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Thermal characterization of homogeneous walls using inverse method
Energy and Buildings 78 (2014) 248–255
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Energy and Buildings journal homepage: www.elsevier.com/locate/enbuild
Thermal characterization of homogeneous walls using inverse method Khaled Chaffar, Alexis Chauchois ∗ , Didier Defer, Laurent Zalewski LGCgE—Laboratory of Civil Engineering and Geo-Environment, Faculty of Applied Sciences of the University of Artois, Technoparc FUTURA, 62400 Béthune, France
a r t i c l e
i n f o
Article history: Received 7 February 2014 Accepted 21 April 2014 Available online 28 April 2014 Keywords: Gypsum tile Inverse method In situ wall thermal properties Infrared thermography Thermophysical properties Building energy saving Experimental methodology
a b s t r a c t Current environmental concerns have promoted efforts to reduce the consumption of energy. In moving towards improving existing buildings, the study of the thermal behaviour of a wall is not easy because its actual thermophysical properties are not well-known. These parameters are nevertheless fundamental for the economic optimisation of building refurbishment or for the verification of their performance in situ. It is thus important to be able to characterize existing building walls. The objective of our study was to develop a method to thermally characterize a wall adapted to in situ applications based on an active approach. The principle of identification consists of thermally examining an access surface by applying a heat flux and studying the response in terms of the temperature recorded by infrared thermography on the opposite surface. Based on signals of flux and of temperatures measured at the edges of the wall, the thermophysical properties (thermal conductivity and volumetric heat) of the wall are estimated by inverse method. The method was applied first to a homogeneous gypsum-tile panel in laboratory. The results were compared to reference values obtained from a classical procedure. Then, the method has been implemented in situ on a homogeneous reinforced concrete shell. © 2014 Elsevier B.V. All rights reserved.
1. Introduction To respond to crucial economic and environmental issues, the energy consumption of buildings has become a major concern of public authorities, of all stakeholders in construction, and of all building managers and users. Among all of the sources of energy waste, the transmission of heat through the envelope of a building is an important energy-performance parameter. In the case of new constructions, planners foresee walls with strong insulating abilities. Nevertheless, once built, walls can exhibit lower performance. Conscientious management of construction, ageing of materials, and humidity all can reduce the thermal resistance of a wall. Materials from agricultural by-products or from recycled products are now more broadly used. These materials often exhibit strong hygroscopicity [1] and a strong ability to settle and lead to a higher variability in the characteristics of walls. For old buildings, the cost of a complete thermal renovation can be high. During a programme of rehabilitation, investments should often be optimised.
∗ Corresponding author. Tel.: +33 3 21 63 71 33/+33 3 21 63 71 31; fax: +33 3 21 63 71 23. E-mail addresses: khaled [email protected] (K. Chaffar), [email protected] (A. Chauchois), [email protected] (D. Defer), [email protected] (L. Zalewski). http://dx.doi.org/10.1016/j.enbuild.2014.04.038 0378-7788/© 2014 Elsevier B.V. All rights reserved.
Different technical options can be considered. For instance replace the windows, the door, upgrade walls insulation and others. The knowledge of thermal properties is essential during the diagnostic phase of wall construction. This knowledge can, among other things, assist in choosing an appropriate renovation strategy. It can allow calculating the return on investment. These problems highlight the interest in being able to estimate the thermal properties of walls in situ. Various approaches have been considered in this regard. There are many methods of non-destructive testing and among them thermal methods [2,3]. Certain methods are based on outfitting walls with temperature and flux sensors [4,5]. These methods require the recording of data during rather long periods, ranging from several hours to several days. The sensors can be left in place for long-term follow-up. A normalised fluxmeter method is presented in the norm EN 12494 [6]. In this case, the conductance of a wall is obtained based on a method of calculating sliding means after at least 72 h of recording. Cucumo et al. [7] have indicated that this method has its limitations and that it is important for the thermal energy stored in the wall to be negligible in comparison with the energy passing through the wall during the test period. These researchers proposed an alternative data analysis based on modelling using finite differences in heat transfer through the wall. Peng et al. [8] made measurements in buildings and used recordings made over the period of one year in three different ways.
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Nomenclature h q0 qe x x ∂/∂x t t Tin Troom Ts
surface film coefficient (W m−2 K−1 ) density of heat flux (W m−2 ) density of surface flux (W m−2 ) Cartesian coordinate axial pitch (cm) spatial derivation time (s) time steps (s) evolution of simulated temperature (◦ C) room temperature (◦ C) surface temperature (◦ C)
Greek symbols thermal conductivity (W m−1 K−1 ) specific heat (J K−1 m−3 ) c Index 0 e n i
heat pulse surface flux index of the parameter considered index
These researchers observed that the conductance values that were obtained experimentally were inferior to those calculated according to the design data. Wu et al. [9] proposed a method based on the frequency analysis of the evolution of flux and temperature. This method allows the conductance and global capacity of the wall to be estimated. Several authors have demonstrated that infrared thermography is a useful tool for inspecting the elements of construction and that it allows for the evaluation of the thermal behaviour of walls [10]. Measurement by infrared thermography [11] has the advantage of being a non-contact, non-intrusive approach and of not modifying the heat exchanges on the surface being observed. However, the radiation perceived by the camera is the result of many phenomena: surface emission, radiation emitted by the atmosphere and its reflection by, for instance, the surface and absorption by the atmosphere. This radiation depends largely on environmental conditions [12]. To the best of our knowledge, in situ applications of this technique for the characterization of walls have only been used in combination with passive approaches, i.e., with specifically implemented thermal stresses. Certain hypotheses on how to fully exploit the quantitative information gathered from measurements performed have been proposed, the validity of which may be debatable. To estimate conductance, Albatici et al. [13] measured, by infrared thermography, the exterior surface temperature of a wall and the interior surface temperature of the surrounding building while suddenly opening a window. This method requires considering the wind speed and the temperature of the object representing the temperature of the exterior environment, as well as estimating the emissivity of the exterior surface of the wall. This article presents an original set-up of thermal solicitation combined with temperature measurements by infrared (IR) thermography intended for the in situ determination of the thermophysical properties of building envelop. The method is different from the classic Flash method [14] as it is applied in situ, and the size of the samples is bigger: in fact, we cannot use optical excitation (e.g., halogen lamps) to perform the measurements in a uniform manner because of the large size of the studied zone (and especially in in situ conditions). The procedure consists of applying a heat solicitation on one of the surfaces of the panel being studied (Fig. 1) and recording the evolution of the temperature on the other
Fig. 1. Scheme of the protocol.
surface by means of an IR camera. This allows a non-contact measurement of temperature evolution and to assess the homogeneity of the temperature. (This verifies that the assumption of unidirectionality is verified.) The characteristics of the panel are obtained using an inverse method based on a finite-difference model. In this first phase, the method is intended to study the running part of a panel, where the conduction of heat can be considered to be unidirectional. To test our procedure, the goal was to be able to determine the thermophysical properties of a panel based on trials lasting approximately one day. The first trials were performed on homogeneous panels in a laboratory. 2. Theoretical aspects In this study, the thermal parameters of a panel were identified by an inversion process [15]. The identification was intended to determine the grouping of the parameters of a model that allows the numerical minimisation of the deviation between the measured and simulated surface temperatures. A numerical model allowing for the calculation of the surface temperature of the wall in response to a flux stress on the other surface was developed. The model was integrated into an inversion algorithm with the goal of identifying the thermophysical parameters of the wall tested. Note that an analytical solution for the temperature evolution of the rear surface of the sample is not given. It could be only given in the case of a Dirac impulsion signal 2.1. Numerical model A numerical model with finite differences was programmed in the Matlab® environment. This model simulates the monodimensional diffusion of heat based on a discretisation of the heat equation. An implicit schema was retained, as it authorises the unconstrained choice of the steps for spatial discretisation and steps for time. The heat equation was discretised based on a secondorder central differentiation.
∂2 T ∂x2
= i,n+1
n+1 n+1 Ti−1 − 2Tin+1 + Ti+1
(x)
2
+ 0 (x)
2
(1)
where T (x, t) = T (i x, n t) = Tin . The panel was assumed to be in a steady initial state. The temperature field within the material depends on temporal variations in temperature and flux density at the geometric limits of the environment. The boundary conditions were defined as follows:at x = 0, the panel is subjected to a heat pulse −
∂T = q0 ∂x
(2)
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where q0 is the density of thermal flux imposed on the “outside surface” of the panel (i.e., x = 0).at x = e, −
∂T = qe ∂x
(3)
where qe designates the density of flux exchanged between the “inside surface” and the environment (i.e., x = e). This process is a global exchange that can be expressed at any moment as follows: qe = h(Ts − Troom )
(4)
where h designates the surface film coefficient, Ts the temperature of the “inside surface”, and Troom is the operative temperature of the environment which corresponds in this study at the operative temperature of the room. At the beginning of the trial, the temperature profile is considered to be linear between the two surfaces of the wall for all 0 < x < e: T (x, 0) = T0 + (TS − T0 ) ×
x e
(5)
The environmental conditions are much more stable in the interior of a building than in the exterior. In the interior, the room temperature evolves slowly during trials, convective phenomena are much less variable, and the surface is not subjected to significant and random radiation. The inside surface was thus selected to be observed by an IR camera, while the flux stress was applied to the outside surface through a flat heating resistance. The heating resistance and the isolating mattress that kept it placed against the panel were installed sufficiently long before the trial such that the conditions for heat transfer in the panel would be close to the steady-state condition. The entering flux and the temperature of the outside surface were measured precisely by a fluxmeter and thermocouples. The temperature of the inside surface monitored by the camera was measured with a degree of uncertainty essentially linked to the characteristics of the camera and the imprecise knowledge of the emissivity of the surface. It is possible to minimise systematic errors with the normalised surface temperature (t), which is defined as follows: (t) =
[T (t) − T (0)] [Tmax − T (0)]
(6)
For the entire duration of the trial, varies from 0 at time t = 0 and reaches 1, decreasing thereafter. Preliminary measurements have shown that the normalised temperatures calculated based on the temperatures recorded by the infrared camera and those given by several thermocouples were almost identical. 2.2. Sensitivity study The thermal characteristics of the panel were determined by minimising the deviation between the normalised experimental inside surface temperature and the normalised temperature simulated using the numerical model described in Section 2.1. The goal of the sensitivity study that was carried out was to verify that the conductivity and specific heat of the panel have a notable effect on the exit temperature and that it will thus be possible to estimate these parameters. This study was based on the calculation of functions of sensitivity. Following experimental procedures, the evolution of the temperature of the rear surface is simulated when the entry surface of the panel is subjected to a heat solicitation. A variation p in one of the unknown parameters is subsequently incorporated into the model to calculate the relative variation in the normalised temperature. The function of sensitivity Xp [16–18] of the normalised temperature at p is accordingly defined by: Xp (p) =
(p) p/p
(7)
In our case, three parameters are considered to be unknown. These parameters are the conductivity of the panel, the specific heat, and the surface film coefficient h. For this study, the thermophysical parameters can be fixed at values close to the unknown parameters because the curves are only used qualitatively. Fig. 2 represents the functions of sensitivity obtained for a gypsum tile measuring 6.5 cm in thickness and having been stressed by a heat solicitation of 134 W m−2 for over 40 min. The temperature of the normalised inside surface was also traced to facilitate the interpretation. Fig. 2 shows that the normalised temperature is sensitive to the three parameters and that the curves are not proportional. Moreover, the sensitivities are not correlated [19]. This finding leads to the assumption that the simultaneous identification of the three parameters is feasible. The study of sensitivity indicates that the period during which the normalised temperature increases seems to be in line with the stated objectives. During this phase, the normalised temperature is sensitive to conductivity and to specific heat above all, which are the most important parameters to be identified in this study. It would be interesting to be able to limit the study to this phase of rising normalised temperature, for this would allow us to experimentally determine the end of the trial and to limit the measurement time while ignoring the cooling period. 2.3. Inverse method The parameters were determined by estimating the grouping of the parameters (i.e., thermal conductivity, specific heat, surface film coefficient), which allowed for the adjustment of the simulated normalised temperature ,c,h to the experimental temperature exp . This was performed by using an iterative minimisation algorithm for the following F error function:
2 1 ,c,h (i) − (i) n n
F (, c, h) =
(8)
i=1
The Levenberg–Marquardt [20,21] algorithm was used in this study. The method of least squares has become a standard technique of minimisation for non-linear problems. 3. Experimental aspects 3.1. Experimental setup The first trials were performed in the laboratory. The experimental design is illustrated in Fig. 3. The panel, which measured 1.8 m × 1.2 m, was constructed of gypsum tile. The panel has a thickness of 6.5 cm. The gypsum tile was the subject of prior characterization using a fluxmeter bench. The conductivity was determined according to the norm ISO NF EN 12664 [22]. The study of the storage phase using this same bench allowed for the determination of the specific heat. We obtained the values = 0.31 W m−1 K−1 and c = 1.2 × 106 J K−1 m−3 . These values are considered to be the reference values for this study. On the outside surface (the side with the stress), a surface measuring 0.9 m × 1.1 m was covered with a flat heating resistance. The resistance was pressed against the panel by a polystyrene panel measuring 18 cm in thickness. The insulation directed most of the power dissipated by the resistance into the panel being tested (i.e., onto a surface area of 0.9 × 1.1 m2 ). The large stressed surface guaranteed unidirectional conduction along the central zone being observed. A 0.5 mm-thick fluxmeter was inserted between the resistance and the gypsum to measure the flux density entering the panel. This measured flux density was taken as the boundary condition for the entry to the panel. The fluxmeter had previously been calibrated [23–25]. The resistance was connected to a
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Fig. 2. Normalised temperature and functions of sensitivity of temperature normalised to parameters.
controllable DC voltage generator. In this study, the resistance was fed by voltage variations. Other forms of stress could be envisaged. In this study, a thermocouple denoted by 1 in Fig. 3 is placed on the inside surface to ensure the stability of the system before beginning heating and to set the initial temperature condition for simulations. The resulting room temperature on the interior side was measured with the aid of a “black ball” type probe (thermometer measuring the radiant temperature). The measured temperature was used in the numerical simulation to determine the surface film coefficient between the panel and the surrounding environment.
On the interior side, an infrared camera was positioned 1 m from the panel [26]. The camera was a CEDIP Silver 420M camera with a matrix of 320 × 240 Insb detectors, which have a spectral sensitivity that is situated in the medium infrared, i.e., 3–5 m. A 24◦ × 32◦ lens was used in this study. A far infrared camera (8–14 microns) should rather be used for this application. It would have given a more powerful signal and a more accurate measurement in the ambient temperature range. It would also have been less affected by reflections. The use of the normalized temperature and the interior conditions of measurement reduced the impact of this choice on our results accuracy. The camera was connected to a
Fig. 3. Schema of the associated experimental protocol.
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Fig. 4. Curve for entering flux.
laptop computer that recorded the images. The camera was controlled with the ALTAIR software programme developed by FLIR. The axis of vision of the camera was perpendicular to the surface. To avoid edge effects, only the central part of the image corresponding to a zone of observation of 30 cm × 37 cm was retained for data analysis. A study of temperature uniformity in this zone showed that the temperature deviations that were observed were on the same order of magnitude as the resolution of the camera. The temperature used in the calculation was obtained by averaging the temperatures for each pixel of the zone observed. A fluxmeter was glued to the edge of this zone. The fluxmeter was used in this study to be able to validate the estimated surface film coefficient [27,28] on the exit surface by the inverse method. This instrument was covered with a very fine lining with the same characteristics for emissivity as the panel. T-type thermocouples were also placed on the inside surface to validate the quality of the normalised temperature obtained based on the measurement by infrared thermography. The thermocouples and the fluxmeters were connected to a multimeter Keithley 2700 datalogger, which measures low voltages with high precision. To avoid the problems associated with cold-juncture correction in the multimeter, the temperatures were measured differentially with respect to a thermal mass with a temperature that was monitored with a precision platinum sensor. 3.2. Conducting a trial The initial conditions of the numerical model correspond to those of steady-state conduction. Each trial begins after a resting time that is sufficiently long to guarantee that the temperature field in the panel is invariant. This condition is easy to obtain in the laboratory. For the in situ trials, it was necessary to install the heating resistance and the insulating plate on the outside surface of the panel several hours before the trial such that the panel would not be subjected to highly variable exterior conditions. The interior conditions were much more stable, allowing the trial to begin under favourable conditions. The infrared camera was switched on two hours before the trial to limit the effect of a possible temperature drift during measurement. The fluxes on the inside and outside surfaces, the resulting room temperature on the inside surface, and the images delivered by the camera are recorded simultaneously. For the trials that produced the results that are presented in this study, the acquisitions were performed every 20 s. The heating resistance was fed by an electrical supply for 40 min. Fig. 4 illustrates the flux density entering the panel measured by the fluxmeter. The flux imposed in this test is from 0 to about 130 W m−2 for about 3000 s then quickly returns to zero (the transitory phases
Fig. 5. Normalised temperature over time (infrared measurement).
indicate that it is important to proceed to measure the flux density). The thick layer of insulation causes the flux to return rapidly to zero. The normalised inside surface temperature obtained through thermographic measurement is plotted in Fig. 5. To show the complete evolution of the fluxes and of the temperatures, the data were recorded for more than 4 h, but for the data analysis, only the elevation phase of the temperature was used. Let us recall that this phase, described in Section 2.2, is the zone that is the most suitable for the identification of the parameters. This phase lasts for approximately 1 h and 30 min for the panel tested in this study. This duration depends on the stress imposed and on the properties of the panel. The inversion scheme was implemented to determine the thermal conductivity, specific heat, and the surface film coefficient, which allowed for the adjustment of the simulated normalised inside surface temperature to the measured temperature. Fig. 6 shows the measured normalised temperature and the optimised normalised temperature as a function of time. A good agreement between the curves can be observed. The optimised normalised temperature was obtained using the following values: = 0.30 W m−1 K−1 and c = 1.1 × 106 J K−1 m−3 and h = 7.5 W m−2 K−1 . The deviation is less than 4% for conductivity with regard to the reference value and less than 8% for specific heat. The stronger sensitivity of the exit temperature to conductivity explains the better precision achieved for this parameter. To assess the quality of the estimation of the surface film coefficient, the coefficient h was calculated for each acquisition based on relation (4) with the temperature and flux measured from the rear surface of the panel. Fig. 7 shows the values of h calculated at each moment.
Fig. 6. Normalised curves measured and simulated for the gypsum tile.
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Table 1 Identified parameters based on the various trials. Identified parameters
Trial
No. 1 No. 2 No. 3 No. 4 No. 5 No. 6 Mean Standard deviation
Experimental parameter
(W m−1 K−1 )
c (J K−1 m−3 )
Global exchange coefficient (W m−2 K−1 )
Experimental (h)
0.30 0.29 0.28 0.31 0.31 0.32 0.30 0.012
1.1 × 106 1.1 × 106 1.15 × 106 1.16 × 106 1.2 × 106 1.2 × 106 1.15 × 106 0.04
7.5 7.4 7 7.1 6.5 6.8 7.04 0.34
7.3 7.8 7.5 7.7 7.1 7.3 7.45 0.24
Table 2 Reference value and the results of the inversion procedure.
Thickness (cm) (W m−1 K−1 ) c (J K−1 m−3 ) h (W m−2 K−1 )
Reference values
Results of the inversion procedure
6.5 0.31 1.2 × 106 7.45
Assumed known value 0.30 1.15 × 106 7.04
Error (%)
3 4 5.5
In the first part of the trial, the deviation in temperature between the surface and the environment appears weak. This produces a reduced exchange between the surface and the surrounding environment and a significant uncertainty regarding the surface film coefficient. Next, the estimated value of the surface film coefficient stabilises. The mean calculated experimental value for times greater than 6000 s is 7.3 W m−2 K−1 . This finding is in good agreement with the predicted value [7.5 W m−2 K−1 ]. The deviation is less than 3%. To study the reproducibility of the method, a series of 6 trials was performed under almost identical conditions. The results are shown in Table 1. The trials were performed in the laboratory, but it was impossible to ensure that surface film coefficients would remain the same from one trial to another. Thus, we observed a more significant dispersion in the value of h. The values shown for Table 1 indicate good reproducibility for the identification procedure. Table 2 shows the mean values that we obtained through this optimisation. The technique produced results close to the reference values with a deviation of 3% for the mean conductivity and of 4% for the mean specific heat. Although the values for the surface film coefficient h depend strongly on the environmental conditions of the trials, the deviation between the optimised mean value and the experimental mean value was low (5.5%).
Fig. 7. The curve of the surface film coefficient as a function of time.
Fig. 8. (In situ) curve for entering flux.
4. In situ experiments 4.1. Experimental setup The wall studied in this part is a reinforced concrete shell of 15 cm thickness. It is an old workshop wall, not isolated. The measurement was performed in summer, which explains the small temperature gradient between the inside and outside. The
Fig. 9. (In situ) normalised temperature over time (infrared measurement).
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Fig. 10. Normalised curves measured and simulated for in situ concrete wall.
experimental conditions are identical to those described in the laboratory experiment. The heating resistance and the insulating plate installed on the outside surface of the wall 10 h before the trial in order to obtain a steady state. The heating time is 120 min. Upon setting of the resistance heater, the infrared camera records every 20 s a thermogram of the rear face of the wall (inside of building where the measurement conditions are much more stable). The data acquisition lasts 22 h, but only the ascending part of the temperature curve (approximately 6 h) is sufficient to obtain the parameters. It is noted that the shape of the flux stress (Fig. 8) can be varied at will during the test based on the observation of the real-time response. Here for example, the injected power was increased during the test by the operator to increase the amplitude of the front temperature. Monitoring the temperature of the entry surface allows to act in real time on request to ensure the best possible dynamic temperatures to improve the signal/noise ratio to identify thermal quantities. On the other hand this is possible because the entering flux used as a boundary condition in the simulation is measured by the fluxmeter. This is one of the advantages of the method which can be applied with any type of stress. Fig. 9 shows the change in temperature of the rear face of the reinforced concrete wall measured at the centre of the image by the infrared camera. The results are shown in Table 3. The trials were performed in situ and in real conditions with occupants and the ambient conditions of the building.
Table 3 In situ identified parameters based on the various trials. Identified parameters
Trial −1
(W m No. 1 No. 2
2.38 2.5
−1
K
)
c (J K−1 m−3 )
h (W m−2 K−1 )
2.35 × 106 2.25 × 106
6.1 5.6
The produced results are close to the reference values (concrete (2% steel) = 2.5 W m−1 K−1 ; concrete (1% steel) = 2.3 W m−1 K−1 ) [29] (Fig. 10). The results, reported in the table above, show that the conductivity and the specific heat of an in situ panel appear to be identified and satisfied relatively close to the reference values; in this way the validity of the present methodology was demonstrated.
5. Conclusion and perspectives The thermophysical parameters of a homogeneous panel can be determined by imposing a flux on one of its surfaces and monitoring the evolution of its temperature on the other surface. A finite-difference model can be used to simulate the temperature response. By the inverse method, thermal conductivity, the specific heat of the panel, and the surface film coefficient between the panel and its surrounding environment can be identified. This method allows the characterization of the thermophysical properties of an in situ panel in a non-destructive way over several hours with a set-up that is light and easy to use. A preliminary series of six trials was performed on a panel of gypsum tiles. Estimates of the conductivity and specific heat were obtained with good reproducibility and with deviations of 3 and 4%, respectively, with respect to the reference values. The results were satisfactory for this first application, and the detection set-up was designed to be portable. Thus, we could consider conducting trials in situ. The wall studied was a reinforced concrete shell of 15 cm thickness. It is a former atelier wall. The results of the conductivity and specific heat were obtained closely to the reference values. As long as the output temperature in response to a flux stress on the other surface can be simulated with sufficient accuracy, the method can be adapted. It is possible in case of 1D or 2D transfer with a suitable model. It seems to be more difficult with glass facades and even impossible with ventilated walls where there is several output for the heat. Regarding heavy or light structures, method accuracy is linked to the answer amplitude and could lead to excitation adjustments. The trial duration changes
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with materials thickness and materials thermophysical properties. Indeed, various developments are envisaged. In the short term, studies on the stress signal will be performed to optimise it. This investigation could improve the quality of the estimates. Another objective is to extend the technique to the multilayer walls of buildings which will allow taking into consideration this common occurrence. Measurement by thermography can also be used profitably to study multidimensional heat transfer, as in the case of masonry walls. Acknowledgements The authors are very grateful to the Pas-de-Calais Habitat and Nord Pas-de-Calais Region for financing Ph.D. thesis of Khaled Chaffar. References [1] M. Kunze, J. Merz, W.-J. Hummel, H. Glosch, S. Messner, R. Zengerle, A micro dew point sensor with a thermal detection principle, Measurement Science and Technology 23 (2012) 014004. [2] Stanislaw Chudzik, Measurement of thermal diffusivity of insulating material using an artificial neural network, Measurement Science and Technology 23 (2012) 065602. [3] J.D. Gabano, T. Poinot, Fractional modelling applied to heat conductivity and diffusivity estimation, Physica Scripta 2009 (2009) 014015. [4] D. Defer, E. Antczak, B. Duthoit, Measurement of low-thermal effusivity of building materials using thermal impedance method, Measurement Science and Technology 12 (2001) 549. [5] Didier Defer, Emmanuel Antczak, Bruno Duthoit, The characterization of thermophysical properties by thermal impedance measurements taken under random stimuli taking sensor-induced disturbance into account, Measurement Science and Technology 9 (1998) 496. [6] EN 12494, European Standard Building Components and Elements. In Situ Measurement of the Surface to Surface Thermal Resistance, CEN, Brussels, 1996 August. [7] M. Cucumo, A. De Rosa, V. Ferraro, D. Kaliakatsos, V. Marinelli, A method for the experimental evaluation in situ of the wall conductance, Energy and Buildings 38 (2006) 238–244. [8] C. Peng, Z. Wua, In situ measuring and evaluating the thermal resistance of building construction, Energy and Buildings 40 (2008) 2076–2082. [9] T. Wu, E. Antczak, D. Defer, T. Chartier, Thermal characteristics in situ monitoring of detached house wall constituted by raw clay, European Journal of Environmental and Civil engineering 14 (2010) 653–667. [10] E. Grinzato, State of the art and perspective of infrared thermography applied to building science, in: C. Meola (Ed.), Infrared Thermography: Recent Advances and Future Trends, Bentham Science Publishers Ltd., Italy, 2012, pp. 200–229, http://dx.doi.org/10.2174/97816080514341120101, eISBN: 9781-60805-143-4. ISBN: 978-1-60805-521-0. (Chapter 9). [11] X.P. Maldague, Theory and Practice of Infrared Technology for Nondestructive Testing, Wiley, New York, NY, 2001. [12] M.Y.L. Chew, Assessing building fac¸ades using infra-red thermography, Structural Survey 16 (1998) 81–86.
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[13] R. Albatici, M. Arnaldo, Tonelli, Infrared thermovision technique for the assessment of thermal transmittance value of opaque building elements on site, Energy and Buildings vol. 42 (2010) 2177–2183. [14] W.J. Parker, W.J. Jenkins, C.P. Butler, G.L. Abbott, Flash method of determining thermal diffusivity, heat capacity and thermal conductivity, Journal of Applied Physics 32 (1961) (1961) 1679–1684. [15] Oleg M. Alifanov, Inverse heat transfer problems, in: International Series in Heat and Mass Transfer, Springer-Verlag Telos, 1994, ISBN-10: 0387536795, ISBN-13: 978-0387536798. [16] O. Carpentier, D. Defer, E. Antczak, A. Chauchois, B. Duthoit, In situ thermal properties characterization using frequential methods, Energy and Buildings 40 (2008) 300–307. [17] Y. Gao, D. Defer, E. Antczak, O. Carpentier, Mise au point d’une sonde destinée à la mesure simultanée de l’effusivité et de la diffusivité thermiques d’un matériau granulaire, in: XXVI Rencontres Universitaires de Génie Civil, 4 au 6 Juin, 2008. [18] A. Chauchois, E. Antczak, D. Defer, O. Carpentier, Formalism of thermal waves applied to the characterization of materials thermal effusivity, Review of Scientific Instruments 7 (2011) 82. [19] F. Brachelet, T. Du, D. Defer, E. Antczak, Détermination de la diffusivité thermique et de l’épaisseur du béton d’enrobage par thermographie infrarouge, in: XXIXe Rencontres Universitaires de Génie Civil, Tlemcen, 29 au 31, Mai, 2011. [20] K. Levenberg, A method for the solution of certain non-linear problems in least squares, Quarterly of Applied Mathematics 2 (2) (1944) 164–168. [21] D.W. Marquardt, An algorithm for the least-squares estimation of non linear parameters, SIAM Journal of Applied Mathematics 11 (2) (1963) 431–441. [22] AFNOR, Association Franc¸aise de Normalisation, NF EN 12664 July 2001 DI 89/106/CE 21/12/1988 Performance thermique des matériaux et produits pour le bâtiment - Détermination de la résistance thermique par la méthode de la plaque chaude gardée et la méthode fluxmétrique - Produits secs et humides de moyenne et basse résistance thermique. [23] D. Leclercq, P. Thery, Apparatus for simultaneous temperature and heat-flow measurements under transient conditions, Review of Scientific Instruments 54 (1983) 374. [24] P. Thery, B. Duthoit, New heat flow sensor for thermal non-destructive testing of wall sections in their natural environment, in: IMEKO TC7. International Symposium on AIMAC91, Japan, 1991, pp. 163–168. [25] S. Lassue, S. Guths, D. Leclercq, B. Duthoit, Natural convection by heat flux measurement and anemometry using thermoelectric effects, Experimental Thermal and Fluid Science 7 no. 1 (2) (1993) 145. [26] S.M. Shepard, Introduction to active thermography for non-destructive evaluation, Anti-Corrosion Methods and Materials 44 (4) (1997) 236–239. [27] L. Zalewski, M. Chantant, S. Lassue, B. Duthoit, Experimental thermal study of a solar wall of composite type, Energy and Buildings 55 (1997) 8–17. [28] S. Lassue, S. Guths, L. Zalewski, Measurement of local convective exchange coefficient with heat flux sensors, in: ASME 2002 Pressure Vessels and Piping Conference Emerging Technologies in Fluids, Structures and Fluid Structure Interactions: Volume 2, Shock, Wave Propagation, Tube Bundle Dynamics, and Structural Dynamics, Vancouver, BC, Canada, August 5–9, 2002, pp. 203–210, http://dx.doi.org/10.1115/PVP2002-1505, Conference Sponsors: Pressure Vessels and Piping Division. ISBN: 0-7918-4657-1. [29] NF EN ISO 13786 July 2008 & ISO 13786:2007 December 2007, Performance thermique des composants de bâtiment – Caractéristiques thermiques dynamiques – Méthodes de calcul. Theme(s): Isolation thermique des bâtiments/Éléments de construction en général.
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Energy and Buildings journal homepage: www.elsevier.com/locate/enbuild
Thermal characterization of homogeneous walls using inverse method Khaled Chaffar, Alexis Chauchois ∗ , Didier Defer, Laurent Zalewski LGCgE—Laboratory of Civil Engineering and Geo-Environment, Faculty of Applied Sciences of the University of Artois, Technoparc FUTURA, 62400 Béthune, France
a r t i c l e
i n f o
Article history: Received 7 February 2014 Accepted 21 April 2014 Available online 28 April 2014 Keywords: Gypsum tile Inverse method In situ wall thermal properties Infrared thermography Thermophysical properties Building energy saving Experimental methodology
a b s t r a c t Current environmental concerns have promoted efforts to reduce the consumption of energy. In moving towards improving existing buildings, the study of the thermal behaviour of a wall is not easy because its actual thermophysical properties are not well-known. These parameters are nevertheless fundamental for the economic optimisation of building refurbishment or for the verification of their performance in situ. It is thus important to be able to characterize existing building walls. The objective of our study was to develop a method to thermally characterize a wall adapted to in situ applications based on an active approach. The principle of identification consists of thermally examining an access surface by applying a heat flux and studying the response in terms of the temperature recorded by infrared thermography on the opposite surface. Based on signals of flux and of temperatures measured at the edges of the wall, the thermophysical properties (thermal conductivity and volumetric heat) of the wall are estimated by inverse method. The method was applied first to a homogeneous gypsum-tile panel in laboratory. The results were compared to reference values obtained from a classical procedure. Then, the method has been implemented in situ on a homogeneous reinforced concrete shell. © 2014 Elsevier B.V. All rights reserved.
1. Introduction To respond to crucial economic and environmental issues, the energy consumption of buildings has become a major concern of public authorities, of all stakeholders in construction, and of all building managers and users. Among all of the sources of energy waste, the transmission of heat through the envelope of a building is an important energy-performance parameter. In the case of new constructions, planners foresee walls with strong insulating abilities. Nevertheless, once built, walls can exhibit lower performance. Conscientious management of construction, ageing of materials, and humidity all can reduce the thermal resistance of a wall. Materials from agricultural by-products or from recycled products are now more broadly used. These materials often exhibit strong hygroscopicity [1] and a strong ability to settle and lead to a higher variability in the characteristics of walls. For old buildings, the cost of a complete thermal renovation can be high. During a programme of rehabilitation, investments should often be optimised.
∗ Corresponding author. Tel.: +33 3 21 63 71 33/+33 3 21 63 71 31; fax: +33 3 21 63 71 23. E-mail addresses: khaled [email protected] (K. Chaffar), [email protected] (A. Chauchois), [email protected] (D. Defer), [email protected] (L. Zalewski). http://dx.doi.org/10.1016/j.enbuild.2014.04.038 0378-7788/© 2014 Elsevier B.V. All rights reserved.
Different technical options can be considered. For instance replace the windows, the door, upgrade walls insulation and others. The knowledge of thermal properties is essential during the diagnostic phase of wall construction. This knowledge can, among other things, assist in choosing an appropriate renovation strategy. It can allow calculating the return on investment. These problems highlight the interest in being able to estimate the thermal properties of walls in situ. Various approaches have been considered in this regard. There are many methods of non-destructive testing and among them thermal methods [2,3]. Certain methods are based on outfitting walls with temperature and flux sensors [4,5]. These methods require the recording of data during rather long periods, ranging from several hours to several days. The sensors can be left in place for long-term follow-up. A normalised fluxmeter method is presented in the norm EN 12494 [6]. In this case, the conductance of a wall is obtained based on a method of calculating sliding means after at least 72 h of recording. Cucumo et al. [7] have indicated that this method has its limitations and that it is important for the thermal energy stored in the wall to be negligible in comparison with the energy passing through the wall during the test period. These researchers proposed an alternative data analysis based on modelling using finite differences in heat transfer through the wall. Peng et al. [8] made measurements in buildings and used recordings made over the period of one year in three different ways.
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Nomenclature h q0 qe x x ∂/∂x t t Tin Troom Ts
surface film coefficient (W m−2 K−1 ) density of heat flux (W m−2 ) density of surface flux (W m−2 ) Cartesian coordinate axial pitch (cm) spatial derivation time (s) time steps (s) evolution of simulated temperature (◦ C) room temperature (◦ C) surface temperature (◦ C)
Greek symbols thermal conductivity (W m−1 K−1 ) specific heat (J K−1 m−3 ) c Index 0 e n i
heat pulse surface flux index of the parameter considered index
These researchers observed that the conductance values that were obtained experimentally were inferior to those calculated according to the design data. Wu et al. [9] proposed a method based on the frequency analysis of the evolution of flux and temperature. This method allows the conductance and global capacity of the wall to be estimated. Several authors have demonstrated that infrared thermography is a useful tool for inspecting the elements of construction and that it allows for the evaluation of the thermal behaviour of walls [10]. Measurement by infrared thermography [11] has the advantage of being a non-contact, non-intrusive approach and of not modifying the heat exchanges on the surface being observed. However, the radiation perceived by the camera is the result of many phenomena: surface emission, radiation emitted by the atmosphere and its reflection by, for instance, the surface and absorption by the atmosphere. This radiation depends largely on environmental conditions [12]. To the best of our knowledge, in situ applications of this technique for the characterization of walls have only been used in combination with passive approaches, i.e., with specifically implemented thermal stresses. Certain hypotheses on how to fully exploit the quantitative information gathered from measurements performed have been proposed, the validity of which may be debatable. To estimate conductance, Albatici et al. [13] measured, by infrared thermography, the exterior surface temperature of a wall and the interior surface temperature of the surrounding building while suddenly opening a window. This method requires considering the wind speed and the temperature of the object representing the temperature of the exterior environment, as well as estimating the emissivity of the exterior surface of the wall. This article presents an original set-up of thermal solicitation combined with temperature measurements by infrared (IR) thermography intended for the in situ determination of the thermophysical properties of building envelop. The method is different from the classic Flash method [14] as it is applied in situ, and the size of the samples is bigger: in fact, we cannot use optical excitation (e.g., halogen lamps) to perform the measurements in a uniform manner because of the large size of the studied zone (and especially in in situ conditions). The procedure consists of applying a heat solicitation on one of the surfaces of the panel being studied (Fig. 1) and recording the evolution of the temperature on the other
Fig. 1. Scheme of the protocol.
surface by means of an IR camera. This allows a non-contact measurement of temperature evolution and to assess the homogeneity of the temperature. (This verifies that the assumption of unidirectionality is verified.) The characteristics of the panel are obtained using an inverse method based on a finite-difference model. In this first phase, the method is intended to study the running part of a panel, where the conduction of heat can be considered to be unidirectional. To test our procedure, the goal was to be able to determine the thermophysical properties of a panel based on trials lasting approximately one day. The first trials were performed on homogeneous panels in a laboratory. 2. Theoretical aspects In this study, the thermal parameters of a panel were identified by an inversion process [15]. The identification was intended to determine the grouping of the parameters of a model that allows the numerical minimisation of the deviation between the measured and simulated surface temperatures. A numerical model allowing for the calculation of the surface temperature of the wall in response to a flux stress on the other surface was developed. The model was integrated into an inversion algorithm with the goal of identifying the thermophysical parameters of the wall tested. Note that an analytical solution for the temperature evolution of the rear surface of the sample is not given. It could be only given in the case of a Dirac impulsion signal 2.1. Numerical model A numerical model with finite differences was programmed in the Matlab® environment. This model simulates the monodimensional diffusion of heat based on a discretisation of the heat equation. An implicit schema was retained, as it authorises the unconstrained choice of the steps for spatial discretisation and steps for time. The heat equation was discretised based on a secondorder central differentiation.
∂2 T ∂x2
= i,n+1
n+1 n+1 Ti−1 − 2Tin+1 + Ti+1
(x)
2
+ 0 (x)
2
(1)
where T (x, t) = T (i x, n t) = Tin . The panel was assumed to be in a steady initial state. The temperature field within the material depends on temporal variations in temperature and flux density at the geometric limits of the environment. The boundary conditions were defined as follows:at x = 0, the panel is subjected to a heat pulse −
∂T = q0 ∂x
(2)
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where q0 is the density of thermal flux imposed on the “outside surface” of the panel (i.e., x = 0).at x = e, −
∂T = qe ∂x
(3)
where qe designates the density of flux exchanged between the “inside surface” and the environment (i.e., x = e). This process is a global exchange that can be expressed at any moment as follows: qe = h(Ts − Troom )
(4)
where h designates the surface film coefficient, Ts the temperature of the “inside surface”, and Troom is the operative temperature of the environment which corresponds in this study at the operative temperature of the room. At the beginning of the trial, the temperature profile is considered to be linear between the two surfaces of the wall for all 0 < x < e: T (x, 0) = T0 + (TS − T0 ) ×
x e
(5)
The environmental conditions are much more stable in the interior of a building than in the exterior. In the interior, the room temperature evolves slowly during trials, convective phenomena are much less variable, and the surface is not subjected to significant and random radiation. The inside surface was thus selected to be observed by an IR camera, while the flux stress was applied to the outside surface through a flat heating resistance. The heating resistance and the isolating mattress that kept it placed against the panel were installed sufficiently long before the trial such that the conditions for heat transfer in the panel would be close to the steady-state condition. The entering flux and the temperature of the outside surface were measured precisely by a fluxmeter and thermocouples. The temperature of the inside surface monitored by the camera was measured with a degree of uncertainty essentially linked to the characteristics of the camera and the imprecise knowledge of the emissivity of the surface. It is possible to minimise systematic errors with the normalised surface temperature (t), which is defined as follows: (t) =
[T (t) − T (0)] [Tmax − T (0)]
(6)
For the entire duration of the trial, varies from 0 at time t = 0 and reaches 1, decreasing thereafter. Preliminary measurements have shown that the normalised temperatures calculated based on the temperatures recorded by the infrared camera and those given by several thermocouples were almost identical. 2.2. Sensitivity study The thermal characteristics of the panel were determined by minimising the deviation between the normalised experimental inside surface temperature and the normalised temperature simulated using the numerical model described in Section 2.1. The goal of the sensitivity study that was carried out was to verify that the conductivity and specific heat of the panel have a notable effect on the exit temperature and that it will thus be possible to estimate these parameters. This study was based on the calculation of functions of sensitivity. Following experimental procedures, the evolution of the temperature of the rear surface is simulated when the entry surface of the panel is subjected to a heat solicitation. A variation p in one of the unknown parameters is subsequently incorporated into the model to calculate the relative variation in the normalised temperature. The function of sensitivity Xp [16–18] of the normalised temperature at p is accordingly defined by: Xp (p) =
(p) p/p
(7)
In our case, three parameters are considered to be unknown. These parameters are the conductivity of the panel, the specific heat, and the surface film coefficient h. For this study, the thermophysical parameters can be fixed at values close to the unknown parameters because the curves are only used qualitatively. Fig. 2 represents the functions of sensitivity obtained for a gypsum tile measuring 6.5 cm in thickness and having been stressed by a heat solicitation of 134 W m−2 for over 40 min. The temperature of the normalised inside surface was also traced to facilitate the interpretation. Fig. 2 shows that the normalised temperature is sensitive to the three parameters and that the curves are not proportional. Moreover, the sensitivities are not correlated [19]. This finding leads to the assumption that the simultaneous identification of the three parameters is feasible. The study of sensitivity indicates that the period during which the normalised temperature increases seems to be in line with the stated objectives. During this phase, the normalised temperature is sensitive to conductivity and to specific heat above all, which are the most important parameters to be identified in this study. It would be interesting to be able to limit the study to this phase of rising normalised temperature, for this would allow us to experimentally determine the end of the trial and to limit the measurement time while ignoring the cooling period. 2.3. Inverse method The parameters were determined by estimating the grouping of the parameters (i.e., thermal conductivity, specific heat, surface film coefficient), which allowed for the adjustment of the simulated normalised temperature ,c,h to the experimental temperature exp . This was performed by using an iterative minimisation algorithm for the following F error function:
2 1 ,c,h (i) − (i) n n
F (, c, h) =
(8)
i=1
The Levenberg–Marquardt [20,21] algorithm was used in this study. The method of least squares has become a standard technique of minimisation for non-linear problems. 3. Experimental aspects 3.1. Experimental setup The first trials were performed in the laboratory. The experimental design is illustrated in Fig. 3. The panel, which measured 1.8 m × 1.2 m, was constructed of gypsum tile. The panel has a thickness of 6.5 cm. The gypsum tile was the subject of prior characterization using a fluxmeter bench. The conductivity was determined according to the norm ISO NF EN 12664 [22]. The study of the storage phase using this same bench allowed for the determination of the specific heat. We obtained the values = 0.31 W m−1 K−1 and c = 1.2 × 106 J K−1 m−3 . These values are considered to be the reference values for this study. On the outside surface (the side with the stress), a surface measuring 0.9 m × 1.1 m was covered with a flat heating resistance. The resistance was pressed against the panel by a polystyrene panel measuring 18 cm in thickness. The insulation directed most of the power dissipated by the resistance into the panel being tested (i.e., onto a surface area of 0.9 × 1.1 m2 ). The large stressed surface guaranteed unidirectional conduction along the central zone being observed. A 0.5 mm-thick fluxmeter was inserted between the resistance and the gypsum to measure the flux density entering the panel. This measured flux density was taken as the boundary condition for the entry to the panel. The fluxmeter had previously been calibrated [23–25]. The resistance was connected to a
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Fig. 2. Normalised temperature and functions of sensitivity of temperature normalised to parameters.
controllable DC voltage generator. In this study, the resistance was fed by voltage variations. Other forms of stress could be envisaged. In this study, a thermocouple denoted by 1 in Fig. 3 is placed on the inside surface to ensure the stability of the system before beginning heating and to set the initial temperature condition for simulations. The resulting room temperature on the interior side was measured with the aid of a “black ball” type probe (thermometer measuring the radiant temperature). The measured temperature was used in the numerical simulation to determine the surface film coefficient between the panel and the surrounding environment.
On the interior side, an infrared camera was positioned 1 m from the panel [26]. The camera was a CEDIP Silver 420M camera with a matrix of 320 × 240 Insb detectors, which have a spectral sensitivity that is situated in the medium infrared, i.e., 3–5 m. A 24◦ × 32◦ lens was used in this study. A far infrared camera (8–14 microns) should rather be used for this application. It would have given a more powerful signal and a more accurate measurement in the ambient temperature range. It would also have been less affected by reflections. The use of the normalized temperature and the interior conditions of measurement reduced the impact of this choice on our results accuracy. The camera was connected to a
Fig. 3. Schema of the associated experimental protocol.
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Fig. 4. Curve for entering flux.
laptop computer that recorded the images. The camera was controlled with the ALTAIR software programme developed by FLIR. The axis of vision of the camera was perpendicular to the surface. To avoid edge effects, only the central part of the image corresponding to a zone of observation of 30 cm × 37 cm was retained for data analysis. A study of temperature uniformity in this zone showed that the temperature deviations that were observed were on the same order of magnitude as the resolution of the camera. The temperature used in the calculation was obtained by averaging the temperatures for each pixel of the zone observed. A fluxmeter was glued to the edge of this zone. The fluxmeter was used in this study to be able to validate the estimated surface film coefficient [27,28] on the exit surface by the inverse method. This instrument was covered with a very fine lining with the same characteristics for emissivity as the panel. T-type thermocouples were also placed on the inside surface to validate the quality of the normalised temperature obtained based on the measurement by infrared thermography. The thermocouples and the fluxmeters were connected to a multimeter Keithley 2700 datalogger, which measures low voltages with high precision. To avoid the problems associated with cold-juncture correction in the multimeter, the temperatures were measured differentially with respect to a thermal mass with a temperature that was monitored with a precision platinum sensor. 3.2. Conducting a trial The initial conditions of the numerical model correspond to those of steady-state conduction. Each trial begins after a resting time that is sufficiently long to guarantee that the temperature field in the panel is invariant. This condition is easy to obtain in the laboratory. For the in situ trials, it was necessary to install the heating resistance and the insulating plate on the outside surface of the panel several hours before the trial such that the panel would not be subjected to highly variable exterior conditions. The interior conditions were much more stable, allowing the trial to begin under favourable conditions. The infrared camera was switched on two hours before the trial to limit the effect of a possible temperature drift during measurement. The fluxes on the inside and outside surfaces, the resulting room temperature on the inside surface, and the images delivered by the camera are recorded simultaneously. For the trials that produced the results that are presented in this study, the acquisitions were performed every 20 s. The heating resistance was fed by an electrical supply for 40 min. Fig. 4 illustrates the flux density entering the panel measured by the fluxmeter. The flux imposed in this test is from 0 to about 130 W m−2 for about 3000 s then quickly returns to zero (the transitory phases
Fig. 5. Normalised temperature over time (infrared measurement).
indicate that it is important to proceed to measure the flux density). The thick layer of insulation causes the flux to return rapidly to zero. The normalised inside surface temperature obtained through thermographic measurement is plotted in Fig. 5. To show the complete evolution of the fluxes and of the temperatures, the data were recorded for more than 4 h, but for the data analysis, only the elevation phase of the temperature was used. Let us recall that this phase, described in Section 2.2, is the zone that is the most suitable for the identification of the parameters. This phase lasts for approximately 1 h and 30 min for the panel tested in this study. This duration depends on the stress imposed and on the properties of the panel. The inversion scheme was implemented to determine the thermal conductivity, specific heat, and the surface film coefficient, which allowed for the adjustment of the simulated normalised inside surface temperature to the measured temperature. Fig. 6 shows the measured normalised temperature and the optimised normalised temperature as a function of time. A good agreement between the curves can be observed. The optimised normalised temperature was obtained using the following values: = 0.30 W m−1 K−1 and c = 1.1 × 106 J K−1 m−3 and h = 7.5 W m−2 K−1 . The deviation is less than 4% for conductivity with regard to the reference value and less than 8% for specific heat. The stronger sensitivity of the exit temperature to conductivity explains the better precision achieved for this parameter. To assess the quality of the estimation of the surface film coefficient, the coefficient h was calculated for each acquisition based on relation (4) with the temperature and flux measured from the rear surface of the panel. Fig. 7 shows the values of h calculated at each moment.
Fig. 6. Normalised curves measured and simulated for the gypsum tile.
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Table 1 Identified parameters based on the various trials. Identified parameters
Trial
No. 1 No. 2 No. 3 No. 4 No. 5 No. 6 Mean Standard deviation
Experimental parameter
(W m−1 K−1 )
c (J K−1 m−3 )
Global exchange coefficient (W m−2 K−1 )
Experimental (h)
0.30 0.29 0.28 0.31 0.31 0.32 0.30 0.012
1.1 × 106 1.1 × 106 1.15 × 106 1.16 × 106 1.2 × 106 1.2 × 106 1.15 × 106 0.04
7.5 7.4 7 7.1 6.5 6.8 7.04 0.34
7.3 7.8 7.5 7.7 7.1 7.3 7.45 0.24
Table 2 Reference value and the results of the inversion procedure.
Thickness (cm) (W m−1 K−1 ) c (J K−1 m−3 ) h (W m−2 K−1 )
Reference values
Results of the inversion procedure
6.5 0.31 1.2 × 106 7.45
Assumed known value 0.30 1.15 × 106 7.04
Error (%)
3 4 5.5
In the first part of the trial, the deviation in temperature between the surface and the environment appears weak. This produces a reduced exchange between the surface and the surrounding environment and a significant uncertainty regarding the surface film coefficient. Next, the estimated value of the surface film coefficient stabilises. The mean calculated experimental value for times greater than 6000 s is 7.3 W m−2 K−1 . This finding is in good agreement with the predicted value [7.5 W m−2 K−1 ]. The deviation is less than 3%. To study the reproducibility of the method, a series of 6 trials was performed under almost identical conditions. The results are shown in Table 1. The trials were performed in the laboratory, but it was impossible to ensure that surface film coefficients would remain the same from one trial to another. Thus, we observed a more significant dispersion in the value of h. The values shown for Table 1 indicate good reproducibility for the identification procedure. Table 2 shows the mean values that we obtained through this optimisation. The technique produced results close to the reference values with a deviation of 3% for the mean conductivity and of 4% for the mean specific heat. Although the values for the surface film coefficient h depend strongly on the environmental conditions of the trials, the deviation between the optimised mean value and the experimental mean value was low (5.5%).
Fig. 7. The curve of the surface film coefficient as a function of time.
Fig. 8. (In situ) curve for entering flux.
4. In situ experiments 4.1. Experimental setup The wall studied in this part is a reinforced concrete shell of 15 cm thickness. It is an old workshop wall, not isolated. The measurement was performed in summer, which explains the small temperature gradient between the inside and outside. The
Fig. 9. (In situ) normalised temperature over time (infrared measurement).
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Fig. 10. Normalised curves measured and simulated for in situ concrete wall.
experimental conditions are identical to those described in the laboratory experiment. The heating resistance and the insulating plate installed on the outside surface of the wall 10 h before the trial in order to obtain a steady state. The heating time is 120 min. Upon setting of the resistance heater, the infrared camera records every 20 s a thermogram of the rear face of the wall (inside of building where the measurement conditions are much more stable). The data acquisition lasts 22 h, but only the ascending part of the temperature curve (approximately 6 h) is sufficient to obtain the parameters. It is noted that the shape of the flux stress (Fig. 8) can be varied at will during the test based on the observation of the real-time response. Here for example, the injected power was increased during the test by the operator to increase the amplitude of the front temperature. Monitoring the temperature of the entry surface allows to act in real time on request to ensure the best possible dynamic temperatures to improve the signal/noise ratio to identify thermal quantities. On the other hand this is possible because the entering flux used as a boundary condition in the simulation is measured by the fluxmeter. This is one of the advantages of the method which can be applied with any type of stress. Fig. 9 shows the change in temperature of the rear face of the reinforced concrete wall measured at the centre of the image by the infrared camera. The results are shown in Table 3. The trials were performed in situ and in real conditions with occupants and the ambient conditions of the building.
Table 3 In situ identified parameters based on the various trials. Identified parameters
Trial −1
(W m No. 1 No. 2
2.38 2.5
−1
K
)
c (J K−1 m−3 )
h (W m−2 K−1 )
2.35 × 106 2.25 × 106
6.1 5.6
The produced results are close to the reference values (concrete (2% steel) = 2.5 W m−1 K−1 ; concrete (1% steel) = 2.3 W m−1 K−1 ) [29] (Fig. 10). The results, reported in the table above, show that the conductivity and the specific heat of an in situ panel appear to be identified and satisfied relatively close to the reference values; in this way the validity of the present methodology was demonstrated.
5. Conclusion and perspectives The thermophysical parameters of a homogeneous panel can be determined by imposing a flux on one of its surfaces and monitoring the evolution of its temperature on the other surface. A finite-difference model can be used to simulate the temperature response. By the inverse method, thermal conductivity, the specific heat of the panel, and the surface film coefficient between the panel and its surrounding environment can be identified. This method allows the characterization of the thermophysical properties of an in situ panel in a non-destructive way over several hours with a set-up that is light and easy to use. A preliminary series of six trials was performed on a panel of gypsum tiles. Estimates of the conductivity and specific heat were obtained with good reproducibility and with deviations of 3 and 4%, respectively, with respect to the reference values. The results were satisfactory for this first application, and the detection set-up was designed to be portable. Thus, we could consider conducting trials in situ. The wall studied was a reinforced concrete shell of 15 cm thickness. It is a former atelier wall. The results of the conductivity and specific heat were obtained closely to the reference values. As long as the output temperature in response to a flux stress on the other surface can be simulated with sufficient accuracy, the method can be adapted. It is possible in case of 1D or 2D transfer with a suitable model. It seems to be more difficult with glass facades and even impossible with ventilated walls where there is several output for the heat. Regarding heavy or light structures, method accuracy is linked to the answer amplitude and could lead to excitation adjustments. The trial duration changes
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