Feasibility study of simplified pipe modeling for analyzing thermal performances of radiant heating and cooling systems

. Energy-efficient radiant heating and cooling require surface temperature and thermal capacity analysis. Simplified pipe modeling is applied to save time and resources for numerical analysis when evaluating the radiant system. Therefore, this study investigated the surface temperature distribution and thermal capacity of a radiant system using simplified pipe modeling. To do this, a steady-state heat transfer simulation was performed using Physibel BISCO. The difference between detailed (circular) and simple (rectangular) pipe models and the effect of material thermal conductivity of various layers were analyzed in three types of radiant heating and cooling systems: Embedded Surface System (ESS), Thermally Activated Building System (TABS), and Cooling Radiant Ceiling Panels (CRCP). The simple and detailed ESS and TABS simulation results showed similar surface temperature and heat capacity in various materials. Also, the CRCP simple and detailed models for materials differed in surface temperature and heat capacity, especially when the pipe thermal conductivity was high. The CRCP simple model overstated surface temperature and thermal capacity, which needs heat resistance to solve this overestimation. Further studies are necessary to investigate the discrepancy with different dimensioning and operation conditions, such as water temperature and flow rate.


Introduction
The radiant system is an attaching panel to indoor surfaces such as floors, walls, and ceilings, or for providing hot or cold water through building structures and for managing the surface temperature of the heat radiating space. The radiant system is a water-based system that offers comfortable cooling to occupants (ASHRAE 2009) and has a positive impact on thermal comfort than conventional HVAC systems (Andrés-Chicote et al., 2012). One of the Radiant systems, chilled ceiling archives have a positive impact on indoor air quality (IAQ), thermal comfort, and energy savings (Hao et al., 2007), and it has a function that occupants can be provided with a neutral condition even when relatively low-temperature hot water is supplied (Safizadh et al., 2007).
Previous studies evaluated the occupant's thermal comfort through radiant ceiling cooling in an office (Tian et al., 2020), and a panel attached to a chamber wall to measure the objective and subjective parameters according to the distance and angle from the occupant (Wang et al., 2022). Furthermore, the cooling capacities of three different types of radiant ceiling panels (i.e., Attached Aluminum Pin type, Attached Adhesion type and, Insert Board type) were evaluated (Park et al., 2014). Likewise, field studies and laboratory studies have been conducted in the literature mostly by attaching panels on indoor surfaces. However, there is * Corresponding author: knrhee@pknu.ac.kr a limitation to evaluating the radiant system through the actual structure of the buildings. Therefore, computer modeling is often used to evaluate the radiant system and compare it to the existing HVAC system in a building. In previous research, EnergyPlus models were analyzed using three energy models (i.e., the existing radiant system, the hypothetical conventional HVAC system, the radiant system with additional energy) to optimize energy efficiency (Khan et al., 2015), and the peak cooling load and 24-hour cooling load were analyzed to compare the radiant cooling system and the air system (Feng et al., 2013). Also, through EnergyPlus, the radiant system and conventional all-air system were evaluated for carbon dioxide emission and energy savings in a variety of European climates (Fabrizio et al., 2012). In previous studies, the radiant system has been investigated from multiple viewpoints via computer simulation, but the detailed comparison between various radiant systems and the effect of characteristics of the structure is still insufficient.
On the other hand, in the literature, the performance of radiant systems was typically evaluated through field investigations, laboratory studies, and computer simulations. To evaluate radiant systems through computer simulation, analyzing surface temperature and thermal capacity is essential for designing radiant heating and cooling systems. As it is common to apply water-circulating pipe to radiant heating and cooling systems, the heat transfer through the water pipe needs to be accurately analyzed to predict the surface temperature and thermal capacity, which can be considered as the fundamental thermal performance of radiant systems. It would guarantee the most accurate result to make the pipe model as it is. The simplified pipe modeling is widely used to reduce time and resources for numerical analysis, despite the organization of tubes and thermal transfer layers varies depending on the type of radiant system. Therefore, In this study, 1) the floor covering (surface) temperature, cooling, and heating capacities of a simple model and a detailed model of a representative radiant cooling and heating system were compared, and 2) the impact of different materials was investigated depending on the model shapes of the radiant systems.

Radiant cooling and heating system
In this study, three representative radiant cooling and heating system types were chosen to compare surface temperature and cooling and heating capacity based on the model shape of the radiant cooling and heating system types, as shown in Fig 1. First, the Thermally Activated Building System (TABS) is a construction that contains a heating layer integrated with the structure. In contrast, the Embedded Surface System (ESS) has an isolated heating layer from the configuration. Finally, the Ceiling Radiant Cooling Panel (CRCP) attached a heating layer to the panel in the radiant system.

Simulation scenarios
In this study, Physibel BISO v.12 was used to calculate a surface temperature and a heating and cooling capacity for each model shape under a twodimensional steady state. Table 1 represents the geometries of simple and detailed baseline models with different system types and material properties. In the simple model, the pipe was modeled as a rectangle. However, in the detailed model, the pipe was modeled as a circle. In the cases of the ESS and TABS, the water temperatures in the pipe were 40 ℃ and 45 ℃, respectively, and the indoor air temperature was 20 to apply the heating mode. For the CRCP, the water temperature was set a 15 ℃ (Shin et al., 2019), and the room temperature was set to 26 ℃ as the cooling mode. The thermal performance of pipes was determined based on the Chlorinated Polyvinyl Chloride's thermal conductivities from the previous study (Patterson & Miers, 2010), and other layers were designed to meet the thermal conductivities of the normally used materials.  In the ESS and TABS, smaller temperature differences were found in distributions between the simple and detailed models. However, in the simplified model of the CRCP, the temperature surrounding the pipe was lower over a larger area than in the detailed model.  Table 2 shows the surface average temperature and average temperature difference between the simple and detailed models when different materials were applied to the layers of each system to verify the effect of the materials. In the case of the ESS, the average surface temperature was similar between the simple model and the detailed model, depending on the materials. However, in the case of the TABS, the surface temperature was 4.5 °C lower than the baseline when the thermal conductivity of concrete was low. In the case of the CRCP, the difference in surface temperature between the simple model and the detailed model represented a range from 0.2 to 1.4 ° C. The trend of the simple and detailed model's average surface temperatures in the baseline was similar to the surface temperature of various conductive layer materials and insulation layer materials. Accordingly, the conductive layer and insulation layer have no significant effect on the surface temperature. Also, according to the thermal conductivity of the pipe, there was a variation in the average surface temperature between the simple and detailed models. However, the average surface temperature did not differ between the simple and detailed models for pipes with high thermal conductivities. Table 2. Average surface temperature with simulation scenarios As the average surface temperature difference between the CRCP simple model and the detailed model was clear except for copper pipe, Fig. 4 showed the surface temperature distribution by section position, except for copper pipe. The surface temperature distribution showed the same trend regardless of the material, with the lowest temperature occurring near the pipe position. The significant variance in surface temperature according to the position of the conductive layer and pipe layer model indicates that the conductive layer and pipe layer affect the distribution of surface temperature. In addition, the surface temperature was generally low when a higher thermal conductivity was used in the pipe material compared to the baseline, demonstrating that the pipe material influenced the CRCP system.

Effect on thermal capacity
Fig . 5 shows the thermal capacity of the simple model and the detailed model based on various materials for each system. In the results, the cooling and heating capacity decreased when the thermal conductivity of the floor covering of the ESS was wood and increased as the thermal conductivity of the screed increased. For the TABS, the cooling and heating capacity decreased when the thermal conductivity of concrete was 0.16 W/mK and 1.65 W/mK and larger when the thermal conductivity was larger than 1 W/mK, demonstrating that the concrete affected the cooling and heating capacity. In the case of the ESS and TABS, the thermal capabilities of the simple model and the detailed model were similar. The thermal capacity increased as the thermal conductivity of the pipe increased relative to the baseline in the CRCP. In addition, when the conductive layer was composed of steel, the thermal capacity of the simplified model was 21% greater than that of the detailed model. However, there was no difference in thermal capacity between the simple model and the detailed model when the pipe material was copper. In summary, the CRCP confirmed that the pipe material affects the thermal capacity and that there is no difference in thermal capacity between the simple model and the detailed model for heat-conductive materials such as copper. Consequently, the ESS and TABS are able to evaluate surface temperature or heating and cooling capability when simple model models are utilized. In the case of the CRCP, however, the simple model must be enhanced, similarly to the surface temperature and heating and cooling capacities of the detailed model.

Discussion
In this study, the surface temperature and heating and cooling capacities in a simple model and a detailed model of three representative radiant systems, and the effect of the materials were confirmed according to the radiant system model shapes. In the ESS and TABS systems that placed the pipe inside the structure, there was no difference in surface temperature and thermal capacity between the simple and detailed models. However, in the case of the ESS, as the thermal conductivity of concrete decreased, the surface temperature and thermal capacity decreased compared to the baseline. In the case of the CRCP, the surface temperature and thermal capacity decreased regardless of the material in the detailed model. The surface temperature of the CRCP was estimated to be lower than the detailed model due to the overestimation of the pipepanel contact area in the simple model. Accordingly, there was no significant barrier in analyzing the surface temperature or heating and cooling capacities of the ESS and TABS when a simple model was applied. However, when a simple model was applied to the CRCP, additional supplementation, such as assuming a virtual thermal resistance between the pipe and the panel, will be required. In addition, future work should be conducted on the generalization of the resistive layer's properties according to the various layer material properties and the operating conditions for the CRCP.

Conclusion
The results of this study compare the surface temperature and thermal capacity of three representative radiant systems by material and model shape.
1) In the case of the ESS, the model shape and material had no influence on the surface temperature and thermal capacity. 2) The physical characteristics of concrete influenced the surface temperature and thermal capacity of the TABS. Thermal capacity showed a similar trend to the increasing and decreasing of concrete thermal capacities. However, the modeling method of the shape had no effect on the surface temperature and thermal capacity. 3) In the case of the CRCP, surface temperature and thermal capacity were affected by the pipe material properties; as the thermal conductivity of the pipe increased, the surface temperature lowered and thermal capacity increased. In addition, the modeling method affected the surface temperature and thermal conductivity and the simple model overestimated the thermal capacity.