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Experimental and numerical analysis of CO2 transport inside a university classroom effects of turbulent models.pdf
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Journal of Building Performance Simulation
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Experimental and numerical analysis of CO2
transport inside a university classroom: effects of
turbulent models
Andrea Carlo D’Alicandro & Alessandro Mauro
To cite this article: Andrea Carlo D’Alicandro & Alessandro Mauro (2023) Experimental
and numerical analysis of CO2 transport inside a university classroom: effects of
turbulent models, Journal of Building Performance Simulation, 16:4, 434-459, DOI:
10.1080/19401493.2022.2163423
To link to this article: https://doi.org/10.1080/19401493.2022.2163423
Published online: 04 Jan 2023.
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3. JOURNAL OF BUILDING PERFORMANCE SIMULATION 435
and Air Conditioning (HVAC) layout, thermal load, natural
ventilation, etc..
Predicting gas or particle transport in an indoor envi-
ronment can be used to reduce their hazard and job-
related risks. An accurate and not excessively time-
consuming numerical simulation aids in this task allowing
the simulation of different scenarios, in a relatively short
time and with reduced cost without the need to work on-
site. Therefore, it is important to find and use the numer-
ical methodology that gives the most accurate results in
the shortest time. In the Eulerian-Eulerian approach, both
the fluid and the transported phases are considered a
continuum and resolved with an Eulerian methodology.
This approach is employed when the transported phase,
which can be solid, liquid or gaseous, can be consid-
ered continuous and the number of particles is enormous
because the computational resources required for this
methodology are independent of the number of parti-
cles. The mass transport is calculated by resolving two
sets of equations, one for the fluid and one for the trans-
ported phase (Hinneburg and Knoth 2005). If the mass
fraction is negligible compared to the fluid fraction, the
mass can be treated as a passive scalar and its transport
is calculated by resolving only the convection–diffusion
equation (Yan, Li, and Ito 2020). This approach is based
on the one-way coupling between mass and fluid. The
fluid flow influences the mass motion while mass does
not modify the fluid flow. This condition is verified if
the Stokes number is smaller than 0.1 (Grau-Bové, Strlič,
and Mazzei 2016; Gao and Niu 2007), which is the case
in this work. In this case, the convective velocity of the
transported phase (CO2) is equal to the fluid convective
velocity, while diffusive flux is caused by the combined
effects of the Brownian and turbulent diffusivity. The con-
vection–diffusion equation has been employed to sim-
ulate the mass transport in different scenarios, such as
particle transport and deposition in indoor environments
(Grau-Bové, Strlič, and Mazzei 2016; Gao and Niu 2007;
Chen, Yu, and Lai 2006), particle transport inside operat-
ing rooms (Mohamed et al. 2020; D’Alicandro and Mauro
2022), gas released by a thermal power plant (Issakhov
and Baitureyeva 2018), pollutants transport in an urban
environment (Simoëns and Wallace 2008; Shen, Cui, and
Zhang 2017), gas transport inside an aircraft (Isukapalli
et al. 2013), CO2 transport in the atmosphere (Pedone
et al. 2017; Chiaramonte, a White, and Trainor-guitton
2014) and in a kitchen (Benchikh Le Hocine, Poncet, and
Fellouah 2020).
The Computational Fluid Dynamics (CFD) uses numer-
ical methodologies to study fluid mechanics and mass
transport. It is indispensable to calculate the fluid flow
field where the mass is transported in the best possible
way and validate the methodology against experimental
measurement, to have the most accurate results to
employ it in the current work and in similar cases. It
does not exist a unified turbulence model which can be
employed for all turbulent simulations, different mod-
els are employed for different phenomena and scenarios.
The Reynolds Averaged Navier-Stokes (RANS) equations
methodology is the most used for engineering applica-
tions, it is based on the calculation of the time-averaged
values for turbulent quantities (Wilcox 2006; Versteeg
and Malalasekera 2007). The RANS equations are cou-
pled with a turbulence model (Ricci et al. 2020), the k-ε
model is one of the most used for engineering appli-
cations due to its robustness, economy and reasonable
accuracy (Wilcox 2006; Versteeg and Malalasekera 2007).
The Large Eddy Simulation (LES) is a numerical method-
ology that explicitly resolves the large eddies and uses
a subgrid-scale model for smaller eddies (Wilcox 2006;
Versteeg and Malalasekera 2007). The LES methodology
has been largely compared with the RANS methodology
for engineering and industrial uses, even if it had better
performance in some cases the very higher computa-
tional load does not make it convenient compared to the
RANS methodology (Ricci et al. 2017, 2022; Blocken 2018;
Zhang, Weerasuriya, and Tse 2020).
Two variations of the Standard k-ε turbulence model
were introduced to remedy poor performances for a spe-
cific class of flows (Pope 2000; Yakhot et al. 1992): the Re-
Normalization Group (RNG) k-ε model (Yakhot and Orszag
1986) and the Realizable k-ε model (Shih and Yang 1995).
The k-ε models perform better than other turbulence
models in most cases (Ricci et al. 2020; D’Alicandro, Mas-
sarotti, and Mauro 2021; Massarotti et al. 2019; Yuce and
Pulat 2018; Vera et al. 2015). The differences between the
k-ε models in closed environments have been studied in
the literature and there is not a k-ε model suitable for
all cases because the best performance depends on the
simulated case and fluid characteristics (Wilcox 2006; Ver-
steeg and Malalasekera 2007; Ricci et al. 2018). The RNG
and Realizable models have better performance than the
Standard model (Chen 1995; Tian et al. 2006; Stavrakakis
et al. 2008; Marzouk and David Huckaby 2010; Shaheed,
Mohammadian, and Kheirkhah Gildeh 2019), even dur-
ing a particle transport simulation (Tian, Tu, and Yeoh
2007), in some cases, the RNG is superior to other mod-
els (Massarotti et al. 2019; Rohdin and Moshfegh 2007;
Burlando et al. 2015). Even if the k-ε turbulence models
have been compared in the thermo-fluid dynamic simu-
lations, there are few works that compared them in gas
transport simulation. Xing et al., compared the standard
k-ε, the RNG k-ε and the SST k-ω for the CO2 transport in a
test chamber (Xing et al. 2013). In this work, the three k-ε
models are compared and validated against experimen-
tal measurements, for the first time in literature, both in
4. 436 A. C. D’ALICANDRO AND A. MAURO
the thermo-fluid dynamic and in the CO2 transport sim-
ulation in a real university classroom equipped with a
Turbulent Mixing Airflow (TMA) system. The aim of those
numerical simulations is to perform a complete analysis
of which is the best model for this scenario, to analyse the
effectofthethermo-fluiddynamicsimulationonthemass
transport simulation and to calculate the CO2 transport.
In a numerical simulation, it is important to use bound-
ary conditions that reproduce the actual condition. The
TMA system, analysed in this case, is composed of swirl
diffusers, those diffusers create a swirl turbulent airflow
and it is pretty hard to reproduce the airflow in each point
at the inlet surface (Rusly and Piechowski 2011). There
are some techniques used to reproduce the airflow of a
swirl diffuser, such as modelling the interior of the dif-
fuser to reproduce the airflow (Massarotti et al. 2019) or
the use of a particle image velocimetry to measure the air
velocity (Massarotti et al. 2019; Li et al. 2017). The first
technique increases a lot the computational load, the sec-
ond technique requires more time and the velocity can
be measured in a discrete number of planes. In this work,
it is proposed an alternative experimental methodology,
which requires common experimental instruments and
a reduced amount of time to approximate with a good
result the swirl turbulent airflow of a swirl diffuser.
In this work, an experimental methodology has been
developed to quickly and without complex measure-
ment instruments evaluate the CO2 transport inside an
indoor environment equipped with a TMA system. The
experimental methodology is coupled with a numerical
methodology, validated on the experimental data col-
lected, to calculate the effects of a generic HVAC system
and find the best suitable RANS k-ε models and, finally, a
methodtoeasilyreproducebutwithgoodapproximation
the boundary conditions of a swirl diffuser. Subsequently,
even the effect of turbulent diffusivity is evaluated on
CO2 transport. The Eulerian method is employed to study
the CO2 transport inside the university classroom and the
CO2 concentration is simulated as a transported passive
scalar. This experimental-numerical methodology can be
applied to study the gas evacuation of an already exist-
ing facility, to test the efficiency of an HVAC system or to
help in the room and HVAC layout design in the project
phase.
The paper is organized as follows: section 2 describes
the experimental setup and the experimental measure-
ment performed; the numerical model, the numeri-
cal methodology, the mesh sensitivity analysis and the
boundary conditions employed are available in section 3;
in section 4 the numerical results and comparison with
experimental measurement are presented, while conclu-
sions are drawn in section 5 and limitations and future
works are explained in section 6.
2. Experimental setup
The experimental measurements have been performed
inside an actual university classroom at the Department
of Engineering of the University of Napoli ‘Parthenope’.
The classroom has maximum dimensions of 8.78 m ×
7.21 m × 2.91 m, there are four rows of banks and one
professor’s desk. The HVAC system that supplies the air is
aTMAsystemcomposedof8helicalswirldiffusers,placed
in two parallel rows at a distance of 2.40 and 5.43 m from
the south wall, the diffusers are placed at a distance of
2.02 m from each other. Each diffuser has 24 rectangular-
shaped openings of the size of 0.10 m × 0.02 m.
The three exhaust grilles are located on the east wall
at a height of 2.50 m, at a distance of 1.60 m from each
other and have a dimension of 0.65 m × 0.28 m. The uni-
versity classroom layout, diffusers (red squares, from 1 to
8), extraction grilles (blue squares), velocity measurement
points (from A to N), the CO2 measurement points (S1
and S2) and the CO2 tank positions are represented in
Figure 1.
The experimental measurements have been divided
into two sets:
(1) Velocity and temperature measurements: inlet volu-
metric flow rate, local air velocity and temperature
measurements have been carried out to determine
the boundary conditions and to validate the velocity
field;
(2) CO2 concentration measurements: these measure-
ments have been carried out to measure the total
CO2 released from the tank, and the CO2 concentra-
tion at two points with the aim to validate the CO2
transport simulation.
During the measurement campaign, the door and the
windows have been closed to avoid air inflow or out-
flow. The total volumetric flow rate from the centralized
HVAC system has been maintained constant at the high-
est possible volumetric flow rate, however, the HVAC sys-
tem supplies air to different classrooms and the air sup-
plied to a specific classroom could not be known a priori.
Therefore, due to this reason and to mediate the sta-
tistical oscillations the air volumetric flow rate has been
measured.
The characteristics of the instruments used during the
experimental measurements are reported in Table 1.
2.1. Velocity and temperature measurements
The air supplied by a TMA system has a three-dimensional
turbulent motion, therefore, to better approximate the
boundary condition at the inlet (diffusers), it has been
5. JOURNAL OF BUILDING PERFORMANCE SIMULATION 437
Figure 1. University classroom layout, the position of velocity measurement points (purple squares, from A to N), CO2 concentration
measurement points (blue circles) and the CO2 cylindrical tank. The inlets (diffusers) are represented in red (from 1 to 8), and the outlets
(rectangular exhaust grilles) are represented in blue.
essential to measure the volumetric flow rate and the
velocity magnitude at each of the eight diffusers. All the
measurements performed have been averaged over an
interval time of 30 s, mainly due to the turbulence airflow,
andrepeatedseventimestocalculatethemeanvalueand
type A uncertainty.
A volume flow hood (Testo s.p.a., Germany) (Figure
2(A)) has been used to measure the volumetric flow rate
6. 438 A. C. D’ALICANDRO AND A. MAURO
Table 1. Instruments characteristics.
Instrument Measured quantity Range Accuracy Resolution
Volume flow hood Volumetric flow rate (m3 h−1) 40–4000 m3 h−1 ±(12 + 3% of m.v.) m3 h−1 1 m3 h−1
Temperature (°C) −20 to +70 °C ±0.5 °C 0.1 °C
Hot wire anemometer Velocity (m s−1) 0–30 m s−1 ±(0.03 + 4% of m.v.) m s−1 0.01 m s−1
Temperature (°C) −20 to +70 °C ±0.5 °C 0.1 °C
NTC temperature sensor (type K) Temperature (°C) −60 to +300 °C ±2.5 °C 0.1 °C
IAQ probe CO2 concentration (PPM) 0–10000 PPM ±(50 + 3% of m.v.) PPM 1 PPM
(m3 s−1) and the air inlet temperature (K) at each diffuser.
The ACH (h−1) in the university classroom has been cal-
culated from the measured volumetric flow rate divided
by classroom volume (Equation (1)) and it is equal to
23.55 h−1.
ACH =
Q
V
· 3600 (1)
where Q is the volumetric flow rate (m3 s−1) and V is the
room volume (m3). 3600 is the conversion factor from s−1
to h−1.
A hot wire anemometer (Testo s.p.a., Germany) (Figure
2(B) and (C)) has been used to measure the magnitude
velocity (m s−1) and the air temperature (K) in the centre
of two openings at a distance of a few millimetres for each
diffuser and in some internal points. The velocity mea-
sured at the internal points (purple squares in Figure 1)
has been used to validate the numerical model. The mea-
surement points have been chosen all over the area of the
classroom occupied by the persons. In particular, three
different measurement lines have been considered: two
lines below the diffusers and one line in the middle of the
area occupied by the students. The internal measurement
points have been located at the coordinates y = 3.00 m,
y = 4.10 m and y = 5.43 m, for each row at the coor-
dinates x = 1.22 m, x = 3.18 m, x = 5.23 m, x = 7.26 m
and at the height z = 1.72 m. The type A uncertainty has
been calculated as the standard deviation of the mea-
surementsandthetypeBuncertaintyhasbeencalculated
from the accuracy and sensitivity value of the instrument
(Joint Committee For Guides In Measurements 2008)
and they have been used to calculate the combined
uncertainty.
The perpendicular velocity at each diffuser has been
calculated from the volumetric flow rate and the dif-
fuser area. While the tangential velocity in the middle
point of the diffuser opening has been calculated from
the perpendicular velocity and the magnitude velocity,
employing Pythagoras’ theorem. The tangential velocity
has been converted into Revolution Per Minute (RPM)
(min.−1). The RPM is then used by the boundary condition
function to calculate the tangential value in each point
at the inlet in the function of the distance by the diffuser
centre. The measured values at the diffusers are reported
in Table 2.
An NTC temperature sensor (type K) (Testo s.p.a., Ger-
many) (Figure 2(D)) has been used to measure the surface
temperature (K) at the windows and at the walls.
The mean temperature difference between the inlets,
the internal points and the surfaces have been ∼ 0.7 K
with the highest difference of 1.1 K between an inlet and
a window. The reason for this small difference is the
very good windows insulation and a temperature differ-
ence of 5 K with the outside air temperature. Therefore,
the air has been considered incompressible, reducing
the complexity and the time required for the numerical
simulation.
2.2. CO2 concentration measurements
The CO2 utilized for the experimental measurements has
been released from a cylindrical tank for water gasifica-
tion, placed in the middle of the first school desk. Two
IAQprobes (Testo s.p.a., Germany) have been placed in the
middle of the third and fourth school desk, respectively at
a distance of 1.76 m (measurement point S1) and 2.64 m
(measurement point S2) from the CO2 source, at a height
of 0.2 m from the desk surface, equivalent to a total height
of 0.98 m from the floor. The points S1 and S2 (sensors)
have been chosen because they are placed in the mid-
dle plane of the classroom on the third and fourth desk
rows. The authors have preferred to not consider the sec-
ond desk row since it is too close to the CO2 source (first
row). The experimental set-up for the CO2 measurements
is represented in Figure 2(E and F).
Before the experiment, the CO2 background concen-
tration value and the CO2 tank weight have been mea-
sured. To release the CO2, the differential valve has been
set at the differential pressure of 1 bar, as soon as the
differential pressure has started dropping the valve has
been closed. The total release time has been 290 s. After
the valve closure, the CO2 concentration has been mea-
sured for another 1240 s to collect data during the evac-
uation process. After the experiment, the CO2 tank has
been weighed to calculate the CO2 mass released. From
an environmental point of view, the total amount of CO2
released has been 315 g which is a negligible quantity.
Another CO2 tank has been used to measure the velocity
and temperature of the CO2 gas expelled from the nozzle,
to use them as a boundary condition value.
7. JOURNAL OF BUILDING PERFORMANCE SIMULATION 439
Figure 2. Experimental setup. (A) Inlet volumetric flow rate measurement with volume flow hood; (B) Inlet magnitude velocity measure-
mentwithahotwireanemometer.(C)Magnitudevelocitymeasurementatavalidationpointwithhotwireanemometer.(D)Temperature
measurement on the wall. (E-F) CO2 concentration measurement set-up, with CO2 probes (S1 and S2) and CO2 tank.
This experimental methodology employed to measure
the CO2 concentration inside an indoor environment can
be used as a proxy to estimate other gas transport and
to quantify the ventilation rate efficiency. The proposed
experimental methodology is:
• Low-cost: the consumable (CO2 tank) is cheap, the
measurement instruments are not expensive and they
can be reused for different applications;
• Safe: CO2 has no harm to human or material goods and
the environmental impact is negligible;
8. 440 A. C. D’ALICANDRO AND A. MAURO
Table 2. Inlet flow rate and velocity measurements at the
diffusers.
Diffuser
Measured
volumetric flow
rate (m3 s−1)
Measured
magnitude velocity
(m s−1)
Calculated RPM
(min.−1)
1 0.14 3.76 139.16
2 0.12 3.05 107.27
3 0.17 3.98 137.9
4 0.16 3.60 89.72
5 0.13 3.08 85.57
6 0.13 3.17 92.20
7 0.12 2.74 91.37
8 0.15 3.44 106.90
• Fast: the measurement can be performed in only a few
hours;
• Easy to perform: it does not require specific training for
the operator.
3. Numerical model
3.1. Numerical domain
The numerical domain has the same dimensions as the
actual classroom, they are reported in section 2. To sim-
plify the computational domain and reduce the compu-
tational load without compromising the accuracy of the
numerical simulation, the chairs, the coat hangers and
other minor geometrical features have not been repro-
duced. The CO2 tank and the attached nozzle have been
explicitly modelled, to better reproduce the CO2 release
in the air. Each diffuser has been modelled with 24 rectan-
gular openings spaced at the same angle along a circum-
ference, instead of reproducing the entire internal struc-
ture, including the directional fins, of the diffuser and,
consequently, simulating the internal airflow. This mod-
elling would have required a considerable increase in the
elements of the mesh and would have made the numer-
ical convergence of the simulation more complicated.
The airflow downstream of the diffuser is not unidirec-
tional; therefore the swirlFlowRateInletVelocity boundary
condition has been used to reproduce the airflow with a
higher grade of accuracy, as explained in the next section.
The numerical geometry with the boundary conditions
applied and the points (green sphere) used in the grid
sensitivity analysis is represented in Figure 3.
3.2. Grid sensitivity analysis
In order to ensure the adequate accuracy of the numeri-
cal results and, at the same time, to save computational
resources a grid sensitivity analysis has been performed.
The open-source Salome software has been used to cre-
ate the mesh. Second-order tetrahedral elements have
been employed to create the surface mesh and the 3D
unstructured meshes. Near the surfaces, a boundary layer
with four prism layers has been created. A total of four
meshes have been created using a refining factor around
1.5. The meshes have a number of cells of 3,827,406
(mesh#1), 5,619,874 (mesh#2), 8,413,665 (mesh#3) and
12,004,351 (mesh#4). The checkMesh, an OpenFoam func-
tion, has been used to ensure the good quality of the
meshes, the following quality indicators and threshold
values have been checked: max non-orthogonality infe-
rior to 70, mean non-orthogonality inferior to 25, max
skewness inferior to 8 and max aspect ratio inferior to
30. Only meshes that satisfy these conditions have been
accepted for the grid sensitivity analysis. The grid sen-
sitivity analysis has been performed using the RNG k-ε
model and comparing the magnitude velocity value in a
point below each diffuser’s centre at the distance of 0.7 m,
for a total of eight points (the points are represented in
Figure 3). Those points have been chosen because the
velocity is higher than other internal points and they are
at an adequate distance from the inlet, neither too close
nor too far. The velocity difference has been compared
in these eight points; the difference between mesh#1
and mesh#4 is in the range of 2.5-10.1%, while between
mesh#2 and mesh#4 is in the range of 0.2-1.1%, while
between mesh#3 and mesh#4 is in the range of 0.1-0.4%,
therefore mesh#2 has been selected for the further step.
After that, another comparison between mesh#2 and
mesh#4 has been performed simulating the CO2 trans-
port and comparing the CO2 concentration values at a
distance of 0.8 m from the nozzle (CO2 source) after a sim-
ulation time of 50 s. The difference is lower than 1.5%,
therefore mesh#2 has been selected for the numerical
simulations.Mesh#2has5,619,874cells,withameannon-
orthogonality value of 16 (max 65), a max skewness of 2.4,
a max aspect ratio of 28 and with an average y+ value
of 2.44 (min. 0.01, max 7.25). The selected mesh is repre-
sented in Figure 4. Then, the OpenFoam function renum-
berMesh has been used to reduce the matrix bandwidth
and the convergence time.
3.3. Thermo-fluid dynamic model
The Reynolds number calculated at the inlet is higher
than 2·105, therefore the airflow can be considered tur-
bulent. The OpenFoam 8 solver buoyantSimpleFoam has
been used to simulate the fluid flow, it is a turbulent
and steady-state solver based on the SIMPLE algorithm,
which resolves the RANS equations coupled with a turbu-
lence model. In this simulation, due to the low temper-
ature gradient, the Boussinesq approximation has been
employed to simulate the buoyancy. A second-order
upwind scheme has been used to discretize the con-
vective terms, while a second-order central difference
9. JOURNAL OF BUILDING PERFORMANCE SIMULATION 441
Figure 3. Numerical geometry with the boundary conditions applied and the points (green sphere) used in the grid sensitivity analysis.
scheme has been implemented for discretizing the diffu-
sion terms. In the actual classroom, there are fluctuations
in the inlet conditions, due to the centralized HVAC sys-
tem air handling unit and other transient phenomena
such as door or window opening. From the numerical
point of view, the steady-state condition is an excellent
approximation of the real airflow inside the classroom
and the computational load is considerably reduced com-
pared to a transient RANS or LES simulation.
The Standard k-ε model, the RNG k-ε model and the
Realizable k-ε turbulence model, coupled with the RANS
equations, have been compared between them and with
the experimental measurements for both the airflow sim-
ulation and the CO2 transport simulation. The theory
and the complete formulation of the RANS equations can
be found in the literature (Wilcox 2006; Versteeg and
Malalasekera 2007; Pope 2000; Moukalled and Mangani
2015). The equations for the kinetic energy k (J kg−1) and
the turbulent kinetic energy dissipation ε (J kg−1 s−1) of
the Standard k-ε model (Equations (2) and (3)) (Jones and
Launder 1972), the RNG k-ε model (Equations (4) and (5))
(Yakhot et al. 1992; Yakhot and Orszag 1986) and the Real-
izable k-ε model (Equations (6) and (7)) (Shih and Yang
1995) are reported:
10. 442 A. C. D’ALICANDRO AND A. MAURO
Figure 4. Mesh employed (mesh#2 with 5,619,874 cells) to perform the thermo-fluid dynamic and CO2 transport simulations.
Standard k-ε model:
∂ρk
∂t
+
∂ρkui
∂xi
=
∂
∂xj
μ +
μt
σk
∂k
∂xj
+ Pk
+ Pb − ρε − YM + Sk (2)
∂ρε
∂t
+
∂ρεui
∂xi
=
∂
∂xj
μ +
μt
σε
∂ε
∂xj
+ C1ε
ε
k
(Pk + C3εPb) − C2ερ
ε2
k
+ Sε
(3)
RNG k-ε model:
∂ρk
∂t
+
∂ρkui
∂xi
=
∂
∂xj
μ +
μt
σk
∂k
∂xj
+ Pk − ρε (4)
∂ρε
∂t
+
∂ρεui
∂xi
=
∂
∂xj
μ +
μt
σε
∂ε
∂xj
+ C1ε
ε
k
Pk − C∗
2ερ
ε2
k
(5)
Realizable k-ε model:
∂ρk
∂t
+
∂ρkui
∂xi
=
∂
∂xj
μ +
μt
σk
∂k
∂xj
+ Pk
+ Pb − ρε − YM + Sk (6)
∂ρε
∂t
+
∂ρεui
∂xi
=
∂
∂xj
μ +
μt
σε
∂ε
∂xj
+ ρC1Sε
− ρC2
ε2
k +
√
νε
+ C1ε
ε
k
C3εPb + Sε (7)
where the subscription i and j (with i=j and i, j = 1, 2, 3)
indicate the axis versors; µ and µt (Pa s) are the dynamic
and turbulent dynamic viscosity; σε and σk are respec-
tively the turbulent Prandtl number for the ε and the k;
Pk and Pb (J kg−1 s−1) are respectively the generations
of turbulence kinetic energy due to the mean velocity
gradients and due to buoyancy; YM (J kg−1 s−1) is the con-
tribution of the fluctuating dilatation in compressible tur-
bulence; Sk (J kg−1 s−1) and Sε(J kg−1 s−2) are respectively
the generic sources terms for the k and ε. The empirical
constants C1ε, C1, C2, C2ε, C∗
2ε and C3ε assume different
values in the function of the application and fluid flow
characteristics (Wilcox 2006; Versteeg and Malalasekera
2007; Pope 2000; Yakhot et al. 1992; Yakhot and Orszag
1986; Shih and Yang 1995; Moukalled and Mangani 2015;
Jones and Launder 1972).
11. JOURNAL OF BUILDING PERFORMANCE SIMULATION 443
The turbulent kinematic viscosity νt (m2 s−1) equation
(Equation (8)) is the same for all three k-ε models:
νt = Cμ
k2
ε
(8)
The difference is in the formulation of the empirical
constant Cµ (Yakhot et al. 1992; Yakhot and Orszag 1986;
Shih and Yang 1995; Jones and Launder 1972), which
results in different νt values. The difference in the k and
ε fields result in a difference in the velocity field, that con-
sequently modifies the CO2 convective transport, instead
the difference in the νt field influences the CO2 diffusivity
transport.
3.4. CO2 transport model
The Eulerian methodology is employed to simulate the
CO2 mass transport and the one-way coupling is guar-
anteed by the very low CO2 mass fraction and Stokes
number lower than 0.1. The continuity of the CO2 phase
is guaranteed because the particle dimension, which is
3.3·10−10 m, is significantly smaller than the Kolmogorov
microscale which is 1·10−3 m in a normally ventilated
room (Gao and Niu 2007; Etheridge and Sandberg 1996).
Due to the high turbulent ventilation and relatively low
density difference between air and CO2, the gas stratifi-
cation is negligible (Badino 2009; Theilacker and White
2006).
The CO2 transport phase is calculated by resolving
the transient advection–diffusion equation (equation 9)
evolving on the previously calculated steady-state airflow
(Gao and Niu 2007).
∂C
∂t + ∇ · (uC) - ∇ · (Dc∇C) = Pc (9)
where C is the CO2 concentration (part. m−3), t is the time
(s), u is the fluid velocity (m s−1), DC is the total diffusiv-
ity (m2 s−1) and PC is the concentration source (part. m−3
s−1).
In order to simulate the CO2 transport, a modified ver-
sionofthetransientscalarTransportFoamsolver,basedon
the PISO algorithm has been employed. The solver has
been modified ad hoc as follows. In the original solver,
there is a single and uniform input value for the diffusivity.
TheactualvalueinaturbulentfieldisthesumoftheBrow-
nian diffusivity D (m2 s−1) and the eddy diffusivity K (m2
s−1). Where D is uniform in the computational domain,
while K (Equation (10)). is calculated from the turbulent
Schmidt number Sct and depends on the fluid νt cell
value. Therefore, the solver has been modified according
totheformulationtohaveanon-uniformdiffusivityvalue.
In each cell, the diffusivity value DC is equal to D + K.
K =
νt
Sct
(10)
The Sct for CO2 transport in the air is 1.14 (Gualtieri et al.
2017) and the νt field is calculated in the thermo-fluid
dynamic simulation. The time required to open and close
the differential valve during the experimental measure-
ments has been ∼2 s, to simplify the numerical simu-
lation it has been considered instantaneous. Therefore,
the switch from the numerical simulation with the noz-
zle opened and CO2 release to the simulation with the
nozzle closed and without CO2 release has been instan-
taneous. A second-order upwind scheme has been used
to discretize the convective terms, while a second-order
central difference scheme has been implemented for dis-
cretizing the diffusion terms. The simulation time step
has been chosen in order to have a max Courant number
lower than 1, resulting in a more accurate result.
3.5. Boundary conditions and simulation procedure
The CO2 transport experiment was divided into two
phases: one where there is the CO2 release (time from 0
to 290 s) and the other one where there is no CO2 release
and there is only the CO2 evacuation (time from 290 to
1530):thereforetonumericallyreproducetheexperiment
two different simulation are needed. One where there is
an inflow from the CO2 tank nozzle, which is equal to an
air inflow during the thermo-fluid dynamic simulation to
model the airflow, while during the CO2 transport simula-
tion there is a CO2 inflow in the domain. The value of the
inlet velocity at the nozzle has been measured during the
experimental measurements. Instead, during the numeri-
cal simulation of the phase without the CO2 release the
nozzle is closed and modelled as a wall. Both phases
have been simulated employing the following k-ε turbu-
lence models: Standard k-ε, RNG k-ε and Realizable k-ε
for a total of six simulations. The initial condition for the
velocityfieldhasbeencalculatedusingthepotentialFoam
solver to reduce the convergence time. The steady-state
quantity fields calculated in the simulation with the noz-
zle closed have been used as initial conditions to reduce
the convergence time in the simulation with the nozzle
opened. To reassume, the steady-state field calculated
with the nozzle opened is used for the CO2 release phase
simulation (time from 0 to 290 s), and then when the gen-
eration phase ends the velocity field is switched to the
steady-state field calculated with the nozzle closed and
then the CO2 evacuation phase is simulated. In these sim-
ulations, only the excess of CO2 concentration has been
simulated therefore both the background and inlet con-
centration value is set at 0 value. The boundary conditions
12. 444 A. C. D’ALICANDRO AND A. MAURO
Table 3. Boundary conditions employed. The OpenFoam boundary condition functions are written in italic.
Physical quantity Inlet – diffusers Inlet – nozzle Outlet Walls
u Volumetric flow rate and
swirl condition;
swirlFlowRateInletVelocity
Velocity;
fixedValue
Free outflow;
zeroGradient
No-slip;
noSlip
T Imposed value;
fixedValue
Imposed value;
fixedValue
Free outgoing flow;
zeroGradient
Adiabatic;
zeroGradient
k Derived value;
turbulentIntensityKinetic
EnergyInlet
Derived value;
turbulentIntensityKinetic
EnergyInlet
Free outflow;
zeroGradient
Wall function;
kLowReWallFunction
ε Derived value;
turbulentMixingLength
DissipationRateInlet
Derived value;
turbulentMixingLength
DissipationRateInlet
Free outflow;
zeroGradient
Wall function;
epsilonWallFunction
α Imposed value;
fixedValue
Imposed value;
fixedValue
Free outgoing;
flow zeroGradient
Wall function;
compressible::alphat
WallFunction
νt Derived value;
calculated
Derived value;
calculated
Derived value;
Calculated
Wall function;
nutUWallFunction
p No outflow;
fixedFluxPressure
No outflow;
fixedFluxPressure
Free outflow;
fixedValue
No outflow;
fixedFluxPressure
CO2 concentration (C) Air with zero concentration;
fixedValue
CO2 generation;
fixedValue
Free outflow;
zeroGradient
Inert wall;
zeroGradient
employed to solve the governing equations, for both
airflow and mass transport simulations, are reported in
Table 3 and represented in Figure 3.
The CO2 fixedValue concentration at the nozzle inlet is
calculated to have the constant CO2 mass outflow each
second equal to 1/290 of the total tank mass lost during
the experiment. The swirlFlowRateInletVelocity boundary
condition needs as input the volumetric flow rate value,
measured with the volume flow hood, and the RPM value
to generate the swirl, this value is derived for each dif-
fuser by the velocity magnitude measured at the inlet and
the volumetric flow rate. In the simulation as in the actual
case, the inflow air has a clockwise direction, due to the
diffuser configuration.
4. Results and discussion
4.1. Fluid flow validation and models comparison
The magnitude velocity fields in the Y-Z plane passing
through the CO2 tank (x = 4.15 m) and in the X-Y plane at
the nozzle height (z = 1.1 m) for all three numerical sim-
ulated cases and with the nozzle closed are represented
in Figure 5. The red circle in the X-Y plane indicates the
nozzle position. All three models provide a similar quali-
tative air velocity field. In all three simulations on the Y-Z
plane, there is a recirculation zone behind the CO2 tank
and a zone with higher velocity below the diffuser line
ahead of the CO2 tank. The Realizable k-ε has more dif-
ference in the velocity distribution with respect to the
two other models that have more similarities between
them. The Realizable k-ε simulation has the lower high-
est velocity and therefore the velocity is more uniform, in
particular, the velocity between the tank nozzle and the
bank rows is very low. Instead, the Standard k-ε simula-
tionhasthehighestvelocitypeakandthereforezonewith
the lowest velocity resulting in a higher velocity gradient
and less uniform velocity. On the X-Y plane, it is possi-
ble to notice that there is a vortex ahead of the CO2 tank
for the Standard k-ε simulation; this will strongly influ-
ence the convective CO2 transport reducing the amount
of CO2 that will reach the sensors. In Figure 6 the mag-
nitude velocity difference between the three turbulent
k-ε models is represented. The velocity magnitude fields
have been obtained by subtracting the velocity magni-
tudes obtained with one turbulent model in the field
obtained with the other turbulent model. The main differ-
ence is below the first row ofdiffusers and it is the position
of the zones with the highest velocity.
The turbulent quantities mean values calculated using
the ParaView function Integrate Variables are reported
in Table 4, while the k and ε distribution on the plane
z = 1.1 m are represented in Figure 7.
The mean value difference for k and ε is low, instead,
there is a difference in the distribution. Both Standard k-
ε and RNG k-ε have zones with higher values and higher
gradients compared to the Realizable k-ε which has a
more uniform distribution. As expected, where the k has
a higher value the magnitude velocity has a higher value
too. The Realizable k-ε has the highest mean value of the
νt that increases the CO2 diffusivity. For all three mod-
els, the νt mean value is several orders of magnitude
higher than the CO2 excess Brownian diffusivity in the air
(Ovando-Chacon et al. 2022).
The velocity magnitude along the three rows at
y = 3.00 m,y = 4.10 mandy = 5.43 m,obtainedemploy-
ing the three k-ε models and with the nozzle closed,
are compared with the experimental measurements per-
formed in the classroom and are represented in Figure 8.
In Figure 8, the bars indicate the expanded combined
uncertainty calculated on the basis of type A and type B
13. JOURNAL OF BUILDING PERFORMANCE SIMULATION 445
Figure 5. Magnitude velocity fields in the Y-Z plane passing through the tank (x = 4.15 m) and in the X-Y plane at the nozzle height
(z = 1.1 m) for all three numerical simulated cases. The black arrows are the velocity magnitude vectors. The red circle in the X-Y plane
indicates the nozzle position.
14. 446 A. C. D’ALICANDRO AND A. MAURO
Figure 6. The magnitude velocity difference between the three turbulent k-ε models.
15. JOURNAL OF BUILDING PERFORMANCE SIMULATION 447
Table 4. Mean value of the turbulent quantities for the three
turbulent k-ε models.
Mean value Standard k-ε RNG k-ε Realizable k-ε
k (J kg−1) 0.0133 0.0141 0.0134
ε (J kg−1 s−1) 0.0394 0.0349 0.0363
νt (m s−1) 0.00385 0.00411 0.00787
uncertainties. In particular, the combined uncertainty has
been expanded by using a coverage factor (km) equal to 1,
corresponding to a confidence level of 68.3% (Joint Com-
mittee For Guides In Measurements 2008). The measured
and calculated velocity values, the Root Mean Square
Deviation (RMSD) and the Mean Absolute Error (MAE) are
reported in Table 5.
The RNG k-ε is the model that reproduces in the most
accurate way the velocity field, in fact the numerical val-
ues are within the uncertainty interval of the experimen-
tal data in 10 points out of 12. Moreover, if the authors
hadchosentoemployacoveragefactorkm = 2(i.e.confi-
dencelevelof95.4%),insteadofequalto1(i.e.confidence
level of 68.3%), the numerical results would have been in
excellent agreement with the experimental data in all the
12 points.
The RMSD and MAE confirm that the RNG k-ε model
is the most accurate while the Standard k-ε model is the
less accurate for this case. The Standard k-ε model has
less agreement with experimental measurements and it
has some velocity spikes. As expected from the litera-
ture analysis the Standard k-ε model is the least suited
turbulence k-ε model to employ for indoor simulations
(Chen 1995; Tian, Tu, and Yeoh 2007). The Realizable
k-ε model has more agreement compared to the Stan-
dard k-ε model but it still presents discrepancies with
the experimental values. The Standard k-ε and the Real-
izable k-ε models have some velocity spikes while the
RNG k-ε model has more contained velocity oscillations
in space. The magnitude velocity is in the range of 0-
0.2 m s−1 for the RNG k-ε model, with some spikes up
to 0.5 m s−1 in the other two models. As a result, the
RNG k-ε model is the most suited and accurate turbu-
lence model to employ in this case. This result is coherent
with other works available in the literature, that com-
pared the k-ε models in indoor environments (Chen 1995;
Tian et al. 2006, 2007; Rohdin and Moshfegh 2007) and in
indoor cross-ventilation environments (Stavrakakis et al.
2008).
In the present paper, the methodology employed to
determinetheinletboundaryconditionforaswirldiffuser
has given good results in agreement with the experi-
mental measurements, especially with the RNG k-ε tur-
bulent model. Therefore, the present methodology can
be employed in future simulations of indoor environ-
ments equipped with swirl diffusers and can be further
improved, by performing measurements in more points
for each diffuser.
Considering that the RNG k-ε model ensures the
most accurate results among the k-ε models tested in
the present paper, the following results, comparing the
airflow field with the nozzle closed and opened, are
obtained by employing the RNG k-ε model. In particular,
in Figure 9 there are the two airflow fields and the dif-
ference between them in the planes at x = 4.15 m and
z = 1.1 m. As it is possible to notice from Figure 9, the
inletvelocityfromthenozzledoesnotgloballymodifythe
velocity field, while it strongly modifies the area around
the nozzle, as it is in the real case.
4.2. CO2 numerical-experimental comparison
Only the concentration excess, with respect to the back-
ground concentration value, has been numerically simu-
lated; therefore, the measured values have been reduced
by the measured background value, moreover, the instru-
ment response time has been considered. The numer-
ically calculated and the experimental measured CO2
concentrations (in both parts. m−3 and PPM), in the mea-
surement points S1 and S2, are represented in Figure 10.
The CO2 transport simulation performed on the
steady-state velocity field calculated with the RNG k-ε
model has the best agreement with the experimental val-
ues even if there is a difference in the peak value and
little time shift (less than 10 s). The difference between
the Realizable k-ε and Standard k-ε curves and the exper-
imental values are mainly caused by the difference in the
velocity fields between the source and the CO2 sensors,
which influence the convective transport, as described
in the previous section. For all three models, there is a
complete mass evacuation without stagnation zones, the
residual CO2 mass in the domain is less than 1% of the
total mass released in the classroom.
The RNG k-ε model has good agreement with exper-
imental data in both velocity and CO2 concentration
measurement, highlighting how it is important to cal-
culate an accurate velocity field to have an accurate
mass transport simulation; especially in a turbulent envi-
ronment where convective transport has a fundamental
role. The highest CO2 concentrations reach values in the
range of 3000–4000 PPM, these values are in accordance
with values measured in other real classrooms (Ovando-
Chacon et al. 2022; Fantozzi et al. 2022), therefore the
CO2 released from a tank does not overestimate the CO2
concentrations in a classroom.
The excess CO2 distribution simulated with the RNG
k-ε model (in both parts. m−3 and PPM) during the evacu-
ation phase (from t = 290 s to t = 1530 s), is represented
at two different heights: at half desk height (Z = 0.5 m) in
16. 448 A. C. D’ALICANDRO AND A. MAURO
Figure 7. Turbulent kinetic energy (k) and turbulent kinetic energy dissipation (ε) fields for the three k-ε turbulent models at the nozzle
height (z = 1.1 m).
17. JOURNAL OF BUILDING PERFORMANCE SIMULATION 449
Figure 8. Numerical-experimentalcomparisonofthevelocitye,obtainedinthesimulationwiththenozzleclosed,alongthethreerows
at y = 3.00 m, y = 4.10 m and y = 5.43 m. The bars indicate the expanded combined uncertainty of the experimental measurement.
Table 5. Experimental values, numerically calculated values, RMSD and MAE for the three simulated cases.
Validation point (m) Measured velocity (m s−1) Standard k-ε (m s−1) RNG k-ε (m s−1) Realizable k-ε (m s−1)
A (1.22, 5.43, 1.72) 0.19 0.12 0.11 0.14
B (3.18, 5.43, 1.72) 0.10 0.30 0.13 0.17
C (5.23, 5.43, 1.72) 0.10 0.32 0.10 0.19
D (7.26, 5.43, 1.72) 0.09 0.12 0.13 0.13
E (1.22, 4.10, 1.72) 0.07 0.09 0.08 0.09
F (3.18, 4.10, 1.72) 0.09 0.24 0.08 0.05
G (5.23, 4.10, 1.72) 0.04 0.11 0.07 0.13
H (7.26, 4.10, 1.72) 0.11 0.08 0.08 0.12
I (1.22, 3.00, 1.72) 0.11 0.01 0.12 0.08
L (3.18, 3.00, 1.72) 0.06 0.33 0.07 0.24
M (5.23, 3.00, 1.72) 0.08 0.37 0.06 0.19
N (7.26, 3.00, 1.72) 0.10 0.15 0.13 0.16
RMSD 0.13 0.02 0.07
MAE 0.12 0.02 0.06
Figure 11 and at the nozzle height (Z = 1.1 m) in Figure
12. The concentration fields have been saved each 248 s
(1/5 of the total simulation time of the evacuation phase),
therefore the excess CO2 distribution is displayed at the
end of the generation phase (t = 290 s), in the next saved
step time (t = 538 s), near the middle time (t = 1034 s)
and at the last simulated second (t = 1530 s). It is impor-
tant to note that the CO2 concentration scale changes in
each time step of Figures 11 and 12. On the left side of the
classroom, where there are no extraction grilles, there is
an accumulation of CO2 that is subsequently evacuated.
On the right side, where the extraction grilles are placed,
there is an accumulation due to the convective motion
of the air which flows through the extraction grilles, then
after the generation ends there is a rapid evacuation of
the CO2. The HVAC system efficiently evacuates the CO2
present in the classroom and, realistically, evacuates all
types of aerosol or gas contaminants in the air.
The total quantity of CO2 inside the university class-
room has been quantified, employing an integration
post-process function at different times. The values have
been normalized with the peak value (t = 290 s) to calcu-
late the CO2 excess still suspended in the air. These values
have been compared with the normalized experimental
measured values in the measurement points S1 and S2.
In the measurement points S1 and S2, and for the overall
classroom, the Air Change per Hour has been calculated
on the basis of the concentration (ACHC) as a function
18. 450 A. C. D’ALICANDRO AND A. MAURO
Figure 9. Comparison of the airflow field calculated with the RNG k-ε turbulent model and with the nozzle closed and nozzle opened.
The planes are at x = 4.15 m and z = 1.1 m.
19. JOURNAL OF BUILDING PERFORMANCE SIMULATION 451
Figure 10. Numerical-experimental comparison of the CO2 concentration in the measurement points S1 and S2.
of the time (Equation (11)) (Chung and Hsu 2001). These
data are reported in Table 6.
The ACHC can be compared with the nominal ACH
(Equation (1)), which is equal to 23.55 h−1 for this case.
The equation for the ACHC is (Chung and Hsu 2001):
ACHC =
ln Ct1 −ln Ct2
|t2−t1|
(11)
Analysing the data reported in the table, it can be seen
that there is a difference between the numerically cal-
culated values referred to the total CO2 in the air and
the experimentally measured values in the points S1
and S2. Therefore, the variation of the concentration in
a specific point (S1 or S2) is not always indicative of
the corresponding value referred to the overall indoor
environment. This aspect could be taken into account
20. 452 A. C. D’ALICANDRO AND A. MAURO
Figure 11. CO2 distribution at half desk height (z = 0.5 m) during the evacuation phase (from t = 290 s to t = 1530 s).
in future works of the authors by using more CO2 sen-
sors, measuring the concentration in an array of points
uniformly distributed in the classroom. If a small num-
ber of sensors is used, such as in the present case, it
is necessary to couple experimental measurements with
numerical data, in order to have an estimation of the
overall evacuation time and ACHC. The ACHC calculated
with the normalized total CO2 in the air is slightly lower
than the ACH based on the volumetric flow rate, mean-
ing that the HVAC system is effective in evacuating
the CO2.
For this case, after ∼12 min (744 s), the CO2 quantity
in the air, numerically calculated, is equal to 0.010 of the
peak value (i.e. 1.0%), while at the simulation end time
(t = 1530s)theresidualvalueisequalto0.001(0.1%).The
measured values are slightly larger than the numerical
ones.
Therefore, 12 min can be considered as the recovery
time, which is the time required to reach concentration
values similar to the background ones. As a term of com-
parison, in an experimental work analysing CO2 and par-
ticulate matter decay in a bigger university classroom
with a lower ACH, the time required to have a concentra-
tion reduction of the 63% is in the range of 12–85 min,
while the recovery time (residual concentration ≤1%) is
much larger (1–2 h) (Westgate and Ng 2022). Therefore,
the present ventilation system can be considered very
effective in evacuating CO2.
21. JOURNAL OF BUILDING PERFORMANCE SIMULATION 453
Figure 12. CO2 distribution at the nozzle height (z = 1.1 m) during the evacuation phase (from t = 290 s to t = 1530 s).
Table 6. ACHC, normalized total CO2 in the air and in the measurement points (S1 and S2) at different times.
Numerical overall classroom Measurement point S1 Measurement point S2
Time (delta time t respect
to the peak time) (s)
Normalized total CO2 in the
air (numerical simulation) ACHC (h−1)
Normalized CO2
measured in S1 ACHC (h−1)
Normalized CO2
measured in S2 ACHC (h−1)
290 ( t = 0) 1.000 / 1.000 / 1.000 /
538 ( t = 248) 0.202 23.244 0.071 38.468 0.219 22.077
786 ( t = 496) 0.047 20.989 0.023 16.401 0.079 14.702
1034 ( t = 744) 0.010 21.323 0.014 6.740 0.023 17.803
1282 ( t = 992) 0.002 21.513 0.009 6.561 0.016 5.084
1530 ( t = 1240) 0.001 21.557 0.008 2.037 0.014 0.476
4.2.1. Effect of the turbulent diffusivity on mass
transport
The effect of the turbulent diffusivity, calculated from the
turbulent viscosity, on mass transport is investigated by
employing the velocity and turbulent viscosity calculated
with the RNG k-ε model. A simulation where the turbulent
and Brownian diffusivities are considered is compared
with a case where the turbulent diffusivity is imposed as
22. 454 A. C. D’ALICANDRO AND A. MAURO
Figure 13. Numerical CO2 concentration in the two measurement points, calculated with and without the turbulent diffusivity. The
experimental measurements are reported as reference.
0 everywhere, therefore the difference in mass transport
is caused only by the additional effect of the turbulent
diffusivity.
The CO2 concentration in the measurement points is
represented in Figure 13, while the CO2 concentration
distribution is represented in Figure 14.
Without the turbulent diffusivity, the total diffusivity
is greatly reduced, therefore the mass follows the air-
flow more and there is less cross-diffusion in the direc-
tion normal to the airflow. This results in a greater
concentration for the case without turbulent diffusiv-
ity in the measurement point S1, which is nearest to
the nozzle, and in a reduced concentration in the far-
thest measurement point (S2) because there is less dif-
fusion, this can be seen in Figure 13. From the analy-
sis of Figure 14 can be noticed that in the case with
turbulent diffusivity enabled the mass diffuses behind
the nozzle and in normal directions with respect to the
flow from the nozzle. At the time t = 538 s, there are
higher concentrations and stagnation zone along the
walls, especially on the left side without extraction grilles,
for the case without turbulent diffusivity. The result of
this comparison highlight how it is important the micro-
scopic mass diffusion (diffusivity) and the effect of the
23. JOURNAL OF BUILDING PERFORMANCE SIMULATION 455
Figure 14. CO2 distribution at the nozzle height (z = 1.1 m) with and without the turbulent diffusivity.
turbulence that can not be ignored if the fluid flow is
turbulent.
5. Conclusions
In the present work, the authors have experimentally
characterized the thermo-fluid dynamic and CO2 trans-
port inside an actual university classroom equipped with
a TMA system. Moreover, the airflow and CO2 transport
have been numerically studied developing an OpenFoam
model.
The numerical simulations have been performed cal-
culating the steady-state airflow employing the RANS
equations, coupled with three different k-ε turbulent
models: the Standard k-ε, the RNG k-ε and the Realizable
k-ε. A modified OpenFoam 8 solver has been employed,
implementing the turbulent diffusivity for the CO2
transport. The numerical results have been compared
and validated against the experimental measurements
acquired by the authors for both air velocity and CO2
concentration.
The main results obtained are:
(1) The proposed experimental methodology to deter-
mine the air inlet boundary conditions for the swirl
diffuser allows to obtain accurate results, if coupled
with the most adequate turbulence model for the
specific case;
(2) The RNG k-ε model can be considered the most
accurate turbulent model, among the three anal-
ysed k-ε models, to be employed for indoor environ-
ments with a layout similar to the present case and
24. 456 A. C. D’ALICANDRO AND A. MAURO
equipped with a TMA system. This consideration is
valid for both the thermo-fluid dynamic and the CO2
transport simulations. The Standard k-ε model is the
least suited for the present case;
(3) The proposed experimental methodology to mea-
sure the CO2 concentration inside an indoor environ-
ment is low-cost, safe, fast and easy to implement,
and could be used as a proxy for IAQ and to estimate
the air ventilation levels;
(4) For the present case, after 20 min (1240 s) almost all
the CO2 excess is evacuated through the extraction
grilles. This value can be used as a reference term for
cases with similar values of ACH, room geometry and
HVAC system.
The proposed numerical and experimental method-
ology can be employed to study different gas transport
in an indoor environment equipped with a TMA system
and swirl diffusers or used to determine the IAQ level and
the efficiency of mechanical and natural ventilation inside
buildings.
6. Limitations and future works
A limitation of the present numerical methodology is that
it can be effectively applied if the windows of the class-
room are closed, and the mechanical ventilation system
is in operation. In the case of cross-ventilation or natural
ventilation, it is difficult to determine realistic boundary
conditions at the opened windows, due to their dynamic
physical behaviour and dependence on meteorological
conditions.
A limitation, related to the present experimental activ-
ity, is that only two CO2 sensors have been used. For
future works, the authors will buy and use more sensors,
in order to place them in the periphery of the room, for
further validation of the model.
Moreover, in the next works, the methodology will
be further developed and employed to simulate gas
transport in different indoor environments, taking into
account specific boundary conditions.
Lastly, instead of using a single large CO2 source, the
authors will employ more smaller sources to simulate the
CO2 exhaled from people in the classroom.
Disclosure statement
No potential conflict of interest was reported by the author(s).
Funding
The authors gratefully acknowledge the financial support
of project PRIN 2020 ‘Optimal refurbishment design and
management of small energy micro-grids – OPTIMISM’, Prot.
20204NXSZH, CUP I65F21001850006, Ministero dell’Università e
della Ricerca (MUR)
Data availability statement
The data that support the findings of this study are available
from the corresponding author, ACD, upon reasonable request.
Nomenclature
Cµ, C1ε, C1, C2, empirical constants of the k-ε models
C2ε, C∗
2ε, C3ε
C CO2 concentration (part. m−3) or (PPM)
D Brownian diffusivity (m2 s−1)
DC total diffusivity (m2 s−1)
K eddy diffusivity (m2 s−1)
k turbulent kinetic energy (J kg−1)
km coverage factor
p pressure (Pa)
PC concentration source (part. m−3 s−1)
Pk generation of turbulence kinetic energy
due to the mean velocity gradients
(J kg−1 s−1)
Pb generation of turbulence kinetic energy
due to the buoyancy (J kg−1 s−1)
Q volumetric flow rate (m3 s−1)
Sct turbulent Schmidt number
Sk generic source terms for the k (J kg−1
s−1)
Sε generic source terms for the ε (J kg−1
s−2)
T temperature (K)
t time (s)
u air velocity (m s−1)
V room volume (m3)
YM contribution of the fluctuating dilatation
in compressible turbulence (J kg−1 s−1)
Greek symbols
α thermal diffusivity (m2 s−1)
σε turbulent Prandtl number for the ε
σk turbulent Prandtl number for the k
ε turbulent kinetic energy dissipation
(J kg−1 s−1)
μ dynamic viscosity (Pa s)
μt turbulent dynamic viscosity (Pa s)
νt turbulent kinematic viscosity (m2 s−1)
Acronyms
ACH = Air Change per Hour (h−1)
ACHC = Air Change per Hour, calculated with Concentra-
tion (h−1)
25. JOURNAL OF BUILDING PERFORMANCE SIMULATION 457
CFD = Computational fluid dynamics
HVAC = Heating ventilation and air conditioning
IAQ = Indoor air quality
LES = Large eddy simulation
MAE = Mean absolute error
RANS = Reynolds averaged navier-stokes
RMSD = Root mean square deviation
RNG = Re-Normalization Group
RPM = Revolution Per Minute (min.−1)
TMA = Turbulent mixing airflow
ORCID
Andrea Carlo D’Alicandro http://orcid.org/0000-0002-1058-
3217
Alessandro Mauro http://orcid.org/0000-0001-8778-7237
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