1、OR-05-5-1 An Integrated Zonal Model for Predicting Indoor Airflow, Temperature, and VOC Distributions Hongyu Huang, PhD Fariborz Haghighat, PhD, PEng Member ASHRAE ABSTRACT This paper presents the development of an intermediate model between CFD models and well-mixed models, the inte- grated zonal m
2、odel (IZM), to predict three-dimensional airflow, temperature, and volatile organic compound (VOC) concentration distributions within a room. The IZMintegrated a zonal model with a three-dimensional air jet model and a three-dimensional building material VOC emissionhink model. The IZM was validated
3、 at three diferent levels: the airflow distribution in a mechanically ventilated room predicted by the IZM was compared with that of the standard k-E CFD model; the temperature distribution for a natural convection case predicted by the IZM was validated with experimental data; and thepredictions of
4、 the total VOCdistri- bution were compared with CFD model predictions. It was found that the integratedzonal model, with quite coarse grids, could provide some global information regarding airflow pattern and thermal and VOC distributions within a room. INTRODUCTION Knowledge of indoor airflow patte
5、rn, air velocity, temperature, and pollutant concentration is important for building engineers either in designing a ventilation system or in evaluating thermal comfort or indoor air quality. Various models have been developed to simulate these parameters within a room. These models can be classifie
6、d as well-mixed models, CFD models, and zonal models. In well-mixed models, a room is treated as a homogeneous mono-zone and the room air velocity, temperature, and contaminant concen- tration are given by a single value, respectively. Therefore, well-mixed models cannot provide detailed airflow pat
7、tern, temperature, and contaminant concentration distributions within a room. Actually, these parameters vary in the space and are influenced by the characteristics of the room. Complete information on air velocity, temperature, andpollut- ant distributions is important for control of local thermal
8、discomfort and pollutants. CFD models can provide detailed knowledge of airflow, temperature, and contaminant distribu- tions within a room, but CFD simulations are too expensive and time consuming to be used as a daily design tool by build- ing engineers. In addition, the accuracy of the CFD result
9、s depends on the users experience and skills in numerical simu- lations. Zonal models are intermediate models between CFD models and well-mixed models. In zonal models, the room is divided into a small number of cells with an order of 1 O- 1 OO. The heat and mass exchange between cells is approximat
10、ely expressed by algebraic or ordinary differential transport rela- tions, and mass and energy conservation principles are applied to each cell to formulate the algebraic equations. The advan- tage ofthis approach lies in its relative straightforwardness for the user to define the problem; on the ot
11、her hand, the formu- lated algebraic equations are relatively small and far easier to solve than the conventional partial differential equations asso- ciated with CFD methods. Therefore, compared to well-mixed models, zonal models can provide users with an estimated view of airflow, temperature, and
12、 contaminant distributions within a room. Zonal models have advantages over CFD models in their simple use, time saving, and satisfactory preci- sion characteristics (Haghighat et al. 2001). Zonal models have been widely applied in building simu- lations for the last 15 years. For indoor airflow and
13、 tempera- ture predictions, promising results have been achieved through integrating zonal models with heat transfer models and air jet models (hard et al. 1996; Wurtz et al. 1999; Musy Hongyu Huang is apost-doctoral fellow and Fariborz Haghighat is a professor in the Department of Building, Civil a
14、nd Environmental Engi- neering, Concordia University, Montreal, Canada. Chang-Seo Lee is a post-doctoral fellow in the Department of Civil Engineering and Applied Mechanics, Faculty of Engineering, McGill University, Montreal. 02005 ASHRAE. 60 1 et al. 2001; Haghighat et al. 2001). This allows us to
15、 consider the integration of pollutant transfer models with zonal models to predict the contaminant concentration within a room. Recently, there have been some concerns about volatile organic compound (VOC) emissions from building material; VOC emitted from building materials have been associated wi
16、th certain symptoms of sick building syndrome, multiple chemical sensitivity, and other health problems. Building materials play a major role in determining the indoor air qual- ity due to their large surface areas and permanent exposure to indoor air. Therefore, predicting indoor VOC concentration
17、distribution is important for building engineers in estimating environmental chemical hazards and occupant exposure and in design of mechanical ventilation systems. This paper first describes in detail the development of an integrated zonal model (IZM) in which a zonal model is incor- porated with a
18、n air jet model and a building material VOC emission Haghighat et al. 2001) or surface-drag flow relations (Axley 2001). The zonal model adopted here applies the commonly used power law viscous loss relations. The physical system considered is a room with a mechanical ventilation system. The room is
19、 in a non- isothermal condition. In the zonal model, the room is subdivided into a number of three-dimensional small cells. The room configuration and partition are shown in Figure 1. Air Mass Conservation Equations. Within each cell, it is assumed that the pressure at the middle of each cell obeys
20、the perfect gas law and the pressure in each cell varies hydro- statically: Pm, = piRTi (1) i,h = ref,i-pigh (2) where Pm,i is the pressure at the middle of cell i (Pa), pi is the air density of cell i (kg/m3), R is the gas constant for air (287.055 Jkg K), is the temperature of cell i (K), PreLiis
21、the reference pressure, which is located at the bottom level of cell i (Pa), h is the height from the bottom of cell i (m), Pi,h is the pressure at the height of h in cell i (Pa), and g is the gravita- tional acceleration (m2/s). Adjacent cells exchange mass through cell interfaces. In each cell, th
22、e general air mass balance can be written as 6 o = c q a, .# IJ (3) j= 1 where qo,v is the airflow rate across the cell i and cellj inter- face (kg/m2s) and A, is the interface area between cell i and cell j (m2). The power law is applied to calculate airflow rate across the cell interface. q a,IJ =
23、 c,pLw“, (4) where APii is the pressure difference between cell i and cellj (Pa), Cdis the coefficient ofpower law (dspa“), usually taken as 0.83, and n is the flow exponent, 0.5 for turbulent airflow and 1 for laminar airflow (Wurtz et al. 1999; Haghighat et al. The pressure at each cell bottom lev
24、el is assumed to be uniform. For horizontal cell interfaces, the airflow rate can be expressed as 200 1). n. Ia.hor e CdPbottom(Pef,top-Pf,bottomPbotrumg If Prf,iop 25D0, V, = Vo x Jet flow Standard flow interface E/ interface A Standard fiow Jwt fiow 4 Figure 3 Configuration ofjet cells. The veloci
25、ty profile at the cross-section: Initial region: +ace E Transition region: X52500, V= Vx= Va x Main region: Jet Cells. Ajet cell includes two subcells; one holds the air belonging to the jet itself and one contains the air from surrounding neighbors, as shown in Figure 3 for a linerjet and a compact
26、 jet. The airflow crossing the interface A (mA), Figure 3, includes the airflow from the jet (mjet) and the airflow from the neighbors (mneighbor). mA = mjei mneighbor (22) The airflow from the jet crossing the interface A, can be modeled as: 604 ASHRAE Transactions: Symposia where Sjet is the jet a
27、irflow passing area (m2). The airflow from surrounding neighbors crossing interface A can be modeled as mneighbor = qa,A(A -jet) (24) where SA is the total area of the interface A (m2) and qa,A is the airflow rate from surrounding neighbors crossing interface A (kg/m2s). Therefore, the airflow cross
28、ing the interface perpendicu- lar to the trajectory of a jet (i.e., A) can be modeled by substi- tuting Equation 21 into Equation 23 and then substituting Equation 23 and Equation 24 into Equation 22; thus, Initial region: Transition region: Main region: (25c) The airflow crossing the interface para
29、llel to the trajectory of the jet (e.g., interface B, Figure 3) can be modeled as the airflow crossing the standard interface. Integrating Material EmissionlSink Model with Zonal Model To predict the VOC concentration distribution within a room, a building material VOC emissiodsink model must be inc
30、orporated with the zonal model. Material EmissiodSink Model. There are two approaches to describe the VOC emissions from dry materials. One approach uses one-phase models (Little and Hodgson 1996; Yang et al. 2001; Huang and Haghighat 2002; Haghighat and Huang 2003), where the dry material is assume
31、d to be a single homogeneous medium. VOC in mate- rials is called in a material phase. Another approach uses multi-phase models (Lee et al. 2002; Tiffonnet 2000) in which the dry material is treated as the solid and fluid as overlapping porous media. VOCs in materials are in the form of gas and adso
32、rbed phases. The multi-phase models consider VOC gas phase difision and ignore adsorbed phase diffusion. Compared with the multi-phase models, the one-phase models are simpler and require less input parameters. In the one-phase model approach, it was suggested that VOC transports from the material t
33、o the room air through three processes (Huang and Haghighat 2002): (1) VOC transfer inside the material is through internal difision and can be described by the tran- sient difision equation. (2) At material/air interface, VOC changes from the material phase to the gas phase. At atmo- spheric pressu
34、re, for low VOC concentration and isothermal condition, the equilibrium relationship between VOC concen- tration in the air phase and VOC concentration in the material phase can be described by a linear isotherm. (3) The gas phase VOC passes through its overlying concentration boundary layer and tra
35、nsports to the room air by difision and convec- tion. The convective mass transfer coefficient is used to express the mass transfer in the boundary layer. Wet building materials, such as paint and glue, can be treated as single homogeneous mediums. Therefore, the one-phase model can also be used to
36、describe the VOC emissions from wet materi- als. Since the VOC internal diffusion and sorption are usually considered as fully reversible phenomena and the mass fluxes depend on the direction of the concentration gradient, the sink behavior of the building materials can be modeled by setting the ini
37、tial VOC concentration lower than the room air VOC concentration. Therefore, the material emissiodsink model becomes (Haghighat and Huang 2003): where, Cmj is the VOC concentration in the jth layer of the material assembly (pg/m3), Dmj is the VOC difision coeffi- cient in thejth layer of the materia
38、l assembly (m2/s), k is the top layer material/air partition coefficient, C,i is the VOC concentration in the near material surface air in cell i (pg/m3), Ca,i is the VOC concentration in the air in cell i (pg/m3), h, is the convective mass transfer coefficient (m/s), Ri is the mate- riai voc emissi
39、on rate in ce11 i (pg/m2s, b is the total material assembly thickness (m), and t is time (s). For a dry material layer, VOC concentration within the material is very low; the dependence of VOC difision coef- ficient on VOC concentration can be ignored. Therefore, each layer of the dry material can b
40、e considered as having homo- geneous difisivity. For a wet material layer, the initiai VOC concentration within the material is usually very high; there- fore, the dependence of VOC difision coefficient on VOC concentration cannot be ignored. Empirical models are usually used to express the difision
41、 coefficient as a function of the concentration. Bodalal(l999) suggested a second-order empirical equation to describe the dependence of the diffusion coefficient of the wet material on VOC concentration. In this study, this equation is used to simulate both the wet phase and the dry phase of the we
42、t material layer. ASH RAE Transactions: Symposia 605 where D, is the VOC diffision coefficient of the wet mate- rial (m2/s), DmO,=, is the initial VOC difision coefficient of the wet material (m2/s), Dm,d, is the VOC diffusion coeffi- cient of the dried wet material (m2/s), C, is the VOC concentrati
43、on in the wet material (pg/m ), and CmO, is the initial VOC concentration in the wet material (pg/m3). The convective mass transfer coefficient, h, can be esti- mated through the correlations among Shenvood number (Sh), Reynolds number (Re), and Schmidt number (Sc) (Huang and Haghighat 2002) as foll
44、ows: 3 For laminar flow, (Rel 500,000): 14 Sh = 0.037Sc3Re: (31) Combined laminadturbulent flow, (Re, Figure 9 Comparison of temperature at X/L = 0.5, Y/W = 0.5. I 1 SRB.0.25Ln 1 I Figure 1 O Geometry of the room. (two-dimensional linear jet) on the top of the west wall (width Lo = 0.06 m). The floo
45、r of the room was covered with polypro- pylene styrene-butadiene rubber (SBR) plate (thickness = 0.25 Lo). The geometry ofthe room is shown in Figure 1 O. The initial total VOC concentration, Co, was 1.92 x lo8 pg/m3, and the difision coefficient of the total VOC was 1.1 x m2/s (at 23C) and 4.2 x Th
46、e total VOC concentration distributions in the room after SBR had been exposed to the air for five days were predicted by the integrated zonal model with a mesh of (1 5 x 1 x S), and results were compared with that of the CFD model(Murakamiet al. 1998), as showninFigure 11 (at 23C) and Figure 12 (at
47、 30C). The lowest VOC concentration was detected in the near ceiling region by both models, since the fresh air came directly along the ceiling. Both models also predicted that the highest VOC concentration was around the m2/s (at 30C) (Murakami et al. 1998). ASHRAE Transactions: Symposia 609 1 I/ I
48、 0.50 1- l .o0 - I- 938 _v_R (X10“) I f lower left corner region. There was good agreement between the prediction results of the concentration distribution by both models, even though there was a small discrepancy. This may be due to the turbulence difhsivity, which is not considered in the integrat
49、ed zonal model. For the average concentration prediction, the discrepancy between the two models was less than 4% at both temperatures. For the above three case studies, it was noted that the simulation results were not sensitive to the grids. The coarse grids were sufficient in generating reasonable results, as well as in providing fast computational speed. The application of this integrated zonal model is not restricted to the above three cases. It can be used to predict the airflow, temperature, and contaminant distributions in a natu- rally andor m
