1 Introduction

The achievement of carbon neutrality requires the reduction of the impact of the building sector, the most energy consuming sector. Buildings, in fact, are responsible for almost 40 % of the total CO2 emissions of European countries [1], whose building stock is strongly heterogeneous and changes at a very slow rate [2]. On average, only one building out of ten was built between 2000 and 2008, while almost one out of two has more than 50 years [3]. This consistent part of the actual building stock, mainly built before the introduction of any energy regulation, has poor energy performance, aggravated by old and obsolete equipment and appliances. The energy saving potential of these buildings is therefore huge. The IEA in 2017 estimated that deep energy renovations of existing building envelopes represent a saving potential greater than all the final energy consumed by the G20 countries in 2015, or around 330 EJ in cumulative energy savings to 2060 [4]. Interventions aimed at improving the energy performance of existing buildings are therefore mandatory in order to achieve not only the reduction of greenhouse gas emissions, but also the ambitious goals of reducing energy consumption for heating and cooling and improving indoor environmental quality. The main applied technologies include interventions on the building envelope, on the heating and cooling systems, on the lighting system, and the integration of renewable energy sources [5]. In order to achieve energy efficiency goals, multiple solutions can be combined. However, despite the consistent number of available technologies, several limitations hinder their application, such as design, complexity, integration, regulatory, economic or behavioural limitations.

In this context, phase change materials (PCMs) have been identified as one of the most interesting solution in building energy refurbishment. Being characterized by high energy storage capacity per unit volume at a nearly constant temperature [6], PCMs act as an almost isothermal reservoir of heat [7], making buildings more energy effective [8]. When integrated in the building envelope, PCM increases the thermal mass of the building envelope while undergoing the phase change [9], thus allowing the storage of significant amount of energy without the uncomfortable temperature swings and the large structural mass necessary with sensible heat storage [10]. The remarkable effect a building envelope has on the energy demand for heating and cooling [11] led to much research over the years focusing on the integration of PCM within various building components [12,13,14,15,16,17,18,19,20]. PCMs can be directly integrated in the building structure, such as in bricks or concrete, or in cladding layers, such as in wallboards or plasters. The addition of PCM into the structural parts is possible only in case of new constructions, while the addition into finishing layers is possible in both new constructions as well as building renovations. As regards the focus of this research, PCMs were mixed within plaster, more specifically lime-based ones, considered more compatible with existing historical buildings. In order to maximise the effect of the PCM, the knowledge of the materials’ properties is essential. In addition to this, when dealing with building materials the actual properties does not always agree with those declared [21]. This may be due to the fact that building materials are poorly characterized at laboratory scale, if considering sample sizing several centimetres [22].

The most used technique for the determination of the PCM thermophysical properties is the Differential Scanning Calorimeter (DSC) [23], which consists in the measure of the amount of heat required to warm up and cool down a sample of the material to be tested, which is estimated in comparison to that of a reference material. However, this technique is affected by some critical limitations due to the sample’s properties. In a DSC measure, in fact, the sample size is normally small, less than 15 mg, and has to be pure and homogeneous [24]. Nevertheless, in case of building envelope applications, PCMs are usually added as encapsulated materials, both micro-encapsulated, in the form of powder or granules, as well as macro-encapsulated, such as within plastic or metallic containers. The characterization of a building material enhanced with PCM, therefore, cannot be considered reliable if carried out through a DSC analysis. To overcome these limitations, an alternative set up was considered necessary in order to roughly estimate the new enhanced materials’ thermal properties. Several researchers had already tried in the past to overcome the main instruments’ limitations by developing their own set up.

Yesilata and Turgut [25], for instance, developed a dynamic measurement technique to measure the effective thermal properties of anisotropic materials.

The challenge however gets even harder when PCMs are integrated in the materials to be tested. As already mentioned, PCMs at lab scale are usually tested by means of DSC, which requires small and homogeneous samples, conditions that are hard to achieve. Several researchers worked for the development of new equipment able to use macroscopic samples, more similar to actual constructive systems. Among them, de Gracia et al. [26] developed a new equipment to test the steady and transient thermal response of building materials containing PCM.

Barreneche et al. [22] at the University of Barcelona developed two devices to characterize the effective thermal conductivity and to register the temperature–time response curves of materials including PCMs at macroscale.

Borreguero et al. [27] developed an experimental set up to evaluate the improvement of the thermal storage capacity of gypsum samples integrated with different percentages of PCMs.

Through the customised set up realised at the University of Ferrara [28], the experimental characterisation of two PCM-enhanced plasters was carried out. The thermo-physical characterisation, carried out by means of steady-state as well as unsteady-state tests, was then followed by the properties validation against experimental data, which were gathered under real outdoor conditions. For this research, polymer-bound organic PCMs were used, with phase change temperatures of 27 °C and 28 °C, hereafter named TK27 and AS28, respectively.

2 Methodology

2.1 Thermo-physical Properties Estimation

At first experimental tests inside the climatic chamber were carried out, aimed at characterizing the plaster’s thermal properties, namely the thermal conductivity, the specific heat and the latent heat capacity, using the set up shown in Fig. 1a. Three plaster samples were realised, a lime-based one used as reference, and two in which 10 % by mass of PCM were added. One had a phase change temperature of 27 °C and was purchased from TITK (TK27) [29], while the other one had a phase change temperature of 28 °C and was purchased from Smart Advanced Systems GmbH (AS28) [30]. The PCMs used are shown in Fig. 1b. Both are polymer-bound PCM granules containing, as stated by the suppliers, approximately 75 % of organic PCM. As regards TK27, the bulk density was declared approximately of 550 kg·m−3 with a maximum storage capacity of 186.4 kJ·kg−1 and a peak melting temperature of 28.9 °C. As regards AS28, the bulk density declared was the same as TK27, the storage capacity was 102.5 kJ·kg−1 and the peak melting temperature 30 °C.

Fig. 1
figure 1

(a) Materials and sensors’ position of the experimental set up; (b) PCMs used: top AS28, bottom TK27

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The thermo-physical properties were estimated following the methodology previously reported in [28]. As regards the thermal conductivity, a steady-state test was carried out in order to estimate it through the Fourier’s law reported in Eq. 1:

$$\overline{{\text{q}} }=-\frac{\uplambda }{{\text{d}}}\cdot \Delta {\text{T}},$$
(1)

where \(\overline{{\text{q}} }\) is the average heat flux [W·m−2], \(\uplambda\) the thermal conductivity [W·(m·K)−1], \({\text{d}}\) the material thickness [m], and \(\Delta {\text{T}}\) the difference between the temperatures on the two surfaces of the material [K]. Since the thickness of the materials used in the tests were known and heat flux and temperatures were constantly measured, the thermal conductivity was the only variable which was hence estimated through the following Eq. 2:

$$\uplambda =\left|\frac{{\text{d}}\cdot \overline{{\text{q}}}}{\Delta {\text{T}} }\right|$$
(2)

The constant temperature difference between the surfaces was maintained by keeping the climatic chamber at constant temperature and a constant voltage on the DC power supply. Once reached the equilibrium, thus with no further changes in the heat fluxes or in the temperatures, it was possible to estimate the thermal conductivity. To limit as much as possible any error, the test was carried out with different voltages on the power supply and setting the climatic chamber on two different temperatures in order to estimate the overall thermal conductivity both when the PCM was in its solid form as well as in the liquid one. The value was then obtained as the average of those estimated during each test.

As regards the specific heat and the latent heat capacity, an unsteady-state test was carried out. This test consisted in a two-step ramp, as depicted in Fig. 2. The two ramps were identical in terms of step duration, heating and cooling rates, difference between maximum and minimum temperature, but they were shifted so that one fully included the phase change, the other one was completely out of it. Since the PCMs used had a declared phase change temperature of 27 °C to 28°C, a ramp between 20 °C and 40 °C was meant to include the phase change while a ramp between 35 °C and 55 °C was intended to be out of it. Both the ramps started when the system reached the equilibrium at the lower temperature, hence 20 °C and 35 °C, respectively. The chamber was then brought to the higher temperature, 40 °C and 55 °C, respectively, with a heating rate of 4 K·min−1 and maintained at that temperature for 6 h, in order to allow the system to reach the thermal equilibrium. After that, the system was brought again at the initial lower temperature with a cooling rate of 4 K·min−1 and maintained at that temperature for 6 h to reach the equilibrium again.

Fig. 2
figure 2

Temperature set inside the climatic chamber during the unsteady-state test

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As regards the specific heat [J·(kg·K)−1], only data acquired during the 35 °C-55°C ramp were used. Knowing the heat flux, the initial and final temperatures and the mass, the specific heat could be estimated through the following Eq. 3:

$${{\text{c}}}_{{\text{p}}}=\frac{{\int }_{{\text{t}}}^{{\text{t}}+\Delta {\text{t}}}\mathrm{q dt}}{{\text{m}}\cdot \Delta {\text{T}}},$$
(3)

where \({\text{q}}\) is the heat flux [W·m−2], \({\text{m}}\) is the sample mass [kg], \(\Delta {\text{T}}\) is the temperature difference between the initial and the final temperature [K], and \(\Delta {\text{t}}\) is the ramp duration.

The latent heat capacity [kJ·kg−1] was estimated comparing the two ramps. In fact, with no changes in the configuration, nor in the heating and cooling rates, nor the steps duration, the differences between the ramps were only related to the PCM latent heat capacity, estimated through Eq. 4:

$$\Delta {\text{h}}=\frac{{\text{A}}\left({\int }_{{{\text{t}}}_{1}}^{{{\text{t}}}_{1}+\Delta {\text{t}}}{{\text{q}}}_{{\text{PC}}}\mathrm{ dt}-{\int }_{{{\text{t}}}_{2}}^{{{\text{t}}}_{2}+\Delta {\text{t}}}{{\text{q}}}_{{\text{noPC}}}\mathrm{ dt}\right)}{{\text{m}}},$$
(4)

where \({{\text{q}}}_{{\text{PC}}}\) [W·m−2] is the heat flux during the phase change, \({{\text{q}}}_{{\text{noPC}}}\) [W·m−2] is the heat flux when the phase change did not occur, \({\text{A}}\) is the sample surface [m2], and \({\text{m}}\) is the mass of the plaster sample containing PCM [kg]. Lastly, \({{\text{t}}}_{1}\) and \({{\text{t}}}_{2}\) are the initial time of the phase change and no-phase change ramps, respectively, and \(\Delta {\text{t}}\) is the ramp duration.

Lastly, the uncertainties of the estimated values were determined using Eq. 5 [31]:

$${{\text{u}}}_{{\text{c}}}^{2}\left({\text{y}}\right)=\sum_{{\text{i}}=1}^{{\text{n}}}{\left(\frac{\partial {\text{f}}}{\partial {{\text{x}}}_{{\text{i}}}}\right)}^{2}{{\text{u}}}^{2}\left({{\text{x}}}_{{\text{i}}}\right),$$
(5)

where \({\text{f}}\) is the function defined as \({\text{Y}}={\text{f}}\left({{\text{X}}}_{1}{,{\text{X}}}_{2},\dots {,{\text{X}}}_{{\text{n}}}\right)\).

2.2 Properties Validation

After the tests carried out at lab scale, a bigger experimental set up was designed and realized to simultaneously monitor different wall samples. On one side, this allowed the monitoring of the behaviour of the PCM-enhanced plasters under real weather conditions, on the other, the validation of the estimated properties against experimental data. The installation of the set up was done exploiting an already existing mock up facility (Fig. 3a) at the TekneHub Laboratory at the University of Ferrara, which was built in 2016 within the European project LIFE Climate Change Adaptation—HEROTILE (High Energy savings in building cooling by ROof TILE shape optimization toward a better above sheathing ventilation) [32].

Fig. 3
figure 3

Mock up at the TekneHub Laboratory of the University of Ferrara, (a) before and (b) after the installation of the set up

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The set up realized has an aluminium structure covered by OSB panels, and was designed to test up to four wall samples at the same time. The set up is approximately 0.90 m × 0.90 m × 0.50 m, while each available slot, containing the wall samples, is 0.38 m × 0.38 m × 0.50 m (Fig. 3b). Each wall sample realized consists of a brick layer covered with plaster both on exterior as well as on the interior side. However, in order to ensure the maximum flexibility and the possibility of changing the configurations to be tested, the wall samples are made of two identical parts, consisting in a 0.03 m masonry tile layer covered by 0.03 m of plaster, which were kept together by means of wooden frames and metal profiles, as depicted in Fig. 4. The wall samples were 0.30 m × 0.30 m and had a 0.04 m insulation frame to limit the heat transfer on the edges, thus establishing a mono-dimensional heat transfer through the walls and prevent them from influencing each other. T-type thermocouples (accuracy: 0.5 K) were positioned on the surface of the exterior and the interior plasters, as well as inside the mock up room to monitor air temperature. Heat flux meters with integrated temperature sensor (heat flux accuracy: 5 %, temperature accuracy: 2 % of value in °C) [33] were positioned between the two brick layers, in the middle of each wall sample. As regards the boundary conditions, data in terms of air temperature, solar radiation, wind speed and wind direction were acquired by a weather station [34] already installed close to the mock up facility. Once the set up was put into operation, a numerical model was implemented in COMSOL Multiphysics v5.6 [35] through which the previously estimated thermo-physical properties were validated against the experimental data gathered. The four wall samples modelled and the physics implemented are depicted in Fig. 5 (where * are the physics used). The validation of the model was carried out using the experimental data acquired over a few consecutive days, in which the outdoor conditions were in line with the season averages, both in terms of air temperature as well as solar irradiance. Given the simple model geometry the mesh implemented was made of 200 regular hexahedrons. Meshes with different number of elements were tried and in all cases the element quality was equal to 1, hence no mesh independence of the solution was considered necessary and investigated.

Fig. 4
figure 4

Schematic representation of the set up: materials and sensors’ position

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Fig. 5
figure 5

Geometry of the plaster samples implemented in COMSOL Multiphysics and conditions applied on the surfaces

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3 Results and Discussion

3.1 Thermo-physical Properties Estimation

At first, the thermal conductivity of the PCM-enhanced plasters was estimated. Data collected during the steady-state tests are reported in Fig. 6a for AS28 and Fig. 6b for TK27. The thermal conductivity was estimating using Fourier’s law as in Eq. 2 and by only using data when the system was in thermal equilibrium, hence when values of the two heat flux meters were almost identical. The thermal conductivity resulted from the test were 0.28 W·(m·K)−1 for AS28 and 0.24 W·(m·K)−1 for TK27. As regards the unsteady-state tests, data collected during the two-step ramp are reported in Fig. 7a and b. The detailed heating and cooling of AS28, comparing the phase change ramp (PC) to the no-phase change one (noPC), are depicted in Fig. 8a and b, respectively. During heating as well as during cooling temperatures changed more slowly in correspondence of the phase change, with peak differences at the melting temperature both above and below the plaster sample. As regards heat fluxes, the peaks reached between the plaster sample and the masonry tile are much lower during heating with reductions of nearly 20 W·m−2.

Fig. 6
figure 6

Data collected during the steady-state test for (a) AS28 and (b) TK27. Lower surface temperatures (first 12 h for AS28 and last 20 h for TK27) were set to estimate the thermal conductivity of the plasters with the PCM in solid state. Analogously, higher surface temperatures (last 15 h for AS28 and first 5 h for TK27) were set to estimate the thermal conductivity of the plasters with PCM in liquid state. Despite all gathered data were reported, only those with the system in equilibrium were considered for the characterisation

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Fig. 7
figure 7

Data acquired during the two-step ramp for (a) AS28 and (b) TK27. On the upper part of both graphs the pattern of the two-step ramp, while on the lower part the heat fluxes monitored. More specifically, the first two peaks (around 3 h and 9 h) indicate the heat flux during melting and solidification of the PCM, respectively, while the last two peaks (around 27 h and 33 h) indicate the heat flux only related to the heating and cooling of the plasters, with no-phase change occurring. As regards the first two peaks, the phase change could be easily detected by the sharp change of the trend in the HFmid line

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Fig. 8
figure 8

Detailed data collected during (a) heating and (b) cooling of AS28 comparing phase change ramp to the no-phase change one. Grey left-axis numbers are referred to the no-phase change ramp (noPC). As highlighted in Fig. 7, the phase change occurring could be detected by the sharp inversion of the heat flux in correspondence of HFmid. Simultaneously to this inversion, the temperature curves started to have a different trend, which up to that point were almost identical

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Moreover, in correspondence of the phase change an inversion of the heat flux (HFmid) is clearly visible, during heating as well as during cooling. Then, detailed heating and cooling in case of TK27, comparing the phase change ramp to the no-phase change one, are depicted in Fig. 9a and b. Analogous considerations to AS28 could be done: temperatures changed at a slower rate reaching peak differences of 2–3 K while heat fluxes reached lower peaks, with reductions of about 30 W·m−2 during melting.

Fig. 9
figure 9

Detailed data collected during (a) heating and (b) cooling of TK27 comparing phase change ramp to the no-phase change one. Grey left-axis numbers are referred to the no-phase change ramp (noPC). Even though peaks and values reached differ from those observed in Fig. 8 with AS28, the trends are almost identical

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In general, even though the PCMs quantities were quite limited, differences between the phase change and no-phase change ramps are clearly visible. As regards the melting of the PCM (20 °C-40°C ramp), in both the plasters a slowdown around 28 °C was visible. During the solidification of the PCM (40 °C-20°C ramp), a slowdown was still visible, but less clearly and also seemed to occur at a different temperature than melting.

To facilitate the comparison between the plasters containing PCMs, data collected during the tests were put together and HFmid heat fluxes are reported in Fig. 10, which were then compared to a reference plaster (REF). During melting, depicted in Fig. 10a, the enhanced plasters reached lower peaks than the reference one, with reduction of about 62 % for AS28 and 73 % for TK27. As observed in the temperatures, where the sharp slowdowns occurred at almost the same temperature, the peak heat flux during the phase change (thus, the positive peaks) were simultaneous, although reaching different peaks, equal to nearly 25 W·m−2 in AS28 and 30 W·m−2 in TK27. Another visible difference between the enhanced plaster regards the melting range of the PCM, which seemed to be narrower in case of AS28 than TK27.

Fig. 10
figure 10

Comparison of heat fluxes collected during (a) heating and (b) cooling. As regards heating, hence the PCM melting, it can be observed that the peak phase change of the two PCMs occur almost simultaneously, with the differences that in case of TK27 the melting range seems to be wider and values are slightly higher (this last due to the higher latent heat capacity of the PCM). During cooling instead, hence the PCM solidification, the peak for TK27 occurs at a lower temperature. Since the range is narrower, the differences between the peak values reached due to the higher latent heat capacity of TK27 are more visible

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Different considerations emerged comparing the heat fluxes during solidification, depicted in Fig. 10b. Both AS28 and TK27 reached lower peaks than the reference one, with reductions of about 30 % and 28 %, respectively, but the greatest difference regards the phase change peak temperature, which seemed to happen at lower temperatures than melting and also different ones. The first to occur, hence at a higher temperature, was in AS28 and then in TK27. From the data obtained during the two-step ramp, the latent heat capacity of the plasters containing PCM were estimated, resulting in 6.8 kJ·kg−1 for the plaster containing AS28 and 10.8 kJ·kg−1 for that containing TK27. Considering the amount of granular PCM contained in each of the enhanced plasters, the latent heat capacity of the granules only was estimated to be about 92 kJ·kg−1 for AS28 and 145 kJ·kg−1 for TK27.

As regards the specific heat, only data gathered from the no-phase change ramp were used. Calculating the cumulative heat stored and released during heating and cooling, respectively, as shown in Fig. 11, and considering each plaster sample mass and the total temperature difference, the values estimated were 1072 J·(kg·K)−1 for AS28 and 1064 J·(kg·K)−1 for TK27. The estimated thermo-physical properties of the two PCM-enhanced plasters along with the calculated uncertainties are summarized in Table 1.

Fig. 11
figure 11

Energy through the plaster samples during heating and cooling. As regards temperatures (gray lines), only one curve for heating and one for cooling are depicted since values monitored for the two plasters were almost identical

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Table 1 Estimated thermo-physical properties of the PCM-enhanced plasters
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3.2 Properties Validation

The validation of the estimated properties was carried out using the model of the experimental set up, described in paragraph 2.2. More specifically, a period of four consecutive days was selected, the first of which was used only to bring the system up to regime, thus excluding the effect of the initial conditions on the results.

For this reason, the results of the model validation, carried out with a timestep of 10 min, are depicted in Fig. 12a for AS28 and Fig. 12b for TK27over a period of three days. The results showed a good agreement between the experimental and the simulated data, supported also by the root mean square error (RMSE) calculated as in Eq. 6 and further reported in Table 2:

$${\text{RMSE}} = \sqrt {\frac{{\mathop \sum \nolimits_{i = 1}^{N} \left( {y_{i} - \hat{y}_{i} } \right)^{2} }}{N}} ,$$
(6)
Fig. 12
figure 12

Comparison between experimental and simulated data for (a) AS28 and (b) TK27

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Table 2 Root mean square error (RMSE) values between experimental and simulated data
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where \({y}_{i}\) is the actual measured value and \({\widehat{y}}_{i}\) is the simulated one.

In terms of temperatures, RMSE values are always lower than 1 °C, with the highest values equal to 0.89 °C and 0.87 °C in case of Tout, namely the temperature on the outer surface of the wall samples. As regards the other temperatures, RMSE values are even lower and between 0.48 °C and 0.59 °C. In term of heat fluxes, RMSE values are 1.90 W·m−2 for AS28 and 2.40 W·m−2 for TK27.

All these values indicate a good agreement between the experimental data, collected during the real scale monitoring, and those simulated with the model implemented in COMSOL Multiphysics whose thermophysical properties were the ones experimentally estimated by means of the ad hoc set up.

4 Conclusion

Phase change materials (PCMs) integrated within building construction materials represent a possible strategy for the energy refurbishment of existing buildings, with special regards to buildings located in particular contexts in which many of the most common techniques are forbidden. The addition of PCMs within plasters, for instance, can be an interesting option to intervene on existing buildings with no alteration of the building design. The heat that is stored when the material is heated up and melt, namely the latent heat, is much greater than the sensible heat that can be stored during the heating up of a common building material, estimated up to 14 times greater. Although the addition of many other aggregates, of biological or non-biological origin, is an extensively studied strategy that allows the improvement of materials’ thermo-physical properties, the increase in the thermal capacity that can be achieved using PCMs in correspondence of their phase change is incomparable in the literature. This means, however, that the integration of PCMs should be accurately designed in order to fully exploit the additional thermal capacity. To maximise the effect of PCMs on building performance, the knowledge of the thermo-physical properties of the new enhanced materials is of outmost importance. However, building materials with PCMs added within are strongly inhomogeneous and standard tests for their thermo-physical characterisation are not suitable. To overcome these issues, an alternative set up was designed and realised ad hoc at the TekneHub laboratory of the University of Ferrara in order to estimate, with different tests but one configuration only, the thermal conductivity, specific heat and latent heat capacity of plasters containing PCMs under the form of granules. The values estimated through steady-state as well as unsteady-state tests were then validated against experimental data. Another experimental set up was in fact designed and realised in order to monitor the dynamic behaviour of up to four wall samples under real outdoor conditions: this allowed not only the monitor of the enhanced plasters over long periods under different conditions, but also the validation of the previously estimated properties. A numerical model of this set up was implemented in COMSOL Multiphysics and simulated data were compared to the experimental ones, and results showed good agreement between the two, with root mean square error values lower than 1 °C and 2.50 W·m−2 for temperatures and heat fluxes, respectively. These results support the reliability of the alternative set up designed as a tool for the thermo-physical characterisation of composite and inhomogeneous materials, being able to overcome the limitations of standard devices and estimate multiple properties with one configuration only. Starting from the results here obtained, the research will be developed on the one hand with the experimentation and monitoring of different plaster samples subjected to real weather conditions, and on the other hand with the simulation of their effects in case of a building scale application.