limonene reactions

Building and Environment 46 (2011) 711e718

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Building and Environment journal homepage: www.elsevier.com/locate/buildenv

Coupled CFD analysis of size distributions on indoor secondary organic aerosol derived from ozone/limonene reactions Kazuhide Ito a, *, Hiroshi Harashima b a b

Interdisciplinary Graduate School of Engineering Science, Kyushu University, 6-1 Kasuga-koen, Kasuga, Fukuoka 816-8580, Japan Obayashi Co. Ltd., Fukuoka, Japan

a r t i c l e i n f o

a b s t r a c t

Article history: Received 11 June 2010 Received in revised form 17 September 2010 Accepted 7 October 2010

Recently, theoretical analysis and experiment have been initiated to investigate the generation of secondary organic aerosols (SOA) by chemical reactions in indoor air. In particular, it has been confirmed that SOA are generated by the reaction of ozone with various terpenoids. The overarching goal of this work was to better understand ozone, VOC (volatile organic compounds) and generated SOA distributions within rooms. We carried out cylindrical test chamber experiments to measure SOA generation from the chemical reaction of ozone and limonene and discussed numerical models to describe it. In this paper, we propose a method for predicting the particle size distribution of SOA generated by ozone and limonene chemical reactions in air. In particular, we discuss an analytical method that involves a sectional modeling approach governing equations of SOA. Although the changes in particle size distribution in a 40-section model were reproduced to a certain extent, rigorous modeling for the generation and growth of SOA and an increased number of sections are needed for improvement of prediction accuracy. Ó 2010 Elsevier Ltd. All rights reserved.

Keywords: Indoor environment CFD Chemical reaction Secondary organic aerosol (SOA)

1. Introduction The quality problem regarding the overall indoor air environment is called IAQ (indoor air quality) and this area has been attracting increasing attention with the increasing health consciousness of residents. In the field of IAQ, it has been pointed out that a specific chemistry exists and causes various chemical reactions and intermediate products and final products are produced as results of chemical reactions. These products have the potential to exert far greater health and physiological effects than compounds prior to reactions [1,2]. In particular, it is confirmed that secondary organic aerosols (SOA) are generated by the reaction of ozone with various terpenoids and theoretical analysis and investigations have begun to evaluate that SOA are generated by chemical reactions in indoor air [3e8]. There is concern that SOA are a serious source of secondary pollution in indoor environments [9]. Many studies have reported associations with ozone-initiated chemistry and subsequent SOA generation in indoor environments. Weschler demonstrated that ozone chemistry produces various products which include primary and secondary ozonides, peroxyhemiacetals, a-hydroxy ketones, and peroxyacyl nitrates. Secondary

* Corresponding author. Tel.: þ81 92 583 7628; fax: þ81 92 583 7627. E-mail address: [email protected] (K. Ito). 0360-1323/$ e see front matter Ó 2010 Elsevier Ltd. All rights reserved. doi:10.1016/j.buildenv.2010.10.003

organic aerosols are important stable products resulting from chemical reaction with ozone. They are formed from low-vaporpressure oxidation products that partition between the gas phase and the surface of pre-existing aerosols or nucleate to form new aerosols. The reaction of ozone with various terpenoids in indoor settings has been shown to contribute tens of mg/m3 to the indoor concentration of sub-micron particles under appropriate conditions [9]. Nazaroff et al. analyzed and reported detailed SOA data from a series of smallchamber experiments in which terpene-rich vapors from household products were combined with ozone under conditions analogous to product use indoors [10e12]. Concerning the numerical prediction of SOA generation and subsequent particle size distribution/change in indoor environments, there are numerous factors that affect the transportation phenomena and reasonable models and numerical procedures to characterize these are needed. We have already carried out cylindrical test chamber experiments to investigate SOA generation resulting from the chemical reaction of ozone and D-limonene in terpenoid chemical substances and have discussed numerical models to describe this phenomenon [13]. We have also reported the results of coupled CFD analysis of flow field and the concentration distributions of ozone and limonene [14]. In this study, we focus on the initial nucleation/generation of SOA and subsequent size distribution and discuss the analytical method by the sectional modeling approach. We also carry out sensitivity

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analysis and comprehensive prediction incorporating a bi-molecular chemical reaction model, SOA generation, and collision/coagulation and deposition models. Furthermore, in order to reproduce the experimental results, a simplified instantaneous nucleation/generation model is introduced and the prediction results were reported. 2. Method for numerical analysis of particle size distribution for SOA Although indoor aerosol transportation and its particle size distribution are similar to those observed in atmospheric environments, there are large differences in terms of generation sources, wall effect (deposition to wall surface) and time spent or residual time in suspension in the air. In indoor environments, because of the short time spent in suspension in the air in comparison with the situation of atmospheric environment, numerical models with high time resolution are required to carry out detailed and accurate prediction [15e19]. The sizes of the particles of indoor aerosols have a wide range from order of nanometer to micrometer and, in general, it is necessary to solve the transportation equations of particle/aerosol size distribution function to predict their generation and later growth [20]. The sectional modeling approach (sectional method or discrete method) is one of the methods used to predict particle size distribution [21]. Multiple aerosol transportation equations divided according to particle size; e.g. diameter or volume, are targeted in the sectional model and the prediction accuracy of the sectional model is improved by increasing the number of sections. The various factors of nucleation/generation model, aggregation and collision/coagulation model, deposition model, and convection and diffusion effects are incorporated into each particle transportation equation. This paper reports the modeling procedure and results of numerical analysis that adopted the instantaneous nucleation model and the sectional modeling approach to reproduce ozone and limonene reactions and the subsequent generation and growth of SOA in indoor environments. 2.1. SOA targeted in this research In this study, the range of SOA size as aerodynamic diameter was set from 10 to 480 nm according to the results of ozoneelimonene reaction experiments in the cylindrical test chamber [13]. The concentration of SOA was about 1011 m3 or less and the density of particles was assumed to be 103 kg/m3 Fig. 1 outlines the SOArelated phenomena targeted in this study. 2.2. Sectional method Here, Eulerian approach will be used to model aerosol dynamics including various factors. Particle transportation involves various factors and can be generally described by the aerosol general dynamic Convection and Turbulence Diffusion Gas C1 C2

Products(Gas) Cp

Ozone. kb C1 C2 kb Limonene Chemical Reaction Molecular Diffusion Deposition

SOA n(v,t)

SOA n(v,t)

Deposition to SOA Surface Y(v,t) p(v,v’) Coagulation, etc.

Coagulation

Brown (+ Gravitational ) Sedimentation Diffusion Deposition

Fig. 1. SOA generation and growth processes.

equation (GDE) shown in equation (1). In this analysis, the GDE of each particle bin will be solved together with the fluid continuity equation and momentum equation; i.e. coupled simulation with computational fluid dynamics (CFD) based on Reynolds Averaged NaviereStokes equation (RANS model). This method is a fully coupled Eulerian- Eulerian simulation of aerosols. The numerical simulation described in section 4 targeted the equations operated ensemble averaging.

vnðv; tÞ ¼ Vunðv; tÞ þ VðDðvÞVnðv; tÞÞ þ Sp þ Ca þ Gs þ Es vt (1) 3

Here, n(v, t) [m ] is the SOA number concentration with particle volumes between v and v þ dv at time t [s]. In this formulation, the particle size is expressed using the volume. The first term of right side of equation (1) indicates convection term; the second term is diffusion term; Sp expresses reaction-generation of aerosols; Ca indicates Collision and Coagulation Term; Gs shows Gravitational Sedimentation and Es is other influencing factors. Though the numerical analysis described later uses the formulation of the ensemble average, the expressions of instantaneous values are used in the formulation in the Section 2.2e2.9. In the present work the smallest nano size aerosols (dp ¼ 10 nm) will fall in free-molecular regime and the larger ones (dp ¼ 480 nm) are in the transition regime as Knudsen number (Kn) ranges between about 0.3 and 14. Here, continuum phase for entire domain is assumed for simplification. In this study, the general dynamic equation shown in equation (1) was solved by sectional representations of aerosol balance equations. In this numerical method, multiple particle transport equations divided into plural sections (the number of sections ‘m’) according to the particle size distribution and the value of volume integration Ql of each section were discretized for numerical simulation. The model parameters (e.g. coagulation constant and diffusion coefficient) that depend on the particle diameter were replaced and represented by representative values for each section.

Zvl Ql ðtÞ ¼

v$nðv; tÞdv

ðl ¼ 1; 2; /; mÞ

(2)

vl1

2.3. Convection and diffusion The first term on the right-hand side of equation (1) expresses the convection term and the second term denotes the diffusion term. u denotes velocity vector and D(v) indicates the Brownian diffusion coefficient of each particle. The order of Brownian diffusion coefficient is estimated as 5.2  108 in the case of 10 nm diameter particles (dp) and 6.8  1011 in the case of 480 nm diameter particles (dp) [22]. These are much smaller than the order of kinematic viscosity of air of 1.8  105 m2/s at 300 K. The volume fraction of generated SOA in this analysis is relatively small compared with the air volume (on the order of ppm), thus the numerical simulation with one-way coupling method, which uses fixed flow field under the assumption that the SOA movement does not affect the flow field, is adopted for scalar transfer of gas phase and SOA phase [23,24]. 2.4. Reaction-generation term The third term on the right-hand side of equation (1); Sp, expresses SOA generation with the bi-molecular chemical reaction of ozone and limonene. In this study, it is assumed that the seeding or nucleating particles such as low-vapor-pressure compounds and

K. Ito, H. Harashima / Building and Environment 46 (2011) 711e718

water vapor in the background become the nuclei that undergo coagulation and aggregation. The time variation in the SOA n(v, t) is described by the second-order rate constant kb [1/ppm/s] for bi-molecular chemical reactions and the fractional aerosol yield Y(v,t) [1/ppm/m3] for partitioning from gas phase to aerosol phase.

Sp ¼ Yðv; tÞ

vCp ¼ Yðv; tÞðkb C1 C2 Þ vt

(3)

Here, Cp denotes the concentration of hypothetical intermediate reaction products [ppm] [29] and C1 and C2 are the concentrations of ozone and limonene [ppm], respectively. kb [1/ppm/s] is the vapor phase rate constant of chemical reaction in the second order. The transport equations for the ozone and limonene concentrations and the bi-molecular chemical reaction are described in Section 2.9. Y(v, t) is defined as the fractional aerosol yield; i.e. a transformation parameter from gas phase to aerosol phase, and here, assumed two types of models; (i) time constant model and (ii) time-dependent formulation to introduce the instantaneous nucleation model (here, we call burst nucleation). Kerminen and Kulmala reported on a theoretical analysis of nucleation in an atmospheric environment and also discussed that the sink (coagulation) effect of nucleation particles onto larger preexisting particles was the dominant factor in nucleation and subsequent particle growth [17]. In this modeling, the nucleation and reaction of particles with a diameter of 10 nm or less were not the analytical targets and the generation of particles with a diameter of 10 nm or more was roughly expressed by equation (3). Under the condition that background particles concentration assumes to be zero, all hypothetical intermediate reaction products will become scalable particles (particle of 10 nm or more in this paper). On the other hand, there are reaction-generation particles in the air as background pre-existing particles after a certain period of time passing. In this point of view, the time-dependent modeling of Y(v, t) is reasonable as a first approximation.

The fourth term on the right-hand side of equation (1) represents a coagulation term that consists of coagulation loss and coagulation gain, and is defined by the following equation [21].

Ca ¼ nðv; tÞ

pðv; v0 Þnðv0 ; tÞdv0

þ

1 2

pðv0 ; v  v0 Þnðv0 ; tÞnðv  v0 ; tÞdv0

(4)

0

Here, p [m3/s] is the collision kernel; i.e. probability of collision/ coagulation for two particles of volume v and v0 (¼v þ dv). Generally, Fuchs’ collision kernel for p is classical and popular. In this case, two types of probability, that of coagulation by Brownian motion and that of turbulent diffusion, are considered. In the coagulation reaction, it is assumed that two particles are lost and a single new particle is generated in one collision. The probability of collision/ coagulation by Brownian motion and turbulent motion (diffusion) can be written as follows.

  KB ¼ 4pða1 þ a2 Þ Dp1 þ Dp2 KT ¼ 4pða1 þ a2 Þ



2nt

st

Dpx ¼

kT Cc 6pmax

(7)

Here, k [m2 kg/s2 K] is the Boltzmann constant, T [K] is air temperature, m [Pa s] is viscosity of air and Cc [] denotes the Cunningham factor. nt is calculated by CFD simulation and st assumed to be 1.0 in this study. The sum of the collision/coagulation probabilities by Brownian motion and turbulent diffusion can be written as equation (8).

pðv; v0 Þ ¼ hðKB þ KT Þ

(8)

Here, h is the collision efficiency of two particles (this is the parameter that expresses the surface intensity between two particles), and is assumed to be h ¼ 1 in this study. Due to the low air velocity, aggregate breakage can be neglected in usual indoor environment (except for the local high and complicate flow region, i.e. the flow through an HVAC blower or near a ceiling fan). 2.6. Gravitational sedimentation The fifth term on the right-hand side of equation (1) represents gravitational sedimentation. This term is defined by the following equation.

  Gs ¼ V vp ðvÞnðv; tÞ

(9)

Here, vp(v) [m/s] is gravitational settling (terminal) velocity and is estimated by Stokes’s law. The gravitational settling velocity of the SOA targeted in this study is estimated as 9.3  106 m/s in the case of dp ¼ 480 nm.

The sixth term Es on the right-hand side of equation (1) denotes other factors, such as volume forces due to electrical and magnetic fields, thermophoresis, electrophoresis, humidity dependence. However, other than the ozon-limonene chemical reaction, we did not consider any such factors in this study. 2.8. Modeling wall surface deposition of SOA

0

Zv

turbulent eddy viscosity and st [] is the turbulent Schmidt number. The Brownian diffusion coefficient is estimated by equation (7).

2.7. Other influential factors

2.5. Coagulation loss and coagulation gain term

ZN

713

(5)

 (6)

Here, a1 and a2 [m] are radii of particles, Dp1 and Dp2 [m2/s] are the Brownian diffusion coefficients of each particle, nt [m2/s] is the

Deposition of aerosols is complicated process that depends on the particle characteristics, air flow conditions and surface characteristics of building materials, and plenty of research results have been reported [25,26]. The concept of deposition velocity vd is generally adopted to estimate deposition flux from air phase onto solid surface. In this study, in order to analyze the flow field and particle transport characteristics in the viscous sub-layer (wall unit yþ<<1), fine grid design and low Reynolds number type turbulent model was used. Assuming the limited phenomenon in the viscous sub-layer (wall unit yþ<<1), wall surface deposition can be expressed by equation (10) using the Brownian diffusion coefficient and concentration gradient.

vn J ¼ DðvÞ j vx B

(10)

It must be emphasized that equation (10) is valid only when the distance to the first grid point is sufficiently small (yþ<<1). As an approximation, the surface SOA concentration on a wall surface is assumed to be zero (assumption of perfect sink) to estimate concentration gradient in vicinity of wall surface.

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2.9. Transport of ozone and limonene in indoor environment The governing equations of ozone and limonene can be written as follows. vC1 vt vC2 vt

¼ VðuC1 Þ þ VðD1 VC1 Þ  kb $C1 $C2 ¼ VðuC2 Þ þ VðD2 VC2 Þ  kb $C1 $C2

(11)

Here, D1 and D2 [m2/s] are the molecular diffusion coefficients of ozone and limonene in the gas phase, respectively, and u [m/s] is velocity. The third term in equation (11) expresses the bi-molecular chemical reaction of ozone and limonene and kb is the secondorder rate constant [27,28]. We have reported the measurement results of kb [] for ozone and limonene [13]. Equation (12) indicates the deposition flux model of gas-phase compounds, ozone and limonene, which was proposed by Sorensen and Weschler [29]. This wall deposition model is derived from molecular theory and expanded to enable its application to the usual CFD grid scale (set by condition yþ (wall unit) < 1) [30].

J ¼ 

ghv4T i

hv i y 1þg T 1 4 D1

C1 jy¼y1

(12)

Here, C1jy¼y1 [ppm] indicates the concentration of ozone (C2jy¼ y1 in case of limonene) denoting the distance to the center of the first computational cell (y1). g [] is reaction probability and denotes the probability of deposition in the vicinity of the wall surface. [m/s] expresses the Boltzmann velocity for the target chemical compound. The deposition flux J, which is expressed by equation (12), is also valid only when the distance to the first grid point is sufficiently small (yþ<<1). We have reported the measurement results of g [] for ozone and limonene onto various wall surfaces [31]. 3. Overview of the experiment using the cylindrical test chamber We have carried out the fundamental experiment of ozone and limonene reactions in air phase using the cylindrical test chamber and already reported the measurement results of the concentration distributions of ozone, limonene and SOA generated in it. Fig. 2 depicts the layout of the cylindrical test chamber and includes photos [13]. The cylindrical test chamber is a duct cavity and consists of three sections (55 mm (diameter)  2500 mm (length)) and these are connected using a U-bend (R ¼ 80 mm). The inner boundaries for air passing through the chamber are made of electro-polished SUS 304 stainless steel. The air inlet velocity (Uin) was set at 1.0 m/s. The inlet air and all the walls were maintained at isothermal conditions (293  0.5 K). The supply air was passed through activated carbon and ULPA filters to keep the concentration of background contaminants (including VOCs and aerosols) low. The relative humidity of supplied air was controlled at 10% and below. In order to prevent photochemical reactions involving ozone, the experiments were carried out in a dark room. Positions (1)e(7) in Fig. 2 show the points of measurement in the chamber. A wide-range particle spectrometer (MSP, Model 1000XP) was used to measure background ultra-fine particles (10 nm 10 mm diameter) and generated SOA. The accuracy of the wide-range particle spectrometer system is 3% for particle diameter and 10% for concentrations. Ozone and limonene were introduced into the cylindrical test chamber from the supply inlet position at constant concentrations (C1, in ¼ 1.00 ppm for ozone, C2,in ¼ 1.75 ppm for limonene). The details of this experiment have been described in a previous paper [13].

Fig. 2. Schematic of cylindrical test chamber.

4. Overview of numerical analysis Numerical simulation based on CFD and sectional model of size distribution of SOA were carried out in accordance with the experimental setup to reproduce the concentration distributions of ozone, limonene and SOA. The inner space of cylindrical test chamber as shown in Fig. 2 was reproduced as target geometry. 4.1. Numerical condition The modeling methodology is based on the Eulerian moment form of the GDE for aerosol transport and dynamics in conjunction with solving the Reynolds averaged NaviereStokes equations (RANS) for bulk fluid modeling. The NaviereStokes governing equations will be discretized by a finite volume based commercial computational CFD code ANSYS/FLUENT 12. Flow fields were estimated using the low Reynolds number type ke3 model (Abe Kondo Nagano model). The QUICK scheme was used for the convection term, and a SIMPLE algorithm was used. To analyze the flow field in the boundary layer and to enable the application of the wall surface deposition model in equation (12), the center of the computational cells closest to the wall surface should be at a non-dimensional distance (wall unit) of yþ<1, where yþ ¼ u* y1 =n and y1 is the distance normal to the wall surface, n is the kinematic viscosity and ffi pffiffiffiffiffiffiffiffiffiffi u* ¼ sw =r is the friction velocity. Here, r is the air density and sw is the wall shear stress. In order to numerically analyze the aerosol GDE, ozone and limonene concentration transport equation in conjunction with CFD based on RANS model, these equations are ensemble averaged. For the cross-correlation function of time fluctuation of scalar concentration and wind velocity caused as a result of the ensemble averaging operation, eddy-viscosity representation is adopted using turbulent eddy viscosity nt and turbulent Schmit Number st. In general, the value of about 0.2e1.3 is adopted as for turbulent Schmidt number and the values 0.7 or 0.9 have been used for most of the CFD studies for turbulent mass diffusion [32]. Here, st ¼ 1.0 was used. The number of meshes was set to about 300,000 and unstructured mesh was used for the analysis. The analysis was carried out in three dimensions. The air inlet velocity and turbulent intensity were set to Uin ¼ 1.0 m/s and 10%, respectively, which are the same as those used in the experiments. The concentrations of ozone and limonene at the inlet position (position (1) in Fig. 2) were set to 1.00 ppm and 1.75 ppm, respectively, and kept constant in accordance with experimental condition. Reaction probabilities [g] with the cylindrical test chamber surface (SUS304) were adopted as g ¼ 3.4  106 (ozone)

K. Ito, H. Harashima / Building and Environment 46 (2011) 711e718

and g ¼ 2.1  105 (limonene) in accordance with a previous report [31]. Concerning the wall surface deposition of SOA, perfect sink condition was assumed (surface SOA concentration set to zero). Analytical conditions are shown in Table 1. 4.2. Cases analyzed and adopted model parameters CFD analyses were carried out for six cases as shown in Table 2. The second-order rate constant kb and the fractional aerosol yield Y (v, t) were estimated using the results of the cylindrical test chamber experiment. kb was assumed to be constant and estimated using the concentration gradient in the cylindrical test chamber [13]. Using the data for the average concentration of the SOA at each sampling point of cylindrical test chamber, the fractional aerosol yield (Y) was estimated from equation (3) as time constant but volume-dependent value [13]. In addition, using the same experimental data for the concentration distribution of the SOA in the test chamber, the time-dependent fractional aerosol yield Y(v, t) was also estimated to reproduce the instantaneous particle generation mode; i.e. we call “burst nucleation” in this paper. In this study, a step change function was introduced to time- and volumedependent Y(v, t) modeling, as shown in Table 2. The concept of age of air (SVE3) was used for estimating elapsed timed of ozone, limonene and SOA [33]. The detail distribution of Y(v, t) as functions of age of air was shown in Appendix A. The gravitational sedimentation was analyzed using settling velocity, the temperature condition was assumed to be an isothermal condition (constant at 293 K) and the humidity effect was disregarded. Concerning the target experiment, the SOA size distribution at sampling point (2) (t ¼ 2.06 s past the inlet position) showed a convex distribution and the peak concentration in the distribution of particle size was about 20 nm (see Fig. 4). In order to reproduce the sharp change in size distribution in the vicinity of a 20 nm diameter, we introduced and divided sections between 10 and 20 nm diameters for the sectional model analysis. The total of three cases; 5 sections, 20 sections and 40 sections, was set in accordance with the following functions.

dp ¼ 10  2:632i

ði ¼ 0; 1; ; 4 for 5 sectionsÞ

(13)

dp ¼ 10  1:226i

ði ¼ 0; 1; ; 19 for 20 sectionsÞ

(14)

dp ¼ 10  1:104i

ði ¼ 0; 1; ; 39 for 40 sectionsÞ

(15)

715

Table 2 Cases analyzed. Case

Sectional Inlet representation velocity

S05-1 S20-1 S40-1 S05-2

5 bin 20 bin 40 bin 5 bin

S20-2 20 bin S40-2 40 bin

kb

Y(v, t)

1.00 [m/s] 1.5  101 6.2  107e1.4  1012 [1/ppm/s] [1/ppm/m3] 1.00 [m/s] 1.5  101 t < 2.06 [s]; [1/ppm/s] Y(v, t) ¼ 6.2  107e1.4  1012 t  2.06 [s] Y(v, t) ¼ 0 [1/ppm/m3]

Here, dp [nm] is the particle diameter and i corresponds to the number of sections. The fundamental data of Brownian diffusion coefficient, probability of collision/coagulation by Brownian diffusion and gravitational settling velocity are shown in Table 3e5 respectively. 5. Results of numerical analysis Fig. 3 denotes comparisons between the measured and predicted concentration distributions of ozone and limonene in cylindrical test chamber. The horizontal axis indicates the distance of each sampling position from supply inlet. These prediction results are superposed on the measurement results of the cylindrical chamber experiment. The results of numerical simulation were able to be reproduced the downward trend of ozone concentration distribution and in good agreement with experimental results. Compared with the experimental results, the prediction result of limonene concentration distribution tended to underestimate the concentration level especially in the wake flow region. Secondorder rate constant kb (in equation (11)) in this analysis adopted the value estimated from the concentration change of ozone in cylindrical test chamber [13,14], thence the reproducibility of the concentration change of ozone by the numerical analysis was relatively high compared with the concentration change pf limonene. It is also thought that one of the reasons of this is caused the uncertainty of concentration measurement of limonene. Fig. 4 shows the numerical results of SOA number concentration distributions at sampling positions (2) and (7) of cylindrical test chamber (see Fig. 2). These prediction results are superposed on the measurement results of the cylindrical chamber experiment. In this prediction, three analysis cases, 5-section model, 20-section model and 40-section model, were set. [ppm]

Table 1 Numerical and boundary conditions. Target space

Duct model (Fig. 2)

Mesh number Turbulence model Scheme Inflow boundary

281,988 (unstructured) Low Re Type ke3 (Abe-Nagano) model Convection term: QUICK Uin ¼ 1.00 m/s, C1,in ¼ 1.00 ppm (ozone), C2,in ¼ 1.75 ppm (limonene) 3/2 kin ¼ 3/2  (0.1Uin)2, 3in¼(C3/4 m kin )/lin Uout ¼ kout ¼ 3out ¼ Cout ¼ free slip Velocity: No-slip, kjwall: No-slip, 3jwall ¼ 2n(vk1/2/vy)2 Wall dep.: g ¼ 3.4  106 (ozone), g ¼ 2.1  105 (limonene) Wall con.: zero (SOA) D ¼ 1.50  105 m2/s (air) D ¼ 1.81  105 m2/s (ozone) D ¼ 6.20  106 m2/s (limonene) ¼ 360 m/s (ozone), 213.4 m/s (limonene) D ¼ kTCc/6pma m2/s (SOA)

Outflow boundary Wall treatment

Molecular diffusion

Brownian diffusion

2.0

Exp(limonene)

Prediction(limonene)

1.5

1.0

0.5 Exp(ozone)

Prediction(ozone)

0.0 (1)

(2) (3)

(4) (5)

(6) (7)

[sampling position] Fig. 3. Concentration distributions of ozone and limonene in cylindrical test chamber.

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K. Ito, H. Harashima / Building and Environment 46 (2011) 711e718 3

9.00E+11

3

[1/m ]

9.00E+11 Experiment CaseS05-1 CaseS05-2

8.00E+11 7.00E+11

3

[1/m ]

9.00E+11 Experiment CaseS20-1 CaseS20-2

8.00E+11

7.00E+11

6.00E+11

6.00E+11

6.00E+11

5.00E+11

5.00E+11

5.00E+11

4.00E+11

4.00E+11

4.00E+11

3.00E+11

3.00E+11

3.00E+11

2.00E+11

2.00E+11

2.00E+11

1.00E+11

1.00E+11

1.00E+11

0.00E+00

0.00E+00 100[nm]

1000

0.00E+00 100 [nm]

10

(a) Sampling point (2)

1000

9.00E+11 Experiment CaseS05-1 CaseS05-2

3

[1/m ]

9.00E+11

Experiment CaseS20-1 CaseS20-2

8.00E+11 7.00E+11

7.00E+11

6.00E+11

6.00E+11

6.00E+11

5.00E+11

5.00E+11

5.00E+11

4.00E+11

4.00E+11

4.00E+11

3.00E+11

3.00E+11

3.00E+11

2.00E+11

2.00E+11

2.00E+11

1.00E+11

1.00E+11

1.00E+11

0.00E+00

0.00E+00 100[nm]

1000

(b) Sampling point (7)

A

Experiment CaseS40-1 CaseS40-2

0.00E+00 100 [nm]

10

1000

(b) Sampling point (7)

B

Case S05

[1/m ]

8.00E+11

7.00E+11

10

1000

(a) Sampling point (2)

3

[1/m ]

8.00E+11

100[nm]

10

(a) Sampling point (2)

3

9.00E+11

Experiment CaseS40-1 CaseS40-2

8.00E+11

7.00E+11

10

[1/m ]

100[nm]

10

1000

(b) Sampling point (7)

C

Case S20

Case S40

Fig. 4. Comparison of the results of prediction and experiment of SOA concentration distribution at each point.

In cases of Case S05-1, S20-1 and S40-1 which adopted time constant modeling of Y(v, t), the prediction accuracy of SOA size distribution and its change over time gradually improved with an increase in the number of sections. In case S20-1 and case S40-1, the numerical results of number concentration and size distribution of SOA at sampling position (2) were reasonably consistent with the experimental results. However, at sampling position (7) that was located at the exhaust outlet and about 8 s past the inlet position, the prediction results of SOA number concentration were overestimated compared with experimental results. In cases of Case S05-2, S20-2 and S40-2 which adopt the burst nucleation model (time-dependent modeling of Y(v, t) with step change function) was confirmed to reproduce the initial nucleation/size distribution of SOA. At sampling position (7), a difference in peak concentration between prediction and experiment was observed. Although the qualitative and quantitative prediction results of peak concentration were not in good agreement with the experimental data, the downward trend of SOA concentration seemed to be identifiable in this modeling. The maximum amount of wall deposition by Brownian motion and gravitational sedimentation was about 3 [%] in this study. Target test chamber is slender duct and the inner wall surface Table 3 Brownian diffusion coefficient [m2/s]. Diameter [m] Dp [m/s]

1.0  1008

2.6  1008

6.9  1008

1.8  1007

4.8  1007

5.2  1008

7.9  1009

1.3  1009

2.6  1010

6.7  1011

area is relatively large compared with chamber volume. This means that wall effect tend to appear to this test chamber geometry. Nevertheless, the wall surface deposition and gravitational sedimentation did not have a predominant influence on the SOA concentration change in this study. And there was also no influence of collision/coagulation model to particle size distribution because the time of passage in the cylindrical chamber was short for about 8 s. 6. Discussion Takahashi reported the time scale of collision/coagulation of particles in various concentration and pointed out that the time scale for changing initial concentration level is approximately 30 s in case of 1016 [m3] as initial particle concentration [20]. This time scale is long enough compared with the average staying time of particles in the cylindrical test chamber (¼8 s). The gravitational settling velocity of the SOA targeted in this study which estimated by Stokes’s law were the order between 108 m/s and 106 m/s, and Table 4 Probability of collision/coagulation by Brownian diffusion KB [m3/s]. Diameter [m] 5.0  1009 1.3  1008 3.5  1008 9.1  1008 2.4  1007

1.0  1008 2.6  1008 6.9  1008 1.8  1007 4.8  1007 1.3  1014 e e e e

1.4  1014 5.2  1015 e e e

2.6  1014 5.5  1015 2.2  1015 e e

6.3 1.1 2.4 1.2 e

   

1014 1014 1015 1015

1.6 2.5 4.6 1.3 8.6

    

1013 1014 1015 1015 1016

K. Ito, H. Harashima / Building and Environment 46 (2011) 711e718

Acknowledgments

Table 5 Gravitational settling velocity [m3/s]. Diameter [m] vp [m/s]

717

1.0  1008

2.6  1008

6.9  1008

1.8  1007

4.8  1007

6.6  1008

1.8  1007

5.3  1007

2.0  1006

9.3  1006

these velocity order were small enough compared with the order of average velocity in test chamber (Uin ¼ 1.0 m/s). The analytical results of particle size and concentration distribution at sampling position (2) (see Fig. 2) using sectional representations of aerosol balance equations were in good agreement with the experimental results at the initial nucleation and particle formation stage. Concerning the prediction of particle size distribution of SOA formed from ozone and limonene reactions, it was confirmed that the sectional modeling approach was valid and had certain accuracy in cases with a sufficient number of sections. In addition, the decreasing trends of the peak SOA concentration over time were also reproduced in this analysis. The initial nucleation and SOA formation progressed in a short period of time and this phenomenon was the dominant effect of subsequent particle size and number concentration distribution. Although the prediction accuracy of initial nucleation and particle size distribution was improved by introducing the burst nucleation model, which incorporated step change function of the fractional aerosol yield Y(v, t) for partitioning from gas phase to aerosol phase as the first approximation, it is necessary to review the physical and chemical bases of this modeling. Concerning the subsequent changes in size and concentration, there was a difference between prediction and experimental results, especially in terms of the position of peak concentration. Sarwar et al. pointed out that the SOA growth wave is likely caused by condensation/absorption of continuously-generated low vapor pressure by-products onto existing or newly-formed SOA and collision/coagulation processes are insignificant [7,8,34]. In this numerical simulation, condensation/adsorption process, i.e. reaction between newly-formed SOA and gas-phase compound (ozone, limonene and low vapor pressure by-products whose diameter is 10 nm or less), was not modeled. The introduction of the reasonable model concerning condensation/adsorption of formed SOA is necessary to improve the prediction accuracy. The numerical errors caused by ensemble averaging of the governing equations and other factors, for example temperature and humidity effects, partial reactions of ozone with sorbed limonene on the wall, must be also considered in order to improve the prediction accuracy.

Anonymous reviewers gave us valuable suggestions on this research. The authors deeply appreciate their kind suggestions. This research was partly supported by a Grant-in-Aid for Scientific Research (JSPS KAKENHI for Young Scientists (S), 21676005). The authors would like to express special thanks to the funding source.

Appendix A In this study, the individual fractional aerosol yield Y(v, t) was set corresponding to each section. Y(v, t) was estimated by cylindrical test chamber experiment and Fig. A1 indicates the example of Y(v, t) distribution as function of SOA diameter for 20 sections case. Fig. A2 shows the time-dependent modeling of Y(v, t) as function of age of air from supply inlet adopted by Case S05-2, S20-2 and S40-2. The results of age of air at each sampling position are shown in Table A1.

Fig. A1 Y(v, t) distribution as function of particle size.

3

Y[1/ppm/m ]

7. Conclusions This paper reported the modeling procedure and results of numerical analysis that adopted the time-dependent nucleation model and the sectional modeling approach to reproduce ozone and limonene reactions and the subsequent generation and growth of SOA in indoor environments. The numerical analysis was carried out in accordance with the experimental scenarios and the results of numerical prediction were in reasonably agreement with experimental results at an early stage of SOA generation. The changes in particle size distribution over time were reproduced to a certain extent by sectional representations of aerosol balance equations, which incorporated coagulation, collision and gravitational settling effects. Concerning the subsequent changes in size and concentration, there was a difference between prediction and experimental results, especially in terms of the position of peak concentration, and modeling of the reaction of a gas-phase compound and aerosol surfaces and other factors affecting SOA change must be considered in order to improve the prediction accuracy.

0

0

1

2

3

4

5

6

7 8 [sec]

Fig. A2 Y(v, t) distribution as function of age of air.

Table A1 Prediction results of age of air (SVE3). Sampling point

(2)

(3)

(4)

(5)

(6)

(7)

Age of air [s]

2.06

2.51

4.78

5.23

7.50

7.99

718

K. Ito, H. Harashima / Building and Environment 46 (2011) 711e718

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