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A comparative assessment of the standardized methods for the in–situ measurement of the thermal resistance of building walls
Energy and Buildings 154 (2017) 198–206
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Energy and Buildings journal homepage: www.elsevier.com/locate/enbuild
Replication Studies paper
A comparative assessment of the standardized methods for the in–situ measurement of the thermal resistance of building walls Ioannis A. Atsonios ∗ , Ioannis D. Mandilaras, Dimos A. Kontogeorgos, Maria A. Founti National Technical University of Athens, School of Mechanical Engineering, Lab. of Heterogeneous Mixtures and Combustion Systems, Heroon Polytechniou 9, 15780 Zografou, Greece
a r t i c l e
i n f o
Article history: Received 4 April 2017 Received in revised form 4 July 2017 Accepted 22 August 2017 Available online 26 August 2017 Keywords: R-value measurement Wall thermal resistance In-situ measurements ISO 9869 ASTM C1155
a b s t r a c t The in-situ thermal resistance (R-value) measurement of building walls is essential for the accurate assessment of the thermal performance of an envelope and is lately a subject of increasing attention. The present study examines the four available standardized methods: for the R-value measurement as described in two international standards: ISO 9869 and ASTM C1155. The required measuring period and the variability of the results of each method are examined by measuring the thermal resistance of three representative walls (drywall, rubble and brick) at different measuring conditions in terms of surface temperature difference and direction of heat flow (stable or alternating during the day). It is concluded that the two most commonly used methods, the Average and the Summation method, require high temperature difference between the indoor and outdoor surfaces of the tested wall in order to provide R-values in short measuring period with low variability. On the contrary, the required measuring period for the other two methods, the Dynamic and the Sum of Least Square method, appears to be independent of the measuring conditions. The resulting values have low variability as long as the direction of heat flow is stable during the measurements. © 2017 Elsevier B.V. All rights reserved.
1. Introduction Energy performance of buildings depends on a variety of factors such as the thermal performance of the envelope, the climatic conditions, the efficiency of heating/cooling systems and electrical appliances and the user behavior. Among them, the performance of the building envelope, partly quantified by means of the thermal resistance value (R-value) of the walls, affects in a critical way the total energy performance of the building since space heating/cooling demands representing a large percentage (35–70%) of the total energy demand [1]. Therefore, limiting the R-value of the walls is one of the most common measures in order to reduce the energy consumption for space heating/cooling [2]. The theoretical calculation of design R-values is essential during the design stage of a building but may vary and deteriorate in practice due to construction irregularities, the quality of workmanship, multi-dimensional heat and moisture flow and material degradation effects [3]. Therefore, in-situ measurement of R-value may be required for post-evaluation of the thermal performance of a building envelope especially in cases of renovation but also
∗ Corresponding author. E-mail address: [email protected] (I.A. Atsonios). http://dx.doi.org/10.1016/j.enbuild.2017.08.064 0378-7788/© 2017 Elsevier B.V. All rights reserved.
for providing real values to BIM platforms and energy efficiency evaluation software. Since the 1980s, in-situ R-value measurement has been the topic of many research works proposing methods that involve measurements of heat flux and temperature at the inner and outer surface of the wall for a period of time [4–12]. The collected time series data can then be analyzed in different ways for the calculation of the R-value. According to the literature there are two main approaches for the analysis: a) modeling of the envelope with R-C networks and use of system identification tools [13–17] and b) the use of standardized methods [18,19] (often with minor modifications). The system identification methods can conditionally provide more accurate results as long as the tools developed are adequately validated and the users are highly experienced [20]. On the other hand, the standardized methods are more likely to produce reliable results when used by non-experienced users and thus, are the most widely used. In any case it is well known that R-value measurements of the same wall using different methods are not always in agreement. Cesaratto et al. [21] employed different analysis tools (both R-C network tools and standardized methods) for the in-situ estimation of thermal resistance for a large number of walls and they found that the results for each wall could deviate significantly (up to 30%) depending on the analysis tool. Ghazi Wakili et al. [22] showed that
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the estimations of R-value for a wall using a R-C network model and a standardized method may deviate up to 10%. Androutsopoulos et al. [20] compared the spread of the results using different system identification tools for the estimation of the thermal resistance of specific walls. They concluded that the measurements should be analyzed by a person with experience in order to obtain reliable results. Regarding the standardized methods, two international standards are currently available for the estimation of the thermal resistance of building envelope components using in-situ measurement data − ISO 9869 and ASTM C 1155 [18,19]. The ISO 9869 standard introduces the Average and the Dynamic Method, while ASTM C 1155 standard introduces the Summation and the Sum of Least Square Method. All methods require the measurement of the internal and external surface temperature and the internal heat flux for at least three days. The Average and the Summation methods are similar to each other with their main advantages being the simplicity in use and the rapid export of results, making them the most widely used methods. However, their precision strongly depends on the measuring conditions [18,19,23]. On the other hand, the Sum of Least Square and the Dynamic method, are more likely to provide reliable results regardless of the measuring conditions [18,19], but require the development of complex algorithms and computational tools for the analysis of the time series data due to their sophisticated methodology. For this reason, these methods are less commonly used. The main limitation of all the standardized methods is that the precision of the R-value measurement depends on the measuring conditions and the duration of the measuring period. Generally, the optimum measuring conditions are the high temperature difference with low temperature variations. Flanders et al. [24] analyzed the estimations of R-value using the two ASTM methods (Summation and Sum of Least Square method) and concluded that the agreement between the two methods was within 1–13% for cases with high internal and external surface temperature difference. Deconinch and Roels [23] and Gaspar et al. [25] compared the two ISO methods (Average and Dynamic method) in terms of different measuring conditions and they concluded that the Average method performs equally well to the Dynamic method when the measuring conditions are optimum. In case of low temperature difference only the Dynamic method leads to reliable results. Roulet et al. [26] compared the same two methods regarding the influence of the indoor/outdoor temperature difference. They concluded that the results of the two ISO methods were stable when the indoor temperature was constant before and during the measuring period. Desogus et al. [27] investigated the results of the Average method for two different measuring conditions. They concluded that the measuring conditions, and particularly the surface temperature difference, greatly influence the results. The smaller the temperature difference the less precise were the results. The second critical measuring parameter is the required duration of the measurements. It can be defined as the minimum duration required by the method in order to provide reliable results. According to the standards this duration can range from 72 h to more than 7 days, depending on the method, the measuring conditions and the type of the tested wall. In case of the Average and Summation methods, it is referred as convergence time and is determined by different criteria for each method. However, in case of the Dynamic and the SLS methods, it is not clearly defined. Gaspar et al. [25] showed that the accuracy of the Dynamic method was significantly improved by extending the measuring period. From the above brief literature review it becomes clear that the main weaknesses of the standardized R-value measurement methods, namely the effect of the measuring conditions and the duration of the measuring period, are limiting the usability of the methods
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and can potentially increase the uncertainty of the results. Gaspar et al. suggested that further investigation regarding the optimum measuring period is needed in order to improve the reliability of the results. Furthermore, Desogus et al. [27] have concluded, that it is difficult to achieve ideal environmental measuring conditions especially in mild climates and the solution to that could be the selection of the appropriate method among the available standardized technique. The main aim of this paper is to address the above issues by evaluating the standardized methods for the in-situ measurements of the R-value of building walls in terms of the required measuring period, the variability of the results and the effect of the measuring conditions on these two parameters. In particular, the examined measuring conditions are the surface temperature difference and the direction of heat flow (stable or alternating during the day). The current study introduces a criterion for the determination of the required measuring period for the Dynamic and Sum of Least Square method. All methods are employed for the Measurement of the R-value of three different building walls (a lightweight drywall construction, a rubble and a brick wall). The results provide guidelines for the in-situ calculation of the thermal resistance of an existing wall, for the pre-processing of measurements and the selection of the appropriate method.
2. Implementation of the four standardized methods The four standardized methods investigated in this paper are extensively described in the relevant ISO and ASTM standards. All methods require measurements of the internal and the external surface temperature and the internal heat flux of the tested wall. The temperature and heat flux sensors should be installed in homogenous locations avoiding thermal bridges. The standards describe in detail the methodology for the calculation of the thermal resistance, as well as the criteria that should be met in order to provide acceptable results (convergence criteria). The equations for the calculation of the R-value, the convergence criteria and the expected error (for 95% probability) of each method are summarized in Table 1. For the scope of this study, FORTRAN codes were developed in order to implement the above mentioned standardized methods. The codes compute the R-value and examine if the convergence criteria are met for a given dataset. For the determination of the R-value according to the Average and Summation methods the heat transfer through the wall is considered one-dimensional quasi-steady state. The model does not take into consideration the thermal storage of the envelope, these methods are sensitive to gradual increase or decrease of the mean (in terms of time and space) wall temperature, especially for massive constructions [19]. Large fluctuations in the internal and external wall surface temperature during and shortly prior to the test increases the required duration of the measurements [28]. A large mean temperature difference between the internal and external surface of the wall is needed for fast and accurate convergence of the methods [6,19,29]. The precision may also depend on the duration of the measurements and the thermal conditions during the test [27]. The Dynamic method requires the development of a model for the solution of the transient heat transfer equation. The model calculates the heat flux at each time interval as a function of the previous measured temperatures and several parameters, among which is the thermal resistance of the wall. The method calculates the R-value in order to minimize the difference between the measured and calculated heat flux values. The method related accuracy depends on the agreement between the calculated and experimental heat flux values and the duration of the measuring period [25].
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Table 1 The characteristics of four methods according to the standards. Method
Estimation of R-value
Convergence Criteria
Error (according to the standards)
For a unique R-value result: - The duration of data should be at least 3 days. - The value calculated at the end of the data set should not deviate more than ±5% from the respective value obtained 24 h before. - The resulting value when applying the method to the first 67% of data should not deviate by more than ±5% from the respective value when analyzing the last 67% of the data. - The change in the stored heat in the wall should not be more than 5% of the heat passing through the wall over the measuring period.
14–28%
For a unique R-value result: A convergence factor (CRn ) is defined: CRn = R(t)−R(t−n) R(t) - The value n is a time interval chosen by the user and varies between 6 and 48 h. - The factor CRn should remain below 0.10 for at least 3 periods of n.
20%
N
(Tsij −Tsej ) Average
R=
j=1
N qj j=1
(Tsij −Tsej ) R=
j=1
N qj j=1
Dynamic
For more results, the coefficient of variation of results should be less than 10%. 2
1. The internal wall heat flux qi (W/m ) at each time interval ti is calculated by the following equation: qi = R1 (Tsi i − Tse i) + K1 T˙ si i + K2 T˙ se i + i−1
Pn
n
i−1
T˙ si j 1 − ˇn ˇn (i − j)+
j=i−p
Qn
n
T˙ se j 1 − ˇn ˇn (i − j)
For a unique R-value result: The goodness of fit between the experimental and the calculated values of heat flux indicates the accuracy of result. The uncertainty (as it is defined by the standard) should be lower than 10% for probability 0.90.
13%
For a unique R-value result: - The goodness of fit between the experimental and the calculated values of heat flux indicates the accuracy of result.
11%
j=i−p
2. A linear system of equations is created and is expressed in a matrix form as: = X · Z q Z an array including all the unknown parameters, including R-value and X the matrix containing the measured temperatures with their derivatives. 3. The solution that minimizes the sum of the differences S 2 = qi,calc − qi
−1
2
between calculated and experimental heat fluxes is
calculated by solving the following equation: →
Z = (X) (X)
Sum of Least Square (SLS)
(X) q
1. The masonry is assumed to be thermally equivalent to a homogenous and one layered wall with the real thickness, d, and unknown thermal properties. 2. The equation of conductive heat transfer in the assumed wall is: governing ∂ ∂x
keq ∂∂Tx
= (Cp )eq ∂∂Tt where keq and (Cp )eq are the thermal conductivity
and the heat capacity of the equivalent wall respectively. 3. The equation can be solved with the Crank-Nicholson method, assuming the thermal properties, keq and (Cp )eq , and defining the measuring data as boundary conditions. 4. The calculated heat flux or temperature values are compared with the experimental values.
For more results, the uncertainty remains within 10% at a 95% confidence interval.
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N
Summation
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This method takes into account the thermal variations by the use of the heat equation. Hence, it can be used when large variations occur in temperature and heat flow rates [18]. A short description of the process for the data analysis is given in [25]. The Sum of Least Square (SLS) method assumes measurements of temperature and heat flux on a homogenous and one layered wall (Table 1). Given also the total thickness of the examined wall the thermal resistance can be calculated. The method requires the development of a code for the numerical solution of the heat transfer equation, which can be derived in two different ways, each one approached as a different method in this study. The first, namely the SLS HF (Sum of Least Square of the error between the measured and the calculated Heat Flux) method, uses the measured internal and external surface temperatures as boundary conditions in order to calculate the heat flux at the internal surface. Next, the sum of squares, f, of the differences between the experimental and the calculated heat flux values, is calculated as follows: f =
N
exp qi
2 − qcalc i
a) For the Average and Summation methods, the required measuring period is the shortest duration in which their convergence criteria are met, as described by their standards. b) For the Dynamic, SLS HF and SLS TIN methods the required measuring period is not defined by the standards. In this study, this period was selected as the duration in which the last three obtained daily values do not deviate more than v = 3%., The reason is that for higher values of v the variability of the results increases to unacceptable levels. Moreover, using more than 3 previous daily values, results to longer required measuring period without further improvement on the variability of the results. The variability of the results is examined by calculating the coefficient of variation, %CV, (often known as relative standard deviation) of the resulting R-values. It expresses an estimation of the amount of random variation expected when applying the method many times and is calculated as follows:
(1)
i=1
where qexp (W/m2 ) and qcalc (W/m2 ) are the measured and the calculated heat flux values respectively and N is the number of measurements. In the second approach, SLS TIN (Sum of Least Square of the error between the measured and the calculated Internal Temperature) method, the measured external surface temperature and the internal wall heat flux are employed as boundary conditions in order to calculate the internal surface temperature. The sum f, is calculated as the sum of squares of the differences between the experimental internal temperatures, Tsi exp (◦ C), and the calculated Tsi cacl (◦ C) ones, as expressed in the following equation for N measurements: f =
N
exp
Tsi j
− Tsi calc j
2 (2)
j=1
In both methods the f value is calculated for different combinations of thermal properties (thermal conductivity, k, density, and specific heat capacity, Cp ) of the tested wall. The thermal properties that minimize f are used for the determination of the R-value of the wall. As in Dynamic method, the fit of the experimental to the calculated values indicates the accuracy of results. The ASTM standard does not refer to any limitation regarding the measuring conditions (temperatures and heat flux) in order to provide acceptable results. The procedure for the calculation of the R-value is given in Table 1. In the current study, both SLS HF and SLS TIN approaches were investigated. 3. Parameters of comparison The standardized methods were compared in terms of the required measuring period and the variability of the results for different measuring conditions. Apart from the duration and the measuring conditions, there are several other factors that can increase the total uncertainty of the results, such as the accuracy of the measuring equipment, the homogeneity of the tested wall, the presence of moisture and the thermal radiation [18]. In the present study, these factors were avoided as possible and their influence was common for all cases. The required measuring period is defined as the shortest duration of data needed to obtain an acceptable result according to the standards. In this study, the R-value was calculated using data series with different durations, from 3 days up to 30 days. The required measuring period was calculated as follows:
201
CV (%) =
M 2
Ri − R
i=1 1 M−1
·
R
· 100%
(3)
where, R is the average R-value and M the number of the resulting R-values (M ≥ 3). The error of the results is estimated with 95.4% confidence level according to the equation: e(%) = 2 · CV (%)
(4)
The standards define the maximum value for the expected coefficient of variation. According to ISO standard, the CV of the Average and Dynamic method is expected to be 10% and 6%, respectively. When the variation exceeds these values, the results are not rejected, but their uncertainty increases accordingly. On the other hand, the CV of the Summation and the two SLS methods expected to be 10% and 6% (for confidence level 95.4%), respectively and when the variation exceeds these values, the results are not accepted, according to ASTM standard. 4. Experimental set-up This section describes the examined walls, the measuring equipment and the environmental conditions under which the in-situ measurements of thermal resistance were performed. 4.1. Wall configurations For the comparison of the standardized methods, three different walls were examined: • Wall A: Drywall construction • Wall B: Traditional rubble wall • Wall C: Brick wall Table 2 presents a section of each wall and the thickness of the construction layers. Wall A is located in a two-storey experimental mock up building inside the campus of National Technical University of Athens. It is a drywall construction based on a cavity wall system incorporating an External Thermal Insulation Composite System (ETICS). A 20 mm layer of vacuum insulated panel (VIP) is included in the ETICS. The drywall materials are anchored on a metal frame structure. The thermal performance of this wall has been also examined in previous work [3] and the theoretical thermal resistance was calculated equal to 4.98 m2 K/W. Wall B is
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Table 2 The configuration and the incorporating material of the three examined walls.
Wall A
Wall B
Total thickness: 365.5 mm
Wall C
n/a
Material
Thickness [mm]
1 2 3 4 5 6 7 8 9 1 2
Finishing coating Finishing mortar Insulation Render Bonding mortar Mineral Wool VIP Cement Board Air Cavity Gypsum Board Stone Mortar
1.5 4 50 5 20 20 25 190 25 60–70% of total thickness 30–40% of total thickness
1 2
Mortar Brick
40 140
Table 3 The measurement conditions of the examined cases.
Wall A Wall B
Wall C
Case
Duration [days]
T [◦ C] = (Tin − Tout )
Direction of heat flow
A B.1 B.2 B.3 C.1 C.2
27 130 130 38 66 28
11.0 −2.2 0.9 −1.6 0.4 0.6
Stable Stable Stable Stable Alternating Stable
a heavy rubble wall situated in a historical building in Athens [30]. The wall consists of approximately 60–70% stone and the rest is mortar. The theoretical thermal resistance is expected to be ca. 0.37 m2 K/W. Wall C is a brick wall located at the same historical building with theoretical thermal resistance equal to 0.36 m2 K/W.
avoiding thermal bridges. The homogeneity of the tested walls was examined using infrared thermography using an IR camera (FLIR, model 595). Solar radiation on the tested sites was avoided either by selecting the North facing exterior walls or by using shaded surfaces.
4.2. Instrumentation 4.3. Measurement conditions The Hukseflux TRSYS01 equipment (Fig. 1a), was used for the insitu temperature and heat flux measurements and the calculation of the thermal resistance [31]. The system is equipped with two heat flux sensors and two pairs of matched thermocouples for differential temperature measurements (Fig. 1b). The thermal resistance of the heat flux sensors is less than 6.25·10−3 m2 K/W and can be considered negligible in relation to the total thermal resistance of the examined walls. The sensitivity of the sensors is approximately 60 Vm2 /W and the expected accuracy lies within ±5% of the measured value. The use of matched thermocouple pairs (K type) assures a differential temperature measurement with accuracy less than ±0.1 ◦ C. High accuracy electronics with sensitivity up to 1 microvolt (CR1000, Campbell Scientific) were used for signal conditioning and measurement. The equipment was installed according to ASTM C 1046-91 [32]. The sensors were placed at thermally homogenous locations
In the present study, six different cases were investigated: one case for wall A, three cases for wall B and two cases for wall C. These cases cover different measuring conditions and measuring periods. In case A, the wall was monitored for a period of 28 days with high temperature difference between the inside and outside environments. To achieve this temperature difference, a temperature controlled system using a fan heater was installed inside the building. Wall B was monitored for three distinct periods (cases B1, B2 and B3). During these cases stable heat flow direction was observed and the mean surface temperature difference was lower than 3 ◦ C. Wall C was monitored for two distinct periods (cases C1 and C2). In these cases low temperature difference was observed. The direction of heat flow through the internal wall was alternating during the day.
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Fig. 1. a) The TRSYS01 equipment and b) the temperature and heat flux sensors.
The data loggers collected data with 1 min interval. However, the data analysis was based on 10 min averaged values. Table 3 presents the total measurement duration, the average value of the temperature difference between the two surfaces of the walls and the direction of heat flow during the measurements (stable or alternating during the day) for the examined cases.
5. Results The standardized methods are evaluated in terms of the required measuring period and the variability of their results. The influence of the measuring conditions (surface temperature difference and direction of heat flow during the day) on the above parameters is investigated.
5.1. Estimation of required measuring period The required measuring period for each method was examined for the six cases. Fig. 2 presents the time evolution of the results provided by the four methods and the required measuring period which has been calculated as described in Section 3. It is noted that the measurements start at day 0 but the first results appear in day 3 according to the standards which define 3 days minimum measuring period before the calculation of the first value. The results of the Average and Summation methods have the same evolution in time, since R-value is calculated by the same equation in Table 1. However, the required measuring period for the two methods varies, because of their different convergence criteria. In case A, where the temperature difference is high (11 ◦ C), the Average and Summation methods require 6 days and 5 days respectively in order to provide a result which satisfies their criteria and the results are close to the R-values of the other three methods. In the other cases, where the surface temperature difference is low, the two methods require 6–20 days to provide results that fulfill the criteria. However, in these cases, the results of Average and Summation methods are different and appear to overestimate the thermal resistance compared with the other three methods. Regarding the Dynamic, SLS HF and SLS TIN methods, it is observed that they provide approximately the same values. The required measuring periods for these methods is always 5–10 days and appear to be independent of the measuring conditions. It is observed that the required measuring periods of these methods are not influenced by the thermal mass of the tested wall. Regarding the two SLS methods, despite the fact that they are based on the same method, their results are different and the required mea-
suring period of SLS HF is always shorter or equal to that of SLS TIN method. 5.2. Estimation of the variability In this section, the coefficient of variation (CV) of the results was calculated for each method in all cases. At least three independent R-values for each method were used in order to calculate the CV. The results were provided by sets of data such that the convergence criteria are fulfilled (Table 1). Additionally, regarding the Dynamic, SLS HF and SLS TIN methods, the obtained results met the criterion for the required measuring period described in Section 3. Fig. 3 illustrates the R-value results for the six cases and the CV for all methods. In case A, the high surface temperature difference between the two sides of the walls results to low variance for all methods. The CV is lower than the expected uncertainty according to the standards. In all other cases (B.1, B.2, B.3, C.1 and C.2) where the surface temperature difference is lower than 3 ◦ C, the CV of the Average and Summation method is significantly higher. The effect of the temperature difference on these two methods is in line with the standards which state that the uncertainty of the results depends on the temperature difference. The CV of the results for the Average and Summation method exceeds the 10%. Hence, the results of Summation method are rejected according to the ASTM. Regarding the Average method, the CV is higher than the expected value, however the ISO standard does not reject the results. Regarding the SLS HF method, the CV is always lower than 5% in all cases, indicating that the variation of this method is not affected by the measuring conditions. Particularly, in case of wall B, the coefficient of variation is extremely low (1.0–1.3%), despite the fact that the duration of the set of data was shorter than 6 days and the wall was heavy. In the cases A, B.1, B.2, B.3 and C.2, where the direction of heat flow is stable during the day (Table 3), the CV of the Dynamic and SLS TIN methods is lower than 6%.On the contrary, in the case C.1 where the direction of heat flow is alternating during the day (Table 3) the CV of these two methods exceeds the 8%. Hence, the results of SLS TIN method are not accepted according to ASTM standards because the CV is higher than 6%. On the other hand, the results of Dynamic method are accepted according to ISO standard, but the uncertainty increase accordingly. The Dynamic and the SLS TIN methods were further investigated for the case C.1. Results were obtained for longer duration of data sets than the period defined according to the criterion of Section 3. Fig. 4 illustrates the calculated values of CV for the two
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Fig. 2. Evolution at the time of R-value results and required measuring period for every method.
methods using R-values obtained from 10, 15 and 20 days. Despite of the increase of the duration of data collection, the CV of these methods remains higher than the expected values. It is demonstrated that the high variation of the results for these two methods is independent of the collection duration of data sets.
6. Conclusions The present work carried out a comparative assessment of the four standardized methods for the in-situ measurement of thermal resistance: the Average, the Summation, the Dynamic and two different approaches of the Sum of Least Square method (SLS HF and SLS TIN). The effect of measuring conditions on the required measuring period and the variability of the results for each method was
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Fig. 3. The R-value results and the respective coefficient of variation (CV) for every method.
investigated. Six cases in total were examined in three different walls. The results showed that the mean temperature difference between the surfaces of the wall and the direction of heat flow during the day strongly influence the duration of the required measuring period and the variability of the results. In particular, the Average and Summation methods require a high temperature difference and, as a consequence, a stable direction of heat flow in order to provide acceptable and reliable results in a short mea-
suring period. In cases where the temperature difference is lower than 3 ◦ C, the results of Average and Summation method have high and not acceptable coefficients of variation, respectively. Hence, the Average and Summation methods should not be used when the temperature difference is too low or their criteria should be stricter. The study also investigated the required measuring period of all methods. For the Dynamic, SLS HF and SLS TIN methods, where it is not determined by their standards, it is defined as the duration in which the last three obtained daily values do not deviate more
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Fig. 4. The CV of the Dynamic and SLS TIN methods for different measuring periods in case C.1.
than 3%. The results showed that this criterion can be used for these methods at any measuring conditions. Regarding the variability of the results, the Dynamic and SLS TIN methods appeared to be affected only by the direction of the heat flow. These methods appeared to require a stable direction of the heat flow during the day in order to provide results with the excepted variability. In case where the direction of the heat flow is stable, their results do not deviate more than 6%, which is the expected value according to the standards. On the other hand, when the heat flow direction is changing during the day, the deviation of the Dynamic and SLS TIN reaches up to 8% and 18% respectively. On the contrary, the SLS HF method is not affected by the measuring conditions providing fast and reliable results at all cases. References [1] Buildings Energy Data Book, 2012. [2] B. Atanasiu, C. Despret, M. Economidou, J. Maio, I. Nolte, O. Rapf, J. Laustsen, P. Ruyssevelt, D. Staniaszek, D. Strong, S. Zinetti, L. Verheyen, Europe’s buildings under the microscope – A country-by-country review of the energy performance of buildings, 2011. [3] I. Mandilaras, I. Atsonios, G. Zannis, M. Founti, Thermal performance of a building envelope incorporating ETICS with vacuum insulation panels and EPS, Energy Build. 85 (0) (2014) 654–665. [4] D.A. McIntyre, In situ measurement of U-values, Build. Serv. Eng. Res. Technol. 6 (1985) 1–6. [5] M.P. Modera, M.H. Sherman, R.C. Sonderegger, Determining the U-value of a wall from field measurements of heat flux and surface temperatures, in: ASTM Workshop on Heat Flow Sensors, Philadelphia PA, 1986. [6] L. Laurenti, F. Marcotullio, F. de Monte, Determination of the thermal resistance of walls through a dynamic analysis of in-situ data, Int. J. Therm. Sci. 43 (3) (2004) 297–306. [7] C. Buratti, S. Grignaffini, Measurement of the thermal resistance of masonry walls, Int. J. Heat Technol. 21 (2) (2003) 107–114. [8] M. Cucumo, A.D. Rosa, V. Ferraro, D. Kaliakatsos, V. Marinelli, A method for the experimental evaluation in situ of the wall conductance, Energy Build. 38 (3) (2006) 238–244. [9] C. Buratti, E. Moretti, Thermal resistance of masonry walls: in situ measurements, 6th World Conference on Experimental Heat Transfer, Fluid Mechanics and Thermodynamics (2005).
[10] C. Peng, Z. Wu, In situ measuring and evaluating the thermal resistance of building construction, Energy Build. 40 (11) (2008) 2076–2082. [11] F. Wang, D. Wang, X. Wang, J. Yao, A data analysis method for detecting wall thermal resistance considering wind velocity in situ, Energy Build. 42 (10) (2010) 1647–1653. [12] P.G. Cesaratto, M. De Carli, S. Marinetti, Effect of different parameters on the in situ thermal conductance evaluation, Energy Build. 43 (7) (2011) 1792–1801. [13] M.J. Jiménez, H. Madsen, Models for describing the thermal characteristics of building components, Build. Environ. 43 (2) (2008) 152–162. [14] M.J. Jiménez, H. Madsen, K.K. Andersen, Identification of the main thermal characteristics of building components using MATLAB, Build. Environ. 43 (2) (2008) 170–180. [15] M.J. Jiménez, B. Porcar, M.R. Heras, Estimation of building component UA and gA from outdoor tests in warm and moderate weather conditions, Sol. Energy 82 (7) (2008) 573–587. [16] M.J. Jiménez, B. Porcar, M.R. Heras, Application of different dynamic analysis approaches to the estimation of the building component U value, Build. Environ. 44 (2) (2009) 361–367. [17] O. Gutschker, Parameter identification with the software package LORD, Build. Environ. 43 (2) (2008) 163–169. [18] ISO, 9869, Thermal Insulation – Building Elements – In situ Measurement of Thermal Resistance and Thermal Transmittance, 1994. [19] ASTM C1155-95 Standard, Standard Practice for Determining Thermal Resistance of Building Envelope Components from the In-situ Data, 2007. [20] A. Androutsopoulos, J.J. Bloem, H.A.L. van Dijk, P.H. Baker, Comparison of user performance when applying system identification for assessment of the energy performance of building components, Build. Environ. 43 (2) (2008) 189–196. [21] P.G. Cesaratto, M. De Carli, A measuring campaign of thermal conductance in situ and possible impacts on net energy demand in buildings, Energy Build. 59 (0) (2013) 29–36. [22] K. Ghazi Wakili, B. Binder, M. Zimmermann, C. Tanner, Efficiency verification of a combination of high performance and conventional insulation layers in retrofitting a 130-year old building, Energy Build. 82 (0) (2014) 237–242. [23] A.-H. Deconinck, S. Roels, Comparison of characterisation methods determining the thermal resistance of building components from onsite measurements, Energy Build. 130 (2016) 309–320. [24] S.N. Flanders, A.O. Desjarlais, T.J. Kunz, A comparison of two techniques for R-value calculcation, using winter in-situ data, Thermal Envelops VI/Heat Transfern in Walls I-Principles (1995) 151–161. [25] K. Gaspar, M. Casals, M. Gangolells, A comparison of standardized calculation methods for in situ measurements of fac¸ades U-value, Energy Build. 130 (2016) 592–599. [26] C. Roulet, J. Gass, I. Marcus, In situ U value measurement: reliable results in short time by dynamic interpretation of the measurement, ASHARE Trans. 93 (1987) 1371–1379. [27] G. Desogus, S. Mura, R. Ricciu, Comparing different approaches to in situ measurement of building components thermal resistance, Energy Build. 43 (10) (2011) 2613–2620. [28] P. Biddulph, V. Gori, C.A. Elwell, C. Scott, C. Rye, R. Lowe, T. Oreszczyn, Inferring the thermal resistance and effective thermal mass of a wall using frequent temperature and heat flux measurements, Energy Build. 78 (0) (2014) 10–16. [29] A. Ahmad, M. Maslehuddin, L.M. Al-Hadhrami, In situ measurement of thermal transmittance and thermal resistance of hollow reinforced precast concrete walls, Energy Build. 84 (0) (2014) 132–141. [30] I. Mandilaras, I. Atsonios, D. Kolaitis, E. Alexandrou, E. Tsakanika Theohari, M. Founti, Large scale measurement campaing to assess the thermal behaviour of an 18th century historic building, in: Ewchp-2013, 3rd European Workshop on Cultural Heritage Preservation, Bolzano, Italy, 2013, pp. 2013. [31] Hukseflux Thermal Sensors, Version 1003, www.hukseflux.com, Delft, The Netherlands, 2015. [32] ASTM C1046-95 Standard, Standard Practice for In-situ Measurement of Heat Flux and Temperature on Building Envelope Components, in, 2013.
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Energy and Buildings journal homepage: www.elsevier.com/locate/enbuild
Replication Studies paper
A comparative assessment of the standardized methods for the in–situ measurement of the thermal resistance of building walls Ioannis A. Atsonios ∗ , Ioannis D. Mandilaras, Dimos A. Kontogeorgos, Maria A. Founti National Technical University of Athens, School of Mechanical Engineering, Lab. of Heterogeneous Mixtures and Combustion Systems, Heroon Polytechniou 9, 15780 Zografou, Greece
a r t i c l e
i n f o
Article history: Received 4 April 2017 Received in revised form 4 July 2017 Accepted 22 August 2017 Available online 26 August 2017 Keywords: R-value measurement Wall thermal resistance In-situ measurements ISO 9869 ASTM C1155
a b s t r a c t The in-situ thermal resistance (R-value) measurement of building walls is essential for the accurate assessment of the thermal performance of an envelope and is lately a subject of increasing attention. The present study examines the four available standardized methods: for the R-value measurement as described in two international standards: ISO 9869 and ASTM C1155. The required measuring period and the variability of the results of each method are examined by measuring the thermal resistance of three representative walls (drywall, rubble and brick) at different measuring conditions in terms of surface temperature difference and direction of heat flow (stable or alternating during the day). It is concluded that the two most commonly used methods, the Average and the Summation method, require high temperature difference between the indoor and outdoor surfaces of the tested wall in order to provide R-values in short measuring period with low variability. On the contrary, the required measuring period for the other two methods, the Dynamic and the Sum of Least Square method, appears to be independent of the measuring conditions. The resulting values have low variability as long as the direction of heat flow is stable during the measurements. © 2017 Elsevier B.V. All rights reserved.
1. Introduction Energy performance of buildings depends on a variety of factors such as the thermal performance of the envelope, the climatic conditions, the efficiency of heating/cooling systems and electrical appliances and the user behavior. Among them, the performance of the building envelope, partly quantified by means of the thermal resistance value (R-value) of the walls, affects in a critical way the total energy performance of the building since space heating/cooling demands representing a large percentage (35–70%) of the total energy demand [1]. Therefore, limiting the R-value of the walls is one of the most common measures in order to reduce the energy consumption for space heating/cooling [2]. The theoretical calculation of design R-values is essential during the design stage of a building but may vary and deteriorate in practice due to construction irregularities, the quality of workmanship, multi-dimensional heat and moisture flow and material degradation effects [3]. Therefore, in-situ measurement of R-value may be required for post-evaluation of the thermal performance of a building envelope especially in cases of renovation but also
∗ Corresponding author. E-mail address: [email protected] (I.A. Atsonios). http://dx.doi.org/10.1016/j.enbuild.2017.08.064 0378-7788/© 2017 Elsevier B.V. All rights reserved.
for providing real values to BIM platforms and energy efficiency evaluation software. Since the 1980s, in-situ R-value measurement has been the topic of many research works proposing methods that involve measurements of heat flux and temperature at the inner and outer surface of the wall for a period of time [4–12]. The collected time series data can then be analyzed in different ways for the calculation of the R-value. According to the literature there are two main approaches for the analysis: a) modeling of the envelope with R-C networks and use of system identification tools [13–17] and b) the use of standardized methods [18,19] (often with minor modifications). The system identification methods can conditionally provide more accurate results as long as the tools developed are adequately validated and the users are highly experienced [20]. On the other hand, the standardized methods are more likely to produce reliable results when used by non-experienced users and thus, are the most widely used. In any case it is well known that R-value measurements of the same wall using different methods are not always in agreement. Cesaratto et al. [21] employed different analysis tools (both R-C network tools and standardized methods) for the in-situ estimation of thermal resistance for a large number of walls and they found that the results for each wall could deviate significantly (up to 30%) depending on the analysis tool. Ghazi Wakili et al. [22] showed that
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the estimations of R-value for a wall using a R-C network model and a standardized method may deviate up to 10%. Androutsopoulos et al. [20] compared the spread of the results using different system identification tools for the estimation of the thermal resistance of specific walls. They concluded that the measurements should be analyzed by a person with experience in order to obtain reliable results. Regarding the standardized methods, two international standards are currently available for the estimation of the thermal resistance of building envelope components using in-situ measurement data − ISO 9869 and ASTM C 1155 [18,19]. The ISO 9869 standard introduces the Average and the Dynamic Method, while ASTM C 1155 standard introduces the Summation and the Sum of Least Square Method. All methods require the measurement of the internal and external surface temperature and the internal heat flux for at least three days. The Average and the Summation methods are similar to each other with their main advantages being the simplicity in use and the rapid export of results, making them the most widely used methods. However, their precision strongly depends on the measuring conditions [18,19,23]. On the other hand, the Sum of Least Square and the Dynamic method, are more likely to provide reliable results regardless of the measuring conditions [18,19], but require the development of complex algorithms and computational tools for the analysis of the time series data due to their sophisticated methodology. For this reason, these methods are less commonly used. The main limitation of all the standardized methods is that the precision of the R-value measurement depends on the measuring conditions and the duration of the measuring period. Generally, the optimum measuring conditions are the high temperature difference with low temperature variations. Flanders et al. [24] analyzed the estimations of R-value using the two ASTM methods (Summation and Sum of Least Square method) and concluded that the agreement between the two methods was within 1–13% for cases with high internal and external surface temperature difference. Deconinch and Roels [23] and Gaspar et al. [25] compared the two ISO methods (Average and Dynamic method) in terms of different measuring conditions and they concluded that the Average method performs equally well to the Dynamic method when the measuring conditions are optimum. In case of low temperature difference only the Dynamic method leads to reliable results. Roulet et al. [26] compared the same two methods regarding the influence of the indoor/outdoor temperature difference. They concluded that the results of the two ISO methods were stable when the indoor temperature was constant before and during the measuring period. Desogus et al. [27] investigated the results of the Average method for two different measuring conditions. They concluded that the measuring conditions, and particularly the surface temperature difference, greatly influence the results. The smaller the temperature difference the less precise were the results. The second critical measuring parameter is the required duration of the measurements. It can be defined as the minimum duration required by the method in order to provide reliable results. According to the standards this duration can range from 72 h to more than 7 days, depending on the method, the measuring conditions and the type of the tested wall. In case of the Average and Summation methods, it is referred as convergence time and is determined by different criteria for each method. However, in case of the Dynamic and the SLS methods, it is not clearly defined. Gaspar et al. [25] showed that the accuracy of the Dynamic method was significantly improved by extending the measuring period. From the above brief literature review it becomes clear that the main weaknesses of the standardized R-value measurement methods, namely the effect of the measuring conditions and the duration of the measuring period, are limiting the usability of the methods
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and can potentially increase the uncertainty of the results. Gaspar et al. suggested that further investigation regarding the optimum measuring period is needed in order to improve the reliability of the results. Furthermore, Desogus et al. [27] have concluded, that it is difficult to achieve ideal environmental measuring conditions especially in mild climates and the solution to that could be the selection of the appropriate method among the available standardized technique. The main aim of this paper is to address the above issues by evaluating the standardized methods for the in-situ measurements of the R-value of building walls in terms of the required measuring period, the variability of the results and the effect of the measuring conditions on these two parameters. In particular, the examined measuring conditions are the surface temperature difference and the direction of heat flow (stable or alternating during the day). The current study introduces a criterion for the determination of the required measuring period for the Dynamic and Sum of Least Square method. All methods are employed for the Measurement of the R-value of three different building walls (a lightweight drywall construction, a rubble and a brick wall). The results provide guidelines for the in-situ calculation of the thermal resistance of an existing wall, for the pre-processing of measurements and the selection of the appropriate method.
2. Implementation of the four standardized methods The four standardized methods investigated in this paper are extensively described in the relevant ISO and ASTM standards. All methods require measurements of the internal and the external surface temperature and the internal heat flux of the tested wall. The temperature and heat flux sensors should be installed in homogenous locations avoiding thermal bridges. The standards describe in detail the methodology for the calculation of the thermal resistance, as well as the criteria that should be met in order to provide acceptable results (convergence criteria). The equations for the calculation of the R-value, the convergence criteria and the expected error (for 95% probability) of each method are summarized in Table 1. For the scope of this study, FORTRAN codes were developed in order to implement the above mentioned standardized methods. The codes compute the R-value and examine if the convergence criteria are met for a given dataset. For the determination of the R-value according to the Average and Summation methods the heat transfer through the wall is considered one-dimensional quasi-steady state. The model does not take into consideration the thermal storage of the envelope, these methods are sensitive to gradual increase or decrease of the mean (in terms of time and space) wall temperature, especially for massive constructions [19]. Large fluctuations in the internal and external wall surface temperature during and shortly prior to the test increases the required duration of the measurements [28]. A large mean temperature difference between the internal and external surface of the wall is needed for fast and accurate convergence of the methods [6,19,29]. The precision may also depend on the duration of the measurements and the thermal conditions during the test [27]. The Dynamic method requires the development of a model for the solution of the transient heat transfer equation. The model calculates the heat flux at each time interval as a function of the previous measured temperatures and several parameters, among which is the thermal resistance of the wall. The method calculates the R-value in order to minimize the difference between the measured and calculated heat flux values. The method related accuracy depends on the agreement between the calculated and experimental heat flux values and the duration of the measuring period [25].
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Table 1 The characteristics of four methods according to the standards. Method
Estimation of R-value
Convergence Criteria
Error (according to the standards)
For a unique R-value result: - The duration of data should be at least 3 days. - The value calculated at the end of the data set should not deviate more than ±5% from the respective value obtained 24 h before. - The resulting value when applying the method to the first 67% of data should not deviate by more than ±5% from the respective value when analyzing the last 67% of the data. - The change in the stored heat in the wall should not be more than 5% of the heat passing through the wall over the measuring period.
14–28%
For a unique R-value result: A convergence factor (CRn ) is defined: CRn = R(t)−R(t−n) R(t) - The value n is a time interval chosen by the user and varies between 6 and 48 h. - The factor CRn should remain below 0.10 for at least 3 periods of n.
20%
N
(Tsij −Tsej ) Average
R=
j=1
N qj j=1
(Tsij −Tsej ) R=
j=1
N qj j=1
Dynamic
For more results, the coefficient of variation of results should be less than 10%. 2
1. The internal wall heat flux qi (W/m ) at each time interval ti is calculated by the following equation: qi = R1 (Tsi i − Tse i) + K1 T˙ si i + K2 T˙ se i + i−1
Pn
n
i−1
T˙ si j 1 − ˇn ˇn (i − j)+
j=i−p
Qn
n
T˙ se j 1 − ˇn ˇn (i − j)
For a unique R-value result: The goodness of fit between the experimental and the calculated values of heat flux indicates the accuracy of result. The uncertainty (as it is defined by the standard) should be lower than 10% for probability 0.90.
13%
For a unique R-value result: - The goodness of fit between the experimental and the calculated values of heat flux indicates the accuracy of result.
11%
j=i−p
2. A linear system of equations is created and is expressed in a matrix form as: = X · Z q Z an array including all the unknown parameters, including R-value and X the matrix containing the measured temperatures with their derivatives. 3. The solution that minimizes the sum of the differences S 2 = qi,calc − qi
−1
2
between calculated and experimental heat fluxes is
calculated by solving the following equation: →
Z = (X) (X)
Sum of Least Square (SLS)
(X) q
1. The masonry is assumed to be thermally equivalent to a homogenous and one layered wall with the real thickness, d, and unknown thermal properties. 2. The equation of conductive heat transfer in the assumed wall is: governing ∂ ∂x
keq ∂∂Tx
= (Cp )eq ∂∂Tt where keq and (Cp )eq are the thermal conductivity
and the heat capacity of the equivalent wall respectively. 3. The equation can be solved with the Crank-Nicholson method, assuming the thermal properties, keq and (Cp )eq , and defining the measuring data as boundary conditions. 4. The calculated heat flux or temperature values are compared with the experimental values.
For more results, the uncertainty remains within 10% at a 95% confidence interval.
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N
Summation
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This method takes into account the thermal variations by the use of the heat equation. Hence, it can be used when large variations occur in temperature and heat flow rates [18]. A short description of the process for the data analysis is given in [25]. The Sum of Least Square (SLS) method assumes measurements of temperature and heat flux on a homogenous and one layered wall (Table 1). Given also the total thickness of the examined wall the thermal resistance can be calculated. The method requires the development of a code for the numerical solution of the heat transfer equation, which can be derived in two different ways, each one approached as a different method in this study. The first, namely the SLS HF (Sum of Least Square of the error between the measured and the calculated Heat Flux) method, uses the measured internal and external surface temperatures as boundary conditions in order to calculate the heat flux at the internal surface. Next, the sum of squares, f, of the differences between the experimental and the calculated heat flux values, is calculated as follows: f =
N
exp qi
2 − qcalc i
a) For the Average and Summation methods, the required measuring period is the shortest duration in which their convergence criteria are met, as described by their standards. b) For the Dynamic, SLS HF and SLS TIN methods the required measuring period is not defined by the standards. In this study, this period was selected as the duration in which the last three obtained daily values do not deviate more than v = 3%., The reason is that for higher values of v the variability of the results increases to unacceptable levels. Moreover, using more than 3 previous daily values, results to longer required measuring period without further improvement on the variability of the results. The variability of the results is examined by calculating the coefficient of variation, %CV, (often known as relative standard deviation) of the resulting R-values. It expresses an estimation of the amount of random variation expected when applying the method many times and is calculated as follows:
(1)
i=1
where qexp (W/m2 ) and qcalc (W/m2 ) are the measured and the calculated heat flux values respectively and N is the number of measurements. In the second approach, SLS TIN (Sum of Least Square of the error between the measured and the calculated Internal Temperature) method, the measured external surface temperature and the internal wall heat flux are employed as boundary conditions in order to calculate the internal surface temperature. The sum f, is calculated as the sum of squares of the differences between the experimental internal temperatures, Tsi exp (◦ C), and the calculated Tsi cacl (◦ C) ones, as expressed in the following equation for N measurements: f =
N
exp
Tsi j
− Tsi calc j
2 (2)
j=1
In both methods the f value is calculated for different combinations of thermal properties (thermal conductivity, k, density, and specific heat capacity, Cp ) of the tested wall. The thermal properties that minimize f are used for the determination of the R-value of the wall. As in Dynamic method, the fit of the experimental to the calculated values indicates the accuracy of results. The ASTM standard does not refer to any limitation regarding the measuring conditions (temperatures and heat flux) in order to provide acceptable results. The procedure for the calculation of the R-value is given in Table 1. In the current study, both SLS HF and SLS TIN approaches were investigated. 3. Parameters of comparison The standardized methods were compared in terms of the required measuring period and the variability of the results for different measuring conditions. Apart from the duration and the measuring conditions, there are several other factors that can increase the total uncertainty of the results, such as the accuracy of the measuring equipment, the homogeneity of the tested wall, the presence of moisture and the thermal radiation [18]. In the present study, these factors were avoided as possible and their influence was common for all cases. The required measuring period is defined as the shortest duration of data needed to obtain an acceptable result according to the standards. In this study, the R-value was calculated using data series with different durations, from 3 days up to 30 days. The required measuring period was calculated as follows:
201
CV (%) =
M 2
Ri − R
i=1 1 M−1
·
R
· 100%
(3)
where, R is the average R-value and M the number of the resulting R-values (M ≥ 3). The error of the results is estimated with 95.4% confidence level according to the equation: e(%) = 2 · CV (%)
(4)
The standards define the maximum value for the expected coefficient of variation. According to ISO standard, the CV of the Average and Dynamic method is expected to be 10% and 6%, respectively. When the variation exceeds these values, the results are not rejected, but their uncertainty increases accordingly. On the other hand, the CV of the Summation and the two SLS methods expected to be 10% and 6% (for confidence level 95.4%), respectively and when the variation exceeds these values, the results are not accepted, according to ASTM standard. 4. Experimental set-up This section describes the examined walls, the measuring equipment and the environmental conditions under which the in-situ measurements of thermal resistance were performed. 4.1. Wall configurations For the comparison of the standardized methods, three different walls were examined: • Wall A: Drywall construction • Wall B: Traditional rubble wall • Wall C: Brick wall Table 2 presents a section of each wall and the thickness of the construction layers. Wall A is located in a two-storey experimental mock up building inside the campus of National Technical University of Athens. It is a drywall construction based on a cavity wall system incorporating an External Thermal Insulation Composite System (ETICS). A 20 mm layer of vacuum insulated panel (VIP) is included in the ETICS. The drywall materials are anchored on a metal frame structure. The thermal performance of this wall has been also examined in previous work [3] and the theoretical thermal resistance was calculated equal to 4.98 m2 K/W. Wall B is
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Table 2 The configuration and the incorporating material of the three examined walls.
Wall A
Wall B
Total thickness: 365.5 mm
Wall C
n/a
Material
Thickness [mm]
1 2 3 4 5 6 7 8 9 1 2
Finishing coating Finishing mortar Insulation Render Bonding mortar Mineral Wool VIP Cement Board Air Cavity Gypsum Board Stone Mortar
1.5 4 50 5 20 20 25 190 25 60–70% of total thickness 30–40% of total thickness
1 2
Mortar Brick
40 140
Table 3 The measurement conditions of the examined cases.
Wall A Wall B
Wall C
Case
Duration [days]
T [◦ C] = (Tin − Tout )
Direction of heat flow
A B.1 B.2 B.3 C.1 C.2
27 130 130 38 66 28
11.0 −2.2 0.9 −1.6 0.4 0.6
Stable Stable Stable Stable Alternating Stable
a heavy rubble wall situated in a historical building in Athens [30]. The wall consists of approximately 60–70% stone and the rest is mortar. The theoretical thermal resistance is expected to be ca. 0.37 m2 K/W. Wall C is a brick wall located at the same historical building with theoretical thermal resistance equal to 0.36 m2 K/W.
avoiding thermal bridges. The homogeneity of the tested walls was examined using infrared thermography using an IR camera (FLIR, model 595). Solar radiation on the tested sites was avoided either by selecting the North facing exterior walls or by using shaded surfaces.
4.2. Instrumentation 4.3. Measurement conditions The Hukseflux TRSYS01 equipment (Fig. 1a), was used for the insitu temperature and heat flux measurements and the calculation of the thermal resistance [31]. The system is equipped with two heat flux sensors and two pairs of matched thermocouples for differential temperature measurements (Fig. 1b). The thermal resistance of the heat flux sensors is less than 6.25·10−3 m2 K/W and can be considered negligible in relation to the total thermal resistance of the examined walls. The sensitivity of the sensors is approximately 60 Vm2 /W and the expected accuracy lies within ±5% of the measured value. The use of matched thermocouple pairs (K type) assures a differential temperature measurement with accuracy less than ±0.1 ◦ C. High accuracy electronics with sensitivity up to 1 microvolt (CR1000, Campbell Scientific) were used for signal conditioning and measurement. The equipment was installed according to ASTM C 1046-91 [32]. The sensors were placed at thermally homogenous locations
In the present study, six different cases were investigated: one case for wall A, three cases for wall B and two cases for wall C. These cases cover different measuring conditions and measuring periods. In case A, the wall was monitored for a period of 28 days with high temperature difference between the inside and outside environments. To achieve this temperature difference, a temperature controlled system using a fan heater was installed inside the building. Wall B was monitored for three distinct periods (cases B1, B2 and B3). During these cases stable heat flow direction was observed and the mean surface temperature difference was lower than 3 ◦ C. Wall C was monitored for two distinct periods (cases C1 and C2). In these cases low temperature difference was observed. The direction of heat flow through the internal wall was alternating during the day.
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Fig. 1. a) The TRSYS01 equipment and b) the temperature and heat flux sensors.
The data loggers collected data with 1 min interval. However, the data analysis was based on 10 min averaged values. Table 3 presents the total measurement duration, the average value of the temperature difference between the two surfaces of the walls and the direction of heat flow during the measurements (stable or alternating during the day) for the examined cases.
5. Results The standardized methods are evaluated in terms of the required measuring period and the variability of their results. The influence of the measuring conditions (surface temperature difference and direction of heat flow during the day) on the above parameters is investigated.
5.1. Estimation of required measuring period The required measuring period for each method was examined for the six cases. Fig. 2 presents the time evolution of the results provided by the four methods and the required measuring period which has been calculated as described in Section 3. It is noted that the measurements start at day 0 but the first results appear in day 3 according to the standards which define 3 days minimum measuring period before the calculation of the first value. The results of the Average and Summation methods have the same evolution in time, since R-value is calculated by the same equation in Table 1. However, the required measuring period for the two methods varies, because of their different convergence criteria. In case A, where the temperature difference is high (11 ◦ C), the Average and Summation methods require 6 days and 5 days respectively in order to provide a result which satisfies their criteria and the results are close to the R-values of the other three methods. In the other cases, where the surface temperature difference is low, the two methods require 6–20 days to provide results that fulfill the criteria. However, in these cases, the results of Average and Summation methods are different and appear to overestimate the thermal resistance compared with the other three methods. Regarding the Dynamic, SLS HF and SLS TIN methods, it is observed that they provide approximately the same values. The required measuring periods for these methods is always 5–10 days and appear to be independent of the measuring conditions. It is observed that the required measuring periods of these methods are not influenced by the thermal mass of the tested wall. Regarding the two SLS methods, despite the fact that they are based on the same method, their results are different and the required mea-
suring period of SLS HF is always shorter or equal to that of SLS TIN method. 5.2. Estimation of the variability In this section, the coefficient of variation (CV) of the results was calculated for each method in all cases. At least three independent R-values for each method were used in order to calculate the CV. The results were provided by sets of data such that the convergence criteria are fulfilled (Table 1). Additionally, regarding the Dynamic, SLS HF and SLS TIN methods, the obtained results met the criterion for the required measuring period described in Section 3. Fig. 3 illustrates the R-value results for the six cases and the CV for all methods. In case A, the high surface temperature difference between the two sides of the walls results to low variance for all methods. The CV is lower than the expected uncertainty according to the standards. In all other cases (B.1, B.2, B.3, C.1 and C.2) where the surface temperature difference is lower than 3 ◦ C, the CV of the Average and Summation method is significantly higher. The effect of the temperature difference on these two methods is in line with the standards which state that the uncertainty of the results depends on the temperature difference. The CV of the results for the Average and Summation method exceeds the 10%. Hence, the results of Summation method are rejected according to the ASTM. Regarding the Average method, the CV is higher than the expected value, however the ISO standard does not reject the results. Regarding the SLS HF method, the CV is always lower than 5% in all cases, indicating that the variation of this method is not affected by the measuring conditions. Particularly, in case of wall B, the coefficient of variation is extremely low (1.0–1.3%), despite the fact that the duration of the set of data was shorter than 6 days and the wall was heavy. In the cases A, B.1, B.2, B.3 and C.2, where the direction of heat flow is stable during the day (Table 3), the CV of the Dynamic and SLS TIN methods is lower than 6%.On the contrary, in the case C.1 where the direction of heat flow is alternating during the day (Table 3) the CV of these two methods exceeds the 8%. Hence, the results of SLS TIN method are not accepted according to ASTM standards because the CV is higher than 6%. On the other hand, the results of Dynamic method are accepted according to ISO standard, but the uncertainty increase accordingly. The Dynamic and the SLS TIN methods were further investigated for the case C.1. Results were obtained for longer duration of data sets than the period defined according to the criterion of Section 3. Fig. 4 illustrates the calculated values of CV for the two
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Fig. 2. Evolution at the time of R-value results and required measuring period for every method.
methods using R-values obtained from 10, 15 and 20 days. Despite of the increase of the duration of data collection, the CV of these methods remains higher than the expected values. It is demonstrated that the high variation of the results for these two methods is independent of the collection duration of data sets.
6. Conclusions The present work carried out a comparative assessment of the four standardized methods for the in-situ measurement of thermal resistance: the Average, the Summation, the Dynamic and two different approaches of the Sum of Least Square method (SLS HF and SLS TIN). The effect of measuring conditions on the required measuring period and the variability of the results for each method was
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Fig. 3. The R-value results and the respective coefficient of variation (CV) for every method.
investigated. Six cases in total were examined in three different walls. The results showed that the mean temperature difference between the surfaces of the wall and the direction of heat flow during the day strongly influence the duration of the required measuring period and the variability of the results. In particular, the Average and Summation methods require a high temperature difference and, as a consequence, a stable direction of heat flow in order to provide acceptable and reliable results in a short mea-
suring period. In cases where the temperature difference is lower than 3 ◦ C, the results of Average and Summation method have high and not acceptable coefficients of variation, respectively. Hence, the Average and Summation methods should not be used when the temperature difference is too low or their criteria should be stricter. The study also investigated the required measuring period of all methods. For the Dynamic, SLS HF and SLS TIN methods, where it is not determined by their standards, it is defined as the duration in which the last three obtained daily values do not deviate more
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Fig. 4. The CV of the Dynamic and SLS TIN methods for different measuring periods in case C.1.
than 3%. The results showed that this criterion can be used for these methods at any measuring conditions. Regarding the variability of the results, the Dynamic and SLS TIN methods appeared to be affected only by the direction of the heat flow. These methods appeared to require a stable direction of the heat flow during the day in order to provide results with the excepted variability. In case where the direction of the heat flow is stable, their results do not deviate more than 6%, which is the expected value according to the standards. On the other hand, when the heat flow direction is changing during the day, the deviation of the Dynamic and SLS TIN reaches up to 8% and 18% respectively. On the contrary, the SLS HF method is not affected by the measuring conditions providing fast and reliable results at all cases. References [1] Buildings Energy Data Book, 2012. [2] B. Atanasiu, C. Despret, M. Economidou, J. Maio, I. Nolte, O. Rapf, J. Laustsen, P. Ruyssevelt, D. Staniaszek, D. Strong, S. Zinetti, L. Verheyen, Europe’s buildings under the microscope – A country-by-country review of the energy performance of buildings, 2011. [3] I. Mandilaras, I. Atsonios, G. Zannis, M. Founti, Thermal performance of a building envelope incorporating ETICS with vacuum insulation panels and EPS, Energy Build. 85 (0) (2014) 654–665. [4] D.A. McIntyre, In situ measurement of U-values, Build. Serv. Eng. Res. Technol. 6 (1985) 1–6. [5] M.P. Modera, M.H. Sherman, R.C. Sonderegger, Determining the U-value of a wall from field measurements of heat flux and surface temperatures, in: ASTM Workshop on Heat Flow Sensors, Philadelphia PA, 1986. [6] L. Laurenti, F. Marcotullio, F. de Monte, Determination of the thermal resistance of walls through a dynamic analysis of in-situ data, Int. J. Therm. Sci. 43 (3) (2004) 297–306. [7] C. Buratti, S. Grignaffini, Measurement of the thermal resistance of masonry walls, Int. J. Heat Technol. 21 (2) (2003) 107–114. [8] M. Cucumo, A.D. Rosa, V. Ferraro, D. Kaliakatsos, V. Marinelli, A method for the experimental evaluation in situ of the wall conductance, Energy Build. 38 (3) (2006) 238–244. [9] C. Buratti, E. Moretti, Thermal resistance of masonry walls: in situ measurements, 6th World Conference on Experimental Heat Transfer, Fluid Mechanics and Thermodynamics (2005).
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