IMPACT OF MULTIZONE MODEL BOUNDARY CONDITIONS ON THE CFD PREDICTION OF ROOM AIRFLOW AND CONTAMINANT CONCENTRATIONS DISTRIBUTION Jacques Ndione†, Hiroshi Yoshino, and Akashi Mochida Department of Architecture & Building Science, Tohoku University, Sendai, Japan
ABSTRACT Coupling CFD and multizone models can avoid their respective drawbacks in predicting airflow and contaminant concentrations distribution in buildings. Two kinds of boundary conditions are commonly exchanged between them. The multizone model can give either pressure or mass flowrate boundary conditions to CFD. This study analyzes in detail the impact of each of the boundary types on the CFD domain, and compares them with a full CFD simulation without coupling. This study shows that in coupling CFD with multizone, the accuracy of the CFD prediction part depends mainly on the accuracy of the boundary conditions being imposed at their interface. When modeling a very small opening, pressure boundary conditions give slightly more accurate results. For a moderate opening height, both pressure and flow rate boundary conditions show good agreement with the CFD-only simulation. For a large opening, the mass flow rate boundary conditions are better to use.
KEYWORDS CFD, multizone models, Exchange of boundary conditions
INTRODUCTION Multizone network model assumptions can lead to incorrect results in flow calculation. CFD simulation of an entire building is expensive in terms of computational resources. As a consequence, multizone models are coupled with CFD. The idea behind this coupling is to apply CFD at selected zones where the well-mixing assumption of multizone models is not satisfied and let the multizone model handle the rest of the building and its surroundings. With the object of refining the entire calculation, the CFD results are fed back into the multizone model. The coupled model can be solved iteratively by exchanging boundary conditions at the interface between the flow network and CFD model. The following two common boundary conditions are used: • Multizone model gives pressure boundary to CFD • Multizone model gives flow rate boundary to CFD Musser [1] investigated the impact of room representation and boundary conditions on predicted contaminant concentrations and airflow profiles in a set of two isothermal rooms connected by an opening of varying sizes. In his study the quantity of air passing to the second room through the opening was controlled. Such a room representation is simplistic and does not reflect the reality of free air movement in buildings. Additionally, he only studied the effect of velocity as a boundary condition. Until now no one has tried to compare the impact of the multizone boundary conditions on the CFD calculation in order to determine which is more effective. In this study we evaluated the impact of the pressure and the flow rate boundary conditions of multizone models on a CFD prediction of room airflow and the distribution of contaminant concentration, and then did a comparison with a CFD-only simulation. †
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INTERFACE BETWEEN CFD AND MULTIZONE MODELS In order to illustrate the interface between the two models, first we describe the coupling principles of the two programs. In figure 1 we have a two-zone building. Multizone airflow models idealize the building as a network of flow elements (e1, e2, and e3 in figure 1). The flow elements can be doors or cracks and they connect at nodes (Figure 1). The nodes represent either a zone such as a room or external conditions with known pressures (P1 and P2). To calculate the airflow and contaminant concentrations passing through each flow element, multizone applies the continuity equation in each zone as indicated in equations 1 and 2
f a ( P ) = C a 1 (Pa − P1 )
na 1
f b ( P ) = C b 2 (Pb − P2 )
nb 2
+ C ab (Pa − Pb )
nab
+ C ab (Pb − Pa )
nab
= 0 (1) = 0 (2)
where the Cij are the flow coefficient paths and the nij the flow exponential coefficients. Pa and Pb are the unknown pressures.
P1
Pa
Pb
e3
P2
e2
e1
Figure 1. Mutlizone modeling of a building The set of non-linear equations which describe the network are solved numerically using a Newton-Raphson algorithm with some modifications. This is described in detail in reference [2]. Since the above formulations are based on the perfect mixing assumption within the zones, when refinements concerning the airflow patterns and contaminant dispersion are necessary in some zones, CFD can be integrated into the network model [3]. The multizone node representing the room where CFD will be applied is replaced then by new nodes that connect to the cell of the CFD domain. An illustration is shown in Figure 2. The arrows show the effect of the CFD domain on the network model.
P1
Pb
CFD
e1 Interface 1
e2 Interface 2 Figure 2. illustration of the coupling of CFD with multizone
P
e3
2
The CFD model also involves the mass conservation principle in the calculated domain. For each cell in the CFD domain, to enforce mass conservation, in the SIMPLER algorithm a pressure equation is used
∑a
nb
Pnb − a p Pp = b p (3)
nb
where subscript P denotes the node at which the equation is approximated and subscript nb runs over the neighboring nodes. aP and anb are the coefficients of the equation. Their expressions can be found in many CFD reference books; P is the pressure, bp is the mass source term The two programs are coupled by linking equation (3) to the system of equations of the multizone model (equations (1) and (2)), where they can exchange information at their interfaces (Figure 2). For example: 1) Multizone model gives pressure P1 and Pb, or mass flow rate across the interfaces to CFD and CFD gives the calculated pressures at the dotted nodes to multizone 2) Multizone model gives pressure P1 and Pb to CFD and CFD gives the flow rate across the interfaces to multizone The next section analyses through numerical experiment the response of the CFD domain in the case of multizone model (COMIS for our study) giving pressures or mass flow rates, and compares them to the results of a CFD-only simulation of the whole building.
METHOD The computational domain used in our investigation is 9 m long, 3 m wide and 3 m high. It is based on the experimental chamber used by Restivo [4], and other researchers for CFD code validation [5]. In that chamber, the air enters through a diffuser located in the upper portion of the front wall, and exits through a passive outlet near the floor at the opposite wall. Later, this configuration was modified by Musser [1] by dividing the room in half with a wall having an opening in it and adding a forced outlet to the lower portion of the front wall. A two dimensional representation is shown in Figure 3. The supply 3 diffuser is now located on the upper portion of the front wall of the first room and supplies 0.214 m /s to room 1. The air is split between the openings, some going out through outlet 1 and some transferred to room 2 via the opening. Air exits room 2 through a passive outlet 2 located on the lower portion of the back wall. In his study, Musser [1] treated outlet 1 as a forced one. This enabled him to fix the quantity of air going to room 2. In our study, there were no such constraints. The quantity of air from the inlet diffuser was freely separated between outlet 1 and the opening in the partition.
Inlet 3m
Room 2
Room 1
Opening Outlet 1
height = h 9m Figure 3. Room geometry and boundary conditions
Outlet 2
The size of the inlet is 0.168 m high and 3 m wide. Outlet 1 and Outlet 2 have the same geometry which is 0.48 m high and 3 m wide. The opening connecting room 1 and room 2 is 1 m wide. By varying its height, three scenarios were considered. The first is when the opening is the size of a h=0.07 m, the second is for a moderate opening height (h=0.63 m) and the last is the case where the opening is the size of an open doorway (1.8 m). In each of the three scenarios, three steady state CFD simulations were conducted: 1) CFD-CFD : both room 1 and room 2 with CFD 2) CFD-COMIS pressure BC: CFD in room 1 using pressure boundary conditions from COMIS 3) CFD-COMIS flow rate BC: CFD in room 1 using flow rate boundary conditions from COMIS These numerical simulations were performed in isothermal conditions with the standard k-ε model st using the 1 order upwind scheme for the convection term and wall function boundary conditions for the tangential velocity components near the walls. The number of grids used in the CFD-CFD simulation is 72 x 32 x 32 and that of the CFD-COMIS simulations 35 x 32 x 32. We decided on these grid configurations after studying the grid dependence solution and determining that there was no difference between these coarse grids and the finest. In the CFD-CFD simulation, outflow (zero gradients) boundary conditions were used at the outlets (Outlet 1 and Outlet 2). For the CFD-COMIS simulations, boundary conditions for Outlet 1 and Outlet 2 was extracted from the results of the multizone model COMIS which can be pressure or velocity (flow rate) boundary conditions. To evaluate the impact of the multizone model boundary conditions on contaminant concentrations prediction by CFD, a contaminant -7 source of 1.10 kg/s was released at the centre of the floor of room 1. In each calculation, velocity and concentration profiles were recorded at 3 poles in room 1 as shown in figure 4. The first pole located at x = 0.75 m is near Outlet 1, the second pole located at x = 2.25 m is at the centre of room 1 and the last pole located at x = 3.75 m is near the opening connection room 1 to room 2. At each pole the velocity was recorded simultaneously at a height of z = 0.5 m, z = 1 m and at z = 1.5 m. in figures 5, 7, and 9 more detailed vertical distributions are shown corresponding to each scenario.
Velocity sensors
Room 1
Room
z=1.5 z=1.0 z=0.5 x=0.75
x=2.25
x=3.75
Figure 4. Location of recording points of velocity
2
3m
RESULTS Figures 5 and 7 compare the velocity and the concentration contour lines when the opening connecting the rooms is 0.07 m respectively.
CFD-CFD CFD-COMIS pressure BC CFD-COMIS flowrate BC
CFD-CFD CFD-COMIS pressure BC CFD-COMIS flowrate BC
1.4
1.4
1.2
1.2
1.2
1.0
1.0
1.0
0.8 0.6
Z [m]
1.4
Z [m]
Z [m]
CFD-CFD CFD-COMIS pressure BC CFD-COMIS flowrate BC
0.8 0.6
0.8 0.6
0.4
0.4
0.4
0.2
0.2
0.2
0.0 -0.7 -0.6 -0.5 -0.4 -0.3 -0.2 -0.1 0.0 0.1
0.0 -1.0
-0.5
U velocity [m/s] (a)
0.0
0.5
1.0
1.5
0.0 -0.6 -0.4 -0.2 0.0 0.2 0.4 0.6 0.8
U velocity [m/s] (b)
U velocity [m/s] (c)
Figure 5. Velocity profiles in case of h=0.07 m recorded at: (a) x=0.75, (b) x=2.25 and (c) x=3.75 m
0.44
0.50
0.06
0.19 0.25 0.38 0.31
0.13
0.38
Room 2
Room 1
0.56 0.50 0.440.38 0.63 0.31 0.69 0.75 0.81 0.88 0.94 1.00 1.06 1.13 1.19 1.25 1.31 1.38 1.50 1.44 1.56 1.63 1.75 1.69 1.81 1.88 1.94 2.00 2.06 2.13 2.19 2.25 2.31 2.38 2.44 2.50 2.56 2.63 2.69 2.75 2.81 2.88 2.94 3.00 3.06 3.13 3.25 3.19 3.31 3.38
0.06
CFD-CFD
0.10 0.05 0.08
0.08
0.03 0.08
0.08 0.08
Room 1
Room 1
0.13 0.100.08 0.15 0.18 0.20 0.05 0.22 0.25 0.27 0.30 0.33 0.35 0.38 0.40 0.45 0.43 0.48 0.50 0.53 0.55 0.58 0.60 0.63 0.65 0.68 0.70 0.73 0.75 0.78 0.80 0.83 0.85 0.88 0.90 0.93 0.95 1.03 1.00 0.98 1.05 1.25 1.20 1.22 1.13 1.15 1.17 1.10 1.08 1.27 1.30 1.32 1.37 1.35 1.45 1.40 1.42 1.62 1.60 1.55 1.57 1.52 1.47 1.50 1.65 1.67 1.70 1.77 1.75 1.72 1.92 1.95 1.90 1.87 1.80 1.82 1.85 2.00 1.97 2.02 2.05 2.07 2.10 2.12 2.15 2.17 2.20 2.22 2.25 2.27 2.30 2.32 2.35 2.37 2.40 2.42 2.45 2.47 2.50 2.52 2.57 2.55 2.60 2.62 2.65 2.67 2.70 2.72 2.75 2.77 2.80 2.82 2.85 2.87 2.95 2.97 2.90 2.92 3.00 3.02 3.05 3.07 3.10 3.12 3.15 3.17 3.20 3.22 3.25 3.27
0.05
CFD-COMIS pressure BC
0.03 0.05 0.08 0.10 0.13 0.15 0.18 0.20 0.22 0.25 0.27 0.33 0.30 0.35 0.38 0.40 0.45 0.43 0.48 0.50 0.55 0.53 0.58 0.60 0.63 0.65 0.68 0.70 0.73 0.75 0.78 0.80 0.83 0.88 0.85 0.90 0.93 1.13 1.15 1.10 1.08 1.05 1.03 1.00 0.98 0.95 1.17 1.25 1.22 1.20 1.40 1.42 1.35 1.37 1.32 1.30 1.27 1.50 1.47 1.45 1.57 1.60 1.55 1.52 1.65 1.67 1.62 1.80 1.82 1.75 1.77 1.72 1.70 1.85 1.87 1.90 1.92 1.95 1.97 2.00 2.02 2.05 2.07 2.10 2.12 2.15 2.17 2.20 2.22 2.25 2.27 2.30 2.32 2.35 2.40 2.42 2.37 2.45 2.47 2.50 2.52 2.60 2.55 2.57 2.62 2.65 2.67 2.70 2.72 2.75 2.82 2.85 2.77 2.80 2.87 2.90 2.92 2.95 2.97 3.00 3.02 3.05 3.07 3.10
CFD-COMIS flow rate BC
Figure 6.Concentration contour lines in case of h=0.07m. CFD-CFD: both room 1 and room 2 with CFD. CFD-COMIS pressure BC: CFD in room 1 imposing pressure boundary conditions from COMIS CFD-COMIS flow rate BC: CFD in room 1 imposing mass flowrate boundary conditions from COMIS
Figures 7 and 8 compare the velocity and the concentration contour lines when the opening connecting the rooms is 0.63 m. respectively
CFD-CFD CFD-COMIS pressure BC CFD-COMIS flowrate BC
CFD-CFD CFD-COMIS pressure BC CFD-COMIS flowrate BC
1.4
1.4
1.2
1.2
1.2
1.0
1.0
1.0
0.8 0.6
0.8 0.6
0.4
0.4
0.2
0.2
0.0 -1.0
-0.5
0.0
0.5
1.0
1.5
Z [m]
1.4
Z [m]
Z [m]
CFD-CFD CFD-COMIS pressure BC CFD-COMIS flowrate BC
0.0 -1.0
0.8 0.6 0.4 0.2
-0.5
0.0
0.5
1.0
1.5
0.0 -0.8 -0.6 -0.4 -0.2 0.0 0.2 0.4 0.6 0.8
U velocity [m/s] (b)
U velocity [m/s] (a)
U velocity [m/s] (c)
Figure 7. Velocity profiles in case of h=0.63 m recorded at: (a) x=0.75, (b) x=2.25 and (c) x=3.75 m
0.08
0.10
0.05 0.03
0.10 0.08
0.08
Room 2
0.08 0.08
Room 1
0.10 0.08 0.13 0.15 0.18 0.20 0.22 0.25 0.05 0.27 0.30 0.33 0.35 0.38 0.40 0.43 0.45 0.48 0.50 0.53 0.58 0.55 0.60 0.63 0.65 0.68 0.70 0.73 0.75 0.80 0.78 0.83 0.85 0.88 0.90 0.93 0.95 0.98 1.00 1.08 1.05 1.03 1.10 1.13 1.17 1.15 1.20 1.27 1.30 1.22 1.25 1.32 1.35 1.40 1.37 1.42 1.45 1.47 1.50 1.52 1.55 1.57 1.60 1.67 1.62 1.65 1.70 1.72 1.75 1.77 1.80 1.85 1.87 1.90 1.82 1.92 1.95 1.97 2.00 2.02 2.05 2.07 2.10 2.12 2.15 2.17 2.20 2.22 2.25 2.27 2.30 2.32 2.35 2.37 2.40 2.42 2.45 2.47 2.60 2.50 2.52 2.55 2.57 2.62 2.65 2.67 2.70 2.72 2.75 2.77 2.80
CFD-CFD
0.17
0.10
0.03
0.07 0.13
0.07 0.13
0.03 0.10
0.13 0.10
Room 1
0.20 0.170.13 0.23 0.10 0.27 0.30 0.33 0.37 0.40 0.43 0.47 0.50 0.53 0.57 0.60 0.63 0.67 0.73 0.70 0.77 0.83 0.80 0.87 0.90 0.93 0.97 1.00 1.03 1.10 1.07 1.30 1.27 1.23 1.17 1.20 1.13 1.37 1.40 1.33 1.43 1.60 1.57 1.53 1.50 1.47 1.63 1.67 1.77 1.73 1.70 1.83 1.80 2.00 1.97 1.90 1.93 1.87 2.03 2.07 2.10 2.13 2.17 2.20 2.23 2.30 2.33 2.27 2.37 2.40 2.43 2.47 2.50 2.53 2.57 2.60 2.63 2.67 2.70 2.73 2.77 2.80 2.83 2.87 2.90 2.93 3.00 3.03 3.07 2.97 3.10 3.13 3.17 3.20 3.23 3.27 3.30 3.33
0.10 0.10
0.10
CFD-COMIS Pressure BC
0.17 0.13 0.10 0.20 0.23 0.27 0.30 0.33 0.37 0.40 0.43 0.47 0.50 0.53 0.57 0.60 0.67 0.63 0.70 0.73 0.77 0.80 0.87 0.83 0.90 0.93 0.97 1.00 1.03 1.07 1.13 1.17 1.20 1.10 1.27 1.23 1.30 1.33 1.47 1.43 1.40 1.37 1.53 1.50 1.57 1.60 1.77 1.73 1.70 1.67 1.63 1.83 1.80 1.90 1.87 1.93 1.97 2.00 2.03 2.10 2.07 2.13 2.17 2.20 2.23 2.27 2.30 2.33 2.37 2.43 2.40 2.47 2.50 2.53 2.63 2.57 2.60 2.67 2.70 2.73 2.77 2.80 2.83 2.87 2.90 2.93 2.97 3.00 3.03 3.07 3.10 3.13 3.17 3.20 3.23
Room 1
0.07
CFD-COMIS Flowrate BC
Figure 8. Concentration contour lines in case of h=0.63 m. CFD-CFD: both room 1 and room 2 with CFD. CFD-COMIS pressure BC: CFD in room 1 imposing pressure boundary conditions from COMIS CFD-COMIS flow rate BC: CFD in room 1 imposing mass flowrate boundary conditions from COMIS
Figures 9 and 10 compare the velocity and the concentration contour lines when the opening connecting the rooms is 1.8 m respectively.
CFD-CFD CFD-COMIS pressure BC CFD-COMIS flowrate BC
CFD-CFD CFD-COMIS pressure BC CFD-COMIS flowrate BC
1.4
1.4
1.2
1.2
1.2
1.0
1.0
1.0
0.8 0.6
Z [m]
1.4
Z [m]
Z [m]
CFD-CFD CFD-COMIS pressure BC CFD-COMIS flowrate BC
0.8 0.6
0.8 0.6
0.4
0.4
0.4
0.2
0.2
0.2
0.0 -1.0
0.0 -1.0
-0.5
0.0
0.5
1.0
1.5
U velocity [m/s] (a)
-0.5
0.0
0.5
1.0
0.0 -0.6 -0.4 -0.2 0.0 0.2 0.4 0.6 0.8
1.5
U velocity [m/s] (b)
U velocity [m/s] (c)
Figure 9. Velocity profiles in case of h=1.8 m recorded at: (a) x=0.75, (b) x=2.25 and (c) x=3.75 m
0.13
0.10
0.03 0.08 0.05
0.10
Room 2
Room 1
0.08 0.13 0.10 0.15 0.08 0.18 0.20 0.22 0.25 0.27 0.30 0.33 0.35 0.38 0.40 0.43 0.45 0.48 0.50 0.53 0.55 0.58 0.60 0.63 0.65 0.68 0.70 0.73 0.75 0.78 0.80 0.83 0.85 0.88 0.90 0.93 0.95 0.98 1.00 1.05 1.03 1.08 1.10 1.13 1.20 1.22 1.17 1.15 1.25 1.27 1.32 1.30 1.45 1.42 1.35 1.37 1.40 1.50 1.47 1.57 1.52 1.55 1.62 1.60 1.67 1.65 1.70 1.72 1.75 1.77 1.80 1.82 1.85 1.92 1.87 1.90 1.95 1.97 2.00 2.02 2.05 2.07 2.10 2.12 2.15 2.17 2.20 2.22 2.25 2.27 2.30 2.32 2.35 2.37 2.40 2.42 2.45 2.50 2.47 2.52 2.55 2.57 2.60 2.62 2.65 2.67 2.70 2.72 2.75 2.77 2.80 2.82 2.85 2.87 2.90 2.92 2.95 2.97 3.00 3.02 3.05 3.07 3.10 3.12 3.15 3.17
CFD-CFD
0.13 0.10 0.20
0.17
0.03
0.07
0.17
Room 1
Room 1 0.13
0.03 0.07 0.10 0.13 0.17 0.20 0.23 0.27 0.30 0.33 0.37 0.40 0.43 0.47 0.53 0.50 0.57 0.60 0.63 0.67 0.70 0.73 0.77 0.80 0.83 0.87 1.00 0.97 0.93 0.90 1.07 1.03 1.10 1.23 1.20 1.13 1.17 1.30 1.27 1.37 1.33 1.43 1.40 1.60 1.57 1.53 1.47 1.50 1.67 1.63 1.70 1.73 1.77 1.80 1.83 1.87 1.90 1.93 1.97 2.00 2.03 2.07 2.13 2.10 2.17 2.20 2.23 2.27 2.30 2.33 2.37 2.40 2.43 2.47 2.50 2.53 2.57 2.60 2.63 2.67 2.70 2.73 2.77 2.80 2.83 2.87
CFD-COMIS Pressure BC
0.23 0.200.170.13 0.27 0.30 0.33 0.37 0.40 0.43 0.47 0.50 0.53 0.57 0.60 0.63 0.70 0.67 0.73 0.77 0.80 0.87 0.83 0.90 0.93 0.97 1.00 1.03 1.10 1.07 1.17 1.20 1.13 1.30 1.27 1.23 1.37 1.33 1.43 1.40 1.57 1.53 1.50 1.47 1.63 1.60 1.70 1.67 1.73 1.77 1.80 1.83 1.87 1.90 1.93 1.97 2.00 2.03 2.07 2.13 2.17 2.10 2.20 2.23 2.27 2.30 2.33 2.37 2.40 2.43 2.47 2.50 2.53 2.57 2.60 2.70 2.63 2.67 2.73 2.77 2.80 2.83 2.87 2.90 2.93 2.97 3.00 3.13 3.03 3.07 3.10 3.17
0.13 0.10
CFD-COMIS Flowrate BC
Figure 10. Concentration contour lines in case of h=1.8 m. CFD-CFD: both room 1 and room 2 with CFD. CFD-COMIS pressure BC: CFD in room 1 imposing pressure boundary conditions from COMIS CFD-COMIS flow rate BC: CFD in room 1 imposing mass flowrate boundary conditions from COMIS
DISCUSSION In the first case (case 1) where the height of the opening connecting the rooms is (0.07m), the velocity profile predictions (Figure 5) show the same trend, but the actual profiles of the CFD-COMIS simulations differ from the CFD-CFD simulation. The reason is that the boundary conditions of the CFD-COMIS simulations were constructed based on the results of multizone model. However such data can be wrong in the sense that multizone models do not predict airflow patterns. For example in this case, the multizone prediction that most of the air flow goes through outlet 1, instead of the opening between the rooms, is not the same as the CFD-CFD prediction. We also see that the contaminant concentration prediction using pressure boundary conditions more closely reflected the ideal situation of the CFD-CFD simulation than the results of the mass flow rate boundary conditions (Figure 6). At an opening height of 0.63 m (case 2), the velocity profile predictions (Figure 7) of the CFD-COMIS simulations show no significant difference whether pressure or velocity boundary conditions are used, and the distribution of the flow rate between the openings almost match the CFD-CFD simulation. The prediction of contaminant concentration contour lines reproduced the same trend as the CFD-CFD calculation (Figure 8) In the final scenario (case 3), when the height of the door is 1.8 m, we see that the velocity profile predictions (Figure 9) using flow rate boundary conditions show good agreement with the CFD-CFD simulation at the three pole locations. Although the velocity profile predictions using pressure boundary conditions did produce the same trend as the CFD-CFD simulations, the difference is relatively large compared to when using flow rate boundary conditions. We also see that the contaminant concentration prediction using mass flow rate boundary conditions more closely reflected the ideal situation of the CFD-CFD simulation than the results of the pressure boundary conditions (Figure 10).
CONCLUSIONS This study shows that in coupling CFD with multizone, the accuracy of the CFD prediction part depends mainly on the accuracy of the boundary conditions being imposed at their interface. When modeling a crack, pressure boundary conditions give slightly more accurate results. For a moderate opening height, both pressure and velocity boundary conditions show good agreement with the CFD-only simulation. For a large opening, the mass flow rate boundary conditions are better to use.
REFERENCES 1. Musser, A. 2001 An analysis of combined CFD and multizone IAQ model assembly issues, ASHRAE Transactions, 107(1) AT-01-13 2. Feustel, H.E., and A. Rayner-Hooson. 1990. Fundamental of the multizone air flow model COMIS. Technical Note AIVC 29. AIVC, Coventry, CB 3. J. Ndione, H. Yoshino, A. Mochida. 2006. Integration of the multizone model COMIS with CFD for indoor environmental analysis. Annual meeting of AIJ. D-2, pp.705-706. 4. Restivo, A. 1979 Turbulent Flow in Ventilated Rooms. University of London, Mechanical Engineering Department. 5. Davidson, L. and P. Nielsen. 1996. Large “Eddy simulation of the Flow in a Three-Dimensional Ventilated Room.” Roomvent ’96. Vol.2.
