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Energy and Buildings 40 (2008) 1513–1520
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Static and dynamic thermal characterisation of a hollow
brick wall: Tests and numerical analysis
J.M. Sala a, A. Urresti a,*, K. Martı́n b, I. Flores b, A. Apaolaza b
b
a
Thermal Engineering Department, Universidad del Paı́s Vasco (UPV/EHU), Alda. Urquijo s/n, 48013 Bilbao, Spain
Construction Quality Control Laboratory of the Basque Government, C/Aguirrelanda n8 10, 01013 Vitoria-Gasteiz, Spain
Received 4 January 2008; accepted 2 February 2008
Abstract
This article explains the adjustment procedure of a calibrated hot-box unit and the execution of the corresponding tests to measure the dynamic
thermal properties of walls needed to calculate the thermal load of buildings. The results of a test for a heterogeneous wall are also presented, in a
dynamic temperature rating. These results are compared with those obtained from a simulation carried out on the performance of the same wall
through the application of a finite volume software. Subsequently, the error introduced by assuming one-dimensional heat flow through a
nonhomogeneous wall is discussed. This is equivalent to considering the heterogeneous layer of the wall as an equivalent homogeneous layer,
which is done in several whole building simulation programs. It is concluded that the error committed may be appreciable, even when the
heterogeneities are not excessive.
# 2008 Elsevier B.V. All rights reserved.
Keywords: Calibrated hot-box test; Dynamic thermal characteristics; Wall transient heat flow; Response factors; Conduction transfer coefficients
1. Introduction
The growing interest in energy saving and efficiency extends
to the field of construction. For this reason, it is necessary to have
an appropriate understanding of the thermal performance of
buildings in order to minimise their thermal load. Because of this,
it is becoming more and more necessary to carry out the thermal
characterisation of construction materials and elements.
Correct evaluation of heat losses through the walls of
buildings requires calculations in a nonstationary framework to
include thermal inertia. For this reason, it is indispensable to
have the dynamic thermal characteristics of these walls. That is
why the hot-box unit of the Construction Quality Control
Laboratory (LCCE) of the Basque Government has been set-up:
to perform dynamic rating tests on walls, specifically, through
the determination of its response factors [1].
Duly validated CFD software is available to verify the data
obtained from the tests and determine the possible errors in
measurement or in determination of the characteristics of walls.
* Corresponding author. Tel.: +34 94 601 4402; fax: +34 94 601 4300.
E-mail address: [email protected] (A. Urresti).
0378-7788/$ – see front matter # 2008 Elsevier B.V. All rights reserved.
doi:10.1016/j.enbuild.2008.02.011
A wall formed of different layers was tested, with one layer
being heterogeneous, made of hollow brick. This means that the
heat flow, at least in the area of the brick layer, is not onedimensional. Numerous thermal load simulation and calculation programs of buildings allow only for the use of multilayer
walls formed of homogeneous layers, that is, they only include
one-dimensional heat flow. In these cases, the tendency is to use
an equivalent homogeneous layer, that is, one has equivalent
properties to the heterogeneous layer which it replaces.
An example of this is the new Spanish Technical
Construction Code [2] which is the transposition of European
Directive 2002/91/CE. There are two procedures for evaluating
the maximum energy demand of a building: the simplified
method and the general method.
The simplified method is similar to that which has existed up
to this time, and is based on establishing the maximum thermal
transmittances to the different types of walls, depending on the
orientation and the climate zone of the building. The general
method is based on the use of software called LIDER which
compares the building in question (object) with a reference
building, so that the object building should work out as having an
energy demand equal to or less than that of the reference building.
The LIDER software simulates the dynamic thermal performance of walls, so their inertia is taken into consideration.
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J.M. Sala et al. / Energy and Buildings 40 (2008) 1513–1520
It is necessary to specify the number of layers of which each
wall is formed and to define the thickness of each layer, the
equivalent specific heat and equivalent thermal conductivity.
Consequently, heterogeneous layers are replaced by the
corresponding equivalent homogeneous layers. With the layers
thus defined, the software calculates the coefficients of the Z
transfer functions [3].
For this reason, using the data obtained from the hot-box
test, the equivalent characteristics of the heterogeneous layer
are obtained. With these properties, the conduction transfer
functions (CTFs) for this wall are calculated via software [4],
considering the equivalent homogeneous layer. With this data,
the test carried out on the specific wall is simulated to estimate
the error committed on considering an equivalent homogeneous
wall. As can be observed, the errors may be considerable, even
when the heterogeneities are not excessive.
2. Description and calibration of the chamber
2.1. Description of the guarded hot-box unit
The unit comprises four chambers:
Fixed chamber for simulation of outdoor conditions.
Mobile chamber for simulation of indoor conditions,
mounted on wheels and rails.
Measuring box, situated within the mobile chamber, and
under the same conditions, so that heat only flows through the
sample.
Attemperated ring, situated around the sample to be tested,
acting as a guard ring to improve the thermal stability of the
sample.
Each chamber is provided with an air-treatment unit, cooling
system with indirect method of thermoregulation and
temperature-control system of the two chambers and ring, in
addition to sensors to measure the temperatures, relative
humidity, air speeds and heat flows. A photograph of the
equipment is shown in Fig. 1.
The mobile chamber covers a temperature range of 0–50 8C,
with a heating/cooling speed of 0.2 8C/min. In the cold chamber,
Fig. 1. Guarded hot-box unit.
the temperature range is 10 8C to +40 8C, with the same
cooling/heating speed. The temperature fluctuation is less than
0.2 8C.
The air-treatment unit is situated within each chamber. The
cooling system is based on a one-stage mechanical unit and has
an indirect thermoregulation system (one per chamber).
Heating is by means of stainless-steel electric heating elements
with double protective thermostat. The forced-air ventilation is
of the vertical type, from the roof to the floor of the chamber.
The samples are 2000 mm 2000 mm and the dimensions
of the measuring box are 1000 1000 as indicated in Standard
UNE-EN ISO 8990:1997 [5]. The control system is based on a
PLC and can be configured with up to 1024 digital and 128
analogue inputs and outputs, with automatic start-up in case of
power failure. The measuring system consists of a Data
Acquisition System, with 64 thermocouples for temperature
reading, with precision of 0.1 8C, 4 sensors for heat flow, 2
air-speed sensors and 2 sensors for relative humidity.
The equipment is provided with a 96-channel data
acquisition system. The system is controlled by an external
PC and includes analogue input and output modules, module
supports, standard network technology and RS232 series for
data transmission.
2.2. Calibration of the calibrated hot box
To carry out the dynamic tests on walls, it is necessary to
know the response of the measuring equipment to temperature
changes [6]. To facilitate temperature regulation in the hot
chamber, the guarded box is removed and is operated as a
calibrated box. This has the added advantage that it is not
necessary to evaluate the dynamic performance of the guarded
box. Because the temperature change will be applied directly on
the circulating air, the only parameter we need to evaluate is the
surface resistance coefficient for both sides of the wall.
The tests were carried out with quite high air speeds, 1–2 m/s
in the hot chamber and 3–4 m/s in the cold chamber, flowing
updown in both cases. These air speeds were used because with
lower speeds it was not possible to maintain homogeneous
surface temperatures in the sample, such that the readings of the
thermocouples of each of the surfaces are within the appropriate
temperature interval.
The measurements were carried out for three air temperature
values of the chamber which simulate outdoor conditions,
namely Tae1 = 0 8C, Tae2 = 5 8C and Tae3 = 10 8C. The surface
temperatures Te and Ti were measured by 32 thermocouples,
distributed on a uniform basis on each surface of the sample, see
Fig. 2.
The measurements were initially performed on a reference
wall, formed of a 5 cm thick layer of extruded polystyrene
(k = 0.035 W/m K). This is a homogeneous material which
responds quickly to variable temperature conditions, so it is
very useful for estimating the response of the chamber itself in
case of variable temperature ratings [6]. The measurements
carried out for the temperatures and values obtained for the
surface thermal resistance on both surfaces are shown in
Table 1.
J.M. Sala et al. / Energy and Buildings 40 (2008) 1513–1520
1515
Fig. 2. Location of thermocouples on the surface of the sample.
It can be verified that the Rse and Rsi maintain noticeably
constant values in the temperature interval considered. The
resulting errors depend on the errors in the determination of the
characteristics of the reference wall tested, specifically, of the
error in thermal conductivity, k, (in our case, this is 2%), the
error in L (the L thickness was measured with a micrometric
screw, with certain variations in the 105 m reading, so this
error is considered negligible), in addition to the errors in
temperature measurement.
These errors are similar in the three tests, so for the
calculation we consider the most unfavourable situation, which
is when the Tae Te, Ti Tai and Ti Te differences are the
least, which occurs in test 2.
On taking all this into consideration, the final result is:
Rse ¼ 0:045 0:004 m2 K=W
The low value of Rsi is due to the high air speed needed to keep
temperature homogeneity on the sample’s surface.
3. Wall tests
3.1. Description of the wall tested
The wall tested consists of three layers: a gypsum layer of
10 mm, a hollow brick layer of 40 mm and an insulating layer
of 30 mm (see diagram in Fig. 3). This prefabricated
construction element forms part of a type of wall that is
typical in our country. The wall is formed of an exterior layer of
facing brick or a 1/2 brick of double hollow brick with a
covering of a single layer of mortar, an air gap of approximately
Table 1
Experimental temperature values and surface air resistance calculated values
1
2
3
Tae
(8C)
0.0
5.0
10.0
Tai
(8C)
20.0
20.0
20.0
Te
(8C)
0.6
5.4
10.3
30 mm, and then the second layer, formed of this construction
element.
The thermophysical properties of the materials have been
obtained from the following sources: the clay of the brick from
NBE-CT-79 [7], the gypsum from EN 12524:2000 [8] and for
the EPS, the values of the official Spanish LIDER program were
used (see Table 2).
3.2. Steady-state test
Rsi ¼ 0:061 0:005 m2 K=W
Test
Fig. 3. The three layers of the wall tested.
Ti
(8C)
19.2
19.4
19.6
Rsi
(m2 K/W)
0.058
0.058
0.061
Rse
(m2 K/W)
0.044
0.041
0.045
First, a static test was performed to determine the total
thermal resistance of the wall and to enable the equivalent
resistance of the heterogeneous layer of the hollow brick to be
calculated.
Prior to the static test of the wall, its response time, ts, was
calculated in order to estimate the duration of the test.
Standard ASTM C1363-97/1 [9] offers two methods for
determining the sample time constant. The simplest method is
through the expression
t s ¼ RT C
(1)
where C is the thermal capacity per unit of transverse area and
RT is the total thermal resistance. Taking into consideration the
dimensions and values listed in Table 2, a thermal capacity
of C = 49.7 kJ/m2 and an approximate thermal resistance of
Table 2
Thermophysical properties of materials
3
r (kg/m )
k (W/m K)
c (J/kg K)
EPS
Clay
Gypsum
15
0.037
1450
1.200
0.490
1050
900
0.300
1010
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J.M. Sala et al. / Energy and Buildings 40 (2008) 1513–1520
RT = 1.15 m2 K/W are obtained. Thus, the value of the time
constant for our wall would be ts = 15.8 h.
In any event, the time constant in composite walls depends
not only on the total resistance and capacity, but also on the
arrangement of the different materials, with different thermal
properties.
The response time of a wall is considerably less than the
value given by the product of RT C [10]. For this reason, we
calculated the ts value from the data obtained on the
computer from the wall performance simulation made with a
finite volumes software (FLUENT). With a being the
quotient limit between the response factors obtained from
the simulation, and D one half of the base of the triangular temperature excitation, the time constant of the wall is
[11]
ts ¼ D
ln a
(2)
The response time obtained from the asymptotic values of the
response factor ratio calculated using FLUENT is ts = 1.47 h.
Once the response time was calculated, the corresponding
tests were carried out to obtain the transmittance of the wall,
according to the standard UNE-EN ISO 8990 [5]. The value
obtained for the thermal transmittance was
U ¼ 0:88 0:04 W=m2 K
Consequently, the total thermal resistance was
RT ¼ 1:14 0:05 m2 K=W
where RT = Rsi + R1 + R2 + R3 + Rse with Ri (i = 1, 3) is the
thermal resistance of each of the layers, and Rsi, Rse, the surface
thermal resistance corresponding to the interior and exterior air,
respectively, obtained at the same conditions as that in the
calibration test.
Once these values have been obtained, the equivalent
conductivity of the hollow brick layer is calculated, from the
total thermal resistance RT and the surface thermal resistance
Rse and Rsi. With R1 = 0.811 m2 K/W, the thermal resistance of
the insulation, and R3 = 0.033 m2 K/W, the thermal resistance
of the gypsum layer, the thermal resistance of the hollow brick
layer is R2 = 0.116 m2 K/W and consequently the equivalent
conductivity of the hollow brick layer is
keq ¼ 0:210 W=m K:
3.3. Dynamic test
The dynamic test is carried out on the by modifying the
exterior air temperature Tae is modified so that it follows a
triangular signal of 10 8C amplitude in an interval of 2 h (10 8C/
h in the upslope and similarly 10 8C/h in the downslope).
Excellent homogeneity in the temperatures of the exterior
environment and a signal of very good quality are obtained.
Once the wall to be tested is installed, the surface
temperatures Ti(t) and Te(t) are measured at 1 min intervals,
with the values being represented in Fig. 4.
Fig. 4. Inside and outside surface temperatures.
The large variation in the exterior surface permits us to
ensure the validity of the results, although the analysis is more
delicate for the interior surface.
The corresponding response factors are obtained from these
surface temperatures, the interior and exterior ambient
temperatures and the Rsi and Rse values, which relate the heat
flow over the excited surface with the temperatures on the
excited surface Xj and the heat flow on the unexcited surface
with the temperatures on this surface, Yj, that is
Xj ¼
qe ð jtÞ
1
¼
½T ae ð jtÞ T e ð jtÞ
10 C Rse 10
(3)
Yj ¼
qi ð jtÞ
1
¼
½T ai ð jtÞ T i ð jtÞ
10 C Rsi 10
(4)
with t being the sampling time interval.
Table 3 shows the values of the response factors obtained up
to an elapsed period of 8 h. Given the thermal capacities of the
layers which constitute the wall tested, it can be verified that it
is sufficient to consider these first 8 h, since effectively the sum
Table 3
Response factors for the wall tested
j
Xj
Yj
0
1
2
3
4
5
6
7
1.10927
0.16088
0.04593
0.02355
0.01214
0.00629
0.00329
0.0174
0.13191
0.32827
0.19153
0.09874
0.05091
0.02636
0.01375
0.00727
J.M. Sala et al. / Energy and Buildings 40 (2008) 1513–1520
of the Xj and Yj factors during this number of hours practically
coincides with the thermal transmittance of the wall.
X
X
X j ¼ 0:864
Y j ¼ 0:842
In the measurements carried out, the triangular signal is
applied in the exterior air temperature and not on the surface of
the wall. Through the exchange of surface heat, a uniform
temperature is obtained on both surfaces of the wall.
4. Numerical analysis
4.1. Steady-state test
First the thermal resistance of the wall tested was calculated
using a CFD code (FLUENT version 6.0). The thermal
resistance Rse and Rsi obtained previously and the temperatures
Te and Ti have been set as contour conditions, and adiabaticity
has been assumed in the upper and lower sides. A calculation
procedure based on Standard UNE-EN ISO 6946:1997 was
used for the apparent thermal conductivity of the air chambers
of the hollow brick layer.
This code was submitted to three validation procedures,
using Standards UNE-EN ISO 10211-1:1995 [12] and UNEEN 1745:2002 [13], with the validity of the software used being
verified in all cases.
The mesh used in the discretisation of the wall is
unstructured and quadrilateral, since this is the mesh that
best suits its geometry. The degree of discretisation is 2 mm,
with this being the value used in the validation according to
Standard UNE-EN 1745:2002. Twelve hundred iterations
were performed. This number was selected after several
simulations.
Table 4 shows the thermal resistance values of the wall
obtained with the CFD, compared with the values obtained in
the tests and with those resulting from applying Standard UNEEN 1745:2002.
1517
Table 4
Thermal resistance of the wall according to different methods
Tests
CFD
RT (m2 K/W)
Deviation (%)
0.88
0.85
3.4
4.2. Dynamic test
The heat transfer function of the CFD code was used to
simulate the dynamic situation, for which the external surface
of the wall was subjected to a triangular excitation of 1 8C
amplitude and 2 h base, with the air temperature of the
unexcited side being kept constant. The heat flow on the excited
and unexcited sides was obtained in this manner and the
response factors were calculated from these flows.
Figs. 5 and 6 present the response factors obtained with the
finite volume code for the heterogeneous solid and those
obtained from the test on the wall.
The values obtained through the two methods are very
similar and have a good agreement with the maximum error of
the data obtained being approximately 5%. It should also be
noted that the highest deviations are in the factors with lower
values, which are those which weigh the least in the subsequent
thermal load calculations.
5. Comparison with homogeneous layer
To verify the suitability of replacing the heterogeneous layer
by a homogeneous one, CTF coefficient calculation software
was used [4], which only accepts homogeneous layers. The
CTF method is used since it is used in many of the building
simulation programs. The equivalent conductivity and the
specific average density and specific heat capacity obtained
from the test were used, which are reproduced in Table 5.
The CTF coefficients were obtained with this software, and
are presented in Table 6.
Fig. 5. X response factors obtained from the test and the CFD code.
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J.M. Sala et al. / Energy and Buildings 40 (2008) 1513–1520
Fig. 6. Y response factors obtained from the test and CFD code.
Table 5
Equivalent layer’s properties
k (W/m K)
r (kg/m3)
c (J/kg K)
0.21
632.35
1041.34
Table 6
CTF coefficients obtained
CTF coefficients
ai
bi
di
1.092077
0.578333
2.56E02
2.95E05
7.42E14
1.64E15
0.1671891
0.3488856
2.32E02
5.24E06
3.35E15
6.10E16
1.000000
0.386967
5.22E04
1.40E12
To compare the data obtained from the test, in the form of
response factors, with those obtained from this software, in the
form of CTF coefficients, the performance of the wall was
simulated in a real temperature variation, for several winter
days in Bilbao. The results of this simulation are shown in
Fig. 7.
As can be seen, the results obtained with the equivalent
homogeneous wall are very similar to those resulting from the
experimental data. The average error between the two
calculations is in the vicinity of 3%, and rarely exceeds 5%.
In any event, it should be noted that the response of the
equivalent wall lags somewhat behind that of the real wall. This
is probably because the dynamic response of walls not only
depends on general characteristics, such as thermal conductivity and capacity, but also on their distribution throughout the
wall [14]. The error in assuming homogeneous layers also
increases slightly when the temperature difference between the
Fig. 7. Interior temperature and heat flow in the Bilbao climate.
J.M. Sala et al. / Energy and Buildings 40 (2008) 1513–1520
1519
Fig. 8. Interior heat flow simulation with sine temperature variation.
exterior and interior environment is reduced. This may be
because under these conditions the heat flow is controlled to a
great extent by the sensible heat stored in the material and,
consequently, in the inertia of the wall itself.
As an example, the calculated response time of the
homogeneous equivalent wall is reduced to 1.36 h, 7% less
than the real time.
If we vary the exterior temperature on a sine basis, with an
amplitude of 5 8C, average temperature equal to the interior, we
obtain the heat flow represented in Fig. 8. For this case, the
average error increases to 60%.
Even so, it should be indicated that in these situations the
heat flow is less, so its contribution to the total balance is not
very noticeable. On carrying out the same calculations for a
typical year in Bilbao, the average error is maintained at
approximately 15%.
6. Conclusions
In calculating the energy demands for buildings and
particularly for bioclimatic systems, it is very important to
characterise the thermal inertia of walls. For this reason, a
calibrated hot-box unit is adjusted for static and dynamic
thermal characterisation of different types of wall, using
2 m 2 m samples.
Numerical analysis is carried out to obtain the thermal
performance of a wall, in stationary and dynamic frameworks.
Dynamic tests are carried out on the basis of the
measurement of the surface temperatures of the wall and
determination of the thermal resistance of the interior and
exterior air layers. On determining these values, and using a
triangular signal in the air temperature of the cold chamber, the
surface temperatures of the sample are measured throughout the
period and the heat flow is calculated.
Finite volume software is used for the numerical calculation of the response factors. Dynamic performance is
analysed considering the heterogeneous wall. The results
obtained permit us to confirm that the test has been correctly
carried out.
The correction of assuming one-dimensional flow in the wall
tested is considered: it contains a heterogeneous hollow brick
layer and, consequently, presents two-dimensional flow paths.
To this end, a simulation based on the Z-transform is used, with
this layer being considered as a homogeneous solid of
equivalent thermal properties. It is demonstrated that although
the homogeneous solid model reproduces the real wall with
some degree of accuracy, certain differences are presented in
respect to the response speed of the wall, which can lead to
important errors in walls where this inertia is significant, or
when the temperature difference between the exterior and
interior is small.
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