1. Introduction
The design of energy-efficient buildings has become a major global challenge for both science and industry. This is mainly driven by the urgent need to significantly reduce the emission of gases that provoke the greenhouse effect and climate change [
1]. The building stock handles over one-third of the global energy consumption, and with this, nearly 40% of total direct and indirect CO
emissions. This sector also remains the single largest energy consumer in the European Union [
2].
Among the existing technologies for improving building energy efficiency, innovative thermal energy storage (TES) systems have shown great potential for saving energy [
3]. Particularly, TES technologies based on latent heat, such as those using phase change materials (PCMs), have attracted significant attention from the construction sector in the last few decades. This interest is because of their high energy storage density; i.e., large amounts of heat energy can be stored in small PCM volumes [
4].
PCMs undergo a phase transition (solid–liquid or liquid–solid) around their utilization temperature, through which they can store (during melting) and release (during solidification) large amounts of heat energy. For most PCMs, this transition is achieved at an almost constant temperature, which is commonly referred to as the melting temperature. Exploiting this physical phenomenon, PCMs can be incorporated into building components to increase their heat storage capacity and achieve a stabilizing thermal effect in indoor spaces [
5].
Thus, by employing PCMs in buildings, it is possible to reduce the energy demand, mitigate peak heating and cooling loads, and improve indoor thermal comfort. PCMs can be actively employed in various ways, such as being integrated into mechanical ventilation systems, embedded in active cooling/heating systems for water or other fluids, and/or encapsulated in pipe networks [
6]. PCMs can also be used passively by integrating them into building components, for example, by direct incorporation, immersion, encapsulation, microencapsulation, and shape-stabilization [
7].
Despite its enormous energy-saving potential, the successful use of passive PCM-based systems in buildings is not implicitly guaranteed. This is because the PCM performance strongly depends on the interplay between the daily thermal cycles. If PCMs are not accurately designed for a specific application, they may not have sufficient benefits or, even worse, they may generate undesired thermal effects. To achieve the accurate performance of PCMs in buildings, a proper design of their thermophysical properties, their quantities, and their positions is required [
8,
9]. However, this is highly influenced by the building typology and local climate conditions, suggesting the use of advanced design methods such as building performance simulation (BPS) software [
10]. These tools are essential for achieving energy-efficient building designs in real climate conditions [
11].
A drawback also present in PCMs is their low thermal conductivity, which often can compromise their proper activation (i.e., solidification/melting). In this regard, plenty of heat transfer enhancements have been proposed in the literature to improve the energy storage/release of latent-based systems such as those which employ PCM-based composites. They are often based on either play/design with the tune geometry of the device or system for TES usage [
12] or to increase the thermal conductivity of the PCM-based composite. The latter can be achieved by using additions and/or high-conducting particles such as carbon microfibers [
13,
14], fine materials such as copper [
15], graphite [
16], aluminum [
17], bronze [
18], nickel and stainless steel [
19], graphene nano-platelets [
20], and carbon nano-tubes [
21].
Regarding the available models to predict the performance of building enclosures with PCMs, there are several approaches of different levels of complexity: simplified, intermediate, and sophisticated models [
22]. However, most of the PCM models integrated into whole-building simulation programs correspond to those classified as intermediate models, which are based on the heat source method, the heat capacity method, and the enthalpy method. Among them, the effective heat capacity method and the heat source method are implemented in ESP-r [
23]. Several PCM models have been developed in TRNSYS, including also the heat capacity (e.g., “TYPE260”) and the heat source methods (e.g., “TYPE1270”) [
22]. Finally, the enthalpy method, which is the most complex one among the intermediate options, is the PCM model implemented in EnergyPlus software [
24].
In the current literature, several studies aim to address the optimization of the PCMs’ thermophysical properties for building applications. Using a parametric analysis, Ascione et al. [
25] studied the proper position and melting temperature of a PCM to achieve nearly zero-energy buildings in Mediterranean climates. They concluded that using a PCM melting temperature of 25
C on the inner side is recommended, and this can achieve reductions in cooling energy demand from 2% (in Madrid) to 13% (in Naples). Saffari et al. [
9] performed a simulation-based optimization analysis of PCM melting temperature to improve the energy performance in buildings across different climate regions regarding the Köppen–Geiger classification. By applying this method, they demonstrated that the optimal selection of the PCM melting temperature can highly influence the total energy consumption of a building, and this strongly depends on the considered climatic conditions. The results also showed that an increment in the PCM quantity can both increase and decrease the performance of the PCMs significantly, affecting their benefits. Therefore, although this work presented significant developments, in some cases, no clear relationships between the PCM thermophysical properties and the heating/cooling energy savings could be derived. This arises from the fact that the research was carried out by employing a single objective optimization approach. Recently, Arıcı et al. [
26] carried out an optimization study about the maximum activation of latent heat of PCM integrated into external building walls for three cities in Turkey. In this work, the influence of location, melting temperature, and layer thickness of PCM on building energy saving was evaluated. However, the PCM design was addressed by adopting a single-objective optimization approach. In addition, the thermal performance of the building was characterized by a single wall heat balance instead of one involving the whole building. This hypothesis can induce non-physical conclusions about the optimal position of the PCM and its melting temperature. For cementitious materials enhanced with microencapsulated PCM (MPCM), most of the current efforts are focused on the development of the materials only and do not evaluate the performance of this technology integrated into buildings regarding real climate conditions [
27,
28,
29].
To address the pinpointed limitations, this work proposes a novel method based on multiobjective optimization to design cement-based systems for building applications enhanced with PCM. In particular, the method is devoted to finding the optimal thermophysical properties of cement-based building panels with embedded MPCM and following annual heating/cooling loads. The PCM melting temperature and the thickness and thermal conductivity of the cement-based panel are the design variables. Thus, this new approach provides a general method to explore the relationship between optimal thermophysical properties of PCM-based systems and the heating/cooling performance of the building incorporating them. This allows for important contributions to a better understanding of the real performance of passive PCM-based systems in buildings.
3. Results
This section reports the analysis and discussion of the optimization results obtained for the proposed case studies. First, the optimization results for Case A are analyzed in
Section 3.1. Then, the corresponding results for Case B are presented in
Section 3.2. Finally, a comparative discussion between both case studies is performed in
Section 3.3. For closer analysis (or their reproduction), all the optimization results are provided as supplementary research data.
3.1. Optimization of Case A
Figure 5 shows the multiobjective optimization results of the annual ideal loads for heating and cooling obtained for Case A. These include the best trade-off (Pareto front) between heating and cooling loads and all the feasible designs evaluated during the optimization procedure. The heating and cooling loads of the baseline model are also displayed to obtain a reference of the improvements reached by the optimized designs.
The first observation is that a reduction in both heating and cooling loads can be obtained by including the PCM-based panel in the building. Moreover, the best performance of the building for heating and cooling has a mutually contradictory response regarding the optimum design of the PCM melting temperature (i.e., T of melting) and the thickness of the panel (d). This means that the best solution for heating is not the best design for cooling and vice versa. This is an important conclusion that demonstrates the necessity of using a multiobjective approach to design passive PCM-based systems in building applications.
Regarding the optimized designs (Pareto front),
Figure 5 also highlights that most of them simultaneously improve the heating and cooling performance compared to the baseline model. Only a few designs show a slightly lower performance for cooling than the baseline model.
Table 6 summarizes the performance of the different optimal designs obtained (Opt-1 to Opt-3) and their relative improvements compared to the baseline model. Regarding the best design for heating (Opt-1), this achieves a large saving of 23.12% for heating, while its cooling performance slightly worsens (−0.35%). Opt-3 is the best design for cooling, which reduces 3.04% of cooling loads and 7.13% of the heating loads. Finally, Opt-2 is the design with the minimum total loads (heating + cooling), achieving a reduction of 11.58%, with improvements of 22.73% and 0.25% for heating and cooling, respectively. From this quantitative analysis, it is noted that all the optimized designs can easier improve the heating performance than the cooling one. Even in the best design for cooling, only an improvement of 3.04% could be achieved, while heating loads can be reduced by 7.13% compared to the baseline model.
Figure 6 shows the relationship between the design variables of all the optimal results (Pareto front) obtained in Case A. This analysis enables a better understanding of the relationship between the optimum design variables and the energy performance of the building. Therefore, it can be seen that the best building performance for heating (Opt-1) is achieved for the thickest panel analyzed (0.35 m) and a T
= 22.31
C. Conversely, the best performance for cooling (Opt-3) is reached by using a thin panel of 0.073 m and a T
= 27.26
C. Moreover, the design that minimizes the total loads (Opt-2) also employs the thickest panel analyzed (0.35 m) but along with a T
= 23.98
C.
Despite a wide range of PCM melting temperatures that are numerically being analyzed, except for Opt-4, the optimum designs are found with T laying between 22.31 and 27.26 C. The physical reason for this range of optimum melting temperature is that the latent heat storage in PCMs with higher or lower T does not considerably affect the heating and cooling loads that are evaluated in the indoor air. Opt-4 is an atypical design defined by the thickest panel (0.35 m) and a T = 29.26 C.
3.2. Optimization of Case B
Figure 7 shows the optimization results obtained for Case B. These include the Pareto front between heating and cooling loads, all the feasible designs evaluated during the optimization, and the baseline model. It can be seen that the limits of the bi-objective space have considerably changed compared to Case A because of incorporating the thermal conductivity in the design space. Here, the designs on the Pareto front achieve good load reductions for both heating and cooling.
To enable a quantitative analysis,
Table 7 summarizes the performance of a few optimum designs obtained along with their relative improvements compared to the baseline model. Here, only the extreme optimal solutions for heating (Opt-1) and cooling (Opt-5) are discussed, since Opt-5 is also the best design for the total loads (heating + cooling).
Opt-1 is the best design for heating, and the same is obtained in Case A. This is because the design space was only enlarged with higher thermal conductivity values than the original PCM-based panel. This aspect is more deeply analyzed in
Section 3.3.
Opt-5 achieves load reductions of 11.81% and 12.38% for heating and cooling, respectively. Unlike the best design for cooling in Case A (Opt-3), Opt-5 achieves a large load reduction for cooling but also obtains a similar improvement for heating.
Figure 8 shows the relationship between the design variables for all the optimum designs (Pareto front) of Case B. Due to all the optimal solutions having the thickest panel allowed (0.35 m), this graph only shows the relationship between the T
and thermal conductivity of the panel (k). As previously introduced, the best building performance for heating (Opt-1) is achieved by using a T
= 22.31
C and the lowest thermal conductivity allowed of k = 0.473 W/(m
K). Conversely, the best building performance for cooling (Opt-5), which is also the best for the total loads, is achieved by using the highest thermal conductivity allowed of k = 10 W/(m
K) and a T
= 26.24
C. As a general guide, starting from the Opt-1 design to improve the cooling performance and going over the optimal designs, these employ a low thermal conductivity (<1 W/(m
K)) while increasing the T
up to 25–26
C. After that sector, the solutions that improve the cooling performance even more keep using a T
= 25–26
C while increasing their thermal conductivity.
3.3. Discussion
Figure 9 shows the Pareto fronts obtained for both case studies (Case A and Case B) and the reference of the baseline model. As shown, the performance of the building for heating and cooling has a mutually contradictory response regarding the optimum design thermophysical properties of the PCM-based panels. This highlights the need of using the multiobjective approach herein proposed to design passive PCM-based systems in building applications. This novel approach presents several advantages compared to previous single optimization approaches found in the literature [
9,
26]; it allows for a better understanding of the real performance of passive PCM-based systems in buildings, such as those discussed next. In
Figure 9, it can be also observed that the optimal solutions of Case B can considerably improve the building performance for cooling compared to either Case A or the reference building. This reveals that when the panel increases its thickness to incorporate more MPCM into the building, the panel must have a high thermal conductivity to guarantee the effectiveness of the extra MPCM incorporated. Therefore, beyond its optimum melting temperature, the PCM has to be thermally coupled with the indoor air to achieve the desired effect. Conversely, if the thickness of the panel increases but keeps a low thermal conductivity, part of the MPCM cannot provide its full storage/release capacity and does not affect the indoor air, which is the real target to reduce the loads. This aspect could be a limitation for standard microencapsulation technology embedded in cement-based pastes.
The volume fraction of the MPCM in cement pastes has a physical limit. Most studies available in the literature employ volume fractions of 20%, while only a few works considered higher amounts (up to a maximum of 40%) [
56]. However, of this volume of MPCM, approximately 60% corresponds to the encapsulating shell, resulting in a very low effective fraction of PCM in the panel. This drives the need to use thicker panels to include more MPCM in the building, but as shown, increasing the thickness is not effective, because a part of the extra PCM added does not result in a thermal coupling with the indoor air and cannot drive a positive effect to it.
Finally,
Figure 10 shows the monthly heating and cooling loads for the designs Opt-2 and Opt-5 compared to the baseline model. Regarding Opt-2, it reduces the heating loads for all the months with noticeable improvements in the autumn months. Conversely, this design has a similar performance to the baseline model regarding the cooling loads. It is worth remembering that the Opt-2 design (attained in the optimization of Case A) has more capacity to reduce the annual heating load (22.73%) than the cooling ones (0.25%).
Regarding Opt-5, the results also show a reduction in the heating loads for all months but with lower performance than the Opt-2 during the winter months. This design also reduces the cooling loads for all the months compared to the baseline model. However, the major cooling load improvements, reducing up to half of the loads, are achieved during moderate temperature months, such as the spring months. It may be worth remembering that this design (Opt-5), achieved in the optimization of Case B, has a good and balanced capacity to reduce the annual heating loads (11.81%) as well as the cooling ones (12.38%).