TY - JOUR AU - Wang,, Lei AB - Abstract In this paper, the phase change plate is made of the organic phase change material (PCM) with the phase change temperature of about 30°C. The PCM is installed in the capillary natural convection radiator with the water supply temperature of 30–60°C. A low-temperature natural convection radiator with heat storage function is formed. The mathematic model is established by enthalpy method and solved by line-by-line iteration method. The applicability and economy of the equipment in Shanghai area are calculated. Taking the time ratio and average temperature of the target domain as the limiting parameters, the operation schemes suitable for three representative days are determined, and the optimum thickness of the phase change plate is 0.05 m for use in Shanghai. The regenerative low-temperature heating radiator provides a new idea for the application of PCMs in the field of low-temperature heating. The conclusions obtained provide a basis for further research and application of the equipment. 1. INTRODUCTION In recent years, phase change energy storage materials have been a research hotspot in the field of energy storage. Phase change materials (PCMs) have broad application prospects in solar energy utilization, industrial waste heat and waste heat recovery, building heating and air conditioning energy saving due to their advantages of phase change latent heat storage, small temperature change and large energy storage density [1]. In the field of construction, there have been a lot of researches on the application of PCMs, which can be divided into passive and active types from the perspective of energy consumption [2–4]. Passive applications include the combination of PCMs with walls, roofs and floors. They depend on the interaction between building characteristics and energy sources [5]. The phase change process is independent of mechanical equipment. Under the premise of not consuming additional electric energy, they can make full use of natural energy to reduce the dependence of indoor light and thermal environment on mechanical equipment, thus achieving the purpose of energy saving. However, this method may not achieve the goal of energy saving while controlling and adjusting the radiator [6–8]. Active application mainly refers to the combination of PCMs with various radiators and heat exchange systems. In low valley or night thermal storage/cold storage, peak electric area, exothermic/cooling, plays the role of peak cutting and valley filling [9]. This method is easy to adjust and install, including the use of PCMs in floor radiation heating system, various air conditioning systems and heat pump systems, as well as in combination with cold radiation ceiling. Summarizing the previous research on active application, most of them focus on the field of cold storage and high-temperature heat storage. With the development of low-temperature PCMs and the large-scale use of low-temperature heat sources in recent years, the application of PCMs in the field of low-temperature heating is an important development direction [10–12]. In this paper, a regenerative low-temperature heating radiator is proposed, which consists of phase change plate and capillary natural convection radiator. Among them, phase change plate is composed of organic material and aluminum plate with phase change temperature of 30°C. Capillary natural convection radiator uses capillary network as heat exchange core and natural convection as operation principle. The equipment shell is composed of adiabatic benzene plate. The upper and lower ends are equipped with air inlet and air outlet, respectively, and the low-temperature water heating at 30–60°C is adopted. In order to study the feasibility of this new type of equipment, this paper takes Shanghai, a typical city in hot summer and cold winter area, as an example, to analyze the applicability and economy of the equipment in winter heating in this area, and put forward the operation plan of the equipment in Shanghai area. The regenerative low-temperature radiator proposed in this paper provides a new idea for the application of PCMs in the field of low-temperature heating. The conclusions obtained provide a basis for further research and application of this radiator. 2. PHYSICAL MODEL 2.1. Structure of phase change plate In general, the thermal conductivity of organic PCMs is small. Aluminum alloy plate is chosen as the main supporting material of phase change plate, and fins are added to strengthen heat transfer. As shown in Figure 1, the aluminum alloy plate is welded with wavy fins of the same material. The wavy fins divide the interior of the phase change plate into several equilateral triangles. Figure 1 Open in new tabDownload slide Structure of PCM. Figure 1 Open in new tabDownload slide Structure of PCM. Fins help to fix the shape of the plate and make it have a good stability. At the same time, fins can greatly improve the average thermal conductivity of the phase change plate and occupy less space, so that the phase change plate can be more filled with the shape-stabilized PCM. The thickness of the selected aluminum alloy plate is 0.5 mm, and the thermal conductivity is 220 W/(m K). The thickness of the phase change plate can be determined according to the volume of the PCM required. In the process of heat storage and release of the phase change plate, if the contact thermal resistance is neglected, the temperature of the internal aluminum alloy plate is the same as that of the upper and lower sides of the aluminum alloy plate. With the addition of fins, the thickness of PCM can be regarded as one-third of the original thickness. The thermal conductivity of PCMs in phase change plates increases three times as much as that of the original ones. 2.2. Physical parameters of phase change materials In order to be used in combination with low-temperature heating radiator, the temperature of PCM is set at 30°C. There are many organic PCMs that meet this condition, such as paraffin, fatty acid and the mixture of fatty acid materials. For the convenience of calculation, this paper chooses the shape-stabilized PCM made by decanoic acid and polyethylene as the basic material. The shape of the phase change plate might change since the volume of PCM might vary under different temperatures. The solid thermal conductivity is 0.255 W/(m K), the liquid thermal conductivity is 0.248 W/(m K), the phase transformation temperature is 30.42°C, the latent heat of phase transformation is 121.50 kJ/kg, the density is 908.12 kg/m3, the solid specific heat capacity is 2.737 kJ/(kg K) and the liquid-specific heat capacity is 2.507 kJ/(kg K). For convenience of calculation, the thermal conductivity of the material is 0.255 W/(m K) of the solid value. The thermal conductivity of PCM-filled plate can be increased by three times as much as that of the original material because of the filling of aluminum alloy plate fins. The thermal conductivity of material is 0.765 W/(m K) in calculation. 2.3. Combination form of phase change plate and radiator The structure of natural convection radiator for low-temperature heating is shown in Figure 2. Figure 2 Open in new tabDownload slide Structure of low-temperature heating terminal device with PCM. Figure 2 Open in new tabDownload slide Structure of low-temperature heating terminal device with PCM. The equipment consists of a shell and an internal capillary network. The shell is made of benzene plate, and the upper and lower ends are equipped with air inlets and air outlets, respectively. The inner capillary network is made of plastic with a density of 897 kg/m3, a thermal conductivity of 0.27 W/(m K) and a specific heat of 2.0 kJ/kg K. The prototype is 0.3 m thick and 1.14 m wide. Three rows of capillary network with 2 × 1 m are installed inside, consisting of 100 capillaries, each row of capillary network spacing 0.02 m. The outer diameter of capillary is 3.4 mm and that of trunk is 20 mm. Considering various factors, the phase change plate is installed on the front and rear surfaces of the radiator, that is, the installation mode of Figure 2. Because of the large surface area of the front and back of the equipment, the installable area of the phase change plate is relatively large, and the contact area between the phase change plate and the heat exchange core is relatively large, which can meet the heat storage requirements of the equipment without affecting the heat dissipation of the equipment. 3. CONTROL EQUATION AND BOUNDARY CONDITIONS 3.1. Control equation Previous experimental data show that the temperature distribution of the equipment is uniform in the width direction. The capillary heat exchanger core is used as a rectangular heat exchanger to dissipate heat. The model can be simplified to two dimensions without considering the heat transfer between the tubes of each row of capillaries. The calculation shows that the airflow in the equipment is laminar, and there is a temperature difference in the vertical direction. The equipment is divided into several subregions in the vertical direction, assuming that the temperature distribution of capillary heat exchanger core, air flow, and air in the cavity is uniform in each subregion. In order to facilitate calculation and analysis, the following assumptions are made for the heat storage and release of phase change plates in each region. Equation (1): the heat transfer is only in Z direction of the thickness of phase change plates, which simplifies the phase change plate into a one-dimensional model. Equation (2): PCMs have constant physical properties in both solid and liquid except for the equivalent specific heat in the phase change region. Equation (3): PCMs have no fluidity in the melting state, ignoring the natural convection in the melting state and the undercooling effect in the solidification state. Equation (4): ignoring the volume change of PCM during phase transition, the density is considered to be a fixed value. Equation (5): ignoring the contact thermal resistance of PCMs and aluminum alloy plates and aluminum alloy fins would not influence the results. Equation (6): ignoring the thickness of aluminum plates and internal fins. To establish the control equation by enthalpy method as formula (1): $$\begin{equation} {\rho}_p\cdot \frac{\partial h(T)}{\partial \tau }={\lambda}_P\cdot \frac{\partial^2T}{\partial{z}^2} \end{equation}$$ (1) Among them, |${\rho}_p$| represents the density of PCM, |${\lambda}_P$| represents the thermal conductivity of PCM, |$h$| represents the enthalpy of PCM and |$T$| represents the thermodynamic temperature of PCM. After calculating the enthalpy by formula (1), it is necessary to convert enthalpy to temperature, and the transformation formula is shown in formula (2). $$\begin{equation} T=\left\{\begin{array}{l}h/{c}_s\kern5.8em h<{cT}_m\\{}{T}_m\kern6em {cT}_m\le h\le{cT}_m+{H}_m\\{}\left(h-{H}_m\right)/{c}_l\kern2em {cT}_m+{H}_m13 15.4 >7 12.1 >10 14.3 9, 13) 33.0 (3, 7) 33.0 (5.5, 10) 39.6 (4, 9) 38.5 (−1, 3) 39.6 (3, 5.5) 36.3 ≤4 13.2 ≤−1 15.4 ≤3 9.9 tmax (°C) Perc (%) tmin (°C) Perc (%) ∆t (°C) Perc (%) >13 15.4 >7 12.1 >10 14.3 9, 13) 33.0 (3, 7) 33.0 (5.5, 10) 39.6 (4, 9) 38.5 (−1, 3) 39.6 (3, 5.5) 36.3 ≤4 13.2 ≤−1 15.4 ≤3 9.9 Open in new tab Table 1 Distribution of outdoor maximum, minimum temperatures and daily range. tmax (°C) Perc (%) tmin (°C) Perc (%) ∆t (°C) Perc (%) >13 15.4 >7 12.1 >10 14.3 9, 13) 33.0 (3, 7) 33.0 (5.5, 10) 39.6 (4, 9) 38.5 (−1, 3) 39.6 (3, 5.5) 36.3 ≤4 13.2 ≤−1 15.4 ≤3 9.9 tmax (°C) Perc (%) tmin (°C) Perc (%) ∆t (°C) Perc (%) >13 15.4 >7 12.1 >10 14.3 9, 13) 33.0 (3, 7) 33.0 (5.5, 10) 39.6 (4, 9) 38.5 (−1, 3) 39.6 (3, 5.5) 36.3 ≤4 13.2 ≤−1 15.4 ≤3 9.9 Open in new tab One day was taken as a representative day for analysis in the two temperature ranges of maximum outdoor temperature, minimum outdoor temperature and large proportion of diurnal difference, for a total of 6 days. They are 27 December, 30 December, 5 January, 24 January, 10 February and 25 February, respectively. The temperature curves of the 6 days are shown in Figure 3. Figure 3 Open in new tabDownload slide The max and min outdoor temperature of typical day. Figure 3 Open in new tabDownload slide The max and min outdoor temperature of typical day. The six curves in the figure can be divided into three groups, namely groups A, B and C. Among them, group A had a higher temperature, group B had a smaller fluctuation and a lower daytime temperature and group C had a larger fluctuation. The mathematical models of air dynamic in the simultaneous room, capillary heat exchanger core, fluid dynamic heat transfer in the equipment and phase change plate are solved. The basic idea of the line-by-line iteration method is to mesh the thermal standpoint in the process of fitting and solving, and calculate iteratively based on each grid line. The discrete equations are established by implicit finite-difference scheme and solved by iteration method using MATLAB program. In the process of calculation, timestep parameters and space-step parameters are adjusted and determined iteratively. 4. ANALYSIS OF EXPERIMENT The economic evaluation of equipment should be carried out in an acceptable range to ensure the indoor temperature. In order to select an appropriate operation plan, an index to measure the indoor temperature limit index should be defined as the ratio of indoor temperature to time in the target domain. The target domain of indoor temperature is defined as 16–20°C, the actual indoor temperature is defined as the actual domain, and the proportion of the actual domain satisfying the conditions of the target domain to the total actual domain is defined as the time proportion of the target domain. The specific calculation method is shown in formula (6). $$\begin{equation} I=n/ sum \end{equation}$$ (6) Among them, |$n$| represents the indoor temperature between 16 and 20°C, |$sum$| represents the daytime working hours and |$I$| represents the temperature–time ratio in target-domain indoor. When the actual indoor temperature is mostly within the target area, that is to say, 80% is acceptable in general sense. In this paper, the proportion of time in the target area is more than 80% as equipment meets the room design requirements. Group A representative day operation plan is divided into four stages. Equation (1): at the valley value of electricity price at night (22:00–6:00 the next day), phase change plate is used for heat storage. The equipment operates under the closed heat storage mode. The water supply temperature is of 60°C and the circulating water flow is 0.05 kg/s. Equation (2): In the peak stage of electricity price (8:00–11:00), the phase change plate releases heat and the equipment stops running. Equation (3): in the normal period of electricity price (11:00–13:00), the phase change plate is used for heat storage, and the equipment is in the open heat storage mode. The water supply temperature is 50°C, and the circulating water flow is 0.05 kg/s. Equation (4): In another peak stage of electricity price (13:00–18:00), the phase change plate releases heat and the equipment stops running. Due to the difference of temperature, B1, B2 and C1, C2 represent the same heat storage and release time as group A representative day, and the operation plan of the equipment is slightly different. Group B represents the following: in the peak period of the day (8:00–11:00), the normal operation of the equipment to recharge heat and the water supply temperature is of 30°C; in the peacetime period (11:00–13:00), open heat storage mode and the water supply temperature of equipment is of 60°C and in the peak time period (13:00–18:00), exothermic mode, normal operation of equipment to recharge heat to the room and the water supply temperature is of 30°C. Group C represents the peak period of the day (8:00–11:00), the normal operation of the equipment to recharge heat and the water supply temperature is of 30°C. In the normal period (11:00–13:00), the heat storage mode initiates and the water supply temperature of the equipment is of 55°C. In peak time period (13:00–18:00), exothermic mode for normal operation of equipment and recharge heat to the room with the water supply temperature is of 30°C. The three schemes are named Plan A, Plan B and Plan C, respectively. Figures 4–9 show the variation of indoor and outdoor temperatures when the equipment operates according to the set scheme. Figure 4 Open in new tabDownload slide Indoor temperature of the typical day A1. Figure 4 Open in new tabDownload slide Indoor temperature of the typical day A1. Figure 5 Open in new tabDownload slide Indoor temperature of the typical day A2. Figure 5 Open in new tabDownload slide Indoor temperature of the typical day A2. Figure 6 Open in new tabDownload slide Indoor temperature of the typical day B1. Figure 6 Open in new tabDownload slide Indoor temperature of the typical day B1. Figure 7 Open in new tabDownload slide Indoor temperature of the typical day B2. Figure 7 Open in new tabDownload slide Indoor temperature of the typical day B2. Figure 8 Open in new tabDownload slide Indoor temperature of the typical day C1. Figure 8 Open in new tabDownload slide Indoor temperature of the typical day C1. Figure 9 Open in new tabDownload slide Indoor temperature of the typical day C2. Figure 9 Open in new tabDownload slide Indoor temperature of the typical day C2. In the primary scheme, the thickness of phase change plate is 0.04–0.07 m, which could not meet the requirement by calculation. Therefore, the thickness of phase change plate is 0.05–0.07 m. There are four curves in each diagram, which are indoor temperature curve and outdoor temperature curve when installing 0.05-, 0.06- and 0.07-m-thick PCB equipment. Each curve contains 1260 nodes. The experimental results show that the indoor temperature of group A is between 17 and 22°C when the representative day runs under the set scheme. The indoor temperature of group B is between 16 and 20°C. The indoor temperature of group C is between 15 and 21°C when it runs under the set scheme on the representative day. The calculation results of the ratio of indoor temperature to time in the target domain are shown in Table 2. Table 2 Time scale I of target domains in typical days. Typical day 0.07 m 0.06 m 0.05 m I (100%) |$\overline{T}$| (°C) I (100%) |$\overline{T}$| (°C) I (100%) |$\overline{T}$| (°C) A1 97.67 18.56 92.00 18.68 93.25 18.67 A2 99.75 18.08 99.67 18.21 99.83 18.26 B1 87.42 16.95 87.50 16.89 89.50 16.87 B2 98.67 17.87 97.67 17.82 97.42 17.80 C1 87.17 17.42 88.50 17.58 87.58 17.59 C2 86.50 18.00 86.42 18.05 87.67 18.02 Typical day 0.07 m 0.06 m 0.05 m I (100%) |$\overline{T}$| (°C) I (100%) |$\overline{T}$| (°C) I (100%) |$\overline{T}$| (°C) A1 97.67 18.56 92.00 18.68 93.25 18.67 A2 99.75 18.08 99.67 18.21 99.83 18.26 B1 87.42 16.95 87.50 16.89 89.50 16.87 B2 98.67 17.87 97.67 17.82 97.42 17.80 C1 87.17 17.42 88.50 17.58 87.58 17.59 C2 86.50 18.00 86.42 18.05 87.67 18.02 Open in new tab Table 2 Time scale I of target domains in typical days. Typical day 0.07 m 0.06 m 0.05 m I (100%) |$\overline{T}$| (°C) I (100%) |$\overline{T}$| (°C) I (100%) |$\overline{T}$| (°C) A1 97.67 18.56 92.00 18.68 93.25 18.67 A2 99.75 18.08 99.67 18.21 99.83 18.26 B1 87.42 16.95 87.50 16.89 89.50 16.87 B2 98.67 17.87 97.67 17.82 97.42 17.80 C1 87.17 17.42 88.50 17.58 87.58 17.59 C2 86.50 18.00 86.42 18.05 87.67 18.02 Typical day 0.07 m 0.06 m 0.05 m I (100%) |$\overline{T}$| (°C) I (100%) |$\overline{T}$| (°C) I (100%) |$\overline{T}$| (°C) A1 97.67 18.56 92.00 18.68 93.25 18.67 A2 99.75 18.08 99.67 18.21 99.83 18.26 B1 87.42 16.95 87.50 16.89 89.50 16.87 B2 98.67 17.87 97.67 17.82 97.42 17.80 C1 87.17 17.42 88.50 17.58 87.58 17.59 C2 86.50 18.00 86.42 18.05 87.67 18.02 Open in new tab Table 2 shows that the average temperature of groups A, B and C is between 17.42 and 18.67°C, and the ratio of indoor temperature to time in the target area is more than 80%, which meets the requirements. Phase change panels with thickness of 0.05, 0.06 and 0.07 m have no effect on the ratio of average temperature to indoor temperature and time. This is because phase change panels do not completely phase change in order to cater to the price range. 5. CONCLUSIONS This paper presents a regenerative low-temperature heating radiator consisting of phase change plate and capillary natural convection radiator. The applicability and economy of the equipment in Shanghai are analyzed by numerical simulation, and the operation scheme of the equipment in Shanghai is put forward. Equation (1): a combination of phase change plate and capillary natural convection radiator is proposed. Among them, phase change plate is composed of organic PCM and aluminum plate whose phase change temperature is about 30°C. In order to improve the heat transfer coefficient, wavy fins are added inside the phase change plate. The phase change plate is mounted on the front and rear inner surfaces of the radiator. Equation (2): three schemes for the operation of the equipment in Shanghai are determined by the trial calculation with the time ratio and the average temperature of the target domain as the limiting parameters. Among them, scheme A is suitable for heating days with high outdoor temperature; scheme B is suitable for heating days with low outdoor temperature and little fluctuation and scheme C is suitable for heating days with low outdoor temperature and large fluctuation. Equation (3): according to the schemes, the average indoor temperature of the three types of representative days is between 17.42 and 18.67°C, and the proportion of indoor temperature time in the target area is more than 80%, which meets the requirements. It shows that the equipment is suitable for operation in Shanghai. Equation (4): considering the comprehensive comfort and economy, the phase change board with thickness of 0.05 m is the best choice for the equipment in Shanghai. The cost savings of installing 0.05m thick PCB equipment under the three schemes are 58.6%, 11.3% and 10.5% respectively. Funding This work is supported by the project of National Import Research Priorities Program of China (2016YFB0801004) and the Science and Technology Project of Jiangsu Province Construction System of China (No. 2017ZD225). References 1 Zwanzig SD , Lian Y , Brehob EG . Numerical simulation of phase change material composite wallboard in a multi-layered building envelope . Energy Convers Manag 2013 ; 69 : 27 – 40 . Google Scholar Crossref Search ADS WorldCat 2 Kuznik F , David D , Johannes K et al. A review on phase change materials integrated in building walls . Renew Sust Energ Rev 2011 ; 15 : 379 – 91 . Google Scholar Crossref Search ADS WorldCat 3 Jin X , Zhang X . Thermal analysis of a double layer phase change material floor . Appl Therm Eng 2011 ; 31 : 1576 – 81 . Google Scholar Crossref Search ADS WorldCat 4 Soaresa N , Costab JJ , Gasparb AR et al. Review of passive PCM latent heat thermal energy storage systems towards buildings energy efficiency . Energy Build 2013 ; 59 : 82 – 103 . Google Scholar Crossref Search ADS WorldCat 5 Ansuini R , Larghetti R , Giretti A et al. Radiant floors with PCM for indoor temperature control . Energy Build 2011 ; 43 : 3019 – 26 . Google Scholar Crossref Search ADS WorldCat 6 Fang G , Wu S , Liu X . Experimental study on cool storage air-conditioning system with spherical capsules packed bed . Energy Build 2010 ; 42 : 1056 – 62 . Google Scholar Crossref Search ADS WorldCat 7 Chidambaram LA , Ramana AS , Kamaraj G et al. Review of solar cooling methods and thermal storage options . Renew Sust Energ Rev 2011 ; 15 : 3220 – 8 . Google Scholar Crossref Search ADS WorldCat 8 Oro E , Gracia A , Castell A et al. Review on phase change materials (PCMs) for cold thermal energy storage applications . Appl Energy 2012 ; 99 : 513 – 33 . Google Scholar Crossref Search ADS WorldCat 9 Noye S , North R , Fisk D . Smart systems commissioning for energy efficient buildings . Build Serv Eng Res Technol 2016 ; 37 : 194 – 204 . Google Scholar Crossref Search ADS WorldCat 10 Kalogirou SA . Building integration of solar renewable energy systems towards zero or nearly zero energy buildings . Int J Low-Carbon Technol 2013 ; 10 : 379 – 85 . Google Scholar Crossref Search ADS WorldCat 11 Lord SF , Noye S , Ure JW et al. Comparative review of building commissioning regulation: a quality perspective . Build Res Inf 2016 ; 44 : 630 – 43 . Google Scholar Crossref Search ADS WorldCat 12 Royapoor M , Roskilly T . Building model calibration using energy and environmental data . Energy Build 2015 ; 94 : 109 – 20 . Google Scholar Crossref Search ADS WorldCat © The Author(s) 2019. Published by Oxford University Press. This is an Open Access article distributed under the terms of the Creative Commons Attribution License (http://creativecommons.org/licenses/by/4.0/), which permits unrestricted reuse, distribution, and reproduction in any medium, provided the original work is properly cited. TI - Energy conservation analysis of regenerative radiator for low-temperature heating JF - International Journal of Low-Carbon Technologies DO - 10.1093/ijlct/ctz055 DA - 2020-02-20 UR - https://www.deepdyve.com/lp/oxford-university-press/energy-conservation-analysis-of-regenerative-radiator-for-low-06bSckW7Lc SP - 40 VL - 15 IS - 1 DP - DeepDyve ER -