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Quantification of the effects of air velocity on VOC emissions from
building materials
Won, D. Y.; Nong, G.; Shaw, C. Y.
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Quantification of the effects of air velocity on VOC emissions from
building materials
Won, D.; Nong, G.; Shaw, C.Y
NRCC-47064
A version of this document is published in / Une version de ce document se trouve dans :
CIB 2004 World Building Congress, Toronto, Ontario, May 2-7, 2004, pp. 1-10
http://irc.nrc-cnrc.gc.ca/ircpubs
Quantification of the Effects of Air Velocity on VOC Emissions from Building Materials
IAQT1S2
D. Won, Ph.D. 1, G. Nong2, and C.Y. Shaw, Ph.D.3
Institute for Research in Construction
National Research Council Canada
Ottawa, Ontario, Canada
ABSTRACT
It has been recognized that volatile organic compound (VOC) emissions from building
materials are affected by environmental factors including surface air movements, temperature,
and relative humidity in a room. Considering a wide range of environmental conditions in
buildings, the effects of environmental factors can be important in simulating indoor levels of
VOCs emitted from building materials. Despite the wide recognition of the issue, most research
effort has been focused on qualitative investigations.
The goal of this research is to determine the correlation between environmental factors
and coefficients of mass-transfer based emission models in a mathematical form. As an initial
step toward the goal, the emissions of decane applied on an oak substrate were tested in a 400 L
dynamic flow chamber with five levels of air velocity and turbulent kinetic energy. The weight of a
specimen was monitored over time. A mass-transfer model that accounts for surface evaporation
and internal diffusion was applied to the measured data to determine the model coefficients. It
was observed that the estimated evaporation coefficient is linearly proportional to the bulk air
velocity in the chamber. Also, there was a power-law relationship between turbulent kinetic
energy and evaporation coefficient.
INTRODUCTION
Environmental factors including surface air movements, temperature, and relative
humidity have been recognized as important factors affecting VOC emissions from building
materials. In consequence, effort has been made to standardize testing methods for data
comparability and/or compatibility. However, the results from standardized emission testing may
not satisfy the needs of incorporating those environmental impacts in the simulations of indoor air
levels of VOCs resulting from building materials.
This paper is intended to address the issue by investing the effects of air velocity on
material emissions. Although it has been reported that increasing ventilation rates or air
velocities over materials can increase the short-term emission rate of VOCs and the long-term
emission rate is almost independent of the ventilation rate or the air velocity (Gunnarsen, 1997;
Zhang et al., 1997; Low et al., 1998; Wolkhoff, 1998; Knudsen et al., 1999), there have been few
attempts to quantify the relationship. One example is the work by Topp et al. (2001), which
shows a correlation between mass transfer coefficient and air velocity or turbulent kinetic energy,
based mainly on CFD simulations.
In this paper, effort has been made to quantify the relationship between air movements
and emissions of decane applied on an oak substrate. Instead of comparing emission rates,
1
D. Won is Research Officer, Indoor Environment Research Program, Institute for Research in
Construction, National Research Council.
2
G. Nong is Technical Officer, Indoor Environment Research Program, Institute for Research in
Construction, National Research Council.
3
C.Y. Shaw is Research Officer, Indoor Environment Research Program, Institute for Research
in Construction, National Research Council.
1
model coefficients, i.e., diffusion and evaporation coefficients estimated from emission data were
compared for different levels of air velocity and turbulence.
METHODOLOGY
Experimental Set-up
The weight of decane applied on an oak substrate was monitored over time with an
electronic balance in a dynamic chamber test. The chamber with a volume of 400 L is designed
to control air velocity and turbulence over a material specimen by incorporating an outer and
inner chamber (Figure 1). The inner chamber (0.297 L) has a upstream section consisting of a
perforated plate and several screens for settling the flow and controlling the turbulence level, a
middle section with relatively uniform air flow for exposing the surface of the test material and a
downstream section consisting of several screens and a buffer plate (Zhang et al., 1996). A tubeaxial fan connected to the downstream section draws air from the upstream to the downstream
section and exhausts it to the outer chamber. Varying the voltage to a DC motor of the fan
provides different levels of air velocity. The size and number of holes of the perforated plate at
the upstream section can also be varied and allow controlling the turbulence level. An enclosure
is attached at the bottom of the inner chamber to house an electronic balance. The height of the
enclosure can be adjusted to allow the specimen surface to be flush with the chamber bottom. A
stainless steel (SS) plate is used to cover the gap between the inner chamber and the balance
enclosure. All parts inside the chamber are made of stainless steel. In particular, the chamber
itself is made of electro-polished stainless steel. More detailed information on the chamber
configuration and performance including air tightness and mixing within the chamber can be
found in Zhang et al. (1996).
FIGURE 1.
Schematic diagram of the 400 L chamber
Air outlet
Hot wire probe
& flow analyzer
Air inlet
Outer chamber
Air flow
Air flow
Screen &
perforated plate
Inner chamber
Screen &
buffer plate
fan
Air flow
DC motor
SS plate
Specimen
Electronic balance
Sensor
(RH & Temp.)
Air velocity was varied in five levels with the DC motor voltage of 5, 10, 15, 20, and 25
volt (V). At the same time, the level of turbulence was varied by using a meshed screen or a
perforated plate. The meshed screen is made of #10 stainless steel wires with 10 x 10 openings
per 6.45 cm2. The size of each opening is 0.19 cm by 0.19 cm. The total opening area is about
2
56.3 %. The perforated plate has 78 holes with a diameter of 1.27 cm. The air velocity and
fluctuations were measured with a flow analyzer equipped with a hot-wire probe (shown as a
dotted line in Figure 1). Figure 2 summarizes the vertical air velocity profile from the surface of a
specimen to the middle of the inner chamber. Figure 2 also shows that difference in the air
velocity caused by different turbulence level (illustrated by solid and dotted lines) is relatively
small. Figure 3 shows turbulent kinetic energy (K) due to velocity fluctuations. Turbulence due to
increased air velocity with the plate with 1.27 cm holes is much greater than that induced by the
meshed screen.
FIGURE 2.
Vertical air velocity (u) profile in the inner chamber
Dimensionless distance from the material surface
(y/ymax)
0.50
0.40
0.30
0.20
0.10
0.00
0
0.05
0.1
0.15
0.2
0.25
0.3
Velocity (m/s)
Meshed Screen-5V
Meshed Screen-25V
Meshed Screen-10V
Perforated Plate-5V
Meshed Screen-15V
Perforated Plate-15V
Meshed Screen-20V
Perforated Plate-25V
Emission Testing and Modeling
Table 1 summarizes the experimental combination with the number of repetition in the 3rd
and 4 column. Decane was chosen to simply the experiment. Oak substrates were preconditioned for 3 days in a full-scale chamber at 23 °C of temperature, 50% of relative humidity,
and 1 air change per hour (ACH). After the application of decane (~4g) on an oak substrate (0.25
x 0.24 m) outside the chamber, the specimen was introduced into the chamber and the weight
was recorded for ~48 hour with an electronic balance. The experimental conditions include 23 ±
1°C of temperature, 50 ± 1.5 % of relative humidity, and 1 ACH.
th
TABLE 1.
Experimental combination
Weight of decane (g)
~4
Voltage (V)
5
10
15
20
25
# of experiment with screen
2
1
5
1
2
# of experiment with plate
2
5
2
3
FIGURE 3.
Vertical profile of turbulent kinetic energy (K) in the inner chamber
Dimensionless distance from the material surface
(y/ymax)
0.50
0.40
0.30
0.20
0.10
0.00
0.0E+00
5.0E-04
1.0E-03
1.5E-03
2.0E-03
2.5E-03
3.0E-03
3.5E-03
4.0E-03
4.5E-03
2
K, (m/s)
Meshed Screen-5V
Meshed Screen-25V
Meshed Screen-10V
Perforated Plate-5V
Meshed Screen-15V
Perforated Plate-15V
Meshed Screen-20V
Perforated Plate-25V
The recorded weight data were used to determine the diffusion and evaporation
coefficient of a mass-transfer based model. The assumptions used to develop the model include:
1. Upon application, decane penetrated into the substrate from the surface and the
substrate can be divided into two regions: Region I with decane and Region II without
decane (See Figure 4).
2. The depth (l) of the region with decane is equal to the volume of decane divided by
the surface area (A) of the substrate.
3. The mass-transfer of decane in Region I is governed by diffusion only with a constant
diffusion coefficient (D).
4. The diffusion is one dimensional and uni-directional, i.e., upwards from the substrate
to the chamber air.
5. The mass-transfer at the specimen surface (x=I) is governed by evaporation.
6. The decane concentration is homogenous (Co) within Region I at t=0, when it is
introduced into the chamber. Co can be estimated from the total mass of decane
applied (Moo), A, and l.
FIGURE 4.
Schematic diagram of the specimen for model development
Evaporation
Diffusion
Negligible masstransfer
{
X=l
Region I: with decane
X=0
Region II: without decane
4
Based on Assumption 3, the decane concentration within Region I can be described by
Equation 1:
∂ 2C
∂C
=D 2
∂x
∂t
(1)
where
C = the concentration of decane in Region I (mg/m3)
D = the diffusion coefficient of decane in Region I (m2/s)
x = the distance upwards from the bottom of Region I (m)
t = time (h)
Two boundary conditions and one initial condition are needed to solve Equation 1. With
Assumption 4, Equation 2 can be used as one boundary condition.
∂C
=0
∂x
at x = 0
(2)
The second boundary condition, Equation 3, is based on Assumption 5.
D
∂C
= α C* − C
∂x
(
)
at x = l
(3)
where
C* = the concentration that would be in equilibrium with the vapour pressure in the
atmosphere remote from the surface (mg/m3);
l = the thickness of Region I (m)
α = the evaporation coefficient (m/h).
Assumption 6 can provide the following initial condition:
C = Co
at t = 0
(4)
Based on equations from 1 to 4, the total mass emitted until a large time t (Mt) can be
found using Laplace transform:


M 
2 L2
ln 1 − t  = ln  2 2
2
 M∞ 
 β1 β1 + L + L
(
where
 β 12 D
− 2 t
l

)
(5)
β1 = the first positive term to satisfy β tan β = L and L = lα
D
M∞ = Mt for an infinite t, which is the total mass of decane applied.
The large time will be defined later. Plotting the logarithmic term on the left hand side of Equation
5 versus time can lead to the diffusion coefficient.
D=−
S l2
(6)
β12
The evaporation coefficient (α) can be described by Equation 7 for the case where the
surrounding air concentration is low, i.e., C* is close to zero. In a chamber experiment, this
condition can be satisfied right after a specimen is introduced into the chamber.
ERo =
α Mo
(7)
l
where
ERo = the initial emission rate (g/h)
Then, β1 can be calculated by manipulating Equation 6,
tan β1
β1
=−
α
Sl
β1 tan β1 = L
and L = lα
D
.
(8)
More detailed information on developing the model can be found in Won and Shaw (2003).
5
RESULTS AND DISCUSSION
Figure 5 shows a typical trend of normalized total mass emitted (Mt/Moo) and emission
rate. The emission rate is shown to be fluctuating around zero after ~2 hours. Additional
measurements done with an electronic balance in a chamber without any emission source
provided a similar type of fluctuations of weight data. Therefore, it is concluded that the
fluctuations of emission data around zero were likely due to fluctuations of environmental
conditions, e.g., air movements rather than mass-transfer phenomena. Consequently, the masstransfer is concluded to be negligible after tf, which is defined as the time when the fluctuation
starts. The rapid increase of Mt/Moo appears to slow down around tf.
FIGURE 5.
Normalized total mass emitted (Mt/Moo) and emission rate (ER) as a function of time
1.2
ER0
Mt/Moo (dimensionless)
Emission rate (g/h)
1.0
0.8
Emission rate
0.6
Mt/Moo
tf
0.4
0.2
0.0
-0.2
0
6
12
18
24
30
36
42
48
Elapsed time (h)
As mentioned previously, Equation 5 is valid for a large time t. The large time is defined
as the time between t0.5 and tf, while t0.5 is defined as the time when Mt/Moo is equal to 0.5
×(M48h/Moo). The R2 value from the regression analysis involving Equation 5 was greater than
0.99 for all experimental data. Prior to determining D with Equation 6, it is necessary to know α
and β1. α was first determined from Equation 7 using ER0 as shown in Figure 5. Equation 8 was
then solved using a commercial Solver to determine β1.
Figure 6 shows a correlation between air velocity (u) at different vertical locations and
evaporation coefficient (α) from the experiments with the meshed screen. The R2 values that are
greater than 0.99 for all correlations demonstrate that there is a strong correlation between air
velocity and evaporation coefficient. However, the type of correlation depends on the location
from the specimen surface. The correlation tends to have a linear form for the bulk air stream
above the velocity boundary layer. On the other hand, α is proportional to air velocity raised to
the power of ~0.3 when the velocity is measured close to the specimen surface. This
demonstrates the importance of specifying the location where air velocity is measured.
Figure 7 shows the effects of turbulence on evaporation coefficients determined from
experiments with the meshed screen. It appears that there is a power-law relationship between
turbulent kinetic energy and evaporation coefficient. The power ranged from 0.17 to 0.33.
6
FIGURE 6.
Evaporation coefficient (α) as function of air velocity (u) with a meshed screen
2.5E-04
0.03
0.06
2.0E-04
0.08
0.11
0.14
1.5E-04
α (m/h)
0.17
0.19
0.22
1.0E-04
y/ymax
Power law
y/ymax
0.03:
y = 0.0005x0.3481
2
R = 0.9946
0.14:
0.06:
y = 0.0004x0.3021
2
R = 0.996
0.17:
0.19:
5.0E-05
0.11:
0.0E+00
0.00
y = 0.0004x
R2 = 0.9939
0.22:
0.3016
y = 0.0003x
R2 = 0.9887
0.05
Linear model
0.28
0.28:
y = 0.0005x + 9E-05
R2 = 0.9978
y = 0.0005x + 0.0001
R2 = 0.9974
0.33:
y = 0.0005x + 9E-05
2
R = 0.9968
y = 0.0005x + 1E-04
2
R = 0.9982
0.39:
y = 0.0005x + 9E-05
R2 = 0.9967
y = 0.0005x + 1E-04
R2 = 0.9992
0.44:
y = 0.0005x + 9E-05
2
R = 0.9959
0.33
0.39
0.44
0.3058
0.08:
y/ymax
Linear model
y = 0.0005x + 0.0001
R2 = 0.994
0.10
0.15
0.20
0.25
Power
(0 08)
0.30
Chamber air velocity (m/s)
FIGURE 7.
Evaporation coefficient (α) as a function of turbulent kinetic energy (K) with a meshed screen
2.5E-04
0.03
2.0E-04
0.06
0.08
0.11
1.5E-04
α (m/h)
0.14
0.17
0.19
1.0E-04
y/ymax
y/ymax
0.03:
y = 0.0015x0.2512
R2 = 0.9987
0.14:
y = 0.0016x0.2597
R2 = 0.9985
0.06:
y = 0.0021x0.2917
2
R = 0.9785
0.17:
y = 0.0028x
R2 = 0.9968
0.19:
y = 0.0028x
R2 = 0.9655
0.22:
y = 0.0029x
R2 = 0.9922
5.0E-05
0.0E+00
0.0E+00
y/ymax
0.08:
y = 0.0017x
R2 = 0.9323
0.11:
y = 0.0013x0.2296
R2 = 0.9061
0.2646
1.0E-04
2.0E-04
0.22
0.28:
y = 0.0025x0.3093
2
R = 0.984
0.33:
y = 0.002x0.2842
2
R = 0.9743
0.3243
0.3237
0.3305
3.0E-04
0.33
0.39
0.44
0.2895
0.39:
y = 0.0021x
2
R = 0.9695
0.44:
y = 0.0021x
R2 = 0.9867
4.0E-04
0.28
0.2923
5.0E-04
6.0E-04
2
Turbulent kinetic energy, (m/s)
Note: Different symbols correspond to different relative distance (y/ymax) from the specimen
surface and lines are from regression analysis.
7
Since it is easier to measure the characteristics of bulk air rather than those of boundary
layer, the effect of bulk air velocity and turbulence on evaporation coefficient is separately shown
in Figure 8. The bulk air velocity and turbulent kinetic energy is the averaged value of two data
points close to the center of the chamber. Figure 8 demonstrates that evaporation coefficient is a
function of both air velocity and turbulent kinetic energy.
FIGURE 8.
Evaporation coefficient (α) as a function of velocity (uoo) and turbulent kinetic energy (Koo) of bulk
air (Lines are from regression analysis)
2
Turbulent kinetic energy (bulk air) (m/s)
0.0E+00
3.0E-04
1.0E-03
2.0E-03
3.0E-03
4.0E-03
2.5E-04
2.5E-04
2.0E-04
2.0E-04
(m/h)
α (m/h)
1.5E-04
1.5E-04
1.0E-04
5.0E-05
0.0E+00
0.00
0.05
0.10
y = 0.0005x + 9E-05
R2 = 0.9963
Meshed screen & velocity
y = 0.0005x + 0.0001
R2 = 0.9979
Perforated plate & velocity
y = 0.0024x0.2912
R2 = 0.9891
Meshed screen & turbulent
kinetic energy
y = 0.0008x0.2176
R2 = 0.9926
Perforated plate & turbulent
kinetic energy
0.15
0.20
0.25
1.0E-04
5.0E-05
0.0E+00
0.30
Velocity (bulk air) (m/s)
The effects of bulk air velocity and turbulent level on diffusion coefficients in Figure 9 are
much weaker than those on evaporation coefficients. Considering the fact that diffusion
coefficients were associated with evaporation coefficients through Equations 6 to 8, the weak
effects appear due to a mathematical propagation rather than a physical phenomenon.
It is interesting to compare these results with published correlations between air velocity
and gas-phase mass transfer coefficients, which have a similar concept to evaporation
coefficients. Sparks et al. (1986) reported that the gas-phase mass-transfer coefficient from
synthetic stain and moth cakes is proportional to air velocity to the power of 0.67. According to
the boundary layer theory associated with heat transfer, heat transfer coefficient is shown to be
proportional to air velocity raised to the power of 0.5 (0.8) for the laminar (turbulent) boundary
condition (Incropera and Dewitt, 1985). On the other hand, Topp et al. (2001) demonstrated that
there is a linear relationship between gas-phase mass-transfer coefficient and air velocity from
one experiment and several CFD simulation cases. Although it was not specifically mentioned in
Topp et al. (2001), there appears to be a power-law correlation between turbulent kinetic energy
and gas-phase mass transfer coefficient.
8
FIGURE 9.
Diffusion coefficient (D) as a function of velocity (uoo) and turbulent kinetic energy (Koo) of bulk air
(Lines are from regression analysis)
Turbulent kinetic energy (bulk air) (m/s)
0.0E+00
1.2E-12
1.0E-03
2.0E-03
2
3.0E-03
4.0E-03
1.4E-12
1.2E-12
1.0E-12
1.0E-12
2
6.0E-13
4.0E-13
2.0E-13
0.0E+00
0.00
D (m /s)
8.0E-13
2
D (m /s)
8.0E-13
0.05
0.10
y = 1E-12x + 7E-13
2
R = 0.6582
Meshed screen & velocity
y = 2E-12x + 6E-13
2
R = 0.9196
Perforated plate & velocity
y = 1E-09x + 7E-13
2
R = 0.9434
Meshed screen & turbulent
kinetic energy
y = 1E-10x + 7E-13
2
R = 0.9819
Perforated plate & turbulent
kinetic energy
0.15
6.0E-13
4.0E-13
0.20
0.25
2.0E-13
0.0E+00
0.30
Velocity (bulk air) (m/s)
CONCLUSIONS
The effects of air velocity and turbulence level on the emissions of decane applied on an
oak substrate were determined using dynamic chamber tests. It was shown that there was a
linear correlation between air velocity and evaporation coefficient, while a power-law correlation
was obtained between turbulent kinetic energy and evaporation coefficient. The correlations of
two factors to diffusion coefficient were shown to be much weaker. Comparisons to published
results suggest that the correlations developed in this paper have a potential of simulating the
effects of air velocity on material emissions in buildings.
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