relative error is high to 46% when the convective mass transfer coefficient is 0.00262 mph (0.00117 m/s) a
3、ccording to the experimental data and simulation. However, the effect of this ignoring on the partition coefficient tends to be small. In addition, a dimen-sionless analysis is introduced to further consider the effect. The proposed method can improve the precision of diffusion coefficient obviously
4、 for the cases studied. INTRODUCTIONMany building materials emit volatile organic compounds (VOCs), which tend to cause sick building syndrome (SBS) (EPA US, 1990; Little et al., 1994; Meininghaus et al., 1999; Haghighat et al., 2005; Xiong et al., 2008). Knowing the emis-sion characteristics of VOC
5、s from building materials is neces-sary to effectively estimate and control indoor air quality. It is found that initial VOC concentration, C0, partition coefficient, K, diffusion coefficient, D, are the three key parameters of build-ing materials controlling the emission process. In order to obtain
6、 such parameters precisely and conveniently, a lot of fascinating work has been done. Haghighat et al. (2002) reviewed researches on the measurement of diffusion coefficients of VOCs for building materials: The cup method (Hansson and Stymne, 2000; Kirchner et al., 1999), twin chamber method (Bodala
7、l et al., 2000; Meininghaus et al., 2000) and porosity test method (Blondeau et al., 2003) were comparised and analyzed. It is found that there can be a difference of up to 700% in the reported data for a given technique.As far as the twin chamber method is concerned, Bodalal et al. (2000, 2001) use
8、d static twin chamber method (i.e. the chamber is sealed and the air flow is in steady state) to measure the diffusion coefficient and partition coefficient. They did not consider the impact of convective mass transfer resistance on the coefficients. Meininghaus et al. (2000) also ignored the convec
9、tive mass transfer effect on the coefficients by using dynamic twin chamber method. Considering those, Haghighat et al. (2002) proposed to apply mass exchanger method to simu-late the VOC transfer of the building material between two CLIMPAQ. In their model, VOC concentration gradients were assumed
10、to be similar as that in the heat exchanger that was unrealistic for many cases due to well mixing of VOC in the chamber. Meininghaus et al. (2000) also pointed out that the flow rate of supply air into the chamber was small compared with the internal recirculation in CLIMPAQ and consequently the co
11、ncentration gradients within the chamber were negligible. So we assume that the chamber air is fully mixed and just consider the convective mass transfer resistance of the boundary layer outside the material in the chamber.Based on the above-mentioned analysis, an improvement for dynamic twin chambe
12、r method to measure VOC diffusion coefficient and partition coefficient is proposed. A formula describing the influence of the improvement on the measured results is derived based on mass transfer mechanism subse-quently. Then the relative error of the traditional dynamic twin chamber method is anal
13、yzed by using the formula. In addition, An Improvement for Dynamic Twin Chamber Method to Measure VOC Diffusion Coefficient and Partition CoefficientJianyin Xiong Yinping Zhang, PhDWei Yan Zhongkai HeJianyin Xiong is a PhD candidate, Yinping Zhang is a professor, Wei Yan is a Masters in Engineering
14、candidate, and Zhongkai He is a PhD candidate in the Department of Building Science, Tsinghua University, Beijing, China.LO-09-090 2009, American Society of Heating, Refrigerating and Air-Conditioning Engineers, Inc. (www.ashrae.org). Published in ASHRAE Transactions 2009, vol. 115, part 2. For pers
15、onal use only. Additional reproduction, distribution, or transmission in either print or digital form is not permitted without ASHRAEs prior written permission.ASHRAE Transactions 955a dimensionless analysis is introduced to further consider the improvement. ANALYSIS OF INFLUENCE OF CONVECTIVE MASS
16、TRANSFER RESISTANCEThe schematic of dynamic twin chamber system is shown in Figure 1. Air with constant VOC concentration, C0, is intro-duced into chamber 1, while clean air is supplied to chamber 2, which means, and . When the mass transfer process arrives at steady state, the mass flux through the
17、 material can be calculated by:(1)where, is the steady state concentration of VOC in cham-ber 2, kg/m3; is the ventilation rate of chamber 2, m3/h; Ais the material area, m2.Since the mass transfer mode of VOC from chamber 1 to material and then to chamber 2 is in series, we have:(2)(3)where, is the
18、 steady state concentration of VOC in cham-ber 1, kg/m3; , are the VOC concentration in the material side of the interfaces respectively, kg/m3; , are the VOC concentration in the air side of the interfaces respectively, kg/m3; hm1, hm2are the convective mass transfer coefficient in both sides of th
19、e material respectively, m/s; D is the apparent diffusion coefficient, m2/s, and De is the effective diffusion coefficient, m2/s.Combined with equations (1) and (2), it yields:(4)(5)Substituting them into equation (3), the following equa-tion can be deduced:(6)This is the improved formula in dynamic
20、 twin chamber for calculating the effective diffusion coefficient which considers the convective boundary layer mass transfer resis-tance. If hm1and hm2approach infinite, the above equation can be written as the traditional formula:(7)Comparing equation (6) with (7), we can see that the traditional
21、formula underestimates the diffusion coefficient by neglecting the item.Applying the similar analysis, a new formula for the parti-tion coefficient can be derived as:(8)where, , are the instantaneous outlet VOC concen-trations in chamber 1 and chamber 2 respectively, kg/m3; is the lapsed time, s.As
22、a comparison, the traditional formula is presented as follows:(9)RESULTS AND DISCUSSIONFor convenience, we analyze the ratios of traditional formula to improved formula for diffusion coefficient and partition coefficient, and this can be implemented by Figure 1 Schematic of dynamic twin chamber meth
23、od.C1,inC0= C2,in0=mC2Q2A-=C2Q2mhm1C1C1a()hm2C2aC2()=mDCm1Cm2L- DKC1aKC2aL- DeC1aC2aL-= =C1Cm1Cm2C1aC2aC1aC1C2Q2Ahm1-=C2aC2C2Q2Ahm2-+=DeC2Q2LC1C2Q2C2A-1hm1-1hm2-+-1A-=De,tradC2Q2LC1C2-1A-=Q2C2A-1hm1-1hm2-+KC0Q1t0C1t()Q1tC2t()Q2td0t0d0t012- C1C2+()VQ2C2V2A-1hm2-1hm1-+-=C1t() C2t()t0KtradC0Q1t0C1t()Q1
24、tC2t()Q2td0t0d0t012- C1C2+()V-=956 ASHRAE Transactionscombining with equations (6), (7), (8) and (9). The results are as follows:(10)(11)Equation (11) indicates that the convection effect will counteract if the mass transfer coefficient on both surfaces of the material is the same, and thus under th
25、is condition, the boundary layer resistance can be ignored for partition coeffi-cient measurement. Xu et al. (2008) published their results about diffusion coefficient and partition coefficient measurements by using dynamic twin chamber method. The data from their paper is summarized in Table 1.Alth
26、ough the paper doesnt list the convective mass trans-fer coefficient, the convective effect can still be estimated from simulation by assuming a series of values for the coefficient. Considering that in many conditions there are no distinct differences of flow field between the two chambers, the con
27、vective mass transfer coefficients between the two cham-bers are taken as the same for analysis for the first step, and thus the convective effect can be ignored for the partition coef-ficient from the above analysis under this premise. Applying the above mentioned data into equations (10) and (11),
28、 the simulated results are obtained and shown in Figure 2. Figure 2 indicates that increases with the increasing convective mass transfer coefficient. If the convective mass transfer coefficient is chosen as a certain value, for example, 0.00262 mph (0.00117 m/s), which is used in Yang (1999)s paper
29、 for the 50L chamber, is then equal to 0.54. This means the relative error, , which is defined as , becomes 46%. This is a large discrepancy between the diffusion coefficient from the improved and tradi-tional formula and thus the convective effect cant be neglected in this situation. The smaller th
30、e convective mass transfer coeffi-cient, the larger the relative error. If we analyze from the view-point of mass transfer resistance, the small convective mass transfer coefficient corresponds to large boundary layer resis-tance (1/hm1) and it becomes analogous to the internal diffusion resistance
31、( ).Then, we consider another condition, that is, the convec-tive mass transfer coefficients are different for the two cham-bers. The convective mass transfer coefficient for chamber 1, hm1, is fixed as 0.00262 mph (0.00117 m/s), and a relation (assuming ) is introduced. The simulated results are sh
32、own in Figure 3.Figure 3 shows that decreases with the increas-ing . When increases from 0.3 to 1.0, the relative error, , Table 1. Experimental Data in Xu et al.s (2008) PaperQ1cfm, m3/hQ2cfm, m3/hC0ug/m3C1ug/m3C2ug/m3Lft, mAft2, m23.8710-2,6.5810-23.8710-2,6.5810-23.721022.311021.351023.2810-2,1.0
33、010-21.04,9.6910-2De,tradDe- 1Q2C2C1C2()A-1hm1-1hm2-+=KtradK- 1Q2C2C1C2+()A-1hm2-1hm1-+=De,tradDeDe,tradDe1DeDe,trad()DeLDe,tradFigure 2 Dependence of De,trad/Deon convective mass transfer coefficient.Figure 3 Dependence of Ktrad/K on .hm2 hm1= 1KtradK 2ASHRAE Transactions 957which is defined as , j
34、ust changes from 14% to 0. This is a relatively small value and it means the partition coefficient is not sensitive to the convective boundary layer resistance.Equation (10) and (11) can be transformed into dimen-sionless forms as a further analysis, which are represented by the following equations:
35、(12)(13)where, Bim1, Bim2are defined as hm1L/De,trad, hm2L/De,trad, respectively; is defined as Thus, the ratios of traditional formula to improved formula for diffusion coefficient and partition coefficient using dynamic twin chamber method are functions of three dimensionless param-eters, Bim1, Bi
36、m2, . Taking the measurement of diffusion coefficient for detailed analysis as an example, by assuming that the parameter Bim1 is equal to Bim2, the relative error can be expressed as:(14)For most building materials in indoor environment condi-tions, Bim1is in the range of 2-700, and thus the relati
37、ve error, , can vary from 0.3% to 100%. Figure 4 shows the variation trend.CONCLUSIONBased on the detailed analysis of mass transfer process of twin chamber method, this paper proposes an improved consideration for measuring diffusion coefficient and partition coefficient, which involves the effect
38、of convective mass trans-fer resistance, and a new formula is deduced to describe this effect. It is found that the traditional model tends to underes-timate the diffusion coefficient and the relative error is high to 46% when the convective mass transfer coefficient is 0.00262 mph (0.00117 m/s) for
39、 the case studied. The measurement of partition coefficient is not sensitive to convective mass transfer resistance and it just causes very small discrepancy by ignor-ing this effect. Further dimensionless analysis indicates that the ratios of traditional formula to improved formula for diffu-sion c
40、oefficient and partition are just functions of three dimen-sionless parameters, Bim1, Bim2, .ACKNOWLEDGMENTSThis research was supported by National Natural Science Foundation of China (grant no.50725620) and by the 11th5 year key project, Dept. of Science of China (grant no. 2006BAJ02A08).REFERENCES
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42、ficients of volatile organic compounds for building materials. Building and Environment, 35: 101-110.Bodalal, A., Plett, E.G., Zhang, J.S., et al., 2001. Correla-tions between the internal diffusion and equilibrium par-tition coefficients of volatile organic compounds (VOC) in building materials and
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46、ndence of on Bim1.1De,tradDe- 1De,tradL-1hm1-1hm2-+ 11Bim1-1Bim2-+=KtradK- 1 C1Bim2-1Bim1-+=CC1C2()C1C2+()C1DeDe,tradDe-2Bim1-=1C958 ASHRAE Transactionscapacities and diffusion coefficients of indoor surface materials exposed to VOCs: proposal of new test proce-dure, Edinburgh. Proceedings of the Ei
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