1. Introduction
Buildings account for 30–40% of the world’s total energy expenditure, as well as 20–30% of total global greenhouse gas (GHG) emissions [
1,
2]. The European Union (EU-28) saw an average annual increase of 6.3% in space cooling energy consumption from 2000 to 2015 [
3]. Adopting energy-efficient measures, such as free cooling techniques, effectively reduces a building’s energy consumption. [
4,
5,
6]. One such technique is ventilative cooling, which utilizes ambient air for space cooling [
7,
8]. Although ventilative cooling can reduce energy consumption, its overall effectiveness is hampered by certain limitations. For example, during heat waves, outdoor temperatures may not be cool enough [
9]. Cooling energy recovery from cold water can offer a substantial amount of free cooling. A 10 °C change in water temperature and a daily water consumption of 1000 L produces approximately 42 MJ of free cooling energy. A recent application is the cooling of subway stations and shelters during heat waves [
10]. Furthermore, past studies have examined the effect of cold recovery from domestic cold water (DCW) on GHG emissions, financial considerations, and water quality [
11,
12,
13].
To recover cooling energy from DCW, DCW can be circulated through pipes embedded in a thermally massive wall before it is dispensed by occupants for regular domestic usage. Hydronic panel heating and cooling systems have extensively employed thermally massive building components, such as concrete walls and floors [
14]. These systems are often referred to as thermally activated building systems (TABS). TABS reduces space heating/cooling energy consumption and mechanical system capacities through thermal energy storage (TES) [
15,
16,
17,
18]. TES stabilizes cooling heat flux (i.e., cooling capacity) fluctuations and wall surface temperature, preventing the surface temperature from falling too quickly to extremely low values. Massive walls are preferable to metal panels since the former can store higher amounts of thermal energy, prevent excessive low wall surface temperature, and elongate the cooling period. TABS also enhances thermal comfort by creating a gradual change in indoor air temperature and evenly distributing the heat flux density [
19].
Several research studies have been conducted to identify the key parameters that affect the cooling performance of TABS. In a parametric study, Antonopoulos et al. [
20] determined that water inlet temperature, pipe spacing, pipe depth, and zone air temperature had significant effects on thermal performance, while other parameters had a negligible impact. These observations have been confirmed by similar studies [
21,
22,
23]. The water cooling capacity (i.e., how well the water removes heat from the wall) and wall surface cooling capacity (i.e., how well the wall removes heat from the associated zone) in hydronic pipe-embedded systems are significantly influenced by the supply water temperature. Antonopoulos et al. [
20] discovered that lowering the supply water temperature from 15 °C to 5 °C resulted in an increase in cooling heat flux density from 45 W/m
2 to 120 W/m
2. Furthermore, different studies have also investigated the use of relatively high-temperature water (18 °C to 25 °C) for space cooling to reduce energy consumption. Šimko et al. [
24] conducted an experiment to determine the maximum cooling capacity for a 16 °C to 25 °C water inlet temperature range. Similar studies [
25,
26,
27] carried out experiments with a supply water temperature range of 18 °C to 21 °C. Raising water supply temperatures would lead to a reduction in energy consumption for chilling water. However, it would also result in a notable decrease in the cooling capacity of the TABS system [
19]. Moreover, further studies [
21,
26,
28] have demonstrated that pipe spacing significantly affects cooling capacity. They found that decreasing the pipe spacing in the same area would result in greater cooling capacity due to an increase in the heat transfer area. Junasová et al. [
29] discovered that by reducing the pipe spacing from 15 cm to 5 cm, the cooling capacity increased by over 40%.
Using thermally massive walls to recover cooling energy from DCW (herein as “DCW-wall”) and assist space cooling does not require complex construction. A diverter valve can be installed to allow DCW to bypass the massive walls during the heating season. Therefore, DCW-walls could potentially reduce capital and operating costs compared with other space cooling technologies due to lower installation costs, downsizing, and ultimately the potential elimination of mechanical cooling systems and their maintenance requirements [
30,
31,
32]. In cold regions such as Canada, where the ground temperature is relatively lower than other regions, more cooling energy can be recovered. In addition, the outlet temperature of DCW will be warmed by room air to make it more suitable for domestic usage (e.g., less mixing with domestic hot water in showers).
The existing literature predominantly focuses on space cooling using chilled water provided by mechanical equipment. However, the authors have observed a research gap in the evaluation of the free cooling potential of DCW before it is used for regular household consumption while also taking into account actual water consumption patterns in residential buildings. Therefore, the primary focus of this study is to address the question: “What is the cooling potential and energy-saving effectiveness of using DCW for space cooling through DCW-walls in residential buildings located in cold-climate regions?” The objective of this paper is to investigate the effectiveness of circulating DCW through thermally massive walls before regular household consumption. Through a comprehensive evaluation of various operational scenarios, such as inlet temperatures, zone temperatures, and engineering designs, this study aims to quantify the range of cooling potential achievable with DCW-walls. Specifically, the focus is on cold climate regions where DCW is relatively cooler, as this presents an opportunity for enhanced energy recovery. Additionally, this study will assess the extent to which the daily cooling energy supplied by a DCW-wall can meet the annual cooling energy requirements of a four-person dwelling in Toronto, Canada, which experiences warm and humid summers.
In terms of the paper’s organization, the research methodology is discussed first, followed by the development and validation of the numerical model. Then, the following
Section 3 has six subsections discussing water outlet temperature, average wall temperature, temperature uniformity, condensation prevention, cooling capacity, delivered (recovered) cooling energy (DCE), the performance difference of the three piping configurations, and the influence of wall surface area on total DCE.
3. Results and Discussion
This section presents the main results and associated analyses. For better clarity, the performance of the spiral configuration is presented first in the first four subsections:
Section 3.1—water outlet and average wall temperatures,
Section 3.2—wall surface temperature uniformity and a general guideline for preventing condensation on the wall,
Section 3.3—cooling heat flux density, and
Section 3.4—delivered cooling energy, based on the following parameters:
Supply water temperature (),
Zone temperature (),
Wall thickness (),
Pipe spacing ().
Section 3.5 compares the performance of the three configurations in the same above-mentioned aspects. The descriptions and figures in these subsections are for the temperature scenario of
= 12 °C,
= 25 °C, and
= 5 cm. The results for cooling heat flux density and delivered cooling energy of the other temperature scenarios, and wall thickness are tabulated in
Section 3.5.
Section 3.6 presents the influence of the wall surface area on the delivery cooling energy.
3.1. Water Outlet and Average Wall Temperatures
The behavior of the wall surface temperature varies depending on the system configuration. It is essential to calculate the surface temperature of the wall because the cooling capacity of the system is directly influenced by the temperature difference between the wall surface and the zone. In addition, calculating the minimum wall temperature is critical to determining the minimum allowable humidity level of the zone air to avoid condensation on the wall surface. Condensation also reduces the effectiveness of radiant cooling systems [
45]. Moreover, thermal comfort can be impacted by the uniformity of the surface temperature.
Figure 6 shows the average surface temperature fluctuations for a spiral configuration over a 24-h period.
The average wall surface temperature reaches its lowest values approximately 2 to 3 h after the water flow rate reaches its highest values, as shown in
Figure 6. The average surface temperature dropped to 19 °C and 20.6 °C at 19:00 for spacings of
= 10 cm and
= 30 cm, respectively. The 10 cm-thick wall is 1 °C less than the 5 cm-thick wall in this situation. As the flow rate approached zero, the surface temperature was close to the zone temperature due to insignificant heat rejection from the wall to the pipe. At the same time, the wall absorbed a significant amount of heat from the zone. Conversely, with an increase in the water flow rate, the wall surface temperature decreases because of a greater heat flux from the wall to the water, which leads to an increase in the water outlet temperature. The temperature range for the water outlet in both spacings of the spiral configuration varied between 16.7 °C and 24.2 °C.
Figure 7 shows the water outlet temperature variation for the spiral counterflow configuration.
3.2. Temperature Uniformity and Condensation Prevention
Temperature distribution on the wall surface is crucial not only for the comfort of the occupants but also for reducing the risk of condensation [
46,
47].
Figure 8 plots the wall surface temperature along the water flow path versus its distance from the water inlet and time of day for the spiral configuration. The coldest temperature is always at the inlet. The warmed temperature takes place between 3 AM and 6 AM at the pipe distance between 20 to 45 m from the inlet, which is at the center of the wall surface.
Figure 8 shows a maximum surface temperature difference of 3.5 °C across the wall at a pipe spacing of 10 cm and a difference of 3 °C at 30 cm.
To avoid condensation, the minimum wall surface temperature should be higher than the dewpoint temperature of the air inside the zone. To establish a conservative yet simple guideline, two minimum wall surface temperatures of all operation scenarios were used as dewpoint temperatures. Thereby, the corresponding relative humidity (RH) is found from a psychrometric chart based on the zone air temperature, as shown in
Table 2. To avoid condensation on the wall surface, indoor RH should not exceed 53.8% and 44.2% when the zone temperature is 25 °C and 30 °C, respectively. These findings are in agreement with the ideal indoor RH, which is between 30% and 50% [
48].
3.3. Cooling Heat Flux Density
In this study, the amount of heat absorbed by the wall surface from the zone per square meter of wall (W/m
2) is referred to as the cooling heat flux density (i.e., cooling capacity). Cholewa et al. [
49,
50] argued that due to heat loss toward the backside of cooled/heated walls, calculations of cooling capacity based on water temperature and flow rate do not always accurately represent the heat flux toward the zone. Cooling capacity can be obtained using Equation (7). According to this equation, the cooling capacity (
q) is always positive when cooling is delivered to the zone air (i.e., the zone air temperature is higher than the average wall surface temperature).
The combined heat transfer coefficient (
) between the zone and wall surface was set to 9.09 W/m
2·K [
33].
Figure 9 shows the changes in cooling capacity for the spiral configuration over a 24-h period.
As shown in
Figure 9, the cooling capacity reached its maximum at 50 W/m
2 for
= 10 cm and at 35.0 W/m
2 for
= 30 cm. The cooling capacity for
= 10 cm was significantly higher than that for
= 30 cm. This can be attributed to the longer pipe length, which provided a larger heat transfer area and a more uniform surface temperature, resulting in fewer hot spots. For both spacings, the minimum cooling capacity was around 10 W/m
2 when the flow rate was almost zero.
3.4. Delivered Cooling Energy
The delivered cooling energy (DCE) in this study was defined as the amount of cooling energy from the water delivered to the room and the wall (i.e., heat loss from the water flow) and was calculated using Equation (8).
where
is the simulation timestep (i.e., 60 s).
Figure 10 illustrates the cumulative DCE (“Total DCE”), the portion of DCE that goes to the room (“DCE to room”), and the amount of energy stored in the wall (“Energy stored in wall”) during a 24-h period.
DCE to room equals the amount of heat transferred between the room and the surface of the wall. Furthermore, the energy stored in the wall is calculated based on the difference between the total DCE and the DCE to room, which can either be heat storage (i.e., the wall temperature increases, negative values in
Figure 10) or cold storage (i.e., wall temperature decreases, positive values in
Figure 10). As shown in
Figure 10, in the first five hours, the accumulated energy stored in the wall (“Energy stored in wall”) was negative (i.e., wall became warmer) because the heat gain from the room was greater than the heat loss to the water due to the low water flow rate. According to
Figure 9, the total DCE for
= 10 cm increased throughout the day to a value of 20.0 MJ at the end of the day. For
= 30 cm, the total DCE reached 15.17 MJ after 24 h.
In order to evaluate the significance of the cooling energy that a DCW-wall can provide, the cooling energy was compared to the space energy demand of Toronto, Ontario, Canada as a benchmark city for the cold climate. Summers in Toronto, typically from June to August, can be quite warm, with temperatures often in the 20–30 °C range, sometimes rising even higher during heatwaves [
51]. Additionally, Toronto often experiences RH levels ranging from 60% to 70% during the summer [
52]. This range of humidity is primarily attributable to the city’s proximity to large water bodies, particularly Lake Ontario. To prevent condensation, it is essential to control the RH level in the zone when using radiant cooling systems. This can be achieved through measures such as the use of dehumidifiers.
To determine the space cooling energy demand in Toronto, calculations were performed using the average space cooling energy consumption of households in the province of Ontario. According to Natural Resources Canada and Statistics Canada [
53,
54], the average energy consumption per household for space cooling in Ontario was 1.9 GJ in 2019. To calculate the energy demand for space cooling, an energy efficiency rating for cooling equipment is necessary. The efficiency of cooling devices is commonly determined using the Seasonal Energy Efficiency Ratio (SEER) [
55]. The SEER is calculated by dividing the amount of heat removed from the air in British Thermal Units (BTUs) by the total energy consumed in watt-hours (Wh). SEER is similar to the Coefficient of Performance (COP), which is a unitless measurement [
55]. With a SEER of 10 BTU/Wh (equivalent to a COP of 2.9) [
56], the energy demand for space cooling can be calculated as 5.6 GJ (i.e., 2.9 × 1.9). Toronto experienced 23 days with mean ambient temperatures above 25 °C [
51]. If a DCW-wall in the above-mentioned configuration was operated for these 23 days, it could provide 0.026 GJ of cooling energy per day and ~0.6 GJ for 23 days. This is approximately 11% of the space cooling energy demand for the entire cooling season in Toronto. More cooling energy can be provided if the wall is operated on other days of the summer. In other words, the DCW-wall system would be credited with a higher contribution percentage if only the cooling demand during heat waves was considered. In this context, the proposed DCW-wall could even eliminate the need for mechanical cooling systems in cities with fewer days of heat waves.
3.5. Comparison of Three Configurations on the Basis of Model Results
This subsection compares the three configurations with respect to water outlet temperature, average wall surface temperature, wall surface temperature distribution, permissible indoor RH to avoid condensation, and cooling potentials.
3.5.1. Water Outlet and Average Wall Temperatures
Figure 11 depicts the changes in the average wall temperature for the three configurations during the 24-h period. When the cooling capacity was at its maximum and the pipe spacing was 10 cm, the average temperature of the wall surface decreased to 19 °C, 18.6 °C, and 18.8 °C for spiral, serpentine, and parallel configurations, respectively. In addition, when the pipe spacing was 30 cm, the spiral and serpentine configurations experienced the same minimum surface temperature of 20.6 °C, while the parallel configuration had a minimum temperature of 21.2 °C. When the cooling capacity reached its maximum value, the surface temperature of a 10 cm-thick wall was 1 °C warmer than that of a 5 cm-thick wall. Also, as the wall thickness was increased from 5 cm to 10 cm, a slower decrease rate of the wall surface temperature and a delay in reaching the minimum temperature by one hour were observed. These changes also had a continuous effect on the temperature of the outlet water. The water outlet temperature for all operation scenarios varied between 16.5 °C and 29 °C. When the flow rate was low, the outlet temperatures approached the zone temperatures.
3.5.2. Temperature Uniformity and Condensation Prevention
Figure 12 illustrates the wall surface temperature contours for all configurations throughout the day. As depicted in
Figure 12, the spiral configuration had a more evenly distributed temperature, with a maximum difference of 4 °C across the wall when compared to the serpentine and parallel configurations, which had maximum temperature differences of 6.5 °C and 6.7 °C, respectively. The variation in temperature uniformity between configurations is caused by the arrangement of pipes in the wall. In a spiral configuration, the cool supply water and less cool return water are parallel and therefore provide a more uniform cooling flux density to the wall. This difference in pipe layout also affects the minimum wall surface temperature, which is crucial for determining the permissible indoor RH.
Table 3 provides a guide to determining the allowable indoor RH to minimize the risk of condensation on the wall surface based on all temperature scenarios for the three piping configurations. Furthermore,
Table 3 displays the cases, along with the corresponding difference between the maximum and minimum wall surface temperature (
). This difference serves as an indicator of temperature uniformity.
For zone temperatures between 25 °C and 30 °C, the spiral configuration permits a higher indoor humidity level compared to the other configurations. The serpentine configuration allows for a 1% higher humidity level than the parallel configuration.
3.5.3. Cooling Heat Flux Density
Figure 13 shows the variation in cooling capacity in all modeled configurations for 24 h. As shown in
Figure 13, the maximum cooling capacity was observed approximately two hours after the water flow rate reached its peak. Among the different configurations, the serpentine configuration exhibited the highest cooling capacity for a pipe spacing of
= 10 cm, followed by the parallel and spiral configurations. Additionally, the difference in cooling capacity between the two spacings (i.e., the maximum distance between the two curves in
Figure 13) was greater for the parallel configuration than for the other two configurations. Similar to
= 10 cm, the serpentine configuration delivered the highest cooling capacity for
= 30 cm, followed by the spiral and parallel configurations.
Table 4 presents the maximum cooling capacity for all scenarios simulated in this study.
Based on
Table 4, the greatest decrease in maximum cooling capacity occurred at
S = 5 cm when the pipe spacing was changed from 10 cm to 30 cm. As a result of increased spacing, the cooling capacity for the serpentine configuration decreased by 33% for
S = 5 cm and 27% for
S = 10 cm. Moreover, when the pipe spacing was increased from 10 cm to 30 cm, the cooling capacity decreased by 40% and 34% for the parallel configuration at
S = 5 cm and
S = 10 cm, respectively. Similarly, for the spiral configuration, the decreases were 30% and 21%. These results suggest that pipe spacing has a more significant impact on maximum cooling capacity than wall thickness does.
To better understand the DCW-wall system performance in the context of existing water-based cooling systems,
Table 5 provides details on the maximum cooling capacity and associated parameters of the DCW-wall system and recent water-based cooling systems.
3.5.4. Delivered Cooling Energy
Figure 14 shows the changes in the cumulative total DCE, DCE to room, and energy stored in the wall over a 24-h period for all configurations. The cumulative DCE trends depicted in
Figure 14 exhibit similar behavior for all configurations and are discussed in
Section 3.4. In this context, although thermal mass did not significantly contribute to heat/cold storage, it could stabilize the wall surface temperature and cooling capacity throughout the day.
Table 6 presents the total DCE values for all scenarios. Similar to cooling capacity, the serpentine configuration showed the highest cooling energy delivered by the system in all temperature scenarios.
3.6. Influence of Wall Surface Area on Total DCE
In addition to the previously mentioned influential parameters, changes in wall dimensions affect the total DCE due to the change in pipe length and, therefore, the area of heat transfer. For the temperature scenario of
= 12 °C and
= 25 °C with a wall thickness of 5 cm,
Table 7 shows the simulation results of the total DCE for all configurations with respect to changes in wall surface area (wall height was fixed at 2 m, but length was subject to change).
As shown in
Table 7, on average, expanding the wall surface area from 4 m
2 to 6 m
2 resulted in a 21% increase in total DCE for pipe spacing of
= 10 cm and a 29% increase for
= 30 cm. Furthermore, for
= 10 cm, when the wall surface area was increased in a 2 m
2 increment, from 6 m
2 to 8 m
2, 8 m
2 to 10 m
2, and 10 m
2 to 12 m
2, the total DCE increased by 10%, 7.2%, and 4.4%, respectively, with a diminishing gain. For
= 30 cm, the values are 11.1%, 10%, and 8.9%, respectively.
Table 7 reveals that while both an increase in wall surface area and a decrease in pipe spacing lead to an increase in total DCE, the impact of the latter is more pronounced.
4. Conclusions
This study aimed to assess the cooling potential of a DCW-wall system and establish guidelines to prevent condensation on the wall surface. A 3D transient thermal model was utilized and validated with experimental data from a similar study. The model incorporated a typical DCW flow rate pattern to calculate various parameters under different operational and boundary conditions. The results indicated that smaller pipe spacing, lower water inlet temperature, and thinner walls led to increased cooling capacity and total DCE. The serpentine configuration exhibited the highest cooling potential, with a maximum cooling capacity of 80.0 W/m2 and a total DCE of 29.97 MJ/day. The free cooling energy provided by the DCW-wall system can effectively reduce or even eliminate reliance on mechanical cooling systems during cooling seasons in cold-climate residential buildings without wasting DCW resources. The findings revealed that the DCW-wall system with spiral configuration supplied almost 11% of the energy demand for space cooling during the cooling season in Toronto, Canada. In addition, the three configurations demonstrated the lowest average wall surface temperature, ranging from 18.6 °C to 21.2 °C across all operation and boundary scenarios. The 10 cm-thick wall had a surface temperature 1 °C higher than the 5 cm-thick wall at peak cooling capacity. The spiral counterflow configuration maintained the most uniform temperature on the wall surface, which is crucial for thermal comfort and condensation prevention. As a result, a conservative, yet simple, guideline was proposed to prevent condensation. Maintaining indoor RH levels between 40.8% and 53.8% would minimize the likelihood of condensation, regardless of the operation and boundary scenario.
This study has certain limitations that are worth considering. First, the research is limited to simulation and validation using experimental data from another similar system. While this approach provides accurate and valuable insights, conducting an experimental study that matches the proposed DCW-wall system configurations will provide more assuring validation. If experimental validation is not possible, using other commercial simulation software to verify the results obtained from the 3D model would be beneficial. Addressing these limitations will enhance the accuracy, applicability, and robustness of the research findings. Additionally, future work could consider incorporating outdoor environmental factors, such as temperature and RH, to account for their impact on indoor conditions. Conducting experimental studies with varied engineering designs, employing additional simulation software for verification, and exploring the influence of outdoor variables on indoor climate should be the focus of future studies.