chapter 2 simulation of indoor air quality -...
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Chapter 2
Simulation of Indoor Air Quality
2.1 Introduction
As was noted in Chapter 1, the two main methods for predicting indoor air flows and
contaminant levels are CFD and macro models. Since full scale computer applications for
building environment simulation began in the early 1960s, dramatic progress has been made in
building simulations (Kusuda, 2001). As mentioned in last chapter, Stewart (1998) carried out
a scoping study for the QUESTOR Centre with the aims of determining the availability and
capabilities of current models for indoor air quality. A detailed literature review of micro and
macro models has been carried out to update Stewart’s review and to describe the advantages
and limitations of current modelling methods and investigate the potential for a sub-zonal
multizone model for use in predicting the distribution of contaminants in indoor air.
This chapter describes the historical development, current status and potential future
capabilities of five categories of indoor air quality models: CFD models (section 2.2),
multizone models (section 2.3), zonal models (section 2.4), CFD with multizone models
(section 2.5), and, a new method − coupling zonal and multizone models as developed for this
project, is described in section 2.6. A summary of the current status of models is given in
section 2.7.
2.2 CFD
2.2.1 The conceptual basis of CFD
As a general purpose simulation technology, Computational Fluid Dynamics (CFD) was not
developed specifically for modelling buildings. Its applications include aircraft aerodynamics,
ship hydrodynamics, meteorology, biomedical engineering, the study of pollutant effluents, the
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design of micro-electronic cooling systems and the design of gas turbines and other
combustion equipment.
The essence of CFD is to numerically model physical processes occurring within a fluid by the
solution of a set of non-linear partial differential equations. These partial differential equations
express the fundamental physical laws that govern the conservation of mass, momentum and
energy.
For room air motion the driving forces are pressure differences, which are caused by wind,
thermal buoyancy, mechanical ventilation systems or combinations of these. The
characteristics of indoor air flow are low velocity and high turbulence intensity. Room air flow
can be considered incompressible as velocities tend to be low, in the order of meters or
centimetres per second (at Mach numbers less than 0.3, i.e. velocity about 100m/s, air may be
considered incompressible). Like many common fluids such as water, air is a Newtonian fluid,
displaying a linear relationship between shear and strain rate. When applying CFD to the IAQ
field, the Navier-Stokes equations are derived by applying the principles of conservation of
mass and momentum to a control volume of fluid (see Schlichting 1968 for details),
conservation of thermal energy and mass for a contaminant species may also be applied. In
three-dimensional Cartesian co-ordinates the following set of partial differential equations
describe room air flow, heat transfer and pollutant transport.
Conservation of momentum in x-direction
∂
∂+
∂∂
∂∂
+∂∂
−=∂∂
+∂∂
+∂∂
+∂∂ )()()()()(
xu
xu
xxpwu
zvu
yuu
xu
tj
jjµρρρρ (2.1)
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Conservation of momentum in y-direction
∂
∂+
∂∂
∂∂
+∂∂
−=∂∂
+∂∂
+∂∂
+∂∂ )()()()()(
yu
xv
xypwv
zvv
yuv
xv
tj
jjµρρρρ (2.2)
Conservation of momentum in z-direction
)()()()()()( TTgz
uxw
xzp
wwz
vwy
uwx
wt
j
jj−−
∂
∂+
∂∂
∂∂
+∂∂
−=∂∂
+∂∂
+∂∂
+∂∂
∞βρµρρρρ (2.3)
Conservation of mass
0)()()( =∂∂
+∂∂
+∂∂ w
zv
yu
xρρρ (2.4)
Conservation of energy
qxTk
xwTc
zvTc
yuTc
xTc
t jjpppp +
∂∂
∂∂
=∂∂
+∂∂
+∂∂
+∂∂ )()()()()( ρρρρ (2.5)
Conservation of contaminants
SxCD
xwC
zvC
yuC
xtC
jj+
∂∂
∂∂
=∂∂
+∂∂
+∂∂
+∂∂ )()()()( (2.6)
where
u = air velocity in the x direction (m/s)
v = air velocity in the y direction (m/s)
w = air velocity in the z direction (m/s)
ρ = air density (kg/m3)
µ = air viscosity (Pa.s)
β = the thermal expansion coefficient of air (K-1)
g = gravitational acceleration (m/s2)
t = time (s)
p = pressure (Pa)
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T = temperature (K)
T∞ = reference temperature (K)
cp = air specific heat (J/kg K)
k = air conductivity (W/m k)
q = the heat within the control volume due to a chemical reaction or a heat source located
within the room (W/m3)
C = concentration of contaminant (kg/m3)
D = molecular diffusion coefficient for the contaminant (m2 /s)
S = volumetric contaminant generation rate (kg/m3 s)
Equations 2.1 to 2.3 characterize the transient fluid flow in the common Navier-Stokes
formulation. The last term of the right side of these equations, for example in Equation 2.1,
shown in compact tensor notation1, represents the net viscous force acting in the positive x-
direction. The tensor notation2 used to express the first term on the right side of Equation 2.5
represents the net diffusion of energy into the control volume due to random molecular motion.
The tensor notation3 in the first term on the right side of Equation 2.6 represents net diffusion
of contaminant into the control volume due to molecular diffusion of contaminant in air. As
can be seen, the energy and concentration equations have similar structures to the momentum
equation. Each contains transient, convection, diffusion and source terms (see Schlichting 1968
for meaning of each term in Navier-Stokes equation).
1
∂
∂+
∂∂
∂∂ )(
xu
xu
xj
jjµ expands to
∂∂
+∂∂
∂∂
+
∂∂
+∂∂
∂∂
+
∂∂
+∂∂
∂∂ )()()(
xw
zu
zxv
yu
yxu
xu
xµµµ
2 )(jj x
Tkx ∂
∂∂∂
expands to )()()(zTk
zyTk
yxTk
x ∂∂
∂∂
+∂∂
∂∂
+∂∂
∂∂
3 )(jj x
CDx ∂
∂∂∂
expands to )()()(zCD
zyCD
yxCD
x ∂∂
∂∂
+∂∂
∂∂
+∂∂
∂∂
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Equations 2.1 to 2.6 fully characterize the transient fluid motion, heat and pollutant transfer
throughout the air volume of a room. There are six unknowns (temperature, pressure,
concentration and three velocity components) in these six equations, so the problem is said to
be closed.
An analytical solution of the coupled, non-linear, partial differential equations for a three
dimensional, turbulent flow field is not possible. The use of numerical methods is inevitable
and therefore the calculation of a flow problem requires the discretisation of that flow field into
space and time using either finite difference (Patankar 1980, Fluent 1995, 1996, 1998) or finite
element (Baker et al. 1994, Williams et al. 1994) methods. The volume of interest (such as a
room) is divided into a large number of small cells, also known as the grid. The generation of
the grid may be the most important stage of the setting up of the CFD code. This is because the
size and distribution of grid cells can affect whether a solution is convergent and its speed and
accuracy.
Most practical flows experience some degree of random turbulent fluctuations, which are
caused by instabilities between inertial and viscous forces. Because the turbulent fluctuations
affect the transport of momentum, energy and pollutants, they must be included in the
formulation and solution of the equations of motion. Although the problem has been
investigated for over a century, there is still no general approach to address turbulent flows.
Tennekes and Lumley (1972) stated that it is impossible to make accurate predictions of
turbulent flows without relying heavily on empirical data.
Techniques of various levels of complexity and computational intensity have been developed
to address this chaotic motion. Some approaches (known as direct numerical simulation and
large eddy simulation) attempt to model the details of the turbulent fluctuations with few or no
assumptions. Direct Numerical Simulation (DNS) requires a fine grid and a small time step to
determine the flow field down to the smallest length scale (in indoor air flow fields the scale
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can be less than 0.1 mm (Murakami and Kato 1989)). The number of required grid cells (in the
order of Re9/4 (Nieuwstadt 1992)) and the limitations in current computer capacity restrict the
application of DNS to flows with a moderate Reynolds number. In Large Eddy Simulation
(LES) the small-scale eddies are removed from the turbulent flow via filtering and only the
large-scale eddies are fully resolved. The effect of the small-scale eddies on the turbulent flow
field is modelled. LES can address a transient solution to the Navier-Stokes equations.
However, in a three dimensional flow field there is still a need for a relatively large amount of
computing time to capture all the essential spatial and time scales at a sufficiently fine mesh
and time step.
In contrast to these high-resolution techniques, turbulence transport models, in which the
equations of motion are filtered with respect to time, are able to apply coarser grids and larger
time steps by treating the random fluctuations with statistical methods. Rather than modelling
the details of the turbulent motion, these methods account for the influence of turbulence on
the time-mean motion. However, the time filtering generates new terms (turbulence terms) in
the equations and the equations of motion are no longer a closed system. Therefore, empirical
information is introduced to evaluate the turbulence terms and bring closure to the system of
equations. Rodi (1980) carries out a detailed review of the various methods which have been
developed to evaluate the turbulence terms. These include Reynolds-stress models, algebraic-
stress models, and zero-, one- and two-equation eddy-viscosity models. The most widely used
turbulence model is the k-ε model. This model works by substituting the instantaneous values
in Equations 2.1-2.3 and Equation 2.5 with the sum of an average value and a fluctuating
component (e.g. ui = iu + ui' ). The averaged terms may be calculated over a coarser grid and
so calculation times are much reduced. When the extra terms are added to the equations
additional unknown terms called the Reynolds terms (- ''jiuuρ and - '' Tuc jpρ ) are introduced.
The new terms appearing in the momentum equations (- ''jiuuρ ) contain the high-frequency
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fluctuating velocity components which are called the Reynolds stress (τij). The second term can
be considered as a diffusion term for the enthalpy or other scalar quantity under consideration.
The determination of Reynolds terms requires extra equations to solve the problem. Most
turbulence models are based on the Boussinesq (1877) assumption that the turbulent stresses
are proportional to the mean velocity gradients,
kxu
xu
uu iji
j
j
itjiij ρδµρτ
32'' −
∂
∂+
∂∂
=−= (2.7)
Similarly, the turbulent heat fluxes are assumed to be proportional to the mean-temperature
gradients,
ipjp x
TcuTc∂∂
Γ=− ''ρ (2.8)
where µt is the turbulent or eddy viscosity, k is the turbulence kinetic energy (where
k=2'2'2'(
21 wvu ++ ), and δij is the Kronecker delta (δij =1 for i =j and δij =0 for i ≠ j). The
molecular viscosity (µ) is a property of the fluid. In contrast µt is a property of the flow: it can
differ significantly from one flow to another and can vary throughout a flow domain. Γ is the
turbulent diffusivity of heat. Like the eddy viscosity, it is a property of the flow rather than of
the fluid. The turbulent Prandtl number, σt, is introduced to relate the turbulent diffusivity of
heat and the eddy viscosity,
Γ= t
tµ
σ (2.9)
Experiments have shown that Γ and µt can vary substantially over a flow or between flows,
whereas σt does not (Rodi 1980). Therefore σt can be assumed constant.
The job of the turbulence model is to calculate the distribution of the eddy viscosity (µt)
throughout the flow domain. In the standard k-ε model, the eddy viscosity at each grid point is
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related to local values of the turbulence kinetic energy (k) and the dissipation rate of turbulence
energy (ε) (Launder and Spalding 1974):
ερµ µ
2kct = (2.10)
where cµ is an empirical constant (cµ = 0. 09; Launder and Spalding 1974). The calculation of
the turbulent viscosity thus requires the derivation of two additional equations to determine k
and ε. These equations are derived from the Navier-Stokes equations and can be found in, for
example, Nieuwstadt 1992.
The eddy viscosity concept eliminates the fluctuating quantities from the Reynolds-averaged
equations of motion, turbulent diffusion now being completely characterized by gradients in
the mean quantities and by the eddy viscosity. By substituting Equations 2.7 to 2.10 into
Equations 2.1 to 2.6 (the ijkδ32 terms are absorbed into the pressure-gradients, as discussed by
Rodi 1980), the governing equations become (the superscript ‘-’, indicating the mean value, is
omitted),
φφφ
φρρφ Sx
Uxt i
ii
=∂∂
Γ−∂∂
+∂∂ )()( (2.11)
where φ represents a mean velocity component (ui) or any mean scalar variable (k, ε, H, C).
The description of the diffusion coefficient (Γφ) and the source terms (Sφ) are given in Table
2.1. The k-ε model also requires several constants which have been determined from
experiments (which are also given in Table 2.1).
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Table 2.1 description of diffusion coefficient (Γφ) and the source terms (Sφ) for variable φ.
Equation φ Γφ Sφ
Continuity 1 0 0
Momentum Uj µe )( rijj
ie
ijg
xU
xxp
ρρµ −+
∂∂
∂∂
+∂∂
−
Enthalpy H µ/Pr + µt/σt q
Concentration C µ/Sc + µt/σc S
Kinetic energy k µe/σk Gs +GB -ρε
Dissipation rate ε µe/σε C1(Gs +GB)ε/k –C2ρε2/k
∂
∂+
∂∂
∂∂
=i
j
j
i
j
its x
uxu
xu
G µ ; it
tiB x
gG
∂∂
=ρ
σµ
ρ; µe = µ +µt.
Empirical constants in the model equations (Gan 1995): C1 = 1.44; C2 = 1.92; σt = 0.9;
σc = 1.0; σk = 1.0; σε= 1.22.
ρr = air density at a reference point.
Pr and Sc are laminar Prandt number and Schmidt number respectively.
In order to solve Equations 2.11 it is necessary to know and specify the appropriate boundary
conditions. Typically, the velocity, temperature and contaminant concentration of air supplied
from forced ventilation or other inlets must be provided. Values of these parameters at outlets
are calculated by the model. Treatment of flow conditions at wall surfaces is important as is
that for heat transfer to or from wall and other room surfaces.
As described in Equations 2.11, the k-ε equations have the same general structure as the
momentum and energy equations. When the discretization, linearization and boundary
condition techniques discussed above are applied, the k-ε equations can be solved in the same
manner as the other governing equations, as described in, for example, Patankar 1980.
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2.2.2 Development
Patankar (1970, 1972, and 1980), Launder and Spalding (1974), Gosman (1977) and their co-
workers have described the numerical method for the solution of equations of air flow and heat
transfer. Nielsen (1974), Nielsen et al. (1979) and Gosman et al. (1980) developed these
algorithms for indoor air flow and heat transfer. After the development of these algorithms
CFD was first deployed for the simulation of fundamental studies of indoor air climate. It took
about ten years before CFD was applied for more practical indoor air quality because of the
limitations of computer processing power. Over the past decade there has been a substantial
body of work completed using CFD methods to examine various aspects of indoor air flows,
air quality and contaminant transport. For example, two IEA annexes (Annex 20, Lemaire et al.
1993; Annex 26, Heiselberg et al. 1998), two ASHRAE research projects (Baker et al. 1992;
Chen and Srebric 1999), and an entire issue of the journal Building and Environment (1989)
have addressed the topic.
Nielsen (1989), Chen (1995), Emmerich (1997), AIVC (1998) and Stewart (1998) provide a
good review of the applications of CFD in predicting indoor air flow and contaminant levels.
The relevant details have been extracted and are summarized in the next sections.
General room airflow
A number of researchers have published details of long term projects to model air flows in
buildings.
Awbi and Gan have developed a k-ε CFD code (known as VORTEX), which takes into
account radiative heat exchange. Details of the VORTEX code are given in Gan and Awbi
(1994). They applied the CFD code to predict thermal comfort and contaminant distribution in
both mechanically and naturally ventilated offices (Awbi 1989, Awbi and Gan 1991, 1993,
Gan 1995). They examined different ventilation systems and their efficiencies which included
the effectiveness of contaminant removal and thermal comfort in rooms with different heat
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sources and openings. After comparing laminar and turbulent cases, they found that turbulence
has a major influence on air movement in a room, and reliable turbulent models and accurate
boundary conditions are very important. Additional applications reported include modelling
mixed convection from heated room surfaces (Awbi and Hatton 2000) and a study of the air
quality in the breathing zone in a room with displacement ventilation (Xing, Hatton and Awbi
2001).
In another major effort, Chen et al. (1988) applied a CFD program and a building energy load
program to predict ventilation efficiency and temperature efficiency in a ventilated room with
different ventilation systems and rates. They found that a large internal gain in the room
lowered the ventilation efficiency but had little influence on the temperature efficiency. In later
work, Chen and Jiang (1992) made a study on the performance of four ventilation system types
in a classroom with a low ventilation rate. In this study the pupils and desks were represented
as aerodynamic blockages generating heat and CO2. They found that buoyancy caused a
secondary flow which dominated the airflow pattern and resulted in similar overall ventilation
effectiveness and thermal comfort for all four cases (except near the diffusers) and similar
average CO2 concentration in all cases. Recently, Chen at al. (1995) applied CFD with
conjugate heat transfer and radiation models to predict a room thermal response. In this study
only surface – surface radiation was included. More recently, Xu and Chen (2001a and 2001b)
have developed a two-layer turbulence model to simulate indoor airflow with combined forced
and natural convection (mixed convection). The results show that their computation data agree
with measurements very well.
Li (1992) developed a CFD code which coupled radiative heat transfer with CFD. The results
show that radiation plays a considerable role in thermal stratification with displacement
ventilation. Li (1994) also developed a method to deal with complex geometries using a non-
body-fitted Cartesian grid. Recently, Li et al. (1996c, 1996d) applied CFD to evaluate several
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measures of ventilation systems. More recently, Li et al. (2000) applied CFD code to predict
natural ventilation in buildings with large openings.
Murakami and Kato (1989) compared the predictions of a 3-D k-ε turbulence model with
experimental measurements in a ventilated clean room with turbulent recirculating flows. They
were able to demonstrate good agreement.
Varying inlet/outlet arrangements
A common application of CFD simulation is to study the performance of ventilation systems
with different diffusers and different inlet and outlet arrangements. Murakami et al. (1989)
analyzed airflow and contaminant diffusion in several types of clean rooms with different
supply and exhaust diffuser arrangements. They examined the effects of varying the number
and arrangement of supply and exhaust ducts on air flow and contaminant distribution and the
contribution of heat sources and sinks to the temperature distribution in a room. The following
conclusions were reached:
• numerical simulation is useful for parametrically analyzing changes in flow conditions for
complex conditions;
• supply outlets have a large influence on both flow fields and contaminant diffusion fields;
• the arrangement of exhaust ducts has a small influence on flow fields but a large influence on
contaminant diffusion fields;
• arrangement of supply ducts in a chequered pattern is superior to a linear pattern in terms of
ventilation effectiveness.
As Moser (1991) predicted, one of the major difficulties in accurate CFD modelling is how to
treat mechanically ventilated inlet airflow from diffusers. Several researchers have conducted
projects comparing a number of ways of representing inlet diffusers. Emvin and Davidson
(1996) discuss four methods of representing a diffuser consisting of 84 jets. The four methods
include detailed modelling of all jets; representing the diffuser as a single jet with an inlet area
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equal to the sum of the individual nozzles (basic model); representing the diffuser as a single
jet with an inlet area equal to the total area of the diffuser with decoupled mass flux and
momentum flux boundary conditions (momentum method); and a ‘box’ model where the
diffuser is represented by a (large) box with boundary conditions given at the box surface.
Only the detailed model was reported to be accurate but it was also expensive.
In another study, Skovgaard and Nielsen (1991) applied two techniques to model diffuser flow
including modelling the diffuser directly and modelling the resulting flow pattern in a volume
in front of the diffuser (PV method). They found that the PV method had the best performance
but it depended on diffuser specific data. Chen and Jiang (1996) applied CFD code to predict
the airflow from a curved surface using three different grid systems including cylindrical co-
ordinates with small step, body-fitted co-ordinates, and unstructured grids. They concluded that
the body-fitted and unstructured grids produced flow patterns that agreed well with flow
visualization techniques but required high labour costs for setting up the simulation. The
cylindrical co-ordinates could not simulate the airflow pattern correctly. Huo et al. (1996)
developed a new method to describe diffuser boundary conditions, called jet main region
specification. They found that the method may be used to accurately predict diffuser boundary
conditions without describing the complicated diffuser geometry and, therefore, saved
simulation time by using a coarser grid.
Recently, Svidt et al. (1998a) applied the CFD code FLOVENT to model airflow through a
slatted floor by using a volume resistance model and a plane resistance model. They found that
the predicted airflow rate was in the range of 10% less than measured. More recently, Bjerg et
al. (2000) applied a 3D k-ε turbulence model to model a wall inlet in livestock rooms. They
found that the numerical results agreed with measurements well very well in the occupied zone
and beneath the ceiling of the test room. Sinha (2001) simulated the behaviour of an inclined
jet on room cooling using CFD. The results show that the angle of the inclined jet has a large
influence on room temperature.
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Occupant effects
There have been several studies (Depecker et al. 1996, Nielsen et al. 1996 and Kalzuka et al.
1992) which examined the impact of occupants on flow regimes and on contaminant
distributions. Occupants are usually treated as sources of both contamination (carbon dioxide
and, sometimes, smoke) and heat. The occupant is usually assumed not to move during the
CFD simulation. Recently, Svidt et al. (1998b) simulated airflow in occupied livestock
buildings using CFD. The results show that it is possible to have a good agreement between a
simple model based on a volume resistance and the laboratory measurements for the specified
case. Nielsen et al. (1998) and Stankov et al. (1999) simulated the influence of furnishings on
indoor flow and pollutant dispersion. Murakami et al. (1998) analysed the influence of
occupants on contaminant distribution.
Displacement ventilation
In a displacement ventilation room, air is supplied near or at the floor and exhausted near or at
the ceiling. In contrast to conventional mechanical ventilation, which is usually arranged to
mix the air in a room, displacement ventilation aims to provide a ‘once through’ system. Some
of the attempts to model displacement ventilation have found that thermal effects from heat
conduction through walls (Li et al. 1996a and 1996b) and radiation through windows can act to
enhance or retard displacement ventilation depending on the conditions.
Some displacement ventilation studies have focused on the thermal environment and/or
ventilation effectiveness. Jiang and Haghighat (1992) studied the effectiveness of a
displacement ventilation system in a partitioned office with five different partition layouts. The
results showed that the arrangement of the partitions was more important to contaminant
concentration and average age of air than the number of partitions. Alamdari et al. (1994)
applied CFD to simulate airflows and temperature distributions in an open-plan office space
with a displacement ventilation system. They concluded that secondary airflows resulting from
infiltration and cold surfaces have adverse effect on the ventilation performance and reduce
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thermal comfort. Awbi (1996) studied the performance of displacement and mixing ventilation
systems for an office and found that the displacement system could provide similar air quality
in the breathing zone with half the ventilation rate of the mixing system.
A few displacement ventilation studies have focused on the effects of heat sources on
displacement ventilation systems. In an early study, Jacobsen and Nielsen (1993) simulated the
thermal environment in a displacement-ventilated room with heat sources and used an
extension of the k-ε turbulence model with a buoyancy factor to account for turbulent viscosity
dependency on vertical temperature gradients. Chen and Chao (1996) studied the flow in a
turbulent buoyant plume and in a displacement ventilated room with obstacles. Recently,
Loomans (1998) performed measurements and simulations on the desk displacement
ventilation system. More recently, Park and Holland (2001) investigated the effect of location
of a convective heat source on displacement ventilation. They found that the effect changed the
temperature field and resulted in a reduction of the cooling load in the occupied zone.
Large enclosures
Many researchers have applied CFD code to simulate airflow within a large enclosure. In one
detailed report, Murakami (1992) describes many of the unique characteristics of large
enclosures (volume, ceiling height and small occupied zone), ventilation design principles, and
prediction methods including simple equations, scale models and CFD modelling.
Many researchers (Kato et al. 1995, Off et al. 1996, Moser et al. 1995, Schild 1996, Awbi and
Baizhan 1994) have applied themselves to the studies of atria. Other researchers (Clancy et al.
1996, Van der Mass and Schaelin 1995, Guthrie et al. 1992, Chow and Fung 1992, Fontaine
and Rapp 1996) studied other types of large enclosures such as auditoriums, airport passenger
terminal buildings, parking garages and gymnasia.
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The IEA initiated a study of Air Flow in Large Enclosures (Annex 26) which was completed in
1996. The final report on this annex has been edited by Heiselberg et al. (1998) and provides
useful information for the study of indoor air quality in industrial buildings. Part of the study
included an assessment of the value of CFD models for large enclosures. Some of the outcomes
from the final report were reported by Stewart (1998):
• conventional computational fluid dynamics approaches incorporating k-ε type turbulence
representation were found to be capable of giving reliable prediction results for temperature,
air velocity and pollutant fields;
• small changes to boundary conditions may significantly affect the main pattern of air flow
and temperature distribution. It was therefore essential that boundary conditions were
accurately represented. The extra effort expended to obtain realistic data is of proven value;
• radiative heat transfer is a sensitive component of energy transport and must be incorporated
in any computational fluid dynamics analysis;
• convective heat transfer from boundaries to the air were not reliably predicted using coarse
grid systems and log-law wall functions. Results tended to be grid spacing dependent. The
use of prescribed convective heat transfer coefficients was proposed as an alternative,
although it was acknowledged that this might not be easy. New wall functions for free
convection heat transfer are presently being tested;
• slow or non-existent convergence of the solution procedure was found in some instances.
This tends to occur when flow is dominated by free convection forces (i.e. thermal
buoyancy). It was demonstrated that this problem could be overcome by using a ‘coupled’
rather that a conventional ‘sequential’ (SIMPLE) solver. In addition, instability in solutions
was found in an isothermal calculation of the air jets in a sports hall in Germany. It is
concluded that such flows may only be modelled by time-dependent computation. A steady-
state model will never converge.
More recently, Li et al. (2000) performed CFD and multizone modelling to predict fog
formation risk in a naturally ventilated industrial building. Mora, Gadgil and Wurtz (2000)
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applied CFD and zonal models to simulate air flows in large indoor spaces. They propose a
way of coupling a model of detailed airflow in large spaces to a multizone infiltration model.
Lam and Chan (2001) simulate a gymnasium using CFD. They found that significant thermal
stratification occurs in the gymnasium and the annual cooling load can be overestimated by
45% for the best exhaust position when the effect of thermal stratification is ignored. Lu et al.
(2001) applied CFD to investigate the air flows field in and around a designated refuge floor,
which was specially designed in high-rise buildings for the purpose of supplying a temporarily
safe place for evacuees under emergency situations. This study shows that air flow could be a
factor affecting the smoke flow pattern.
Natural ventilation
Natural ventilation relies on wind pressure, appropriately placed openings and thermal
buoyancy to provide clean fresh air to buildings and therefore reduces the energy requirements
of mechanical ventilation systems. Many researchers have taken an interest in this ventilation
method. Tsutumi et al. (1992) and Iwamoto et al. (1992) applied CFD to study cross-
ventilation in residential buildings. Barozzi et al. (1991) performed simulations and
experiments on a solar driven passive ventilation system. Jones et al. (1991) studied infiltration
rates in a naturally ventilated industrial building using both CFD and multizone models.
Kornaat and Lemaire (1994) investigated carbon monoxide levels in an indoor car park with
natural ventilation and determined that a mixing fan was needed to avoid unacceptably high
local concentrations.
More recently, Peppes et al. (2001) performed CFD and measurements to simulate buoyancy-
driven flow within a naturally ventilated residential building. They concluded that all floors
connected to a stairwell proved to behave as different zones.
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Contaminant transport
Many studies have reported CFD simulations for steady state cases of airflow and inert
contaminant transport.
Nagano and Mimi (1992) studied airflow and pollutant concentrations in a rectangular, two-
dimensional space with different combinations of floor and ceiling supplies and exhausts and
Reynolds numbers from 5 to 10,000. They predicted that, for most cases, ceiling supply offered
better ventilation efficiency than floor supply. Schaelin et al. (1992) used the commercial CFD
code PHOENICS to model air flow, temperature and contaminant distribution in a kitchen with
a workbench containing a cooking plate with an overhead exhaust fan, and in another building
with a heating radiator and various combinations of open and closed windows with and without
external pressure caused by wind. The calculations were performed in steady state but could
also be solved for time-varying boundary conditions though in most cases it was usually
preferable to calculate stationary solutions for three or four different boundary conditions
rather than the dynamic behaviour of the room air flow.
Kato et al. (1996) simulated contaminant distribution in a room with a displacement ventilation
system and one occupant. The contaminant source configuration included generation
throughout the room, from the ceiling, from a point source and the surface of the occupant.
Murakami et al. (1989) and Kato et al. (1992) also predicted steady state contaminant
concentrations in clean rooms.
Cafaro et al. (1992) applied CFD to model transient cases of both air flow and contaminant
transport. They studied contaminant transport in a simple room to gain insight into the issue of
natural gas leaks. The situations analyzed included both pollutant decay from an initial uniform
concentration and pollutant build up due to a source.
33
The more common approach taken for transient contaminant transport studies involves using a
steady-state flow solution to solve for transient pollutant concentrations generated by a source.
This approach was applied by Roy et al. (1993), Suyama and Aoyama (1992), Haghighat et al.
(1994) and Riffat and Shao (1994).
There have also been attempts to model the distribution of particles or aerosols which is more
difficult because of the need to model deposition and possibly suspension. Lu and Howarth
(1996) and Fontaine et al. (1994) used Lagrangian particle tracking methods with assumptions
of no heat and mass transfer between air and particles, no particles rebound from surface,
spherical solid particles, and motion governed by Newton’s second law. They concluded that
deposition and migration are mostly influenced by airflow patterns and particle properties, the
majority of particle migrations occur within the first 10 minutes of particle tracking time, large
particles deposit much faster than small, and small particles can remain in suspension for
longer than two hours.
More recently, Lin et al. (2000) applied CFD to simulate concentration distribution of CO2,
radon and moisture in a typical Hong Kong industrial workshop with displacement ventilation.
They concluded that prediction of contaminant distribution is more difficult than air
temperature and flow distribution. Topp, Nielsen and Heiselberg (1999) modelled emission
from building materials with CFD. They reported that the model predictions agreed with
experimental results very well. Papakonstantinou et al. (2000) calculated velocity, pollutant
concentrations and temperature fields within the archaeological museum of Athens using a
three-dimensional CFD model. The air pollutants considered were O3, CO, SO2, NOx, Pb and
CO2. Nazaroff (2001) performed experiments and CFD modelling on particle deposition in
cracks, ducts and rooms.
34
2.2.3 General capabilities of current models
General
All CFD models are based on the conservation laws of mass (continuity equation), energy
(internal-energy equation) and momentum (Navier-Stokes equations), collectively called the
governing equations for fluid flow and listed in Section 2.2.1.
Most applications of CFD for room air flow and heat transfer simulation have employed the k-
ε model which was originally developed for high-Reynolds number (i.e. fully turbulent) flows.
Strictly speaking the standard k-ε turbulence model is only valid for fully-developed
turbulence. However, in general, room air flows are not fully turbulent. Baker et al. (1994)
state that most room air flows are locally turbulent, but flows away from HVAC (Heating,
Ventilation and Air Condition) supply systems and obstructions with edges tend to be subtly
turbulent. He indicated that the standard k-ε model would overpredict the transfer of heat and
momentum in regions where the flow is “subtly” turbulent. Although air flow at diffuser
outlets tends to be turbulent, measurements indicate that the flow in the main body of
ventilated rooms may be transitional (Jones and Whittle 1992). A mix of flow regimes was
found near most heated or cooled surfaces, such as radiators and windows.
There are two main approaches which may be used to overcome this problem. The first uses
‘boundary layer theory’ to treat air flows near solid walls, where viscous diffusion dominates
turbulent diffusion. The common approach is to use the wall function method (Launder and
Spalding 1974). This method does not attempt to calculate the flow within the laminar and
semi-laminar regions of the boundary layer where molecular diffusion is significant. The wall
function method assumes the form of velocity and temperature profiles within the boundary
layer while the next-to-wall grid points are placed in the fully-turbulent region. Variations in k
and ε are made consistent with these velocity functions. Of the many constructs of wall
functions that had been developed and applied, Launder and Spalding (1974) recommended
these semi-empirical formulations based on their experience with fully turbulent flows.
35
Because the logarithmic velocity profile (see White 1979, for example) for forced flow is the
foundation of Launder and Spalding’s wall functions, they are often referred to as the “log-
law” wall functions. The standard form of the k-ε model in conjunction with log-law wall
functions has been widely applied in predicting room air flow and heat transfer.
The second approach is alternate turbulence modelling, which includes low-Reynolds number
modelling with k-ε, alternate k-ε models, higher resolution options to k-ε, alternate near-wall
approaches for k-ε and zero-equation turbulence models (Beausoleil-Morrison, 2000). These
are described briefly in the following paragraphs.
Low-Reynolds number modelling
In low-Reynolds number modelling (Launder and Spalding 1974, Lam and Bremhorst 1981)
grid points are placed within the boundary layer, including the laminar region. Then some of
the empirical constants (as described in Section 2.2.1) will vary with the local turbulence
Reynolds number. Low-Reynolds number models have been applied for indoor air flow
modelling (Chen 1995, Nielsen 1998, Awbi 1998). Some improvements relative to wall
function methods have been demonstrated, but at the expense of substantially higher
computational requirements and reduced stability.
Alternate k-ε models
Beausoleil-Morrison (2000) reported that there are three alternate formulations: two-layer
model, two-scale model and renormalization-group model. He stated that the alternative k-ε
formulations performed well in some cases, poorly in others.
Higher resolution options to k-ε
As mentioned in Section 2.2.1, Large eddy simulation (LES) methods can address a transient
solution to the Navier-Stokes equations at the expense of relatively large amounts of
computing time. Nielsen (1998) and Emmerich and McGrattan (1998) have applied LES to
36
buildings for isothermal air flows. Performance has been adequate, but not substantially better
than the standard k-ε model. Further refinement will be necessary before this method can be
widely used in buildings. Chen (1996) has applied a Reynolds-stress model to predict room air
flow and heat transfer. Only slight accuracy improvements relative to the standard k-ε model
were found at the expense of substantially higher computational requirements and stability.
Alternate near-wall approaches for k-ε
Takemasa et al. (1992), Yuan et al. (1994), Xu et al. (1998) and Neitzke (1998) have developed
new wall functions for use with the standard k-ε model. These models can not be extended to
the general case yet.
Zero-equation turbulence models
Rather than solving the k and ε equations to calculate µt using Equation 2.10, zero-equation
models use a fixed value for the eddy viscosity or relate it to the mean velocity distribution.
This substantially reduces computational requirements relative to the k-ε model. Chen and Xu
(1998) and Srebric et al. (1999) have applied this method for some cases. They found good
agreement between the computed and measured air velocity and temperature profiles.
At this time, none of the other alternatives have been proven to be suitable universal
replacements for the standard k-ε model (Beausoleil-Morrison 2000).
Some widely used CFD programs, including those for the Annex 20 work are listed in Table
2.2 (from Lemaire 1992).
37
Table 2.2 Computer codes suitable for modelling indoor air flows
(adapted from Table 2.4, Lemaire 1992, p12)
Name Country Origin of code Type Method
ARIA UK Abacus C FVASTEC UK Harwell C FVCALC-BFC S Chalmers R FVCHAMPION NL TUD R FVEOL – 3D F INRS R FVEXACT3 USA NIST R FVFEAT UK C FEFIDAP USA FDI C FEFIRE A AVL C FVFLOTRAN Compuflow C FEFloVENT UK FLOMERICS C FVFLOW-3D UK Harwell C FVFLUENT USA Fluent Inc. C FVJASMINE UK BRE-FRS R FVKAMELEON N SINTEF R FVPHOENICS UK CHAM C FVSIMULAR AIR A AVL C FVSTAR-CD UK CD C FVTEACH -3D DK Aalborg R FVTEMPEST USA Batelle R FVWISA-3D NL TNO R FV
Note: R= research code, C = commercial code, FV = finite volume, FE = finite element.
Conclusions from Annex 20
Stewart (1998) stated that apart from the details presented for work on large enclosures, the
most useful source for an evaluation of currently available models for indoor air quality is the
report Room Air and Contaminant Flow, Evaluation of Computational Methods (Lemaire et al.
1993), which included details of work carried out for Annex 20 of the IEA.
Researchers in thirteen countries worked on the project over a period of 3.5 years and
completed fifty individual research projects which included specification of test cases covering
a wide range of application and environmental scenarios, experimental measurements for the
test cases, simulations and evaluations.
38
Stewart’s (1998) summary of the conclusion of the Annex 20 report is given below.
Application of models as design tools
• CFD simulations are useful when variables needed in all points of the flow field are difficult
to measure.
• CFD simulations are useful to study the sensitivity of flow patterns to small changes of
conditions.
• When neither similar experience nor measured data exist (large spaces, unconventional
ventilating systems, strong buoyancy effects), CFD simulations are useful to predict air flow
patterns for critical projects.
• Simplified methods are useful to estimate the throw of supply air jets, the maximum velocity
in the occupied zone, or the thermal plume in a radiator-window configuration.
• A catalogue of pre-calculated cases is useful to get a quick overview of flow patterns that
may develop in standard office rooms under various conditions.
In general, CFD codes can make a valuable contribution to understanding air movement in
spaces and can predict room air movement with sufficient realism to be used for design
purposes. It is necessary, however, that CFD codes are used with care and, most importantly,
with the exercise of sound engineering judgement.
Performance of models in prediction of flow parameters
As part of Annex 20, measurements were made under isothermal and buoyant conditions
encompassing forced and free convection. The following general conclusions concerning the
performance of the models in the prediction of flow parameters were presented.
• The isothermal air flow pattern and velocity decay can be predicted with an acceptable
degree of realism by almost all the CFD models. In many cases the predicted occupied zone
velocities are within a band indicating general compliance with expectation. However, in
some case velocities are underpredicted. Small recirculation areas in the corners of the room
39
were usually not predicted although their impact is believed small. In the one case where
corner recirculation was reproduced a low Reynolds number model was used.
• CFD models can predict flow pattern, velocity and temperature distribution in buoyant flow,
although with a reliability reduced from that demonstrated for isothermal flow. It was
difficult to obtain converged and grid independent results.
Technical problems
During the work undertaken for Annex 20, a number of technical problems were identified and
it was suggested that attention should be given to these in future work.
• It was suggested that the use of low Reynolds number models be further investigated for the
turbulence models used for the range of Reynolds numbers encountered near walls.
• It is particularly difficult to model supply jet characteristics.
• Thermal wall functions are required to predict heat transfer from natural and mixed
convection at warm or cold surfaces, which proved difficult to predict for some of the tests.
• Convergence of flow fields with buoyant conditions was generally poor.
2.2.4 Difficulties with CFD
Most applications of CFD for room air flow and heat transfer simulation have used the k-ε
turbulence model. An important restriction for the use of this type of model is that the solution
of the system of equations converges to a ‘steady-state’ result. Since many of the contaminant
dispersion situations of interest will be transient or dynamic, this must be a serious drawback
for the use of this type of CFD model. A further practical limitation is the time taken for the
model to converge to a solution. There is always a trade-off between the number of grid cells
used and therefore the grid size and the time needed for the computation. There are many
examples in the literature of analyses conducted on fast PC’s, but these often have run of times
of tens to hundreds of hours and grid sizes of 10,000 to 30,000 cells. It has been reported that it
took a week or more to carry out the cycle of setting up, executing and analysing the results for
one configuration.
40
In large spaces air flows tend to be dominated by thermal effects (rather than momentum from
air supplied by a mechanical ventilation system) and thermal coupling with outside air
(because of the significant area of external walls) may also be important. Unfortunately, it is
difficult for CFD codes to model natural convection.
CFD models are complicated and their application requires much specialized knowledge and
sound engineering judgement. When CFD is applied, it is often difficult to set up the model,
identify and specify appropriate boundary conditions.
2.2.5 Future development
There are ongoing developments in most aspects of the use of CFD for air flow and air quality
modelling.
As discussed in Section 2.2.3 there are a number of efforts to improve turbulence modelling,
especially for the near-wall regions. Many of these methods are being developed for indoor air
flow.
It is a challenge for current CFD models to simulate natural ventilation. Given the increasing
interest in natural ventilation, attention should be directed towards modelling and especially to
identification of the boundary conditions.
Commercial software is also improving, especially in terms of the provision of user interfaces
which aid the less expert user to correctly set up and execute a simulation and to interpret the
results.
Several research teams have combined CFD with multizone models (see Section 2.5).
41
Heiselberg et al. (1998) give a review of some recent work using CFD models for indoor air
flow and air quality modelling. In addition to improved turbulence modelling, advances are
under way in most areas of CFD modelling including the provision of:
• improved methods for solving the systems of equations;
• improved numerical schemes for the convection term;
• improved computational accuracy and error estimation;
• better fitting of structures using unstructured computational grids;
• more sophisticated treatment of inlet and outlet openings and wall boundary layer flows;
• investigation of solar heat gain models.
The Heiselberg report also includes details of a wide range of tests and comparisons of the use
of multizone and CFD models with experimental data.
2.3 Multizone models
2.3.1 The conceptual basis of multizone models
The distribution of air flows inside a building is driven by pressure differences which may arise
from any combination of wind, thermal buoyancy effects and mechanical ventilation. The
distribution of openings on the external and internal divisions, some of which may be varied by
the occupants, will also lead to significant pressure differences within a building (see Feustel,
1989, p160). Figure 2.1, taken from Feustel (1989), shows how these factors combine to
influence pressure and hence air flow distribution.
As mentioned previously, air flow modelling is a necessary pre-cursor to air quality modelling.
Air flow into, out of and within buildings and their compartments may be simulated for
buildings if the air leakage rates, current weather and external shielding conditions are known.
As noted in Section 2.1, Macro modelling is an alternative method to CFD for predicting
42
indoor air quality. Macro models include multizone models and zonal models. They are
discussed in this section and the next section respectively.
Figure 2.1 Influences on air flow distribution in buildings (from Feustel 1989)
In their survey of air flow models for multizone structures, Feustel and Dieris (1992) identified
two main model categories, single-zone and multizone.
Wind velocity and direction
Surroundings
Shape of the building
Wind pressure distribution
Temperature differences
Mechanicalventilation system
Vertical flow resistance
Thermal buoyancy
Building
Fan and duct characteristics
Imposed pressure
Leakage configuration
Inside pressure distribution
Air flow distribution
Inhabitants behaviour
43
Single-zone models assume that a building can be described by a single, well-mixed zone.
These models are most often used for single-story, single-family houses with no internal
partitions (e.g. all internal doors are open) which will hardly ever be true for large industrial
buildings.
Single-zone models can be classified as empirical and physical models (Feustel 1989).
Empirical infiltration models are based solely on knowledge from infiltration measurements.
Infiltration rate can be assumed to be constant or obtained from tracer gas measurements by a
regression method.
Physical models became possible after pressurization measurement techniques for building
components or whole buildings were developed. They can be divided into two groups: crack
models and single-zone network models. The crack model was the first real attempt to estimate
leakage of a building’s envelope. In this method the infiltration is assumed to be proportional
to the product of crack coefficient and crack length and can be expressed by an empirical
power law function (Feustel 1989),
nn pCpalQ ∆=∆= (2.12)
where
Q = infiltration rate
a = crack flow coefficient
l = crack length
C = flow coefficient
∆p = design pressure
n = flow exponent
Values for the exponent range between n = 0.5 for fully turbulent jets or turbulent flow and n =
1.0 for fully laminar flow. It is common to use n = 2/3 for the crack method (Feustel 1989).
Crack flow coefficients are published in various handbooks and infiltration standards (German
Standard 1959, Reinhold and Sonderegger 1983 and Liddament 1986).
44
Single-zone network models are based on a mass balance equation which takes into account all
flow paths between the outside and the building. For a building with k flow paths the mass flow
balance is written as,
∑=
−
−−=
k
j ioj
iojniojj
pp
ppppC
0
0 ρ (2-13)
where
ρ = density of air
Cj = flow coefficient flow path j
Poj = external pressure for flow path j
Pi = internal pressure
n = flow exponent
The principal disadvantage of this approach is its data requirements, which include flow path
distribution, flow path characteristics, weather data, shielding and terrain roughness conditions
and the characteristics of the mechanical ventilation system. In order to overcome this limit
some simplified single-zone models have been developed. For example, the LBL-model
(Sherman 1980), the NRCC model (Shaw and Tamura 1977) and the BRE-model (Warren and
Webb 1980). These models often assume that the distribution of whole house leakage can be
obtained from pressurization tests. Infiltration rates induced by wind and stack are calculated
separately and superimposed later.
In single-zone models, a zone is defined as a fully mixed volume with a constant concentration.
Therefore, there are no single-zone buildings in reality. However, a smaller building without
internal partitions or at least with open internal doors can be simulated with reasonable
accuracy by single zone models (Feustel 1989). Unfortunately, single-zone models are also
often used to calculate air flows in multizone structures, which goes beyond the application
range of these models.
45
Multizone models are suitable for buildings containing more than one well-mixed zone. In
fact, most buildings should be characterized as multizone structures even when no internal
partitions are present (e.g., airplane hangers). The essence of multizone models is that the
internal pressures in each identified zone must be known (or be determined) and that flows
from zone to zone are determined by a combination of pressure difference and a description of
the flow path between the zones. These are network models made up from nodes (representing
zones) and inter-node flow paths. Figure 2.2 shows how a two-room building would be
represented in a multizone model (from Stewart 1998). The two rooms are represented by the
black numbered circles. Room 1 has two windows, an extractor fan and an internal door to
room 2. Room 2 has a window, an external door and an internal door to Room 1. Nodes outside
the building are represented by the un-numbered black circles which describe the boundary
conditions for the pressure. The diagram illustrates clearly that this type of model simulates
flows between zones rather than within zones (i.e. inside the rooms of a building). A series of
inter-related mass balance equations must be solved simultaneously to derive a solution.
As for their single-zone counterparts, multizone models are based on the following mass
balance equation,
∑ ∑= =
−
−−=
m
l
k
j iioj
iiojniiojij
pp
ppppC ij
0 0 ,
,,,
,0 ρ (2.14)
where
m = number of zones
k = number of links of zone i
ρ = density of air
Cj,i = flow coefficient for flow path j of zone i
Poj,i = external pressure for flow path j of zone i
Pi = internal pressure of zone i
nj,i = flow exponent for flow path j of zone i
46
Unlike the single-zone models, where there is only one internal pressure to be determined, in
multizone models one pressure for each of the zones must be determined. This has led to
considerable complexity of the numerical solution algorithm. These models have wide
potential in predicting infiltration and ventilation air flow distribution. Their weakness for
indoor air contaminant work is that the air in each zone is assumed to be well mixed. This will
generally lead to incorrect assumptions about the risk of exposure to contaminants. In spaces
with high ceilings stratification effects may lead to contaminants being concentrated in either
Elevation
Plan
Vent
Window
Window Window
Door
12
Figure 2.2 Representation of a two-room building in a multizone model
(adapted from Stewart 1998)
Door
47
the upper or lower regions. Estimation of transfer of contaminants to other parts of the
building, or to outside, will be incorrect if the connection path starts in an area where the local
concentration is very different from the assumed mean concentration.
2.3.2 Development of multizone models
A survey by Feustel and Kendon (1985) revealed 26 papers describing 15 different multizone
infiltration models. A literature review and questionnaire survey undertaken by Feustel and
Dieris (1992) describes fifty different models.
One of the first models they found was Jackman’s model LEAK which was published in 1970.
This was followed by the National Research Council of Canada’s model (Sander, 1984) in
1974, which was the first one made available to interested parties. Indeed this numerical tool
was probably still the most widely used multizone infiltration model in the 1990s.
Feustel and Dieris go on to document continuing progress throughout the 1970s and 1980s
when new models were produced with gradually increasing sophistication. Several multizone
models were developed in the aftermath of the oil price crisis. The program STROM (Feustel
1977) was developed at Technische Universitaet, Berlin. Concurrent with STROM, ELA 4 (de
Gids, 1977) was developed. The models VENT1 and VENT2 (Etheridge and Alexander, 1980)
as well as BREEZE (Evers and Waterhouse, 1978) were developed in the late 1970s by
researchers from British Gas and the Building Research Establishment. Models such as
AIRNET (Walton, 1983) and MOVECOMP (Herrlin, 1985) were the first to attempt to solve
the set of non-linear equations which arise if a building contains zones with widely differing
leakage characteristics. Treatment of open doorways in otherwise airtight buildings can lead to
failure to converge to a single solution. Newton’s method for mathematical solutions with
under-relaxation factors was applied to overcome the problem.
48
They also discovered some models developed in Japan, France, and Brazil. Work done in
Japan was published by Hayakawa and Togari (1979), Ishida and Udagowo (1988), Hayashi et
al. (1985), Sasaki (1987), Okuyama (1987), and Matsumoto and Yoshino (1988). Some
multizone models developed in CSTA, INSA (Cacavelli et al. 1988) and EDF, France, are
listed. From Brazil, the model FLOW2 (Melo, 1987) was also described by Feustel.
One of the most recently developed models is COMIS (Feustel and Raynor-Hoosen, 1990,
Feustel, 1999). COMIS was produced by an international co-operative project team as part of
an International Energy Agency project. It has very sophisticated treatment of all aspects of
indoor air flow and air quality. COMIS was developed under the IEA’s Annex 23‘Multizone
Air Flow Modelling’ initiative. COMIS, together with the CONTAM series (Walton, 1997,
Dols, 2001) under the development at the National Institute of Science and Technology in the
USA, probably represent current state-of-the-art in multizone models.
Feustel and Dieris gave a useful summary table of their survey which is reproduced as Table
2.3. Stewart (1998) gave further comment on the details. Some of them are summarized below.
• The rapidly increasing power of PCs means that most, if not all, programs of this type will
run on such machines without the capacity limits mentioned.
• Those air flow models which are combined with a thermal model are expected to give more
accurate simulations. Only programs combined with a pollution model are useful for indoor air
quality analysis.
• Only those models which are available to third parties and which have been, or can be,
validated can be expected to be widely used. A conventional FORTRAN code with a modular
structure and good input and output features has this potential.
2.3.3 General capabilities of current models
As mentioned in the last section the CONTAM and COMIS models probably represent state-
of-the-art in multizone models. They are useful tools for analyzing airflow and contaminant
49
Program language:FORTRANBASICPascalCHPLdBaseIV
34 4 1 2 3 1
Computer type:Main frameWork stationPC
14 11 15
Solver:Hardy-Cross methodNewton-Raphson methodLevenberg-Marquard methodBrown-Conte methodSecant methodRule ‘ falsi’Gaussian eliminationBeta-method (Newark)
1 25 1 1 3 1 1 1
Limits:Max. number of zonesMax. number of openings/zonesMax. number of shafts/corridors/floorsMax. number of mechanical ventilationsystem
<= 100 18 17 17 18
> 100 7 3 2 2
NO limit 18 23 23 20
Input features:Interactive inputCAD inputWeather data from files3-D building descriptionSchedules (e.g. occupants)
Yes 15 1 24 10 19
No 21 30 14 26 17
Not specified 14 19 13 14 14
Output features:File of arrays used by modelGraphical outputStatistical functions
Yes 29 12 5
No 6 23 29
Not specified 15 15 16
Structure:Separate input programModular structure
Yes 24 20
No 14 14
Not specified 12 16
Combination with other models:Combined with thermal modelCombined with pollution model
Yes 15 13
No 24 26
Not specified 11 11
Availability:Program available to third parties
No 15
Yes 15
Yes, but 12
Table 2.3 Summary of multizone air flow infiltration network model
(from Feustel and Dieris, 1992)
50
transport in complex multizone buildings on a macro level. They are well documented, have
modular structure and sophisticated graphical user interfaces, have been extensively tested and
characterized, have links to thermal energy codes and are in the public domain.
More details on the COMIS program have been published than for CONTAM and it will be
used here to describe the capabilities of multizone models.
Program description
COMIS (Conjunction Of Multizone Infiltration Specialists) is a multizone air flow and
contaminant transport model with a modular structure, developed as a result of an international
research collaborative effort under the auspices of the International Energy Agency. The actual
simulation code, written in Fortran 77, was previously named COMVEN. More than 200
copies are being used in 15 countries and there is obvious potential for it to become a standard
for multizone air flow modelling.
The program includes the following flow elements: cracks, duct systems, fans, flow controllers,
vertical large openings (windows and/or doors), kitchen hoods and passive stacks. COMIS
allows the user to define schedules describing changes in the indoor temperature distribution,
fan operation, pollutant concentration in the zones, pollutant sources and sinks, opening of
windows and doors, and the weather data. The flexible time step implemented in COMIS
enables modelling to be independent of the frequency with which the weather data are
provided. The COMIS air flow calculation is based on the assumption that indoor air flows
reach steady-state at each time step. The contaminant transport is based on a dynamic model
and has its own time step, based on the time constant of the most critical zone. The two models
are coupled. Results for air flows and contaminant levels are reported in data tables by COMIS
and in graphical form by some of the user-interfaces.
51
The principal underlying the COMIS model is that buildings are complicated interconnected
networks of air-mass flow paths. Zones in the building (rooms or groups of rooms) are
connected by the flow paths. Each path has some flow resistance whether it is an open or
closed door or window or leakage through walls, joints or other cracks. COMIS includes
airflow equations for large vertical openings, single-sided ventilation, and different opening
situations for various window types. The boundary conditions for the pressure distribution
inside the building are described by nodes or grid points outside the building. More details can
be found in the COMIS web site at http://www-epb.lbl.gov/comis/ (most recent update, March
2, 2000).
Two user interfaces are available for PCs: COMERL, a simple text editor based user interface
with an integrated database, and COMIS/IISiBat, a graphical, sophisticated user interface,
developed at the Building Technology and Scientific Centre, CSTB at Sophia Antipolis in
France (IISiBat, 1997), which is available on the internet: http://evl.cstb.fr/iisibat.htm.
Feustel and Raynor-Hoosen (1990), and Feustel (1999) have described COMIS in detail. A
summary is presented in the following sections.
Air flow components
(1) Crack flow
All multizone models need to calculate the flows through cracks in the building. Air leakage
characteristics can be represented by a power law equation based both on theory and
measurement:
( )npCQ ∆= (2.15)
where
Q = air flow rate
∆p = pressure difference
C = air leakage coefficient
52
n = pressure exponent
In COMIS cracks are classified as windows, walls, doors, etc. and appropriate correction
factors are introduced. A temperature correction factor is also introduced to increase the
accuracy.
(2) Air flow through large openings
Airflow through doorways, windows and other large openings are a significant way in which
air, pollutants and thermal energy are transferred from one zone of a building to another or to
the outside. Predicting air flow through a large opening is difficult. A general solution is
applied in COMIS to include large openings in the pressure network of a multizone model,
which is generally applicable for most large openings. This model is based on a combination of
Bernoulli’s assumptions and of empirical knowledge acquired from experiments in real
configurations. COMIS takes pressure and density differences into account at several levels
spaced in the opening. The mass flow is calculated for each interval representing a fraction of
the pressure difference profiles. The total flow is obtained by summation over the whole
opening.
The calculation is split into different cases corresponding to a range of possible openings:
• closed opening (opening factor = 0) – summation of top and bottom crack plus integration
over two vertically distributed cracks. Equation (2.15) is applied for crack calculations.
• normal rectangular vertical openings – integration over n openings with the actual open width
and height of interval. The basic equation as implemented in COMIS source code is,
ii
ni
iid phWcm ∆= ∑
=
=
ρ21
(2.16)
where
m = mass flow rate (kg/s)
cd = actual value for discharge coefficient (-)
W = actual open width (m)
53
n = number of integration intervals for a large opening (n = 20 in COMIS)
hi = interval of opening i (m)
ρi = air density of opening i (kg/m3)
∆pi = effective pressure difference of opening i (n), which is the sum of the
stack pressure difference and the difference of actual pressure at reference
height
• horizontally pivoted window (flow direction assumed strictly perpendicular to the plane of
the opening) – integration over normal rectangular openings at top and bottom of a large
opening plus a rectangular opening in series with two triangular openings in the middle of the
large opening (most general situation).
(3) Ducts
Pressure losses in ducts are calculated taking into account both friction losses (∆pfriction) and
dynamic losses due to duct fittings (∆pfittings). They are expressed as:
fittingsfriction ppp ∆+∆=∆ (2.17)
dynamicfriction pdlp λ=∆
dynamicfittings pp ×=∆ ζ
where
λ = dimensionless friction factor (−)
l = length of the duct (m)
d = diameter of the duct (m)
pdynamic = dynamic pressure of the air flow (Pa)
ζ = dimensionless coefficient (−)
A passive stack is a link from a zone in a building to the outside (roof), which is also
considered in COMIS.
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(4) Fans
Fan performance is expressed by the total pressure difference and the volume flow rate, which
can be based on fan laws or an expression for the fan operating curve. The fan laws relating to
the effects of fan rotating speed (N) and air density (ρ) are expressed by (Feustel and Raynor-
Hoosen, 1990):
2
121 N
NQQ ×= (2.18)
2
12
2
12,1, ρ
ρ×
×=
NN
pp FF (2.19)
Subscript 1 denotes that the variable is for the fan under consideration; subscript 2 denotes that
the variable is for the test fan.
Fan performance may be expressed by a polynomial approximate formula using the least
square method, on the basis of at least three data pairs of the volume flow rate and the pressure
difference.
(5) Flow controllers
Four types of flow controller (ideal symmetric, ideal non-symmetric, non-ideal symmetric,
non-ideal non-symmetric) were described in COMIS.
Flow controllers usually have a valve to change the cross-section of the flow path, thereby
changing the relation between the flow through and the pressure across the controllers. In
COMIS flow controllers are described by their performance characteristic.
(6) Kitchen hood
COMIS models kitchen hoods by means of a set of power law equations or by using a
component that calculates the spread of pollutants into the zone.
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Boundary conditions
The boundary conditions describe the interaction of the building with the external environment,
particularly those forces which act to drive the air flow around and through a building.
COMIS includes dimensionless pressure coefficients to describe the wind pressure distribution
on the building envelope which is the ratio of the surface dynamic pressure to the dynamic
pressure in the undisturbed flow pattern measured at a reference height. The pressure
coefficient Cp at point k(x, y, z), with reference dynamic pressure pdyn related at height zref, for
a given wind direction φ can be described by (Feustel and Raynor-Hoosen, 1990),
)()(
),(refdyn
okrefpk zp
zppzC
−=φ (2.20)
with
)(21)( 2
reforefdyn zwzp ρ= (2.21)
For the Cp calculation COMIS takes into account climate parameters (wind velocity profile w
and incident angle), environment parameters (plan area density and relative building height)
and building parameters (relative position, etc.). The effect of thermal buoyancy is also
considered in COMIS.
Additional features
COMIS allows users to add new models for air flow components, which is very convenient
when modifying the program to include more links.
Individual zones can be divided into layers to account for variations in temperature when a
vertical temperature gradient exists in a zone.
Contaminant transport is simulated by assuming that concentration in a zone is uniform and air
pollutants are transported from zone to zone by the air flow between zones. Filtration effects
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are introduced to represent absorption onto solid surfaces or any kind of chemical reaction or
phase change resulting from contact with a solid material as the pollutant flows from one zone
to another.
There are two different time steps in COMIS, one for air flow calculations and the other for
contaminant transport calculations. Under assumption of air flows being a ‘quasi-steady-state’
phenomenon, the time step used for air flow simulation is based on external events such as
windows or doors opening or closing, starting or stopping fans or changes in external
pressures.
Contaminant dispersion is a dynamic process and the time step used is based the shortest time
constant of all the zones accounted for in a particular simulation.
Users can provide schedules describing changes with time of various input parameters
including weather data, window openings, fan schedules, zone temperatures or humidity,
occupant activities and sources and sinks of up to five pollutants. When any of these changes
occurs, COMIS will recalculate the air flow field.
Evaluation of COMIS
Fürbringer, Roulet and Borchiellini (1996) edited a report on the evaluation of COMIS. They
stated that COMIS simulation results were compared with over fifty benchmarks or test cases
with either an analytical or a numerical solution to ensure that the code did not contain
numerical errors. User tests were also carried out to evaluate the influence of the user on the
program results, i.e. their ability to understand the program documentation and how to set up
and execute a simulation. The test results show that user ability is a critical factor in securing
reliable predictions.
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The program was also checked against 14 other simulation programs performed by 5 different
laboratories with various objects and against 9 experimental studies conducted within Annex
23. Sensitivity analysis was also made.
2.3.4 Recent development and future work
There is active on-going research in the area of multizone modelling, especially for CONTAM
and COMIS. More recently, Dols (2001) described the latest version of CONTAM-
CONTAMW. In January 2001, COMIS v3.1/w IISiBat v2.4 was presented at a workshop at
EMPA in Zürich. A commercial version of the program (COMIS v3.1/IISiBat v2.4) can now
be ordered from CSTB via the following web site: http://software.cstb.fr. COMIS has been
integrated with the building and systems simulation code TRNSYS (Dorer and Weber 1999)
and with the building energy simulation program EnergyPlus (Huang et al. 1999) to simulate
heat transport in buildings. Work is planned on the inclusion of new methods for the treatment
of chemical reactions and for emissions and transport of aerosols and particulates.
One of the most recent advances in multizone methods involves nesting a zonal model within a
multizone model. This is still under development and has the potential to become a practical
tool for investigating indoor air quality issues (see section 2.6). It is one of the most relevant
areas of research for this project.
2.4 Zonal models
2.4.1 The conceptual basis of zonal models
Zonal models have been developed because the room-by-room isothermal assumption is not
sufficient to predict a building’s thermal behaviour.
To tackle this issue, Lebrun (1970) proposed splitting a room into different zones
characterizing the main driving flows and connecting these zones by mass conductance. This
method made it possible to predict more accurately the thermal behaviour of rooms and to
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make easier the coupling between rooms and heating systems. Since Lebrun’s pioneering work,
various researchers developed this idea and today these methods are known as ‘zonal models’.
In zonal models the inside of a room is divided into a small number of zones or cells. Mass
balance and heat balance equations are applied to the individual zones (cells). The solution of
the set of coupled equations gives the air flow and temperature distribution in the room. Their
development is discussed in the next section.
2.4.2 Development
Allard and Inard (1992) gave a short review of typical zonal models. The relevant details have
been extracted and are summarized below.
The first zonal models (Lebrun 1970, Laret 1980, Howarth 1980 and Inard 1988) were based
on fixed air flow directions and on the application of specific flow laws for plumes, jets and
boundary layers. In order to improve the use of zonal models, Overby and Steen-Thode (1990)
and Inard and During (1991) extended the previous models to the unsteady state. The
comparisons of their numerical predictions with experiments agree reasonably well. Sandberg
and Linström (1987) proposed a two-zone unsteady box model to predict the evolution of the
contaminant concentration in a room ventilated by displacement. The numerical prediction
appears to be in good agreement with experimental results. They also point out that the quality
of the results is directly related to the quality of the description of the driving flows.
As a generalization of the concept of a zonal model, Grelat (1987) and Dalicieux and Bouia
(1991) developed pressure zonal models. The idea is that the main problem of the usual zonal
model is related to the prediction of the transport terms between zones that are not directly
described by the main flow equations. A heated room can be spilt into two different kinds of
zone: the ‘plume’ and the ‘current’ zones. For the zones that are not located within a driving
flow, Bernoulli’s equation is applied to estimate the reference pressure at any location in the
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room. Mass balance and energy equations are made for each zone. The calculation converges
iteratively to a solution giving the temperature and reference pressure in each zone. Inard,
Bouia and Dalicieux (1996) increased this generality of this kind of model. However, these
models are applicable only to a few simple configurations (Musy et al. 2001).
Other models (Bouia 1993, Wurtz et al. 1996) made the inter-cell air flow rates a function of
the pressure distribution. It has been shown that this approach cannot correctly represent the
driving flows (Musy et al. 1997).
More recently, Musy et al. (1999) and Musy et al. (2001) improved zonal models to predict
thermal comfort and simulate natural convection in a room with a radiative/convective heater
with the SPARK object-oriented simulation environment. Haghighat et al. (2001) developed a
Pressurized zOnal Model with Air-diffuser (POMA) to predict the airflow pattern and thermal
distributions within a mechanically ventilated room.
2.4.3 Limits of current models
Allard and Inard (1992) stated that zonal models are always based on two main assumptions:
that we are able to predict the main driving flows (boundary layer, jet or thermal plume) and
we have a sufficiently good empirical knowledge of these structures to calculate their
characteristics. These two assumptions remain as limits to the use of these models in a
prediction process. Although some efforts have been made to predict driving flows, there is
still much work needed to improve our knowledge about these. Current zonal models are only
applied to single rooms with a limited set of driving forces. Musy et al. are developing a new
zonal model for multiple rooms (Musy et al. 2001).
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2.5 Coupling CFD with multizone models
Introduction
Each model type (CFD, multizone model, or zonal model) has its advantages and limits. In
recent years several researchers have tried to link multizone and CFD models in order to
realize the benefits of both. A CFD model is applied to describe a particular room while a
multizone model is used to predict flows and transport in the rest of the building. They interact
with each other: the multizone model provides some of the boundary data needed for the CFD
code and the results of the CFD code are fed back to the multizone model.
Development and general capacities
Schaelin et al. (1992) described an approach called ‘method of detailed node values’. This
method relies on the user to set up and run two separate models. They used COMIS for the
multizone part and PHOENICS for the CFD calculations. Parameter transfer between COMIS
and CFD (PHOENICS) was achieved ‘externally’ by the user and was described for different
flow paths of practical importance. They stated that this approach could considerably enhance
the accuracy of results of multizone simulations.
Clarke et al. (1995) developed a more integrated approach in which they combined multizone
methods with thermal energy modules and a CFD code. They described the techniques used to
couple CFD grid cells at boundaries with the nodes and flow paths in the multizone model, in
which the direction of the flow must be known in order to determine the appropriate
connection points. The two models iterate between each other to reach a final solution by the
‘internal’ connection between the codes.
Further developments
At the date of the publications listed (1992 and 1995) both research groups indicated that the
methods had only been developed sufficiently to predict their feasibility and their potential for
improved prediction of air flow rates in buildings. More work on specifying the boundary
61
conditions, especially for the CFD part of the calculations, was needed to refine and improve
the models.
A multizone model coupled with CFD still suffers from the inherent difficulties of the CFD
approach. Multizone models coupled with coarse-grid CFD models are also under development
and may prove to be a useful combination.
2.6 Coupling zonal models with multizone models
Introduction
As mentioned previously, efforts to determine air movement and contaminant dispersal within
buildings have focused either on the macroscopic features of airflow and dispersal within
whole buildings using single or multizone methods, or on the microscopic features of airflow
and contaminant dispersal in small portions of building system (e.g., single rooms) using CFD
methods. The project tackled here is that the central task of indoor air quality analysis is the
prediction of the spatial and temporal variation of contaminant concentrations within buildings,
especially for large industrial buildings. A practical method is needed to analyze the dispersal
of contaminants within whole buildings while also providing some information regarding the
degree of spatial variation of these contaminants within single rooms. A multizone model
coupled with CFD has this functionality, but it still suffers from the inherent difficulties of the
CFD approach and is likely to be of limited practical use at least in the medium term. The
question then arises, is it possible to formulate models that are not as demanding of resources
and skills as CFD yet provide more detailed information than multizone models?
In this project the problem has been addressed from the whole building perspective, employing
a multizone model (COMIS), while using a zonal model to obtain the details of dispersal
within individual rooms of the building. This new method is described in the next section.
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Description of nesting a zonal model within a multizone model
One of the most relevant areas of research for this project involves nesting a zonal model
within a multizone model. The main idea behind this method is that when a room or space in a
building is not well mixed (for example, there is thermal or concentration stratification), the
room is sub-divided into regions with similar air flow patterns and temperature regimes. Other
well-mixed rooms are treated as single zones. For clarity the term sub-zone will be used to
indicate a sub-divided air space in an individual room. Two types of sub-zone are used:
standard sub-zones and mixed sub-zones. Standard sub-zones are assumed to have a uniform
air temperature and pressure which does not differ markedly from their immediate
neighbouring sub-zones. The important characteristic of these sub-zones is that flow velocities
(and momentums) between them are small and primarily driven by pressure differences. Mass
flows between adjacent sub-zones are calculated in different ways for horizontal and vertical
interfaces. A mixed sub-zone contains two parts: one contains air belonging to the flow
element and one contains air from the surroundings. The driving forces of flow elements are
jets, thermal plumes, boundary layers, and fans etc. Specific models have been developed to
describe flows for some typical examples of these. The equations for standard sub-zones are
reused to calculate air flows from the surroundings. Mass and energy balances are made for
each zone (sub-zone). The solution of the non-linear systems of equations, based on mass and
energy balances for each zone (sub-zone), provides the pressure and temperature fields. When
source strength is known or a source emission model has been used, concentration fields can
also be calculated for pollutants based on the conservation of mass for each contaminant
species in each zone (sub-zone). This type of model is still under development and more work
is needed on the various driving forces.
2.7 Summary
A comprehensive literature review on the simulation of indoor air quality indicates current
state-of-the-art in modelling, its capabilities and limitations. The main findings of this study are
summarized below.
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Currently, multizone and computational fluid dynamics (CFD) models are used widely in the
analysis of airflow, temperature and contaminant distributions. Multizone modelling is the
simplest method. It takes a room within a building as one uniform zone that is connected to
others by links or flow paths between rooms and/or the outside. The links are specified by their
flow properties and flow rates determined by pressure differences across the links. The network
of links is then described by a series of flow equations which are solved simultaneously to
provide a mass conserving solution. COMIS, together with the CONTAM series probably
represent state-of-the-art in multizone models. This approach has the advantage of ease of use
in terms of problem definition, straightforward internal representation and calculation
procedure, which allow the prediction of bulk flows through the whole building as caused by
wind, temperature difference, and/or mechanical systems. However, these models cannot
predict detailed temperature and airflow distribution within single rooms of a building. So for
practitioners who focus on the macroscopic features of airflow and contaminant dispersal
among rooms, not within rooms, multizone models are effective tools.
CFD methods can simulate the detailed intra-zonal airflow and temperature distributions within
a room by simultaneously solving the Navier-Stokes equations and other related equations.
Despite the richness of results in terms of information regarding the airflow and temperature
distributions within a room, CFD models require huge user effort in terms of problem
definition, computational effort and post-processing. Numerical solutions of microscopic
formulations of free and forced convection problems remain computationally challenging.
Their application requires much specialized knowledge and sound engineering judgement.
Thus, it is practically difficult to apply this approach as a daily design tool and to integrate it
into a general building energy simulation program or a multizone air infiltration model. CFD
models are good choices for users who focus on the microscopic features of airflow and
contaminant dispersal in small portions of buildings (e.g., single rooms).
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A zonal model is an intermediate approach between CFD and multizone models. In this
approach a room is divided into several macroscopic homogeneous zones in which mass and
heat conservation must be obeyed. The model will provide some information about thermal
airflow within a room, and it should be relatively easy for users to define the problem. It could
easily be incorporated into building thermal analysis software and multizone infiltration
models. Zonal models are always based on two main assumptions: that we are able to predict
the main driving flows (boundary layer, jet or thermal plume) and we have a sufficiently good
empirical knowledge of these structures to calculate their characteristics. There is still much
work needed to improve knowledge about these. Current zonal models are only applied to
single rooms with a limited set of driving forces.
It would be a significant step forward to add the potential to predict varying conditions inside
one or more rooms to a multizone model which predicts conditions throughout a building and
accounts for the influence of the external atmosphere. Multizone models include such
boundary and driving conditions as ex/infiltration through windows, doors, cracks and
ventilation systems. It would be necessary to enhance any candidate zonal model to cope with
all of the potential flow paths in a 'parent' multizone model.
COMIS (Conjunction Of Multizone Infiltration Specialists) is a multizone air flow and
contaminant transport model with a modular structure, developed by an international research
collaborative effort under the auspices of the International Energy Agency. It is the most
popular public domain multizone model and there is obvious potential for it to become a
standard for multizone air flow modelling. I have chosen to use COMIS as the starting point
for my work and to add the necessary functionality to COMIS.