CFD modeling of particle dispersion and deposition coupled with particle dynamical models in a ventilated room

Accepted Manuscript CFD modeling of particle dispersion and deposition coupled with particle dynamical models in a ventilated room Guangping Xu, Jiasong Wang PII:

S1352-2310(17)30468-5

DOI:

10.1016/j.atmosenv.2017.07.027

Reference:

AEA 15441

To appear in:

Atmospheric Environment

Received Date: 5 December 2016 Revised Date:

14 July 2017

Accepted Date: 16 July 2017

Please cite this article as: Xu, G., Wang, J., CFD modeling of particle dispersion and deposition coupled with particle dynamical models in a ventilated room, Atmospheric Environment (2017), doi: 10.1016/ j.atmosenv.2017.07.027. This is a PDF file of an unedited manuscript that has been accepted for publication. As a service to our customers we are providing this early version of the manuscript. The manuscript will undergo copyediting, typesetting, and review of the resulting proof before it is published in its final form. Please note that during the production process errors may be discovered which could affect the content, and all legal disclaimers that apply to the journal pertain.

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ACCEPTED MANUSCRIPT 1

CFD modeling of particle dispersion and deposition coupled with particle dynamical

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models in a ventilated room

3 Guangping Xu, Jiasong Wang*

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School of Naval Architecture, Ocean and Civil Engineering, Shanghai Jiao Tong University, Shanghai, 200240, China

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Abstract

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Two dynamical models, the traditional method of moments coupled model (MCM) and Taylor-series

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expansion method of moments coupled model (TECM) for particle dispersion distribution and

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gravitation deposition are developed in three-dimensional ventilated environments. The turbulent

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airflow field is modeled with the renormalization group (RNG) k–ε turbulence model. The particle

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number concentration distribution in a ventilated room is obtained by solving the population balance

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equation coupled with the airflow field. The coupled dynamical models are validated using

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experimental data. A good agreement between the numerical and experimental results can be

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achieved. Both models have a similar characteristic for the spatial distribution of particle

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concentration. Relative to the MCM model, the TECM model presents a more close result to the

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experimental data. The vortex structure existed in the air flow makes a relative large concentration

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difference at the center region and results in a spatial non-uniformity of concentration field. With

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larger inlet velocity, the mixing level of particles in the room is more uniform. In general, the new

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dynamical models coupled with computational fluid dynamics (CFD) in the current study provide a

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reasonable and accurate method for the temporal and spatial evolution of particles effected by the

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deposition and dispersion behaviors. In addition, two ventilation modes with different inlet velocities

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are proceeded to study the effect on the particle evolution. The results show that with the ceiling

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ventilation mode (CVM), the particles can be better mixed and the concentration level is also higher.

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On the contrast, with the side ceiling ventilation mode (SVM), the particle concentration has an

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obvious stratified distribution with a relative lower level and it makes a much better environment

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condition to the human exposure.

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*Corresponding author. Tel.: +86 21 34205311; fax: +86 21 34205311 E-mail address: [email protected] (J.S.Wang).

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Keywords: Computational fluid dynamics; dynamical model; indoor particles; deposition;

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ventilation

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1. Introduction In recent years, air pollution is one of the most social concerns especially in developing countries.

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When people in daily life spend most of their time in different indoor environments, the air quality

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becomes the focus of our attention (Steinleet al. 2013; Matz et al. 2014). Aerosol particles are one of

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the main components in indoor air pollutants. These suspended particles in the air, such as dust,

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smoke, and fumes strongly impact the human respiratory system and cause kinds of certain sick

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syndromes. Epidemiological studies have shown that the ultrafine particle number concentration

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associates strongly with morbidity and mortality (Lippmann et al. 2014; Mataloni et al. 2016).

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Therefore, the understanding of evolution rule of the particulate matters appears to be particularly

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important.

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The evolution of particles is effected by various dynamical behaviors such as deposition,

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coagulation, and nucleation. Generally in indoor environments with the existence of relative low

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particle concentration, deposition and dispersion are the main dynamical behavior which dominate

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the evolution of particles. Many studies on particle deposition have been conducted in the last few

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decades. In the work of Lai and Nazaroff (2000), the particle deposition velocities at vertical and

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horizontal surfaces were acquired, which have been applied in many studies about particle deposition

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as a good reference. Nazaroff (2004) then concentrated on summarizing different modeling

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techniques to deal with indoor particle dynamics including deposition, indoor source emission,

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dispersion, and filtration. More recently, the researchers studied the characteristics of fine and

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ultrafine particles deposition in different real indoor environments (El et al. 2008; Laiman et al.

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2014). However, these reviews and researches are based on the assumption that the air condition of

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room and particles is well-mixed, which is hardly satisfied in real conditions. The particles

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dispersion and deposition are always effected by turbulent flow significantly and result in spatial

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non-uniformity. For this reason, it is essential to couple with air flow field to consider the spatial

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distribution of particles.

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ACCEPTED MANUSCRIPT Computational fluid dynamics (CFD) is a strong useful tool applied to predict various flow fields.

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It has been used for studying particle dispersion and spatial distribution with different models

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controlling particle evolution. Theoretically, there are two approaches used extensively to estimate

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the process of particle transport coupled with CFD models: the Lagrangian and the Eulerian methods.

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In the Lagrangian method, the particles are treated as discrete phase and the dynamics of single

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particle is focused by trajectory approach. The motion equations on account of various forces

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exerting on an individual particle is solved to acquire the history information of every single particle.

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On the other hand, the Eulerian method treats particles as a continuum. The particle concentration

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field is obtained by solving governing equations derived from the species conservation condition.

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In particle dynamics studies, each method has its own applicable and appropriate situations.

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From one perspective, the Eulerian method can easily incorporate the particle diffusion effect since

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the randomness of the particle phase is included in the diffusion term of governing equation. From

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the aspect of numerical simulation cost, the computational requirement of the Eulerian method is

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obviously lower than that required by the Lagrangian method. Among the Eulerian approaches, the

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method of moment (MOM) is extensively adopted in literatures studying particle dynamics.

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Settumba and Garrick (2004) coupled MOM with CFD code to study the coagulation behavior in

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temporal mixing layers. The same method was also applied to study the planar jet flow (Yu et al.

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2006) and the poiseuille flow (Song and Lin 2008). More recently, Yu et al (2008) extended a new

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moment method called Taylor-expansion moment method (TEMOM), which could give more

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reasonable and accurate simulation results. This new method was then applied on some particle

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dynamics behaviors including coagulation (Lin et al 2010; 2012), nucleation (Yu et al 2009) and

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breakage (Gan et al 2010) coupled with different flow fields. However, there is little research about

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the two moment methods on the study of particle deposition in indoor environments as we have

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known.

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The approaches proposed in the previous studies could only be valid for the specific issue such as

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the deposition mechanism. However, these methods are not suitable for relative high concentration

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environments that the particles are dominated not only by deposition but also by coagulation

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behavior. Therefore, it is very limited to predict the particles evolution especially in more

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complicated indoor environments. For this reason, it is essential to find another way with more

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extensive applicability that could be applied in more real-world conditions. The moment method

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used in this study has the ability to predict particles evolution under multiple dynamic behaviors

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coupled with flow fields. Compared with the previous Eulerian methods used in the study of deposition, the method of

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moment could easily extend to other particle dynamics, as well as provide more evolution laws about

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not only particle concentration but also geometric diameter and polydispersity as concerned in

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real-world conditions that existing more than one dynamic behavior simultaneously. In many indoor

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environments as described in the previous studies such as Elghobashi (1994) and Zhao et al. (2004),

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with the assumption that the particle sources are all from the outdoor with lower volume fraction of

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particles, as well as there are no particles in the initial indoor environment condition, the deposition

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and dispersion are the main influence factors on indoor particles evolution. When the particle

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concentration in an indoor environment is much higher, the coagulation behavior greatly affect the

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particles evolution, and both the coagulation and deposition behaviors should be considered together.

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However, in other more common indoor environment cases that there exist some particle emission

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sources indoors or lower ventilation rates, the particles evolution is not only dominated by deposition

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but also by other dynamical mechanisms such as coagulation and condensation. For example,

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Glytsos et al. (2010) monitored ultrafine particles (UFP) number concentrations due to several indoor

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sources and indicated that strong coagulation effects shift the particle size distribution to larger sizes

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during candle burning, smoking, onion frying, and hair dryer operation. Similarly, Rim et al. (2016)

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also validated that the coagulation effect can be significant during the source emission due to high

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concentration and high mobility of nano-size particles when there exist indoor UFP sources: an

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electric stove, a natural gas burner, and a paraffin wax candle. In addition, in the study of Rivas et al.

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(2015), the authors had given a result that the coagulation and condensation processes might affect

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UFP indoors when investigating the correlation of indoor and outdoor particle concentrations. The

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higher concentrations of indoor-generated particles were observed in school rooms when closed

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windows hindered dispersion (cold season). This means the low ventilation rate condition indoors

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could also make the particle concentration higher with time elapses and the effect of coagulation

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needs to be considered simultaneously. In addition, Furthermore, when existing in a flow field with

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high turbulence intensity, the particles are dominated by both coagulation and breakage. Besides,

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ACCEPTED MANUSCRIPT when emitted from the tailpipe of motor vehicles, the particles are dominated by deposition,

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coagulation, condensation, and nucleation together. These complicated conditions could not be

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solved by the common Eulerian or Lagrangian model. On the contrary, the method for deducing the

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new models is easy to extend to other mechanisms and has the ability to deal with these situations.

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Previous studies have done some work with respect to coagulation or nucleation coupled with flow

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field. However, there is no related studies, as we have known, on the interaction between the

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deposition and flow field by using this method. This study could provide a basis for studying the

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particles evolution under multiple dynamics behaviors in different type of flow fields.

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In this study, it is aimed to develop new dynamical models coupled with CFD by using the two

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moment methods to the study particle transport and distribution in ventilated indoor environments.

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The main work and the challenge is to transform the mathematical equation describing the deposition

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behavior by the two moment methods into the proper form that could be coupled with turbulence

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models and be solved numerically. The two dynamical models are argued for their applicability and

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accuracy when simulating particle indoor dispersion. A three dimensional ventilated room with

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detailed measured data reported in the literature is selected as the case for comparisons, and the

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simulated results by the two models with measurement are discussed. Moreover, the particle

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concentration in a simulated room with some lay outs and human body is studied to see the effects of

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different ventilation modes and inlet velocities on the particles temporal and spatial evolution.

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2. CFD modeling

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2.1 The turbulent air flow modeling

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In ventilated indoor air conditions, airflow is often considered to be turbulent and particles are

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much easier to transport and disperse affected by turbulence. In order to analyze the particle transport

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process, it is essential to know the airflow field in which particles are suspended. The air phase here

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is treated as a continuum and the Eulerian method is used in the numerical analysis. The interaction

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between fluid phase and particle phase is assumed to be one way, and the impact from particle phase

139

to fluid phase is negligible. This assumption is feasible since particle volume fraction is sufficiently

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small. Among Eulerian methods, the k–ε two-equation turbulence models are computationally

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ACCEPTED MANUSCRIPT efficient and stable compared to more complicated Reynolds stress models. Compared to the

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standard k–ε model, the renormalization group (RNG) k–ε turbulence model has its own advantage

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on simulating turbulent flows. The coefficients of the RNG model are derived theoretically rather

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than experimental fitting adopted in the standard model. The dissipation rate equation has an

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additional strain term. The strong anisotropy at regions occurring large shear can also be considered

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in the RNG model. Wang (2009) has also showed that the RNG k–ε turbulence model has much

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better ability of predicting the vortex structure and flow separation characteristics than the standard

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k–ε model. It is more proper to use RNG k–ε model for simulating indoor airflow and the previous

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researches have also showed better agreements between simulated results and experiment data

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compared to other turbulence models (Posner et al 2003; Kuznik et al 2007). For these reasons, the

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RNG k–ε model is selected to predict the incompressible turbulent airflow in a room.

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The general form of the governing equations can be generalized as:

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∂ + ∂

=

+

, 1

represents the independent variables: time-averaged velocity components u, v, w, turbulent

153

where

154

kinetic energy k, and dissipation rate of turbulent kinetic energy ε. When

155

represents the conservation of mass.

156

and

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source term of the general equation. The modeled equations for the turbulent kinetic energy and its

158

dissipation rate are written as:

TE D

is the velocity component in the coordinate

is the effective diffusion coefficient for each dependent variable

EP

is time.

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+

+

159

where

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for

=

∙

=

∙

is the effective kinetic viscosity,

+ and

+ !

'

+

where ν% is the turbulent viscosity and is written as:

'

direction, .

is the

− , 2 −

"

"

−

, 3

are the inverse effective Prandtl numbers

and , respectively. The generation term of turbulence kinetic energy = ν% &

161

is unity, the equation

(

'

is expressed as:

, 4

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ACCEPTED MANUSCRIPT ν% = is given by = 163

*-

1 − -⁄-/ 1 + 1-.

.

"

, 6

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And the expression for the

. 5

where -=

3&

'

*,

+

'

,

,

(

' !

4

!⁄"

"

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The constants in the RNG k–ε model,

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1.393, 1.393, 1.42, 1.68, 4.38 and 0.012 (Yakhot et al. 1992).

, -/ , and 1, are specified as 0.0845,

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*

"

The air is assumed to be incompressible and isothermal. The turbulent model is solved by the

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form of discretized algebraic equations. The discretization scheme used for all variables except the

168

pressure term is the second-order upwind scheme, and for pressure the standard scheme is selected.

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The transient formulation is solved by the first-order implicit scheme. Finally, this study used the

170

SIMPLE algorithm to couple pressure and velocity fields.

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2.2 The particle phase modeling

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The transport of ultrafine particles dispersed through the fluid is governed by the general

173

dynamics equations (GDE). The GDE describes the particle dynamics under the effect of different

174

physical and chemical processes: advection, diffusion, deposition, coagulation and other dynamical

175

behaviors (Friedlander, 1977). In this study, only the deposition behavior is considered, and the

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dynamics equation is written as:

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∂6 + ∂

6

=

∙

78 + 7%

6

+

96 , 8 9

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where 6 is the particle number concentration,78 is the Brownian diffusion coefficient, which is

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given by Stokes-Einstein expression: 78 =

;< = , 9 3>?9@

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in which ;< is the Boltzmann constant, = is the air absolute temperature, ? is the gas viscosity, 9@ is the particle diameter, and

is the slip correction factor, which is represented as follows:

= 1+

0.43359@ 2B 31.264 + 0.418exp &− (4, 10 9@ B

where B is the mean free path length of the gas molecules.7% is the turbulent diffusivity, which is

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given by: 7% =

G

?

H%

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, 11

where ?

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Schmidt number, which is selected to be 0.7 (Li and Stathopoulos 1997;Tominaga and Stathopoulos 2007). And the source term, 96⁄9 is given by

H%

is the turbulent

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is the dynamic viscosity of fluid, G is the fluid density, and

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96 = −1 I ∙ 6 I, , 12 9

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where I is the particle volume, and 1 I is the deposition rate or the wall loss rate, which is given

187

by:

K! ⁄ .

TE D

1 I = J ∙ I K"

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where J = 4>⁄3

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the mean free path length of the gas molecules;

1.664B

8 = ⁄6>?

K! ⁄

EP

" K! ⁄.

8

+ L ∙ I "⁄. , 13

Q MN ∙ ON6 >⁄N ∙ ∙ P

⁄>R S, in which B is

is the Boltzmann constant; = is the absolute

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temperature; ? is the gas viscosity; N is an empirical value which is selected to be 2.6 (Cheng 1997;

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Park et al. 2001);

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is coefficient of the eddy diffusivity;

is the total surface area of the enclosed

chamber; R is the volume of the chamber. And L = 3⁄4>

"⁄.

2GT⁄9?U , where G is the

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particle density; U is the height of the chamber. In Eq. (13), the two terms on the right hand refer to

194

the diffusion term and the gravitation term respectively. Eq. (12) is not able to be solved directly by

195

numerical methods, and it has to be changed into other forms. Here, a moment method is introduced

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to describe the particle field in time and space. The kth order moment V of the particle distribution

197

is defined as: X

V = W I 6 I 9I . 14 /

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By multiplying both sides of Eq. (2) with I

applying the definition of moment, the transport equation for the moment V can be expressed as: ∂V + ∂

200

after substituting Eq. (13) into Eq. (12) and

V

=

V

& 78 + 7%

where 9V ⁄9 = −MJ ∙ VK"

(+

9V , 9

= 0,1,2 15

+ L ∙ V"⁄. S is the source term due to the deposition effect.

K! ⁄ .

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The first three moment variables V/ , V! , and V" are used to describe the particle properties,

202

representing the particle number concentration, the volume concentration and the scattered level,

203

respectively. Here, the two methods of dealing with the source term are given as below.

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The first method proposed by Park and Lee (2000) is making an assumption that the initial particle number concentration follows lognormal form as: 6 I,

206

in which Y

=

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Y

3I√2>[6\]

^ _ 3−

[6" MI⁄I] 18[6" \]

S

4, 16

is the total particle number concentration at time , I]

is the geometric mean

207

volume, and \]

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in the moment equations can get closed. According to the prior proposed method of moment (MOM),

209

the source term can be converted into the first three moments form and the final expression of the

210

traditional method of moments coupled model (MCM) can be expressed as:

V!

∂V" + ∂t

TE D

∂V! + ∂t

=

a 78 + 7%

EP

V/

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∂V/ + ∂t

is the standard deviation. Consequently, the fractional moment variables existed

V"

=

a 78 + 7%

=

a 78 + 7%

V/

V!

⁄

⁄

⁄d

b − J ∙ V/!c d V!Ke d V"" ⁄

⁄

⁄

⁄

⁄

⁄

⁄

⁄

⁄d

− L ∙ V/K! d V!g d V"g d , 18

⁄d

− L ∙ V/g d V!K!h d V""/ d . 19

b − J ∙ V/" d V!f d V"K!

V"

⁄

− L ∙ V/" d V!f d V"K! d , 17

b − J ∙ V/K! d V!g d V"g

⁄

⁄

⁄

⁄

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Another approach of treating the fractional moment variables is using the Taylor-series expansion

212

method of moment, which is proposed by Yu et al. (2008) for studying the coagulation behavior. This

213

approach has no prior requirement for the particle size spectrum, and the limitation inherent in the

214

lognormal distribution theory automatically disappears. This advantage has greatly expanded the

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feasibility of the moment method in real environment conditions. However, this new approach has

216

not been used in studying the deposition behavior of fine particles as far as we have known. Here, the

217

coupled dynamics model is reestablished to study the distribution of particles in a ventilated room

218

condition. In the source term, the first three moment equations are written as:

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9V/ = −MJ ∙ VK!h⁄.d + L ∙ V"⁄. S, 20 9 9V! = −MJ ∙ VK".⁄.d + L ∙ Vg⁄. S, 21 9

SC

9V" = −MJ ∙ VKh"⁄.d + L ∙ Vf⁄. S, 22 9

221

in which the fractional variables are treated by Taylor-series expansion. In Eq. (14), I expanded about point I = _ as follows: I = _ + _

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"

−

I−_ +

K!

2

_

I

K" "

_

+ −_

K"

K! "

TE D

=

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−1 I−_ 2

+ 2_

K!

Then substituting Eq. (17) into Eq. (8), it is obtained as V =

"

2

2−3 +

"

V/ + _

K!

2 −

"

V! +

"

I+

_

K"

2

is first to be

"

−3 2

"

−

_

. 23

V" , 24

and the expansion point _ is defined as the mean particle size V! ⁄V/ (Yu et al 2008). By applying

224

Eq. (24), the fractional moment variables in Eqs. (20) to (22) can be eliminated and substituted by the first three moments V/ , V! , and V" as follows:

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EP

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VK!h⁄.d = VK".⁄.d = VKh"⁄.d =

1081 gg⁄.d K!h⁄.d 440 dc⁄.d Kdc⁄.d V V! + V V! V" , 25 1521 / 1521 / 1705 !h⁄.d ".⁄.d 184 gg⁄.d Kgg⁄.d V V! − V V! V" , 26 1521 / 1521 /

2234 K".⁄.d Kh"⁄.d 713 !h⁄.d K!h⁄.d V V! + V V! V" , 27 1521 / 1521 /

1 ⁄ 10 ⁄ ⁄ ⁄ V"⁄. = − V/c . V!Kc . V" + V/! . V!" . , 28 9 9

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ACCEPTED MANUSCRIPT Vg⁄. = Vf⁄. =

5 !⁄. K!⁄. 4 ⁄ ⁄ V/ V! V" + V/K" . V!g . , 29 9 9

20 K"⁄. "⁄. 11 ⁄ ⁄ V/ V! V" − V/Kg . V!f . . 30 9 9

Then the final form of the Taylor-series method of moments coupled models (TECM) can be written

227

as:

∂V! + ∂t

V!

a 78 + 7%

V/

1081 gg⁄.d K!h⁄.d 440 dc⁄.d Kdc⁄.d V V! + V V! V" 1521 / 1521 /

b−J∙

1 ⁄ 10 !⁄. "⁄. ⁄ −L ∙ − V/c . V!Kc . V" + V V! , 31 9 9 / =

a 78 + 7% −L ∙

V" =

a 78 + 7%

V!

1705 !h⁄.d ".⁄.d 184 gg⁄.d Kgg⁄.d V V! − V V! V" 1521 / 1521 /

b−J∙

5 !⁄. K!⁄. 4 ⁄ ⁄ V/ V! V" + V/K" . V!g . , 32 9 9 V"

b−J∙

2234 K".⁄.d Kh"⁄.d 713 !h⁄.d K!h⁄.d V V! + V V! V" 1521 / 1521 /

TE D

∂V" + ∂t

=

SC

V/

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∂V/ + ∂t

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20 K"⁄. "⁄. 11 ⁄ ⁄ V/ V! V" − V/Kg . V!f . . 33 9 9

EP

−L ∙

Now, we can use the new MCM model of Eqs. (17-19) and the new TECM model of Eqs.

229

(31-33) coupled with the RANS equations of (1-8) to obtain the particle dispersion distribution and

230

gravitation deposition under indoor ventilated environments.

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2.3 Boundary condition

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In this study, the semi-empirical particle deposition model developed by Lai and Nazaroff (2000)

233

is selected to account for the boundary condition. This method is widely employed in studying

234

indoor particle deposition performance (Zhao et al. 2008; Guichard et al. 2014). The particle mass

235

flux at wall surface, ij , is calculated by

ij = Ik ∙

8

∙ G@ ∙ Jj , 34

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ACCEPTED MANUSCRIPT 236

where Ik is the deposition velocity of particles;

8

is defined as the particle concentration at the

237

first near-wall cell, and the concentration in a small cell is considered to be uniform; and Jj is the

238

total area of each boundary surface.

241 242

surfaces were used in this study.

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In the study of Lai and Nazaroff (2000), the detailed expressions of Ik at different wall The deposition velocity at the vertical surface (IkX ), the upward horizontal surface (Ikl ), and

the downward surface (Ikk ) is expressed respectively as follows: ∗

IkX =

Ikk = ∗

; 35

Ip

X s

1 − exp q− lr∗ t

; 36

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Ikl =

n

SC

239

Ip

X s

exp q− lr∗ t − 1

, 37

is friction velocity, Ip is the gravitational settling velocity of particle, and I is an

in which

244

integral term which is shown as:

TE D

243

n = u3.64

H

"⁄.

.

v − w + 39x, 38

EP

M10.92 H K!⁄. + 4.3S 1 8.6 − 10.92 v = ln { | + √3 tanK! 3 K! 2 + 0.0609 √3 × 10.92 H M10.92

AC C

1 w = ln { 2

H

K!

H

K!⁄.

+ •€S

.

+ 7.669 × 10Kc • €

.

| + √3 tan

• € = 9@

∗⁄

K!

H

H

K!⁄.

K!⁄.

4, 39

2• € − 10.92 H K!⁄. 3 4, 40 ⁄ √3 × 10.92 H K! .

2 , 41

is the kinematic viscosity of air, 9@ is particle diameter. And the total deposition velocity

245

where

246

is expressed as: Ik =

IkX JX + Ikl Jl + Ikk Jk . 42 J

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ACCEPTED MANUSCRIPT 247

The accuracy of the calculated deposition velocity by this equation has been validated by the study of

248

Zhao et al. (2008) that compared the result with the experimental data. Also, this method has been

249

widely used in indoor environment conditions.

250

The inlet profile of velocity is set to be uniform, which is consistent with the real condition of the

251

experiment of Chen et al (2006). The parameter k in the RNG k–ε turbulence model is set to 3.828×

252

10-8 m2/s2, which is determined by

253

the turbulent intensity, which is defined as n% = 0.16 •^‚

254

inlet). The parameter epsilon ( *

.⁄c .⁄"

„ 0.07ƒ , where

*

K!⁄f

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=

n% " ⁄2, in which u is the mean inlet velocity, and n% is

(•^‚ is the Reynolds number at the

) is set to 2.119 × 10-10 m2/s3, which is defined as

is an empirical constant specified in the turbulence model

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=3

(approximately 0.085), and ƒ is the relevant dimension of the inlet. The outlet boundary condition is

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set to be outflow, which is usually applied in the uncompressible flow. And the particle concentration

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at the outlet is set to zero according to the experimental setup.

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3. Results and discussion

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3.1 Model validation for coarse particles

262

3.1.1 Modeling setup based on the experiment

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In order to validate the numerical model for particle transport and deposition in a room, the

264

experiment data including airflow and particle concentration measured by Chen et al (2006) is

265

selected as the comparison case. The model room geometry is 0.8 m length, 0.4 m width and 0.4 m

266

height. The inlet and outlet are both 0.04 m × 0.04 m at the center plane Y=0.2 m as shown in Fig. 1.

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Fig. 1 Schematic of the ventilated chamber used for experiments by Chen et al. (2006)

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The particle density is 1400 kg/m3, and its diameter is tested to be 10 µm. The particle

271

concentration is normalized by the inlet concentration (a lower concentration level that the particle

272

coagulation effect could be neglected) and set to be 1.0. Simulations were conducted for two inlet

273

velocities (Vinlet), 0.225 m/s and 0.45 m/s, respectively. A monitoring point at the center of outlet is

274

set up to estimate the time for the steady state of concentration field. Three sets of uniform structured

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grids 16,000, 128,000 and 512,000 are tested for the transient simulation. The 128,000 (40×40×80)

276

grids for the velocity profile, the turbulent intensity and the particle concentration along the

277

x-direction of inlet center at the center plane shows a quite similar result to those of the 512,000 grids

278

as shown in Fig. 2. Hence, all the following simulations are based on the 128,000 grids to save the

279

simulation time. All the simulations are carried out by the ANSYS Fluent (version 17.0) software.

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Fig. 2 Grids number independence test; (a) velocity; (b) turbulent intensity; (c) particle concentration

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3.1.2 Comparison of simulation results with the experiment of Chen et al. (2006) After simulated for about 400 s with the two inlet velocities as shown in Fig. 3, the concentration

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value at the monitoring point has no longer changed, which could be considered to reach a steady

292

state for both flow and concentration fields to present the final results of the simulation. The mixing

293

time for inlet velocity 0.225 m/s is about 386 s and for inlet velocity 0.45 m/s is about 323 s. The

294

mixing time of higher inlet velocity case is significantly smaller. It is evident that higher ventilation

295

rate could provide better mixing efficiency.

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Vinlet=0.45 m/s

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Fig. 3 Particle concentration variation at the monitoring points with time elapses for two inlet velocities 0.225 m/s

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and 0.45 m/s

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The numerical results of the three-dimensional ventilation flow field are first presented. Fig. 4

302

shows the comparison of simulated x direction velocity by RNG k–ε model with the experimental

303

data for the case with Vinlet=0.225 m/s. The agreement between predicted and measured results is very

304

good although there exists a little difference. The result shows that the selected turbulent model is

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appropriate to calculate the air flow field in a ventilated chamber. The particle concentration is

306

solved simultaneously based on the airflow field calculated by RNG k–ε turbulent model.

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Fig. 4 Comparison of measured and predicted x-direction velocities at three different locations of center plane

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x=0.2m, 0.4 m, and 0.6 m (inlet velocity 0.225 m/s).

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Fig. 5 shows the comparisons of simulated particle concentration by the MCM and TECM

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models with the experimental data under two inlet velocities 0.225 m/s and 0.45 m/s at 400 s. In

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contrast to the measured results obtained by Chen et al (2006), the simulated concentration

314

distribution shows reasonable agreement at three locations. In most positions, the simulated data are

315

close to the experiment data within the uncertainty range except at locations near the ceiling area.

316

The relative error to the measurement is acceptable. The discrepancy means that the simulation

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results overestimate the particle flux to the ceiling wall. It is supposed that this may be mainly caused

318

by the complicated turbulence effect on the deposition which is not accurately estimated. The MCM model essentially captured the characteristics of particle and in a reasonable

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agreement with the experiment. It gives good predictions that the data is in the measured range of

321

deviation at most positions. Relative large discrepancies occur at the ceiling wall area, where the

322

particle concentration are overestimated. This may result from the complicated air flow condition

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near the wall surface which has strongly effect on the particle concentration. And the concentration

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on the boundary surface are also acquired by the semi-empirical model, which may also a possible

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reason for the difference.

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Compared with the MCM model, the TECM model gives a relative smaller simulation values at

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almost all the locations. When the inlet velocity is 0.225 m/s, the difference is very close below

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0.35m, and presents a little larger as well as more close to the measured data when the velocity is

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0.45 m/s. At the locations above 0.35m, it also presents more accurate simulation results although

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some discrepancies existed. The difference of results between MCM and TECM models may come

331

from the derivation of the moment equations. The MCM model is based on the assumption that the

332

particle size distribution is taken as lognormal, which is not consistent with this measurement setup.

333

This could make some inevitable mathematical errors during calculation process. On the other hand,

334

the TECM model is not included any assumption and this difference makes the discrepancy of the

335

final simulation results. On the whole, the two moment equation models could give a reasonable and

336

accurate simulation result about the particle concentration evolving with time and space. Compared

337

with the MCM model, the results calculated by TECM model are more close to the experiment data

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although there still exists some discrepancies in several locations near the ceiling wall.

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Fig.5 Comparison of measured and simulated particle concentrations at three different locations of center plane; (a)

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inlet velocity 0.225 m/s; (b) inlet velocity 0.45 m/s.

344

In order to make a quantitative comparison, the relative errors, defined as |

p

−

|/ , where

p

345

is the simulated value and

is the experimental value, at the nine monitoring points with two inlet

346

velocities are shown in Fig. 6. The numbers are set from 1 to 9, representing the points from the

347

bottom to the top. The simulation results with the two methods are compared with that of Chen et al.

348

(2006). When the inlet velocity is 0.225 m/s, the relative errors of MCM and TECM are smaller at

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ACCEPTED MANUSCRIPT point 1 to 4. The mean error of MCM is 13.26%, which is a little smaller than the 16.27% of Chen et

350

al. (2006), and the mean error of TECM is 16.82%, which is almost the same with that of Chen et al.

351

(2006). Meanwhile, when the inlet velocity is 0.45 m/s, the relative errors of MCM and TECM are

352

smaller at most locations except at the point 9. The mean relative errors of MCM, TECM and Chen

353

et al. (2006) are 16.16%, 12.15% and 15.99%, respectively as shown in Table 1. This result shows

354

that the TECM performs better on simulating the deposition behavior with lager inlet velocity, and

355

the MCM model gives the same level of relative errors compared with the results of Chen et al.

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(2006). It can be considered that the TECM model performs a more accurate result than the MCM

357

model, which gives a result with almost the same level of relative error compared with Chen et al.

358

(2006).

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Fig. 6 Relative errors of different models for the simulation

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Table 1 Mean relative error between the simulated values and the experimental data

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Inlet velocity

Mean relative error (%) MCM

TECM

0.225 m/s

16.27

13.26

16.82

0.45 m/s

15.99

16.16

12.15

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Fig. 7 shows the concentration evolution profiles at the center plane simulated by the two

366

moment methods when the inlet velocity is 0.225 m/s. For both cases, the highest concentrations are

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ACCEPTED MANUSCRIPT around the inlet area, as is treated to be the source of particles. Due to the effect of dispersion and

368

gravitation, the concentration gradually decreases along the x-direction at the centerline of inlet. The

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concentration at the above part of the center plane is always higher than that at the below, where the

370

gravitational settling effect is more obvious than the turbulent dispersion. The particle number

371

concentrations have the similar distribution law with the two models. In the middle region, the MCM

372

model gives a little higher concentration distribution result compared with the TECM model. In

373

addition, the lowest particle concentrations are both at the left bottom of the center plane.

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Fig. 8 shows the same concentration condition when the inlet velocity is 0.45 m/s. Like the case

375

in Fig.5, the result calculated by MCM is relative larger than that by TECM especially at the region

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below Y=0.3 m. Compared with the case when the inlet velocity is 0.225 m/s, it also presents that

377

with the inlet velocity increases or larger turbulent intensity exists, the particle mixing level is

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enhanced, and the particle concentration distribution is more uniform.

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Fig.7 Simulation result of particle concentration distribution at the center surface when inlet velocity is 0.225 m/s.

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(a) MCM model; (b) TECM model.

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Fig.8 Simulation result of particle concentration distribution at the center surface when inlet velocity is 0.45 m/s. (a)

385

MCM model; (b) TECM model.

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ACCEPTED MANUSCRIPT Fig. 9 shows the particle number concentration distribution in the whole flow field with two inlet

387

velocities by the TECM model. It is evident that the concentration at the right part is much higher

388

than that at the left part due to the air flow. The lowest concentration is at the corner near the floor

389

down the inlet. Meanwhile, the streamlines from the inlet are presented to show the vortex structures

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in the simulated room. From the distribution of streamlines, it can be seen that a large vortex

391

structure exists in the center part of the room, which makes the particle concentration lower at the

392

center region of the vortex than that at the place around. This indicates that this type of flow structure

393

strongly affect the particle concentration distribution and produce a lower concentration region at the

394

center of the vortex. When the inlet velocity is 0.45 m/s, the effect of the vortices presents a similar

395

vortex structure, and a lower concentration region also appears in the center region. However, due to

396

the stronger turbulent dispersion, the concentration mixing level is promoted.

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Fig. 9 Spatial distribution of particle concentration and streamlines (dashed lines with arrows) from the inlet in the

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ventilated room. (a) Vinlet =0.225 m/s; (b) Vinlet =0.45 m/s.

401 402

3.2 Model validation for fine particles

403

For further validate the accuracy of the new models for fine particles, another experiment by Zhao

404

et al. (2009) is selected to make the comparison as shown in Fig. 10. In this experiment, the NaCl

405

particles with diameter of 101.8 nm are injected into the room at the inlet. Three grids sets of 3,6550,

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ACCEPTED MANUSCRIPT 14,6200, and 58,4800 are tested and the set of 14,6200 grids is selected , which gives a relative good

407

result considering the numerical simulation cost. The simulated particle concentration at the 27

408

locations of the lines across the 9 places vertically as shown in Fig. 11 are compared with the

409

experimental data, and both the MCM and the TECM give good agreements. Similar situation with

410

the above experiment, the TECM performs much better at the location A, C, D and F. The mean

411

relative errors of MCM, TECM and Zhao et al. (2009) are also calculated, which are 16.16%, 12.15%

412

and 15.99%, respectively. It can be considered that the accuracy of the MOM and the model in the

413

reference are at the same level, and the TECM could give a result with relative less error. Therefore,

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the two models could better simulate the particle deposition behavior in the flow field.

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Fig. 10 Experiment set up by Zhao et al. (2009)

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Fig. 11 Comparison of particle concentration between the simulation and the experimental data

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3.3 Characteristic of particle dispersion in different ventilation systems

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3.3.1 Case description After the validations above, the present developed dynamical model TECM can be taken as a

424

reliable model used to study the particle dispersion and deposition characteristics under different

425

ventilation conditions in a hypothetic room, which is representative in daily life. The dimension

426

room is 5.0 m length, 3.5 m width, and 2.5 m height as shown in Fig. 12. Two ventilation modes

427

named ceiling ventilation mode (CVM) and side ventilation mode (SVM) are designed to supply air

428

flow by two inlets located at the ceiling wall and the side wall with particles and an exhaust at the

429

floor level. Two inlet velocities 0.3 m/s and 1.2 m/s are selected to provide low and high levels of air

430

flow. The particle diameter is set to 10 µm, and its density is 1400 kg/m3, which are the same set as

431

in the experiment above. In addition, the other sets for the turbulent flow field and the particle phase

432

are also the same as that in the above simulation. A monitoring point is set at the location (X=4.0,

433

Y=1.8, Z=1.2) near the head of the human body to simulate human exposure and evaluate the particle

434

concentration level. The wall surfaces are treated to be adiabatic and the temperature difference is

435

also neglected. Three grids sets of 3,1800, 12,7100, and 50,8400 are tested, and the set of 12,7000

436

could give a relative good result with consideration of numerical simulation cost.

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Fig. 12 Configuration of the simulated office room with 5.0 m length (X), 3.5 m width (Y), and 2.5 m height (Z); the

440

dimension of the SVM inlet is 0.4 m × 0.4 m, the CVM inlet is 0.4 m × 0.4 m, and the outlet is 0.4 m × 0.3 m

441

respectively. The human body is simplified by a squre cylinder with 1.2 m height.

443

3.3.2 Particle distribution with CVM and SVM

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The temporal evolution of particle concentration at the monitoring point with two inlet velocities

445

under CVM and SVM conditions are shown in Fig. 13. With CVM, it takes about 11 minutes to

446

reach the final steady concentration for the inlet velocity of 0.3 m/s, and 19 minutes for the inlet

447

velocity of 1.2 m/s. It is evident that with a larger inlet velocity, the concentration increases more

448

quickly to the ultimate stable value. The required time to reach 90% of the final concentration for the

449

two inlet velocities are about 9.1 minutes and 5.2 minutes respectively, and the terminal

450

concentrations reach to the 79% and 65% levels of the supplied inlet concentration. This implies that

451

with CVM, the particles in the room are much easy to disperse to other places by the effect of

452

turbulent flow. When the inlet velocity increases, it changes the increase rate of particle

453

concentration, and makes a little lower level of the final concentration to the human exposure. It can

454

be considered that the CVM is not obviously reduce the particle concentration around the occupant

455

with an arbitrary inlet velocity. On the contrast, with SVM, the time to reach the final steady

456

concentration when the inlet velocity is 0.3 m/s is 7.9 minutes, and 2.9 minutes when the inlet

457

velocity is 1.2 m/s. Meanwhile, the final stable concentrations are 0.186 and 0.468 respectively.

458

Under the same inlet velocity, the time values for the two cases may depend on the inlet location.

459

However, the final stable concentrations under the two inlet velocities decrease by more than half,

460

and there also exists a large discrepancy between the two inlet velocities, which is very different with

461

the case of SVM. It implies that when the inlet velocity is larger, the particles are easier to disperse

462

than the deposit to the wall surfaces so that the particle concentration decreases effectively.

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Fig. 13 Temporal particle concentration at the monitoring point in the CVM and SVM cases with two inlet

465

velocities 0.3 m/s and 1.2 m/s.

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Fig. 14 shows the particle concentrations at different height levels at one location at front of the

467

human body (X=4.1 m, Y=1.7 m). With CVM as shown in Fig. 11(a), the concentration varies in a

468

small range with different height levels. With 1.2 m/s inlet velocity, this difference is very slight.

469

This implies that the particles are in a well-mixed state in the ventilated room, and the effect of

470

dispersion dominated by the turbulent flow makes particles suspend in the air. The higher

471

concentration at Y=1.1 m height is resulted from the particle deposition on the desk where the

472

particles are not easy to disperse. Compared with the case of CVM, the vertical concentration with

473

SVM as shown in Fig. 11(b) presents obvious stratification, which may result from the particles

474

brought to the upper zone by the upward airflow, as well as the particles at the lower places deposit

475

to the floor due to the gravitational settling. For this reason, the particle concentration to the human

476

body (Y=1.2 m) is much lower than that with the CVM. With larger inlet velocity, the turbulent

477

airflow is more likely to make particles stay in the air and make a relative higher concentration level

478

as well.

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Fig. 14 Vertical distribution of particle concentration at the seated human body under two ventilation modes. (a)

482

CVM and (b) SVM.

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Fig. 15 Particle concentration distribution at the pla ne (Y=1.8) across the human body. (a) CVM when Vinlet is 0.3

485

m/s; (b) CVM when Vinlet is 1.2 m/s; (c) SVM when Vinlet is 0.3 m/s; (d) SVM when Vinlet is 1.2 m/s.

27

ACCEPTED MANUSCRIPT 486

Fig. 15 shows the particle concentration distribution at the plane across the human body with

488

CVM and SVM. With CVM (Fig. 15(a) and Fig. (15b)), the particle concentration at the places with

489

human body is much lower which is caused by the particles deposition on more surfaces that less

490

particles are dispersd by the air flow. On the contrast, with SVM (Fig. 15(c) and Fig. (15d)), the

491

concentration around the human body is much higher compared with the other places at the plane.

492

Some particles are dispersed and suspended to the places far away from the particle inlet by the air

493

flow, and the concentration level is dependent on the inlet velocity. Generally, due to the deposition

494

effect, the particle concentration near the floor is also higher than that at the upper places. Meanwhile,

495

there also exist some lower concentration regions at the middle places due to the vortex structure

496

induced by the turbulent flow. In addition, the average particle concentration at the outlet with SVM

497

is much lower than that with CVM as shown in Fig. 16. It is also proved that the particle deposition

498

effect on the evolution of number concentration is more evident with the SVM.

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Inlet velocity is 1.2 m/s

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Inlet velocity is 0.3 m/s

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499 500

CVM

SVM

Fig. 16 Average particle concentration at outlet with CVM and SVM

501 502

Fig. 17 shows the spatial distribution of particle concentraiton with CVM and SVM under two

503

inlet velocities 0.3 m/s and 1.2 m/s. With CVM as shown in Fig. 17(a) and Fig. 17(b), the particle

504

concentration at the places around the human body is at a relative lower level than that at the other

505

half of the room. This difference is supposed to be caused by the exsistence of canbinet, desk and

28

ACCEPTED MANUSCRIPT human body which could increase the particle deposition chance so as to reduce the concentration,

507

which can also be illustrated in Fig. 15(a) and Fig. 15(b). In the core region of the vortex structures

508

presented by the streamlines in the figures, the particle concentration is relative lower than that at the

509

places around due to the turbulence agglomeration effect. With SVM as shown in Fig. 17(c) and Fig.

510

17(d), the concentration presents stratified obviously. At the places far away from the inlet, the

511

turbulent flow gets more weak that the deposition effect dominates the evolution of particles to make

512

the concentraiton decrease greatly. Meanwhile, the turbulent air flow takes less particles to the places

513

near the ceiling surfaces due to the flow field structure. As a result, the concentration level near the

514

floor surfaces is much higher than that at the upper region. In addition, the larger supplied air

515

velocity can imporve the mixing level with both the ventilation situations. It can be concluded that

516

under the same inlet velocity, compared with CVM, the SVM could get a better environment for the

517

seated person in the room with a relative lower particle concentration.

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Fig. 17 Spatial distribution of particle concentration with CVM and SVM. (a) CVM when Vinlet is 0.3 m/s; (b) CVM

523

when Vinlet is 1.2 m/s; (c) SVM when Vinlet is 0.3 m/s; (d) SVM when Vinlet is 1.2 m/s.

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4. Conclusions

In this paper, two moment based coupled dynamical models, MCM and TECM, coupled with

527

flow field are established to simulate spatial and temporal distribution of particle number

528

concentration dominated by deposition in a ventilated indoor environment. Both the effects of

529

dispersion and gravitation settling are considered during the process of particle evolution. The air

530

flow field is simulated by RNG k–ε turbulent model, and the result shows a good agreement with the

531

experiments. The numerical simulation of particle number concentration is also validated by the

532

measured data under two inlet velocities, 0.225 m/s and 0.45 m/s, as well as two diameters of 10 µm

533

and 0.1018 µm.

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According to the comparison with the two experimental results, the new models could better

535

simulate the particles evolution dominated by deposition and air flow with different particle sizes.

536

Compared with the MCM model, the TECM model gives relative smaller concentration values at

537

most locations, and it is shown that the results agree much better with the measured data. The

538

particle concentration calculated by both two models have a similar spatial distribution, and with a

539

large vortex structure, the particle concentration at the center region is much lower than that at the

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ACCEPTED MANUSCRIPT 540

places around. Moreover, with larger inlet velocity or higher turbulence intensity, the mixing level is

541

more uniform. The discrepancy between the results acquired by the two moment models may result from the

543

different derivation of the moment equations, and the TECM model seems to give a better simulation

544

result. In general, the two moment dynamical models are found to be effective methods to study the

545

indoor particle transport and concentration distribution, although there still exist some errors at some

546

locations. Furthermore, another good feature of the moment method is the expansibility to deal with

547

other dynamical behaviors, like coagulation or nucleation, which may be considered simultaneously

548

for further applications.

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The simulation results of concentration comparison between the two ventilated modes, CVM and

550

SVM, indicate that the supplied air with particle pollutants from the ceiling wall surface can produce

551

a more uniform and higher concentration field. Compared with CVM, the SVM produces a more

552

stratified, as well as a lower concentration level that the human exposure could be less serious. The

553

mixing level gets also higher with the inlet velocity increases for both CVM and SVM.

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ACCEPTED MANUSCRIPT Steinle S, Reis S, Sabel C E. Quantifying human exposure to air pollution—Moving from static monitoring to spatio-temporally resolved personal exposure assessment[J]. Science of the Total Environment, 2013, 443: 184-193.

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ACCEPTED MANUSCRIPT Highlights Two moment based coupled dynamical models, MCM and TECM, coupled with flow field are established to simulate particles deposition in ventilated rooms.

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Both models could give good results on particles evolution in the indoor air flow, and the TECM performs relative better compared with MCM.

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Compared with CVM, the SVM could produce a more stratified and lower concentration level.