15 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
Transcript
15
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),
(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.
32
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.
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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
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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
