Effect of Non-Isothermal Conditions on Hygrothermal

Transcription

Proceedings of BS2015:
14th Conference of International Building Performance Simulation Association, Hyderabad, India, Dec. 7-9, 2015.
EFFECT OF NON-ISOTHERMAL CONDITIONS ON HYGROTHERMAL
BEHAVIOUR OF A HEMP CONCRETE BUILDING ENVELOPE
Anh Dung Tran Le1, Driss Samri2 , Chadi Maalouf3, Mourad Rahim1, Omar Douzane1,
Geoffrey Promis1, Thierry Langlet1
1
Laboratoire des Technologies Innovantes (LTI), Université de Picardie Jules Verne
Avenue des Facultés, 80025 Amiens Cedex 1, France
2
Cerema, Direction territoriale Sud-Ouest, Rue Pierre Ramond CS 60013 33166 Saint
Médard en Jalles Cedex, France
3
GRESPI, Faculté des Sciences, Université de Reims, BP1039, 51687, Reims, France
ABSTRACT
The objective of this work is to study the effect of
taking into account the non-isothermal conditions on
the prediction of hygrothermal behavior of a hemp
building envelope and on the hygrothermal comfort
in building. At the beginning, two mathematical
models (non isothermal and isothermal models) to
describe the coupled heat and mass transfer in porous
materials have been investigated. Both models are
one-dimensional and analyzed, using finite difference
technique with an implicit scheme. Then, numerical
results are compared to experimental data. The
comparison has shown that the model which
disregards the effect of temperature on the sorption
cannot predict correctly one-dimensional heat and
moisture transfer through the building envelope.
Finally, the application of both models at whole
building level for predicting the hygrothermal
comfort conditions has been conducted.
INTRODUCTION
Temperature and relative humidity are important
parameters influencing perceived indoor air quality
and human comfort. High moisture levels can
damage construction and inhabitant’s health. High
humidity harms materials, especially in case of
condensation and it helps moulds development
increasing allergic risks. Consequently, several
researchers have studied the use of various
hygroscopic materials to moderate indoor humidity
levels. The material that absorbs and desorbs water
vapor can be used to moderate the amplitude of
indoor relative humidity and therefore to participate
in the improvement of the indoor quality and energy
saving (Olalekan and Simonson, 2006; Tran Le et al.,
2010; Colinart et al., 2012). Vegetal fiber materials
are an interesting solution as they are eco materials
and have low embodied energy. Hemp concrete is
one of these materials which is more and more
recommended by the eco-builders for its low
environmental impact. The physical properties of
hemp concrete has been measured by many authors (
Rahim et al., 2015, Collet et al., 2008; Cerezo, 2005;
Evrard and De Herde, 2010; Pretot et al., 2014). It is
highlighted that the one presents high moisture
buffering capacity and a good compromise between
insulation and inertia materials (Maalouf et al.,
2014).
MATHEMATICAL MODELS
Heat and moisture transport in porous building
materials
Mechanisms of moisture transport in a single
porous building material have been extensively
studied (Philip and De Vries, 1957; Kunzel, 1995;
Mendes et al., 2003). Most of the models have nearly
the same origin; the main difference among them is
related to particular assumptions used. In this article,
the model that takes into account liquid and vapor
moisture transport is used (Mendes et al., 2003).
Forms of moisture transport depend on the pore
structure as well as on the environmental conditions.
The liquid phase is transported by capillarity whereas
the vapor phase is due to the gradients of partial
vapour pressure. With these considerations, the mass
conservation equation becomes:
∂θ
∂ 
∂T  ∂ 
∂θ 
=  DT
 +  Dθ

(1)
∂t ∂x 
∂x  ∂x 
∂x 
with the following boundary conditions
respectively for the external (x=0) and internal (x=L)
surfaces of the wall:
∂T
∂θ 

− ρl  DT
+ Dθ
= hM , e ρ v, a,e − ρv, s,e

∂
x
∂x  x = 0,e

(
)
(2)
∂T
∂θ 

− ρl  DT
+ Dθ
= hM ,i ρ v, s,i − ρ v, a ,i

∂x
∂x  x = L,i

(
)
(3)
where the subscript a represent the adjacent air
and s the solid surface of the material, while the
subscripts e and i correspond respectively to the
external and internal neighbouring environment (a)
or solid surface (s).
One dimension of the energy conservation
equation with coupled temperature and moisture for a
porous media is considered and the effect of the
- 2222 -
adsorption or desorption heat is added. This equation
is written as:
ρ 0 Cp m
∂T
∂  ∂T
= λ
∂t ∂x  ∂x
 ∂ 
∂T 

 + Lv ρ l   DT ,v
+
∂
x
∂x 

 
∂ 
∂θ  
 Dθ ,v

(4)
∂x 
∂x  
where Cpm is the average specific heat which
takes into account the dry material specific heat and
the contribution of the specific heat of liquid phase.
+
Cpm = Cp0 + Cpl
ρl
θ
ρ0
(5)
λ is thermal conductivity depending on moisture
content.
,
Indoor
conditions
,
Outdoor
conditions
,
,
Convective heat
and mass transfer
Convective heat
and mass transfer
,
,
Heat and mass transfer
Figure 1 Schematic representation of heat and
moisture transfer through the wall.
Figure 1 shows the boundary conditions that take
into account convective heat transfer, radiative heat
transfer and heat associated to phase changes, as
expressed in the right side of Eqs. (6) and (7) for the
external and internal surfaces, respectively.
−λ
∂T
∂T
∂θ 

− Lv ρl  DT ,v
+ Dθ ,v 
= hT ,e Ta,e − Ts,e
∂x
∂x
∂x x=0,e

(
(
+ L v h M ,e ρ ve , a , e − ρ ve , s ,e
)
(
(
)
Effect of temperature on the sorption
characteristics
Up to now, many studies have been carried out to
measure the general shape of the isothermal sorption
characteristic. However, the physics related to the
isothermal sorption curves are still disputed. The
researches showed that the sorption capacity of
materials depends on the temperature (Carsten and
Clorius, 2004; Ait Oumeziane, 2014; Navi and
Herger, 2005). Increasing temperature will entail that
the isosteric moisture content be reached in
equilibrium with a higher relative humidity. The
study of its effect on the hgrothermal behavior for the
bio-based materials is new (Carsten and Clorius,
2004). Concerning the hemp concrete, Ait
Ouméziane (2014) showed that taking into account
its influence is necessary. In this article, we use two
models describing the relation between sorption
characteristics at different temperatures: Milly's
model (Milly, 1982) and Poyet's model (Poyet and
Charles, 2009).
Milly's model is based on the effect of temperature
on the intrinsic properties of water to establish the
sorption curves. The temperature dependent sorption
characteristics are expressed as:
Cϕ (T2 −T1 )
ϕ2 (θ , T2 ) = ϕ1(θ , T1)e
(6)
∂T
∂T
∂θ 

− λ − Lvρl  DT ,v
+ Dθ ,v 
= hT ,i Ts,i −Ta,i
∂x
∂
x
∂x  x=L,i

+ L v h M ,i ρ ve , s ,i − ρ ve, a ,i
)
Pvs (T ) ∂ϕ
(8)
ρl ∂θ
The equations contain several parameters that are
themselves function of the state variables. The
special interests of the model are the dependencies of
moisture content, moisture transport coefficient,
thermal conductivity ,etc. upon the relative humidity
and temperature. This makes possible to take into
account the temperature-sorption dependence into the
model, which will be presented in the next subsection.
Dθ = π
(9)
where the coefficient Cϕ is given as:
1 ∂ϕ
(10)
ϕ ∂T
However, Poyet (2009) showed that this
consideration is not sufficient to well predict the
hygrothermal behavior of concrete. Thus, the authors
propose one another model based on the differential
heat of sorption, which is written as:
Cϕ =
)
(7)
In the case lacking a data base of moisture
transport coefficients, simplified models should be
used. The use of simplified mathematical models has
varying effects on accuracy and has been discussed
in (Mendes et al., 2003). In this article, the effect of
temperature gradient on moisture diffusion is
neglected which is generally accepted. The moisture
diffusion coefficient related to moisture content
gradient is evaluated as:
qst (θ )
P (T )
ϕ(T2,θ ) = ϕ(T1,θ ) sat 1 e
Psat(T2)
Ml  T2 −T1 


R  T1T2 
(11)
where: Ml: molar mass of water [kg.mol-1]; R:
ideal gas constant [J.mol-1 K-1]; qst : isosteric heat
[J.kg-1], which is calculated from two sorption
isotherms at two different temperatures (T1 and T2).
- 2223 -
Air model
In order to model heat and mass transfer in the room,
we used the nodal method, which consider the room
as a perfectly mixed zone. The energy equation and
the mass balance equation for room air can be written
as:
∂T
ρi c pV
= ΦWest − Φ East + Φ South − Φ North
∂t
+ΦBottom − ΦTop + ΦSource
(12)
V
H: enthalpy of moist air (KJ/kg)
Acceptability scale ranges from +1 (clearly
acceptable) to -1 (clearly unacceptable).
The empirical coefficients a and b have been
calculated for polluted and unpolluted air with five
building materials at two different loading levels. For
clean air and air polluted with carpet and sealant, the
constants a, b and the acceptability function are
shown in Table 1. These formulas have been used to
predict the PD and the indoor air acceptability.
∂ρ i
= QmWest − QmEast + QmSouth − QmNorth
∂t
+QmBottom − QmTop + QmSource
Table 1 a, b and acceptability for the clean air and
air polluted air (based on Fang et al., 1998).
(13)
where:
ρi : air density (kg.m-3)
Φ: Heat flux (W)
Qm : Air flow rate (kg.s-1)
Φsource : Heat source power (W)
w : Humidity ratio (kg.kg-1).
Prediction of percentage perceived discomfort
(PD) and indoor air acceptability (Acc)
The literature shows that indoor humidity has a
strong effect on the acceptability and freshness of
indoor air. Toftum (1998) found that 1°C change in
air temperature had the same effect on acceptability
and freshness as 121 and 130 Pa change in vapour
pressure, respectively. For thermal sensation, a 1°C
change in air temperature corresponded to 231 Pa
change in vapour pressure.
Investigations showed that complaints about bad
indoor air quality increased with a higher enthalpy
(H) of the air (Hens, 2011). The enthalpy of moist air
is the sum of the enthalpy of the dry air and the
enthalpy of the water vapour. The enthalpy of moist
air can be described as:
H=1.008T+w (2500.8+1.805T)
(14)
Where:
T: dry-bulb temperature of air-vapour mixture (°C);
w: humidity ratio, kg of water vapour/kg of dry air.
The statistical relation found between enthalpy and
number of dissatisfied (with 20% dissatisfied is
handled as the limit) looks like (Hens, 2011):
exp[− 0.18 − 5.28(−0.0333H + 1.662)]
PD =
(15)
1 + exp[− 0.18 − 5.28(−0.0333H + 1.662)]
Fang (1998) studied 40 subjects which were facially
exposed to air supplied through a diffuser under
laboratory conditions. The subjects assessed the
acceptability of polluted and unpolluted air at
different humidity and temperatures. Based on the
response of the subjects, the acceptability of air can
be expressed as function of the enthalpy of air:
Acceptability= a. H + b
(16)
Where:
a and b: empirical coefficients
Case study
Clean air
a
-0.033
b
1.662
Air polluted
with carpet
Air polluted
with sealant
-0.023
0.966
-0.013
0.263
Acceptability
Acceptability= 0.033H + 1.662
In order to solve the previous equation system, the
numerical solution is based on the finite difference
technique with an implicit scheme. To solve this
system of equations, we used the Simulation Problem
Analysis and Research Kernel (SPARK) which is
especially suited to solve efficiently differential
equation systems (Sowell and Haves, 2001;
Mendonça, 2004; Wurtz, 1995).
NUMERICAL STUDY AND
EXPERIMENTAL VALIDATION AT
WALL LEVEL
Experiment and simulation conditions
This section concerns the validation of the
numerical model by comparing the simulation results
with experimental ones. For this, we use the results
obtained from the experimental facility developed at
the laboratory by Samri (2008). One side of tested
wall was submitted to various outdoor conditions of
temperature and relative humidity using a climate
chamber, while other side of the wall was in contact
with the laboratory ambient where temperature and
relative humidity are relatively constant. The test
wall was instrumented with sensors which are
connected to an acquisition system to measure the
hygrothermal profiles. It consists of a hemp concrete
wall with 30 cm of thickness. The wall was subjected
to cyclic step-changes in relative humidity and
temperature: 20°C/50% RH during 24h followed of
10°C/80% RH during 24h; 40°C/45% RH during
24h and finally finished with 20°C/50% during 24h
(see Figure 2).
- 2224 -
In addition, to test the effect of using the different
sorption curves, for each model, three cases have
been considered:
• Adsorption curve
• Desorption curve
• Mean sorption curve obtained from the
average between adsorption and desorption.
In this paper, the isosteric heat adsorption of hemp
concrete has been determined by using the sorption
isotherms at 10° and 23°C (Ait Oumeziane, 2014).
For the both indoor and outdoor surfaces, the heat
and mass transfer coefficients are 9 W.m-2.K-1 and
0.003 m.s-1, respectively. The time step is 240
seconds and the wall was discretized into 25 nodes
according to one sensitive study conducted by Tran
Le (2009). In order to facilitate the investigation,
only the results obtained in the middle of the wall
(point C) will be presented.
Step-changes in
relative humidity
and temperature
80
80
60
60
50
40
T
40
HR
30
20
20
10
Relative humidity (%)
Temperature (°C)
70
Isothermal hygrothermal behavior of hemp
concrete wall: Isoth model
The comparison between the variation of
temperature and relative humidity at point C obtained
from the simulation using the Isoth model and the
one from the experimental measurement is presented
in Figure 3 and Figure 4.
0
0
12
24
36
48
60
Time (h)
72
84
96
Figure 2 Experimental procedure : Step-changes
in relative humidity and temperature.
Table 2 Hygrothermal properties of hemp
concrete (Ait Oumeziane, 2014)
T at C Testing
T at C Simulation_Adsorption
T at C Simulation_Mean curves
T at C Simulation_Desorption
T outside
60
Density
Thermal
conductivity
Specific
heat
capacity
Water vapor
permeability
kg/m3
320
W/(m.K)
0.091
J/(kg.K)
1250
Kg/(m.s.Pa)
1.10-10
Temperature (°C)
50
40
30
20
10
0
The hygrothermal properties of hemp concrete
measured by (Ait Oumeziane, 2014) are used for the
simulation. Some basic hygrothermal data of hemp
concrete is given in Table 2. It is noticed here that
some authors have validated their models with
constant coefficients using the results of this
experimental case (Tran Le et al., 2014; Samri,
2008). However, the fact that a value of about 3.10-7
(m²/s) of mass transport coefficient associated to a
moisture content gradient was used for their
validations is not realistic. Therefore, this article
focuses on a more completed model that takes into
account the effect of the temperature-dependent
sorption characteristics on the hygrothermal response
of hemp concrete wall. The simulation has been
realized for two following models:
• Isoth: Using the isothermal sorption
characteristics in the simulation
• Non-Isoth: Taking into account the effect of
temperature on the sorption curve by using
the Poyet's model or Milly's model
20
40
60
Time (h)
80
100
Figure 3 Variation of temperature at point C – Isoth
model and experimental measurement
One can observe that the variation of temperature is
very similar for the three studied cases (adsorption,
desorption and average curve). The model gives a
quite satisfactory prediction of temperature within
the wall, despite some discrepancy between
experimental and predicted values. Concerning the
variation of relative humidity, the computed results
did not fit to the experimental ones. This should be
explained by the fact that the studied model
neglected the effect of temperature on the moisture
sorption capacity of the material, in which increasing
temperature results in increase of the relative
humidity at given water content. Therefore, the
dependency of sorption characteristic on temperature
has been taken into account in the physical model
and the result will be presented in the following
subsection.
- 2225 -
experimental ones is 3% RH. This value is small
compared to the accuracy of sensor inserted in the
tested wall, which is ±1.5% of RH.
RH at C Testing
100%
RH at C Simulation_Mean curves
RH at C Testing
RH at C Simulation_Desorption
80%
100%
RH at C Simulation_Adsoprtion
RH outside
RH at C Simulation_Adsoprtion
60%
40%
0
20
40
60
80
RH at C Simulation_Mean curves
RH at C Simulation_Desorption
80%
RH outside
60%
100
Time (h)
40%
0
Figure 4 Variation of relative humidity at point C –
Isoth model and experimental measurement
T at C Testing
T at C Simula tion_Adsorption
T at C Simula tion_Mea n curves
T at C Simula tion_Desorption
T outside
Temperature (°C)
50
40
30
20
10
0
20
40
60
80
40
60
80
100
Time (h)
Non-Isothermal hygrothermal behavior of hemp
concrete wall: Non-Isoth model
As mentioned above, both Milly's model and
Poyet's model have been used to study the impact of
non-isothermal conditions on the hygrothermal
behavior of hemp concrete. Because the results
obtained from the Milly's model is very close to those
from Isoth model, they are not depicted here. This
subsection focuses only on the results obtained by
using Poyet's model and the comparison between its
results and experimental data are shown in Figure 5
and Figure 6.
60
20
100
Time (h)
Figure 5 Variation of temperature at point C – NonIsoth model and experimental measurement
As can be seen from Figure 5 , the numerical
results are in accordance to the experimental results.
In addition, they are very close to those obtained by
using the Isoth model (by comparing Figure 5 with
Figure 3). Figure 6 showed that compared to the final
one, the Non-Isoth model results in significantly
better prediction of the relative humidity variation in
the tested wall. Concerning three cases studied, the
results are dependent on which the sorption curve is
used for the simulations. The results calculated with
the adsorption allow a better prediction of the relative
humidity variation than those for the model that uses
desorption curve or an average sorption curve
between adsorption and desorption. The maximum
difference between the computed results for the
model that uses adsorption curve and the
Figure 6 Variation of relative humidity at point C –
Non-Isoth model and experimental measurement
It can be drawn a conclusion that it is necessary to
take into account the non-isothermal conditions on
the sorption curves in order to well predict the
hygrothermal behavior of the wall submitted to the
dynamic conditions of temperature and relative
humidity.
EFFECT OF NON-ISOTHERMAL
CONDITONS AND MASS TRANSFER
WITHIN THE BUILIDNG ENVELOPE
ON THE HYGROTHERMAL COMFORT
To investigate the effect of the dependency of
sorption characteristic on temperature on the
hygrothermal comfort at whole building level, the
hygrothermal behaviour of a bedroom which has a
space area of 20 m2 and a volume of 57 m3 has been
studied. It is noted that the numerical model for the
whole building level has been fully validated in
(Tran Le et al., 2010).The plan of the studied room is
depicted in Figure 7. The west and south facades are
in contact with outdoor conditions while other walls
are considered as internal partitions and in contact
with heated space at 19°C temperature and 50 %
relative humidity. External and internal walls are
made of hemp concrete and have 40 cm and 20 cm
thickness respectively. It is considered that no
moisture diffusion occurs through the floor and the
ceiling.
The bedroom is equipped with a radiator and a PI
controller that keeps operative temperature at 19 °C.
The bedroom is ventilated at 0.5 Ach. Heat transfer
coefficients are hT,e= 16 W/m2.K for the outdoor
surfaces and hT,i= 4 W/m2.K for indoor surfaces. The
mass convection coefficients were calculated by
using the Lewis relation and considering the Lewis
number equals to 1. The room is occupied from 23.00
pm to 7.00 am by two persons. The initial relative
humidity and temperature in the walls and the studied
room are respectively 50 % and 19 °C.
- 2226 -
variation of temperature in this thin layer results in a
small effect of temperature-sorption dependence on
the indoor humidity.
By comparing the Th model with other ones, the
results show that moisture buffering of hemp
concrete could considerably dampen the indoor
relative humidity variation and thus notably reduce
the enthalpy of moisture air. Following this, it
reduces the PD values which are shown in Figure 9
because bad indoor air quality increased with a
higher enthalpy. For example, at 71th day, during the
occupied period, the maximum value of PD of the
Non-Isoth model is 13.5% compared to 27 % of Th
model, so a relative increase of 50% was observed.
PD _Isoth model
PD_Non-Isoth model
PD _Th model
Water vapour source (g/h)
400
320
20%
400
320
60%
240
160
40%
80
20%
160
10%
80
0%
0
70
71
71
72
73
74
73
74
75
Time (day)
Figure 9 Percentage of dissatisfied of the indoor air
for the studied models
Figure 10 presents the indoor air acceptability
calculated for the "clean air" case during the
occupation time. The Acc values of Th model are
lower than those of Non-Isoth or Isoth models. This
fact signifies that the indoor air quality is more
clearly acceptable when the moisture exchange
between the building envelope and surrounding air is
taken into account. Concerning the effect of nonisothermal conditions on PD and Acc, it is very small
and neglected.
Acc_Isoth model
Acc_Non-Isoth model
Acc_Th model
0
70
72
75
Time (day)
0,8
400
320
0,6
Acc
Figure 8 Indoor relative humidity for the studied
models
Figure 8 compares the predicted indoor relative
humidity simulated of three models during 5 days
(from 70th to 75th day). It can be seen that the effect
of temperature-sorption dependence on the indoor
relative humidity is neglectable even if its effect is
important on wall level, which has shown in the last
section. It is because only the moisture buffering
capacity of a thin layer at the indoor surface that
exchanges the moisture with indoor air contributes
principally to moderating the variation of indoor
relative humidity. Therefore, a significantly reduced
- 2227 -
240
0,4
160
0,2
80
0,0
0
70
71
72
73
74
75
Time (day)
Figure 10 Acceptability of the indoor air for the
studied models
80%
Simulations are run for three months in winter
using Nancy weather data (in France) by considering
three models:
• Isoth and Non-Isoth (Poyet's approach)
models that use adsorption curve
• Th model which neglects the water vapour
exchange between the building envelope
and indoor/outdoor air (only heat transfer is
considered and the envelope is fully coated
with aluminum foil)
Indoor RH _Isoth model
Indoor RH _Non-Isoth model_ads
Indoor RH _Th model
240
PD (%)
Figure 7: Plan of the studied room
30%
CONCLUSION
This article focuses on the development and use of
a numerical model that takes into account the effect
of temperature on the sorption characteristics in the
transient modeling of coupled heat and mass transfer
in porous materials. In order for this to be done, two
models (Isoth and Non-isoth that uses the approaches
proposed by Milly and Poyet) have been carried out
and implemented in the simulation environment
SPARK which is suited to solve efficiently
differential equation systems.
The numerical results were then compared to the
experimental ones. The results showed that taking the
influence of temperature on the sorption curves into
account is necessary for better prediction of the
hygrothermal behavior of a hemp concrete wall. Both
Isoth and Non-isoth models predicted well the
variation of temperature. However, only Non-isoth
model that uses the Poyet's approach is adapted to
study the variation of the relative humidity in the
wall.
At whole building level, it can be drawn a
conclusion that that moisture buffering capacity of
hemp concrete could considerably dampen the indoor
relative humidity variation and thus notably reduce
the percentage perceived discomfort and increase
indoor air acceptability during occupied period. In
addition, the effect of temperature-sorption
dependence on the hygrothermal comfort is very
small and could be neglected.
H
Enthalpie of mois air
KJ.kg-1
hM
Mass transfer convection
coefficient
m .s-1
hT
Heat transfer convection
coefficient
W.K-1.m-2
Lv
Heat of vaporization
J.kg-1
T
Temperature
°C
t
Time
s
x
Abscise
m
θ
Moisture content
m3 .m-3
λ
Thermal conductivity
W.m-1.K-1
ρ0
Mass density of dry material
kg.m-3
ρl
Mass density of water
kg.m-3
ρv
Mass density of vapor water
kg.m-3
φ
Relative humidity
%
ρi
Air density
kg.m-3
Φ
Heat flux
W
Qm
Air flow rate
kg.s-1
Φsource
Heat source power
W
w
Humidity ratio
kgkg-1
i
Internal
e
External
ACKNOLEGEMENT
REFERENCES
The authors wish to thank the reviewers for their
constructive comments on this article.
Ait
NOMENCLATURE
Symbol Definition
Unity
C
Specific heat
J.kg-1.K-1
C0
Specific heat of dry material
J.kg-1.K-1
Cl
Specific heat of water
J.kg-1.K-1
DT
Mass transport coefficient
associated to a temperature
gradient
m2.s-1.K-1
DT,v
Vapour transport coefficient
associated to a temperature
gradient
m2.s-1.K-1
Dθ
Mass transport coefficient
associated to a moisture
content gradient
m2.s-1
Dθv
Vapour transport coefficient
associated to a moisture
content gradient
m2.s-1
Oumeziane, Y. 2014. Evaluation des
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Effect of Non-Isothermal Conditions on Hygrothermal

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