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Static and dynamic thermal characterisation of a hollow brick wall: Tests and numerical analysis
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Energy and Buildings 40 (2008) 1513–1520 www.elsevier.com/locate/enbuild
Static and dynamic thermal characterisation of a hollow brick wall: Tests and numerical analysis J.M. Sala a, A. Urresti a,*, K. Martı´n b, I. Flores b, A. Apaolaza b b
a Thermal Engineering Department, Universidad del Paı´s 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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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.
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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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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.
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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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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
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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. References [1] D.G. Stephenson, G.P. Mitalas, Cooling load calculations by Thermal Response Factor method, ASHRAE Transactions 73 (1) (1967). [2] Real Decreto 314/2006, Ministerio de Vivienda, Boletin Oficial del Estado, n8 74, March 2006. [3] G.P. Mitalas, J.G. Arsenaut, Z Transfer functions for the calculation of transient heat transfer through walls and roofs, in: Proceedings 1st Symposium Use of Computers for Environmental Engineering related to Buildings, 1970. [4] G.P. Mitalas, J.G. Arsenaut, FORTRAN IV program to calculate z-transfer functions for the calculation of heat transfer through walls and roofs, DBR Computer Program No. 33, National Research Council Canada, Ottawa, 1972. [5] UNE-EN ISO 8990:1997. Thermal Insulation: Determination of Steady State Thermal Transmission Properties Calibrated and Guarded Hot Box. [6] W.C. Brown, D.G. Stephenson, A guarded hot box procedure for determining the dynamic response of full-scale wall specimens. Part I, ASHRAE Transactions 99 (1993) 632–642. [7] Real Decreto 2429/1979, Normativa Ba´sica de Edificacio´n. Condiciones Te´rmicas de los edificios, Boletin Oficial del Estado, n8 253, October 1979. [8] EN 12524:2000. Building Materials and Products. Hygrothermal Properties. Tabulated Design Values. [9] ASTM C1363-97/1. Standard Test Method for the Thermal Performance of Building Assemblies by Means of a Hot Box Apparatus.
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[10] E. Kossecka, J. Kosny, Correlations between time constants and structure factors of building walls, Archives of Civil Engineering (2004) 175–188. [11] T. Kusuda, Thermal response factors for multi-layer structures of various heat conduction systems, ASHRAE Transactions 75 (I) (1969) 246–271. [12] UNE-EN ISO 10211-1:1995. Thermal Bridges in Building Construction. Heat Flows and Surface Temperatures. Part I: General Calculation Methods.
[13] UNE-EN 1745:2002. Masonry and Masonry Products. Methods for Determining Design Thermal Values. [14] E. Kossecka, J. Kosny, Relations between structural and dynamic thermal characteristics of building walls, in: Proceedings of 1996 International Symposium of CIB W67, Energy and Mass Flows in the Life Cycle of Buildings, Vienna, 1996.
Energy and Buildings 40 (2008) 1513–1520 www.elsevier.com/locate/enbuild
Static and dynamic thermal characterisation of a hollow brick wall: Tests and numerical analysis J.M. Sala a, A. Urresti a,*, K. Martı´n b, I. Flores b, A. Apaolaza b b
a Thermal Engineering Department, Universidad del Paı´s 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
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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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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
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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.
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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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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
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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. References [1] D.G. Stephenson, G.P. Mitalas, Cooling load calculations by Thermal Response Factor method, ASHRAE Transactions 73 (1) (1967). [2] Real Decreto 314/2006, Ministerio de Vivienda, Boletin Oficial del Estado, n8 74, March 2006. [3] G.P. Mitalas, J.G. Arsenaut, Z Transfer functions for the calculation of transient heat transfer through walls and roofs, in: Proceedings 1st Symposium Use of Computers for Environmental Engineering related to Buildings, 1970. [4] G.P. Mitalas, J.G. Arsenaut, FORTRAN IV program to calculate z-transfer functions for the calculation of heat transfer through walls and roofs, DBR Computer Program No. 33, National Research Council Canada, Ottawa, 1972. [5] UNE-EN ISO 8990:1997. Thermal Insulation: Determination of Steady State Thermal Transmission Properties Calibrated and Guarded Hot Box. [6] W.C. Brown, D.G. Stephenson, A guarded hot box procedure for determining the dynamic response of full-scale wall specimens. Part I, ASHRAE Transactions 99 (1993) 632–642. [7] Real Decreto 2429/1979, Normativa Ba´sica de Edificacio´n. Condiciones Te´rmicas de los edificios, Boletin Oficial del Estado, n8 253, October 1979. [8] EN 12524:2000. Building Materials and Products. Hygrothermal Properties. Tabulated Design Values. [9] ASTM C1363-97/1. Standard Test Method for the Thermal Performance of Building Assemblies by Means of a Hot Box Apparatus.
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[10] E. Kossecka, J. Kosny, Correlations between time constants and structure factors of building walls, Archives of Civil Engineering (2004) 175–188. [11] T. Kusuda, Thermal response factors for multi-layer structures of various heat conduction systems, ASHRAE Transactions 75 (I) (1969) 246–271. [12] UNE-EN ISO 10211-1:1995. Thermal Bridges in Building Construction. Heat Flows and Surface Temperatures. Part I: General Calculation Methods.
[13] UNE-EN 1745:2002. Masonry and Masonry Products. Methods for Determining Design Thermal Values. [14] E. Kossecka, J. Kosny, Relations between structural and dynamic thermal characteristics of building walls, in: Proceedings of 1996 International Symposium of CIB W67, Energy and Mass Flows in the Life Cycle of Buildings, Vienna, 1996.