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A quantitative methodology to evaluate thermal bridges in buildings
Applied Energy 97 (2012) 365–373
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A quantitative methodology to evaluate thermal bridges in buildings Francesco Asdrubali ⇑, Giorgio Baldinelli, Francesco Bianchi CIRIAF, University of Perugia, Via G. Duranti, 67, 06125 Perugia, Italy
a r t i c l e
i n f o
Article history: Received 6 July 2011 Received in revised form 13 December 2011 Accepted 14 December 2011 Available online 5 January 2012 Keywords: Buildings Insulation Thermal bridges Infrared thermography Numerical analysis
a b s t r a c t The use of multi-layer walls with high thermal resistance values is widely used to reduce heat losses in buildings during wintertime. Nevertheless, it is extremely important to treat also weaker components of the envelope such as doors, windows and all the various thermal bridges, otherwise the efforts in increasing walls thermal resistance can be vanished. If the improvement of the thermal performance of windows and doors has reached a significant development and a high level of standardization, the same is not true for the corrections related to thermal bridges, which therefore require a specific analysis in the design phase. Thermal bridges, of whatever nature, are therefore a crucial point in the energy analysis of the building envelope. The analysis on existing constructions can be performed on site with thermographic techniques that describe in first approximation the qualitative energy performance of the building and put in evidence the main heat losses. The paper proposes a methodology to perform a quantitative analysis of some types of thermal bridges, through simple thermographic surveys and subsequent analytical processing. From the simple measurement of the air temperature and the analysis of the thermogram, the thermal bridge effect can be estimated as a percentage increase of the homogenous wall thermal transmittance. This term is obtained without further information on the structure of both the thermal bridge and the stratigraphy of the wall. The analytical methodology – which was validated with experimental and numerical analyses – is described and the results of surveys on different types of thermal bridges are reported. This method represents a quick and effective tool to define the actual heat loss of high-insulation buildings and to evaluate the benefits in treating thermal bridges. Ó 2011 Elsevier Ltd. All rights reserved.
1. Introduction The study and reduction of buildings heat losses play an important role on an integrated energy-saving policy. The infrared (IR) thermography imaging technique results useful to conduct in situ analyses, since it allows a qualitative survey to evaluate the surface temperatures of the envelope surfaces. Following the standard procedure, a comparative analysis has to be conducted with reference thermograms that describe the main defects. The qualitative approach of this investigation leads to the assessment of easily recognizable imperfections such as air infiltration, bad insulation, and mold. On the other hand, a comparative analysis among different kinds of thermal bridges becomes difficult when it is performed through purely qualitative evaluations. The present work tries to define a quantitative approach based on the analysis of the thermogram that describes the temperature field on the internal or external surface of a part of the envelope. The aim
⇑ Corresponding author. Tel.: +39 075 585 3716; fax: +39 075 585 3697. E-mail address: [email protected] (F. Asdrubali). 0306-2619/$ - see front matter Ó 2011 Elsevier Ltd. All rights reserved. doi:10.1016/j.apenergy.2011.12.054
consists of evaluating the thermal bridge effect, providing a percentage increase of the homogenous wall thermal transmittance. The IR thermographic analysis is influenced by many factors affecting the accuracy of the absolute temperature reading. After a quick analysis on the determination of the parameters involved in the IR camera temperature output, the analytical description of the quantitative incidence factor of the thermal bridge is introduced. The validation of the methodology has been executed with the realization of a thermal bridge in a controlled environment, so giving the possibility of comparing the proposed technique to other experimental data and to a finite volumes analysis. After the process validation, the investigation has been extended to other types of envelope singularities.
2. Literature review The application of IR thermography in buildings may be characterized by different levels of deepening: a first step qualitative analysis is described by Balaras and Argirious [1], with diagnosis oriented not only to buildings energy losses, but also to non-destructive tests of ventilation, heating, air conditioning and electric systems.
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Nomenclature A CFD D h I L l N Q T U W
e u s w
area (m2) computational fluid dynamics distance (m) liminar coefficient (W/m2 K) incidence factor (–) thermal coupling coefficient (W/K) length (m) number (–) thermal flux (W) temperature (K, °C) thermal transmittance (W/m2 K) energy (J) thermal emittance (–) heat flux density (W/m2) atmosphere transmittance (–) linear thermal transmittance (W/m K)
Quantitative IR thermography has to take into account a number of variables linked to the heat transfer phenomena. Barreira and de Freitas [2] conducted a sensitivity analysis of the process to the emissivity, reflection, environmental conditions and surface color, by means of laboratory measurements and in situ campaigns. Avdelidis and Moropoulou [3] proposed a detailed investigation on the influence of emissivity, while Datcu et al. [4] used experimental methodologies for the determination of the reflected temperature. Li et al. [5] suggested that a preparatory study in a laboratory gives important indications for the elimination of reflection bias. Active thermography is suitable for the detection of internal defects, as explained by Grinzato et al. [6]. Albatici and Tonelli [7] defined a methodology for the evaluation of the thermal transmittance of an opaque component, through the IR thermography and the contemporary measurements of the external and internal air temperatures, comparing the results of three cases with data obtained from heat flow meters. As far as the specific application of IR thermography to thermal bridges, Zalewski et al. [8] studied the effect of a steel junction inside a prefabricated panel with a preliminary thermographic analysis, making a further refinement by heat flow meters and three-dimensional numerical models. Finite element codes in conjunction with IR cameras were also used by Heinrich and Dahlem [9] (for the investigation of low consumption buildings) and Wròbel and Kisilewicz [10] (for testing structural thermal bridges). Finally, Benko [11] indicated a quantitative analysis factor associated to the thermal bridges heat dispersion, obtained by means of the sole study of the thermogram of the external surface of a building.
Subscripts 1D one-dimensional 2D two-dimensional atm atmospheric HFM evaluated with heat flow meter i internal obj object pixel relative to each pixel refl reflected s surface tb thermal bridge tot total 1 part of thermal bridge 2 part of thermal bridge 3 part of thermal bridge
Most of the authors tried to evaluate the thermal bridges heat loss embracing a numerical approach: Cappelletti et al. [12] investigated with these tools the discontinuity deriving from the coupling wall-window; Dèquè et al. [13] focused their attention on structural thermal bridges effects; Martin et al. [14] added a contribution on thermal bridges behavior in dynamic conditions. In any case, the CFD analysis constitutes a tool that requires the knowledge of the composition of the structures investigated, and it does not represent an immediate instrument to define in situ the thermal bridge characteristics. 3. Infrared thermography outlines In Fig. 1 the heat transfer processes of a thermographic analysis are sketched [15]. The energy balance is synthesized by the following equation:
W tot ¼ esW obj þ ð1 eÞsW refl þ ð1 sÞW atm
ð1Þ
where Wtot represents the total energy that hits the camera when the object to be analyzed is focused; the only term of interest for a quantitative analysis is Wobj, the energy radiated from the object, that is a function of its temperature. The other two addenda are related to contributions from different sources standing around the measurement field (Wrefl) and the atmosphere absorption (Watm). Wrefl depends on the temperature of the objects facing the surface under investigation as well as on the reflective properties of the surface itself; the correction is defined by the determination of the reflected temperature, described below. Watm is linked to the air temperature and relative humidity
Fig. 1. Infrared thermography: schematization of the heat transfer processes [15].
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and to the distance between the camera and the surface; these parameters have to be used in the IR camera setup. Once the last two terms are identified, the remaining uncertainty arises from the definition of the emissivity properties of the object under investigation. Therefore, IR thermography cameras need a series of parameters to take into account of the physics of heat transfer: object emissivity, reflected temperature, atmosphere temperature, relative humidity, distance from the object. The emissivity could be determined by the parallel measurement of the surface temperature with other instruments or using tapes with known emissivity, applied on the examined surface. The environment where the thermographic measurement is conducted should be kept as much as possible at constant temperature, at the aim of minimizing the terms different from the object emissivity (in particular, the reflected energy), so reducing their contribution to the accuracy reduction. The reflected temperature is obtained lying a rubbed aluminum foil on the object surface, setting at the same time the camera emissivity to the unitary value. Because of the aluminum high reflectivity, the rub and the IR camera setting, the thermogram generated gives the reflected temperature Trefl linked to the radiative heat sources present in the measurement environment. Finally, the imaging has to be executed with the camera lens not perpendicular to the object analyzed, at the aim of avoiding the socalled ‘‘Narcissus effect’’: the camera sees its lens reflected on the object [16]. These precaution was taken even if the lens were far enough from the surface investigated. All the previous actions are necessary to improve the quantitative thermography, minimizing the sources of errors and uncertainty [17].
Generally speaking, a thermal bridge is individuated by the linear thermal transmittance, obtained by a two-dimensional calculation [18] and defined by the following equation:
w ¼ L2D
n X
U k lk
Each image obtained by an IR camera gives the temperature of each pixel hit by the radiation emitted form the object examined, so defining the entire thermal field of the area covered by the camera optic. IR thermography applications for the evaluation of heat dispersions in buildings perform at their best if a minimum temperature difference of 10–15 °C between the external and internal environment is guaranteed [15]. Analyzing, for example, the inner side of envelope components during the heating season, a decrease of surface temperature is easily registered (Fig. 2). The aim of the present work is to introduce a parameter able to express the thermal bridge effect on the building dispersions, using only the information captured from the thermogram.
ð2Þ
k¼1
where L2D is the linear thermal coupling term derived by the twodimensional calculation, Uk is the thermal transmittance of the kth one-dimensional component (width lk, 1 m length) that separates the internal side from the external environment. Thus, the quantitative classification of thermal bridges is identified by the value of w, that gives the thermal flux transferred per length and temperature units in steady-state conditions. Besides, the linear thermal transmittance determines the thermal field visualized by the IR camera: in winter season, with the same indoor–outdoor temperature difference, thermal bridges with higher dispersions generate thermograms with lower temperature values in the internal side. Hence, starting from the acquisition of the thermal field, it is theoretically possible to go backward to the quantitative evaluation of the thermal bridge, that is the aim of the new parameter definition developed in this work. The definition itself of thermal bridge [19] puts in evidence that it represents a zone with thermal properties significantly different from the rest of the envelope; as a consequence, the temperature of the inner side will be interested by considerable variations in the area influenced by the thermal bridge, assuming on the contrary an almost constant value in the part of the structure where the heat flux can be considered one-dimensional. In this ‘‘undisturbed’’ zone, the temperature is a function of the thickness and thermal conductivity of the layers that constitute the wall; in stationary conditions, the heat flowing through the one-dimensional wall can be written with as follows:
Q 1D ¼ h1D i A1D ðT i T 1D is Þ 4. Description of the methodology adopted for the quantitative analysis of thermal bridges
367
ð3Þ
where h1D_i is the internal liminar coefficient (the reciprocal of the internal surface resistance, which takes into account of both convection and radiation heat transfer), A1D is the area considered and the temperatures Ti and T1D_is represent respectively the inner air temperature (that could be considered equal to the temperature of the inner objects exchanging heat by radiation with the inner wall) and the wall inner surface temperature. When in situ measurements are performed, it is difficult to achieve steady-state conditions, because of the variation of the external temperature and the presence of potentially disturbing factors, therefore, the IR images have to be taken with particular care. In the case of the introduction of a thermal bridge in the area A1D, Eq. (3) is not applicable since the temperature is far from being uniform throughout the entire surface. Analyzing the area with an IR camera, the thermal field of the wall under investigation is available, therefore, a temperature value Tpixel_is could be associated to
Fig. 2. Example of a structural thermal bridge and window thermal bridge at the coupling of glass and frame.
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each pixel that is representative of a part Apixel of the wall surface; the extension of Apixel depends from the instantaneous field of view of the chosen IR camera. Hence, the evaluation of the heat flux is possible in each pixel, obtaining a formulation of the whole area dispersion:
Q tb ¼ htb i Apixel
N X ðT i T pixel is Þ
ð4Þ
p¼1
with the hypothesis of constant liminar coefficient and being N the number of pixels that compose the entire area, according to the relation:
A1D ¼ NApixel
ð5Þ
Then, the incidence factor of the thermal bridge Itb is defined as the ratio between the heat flowing in real conditions and the heat flowing in absence of the thermal bridge:
PN Q tb htb i Apixel p¼1 ðT i T pixel is Þ Itb ¼ ¼ Q 1D h1D i A1D ðT i T 1D is Þ
ð6Þ
i
Therefore, also recalling Eq. (5), the incidence factor of the thermal bridge becomes:
ð7Þ
This quantitative factor could be also expressed in terms of an increase of the thermal transmittance U1D of the undisturbed zone; considering the influence of the thermal bridge, and using the hypothesis of steady-state conditions, the actual value of the wall thermal transmittance Utb can be written as follows:
U tb ¼ U 1D Itb
ð8Þ
The incidence factor of the thermal bridge is connected to the linear thermal transmittance w as defined in Eq. (2), when the thermal transmittance U1D of the undisturbed zone is known:
Itb ¼
Simply subtracting 1 to Itb and multiplying the result by the heat exchanged through the undisturbed wall Q1D, the heat loss due to the thermal bridge is obtained. On the basis of Eq. (6), a methodology of imaging is proposed, aimed at obtaining the data necessary for the evaluation of the two heat fluxes with the only help of the acquisition of the internal environment temperature, minimizing at the same time the sources of errors. For example, considering a structural thermal bridge constituted by a wall angle infinitely high, the thermogram will show a minimum in correspondence of the angle, moving then towards an asymptote that represents the wall behavior in the one-dimensional zone, where the effect of the thermal bridge is negligible (Fig. 3). The choice of the area covered by the imaging plays a fundamental role, since the distance D (Fig. 3) has to be sufficient to include the undisturbed zone, whose temperature value is the term T1D_is of Eq. (6). The advantage of acquiring in the same thermogram both the temperature of the thermal bridge area and the thermal field of the one-dimensional wall consists of avoiding the introduction of further errors linked to different instants of reading or different angles of view. When surfaces with different orientation are contemporarily observed, in fact, the effect of the angle between the viewing direction and the normal to the surface has be taken into account, since the thermal emittance may depend on that angle. Besides, since the domain is limited and the image is captured in the same instant for all the surface, the liminar coefficient could be considered constant throughout the entire area:
h1D i ¼ htb
P P htb i Apixel Np¼1 ðT i T pixel is Þ Apixel Np¼1 ðT i T pixel is Þ ¼ h1D i A1D ðT i T 1D is Þ NApixel ðT i T 1D is Þ PN p¼1 ðT i T pixel is Þ ¼ NðT i T 1D is Þ
Itb ¼
U 1D ðltb þ l1D Þ þ w U 1D ðltb þ l1D Þ
ð9Þ
or
w ¼ ðItb 1ÞU 1D ðltb þ l1D Þ
ð10Þ
5. Model validation In this section the validation process of the methodology described in the previous paragraph is reported. The thermal bridge selected for the purpose is the one generated in a window, by the coupling between the glass and frame (Fig. 2). The choice was dictated by the possibility of installing the window inside an available climatic chamber [20], whose characteristic and dimensions do not permit the testing of a structural thermal bridge. The sample is mounted between two rooms with a temperature difference of about 20 °C, in steady-state, monitored and controlled conditions. The validation of the proposed methodology has been assessed with two different approaches: an instrumental heat flow analysis, where the heat transfer is measured point by point through the window area; a numerical analysis, implementing a two-dimensional model of the node of the window considered 5.1. Thermographic analysis Infrared thermographic measurements were carried out in the lab to verify the various parameters influencing the phenomenon, including steady-state conditions. The window was positioned between a conditioned space, kept at 1 °C, and the laboratory, kept at constant temperature too. The attention was focused on the window’s lower thermal bridge, whose section is characterized by aluminum with polyamide washers to assure the thermal cut.
Fig. 3. Example of an angular thermal bridge and relative thermogram output.
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The glazing (mm 6/7 + mm 15 + mm 8/9, with an aluminum spacer) has the inner side of the external layer covered by a lowemission coating. The IR camera is manufactured by FLIR, model B360 with a FPA microbolometer without cooling, a spectral range from 7.5 and 13.0 lm, and a 320 240 pixel resolution. To quantitatively evaluate the thermal field, it was necessary to perform calibration measurements and to acquire the various parameters to be inserted into the instrument to correct the thermogram. The surface thermal emittance was calculated thanks to surface temperature probes, varying the emissivity in the IR camera, so to obtain the measured temperatures. The reflected temperature was then evaluated with the methodology described in paragraph 2, using an aluminum foil (Fig. 4). Thanks to thermohygrometric probes, environmental conditions were evaluated during the measurements. Also the distance between the sample and the IR camera was registered. A particular attention was paid to the framing, to respect the value of the distance D defined in the previous paragraph. From the standard EN ISO 10077-2 [21], which deals with the numerical calculations for the frames, it emerged that to include in the thermographic image the glass undisturbed area, a distance D from the frame edge of at least 200 mm has to be considered. Fig. 5 shows the thermogram which will be studied, also calculating the incidence factor of the thermal bridge; the thermal bridge is actually composed by the junction between the frame and the glass but, since the length of the opaque part is reduced to few centimeters, the analysis is limited to the transparent portion of the window. The domain considered for the validation process is constituted by an imaginary line (Fig. 5) on the central area of the glass (far away from the lateral thermal bridges). The trend of temperature along the line is shown in the
Fig. 5, where the asymptotic behavior is clearly visible towards the temperature of the undisturbed area (17.7 °C). Calculating the number of pixels that compose the line and applying the above procedure for the evaluation of the incidence factor of the thermal bridge, the value of 1.174 is obtained, with an uncertainty of 6.4%, considering a confidence level equal to 95%. The error rate was estimated referring to the standard ISO/ IEC Guide 98-3:2008 [22], taking into account of the uncertainty associated with the temperature read by the camera, provided its technical data. 5.2. Heat flow analysis Before the execution of the thermographic analysis, a group of temperature and heat flow probes have been placed in the area subjected to investigation. Fig. 6 shows the arrangement, with the sensors following the imaginary line described above. The heat flow probes allow the measurement of the heat flux density (W/ m2) in the undisturbed zone and throughout the whole area of the thermal bridge; the Table 1 reports the values of the heat flow, with the relative areas of interest. In the undisturbed zone only one heat flow meter was placed, while the part closest to the frame and affected by the thermal bridge has been inspected with three heat flow meters, placed one above the other. The incidence factor of the thermal bridge is estimated in the whole surface covered by the measurement line of Fig. 6 using the following equation:
Itb
HFM
¼
Q tb u1D A1D þ utb 1 Atb 1 þ utb 2 Atb 2 þ utb 3 Atb ¼ Q 1D u1D ðA1D þ Atb 1 þ Atb 2 þ Atb 3 Þ
Fig. 4. Measurement of the reflected temperature.
Fig. 5. Thermogram of the lower part of the window and trend of temperature along the imaginary line.
3
ð11Þ
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with an uncertainty of 4.6% (confidence level equal to 95%), derived from the indications of the standard EN ISO 10077-2. 5.4. Comparison between the methodologies Fig. 8 shows the temperature trends of the three different methods along the imaginary line. In the case of the heat flow analysis, the sole points where the temperature probes were placed are reported; from a qualitative point of view, the temperature trend in the thermogram can be compared to the results of some studies found in literature [24]. The three methods show a good agreement, with a light difference in the central area of the thermal bridge. In Fig. 9 the results in terms of the incidence factor of the thermal bridge are sketched, together with the relative uncertainties; it is evident that, considering the confidence interval, data overlap, indicating compatible results and demonstrating the correctness of the method. 6. Application of the methodology to in situ thermal bridges
Fig. 6. Heat flow meters to evaluate the thermal bridge in the transparent part of the window.
Table 1 Heat flow meters results, with the relative areas of interest. Heat flux density (W/m2)
u1D utb_1 utb_2 utb_3
32.8 38.5 46.1 63.4
Area (m2) A1D Atb_1 Atb_2 Atb_3
0.11 0.03 0.03 0.03
The incidence factor of the thermal bridge results equal to 1.228 with an uncertainty of 7.4% (confidence level equal to 95%), associated to the presence of the heat flow probes [22]. 5.3. Numerical analysis The commercial code FLUENT [23] was used for the Computational Fluid Dynamic analysis. The section of the window was modeled taking into account the standard EN ISO 10077-2 [21], to evaluate the thermal properties of the air space and of the materials. Boundary conditions are convective and the cool and hot side temperatures are defined by the laboratory measurements (hot side temperature: 22.2 °C, cold side temperature 0.7 °C), while the liminar coefficients are derived from the standard. As a matter of fact, the window is placed between two spaces whose environmental conditions are similar to the real ones; the cold side is characterized by forced convection while the hot one by natural convection. As far as convection, simulations were therefore carried out with standard conditions, so that the results could be easily extended to the real buildings conditions. The mesh is a triangular one, with a step of about 0.5 mm. Fig. 7 shows the temperature field in the section of the two-dimensional model, together with the temperature trend along the imaginary line of Fig. 6. To evaluate the incidence factor of the thermal bridge, the imaginary line was divided into small segments of the same length of the mesh. The hypothesis allowed to compare the simulation output data with the data taken from the thermogram, assimilating the behavior of a pixel to the one of a single mesh. The value of the incidence factor of the thermal bridge obtained from the simulation is equal to 1.169,
Two different configurations of a floor with a low beam were chosen in situ to evaluate the incidence factor of the thermal bridge. The first configuration presents a correction of the thermal bridge with insulating panels (both inside and outside) while the second one is not insulated at all. In both cases a thermographic image was acquired, including the undisturbed area and measuring at the same time the air temperature. The wall was not exposed to solar radiation; steady-state conditions were assumed, having evaluated the environmental conditions during the periods before the measurement. Also in this case, an imaginary line was considered starting from the internal edge between the floor and the wall (Figs. 10 and 11). Analyzing the trends, two completely different thermal fields can be observed; it is also possible to see the asymptotic part and evaluate the temperature of the undisturbed area. The difference between the two configurations is evident if we compare the two values of the incidence factor of the thermal bridge, which is equal to 1.606 for the configuration with the insulated beam and to 2.000 for the configuration with the non-insulated beam. A further analysis was carried out for the investigated walls, evaluating thanks to a heat flux meter the thermal transmittance (U1D) without the influence of the thermal bridge; the indications of the standard ISO 9869 [25] were followed, using the average method, suitable for the unsteady conditions of the in situ analyses. A plate heat flux meter was positioned in the inner side of the wall, adding a protection from unwanted radiation sources such as artificial lighting, sun or household appliances; the measurement apparatus is completed by the installation of two temperature probes on the internal and external surface of the wall. The average method consists of calculating the instantaneous thermal transmittance as a function of the previous heat flux and temperature values; after a proper acquisition time (minimum three days, seven days for this measurement campaign), the thermal transmittance tends to an asymptote that represents its actual value (Fig. 12). Thanks to the results, it was possible to evaluate the increase in the thermal transmittance of the wall, in the area of the thermal bridge, according to Eq. (8) (Table 2). It is therefore possible to obtain, thanks to the incidence factor of the thermal bridge, quantitative data concerning the thermal bridge even without a detailed knowledge of the stratigraphy of the wall. In the case of the non insulated beam, a further analysis was carried out, since the stratigraphy was known. A computational analysis of the thermal bridge was therefore performed, obtaining
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Fig. 7. Numerical analysis: thermal field in a generic section of the window and temperature trend along the imaginary line.
Fig. 8. Comparison between the temperature trends obtained from the thermogram, the temperature probes and the simulations.
Fig. 9. Plot of the incidence factor of the thermal bridge evaluated through the three different methods, with the relative uncertainties.
a trend of temperatures similar to the real ones and a value of the incidence factor of the thermal bridge equal to 2.111. A model in FLUENT was created to simulate also the correction of the thermal bridge (insulation of the beam); Fig. 13 reports the
comparison between the temperature values along the insulated and the non-insulated beams. It is interesting to note that the curves result very similar to the real ones, reported in Figs. 10 and 11. The calculated value of the incidence factor of the thermal
Fig. 10. Thermogram of the insulated beam and temperature trend along the imaginary line.
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Fig. 11. Thermogram of the non-insulated beam and temperature trend along the imaginary line.
Fig. 12. Specific heat flux, internal–external temperatures and thermal transmittance trends for the in situ measurement of the undisturbed wall insulating properties.
Table 2 Thermal transmittances of both configurations (undisturbed area and area of the thermal bridge).
Insulated beam Non insulated beam
U1D (W/m2 K)
Itb
Utb (W/m2 K)
0.42 0.39
1.606 2.000
0.67 0.78
UNI TS 11300 [26]; an overall heat loss in wintertime of 4684 W was evaluated, 13.4% of which due to the thermal bridge. The correction of the thermal bridge reduces the heat loss to a value of 4307 W and the incidence of the thermal bridge to 8.8%. The analysis allows to evaluate the global effects of the presence of thermal bridges in the envelope’s heat losses and to therefore in the energy primary demand of a building during wintertime. 7. Conclusions
Fig. 13. Simulated temperature trends: comparison between the insulated and the non insulated beam.
bridge is equal to 1.262, so there is a reduction in the thermal bridge heat loss of about 40%. In global terms, it is also possible to evaluate the benefits of such a correction in the heat losses of the whole flat. Simulations of the energy behavior of the flat were carried out according to
The analysis of thermal bridges conducted with the IR thermography can be developed through various approaches, from qualitative investigations to the quantitative techniques of the active thermography. In this work a quantitative factor was introduced, at the aim of evaluating in a simple and effective manner the effect of thermal bridges on the global dispersions of buildings. It was analytically defined the incidence factor of the thermal bridge that depends from the internal air temperature and the internal wall surface temperature, read by the IR camera. Afterwards, results acquired with the thermographic investigation were compared with data obtained by heat flow meters, and the findings of a finite volume analysis; this test was realized in a laboratory setup, where it was possible to monitor the boundary conditions, keeping the stationary conditions for the thermal bridge generated in a window from the coupling of glass and frame. It emerged that the thermal field obtained with the three methods is very similar, producing close values of the incidence factor of the thermal bridge. Two in situ thermal bridges were then investigated, verifying the effect of the insulation on a floor beam; it came out that the incidence factor of the thermal bridge describes correctly the dispersion grade of the singularity, quantifying the result of the thermal bridge correction.
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The factor could be linked the linear thermal transmittance of the thermal bridge and it could be also used to define an increase percentage of the undisturbed wall thermal transmittance, so proposing a simple and useful tool to calculate the actual heat dispersions of buildings by quick and easy in situ thermographic measurements, suggesting at the same time possible interventions for the improvement of insulation. The quantitative thermographic imaging constitutes also a useful mean to analyze, improve and validate 3D simulation tools especially designed for the evaluation of building energy performance [27], since they are capable of evaluating the outdoor and indoor walls thermal fields.
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[10] Wròbel A, Kisilewicz T. Detection of thermal bridges – aims, possibilities and conditions. Qirt 2008. Kracow, Poland, July 2–5, 2008. [11] Benko I. Quantitative analysis of thermal bridges of structures through infrared thermograms. Qirt 2002. Dubrovnik, Croatia, September 24–27, 2002. [12] Cappelletti F, Gasparella A, Romagnoni P, Baggio P. Analysis of the influence of installation thermal bridges on windows performance. The case of clay block walls. Energy Build 2011;43(6):1435–42. [13] Déqué F, Ollivier F, Roux JJ. Effect of 2D modelling of thermal bridges on the energy performance of buildings – numerical application on the Matisse apartment. Energy Build 2001;33(6):583–7. [14] Martin K, Erkoreka A, Flores I, Odriozola M, Sala JM. Problems in the calculation of thermal bridges in dynamic conditions. Energy Build 2011;43(2–3):529–35. [15] Flir System. User’s manual; 2008. [16] Boizumault F, Harmand S, Desmet B. Experimental determination of the local heat transfer coefficient on a thermally thick wall downstream of a backwardfacing step. Qirt 1996. Stuttgart, Germany, September 2–5, 1996. [17] Minkina W, Dudzik S. Infrared thermography – errors and uncertainties. West Sussex, UK: Wiley; 2009. [18] EN ISO 10211. Thermal bridges in building construction. Heat flows and surface temperatures – detailed calculations; 2008. [19] EN ISO 14683. Thermal bridges in building construction. Linear thermal transmittance – simplified methods and default values; 2008. [20] Asdrubali F, Baldinelli G. Thermal transmittance measurements with the hot box method: calibration, experimental procedures, and uncertainty analyses of three different approaches. Energy Build 2011;43:1618–26. [21] EN ISO 10077-2. Thermal performance of windows, doors and shutters. Calculation of thermal transmittance – numerical method for frames; 2004. [22] ISO/IEC Guide 98-3:2008. Uncertainty of measurement – part 3: Guide to the expression of uncertainty in measurement; 2008. [23] Fluent version 12.1. User’s guide. USA; 2009. [24] Griffith BT, Türler D, Arasteh D. Surface temperatures of insulated glazing units: infrared thermography laboratory measurements. ASHRAE Trans 1996;102(Pt. 2). [25] ISO 9869. Thermal insulations – building elements. In-situ measurements of thermal resistance and thermal transmittance; 1994. [26] UNI/TS 11300-1. Energy performance of buildings – part 1: evaluation of energy need for space heating and cooling; 2008. [27] He J, Hoyano A, Asawa T. A numerical simulation tool for predicting the impact of outdoor thermal environment on building energy performance. Appl Energy 86:1596–605.
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Applied Energy journal homepage: www.elsevier.com/locate/apenergy
A quantitative methodology to evaluate thermal bridges in buildings Francesco Asdrubali ⇑, Giorgio Baldinelli, Francesco Bianchi CIRIAF, University of Perugia, Via G. Duranti, 67, 06125 Perugia, Italy
a r t i c l e
i n f o
Article history: Received 6 July 2011 Received in revised form 13 December 2011 Accepted 14 December 2011 Available online 5 January 2012 Keywords: Buildings Insulation Thermal bridges Infrared thermography Numerical analysis
a b s t r a c t The use of multi-layer walls with high thermal resistance values is widely used to reduce heat losses in buildings during wintertime. Nevertheless, it is extremely important to treat also weaker components of the envelope such as doors, windows and all the various thermal bridges, otherwise the efforts in increasing walls thermal resistance can be vanished. If the improvement of the thermal performance of windows and doors has reached a significant development and a high level of standardization, the same is not true for the corrections related to thermal bridges, which therefore require a specific analysis in the design phase. Thermal bridges, of whatever nature, are therefore a crucial point in the energy analysis of the building envelope. The analysis on existing constructions can be performed on site with thermographic techniques that describe in first approximation the qualitative energy performance of the building and put in evidence the main heat losses. The paper proposes a methodology to perform a quantitative analysis of some types of thermal bridges, through simple thermographic surveys and subsequent analytical processing. From the simple measurement of the air temperature and the analysis of the thermogram, the thermal bridge effect can be estimated as a percentage increase of the homogenous wall thermal transmittance. This term is obtained without further information on the structure of both the thermal bridge and the stratigraphy of the wall. The analytical methodology – which was validated with experimental and numerical analyses – is described and the results of surveys on different types of thermal bridges are reported. This method represents a quick and effective tool to define the actual heat loss of high-insulation buildings and to evaluate the benefits in treating thermal bridges. Ó 2011 Elsevier Ltd. All rights reserved.
1. Introduction The study and reduction of buildings heat losses play an important role on an integrated energy-saving policy. The infrared (IR) thermography imaging technique results useful to conduct in situ analyses, since it allows a qualitative survey to evaluate the surface temperatures of the envelope surfaces. Following the standard procedure, a comparative analysis has to be conducted with reference thermograms that describe the main defects. The qualitative approach of this investigation leads to the assessment of easily recognizable imperfections such as air infiltration, bad insulation, and mold. On the other hand, a comparative analysis among different kinds of thermal bridges becomes difficult when it is performed through purely qualitative evaluations. The present work tries to define a quantitative approach based on the analysis of the thermogram that describes the temperature field on the internal or external surface of a part of the envelope. The aim
⇑ Corresponding author. Tel.: +39 075 585 3716; fax: +39 075 585 3697. E-mail address: [email protected] (F. Asdrubali). 0306-2619/$ - see front matter Ó 2011 Elsevier Ltd. All rights reserved. doi:10.1016/j.apenergy.2011.12.054
consists of evaluating the thermal bridge effect, providing a percentage increase of the homogenous wall thermal transmittance. The IR thermographic analysis is influenced by many factors affecting the accuracy of the absolute temperature reading. After a quick analysis on the determination of the parameters involved in the IR camera temperature output, the analytical description of the quantitative incidence factor of the thermal bridge is introduced. The validation of the methodology has been executed with the realization of a thermal bridge in a controlled environment, so giving the possibility of comparing the proposed technique to other experimental data and to a finite volumes analysis. After the process validation, the investigation has been extended to other types of envelope singularities.
2. Literature review The application of IR thermography in buildings may be characterized by different levels of deepening: a first step qualitative analysis is described by Balaras and Argirious [1], with diagnosis oriented not only to buildings energy losses, but also to non-destructive tests of ventilation, heating, air conditioning and electric systems.
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Nomenclature A CFD D h I L l N Q T U W
e u s w
area (m2) computational fluid dynamics distance (m) liminar coefficient (W/m2 K) incidence factor (–) thermal coupling coefficient (W/K) length (m) number (–) thermal flux (W) temperature (K, °C) thermal transmittance (W/m2 K) energy (J) thermal emittance (–) heat flux density (W/m2) atmosphere transmittance (–) linear thermal transmittance (W/m K)
Quantitative IR thermography has to take into account a number of variables linked to the heat transfer phenomena. Barreira and de Freitas [2] conducted a sensitivity analysis of the process to the emissivity, reflection, environmental conditions and surface color, by means of laboratory measurements and in situ campaigns. Avdelidis and Moropoulou [3] proposed a detailed investigation on the influence of emissivity, while Datcu et al. [4] used experimental methodologies for the determination of the reflected temperature. Li et al. [5] suggested that a preparatory study in a laboratory gives important indications for the elimination of reflection bias. Active thermography is suitable for the detection of internal defects, as explained by Grinzato et al. [6]. Albatici and Tonelli [7] defined a methodology for the evaluation of the thermal transmittance of an opaque component, through the IR thermography and the contemporary measurements of the external and internal air temperatures, comparing the results of three cases with data obtained from heat flow meters. As far as the specific application of IR thermography to thermal bridges, Zalewski et al. [8] studied the effect of a steel junction inside a prefabricated panel with a preliminary thermographic analysis, making a further refinement by heat flow meters and three-dimensional numerical models. Finite element codes in conjunction with IR cameras were also used by Heinrich and Dahlem [9] (for the investigation of low consumption buildings) and Wròbel and Kisilewicz [10] (for testing structural thermal bridges). Finally, Benko [11] indicated a quantitative analysis factor associated to the thermal bridges heat dispersion, obtained by means of the sole study of the thermogram of the external surface of a building.
Subscripts 1D one-dimensional 2D two-dimensional atm atmospheric HFM evaluated with heat flow meter i internal obj object pixel relative to each pixel refl reflected s surface tb thermal bridge tot total 1 part of thermal bridge 2 part of thermal bridge 3 part of thermal bridge
Most of the authors tried to evaluate the thermal bridges heat loss embracing a numerical approach: Cappelletti et al. [12] investigated with these tools the discontinuity deriving from the coupling wall-window; Dèquè et al. [13] focused their attention on structural thermal bridges effects; Martin et al. [14] added a contribution on thermal bridges behavior in dynamic conditions. In any case, the CFD analysis constitutes a tool that requires the knowledge of the composition of the structures investigated, and it does not represent an immediate instrument to define in situ the thermal bridge characteristics. 3. Infrared thermography outlines In Fig. 1 the heat transfer processes of a thermographic analysis are sketched [15]. The energy balance is synthesized by the following equation:
W tot ¼ esW obj þ ð1 eÞsW refl þ ð1 sÞW atm
ð1Þ
where Wtot represents the total energy that hits the camera when the object to be analyzed is focused; the only term of interest for a quantitative analysis is Wobj, the energy radiated from the object, that is a function of its temperature. The other two addenda are related to contributions from different sources standing around the measurement field (Wrefl) and the atmosphere absorption (Watm). Wrefl depends on the temperature of the objects facing the surface under investigation as well as on the reflective properties of the surface itself; the correction is defined by the determination of the reflected temperature, described below. Watm is linked to the air temperature and relative humidity
Fig. 1. Infrared thermography: schematization of the heat transfer processes [15].
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and to the distance between the camera and the surface; these parameters have to be used in the IR camera setup. Once the last two terms are identified, the remaining uncertainty arises from the definition of the emissivity properties of the object under investigation. Therefore, IR thermography cameras need a series of parameters to take into account of the physics of heat transfer: object emissivity, reflected temperature, atmosphere temperature, relative humidity, distance from the object. The emissivity could be determined by the parallel measurement of the surface temperature with other instruments or using tapes with known emissivity, applied on the examined surface. The environment where the thermographic measurement is conducted should be kept as much as possible at constant temperature, at the aim of minimizing the terms different from the object emissivity (in particular, the reflected energy), so reducing their contribution to the accuracy reduction. The reflected temperature is obtained lying a rubbed aluminum foil on the object surface, setting at the same time the camera emissivity to the unitary value. Because of the aluminum high reflectivity, the rub and the IR camera setting, the thermogram generated gives the reflected temperature Trefl linked to the radiative heat sources present in the measurement environment. Finally, the imaging has to be executed with the camera lens not perpendicular to the object analyzed, at the aim of avoiding the socalled ‘‘Narcissus effect’’: the camera sees its lens reflected on the object [16]. These precaution was taken even if the lens were far enough from the surface investigated. All the previous actions are necessary to improve the quantitative thermography, minimizing the sources of errors and uncertainty [17].
Generally speaking, a thermal bridge is individuated by the linear thermal transmittance, obtained by a two-dimensional calculation [18] and defined by the following equation:
w ¼ L2D
n X
U k lk
Each image obtained by an IR camera gives the temperature of each pixel hit by the radiation emitted form the object examined, so defining the entire thermal field of the area covered by the camera optic. IR thermography applications for the evaluation of heat dispersions in buildings perform at their best if a minimum temperature difference of 10–15 °C between the external and internal environment is guaranteed [15]. Analyzing, for example, the inner side of envelope components during the heating season, a decrease of surface temperature is easily registered (Fig. 2). The aim of the present work is to introduce a parameter able to express the thermal bridge effect on the building dispersions, using only the information captured from the thermogram.
ð2Þ
k¼1
where L2D is the linear thermal coupling term derived by the twodimensional calculation, Uk is the thermal transmittance of the kth one-dimensional component (width lk, 1 m length) that separates the internal side from the external environment. Thus, the quantitative classification of thermal bridges is identified by the value of w, that gives the thermal flux transferred per length and temperature units in steady-state conditions. Besides, the linear thermal transmittance determines the thermal field visualized by the IR camera: in winter season, with the same indoor–outdoor temperature difference, thermal bridges with higher dispersions generate thermograms with lower temperature values in the internal side. Hence, starting from the acquisition of the thermal field, it is theoretically possible to go backward to the quantitative evaluation of the thermal bridge, that is the aim of the new parameter definition developed in this work. The definition itself of thermal bridge [19] puts in evidence that it represents a zone with thermal properties significantly different from the rest of the envelope; as a consequence, the temperature of the inner side will be interested by considerable variations in the area influenced by the thermal bridge, assuming on the contrary an almost constant value in the part of the structure where the heat flux can be considered one-dimensional. In this ‘‘undisturbed’’ zone, the temperature is a function of the thickness and thermal conductivity of the layers that constitute the wall; in stationary conditions, the heat flowing through the one-dimensional wall can be written with as follows:
Q 1D ¼ h1D i A1D ðT i T 1D is Þ 4. Description of the methodology adopted for the quantitative analysis of thermal bridges
367
ð3Þ
where h1D_i is the internal liminar coefficient (the reciprocal of the internal surface resistance, which takes into account of both convection and radiation heat transfer), A1D is the area considered and the temperatures Ti and T1D_is represent respectively the inner air temperature (that could be considered equal to the temperature of the inner objects exchanging heat by radiation with the inner wall) and the wall inner surface temperature. When in situ measurements are performed, it is difficult to achieve steady-state conditions, because of the variation of the external temperature and the presence of potentially disturbing factors, therefore, the IR images have to be taken with particular care. In the case of the introduction of a thermal bridge in the area A1D, Eq. (3) is not applicable since the temperature is far from being uniform throughout the entire surface. Analyzing the area with an IR camera, the thermal field of the wall under investigation is available, therefore, a temperature value Tpixel_is could be associated to
Fig. 2. Example of a structural thermal bridge and window thermal bridge at the coupling of glass and frame.
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each pixel that is representative of a part Apixel of the wall surface; the extension of Apixel depends from the instantaneous field of view of the chosen IR camera. Hence, the evaluation of the heat flux is possible in each pixel, obtaining a formulation of the whole area dispersion:
Q tb ¼ htb i Apixel
N X ðT i T pixel is Þ
ð4Þ
p¼1
with the hypothesis of constant liminar coefficient and being N the number of pixels that compose the entire area, according to the relation:
A1D ¼ NApixel
ð5Þ
Then, the incidence factor of the thermal bridge Itb is defined as the ratio between the heat flowing in real conditions and the heat flowing in absence of the thermal bridge:
PN Q tb htb i Apixel p¼1 ðT i T pixel is Þ Itb ¼ ¼ Q 1D h1D i A1D ðT i T 1D is Þ
ð6Þ
i
Therefore, also recalling Eq. (5), the incidence factor of the thermal bridge becomes:
ð7Þ
This quantitative factor could be also expressed in terms of an increase of the thermal transmittance U1D of the undisturbed zone; considering the influence of the thermal bridge, and using the hypothesis of steady-state conditions, the actual value of the wall thermal transmittance Utb can be written as follows:
U tb ¼ U 1D Itb
ð8Þ
The incidence factor of the thermal bridge is connected to the linear thermal transmittance w as defined in Eq. (2), when the thermal transmittance U1D of the undisturbed zone is known:
Itb ¼
Simply subtracting 1 to Itb and multiplying the result by the heat exchanged through the undisturbed wall Q1D, the heat loss due to the thermal bridge is obtained. On the basis of Eq. (6), a methodology of imaging is proposed, aimed at obtaining the data necessary for the evaluation of the two heat fluxes with the only help of the acquisition of the internal environment temperature, minimizing at the same time the sources of errors. For example, considering a structural thermal bridge constituted by a wall angle infinitely high, the thermogram will show a minimum in correspondence of the angle, moving then towards an asymptote that represents the wall behavior in the one-dimensional zone, where the effect of the thermal bridge is negligible (Fig. 3). The choice of the area covered by the imaging plays a fundamental role, since the distance D (Fig. 3) has to be sufficient to include the undisturbed zone, whose temperature value is the term T1D_is of Eq. (6). The advantage of acquiring in the same thermogram both the temperature of the thermal bridge area and the thermal field of the one-dimensional wall consists of avoiding the introduction of further errors linked to different instants of reading or different angles of view. When surfaces with different orientation are contemporarily observed, in fact, the effect of the angle between the viewing direction and the normal to the surface has be taken into account, since the thermal emittance may depend on that angle. Besides, since the domain is limited and the image is captured in the same instant for all the surface, the liminar coefficient could be considered constant throughout the entire area:
h1D i ¼ htb
P P htb i Apixel Np¼1 ðT i T pixel is Þ Apixel Np¼1 ðT i T pixel is Þ ¼ h1D i A1D ðT i T 1D is Þ NApixel ðT i T 1D is Þ PN p¼1 ðT i T pixel is Þ ¼ NðT i T 1D is Þ
Itb ¼
U 1D ðltb þ l1D Þ þ w U 1D ðltb þ l1D Þ
ð9Þ
or
w ¼ ðItb 1ÞU 1D ðltb þ l1D Þ
ð10Þ
5. Model validation In this section the validation process of the methodology described in the previous paragraph is reported. The thermal bridge selected for the purpose is the one generated in a window, by the coupling between the glass and frame (Fig. 2). The choice was dictated by the possibility of installing the window inside an available climatic chamber [20], whose characteristic and dimensions do not permit the testing of a structural thermal bridge. The sample is mounted between two rooms with a temperature difference of about 20 °C, in steady-state, monitored and controlled conditions. The validation of the proposed methodology has been assessed with two different approaches: an instrumental heat flow analysis, where the heat transfer is measured point by point through the window area; a numerical analysis, implementing a two-dimensional model of the node of the window considered 5.1. Thermographic analysis Infrared thermographic measurements were carried out in the lab to verify the various parameters influencing the phenomenon, including steady-state conditions. The window was positioned between a conditioned space, kept at 1 °C, and the laboratory, kept at constant temperature too. The attention was focused on the window’s lower thermal bridge, whose section is characterized by aluminum with polyamide washers to assure the thermal cut.
Fig. 3. Example of an angular thermal bridge and relative thermogram output.
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The glazing (mm 6/7 + mm 15 + mm 8/9, with an aluminum spacer) has the inner side of the external layer covered by a lowemission coating. The IR camera is manufactured by FLIR, model B360 with a FPA microbolometer without cooling, a spectral range from 7.5 and 13.0 lm, and a 320 240 pixel resolution. To quantitatively evaluate the thermal field, it was necessary to perform calibration measurements and to acquire the various parameters to be inserted into the instrument to correct the thermogram. The surface thermal emittance was calculated thanks to surface temperature probes, varying the emissivity in the IR camera, so to obtain the measured temperatures. The reflected temperature was then evaluated with the methodology described in paragraph 2, using an aluminum foil (Fig. 4). Thanks to thermohygrometric probes, environmental conditions were evaluated during the measurements. Also the distance between the sample and the IR camera was registered. A particular attention was paid to the framing, to respect the value of the distance D defined in the previous paragraph. From the standard EN ISO 10077-2 [21], which deals with the numerical calculations for the frames, it emerged that to include in the thermographic image the glass undisturbed area, a distance D from the frame edge of at least 200 mm has to be considered. Fig. 5 shows the thermogram which will be studied, also calculating the incidence factor of the thermal bridge; the thermal bridge is actually composed by the junction between the frame and the glass but, since the length of the opaque part is reduced to few centimeters, the analysis is limited to the transparent portion of the window. The domain considered for the validation process is constituted by an imaginary line (Fig. 5) on the central area of the glass (far away from the lateral thermal bridges). The trend of temperature along the line is shown in the
Fig. 5, where the asymptotic behavior is clearly visible towards the temperature of the undisturbed area (17.7 °C). Calculating the number of pixels that compose the line and applying the above procedure for the evaluation of the incidence factor of the thermal bridge, the value of 1.174 is obtained, with an uncertainty of 6.4%, considering a confidence level equal to 95%. The error rate was estimated referring to the standard ISO/ IEC Guide 98-3:2008 [22], taking into account of the uncertainty associated with the temperature read by the camera, provided its technical data. 5.2. Heat flow analysis Before the execution of the thermographic analysis, a group of temperature and heat flow probes have been placed in the area subjected to investigation. Fig. 6 shows the arrangement, with the sensors following the imaginary line described above. The heat flow probes allow the measurement of the heat flux density (W/ m2) in the undisturbed zone and throughout the whole area of the thermal bridge; the Table 1 reports the values of the heat flow, with the relative areas of interest. In the undisturbed zone only one heat flow meter was placed, while the part closest to the frame and affected by the thermal bridge has been inspected with three heat flow meters, placed one above the other. The incidence factor of the thermal bridge is estimated in the whole surface covered by the measurement line of Fig. 6 using the following equation:
Itb
HFM
¼
Q tb u1D A1D þ utb 1 Atb 1 þ utb 2 Atb 2 þ utb 3 Atb ¼ Q 1D u1D ðA1D þ Atb 1 þ Atb 2 þ Atb 3 Þ
Fig. 4. Measurement of the reflected temperature.
Fig. 5. Thermogram of the lower part of the window and trend of temperature along the imaginary line.
3
ð11Þ
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with an uncertainty of 4.6% (confidence level equal to 95%), derived from the indications of the standard EN ISO 10077-2. 5.4. Comparison between the methodologies Fig. 8 shows the temperature trends of the three different methods along the imaginary line. In the case of the heat flow analysis, the sole points where the temperature probes were placed are reported; from a qualitative point of view, the temperature trend in the thermogram can be compared to the results of some studies found in literature [24]. The three methods show a good agreement, with a light difference in the central area of the thermal bridge. In Fig. 9 the results in terms of the incidence factor of the thermal bridge are sketched, together with the relative uncertainties; it is evident that, considering the confidence interval, data overlap, indicating compatible results and demonstrating the correctness of the method. 6. Application of the methodology to in situ thermal bridges
Fig. 6. Heat flow meters to evaluate the thermal bridge in the transparent part of the window.
Table 1 Heat flow meters results, with the relative areas of interest. Heat flux density (W/m2)
u1D utb_1 utb_2 utb_3
32.8 38.5 46.1 63.4
Area (m2) A1D Atb_1 Atb_2 Atb_3
0.11 0.03 0.03 0.03
The incidence factor of the thermal bridge results equal to 1.228 with an uncertainty of 7.4% (confidence level equal to 95%), associated to the presence of the heat flow probes [22]. 5.3. Numerical analysis The commercial code FLUENT [23] was used for the Computational Fluid Dynamic analysis. The section of the window was modeled taking into account the standard EN ISO 10077-2 [21], to evaluate the thermal properties of the air space and of the materials. Boundary conditions are convective and the cool and hot side temperatures are defined by the laboratory measurements (hot side temperature: 22.2 °C, cold side temperature 0.7 °C), while the liminar coefficients are derived from the standard. As a matter of fact, the window is placed between two spaces whose environmental conditions are similar to the real ones; the cold side is characterized by forced convection while the hot one by natural convection. As far as convection, simulations were therefore carried out with standard conditions, so that the results could be easily extended to the real buildings conditions. The mesh is a triangular one, with a step of about 0.5 mm. Fig. 7 shows the temperature field in the section of the two-dimensional model, together with the temperature trend along the imaginary line of Fig. 6. To evaluate the incidence factor of the thermal bridge, the imaginary line was divided into small segments of the same length of the mesh. The hypothesis allowed to compare the simulation output data with the data taken from the thermogram, assimilating the behavior of a pixel to the one of a single mesh. The value of the incidence factor of the thermal bridge obtained from the simulation is equal to 1.169,
Two different configurations of a floor with a low beam were chosen in situ to evaluate the incidence factor of the thermal bridge. The first configuration presents a correction of the thermal bridge with insulating panels (both inside and outside) while the second one is not insulated at all. In both cases a thermographic image was acquired, including the undisturbed area and measuring at the same time the air temperature. The wall was not exposed to solar radiation; steady-state conditions were assumed, having evaluated the environmental conditions during the periods before the measurement. Also in this case, an imaginary line was considered starting from the internal edge between the floor and the wall (Figs. 10 and 11). Analyzing the trends, two completely different thermal fields can be observed; it is also possible to see the asymptotic part and evaluate the temperature of the undisturbed area. The difference between the two configurations is evident if we compare the two values of the incidence factor of the thermal bridge, which is equal to 1.606 for the configuration with the insulated beam and to 2.000 for the configuration with the non-insulated beam. A further analysis was carried out for the investigated walls, evaluating thanks to a heat flux meter the thermal transmittance (U1D) without the influence of the thermal bridge; the indications of the standard ISO 9869 [25] were followed, using the average method, suitable for the unsteady conditions of the in situ analyses. A plate heat flux meter was positioned in the inner side of the wall, adding a protection from unwanted radiation sources such as artificial lighting, sun or household appliances; the measurement apparatus is completed by the installation of two temperature probes on the internal and external surface of the wall. The average method consists of calculating the instantaneous thermal transmittance as a function of the previous heat flux and temperature values; after a proper acquisition time (minimum three days, seven days for this measurement campaign), the thermal transmittance tends to an asymptote that represents its actual value (Fig. 12). Thanks to the results, it was possible to evaluate the increase in the thermal transmittance of the wall, in the area of the thermal bridge, according to Eq. (8) (Table 2). It is therefore possible to obtain, thanks to the incidence factor of the thermal bridge, quantitative data concerning the thermal bridge even without a detailed knowledge of the stratigraphy of the wall. In the case of the non insulated beam, a further analysis was carried out, since the stratigraphy was known. A computational analysis of the thermal bridge was therefore performed, obtaining
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Fig. 7. Numerical analysis: thermal field in a generic section of the window and temperature trend along the imaginary line.
Fig. 8. Comparison between the temperature trends obtained from the thermogram, the temperature probes and the simulations.
Fig. 9. Plot of the incidence factor of the thermal bridge evaluated through the three different methods, with the relative uncertainties.
a trend of temperatures similar to the real ones and a value of the incidence factor of the thermal bridge equal to 2.111. A model in FLUENT was created to simulate also the correction of the thermal bridge (insulation of the beam); Fig. 13 reports the
comparison between the temperature values along the insulated and the non-insulated beams. It is interesting to note that the curves result very similar to the real ones, reported in Figs. 10 and 11. The calculated value of the incidence factor of the thermal
Fig. 10. Thermogram of the insulated beam and temperature trend along the imaginary line.
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Fig. 11. Thermogram of the non-insulated beam and temperature trend along the imaginary line.
Fig. 12. Specific heat flux, internal–external temperatures and thermal transmittance trends for the in situ measurement of the undisturbed wall insulating properties.
Table 2 Thermal transmittances of both configurations (undisturbed area and area of the thermal bridge).
Insulated beam Non insulated beam
U1D (W/m2 K)
Itb
Utb (W/m2 K)
0.42 0.39
1.606 2.000
0.67 0.78
UNI TS 11300 [26]; an overall heat loss in wintertime of 4684 W was evaluated, 13.4% of which due to the thermal bridge. The correction of the thermal bridge reduces the heat loss to a value of 4307 W and the incidence of the thermal bridge to 8.8%. The analysis allows to evaluate the global effects of the presence of thermal bridges in the envelope’s heat losses and to therefore in the energy primary demand of a building during wintertime. 7. Conclusions
Fig. 13. Simulated temperature trends: comparison between the insulated and the non insulated beam.
bridge is equal to 1.262, so there is a reduction in the thermal bridge heat loss of about 40%. In global terms, it is also possible to evaluate the benefits of such a correction in the heat losses of the whole flat. Simulations of the energy behavior of the flat were carried out according to
The analysis of thermal bridges conducted with the IR thermography can be developed through various approaches, from qualitative investigations to the quantitative techniques of the active thermography. In this work a quantitative factor was introduced, at the aim of evaluating in a simple and effective manner the effect of thermal bridges on the global dispersions of buildings. It was analytically defined the incidence factor of the thermal bridge that depends from the internal air temperature and the internal wall surface temperature, read by the IR camera. Afterwards, results acquired with the thermographic investigation were compared with data obtained by heat flow meters, and the findings of a finite volume analysis; this test was realized in a laboratory setup, where it was possible to monitor the boundary conditions, keeping the stationary conditions for the thermal bridge generated in a window from the coupling of glass and frame. It emerged that the thermal field obtained with the three methods is very similar, producing close values of the incidence factor of the thermal bridge. Two in situ thermal bridges were then investigated, verifying the effect of the insulation on a floor beam; it came out that the incidence factor of the thermal bridge describes correctly the dispersion grade of the singularity, quantifying the result of the thermal bridge correction.
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The factor could be linked the linear thermal transmittance of the thermal bridge and it could be also used to define an increase percentage of the undisturbed wall thermal transmittance, so proposing a simple and useful tool to calculate the actual heat dispersions of buildings by quick and easy in situ thermographic measurements, suggesting at the same time possible interventions for the improvement of insulation. The quantitative thermographic imaging constitutes also a useful mean to analyze, improve and validate 3D simulation tools especially designed for the evaluation of building energy performance [27], since they are capable of evaluating the outdoor and indoor walls thermal fields.
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