Trombe Wall Thermal Behavior and Energy Efficiency of a Light Steel Frame Compartment: Experimental and Numerical Assessments

Buildings are seeking renewable energy sources (e.g., solar) and passive devices, such as Trombe walls. However, the thermal performance of Trombe walls depends on many factors. In this work, the thermal behavior and energy efficiency of a Trombe wall in a lightweight steel frame compartment were evaluated, making use of in situ measurements and numerical simulations. Measurements were performed inside two real scale experimental identical cubic modules, exposed to natural exterior weather conditions. Simulations were made using validated advanced dynamic models. The winter Trombe wall benefits were evaluated regarding indoor air temperature increase and heating energy reduction. Moreover, a thermal behavior parametric study was performed. Several comparisons were made: (1) Sunny and cloudy winter week thermal behavior; (2) Office and residential space use heating energy; (3) Two heating set-points (20 ◦C and 18 ◦C); (4) Thickness of the Trombe wall air cavity; (5) Thickness of the thermal storage wall; (6) Dimensions of the interior upper/lower vents; (7) Material of the thermal storage wall. It was found that a Trombe wall device could significantly improve the thermal behavior and reduce heating energy consumption. However, if not well designed and controlled (e.g., to mitigate nocturnal heat losses), the Trombe wall thermal and energy benefits could be insignificant and even disadvantageous.


Introduction
Energy is one of the main concerns when addressing sustainable development, especially since the world's energy matrix is still very dependent on fossil fuels, as oil and coal. The building's sector plays an important role, as buildings consume approximately 40% of the total energy in Europe, being also responsible for about 36% of the CO 2 emissions [1]. Aiming to improve the energy efficiency of buildings, the European Union (EU) has established the energy performance of buildings directive (EPBD) [2], in which two key concepts are defined: (1) the cost-optimal energy, regarding cost-efficiency of strategies [3], and (2) the nearly zero-energy buildings (nZEB)-buildings with very high energy efficiency-that cover their energy needs with energy produced by renewable sources, on-site or nearby [4]. To meet the EPBD requirements, the optimization of construction systems and the development of strategies to decrease energy consumption by buildings are key [5].
A sustainable strategy to improve the thermal and energy performance of buildings is exploiting solar energy, which also meets the EPDB establishments. A Trombe wall (TW) is a passive solar device that can be present in a building's façade to accumulate solar heat, heating, and even cooling indoor spaces, fostering natural ventilation [6]. This passive solar device was patented in 1881 by the

Materials and Methods
The materials and methods used in this research have been described in detail in this section, starting with the experimental and numerical approaches, followed by the calibration and validation of the advanced dynamic thermal simulation models of the LSF modules and water Trombe wall.

LSF Experimental Modules
The experimental measurements were performed on two similar lightweight steel frame (LSF) modules constructed near the Department of Civil Engineering (DEC) of the University of Coimbra (Portugal), as illustrated in Figure 1, having a GPS coordinates: 40.  The external dimensions of the experimental modules, as well as the material specifications of the LSF construction elements, such as the number of layers, materials, and thicknesses, are schematically illustrated in Figure 2, while Table 1 displays the thermal conductivities of the materials. In these experimental modules, the LSF system B(A) a was adopted and manufactured by Urbimagem company [29], making use of steel profiles C100 × 45 × 1.5 mm. The structural sheathing was provided by 12 mm oriented strand board (OSB) panels [30] on both sides of the walls' steel frame. The ceiling was also inferiorly lined with OSB panels, as well as the upper side of the roof steel frame beams. To allow access to the interior, both modules had a similar wooden door (2.00 m high by 0.78 m wide), which was thermally insulated with the same expanded polystyrene (EPS) external thermal insulation composite system (ETICS) system of the walls. There were no windows in the experimental TW modules. This was justified by the intention to isolate the TW effect in the evaluated compartments. A glazed window (e.g., south orientated) would provide additional solar heat gains, which would be overlapped and more difficult to distinguish from the heat gains provided by the TW device.
Notice that, as illustrated in Figure 2, the experimental modules were designed to have gypsum plasterboard (GPB) as an inner sheathing layer of walls and ceiling, but later it was decided not to apply these GPB panels. The batt insulation was provided by 100 mm mineral wool (MW) [31], fulfilling the air-cavity between the steel frame. The exterior thermal insulation composite system (ETICS) was made with EPS thermal insulation [32] (50 mm thick) and finished by a reinforced plaster layer (5 mm). The exterior thermal insulation of the roof was made of extruded polystyrene (XPS) [33] with the same thickness. To avoid moisture direct contact from the ground, the floor was 300 mm elevated, creating a small crawl space below, as illustrated in Figure 2, having an 18 mm OSB panel [30] below and another above the continuous XPS [34] thermal insulation layer (60 mm thick). The inclined flat roof was waterproofed by a polyvinyl chloride (PVC) membrane [35] (1.5 mm thick), forming a plenum above the ceiling with variable thickness. The external dimensions of the experimental modules, as well as the material specifications of the LSF construction elements, such as the number of layers, materials, and thicknesses, are schematically illustrated in Figure 2, while Table 1 displays the thermal conductivities of the materials. In these experimental modules, the LSF system B(A) a was adopted and manufactured by Urbimagem company [29], making use of steel profiles C100 × 45 × 1.5 mm. The structural sheathing was provided by 12 mm oriented strand board (OSB) panels [30] on both sides of the walls' steel frame. The ceiling was also inferiorly lined with OSB panels, as well as the upper side of the roof steel frame beams. To allow access to the interior, both modules had a similar wooden door (2.00 m high by 0.78 m wide), which was thermally insulated with the same expanded polystyrene (EPS) external thermal insulation composite system (ETICS) system of the walls. There were no windows in the experimental TW modules. This was justified by the intention to isolate the TW effect in the evaluated compartments. A glazed window (e.g., south orientated) would provide additional solar heat gains, which would be overlapped and more difficult to distinguish from the heat gains provided by the TW device.
Notice that, as illustrated in Figure 2, the experimental modules were designed to have gypsum plasterboard (GPB) as an inner sheathing layer of walls and ceiling, but later it was decided not to apply these GPB panels. The batt insulation was provided by 100 mm mineral wool (MW) [31], fulfilling the air-cavity between the steel frame. The exterior thermal insulation composite system (ETICS) was made with EPS thermal insulation [32] (50 mm thick) and finished by a reinforced plaster layer (5 mm). The exterior thermal insulation of the roof was made of extruded polystyrene (XPS) [33] with the same Energies 2020, 13, 2744 5 of 25 thickness. To avoid moisture direct contact from the ground, the floor was 300 mm elevated, creating a small crawl space below, as illustrated in Figure 2, having an 18 mm OSB panel [30] below and another above the continuous XPS [34] thermal insulation layer (60 mm thick). The inclined flat roof was waterproofed by a polyvinyl chloride (PVC) membrane [35] (1.5 mm thick), forming a plenum above the ceiling with variable thickness. Table 1. Thermal conductivity (λ ) of the materials used in the lightweight steel frame (LSF) modules.

Materials ((m•K)/W) Reference
Reinforced plaster (ETICS 1 finish) 0.720 [37] EPS 2 (ETICS 1 thermal insulation) 0.036 [32] OSB 3 (LSF sheathing) 0.130 [30] Mineral wool (cavity insulation) 0.037 [31] Steel (profiles C100 × 45 × 1.5 mm) 50.000 [38] XPS 4 (roof insulation) 0.036 [33] (floor insulation) 0.035 [34] Vinyl floor cover 0.250 [39] PVC 5 membrane (roof waterproofing) 0.170 [35] Table 2 displays, for each LSF element, the materials and thicknesses of the layers, as well as the computed thermal transmittance (U-value). Notice that two types of layers were assessed in these LSF elements: (1) homogeneous, where the steel frame was not included in the thermal computations, given its location outside the insulation and sheathing materials, and (2) inhomogeneous, where the steel frame crossed through the insulation materials (e.g., mineral wool). The U-value for the elements with homogeneous layers (floor, roof, and door) was computed following the analytical calculation procedures prescribed by standard ISO 6946 [41]. The U-values of the LSF elements Energies 2020, 13, 2744 6 of 25 containing inhomogeneous layers (walls and ceiling) were computed, making use of bi-dimensional (2D) finite element method (FEM) models built in the THERM software [42], as has been detailed next in Section 2.2.1. The obtained U-values (Table 2) ranged from 0.326 W/(m 2 ·K) in the walls up to 0.670 W/(m 2 ·K) in the ceiling. The Trombe wall prototype (2.80 m high and 0.55 m wide) was placed on the south-oriented wall of module 2 ( Figure 1). Figure 3a schematically illustrates the geometry of this Trombe wall prototype, which was developed and executed during a Ph.D. research work [36]. Notice that the dimensions of this modular TW prototype were defined, taking into account the ceiling height (2.80 m) and the usual vertical steel stud spacing in LSF construction (0.60 m). The thermal storage wall was made with a black-painted steel sheet tank fulfilled with water, having 50 mm of thickness. On the outer side, there was an aluminum frame glazing system with double glass (4 mm + 16 mm of argon + planistar 6 mm), having an effective solar absorption area of 1.1 m 2 . The glazing panel had a solar heat gain coefficient (SHGC) equal to 0.743, while the direct solar transmission was 0.667, and the thermal transmittance was 2.552 W/(m 2 ·K), as displayed in Figure 3b. Trombe wall: (1) an upper air vent, 0.50 m wide by 0.10 m high, and (2) a bottom air vent with the same width but a smaller height (0.05 m).

Monitoring Equipment
To reproduce the thermal behavior of the experimental modules exposed to exterior weather conditions, it was needed to have access to hourly weather data recorded nearby. With this purpose, two weather stations were used: (1) Department of Mechanical Engineering (DEM) [43], also located in the Engineering campus of the University of Coimbra (GPS: 40.1849° N, 8.4132° W), and (2) CoolHaven company [44], located in Coimbra iParque, Antanhol (GPS: 40.1792° N, 8.4654° W).
The nearest weather data station (DEM) was used for most of the data needed to perform advanced dynamic simulations, including air temperature, dew-point temperature, relative humidity, wind direction, wind speed, atmospheric pressure, and precipitation. However, this weather station did not provide some additional relevant weather data, such as the parameters related to solar radiation, i.e., global horizontal radiation, diffuse horizontal radiation, and direct normal radiation. This essential detailed solar radiation information was obtained in the CoolHaven weather station, located about 7 km from the experimental modules.
Regarding the hardware, the DEM weather station is a wireless Davis Vantage Pro2 Plus [45], while the CoolHaven is constituted of several sensors, with the pyranometer being a sunshine sensor Delta-T BF5 [46].
Notice that according to the Köppen-Geiger climate classification [47], the city of Coimbra (Portugal) is located in a Csb climate region, which is characterized by a temperate climate with rainy winter and dry summer slightly hot, being a very frequent climate within the Mediterranean region [16].
The indoor air temperature and humidity were measured simultaneously, inside both LSF modules, to monitor their thermal behavior and verify the influence of the solar Trombe wall. With  This glazed aluminum frame had a top and lower exterior openings for exterior ventilation, which were not used during these experiments, being all the time closed. Between the storage wall and the outer glazing, there was a 100 mm thick air cavity. On the inner surface of the storage wall, there was a layer of 0.10 m of mineral wool, covered by an OSB panel (12 mm). To allow air circulation between the outer air cavity and the indoor environment, there were two rectangular air vents on the Trombe wall: (1) an upper air vent, 0.50 m wide by 0.10 m high, and (2) a bottom air vent with the same width but a smaller height (0.05 m).

Monitoring Equipment
To reproduce the thermal behavior of the experimental modules exposed to exterior weather conditions, it was needed to have access to hourly weather data recorded nearby. With this purpose, two weather stations were used: The nearest weather data station (DEM) was used for most of the data needed to perform advanced dynamic simulations, including air temperature, dew-point temperature, relative humidity, wind direction, wind speed, atmospheric pressure, and precipitation. However, this weather station did not provide some additional relevant weather data, such as the parameters related to solar radiation, i.e., global horizontal radiation, diffuse horizontal radiation, and direct normal radiation. This essential detailed solar radiation information was obtained in the CoolHaven weather station, located about 7 km from the experimental modules. Regarding the hardware, the DEM weather station is a wireless Davis Vantage Pro2 Plus [45], while the CoolHaven is constituted of several sensors, with the pyranometer being a sunshine sensor Delta-T BF5 [46].
Notice that according to the Köppen-Geiger climate classification [47], the city of Coimbra (Portugal) is located in a Csb climate region, which is characterized by a temperate climate with rainy winter and dry summer slightly hot, being a very frequent climate within the Mediterranean region [16].
The indoor air temperature and humidity were measured simultaneously, inside both LSF modules, to monitor their thermal behavior and verify the influence of the solar Trombe wall. With this purpose, one Tinytag Ultra 2-TGU-4500 [48] air temperature and humidity sensor was installed inside each module, being suspended in the middle ceiling, at mid-height. These sensors were factory calibrated, having a precision of ±0.45 • C for temperature and ±3% for relative humidity. The measured data was averaged and recorded every 10 minutes, having a sampling interval of 10 seconds. The in situ measurements took place from the 26 th of July 2019 until the 19 th of January 2020.

2D FEM Thermal Computations
As mentioned before (see Section 2.1.1), the U-values of the inhomogeneous LSF elements (walls and ceiling) were computed, making use of bi-dimensional (2D) models implemented in a finite element method (FEM) software: THERM [42]. The FEM mesh was refined to have a maximum error of 2%.

LSF Ceiling Element
For the ceiling element, as the steel profiles are placed only in one direction (see the yellow region in Figure 4a), the U-value was directly obtained from the 2D FEM model, as illustrated in Figure 4b. The model had a width of 600 mm, i.e., equal to the distance between the steel studs within the ceiling. The steel C stud was positioned in the middle of the model, as shown in Figure 4b, and this is a representative part of the LSF ceiling slab. Moreover, the ceiling mineral wool (MW) insulation was considered only between steel sections since, in practice, it was not possible to put MW inside the corresponding steel lattice beam, where it was considered an air gap. Figure 4c displays the temperature distribution predicted in the ceiling cross-section, where the thermal bridged effect was clear due to the MW thermal insulation discontinuity. The global U-value computed from the THERM model was 0.670 W/(m 2 ·K). Notice that assuming homogeneous layers, i.e., considering continuous MW insulation and neglecting the steel studs, the U-value obtained was 0.334 W/(m 2 ·K), being 50% smaller.

LSF Wall Element
Since the LSF walls had steel studs in vertical, horizontal, and diagonal planes (see Figure 5a), the bi-dimensional U-value computation procedure was different from the ceiling element, where the U-value was directly obtained from the THERM model. It is well known that an insulated LSF element has two distinct thermal zones [49,50]: (1) an increased heat transfer zone (lower thermal resistance) in the vicinity of the steel studs, given the high thermal conductivity of steel, and (2) a more reduced heat transfer zone (higher thermal resistance) in the insulated cavity between the steel studs. Thus, the global thermal transmittance (U global ) of LSF elements with complex steel frame could be estimated, making an area-weighted summation of the U-values for each thermal zone mentioned before ("stud" and "cav"), as given in the following equation: where A global is the total area of the LSF element (internal dimensions), A stud is the total area of influence of the steel stud on the LSF element, and A cav is the remaining cavity area of the LSF wall. For this specific LSF wall, the areas considered in the computations are displayed in Figure 5a. Both U-values (U stud and U cav ) were obtained, making use of a THERM model, as illustrated in Figure 5b. This simplified LSF wall model had a length equal to the spacing between the vertical steel studs, i.e., 600 mm. To obtain the two representative U-values, two "measurement" zones were simulated in the LSF wall model: one right under the steel stud and another one in the edge of the wall cavity. These "measurement" zones were modeled having the same width as the steel stud flange, i.e., 45 mm, and is delimited in Figure 5 by two dashed white lines. Figure 5c displays the obtained temperature ( • C) color distribution along the cross-section of the LSF wall model and is well visible in the thermal bridge originated by the central steel stud and its correspondent temperature disturbance. Figure 5d shows the computed heat flux (W/m 2 ) distribution within the cross-section of the LSF wall, as well as the two U-values computed in the steel stud vicinity and in the edge of the wall cavity. As expected, the U stud (0.797 W/m 2 ·K) was considerably higher (+260%) than the U cav (0.221 W/m 2 ·K), confirming the huge relevance of the steel stud (only 1.5 mm thick) in the thermal performance of the LSF wall.
seconds. The in situ measurements took place from the 26 th of July 2019 until the 19 th of January 2020.

2D FEM Thermal Computations
As mentioned before (see Section 2.1.1), the -values of the inhomogeneous LSF elements (walls and ceiling) were computed, making use of bi-dimensional (2D) models implemented in a finite element method (FEM) software: THERM [42]. The FEM mesh was refined to have a maximum error of 2%.

LSF Ceiling Element
For the ceiling element, as the steel profiles are placed only in one direction (see the yellow region in Figure 4a), the -value was directly obtained from the 2D FEM model, as illustrated in Figure 4b. The model had a width of 600 mm, i.e., equal to the distance between the steel studs within the ceiling. The steel C stud was positioned in the middle of the model, as shown in Figure 4b, and this is a representative part of the LSF ceiling slab. Moreover, the ceiling mineral wool (MW) insulation was considered only between steel sections since, in practice, it was not possible to put MW inside the corresponding steel lattice beam, where it was considered an air gap. Figure 4c displays the temperature distribution predicted in the ceiling cross-section, where the thermal bridged effect was clear due to the MW thermal insulation discontinuity. The global -value computed from the THERM model was 0.670 W/(m 2 •K). Notice that assuming homogeneous layers, i.e., considering continuous MW insulation and neglecting the steel studs, the -value obtained was 0.334 W/(m 2 •K), being 50% smaller.

LSF Wall Element
Since the LSF walls had steel studs in vertical, horizontal, and diagonal planes (see Figure 5a), the bi-dimensional -value computation procedure was different from the ceiling element, where the -value was directly obtained from the THERM model. It is well known that an insulated LSF element has two distinct thermal zones [49,50]: (1) an increased heat transfer zone (lower thermal resistance) in the vicinity of the steel studs, given the high thermal conductivity of steel, and (2) a more reduced heat transfer zone (higher thermal resistance) in the insulated cavity between the steel studs. Thus, the global thermal transmittance ( ) of LSF elements with complex steel frame could be estimated, making an area-weighted summation of the -values for each thermal zone mentioned before ("stud" and "cav"), as given in the following equation: where is the total area of the LSF element (internal dimensions), is the total area of influence of the steel stud on the LSF element, and is the remaining cavity area of the LSF wall. For this specific LSF wall, the areas considered in the computations are displayed in Figure 5a.
Both -values ( stud and cav) were obtained, making use of a THERM model, as illustrated in Figure 5b. This simplified LSF wall model had a length equal to the spacing between the vertical steel studs, i.e., 600 mm. To obtain the two representative -values, two "measurement" zones were simulated in the LSF wall model: one right under the steel stud and another one in the edge of the wall cavity. These "measurement" zones were modeled having the same width as the steel stud flange, i.e., 45 mm, and is delimited in Figure 5 by two dashed white lines. Figure 5c displays the obtained temperature (°C) color distribution along the cross-section of the LSF wall model and is well visible in the thermal bridge originated by the central steel stud and its correspondent temperature disturbance. Figure 5d shows the computed heat flux (W/m 2 ) distribution within the cross-section of the LSF wall, as well as the two -values computed in the steel stud vicinity and in the edge of the wall cavity. As expected, the stud (0.797 W/m 2 •K) was considerably higher (+260%) than the cav (0.221 W/m 2 •K), confirming the huge relevance of the steel stud (only 1.5 mm thick) in the thermal performance of the LSF wall.
Finally, knowing the three areas ( Figure 5a) and the two -values ( Figure 5d) and making use of Equation (1), a global -value equal to 0.326 W/(m 2 •K) was obtained. Notice that when the steel studs were neglected and homogenous layers were assumed, the -value reduced to 0.225 W/(m 2 •K) (31% smaller). It is important to highlight that there are several strategies to mitigate the thermal bridges originated by steel studs within an LSF component, reducing their -value, such as the use of thermal break (TB) strips within steel studs flange [51]. These TB strips could be made of different materials, such as recycled tire rubber [52]. Shortly, it was intended to use this type of TB strips to improve the thermal performance of these experimental LSF modules.

Advanced Dynamic Simulations
The advanced dynamic thermal simulations were performed in the software DesignBuilder version 5.5.0.012 (DesignBuilder Software Ltd, Stroud, Gloucester, UK) [37]. The computations were performed, making use of hourly interval data. A replica of the two LSF experimental modules photographed in Figure 1 was modeled, taking into account the location/climate, the geometry/dimensions, the construction elements composition (e.g., walls, floor, ceiling, roof, door, and Trombe wall), the material properties, the airtightness, the activity, and occupation parameters.  Finally, knowing the three areas ( Figure 5a) and the two U-values ( Figure 5d) and making use of Equation (1), a global U-value equal to 0.326 W/(m 2 ·K) was obtained. Notice that when the steel studs were neglected and homogenous layers were assumed, the U-value reduced to 0.225 W/(m 2 ·K) (31% smaller).
It is important to highlight that there are several strategies to mitigate the thermal bridges originated by steel studs within an LSF component, reducing their U-value, such as the use of thermal break (TB) strips within steel studs flange [51]. These TB strips could be made of different materials, such as recycled tire rubber [52]. Shortly, it was intended to use this type of TB strips to improve the thermal performance of these experimental LSF modules.

Advanced Dynamic Simulations
The advanced dynamic thermal simulations were performed in the software DesignBuilder version 5.5.0.012 (DesignBuilder Software Ltd, Stroud, Gloucester, UK) [37]. The computations were performed, making use of hourly interval data. A replica of the two LSF experimental modules photographed in Figure 1 was modeled, taking into account the location/climate, the geometry/dimensions, the construction elements composition (e.g., walls, floor, ceiling, roof, door, and Trombe wall), the material properties, the airtightness, the activity, and occupation parameters. Figure 6 exhibits a print-screen view of the two models: (1) module 1, used as reference (Figure 6a), and (2) module 2, containing the Trombe wall (Figure 6b).
The airtightness of these experimental modules was measured in-situ [36], and the obtained value (0.05 air changes per hour) was implemented in the DesignBuilder model as a constant value and without any natural ventilation since, during the measurements, the openings (back door and Trombe wall exterior vents) were always closed. Moreover, the modules were kept empty, i.e., without anyone inside. Thus, the occupancy was set as "null", and the activity tab as "none". Notice that the color of the materials was also reproduced, in particular, the black color of the Trombe wall (Figure 6b).

Calibration and Model Validation
To ensure good reliability of the DesignBuilder [37] advanced dynamic models ( Figure 6) thermal behavior predictions, the obtained simulation results were compared with the air temperature in-situ measurements (see Section 2.1.3), performed inside the LSF modules (Figure 1), subjected to natural Energies 2020, 13, 2744 11 of 25 outdoor weather conditions (recorded nearby, as previously explained in Section 2.1.3), allowing to validate these models, as shown next.

Advanced Dynamic Simulations
The advanced dynamic thermal simulations were performed in the software DesignBuilder version 5.5.0.012 (DesignBuilder Software Ltd, Stroud, Gloucester, UK) [37]. The computations were performed, making use of hourly interval data. A replica of the two LSF experimental modules photographed in Figure 1 was modeled, taking into account the location/climate, the geometry/dimensions, the construction elements composition (e.g., walls, floor, ceiling, roof, door, and Trombe wall), the material properties, the airtightness, the activity, and occupation parameters. Figure 6 exhibits a print-screen view of the two models: (1)    The airtightness of these experimental modules was measured in-situ [36], and the obtained value (0.05 air changes per hour) was implemented in the DesignBuilder model as a constant value and without any natural ventilation since, during the measurements, the openings (back door and Trombe wall exterior vents) were always closed. Moreover, the modules were kept empty, i.e., without anyone inside. Thus, the occupancy was set as "null", and the activity tab as "none". Notice that the color of the materials was also reproduced, in particular, the black color of the Trombe wall ( Figure 6b).

Calibration and Model Validation
To ensure good reliability of the DesignBuilder [37] advanced dynamic models ( Figure 6) thermal behavior predictions, the obtained simulation results were compared with the air temperature in-situ measurements (see Section 2.1.3), performed inside the LSF modules ( Figure 1), subjected to natural outdoor weather conditions (recorded nearby, as previously explained in Section 2.1.3), allowing to validate these models, as shown next.

Trombe Wall LSF Model
The accuracy of the Trombe wall LSF model was also verified by comparison among predicted and measured indoor air temperatures. Figure 8 displays the obtained results plot, in which a good agreement between both curves was observed. The RMSE for this model was 0.5 °C, confirming also a good accuracy performance of this second model.

Trombe Wall LSF Model
The accuracy of the Trombe wall LSF model was also verified by comparison among predicted and measured indoor air temperatures. Figure 8 displays the obtained results plot, in which a good agreement between both curves was observed. The RMSE for this model was 0.5 • C, confirming also a good accuracy performance of this second model.

Trombe Wall CFD Assessment
To verify if the modeled Trombe wall is operating coherently, a computational fluid dynamics (CFD) analysis was also conducted on DesignBuilder, which has a built-in CFD tool. Figure 9 displays the results of the CFD analysis, carried for the 16:00 hours of the 4 th of September, with both air velocity and temperature in a color scale being displayed, as well as velocity vectors.
Looking at the results of the horizontal plane plotted in Figure 9a was well visible the colder air entrance to the Trombe wall air cavity through its lower vent, as well as the warmer air flowing out of the upper vent near the ceiling. Moreover, in Figure 9b (the vertical plane in front of the Trombe wall), the air stratification in height and also the air being heated near the Trombe wall were again visible, which was exposed to direct solar radiation (4 pm) and, consequently, was flowing up to the ceiling. Therefore, these CFD simulation results made sense and were coherent with the expected ones for a compartment with a Trombe wall exposed to direct solar radiation, which ensured the reliability of the implemented models.

Trombe Wall CFD Assessment
To verify if the modeled Trombe wall is operating coherently, a computational fluid dynamics (CFD) analysis was also conducted on DesignBuilder, which has a built-in CFD tool. Figure 9 displays the results of the CFD analysis, carried for the 16:00 hours of the 4 th of September, with both air velocity and temperature in a color scale being displayed, as well as velocity vectors.

Trombe Wall CFD Assessment
To verify if the modeled Trombe wall is operating coherently, a computational fluid dynamics (CFD) analysis was also conducted on DesignBuilder, which has a built-in CFD tool. Figure 9 displays the results of the CFD analysis, carried for the 16:00 hours of the 4 th of September, with both air velocity and temperature in a color scale being displayed, as well as velocity vectors.
Looking at the results of the horizontal plane plotted in Figure 9a was well visible the colder air entrance to the Trombe wall air cavity through its lower vent, as well as the warmer air flowing out of the upper vent near the ceiling. Moreover, in Figure 9b (the vertical plane in front of the Trombe wall), the air stratification in height and also the air being heated near the Trombe wall were again visible, which was exposed to direct solar radiation (4 pm) and, consequently, was flowing up to the ceiling. Therefore, these CFD simulation results made sense and were coherent with the expected ones for a compartment with a Trombe wall exposed to direct solar radiation, which ensured the reliability of the implemented models.   Looking at the results of the horizontal plane plotted in Figure 9a was well visible the colder air entrance to the Trombe wall air cavity through its lower vent, as well as the warmer air flowing out of the upper vent near the ceiling. Moreover, in Figure 9b (the vertical plane in front of the Trombe wall), the air stratification in height and also the air being heated near the Trombe wall were again visible, which was exposed to direct solar radiation (4 pm) and, consequently, was flowing up to the ceiling. Therefore, these CFD simulation results made sense and were coherent with the expected ones for a compartment with a Trombe wall exposed to direct solar radiation, which ensured the reliability of the implemented models.

Results and Discussion
In this section, the obtained results have been presented and discussed, starting with the Trombe wall benefits, regarding the thermal behavior and heating energy savings. Thereafter, the results of the sensibility analysis, for several Trombe wall parameters, have been described and discussed.

Trombe Wall Benefits
In this section, the water Trombe wall benefits were assessed, making use of in situ indoor air temperature measurements (Section 3.1.1.) and advanced dynamic numerical simulations for the heating energy reduction predictions (Section 3.1.2.). These assessments were performed by comparison between module 1 (the reference one) and module 2 (the one with a Trombe wall) located in the city of Coimbra (Portugal), during winter.

Indoor Temperature Increase
The indoor air temperature comparisons were made using the data from measurements taken simultaneously with the temperature and humidity sensors [48], on both modules (with and without the Trombe wall) and are plotted in Figure 10, as well as the exterior environment air temperature. Two distinct winter weeks were chosen to demonstrate the behavior of the modules under different weather conditions. In Figure 10a, the records for a sunny week (from 28 th of December to 3 rd of January) are displayed, while in Figure 10b, the measurements for a cloudy week (from 16th to 22nd of December) are shown.
In the sunny winter week (Figure 10a), the indoor air temperature increase in module 2 due to the Trombe wall was well visible, having an average temperature of 16.2 • C, i.e., a temperature increase of 3.3 • C relative to module 1. Notice that even with a Trombe wall, the indoor comfort air temperature (e.g., 18 • C) was not reached. Another interesting feature was that the daily indoor air temperature amplitude (or fluctuation) was also greater in the experimental module with the Trombe wall (module 2), having a higher temperature increase rate during the day (due to the solar heat gains) and also a higher temperature decrease rate during the night (due to the higher heat losses through the Trombe wall, which did have any night shutter device).

Results and Discussion
In this section, the obtained results have been presented and discussed, starting with the Trombe wall benefits, regarding the thermal behavior and heating energy savings. Thereafter, the results of the sensibility analysis, for several Trombe wall parameters, have been described and discussed.

Trombe Wall Benefits
In this section, the water Trombe wall benefits were assessed, making use of in situ indoor air temperature measurements (Section 3.1.1.) and advanced dynamic numerical simulations for the heating energy reduction predictions (Section 3.1.2.). These assessments were performed by comparison between module 1 (the reference one) and module 2 (the one with a Trombe wall) located in the city of Coimbra (Portugal), during winter.

Indoor Temperature Increase
The indoor air temperature comparisons were made using the data from measurements taken simultaneously with the temperature and humidity sensors [48], on both modules (with and without the Trombe wall) and are plotted in Figure 10, as well as the exterior environment air temperature. Two distinct winter weeks were chosen to demonstrate the behavior of the modules under different weather conditions. In Figure 10a, the records for a sunny week (from 28 th of December to 3 rd of January) are displayed, while in Figure 10b, the measurements for a cloudy week (from 16th to 22nd of December) are shown.
In the sunny winter week (Figure 10a), the indoor air temperature increase in module 2 due to the Trombe wall was well visible, having an average temperature of 16.2 °C, i.e., a temperature increase of 3.3 °C relative to module 1. Notice that even with a Trombe wall, the indoor comfort air temperature (e.g., 18 °C) was not reached. Another interesting feature was that the daily indoor air temperature amplitude (or fluctuation) was also greater in the experimental module with the Trombe wall (module 2), having a higher temperature increase rate during the day (due to the solar heat gains) and also a higher temperature decrease rate during the night (due to the higher heat losses through the Trombe wall, which did have any night shutter device).
When the sky was cloudy (Figure 10b), as expected, the daily temperature variation was very smothered, and the air temperature difference inside the modules became very reduced, which was only 1 °C higher for this week inside module 2. Comparing both weeks (sunny and cloudy), the average environment exterior air temperature was lower during the sunny week (Figure 10a) (12.2 °C) in comparison with the cloudy week (13.4 °C), which was 1.2 °C higher. This was due to the night cooling effect, which was much higher in a winter clear sky in comparison with a cloudy sky. Thus, this feature also demonstrated how important it was to control the night heat losses, mainly when the sky was clear, in order to optimize the thermal performance of the Trombe wall during the heating season.

Heating Energy Decrease
In this section, the heating energy decrease due to the existence of a Trombe Wall was predicted, making use of advanced numerical dynamic simulation models, as previously detailed in Section 2.2.2 and validated in Section 2.3. The hourly weather data was obtained from the EnergyPlus IWEC database [53] for Coimbra city (Portugal), and the computations were performed for all winter season (from 22 nd of December until the 20 th of March). The modeled air-conditioning heating system was a "split" type with no fresh air, having a coefficient of performance (COP) for heating mode equal to 2.35, with the adopted energy source the electricity from the grid.
To compare its relevance in the heating energy demand, two heating set-points were simulated, namely, 20 °C and 18 °C, respectively; the former and current thermal comfort temperatures considered for calculating residential heating energy needs in Portugal [54].
Moreover, two occupation schedules and use types were considered, namely, (1) an office space occupied from 08:00 to 18:00 during weekdays (Monday to Friday), and (2) a residential space occupied from 19:00 to 07:00 during all days. The predicted energy demand for heating (electricity) was displayed and analyzed as a total value (kWh) and as normalized values (kWh/m 2 ).

Residential Space Use (Heating during the Night)
The heating energy demand predicted for residential space use (night occupation) is displayed in Figure 11 for both LSF modules and two heating set-points. As expected, reducing the heating setpoint (18 °C instead of 20 °C) allowed reducing also the heating energy consumption. This energy reduction was significant (Figure 11b), ranging from −33%, in the reference LSF module 1, to −40% in the Trombe wall LSF module 2.
The heating energy consumption in module 2 was 5% lower than in module 1 for an 18 °C heating set-point, confirming the energy efficiency advantage of the Trombe wall (TW) in the second LSF module. However, when the heating set-point was higher (20 °C), the computed results showed a 5% increase in the heating energy for the TW module 2 (24.79 kWh/m 2 ) in comparison with the reference module 1 (23.60 kWh/m 2 ). This surprising feature was related to the increased heat losses during the night due to the existence of the TW in module 2, which were not enough to balance the solar heat gains during the daytime, and this assumption has been explained in detail in the following paragraphs.
The space heating energy demand, besides the efficiency of the air-conditioning system (assumed to be 2.35 for the heating mode in this work), depended on the heat balance (gains versus losses) for each module. When this heat balance was positive (e.g., during a sunny day due to significant solar heat gains), the indoor temperature arose. When this heat balance was negative (e.g., When the sky was cloudy (Figure 10b), as expected, the daily temperature variation was very smothered, and the air temperature difference inside the modules became very reduced, which was only 1 • C higher for this week inside module 2. Comparing both weeks (sunny and cloudy), the average environment exterior air temperature was lower during the sunny week (Figure 10a) (12.2 • C) in comparison with the cloudy week (13.4 • C), which was 1.2 • C higher. This was due to the night cooling effect, which was much higher in a winter clear sky in comparison with a cloudy sky. Thus, this feature also demonstrated how important it was to control the night heat losses, mainly when the sky was clear, in order to optimize the thermal performance of the Trombe wall during the heating season.

Heating Energy Decrease
In this section, the heating energy decrease due to the existence of a Trombe Wall was predicted, making use of advanced numerical dynamic simulation models, as previously detailed in Section 2.2.2 and validated in Section 2.3. The hourly weather data was obtained from the EnergyPlus IWEC database [53] for Coimbra city (Portugal), and the computations were performed for all winter season (from 22 nd of December until the 20 th of March). The modeled air-conditioning heating system was a "split" type with no fresh air, having a coefficient of performance (COP) for heating mode equal to 2.35, with the adopted energy source the electricity from the grid.
To compare its relevance in the heating energy demand, two heating set-points were simulated, namely, 20 • C and 18 • C, respectively; the former and current thermal comfort temperatures considered for calculating residential heating energy needs in Portugal [54].
Moreover, two occupation schedules and use types were considered, namely, (1) an office space occupied from 08:00 to 18:00 during weekdays (Monday to Friday), and (2) a residential space occupied from 19:00 to 07:00 during all days. The predicted energy demand for heating (electricity) was displayed and analyzed as a total value (kWh) and as normalized values (kWh/m 2 ).

Residential Space Use (Heating during the Night)
The heating energy demand predicted for residential space use (night occupation) is displayed in Figure 11 for both LSF modules and two heating set-points. As expected, reducing the heating set-point (18 • C instead of 20 • C) allowed reducing also the heating energy consumption. This energy reduction was significant (Figure 11b), ranging from −33%, in the reference LSF module 1, to −40% in the Trombe wall LSF module 2.
Obviously, when the indoor air temperature set-point was elevated from 18 °C up to 20 °C, the temperature difference between indoor and outdoor conditions also increased, leading also to an increase in the heat losses, which originated a higher space heating energy consumption to maintain the defined set-point indoor temperature. Once again, this feature reinforced the importance of mitigating heat losses through the TW, mainly during winter season night-time, for example, making use of a controllable night shutter device. Office Space Use (Heating during the Day) The heating energy demand simulation results, assuming an office space use, i.e., during the daytime, in both LSF modules, are displayed in Figure 12. Now, the energy efficiency benefits of the TW use were significantly higher in comparison with the residential daytime use (Figure 11). The heating energy reduction ranged from −14%, for a 20 °C heating set-point, to −27% for an 18 °C setpoint. This improved energy efficiency was because the heating schedule of the air-conditioning system matched the higher TW solar heating gains during the daytime. Consequently, the indoor temperature increased, and the heating energy use decreased for both heating set-points.
Comparing the energy demand for both heating set-points, the energy reduction in percentages was similar to the previous ones, i.e., residential space use (Figure 11b), ranging from −32% up to −42% (Figure 12b), for reference LSF module 1 and TW module 2, respectively. However, in absolute values, this energy consumption reduction was smaller, i.e., −5.41 kWh/m 2 (office daytime use) instead of −7.80 kWh/m 2 (residential night-time use) for module 1, while for module 2, it was −6.09 kWh/m 2 instead of −9.84 kWh/m 2 , for office and residential space use, respectively. The heating energy consumption in module 2 was 5% lower than in module 1 for an 18 • C heating set-point, confirming the energy efficiency advantage of the Trombe wall (TW) in the second LSF module. However, when the heating set-point was higher (20 • C), the computed results showed a 5% increase in the heating energy for the TW module 2 (24.79 kWh/m 2 ) in comparison with the reference module 1 (23.60 kWh/m 2 ). This surprising feature was related to the increased heat losses during the night due to the existence of the TW in module 2, which were not enough to balance the solar heat gains during the daytime, and this assumption has been explained in detail in the following paragraphs.
The space heating energy demand, besides the efficiency of the air-conditioning system (assumed to be 2.35 for the heating mode in this work), depended on the heat balance (gains versus losses) for each module. When this heat balance was positive (e.g., during a sunny day due to significant solar heat gains), the indoor temperature arose. When this heat balance was negative (e.g., during the night due to the exterior temperature drop and absence of solar radiation), the indoor temperature decreased.
As measured and previously plotted in Figure 10a, the indoor temperature increase rate during the day was bigger in module 2 (red line) due to the higher solar heat gains provided by the Trombe wall. However, as also displayed in the same figure, during the night, the indoor temperature decrease rate was also bigger in the TW module 2, compared to the reference module 1 (black line), due to higher heat losses through the Trombe wall.
In fact, the thermal transmittance (U-value) of the TW device, due to air circulation between the glazed air-cavity and the interior of the module, was increased to the U-value of the glazing panel (2.552 W/(m 2 ·K), see Figure 3b). Comparing this U-value with the one provided by the LSF wall (0.326 W/(m 2 ·K), see Table 2), for the same area and temperature difference, the heat losses through the glazing panel of the TW were almost 7 times higher (+683%).
Obviously, when the indoor air temperature set-point was elevated from 18 • C up to 20 • C, the temperature difference between indoor and outdoor conditions also increased, leading also to an increase in the heat losses, which originated a higher space heating energy consumption to maintain the defined set-point indoor temperature. Once again, this feature reinforced the importance of mitigating heat losses through the TW, mainly during winter season night-time, for example, making use of a controllable night shutter device.
Office Space Use (Heating during the Day) The heating energy demand simulation results, assuming an office space use, i.e., during the daytime, in both LSF modules, are displayed in Figure 12. Now, the energy efficiency benefits of the TW use were significantly higher in comparison with the residential daytime use (Figure 11). The heating energy reduction ranged from −14%, for a 20 • C heating set-point, to −27% for an 18 • C set-point. This improved energy efficiency was because the heating schedule of the air-conditioning system matched the higher TW solar heating gains during the daytime. Consequently, the indoor temperature increased, and the heating energy use decreased for both heating set-points. Jaber and Ajib [55] also performed hourly energy computer simulations to analyze the energy performance of a Trombe wall system for a typical Jordanian residential building (Mediterranean region). The studied house had a rectangular shape, having a floor area of about 154 m 2 . The heavyweight façade walls had a very reduced thermal transmittance value, 0.133 W/(m 2 •K), which corresponded to 41% of the LSF walls' -value in the experimental modules, i.e., 0.326 W/(m 2 •K) (see Table 2).
Their simulations were performed for a 20 °C heating set-point [55]. The predicted normalized heating energy consumption for the Jordanian building, without a Trombe wall, was 15.27 kWh/m 2 , which was reduced to 12.09 kWh/m 2 (−21%), simulating a TW filling 18% of the south-oriented façade area (two bedrooms). They performed several simulations for different TW area ratios, ranging from 0% up to 50%, and based on the obtained results, they adjusted a polynomial curve (2nd order regression) to estimate the percentage of energy saving.
Making use of the previously mentioned estimation curve and applying the area ratio for the modular water TW evaluated in this paper, which was about 20%, the predicted energy saving would be around 22%. Not surprisingly, due to our reduced exterior walls insulation level, this energysaving prediction was considerably higher than the ones obtained here for the 20 °C indoor set-point temperature.

Parametric Study
After analyzing the Trombe wall (TW) benefits in terms of indoor air temperature increase and heating energy decrease, in this section, a parametric study was conducted to assess the impact of the changes of some TW-related parameters on its thermal behavior. In this sensibility analysis, all the simulations were performed for the TW LSF module 2, having as reference for comparison the DesignBuilder model, previously validated in Section 2.3.2, i.e., an unoccupied module. Notice that only one parameter was changed for each evaluated scenario, as displayed in Table 3. Four different parameters were evaluated: (1) Air cavity thickness; (2) Air vents dimensions; (3) Storage thickness; (4) Thermal storage material. For each parameter, two additional scenarios were assessed, besides the reference model scenario. Again, the hourly weather data for Coimbra (Portugal) was used [53], and a sunny winter week was chosen (23rd-29th January) for these simulations.

Parameter
Model Value Reference 10 cm Comparing the energy demand for both heating set-points, the energy reduction in percentages was similar to the previous ones, i.e., residential space use (Figure 11b), ranging from −32% up to −42% (Figure 12b), for reference LSF module 1 and TW module 2, respectively. However, in absolute values, this energy consumption reduction was smaller, i.e., −5.41 kWh/m 2 (office daytime use) instead of −7.80 kWh/m 2 (residential night-time use) for module 1, while for module 2, it was −6.09 kWh/m 2 instead of −9.84 kWh/m 2 , for office and residential space use, respectively. Jaber and Ajib [55] also performed hourly energy computer simulations to analyze the energy performance of a Trombe wall system for a typical Jordanian residential building (Mediterranean region). The studied house had a rectangular shape, having a floor area of about 154 m 2 . The heavyweight façade walls had a very reduced thermal transmittance value, 0.133 W/(m 2 ·K), which corresponded to 41% of the LSF walls' U-value in the experimental modules, i.e., 0.326 W/(m 2 ·K) (see Table 2).
Their simulations were performed for a 20 • C heating set-point [55]. The predicted normalized heating energy consumption for the Jordanian building, without a Trombe wall, was 15.27 kWh/m 2 , which was reduced to 12.09 kWh/m 2 (−21%), simulating a TW filling 18% of the south-oriented façade area (two bedrooms). They performed several simulations for different TW area ratios, ranging from 0% up to 50%, and based on the obtained results, they adjusted a polynomial curve (2nd order regression) to estimate the percentage of energy saving.
Making use of the previously mentioned estimation curve and applying the area ratio for the modular water TW evaluated in this paper, which was about 20%, the predicted energy saving would be around 22%. Not surprisingly, due to our reduced exterior walls insulation level, this energy-saving prediction was considerably higher than the ones obtained here for the 20 • C indoor set-point temperature.

Parametric Study
After analyzing the Trombe wall (TW) benefits in terms of indoor air temperature increase and heating energy decrease, in this section, a parametric study was conducted to assess the impact of the changes of some TW-related parameters on its thermal behavior. In this sensibility analysis, all the simulations were performed for the TW LSF module 2, having as reference for comparison the DesignBuilder model, previously validated in Section 2.3.2, i.e., an unoccupied module. Notice that only one parameter was changed for each evaluated scenario, as displayed in Table 3. Four different parameters were evaluated: (1) Air cavity thickness; (2) Air vents dimensions; (3) Storage thickness; (4) Thermal storage material. For each parameter, two additional scenarios were assessed, besides the reference model scenario. Again, the hourly weather data for Coimbra (Portugal) was used [53], and a sunny winter week was chosen (23rd-29th January) for these simulations.

Air Cavity Thickness
The first TW parameter analyzed was the air cavity thickness between the storage wall and the glazed exterior frame. Three different air cavity thicknesses were evaluated: 10 cm (reference), 20 cm (scenario 1), and 30 cm (scenario 2), as illustrated in Figure 13. The increase in the air cavity thickness originated an indoor air temperature decrease. While the reference model had an average temperature of 18.2 • C, when the air cavity thickness was doubled (20 cm) and tripled (30 cm), the indoor temperature decreased to 0.9 • C and 1.2 • C, respectively. These results allowed to conclude that, for this TW configuration, the better thermal performance was achieved for the smaller air cavity (10 cm), which could be related to the lower air volume to be heated inside the air cavity and the higher buoyancy effect, promoting an increased upwards air convection and consequent higher heat flow through the upper vent to the interior of the module. The first TW parameter analyzed was the air cavity thickness between the storage wall and the glazed exterior frame. Three different air cavity thicknesses were evaluated: 10 cm (reference), 20 cm (scenario 1), and 30 cm (scenario 2), as illustrated in Figure 13. The increase in the air cavity thickness originated an indoor air temperature decrease. While the reference model had an average temperature of 18.2 °C, when the air cavity thickness was doubled (20 cm) and tripled (30 cm), the indoor temperature decreased to 0.9 °C and 1.2 °C, respectively. These results allowed to conclude that, for this TW configuration, the better thermal performance was achieved for the smaller air cavity (10 cm), which could be related to the lower air volume to be heated inside the air cavity and the higher buoyancy effect, promoting an increased upwards air convection and consequent higher heat flow through the upper vent to the interior of the module.
Hong et al. [56] performed a three-dimensional CFD thermal simulation of a Trombe wall with Venetian blind structure located in Hefei (China), assuming adiabatic surfaces for the air vents and internal wall. They compared several air cavity thicknesses, ranging from 8 cm up to 18 cm, with an increment of 2 cm. No significant thermal performance improvement was found for a thickness of the air cavity higher than 14 cm. Thus, they suggested a thickness equal to 14 cm.

Air Vents Dimensions
The second parameter analyzed was the dimension of the interior vents present on the storage wall to allow vertical air convection and airflow to/from the LSF module. The reference model had an upper vent with dimensions of 50 × 10 cm and a lower vent with 50 × 5 cm. Two additional scenarios were evaluated by modeling increased vents dimensions: 50 × 13 cm (upper) and 50 × 8 cm Hong et al. [56] performed a three-dimensional CFD thermal simulation of a Trombe wall with Venetian blind structure located in Hefei (China), assuming adiabatic surfaces for the air vents and internal wall. They compared several air cavity thicknesses, ranging from 8 cm up to 18 cm, with an increment of 2 cm. No significant thermal performance improvement was found for a thickness of the air cavity higher than 14 cm. Thus, they suggested a thickness equal to 14 cm.

Air Vents Dimensions
The second parameter analyzed was the dimension of the interior vents present on the storage wall to allow vertical air convection and airflow to/from the LSF module. The reference model had an upper vent with dimensions of 50 × 10 cm and a lower vent with 50 × 5 cm. Two additional scenarios were evaluated by modeling increased vents dimensions: 50 × 13 cm (upper) and 50 × 8 cm (lower) in scenario 3, and; 50 × 16 cm (upper) and 50 × 11 cm (lower) in scenario 4. Figure 14 displays the obtained results, where a slightly indoor air temperature increase was visible with an increase in the dimensions of the air vents (+0.4 • C for scenario 3 and +0.5 • C for scenario 4). As expected, this indoor temperature increase was greater during the daytime, near noon, when the solar radiation was also higher. This better thermal performance could be justified by the increased natural air convection and airflow exchange between the TW air cavity and the interior of the module. Moreover, it could be deduced that forced air convection, making use of small fans, might improve, even more, the TW thermal performance.
Energies 2020, 13,2744 18 of 25 Figure 14 displays the obtained results, where a slightly indoor air temperature increase was visible with an increase in the dimensions of the air vents (+0.4 °C for scenario 3 and +0.5 °C for scenario 4). As expected, this indoor temperature increase was greater during the daytime, near noon, when the solar radiation was also higher. This better thermal performance could be justified by the increased natural air convection and airflow exchange between the TW air cavity and the interior of the module. Moreover, it could be deduced that forced air convection, making use of small fans, might improve, even more, the TW thermal performance.
Hong et al. [56] also evaluated the influence of the inlet/outlet vent dimensions in the Trombe wall (2.00 m high × 1.00 m width) thermal performance. They assumed equal sized upper and lower vents and fixed their height to 10 cm. The vents width ranged from 20 cm up to 70 cm, with an increment of 10 cm. They found a slight decrease in the TW thermal performance for 70 cm width vents and suggested the use of vents with the following dimensions: 60 cm width × 10 cm height.

Storage Wall Thickness
The third parameter analyzed was the thickness of the water storage wall of the Trombe wall. The reference model had a 5 cm water storage wall composed of black painted steel, filled with water. Two additional scenarios with increased storage wall thickness were evaluated: 10 cm for scenario 5 and 15 cm for scenario 6. Figure 15 exhibits the obtained results, where a decrease in indoor air temperature was visible in scenarios 5 (−0.7 °C) and 6 (−1.0 °C). This worst TW thermal performance could be justified by the larger volumes of water to be heated, inside the storage walls, by the same solar radiation and the consequent lower temperatures achieved.
Briga-sá et al. [9] also evaluated the influence of the storage wall thickness (15 cm up to 40 cm), made of concrete, on ventilated and non-ventilated Trombe walls for the climate of Vila Real, a city located in the north of Portugal. Making use of a simplified calculation methodology prescribed by standard ISO13790:2008, they found that the heat gains were reduced when increasing the thickness for non-ventilated TWs, while for ventilated TWs, the heat gains increased. Hong et al. [56] also evaluated the influence of the inlet/outlet vent dimensions in the Trombe wall (2.00 m high × 1.00 m width) thermal performance. They assumed equal sized upper and lower vents and fixed their height to 10 cm. The vents width ranged from 20 cm up to 70 cm, with an increment of 10 cm. They found a slight decrease in the TW thermal performance for 70 cm width vents and suggested the use of vents with the following dimensions: 60 cm width × 10 cm height.

Storage Wall Thickness
The third parameter analyzed was the thickness of the water storage wall of the Trombe wall. The reference model had a 5 cm water storage wall composed of black painted steel, filled with water. Two additional scenarios with increased storage wall thickness were evaluated: 10 cm for scenario 5 and 15 cm for scenario 6. Figure 15 exhibits the obtained results, where a decrease in indoor air temperature was visible in scenarios 5 (−0.7 • C) and 6 (−1.0 • C). This worst TW thermal performance could be justified by the larger volumes of water to be heated, inside the storage walls, by the same solar radiation and the consequent lower temperatures achieved.

Thermal Storage Material
The fourth and last parameter studied was the thermal storage material of the Trombe wall. As stated before, the reference TW thermal storage material was water. Two additional scenarios were simulated, making use of two other materials: concrete in scenario 7 and basalt stone in scenario 8. The thermal properties (thermal conductivity, specific heat, and density) of these three materials are displayed in Table 4. Regarding the optical properties, all these materials were modeled as being black painted, i.e., having solar and visible absorptances equal to 0.9. Table 4. Thermal conductivity ( ), specific heat ( ), and density () of thermal storage materials evaluated [37].

Material ((m•K)/W) (J/(kg•K))
 (kg/m 3 )  Figure 16 exhibits the obtained results, showing a slight decrease in the average indoor air temperature inside module 2 for the newly evaluated thermal storage materials: −0.4 °C for concrete (scenario 7) and −0.8 °C for basalt stone (scenario 8). Concrete storage material exhibited a higher temperature increase rate but also the higher temperature decrease rate during the cooling afternoon and night time, perhaps due to the significant lower specific heat (about four times smaller) and higher thermal conductivity (almost two times greater). The basalt stone temperature curve (scenario 8) exhibited a similar trend to the water temperature curve (Ref.), but with slightly lower indoor air temperature values (−0.8 °C).
As stated by Saadatian et al. [7], "Because the specific heat of water ( ) is higher than that of other types of building material, such as concrete, bricks, adobe, and stone, water stores more heat than the other materials. Similarly, because water convects, the transfer of heat to the interior space occurs faster than with classic Trombe walls.". Hu et al. pointed out another advantage of water as a thermal storage material: "Because the specific heat of water is higher than that of the building materials, the water's surface temperature does not rise as high as that of the masonry. Therefore, less heat is reflected back through the glazing." Nevertheless, Saadatian et al. [7], regarding water TWs, also stated that: "in harsh colder climates the glass layer should be insulated. Otherwise, the loss of heat from the warm wall to the outside would be significant.". Briga-sá et al. [9] also evaluated the influence of the storage wall thickness (15 cm up to 40 cm), made of concrete, on ventilated and non-ventilated Trombe walls for the climate of Vila Real, a city located in the north of Portugal. Making use of a simplified calculation methodology prescribed by standard ISO13790:2008, they found that the heat gains were reduced when increasing the thickness for non-ventilated TWs, while for ventilated TWs, the heat gains increased.

Thermal Storage Material
The fourth and last parameter studied was the thermal storage material of the Trombe wall. As stated before, the reference TW thermal storage material was water. Two additional scenarios were simulated, making use of two other materials: concrete in scenario 7 and basalt stone in scenario 8. The thermal properties (thermal conductivity, specific heat, and density) of these three materials are displayed in Table 4. Regarding the optical properties, all these materials were modeled as being black painted, i.e., having solar and visible absorptances equal to 0.9. Table 4. Thermal conductivity (λ), specific heat (c), and density (ρ) of thermal storage materials evaluated [37].  Figure 16 exhibits the obtained results, showing a slight decrease in the average indoor air temperature inside module 2 for the newly evaluated thermal storage materials: −0.4 • C for concrete (scenario 7) and −0.8 • C for basalt stone (scenario 8). Concrete storage material exhibited a higher temperature increase rate but also the higher temperature decrease rate during the cooling afternoon and night time, perhaps due to the significant lower specific heat (about four times smaller) and higher thermal conductivity (almost two times greater). The basalt stone temperature curve (scenario 8) exhibited a similar trend to the water temperature curve (Ref.), but with slightly lower indoor air temperature values (−0.8 • C).

Conclusions
In this work, the influence of a passive modular water Trombe wall (TW) in the thermal behavior and energy efficiency of a lightweight steel frame (LSF) compartment was evaluated. Two real scale experimental identical LSF cubic modules, located in Coimbra (Portugal), exposed to natural exterior weather conditions, were used for in situ measurements. Module 1 was used as a reference, while the other one (module 2) was used to measure the influence of the TW, positioned in the south façade, on their thermal behavior by making a direct comparison between both modules. Additionally, these measurements allowed to calibrate and validate two numerical models (without and with a TW), with very good accuracy, i.e., having a root mean square error (RMSE) equal to 0.3 °C, for the reference model, and 0.5 °C for the TW model. These two validated models were used to perform advanced dynamic thermal simulations, making use of DesignBuilder software. Finally, these validated models allowed to predict the TW benefits in the heating energy consumption, as well as to perform a parametric study to evaluate the influence of four TW-related parameters on its thermal performance.
The first conclusion remark was that in this work, it was possible to evaluate the thermal behavior influence of a TW by in situ direct measurements and also performing advanced thermal dynamic simulations. The assessment was performed by quantifying the TW benefits (thermal and heating energy) and carrying out a thermal behavior parametric study. Several comparisons were performed, regarding (1) Sunny and cloudy winter week thermal behavior; (2) Office and residential space use heating energy; (3) Two heating set-points (20 °C and 18 °C); (4) Thickness of the TW air cavity; (5) Thickness of the thermal storage wall; (6) Dimensions of the interior upper/lower vents, and (7) Material of the thermal storage wall.
Regarding the obtained results for the TW benefits evaluation, the following main conclusions could be pointed out:

•
In both sunny and cloudy winter weeks, the measured temperature was higher in module 2 (with a TW passive device). However, the warmer effect of the TW was much more effective during the sunny week, increasing the average indoor air temperature significantly, i.e., +3.3 °C and +4.0 °C relative to the interior of module 1 (reference) and exterior environment temperatures, respectively. • During the winter season, it was found that a TW was significantly more efficient for an office use schedule (during daytime), instead of a residential use schedule (during nigh-time). The heating energy consumption was reduced from 14.95 kWh/m 2 , for residential space, down to 8.53 kWh/m 2 for office space (−43%), for an 18 °C indoor comfort temperature.

•
A smaller heating set-point (18 °C instead of 20 °C) allowed to significantly reduce the heating energy consumption with and without a TW device, more than 40% and 32% reductions, respectively. As stated by Saadatian et al. [7], "Because the specific heat of water (c) is higher than that of other types of building material, such as concrete, bricks, adobe, and stone, water stores more heat than the other materials. Similarly, because water convects, the transfer of heat to the interior space occurs faster than with classic Trombe walls.". Hu et al. pointed out another advantage of water as a thermal storage material: "Because the specific heat of water is higher than that of the building materials, the water's surface temperature does not rise as high as that of the masonry. Therefore, less heat is reflected back through the glazing." Nevertheless, Saadatian et al. [7], regarding water TWs, also stated that: "in harsh colder climates the glass layer should be insulated. Otherwise, the loss of heat from the warm wall to the outside would be significant.".

Conclusions
In this work, the influence of a passive modular water Trombe wall (TW) in the thermal behavior and energy efficiency of a lightweight steel frame (LSF) compartment was evaluated. Two real scale experimental identical LSF cubic modules, located in Coimbra (Portugal), exposed to natural exterior weather conditions, were used for in situ measurements. Module 1 was used as a reference, while the other one (module 2) was used to measure the influence of the TW, positioned in the south façade, on their thermal behavior by making a direct comparison between both modules. Additionally, these measurements allowed to calibrate and validate two numerical models (without and with a TW), with very good accuracy, i.e., having a root mean square error (RMSE) equal to 0.3 • C, for the reference model, and 0.5 • C for the TW model. These two validated models were used to perform advanced dynamic thermal simulations, making use of DesignBuilder software. Finally, these validated models allowed to predict the TW benefits in the heating energy consumption, as well as to perform a parametric study to evaluate the influence of four TW-related parameters on its thermal performance.
The first conclusion remark was that in this work, it was possible to evaluate the thermal behavior influence of a TW by in situ direct measurements and also performing advanced thermal dynamic simulations. The assessment was performed by quantifying the TW benefits (thermal and heating energy) and carrying out a thermal behavior parametric study. Several comparisons were performed, regarding (1) Sunny and cloudy winter week thermal behavior; (2) Office and residential space use heating energy; (3) Two heating set-points (20 • C and 18 • C); (4) Thickness of the TW air cavity; (5) Thickness of the thermal storage wall; (6) Dimensions of the interior upper/lower vents, and (7) Material of the thermal storage wall.
Regarding the obtained results for the TW benefits evaluation, the following main conclusions could be pointed out:

•
In both sunny and cloudy winter weeks, the measured temperature was higher in module 2 (with a TW passive device). However, the warmer effect of the TW was much more effective during the sunny week, increasing the average indoor air temperature significantly, i.e., +3.3 • C and +4.0 • C relative to the interior of module 1 (reference) and exterior environment temperatures, respectively. • During the winter season, it was found that a TW was significantly more efficient for an office use schedule (during daytime), instead of a residential use schedule (during nigh-time). The heating energy consumption was reduced from 14.95 kWh/m 2 , for residential space, down to 8.53 kWh/m 2 for office space (−43%), for an 18 • C indoor comfort temperature.

•
A smaller heating set-point (18 • C instead of 20 • C) allowed to significantly reduce the heating energy consumption with and without a TW device, more than 40% and 32% reductions, respectively. • A 27% reduction in heating energy due to TW device for an office 18 • C set-point was found, and this energy reduction was smaller (−14%) for the heating 20 • C set-point.
For residential use, the TW energy benefits were very reduced (only 5% decrease for 18 • C set-point), and there was even a heating energy consumption increase (+5%) when the set-point was 20 • C, due to nocturnal heat losses through the TW device.
Regarding the TW device parametric study, the main conclusions could be summarized as follows: • An increase in the original TW air cavity thickness (10 cm) did not show any thermal performance improvement, and a decrease in the average indoor air temperature was found (−0.9 • C and −1.2 • C).

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An increase in the original thermal storage wall thickness (5 cm) did not show any thermal performance improvement, and a decrease in the average indoor air temperature was obtained (−0.7 • C and −1.0 • C).

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Changing the material of the storage wall (water) reduced the thermal performance of the TW device, originating a decrease in the average indoor air temperature (−0.4 • C and −0.8 • C).
In short, a TW device could, in fact, significantly improve the thermal behavior of an LSF compartment and reduce heating energy consumption during winter in a Csb Köppen-Geiger [47] Mediterranean climate. However, there were many factors that could influence the TW thermal performance, with adequate design and control to mitigate nocturnal heat losses very important. Otherwise, their thermal performance and energy efficiency improvement could be very insignificant and even decreased.
As most of the research studies, this work also had some limitations, including the assessment of only one climate/location, only one TW orientation (south exposed), only one isolated small compartment (not an entire building) without any window, only one construction system (LSF), only the heating mode during the winter season was evaluated (not an entire year), etc. Thus, in real buildings, thermal behavior and energy performance are much more complex, depending on many more factors. Nevertheless, the obtained results and conclusions could be very useful to identify the main benefits and possible drawbacks of a solar passive TW device in an LSF compartment, as well as to enhance the importance of the indoor set-point temperature and the occupation schedule of the compartment.