Du Huiting1, Diao Yanhua1, Zhao Yaohua1, Wang Zeyu2, Wang Guozhen1
1. Beijing University of Technology, Beijing 100124, China
2. China Nuclear Power Engineering Co., Ltd., Beijing 100840, China
† 通信作者：刁彦华,E-mail：[email protected]
About author:DU Huiting (2000-), female, master candidate, mainly engaged in the research of high-efficiency phase change energy storage technology. Diao Yanhua (1973-), male, Ph.D., associate professor, mainly engaged in solar thermal utilization, phase change heat storage, heat recovery and enhanced heat exchange technology research.
Received: 2023-08-10 Revised: 2023-09-08
Funds: Beijing Natural Science Foundation (3192009)
summary
Industrial waste heat is wasted, the utilization rate is low, and the practical application process is limited by time and space, and efficient heat storage technology and devices are needed to solve such problems. In this paper, a new type of phase change accumulator combining multi-channel parallel flow flat tubes and compact fins is proposed, with water as the heat-carrying fluid and lauric acid as the phase change material. The effects of heat-carrying fluid injection mode, flow rate and inlet temperature on the heat storage/release performance of the heat accumulator were studied experimentally, and the heat transfer characteristics of the heat accumulator under small temperature difference were analyzed. The results show that the PCM filling rate of the accumulator is 82.5%, and the use of compact fins greatly strengthens the heat exchange process on the PCM side, and the heat storage/release performance is excellent. When the inlet temperature of the heat-carrying fluid is 45β°C and 41β°C, respectively, the phase change is completed in about 270 min and 75 min, and the minimum heat storage/release temperature difference can reach 2β°C, and the average heat storage specific power at the minimum temperature difference is 25.18 W/kg and the average heat extraction specific power is 20.23 W/kg.
Key words: phase change heat storage; Multi-channel parallel flow flattened tubes; compact fins; Small temperature differences
CLC Number: TK513.5 Document Identification Code: A Article Number: 2095-560X(2024)02-0141-10
Heat Charge/Discharge Characteristics of Multi-Channel Parallel Flow Flat Tube-Compact Finned Latent Heat Storage Device
DU Huiting1, DIAO Yanhua1,†
, ZHAO Yaohua1, WANG Zeyu2, WANG Guozhen1
1. Beijing University of Technology, Beijing 100124, China
2. China Nuclear Power Engineering Co. Ltd., Beijing 100840, China
Abstract
In view of the serious waste, the low utilization rate and the great limitation in time and space in the actual application process of industrial waste heat, efficient heat storage technology and devices are needed to solve such problems. This paper proposed a new phase change heat storage device combining multi-channel parallel flow flat tube with compact fins, which used water as the heat transfer fluid and lauric acid as the phase change material.
The effects of injection method, flow rate and inlet temperature on the heat storage and release performance of the device were studied experimentally. Besides, the thermal performance of the device under small temperature difference was analyzed. The results show that the phase change material filling rate of the device is 82.5%, and the use of compact fins greatly strengthens the phase change materialʹs side heat transfer process, as well as its excellent heat storage and release performance. When the inlet temperature of the heat exchange fluid is 45 °C/41 °C respectively, the phase change material completes the phase change at about 270 min/75 min.
So the heat storage and heat release temperature difference can reach 2 °C. The average heat storage specific power at the minimum temperature difference can reach 25.18 W/kg and the average heat extraction ratio power can reach 20.23 W/kg.
Key words: phase change heat storage; multi-channel parallel flow flat tube; compact fins; small temperature difference
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0 Introduction
The industrial energy consumption in mainland China accounts for about 70% of the country's total energy consumption, of which only part of the energy is effectively utilized, and the remaining 17% ~ 67% of the energy is eventually converted into waste heat [1]. The mainland is rich in industrial waste heat resources, but due to the various forms of industrial waste heat and the limitation of time and space in the actual application process, the utilization rate of waste heat resources is low and the waste is serious. The application of heat storage technology to waste heat utilization can well alleviate the problem of uneven distribution or continuous utilization of heat energy in time, space, and intensity, and improve the utilization rate of industrial waste heat [2].
Phase change materials have a high phase change heat storage density [3], and organic phase change materials have the advantages of good formability in the solid state, stable performance, and low subcooling and phase separation phenomena [4, 5].
In practical engineering applications, the disadvantages of low thermal conductivity and large heat transfer resistance of PCM have become the main reasons limiting the application of latent heat accumulators, so it is necessary to take measures to strengthen heat exchange, such as improving the thermal conductivity of PCM, adding fins, and optimizing the structure of the device [6]. IN THE RESEARCH OF PHASE CHANGE MATERIALS, SIAHPUSH ET AL. [7] ADDED COPPER FOAM TO EICOSANE, WHICH GREATLY IMPROVED THE THERMAL CONDUCTIVITY OF PHASE CHANGE MATERIALS. In addition, the addition of fins to the accumulator can increase the heat exchange area of the accumulator and improve the energy storage efficiency. NICHOLLS ET AL. [8] COMPARED AND STUDIED THE EFFECTS OF FINLESS AND DIFFERENT FORMS OF FINS ON CASING HEAT EXCHANGERS. The results show that the addition of different forms of fins can improve the heat transfer efficiency and shorten the heat exchange time to different degrees.
Latent heat accumulator structures are divided into shell-and-tube, modular package, and auxiliary heat pipe types [9]. Research at home and abroad has mainly focused on shell-and-tube accumulators, which are characterized by embedding heat-carrying fluid channels into large vessels containing phase change materials. Heat-carrying fluid channels can be divided into straight tubes, U-shaped tubes, spiral tubes, and serpentine tubes. RATHOD ET AL. [10] INSTALLED LONGITUDINAL FINS ON HEAT-CARRYING FLUID STRAIGHT TUBES, AND THE RESULTS SHOWED THAT THE INSTALLATION OF LONGITUDINAL FINS COULD REDUCE THE PHASE CHANGE TIME OF THE PHASE CHANGE MATERIAL BY HALF. TORREGROSA-JAIME ET AL. [11] PROPOSED AN ENERGY STORAGE TANK USING A COUNTERCURRENT SPIRAL COIL-TYPE HEAT-CARRYING FLUID CHANNEL, WHICH HAS A STRONGER HEAT TRANSFER AND IS MORE AFFECTED BY NATURAL CONVECTION THAN THE STRAIGHT PIPE CHANNEL. However, the traditional shell-and-tube heat accumulator has deficiencies in the filling rate of phase change material, the volume of the equilibrium device, the heat exchange area, the heat storage power and the heat storage density.
CHEN ET AL. [12] PROPOSED A PHASE CHANGE HEAT ACCUMULATOR WITH A POROUS CHANNEL FLAT TUBE ATTACHED TO A STRAIGHT RECTANGULAR FIN AS THE CORE HEAT EXCHANGE ELEMENT, AND THE RESULTS SHOWED THAT THE PHASE CHANGE MATERIAL FILLING RATE OF THE DEVICE WAS 82%, THE HEAT EXCHANGE AREA WAS LARGE, AND THE CONVECTIVE HEAT TRANSFER COEFFICIENT WAS HIGH. Chen et al. [13] simulated and studied the heat storage performance of four types of porous flat tube phase change heat accumulators, and found that the natural convection can be strengthened and the heat transfer time can be shortened when the length of the porous channel is perpendicular to the gravity direction.
In summary, compared with the traditional shell-and-tube heat accumulator in the form of straight pipes, the multi-channel parallel flow flat tube can improve the heat transfer coefficient while ensuring the filling rate of the phase change material of the heat accumulator, and its internal tiny fins can strengthen the heat transfer and shorten the completion time of heat storage/heat release.
In this study, a set of phase change heat accumulators combining multi-channel parallel flow flat tubes and compact fins were designed and built to further strengthen the heat transfer of phase change materials on the basis of previous studies. The heat storage/release performance of the heat accumulator under different heat-carrying fluid injection modes, flow rates and inlet temperatures was studied, and the heat storage/release capacity of the heat accumulator under small temperature difference was analyzed. Through the experimental research and theoretical analysis of the performance of the accumulator, the variation law of its performance was investigated, in order to provide a theoretical basis for the development of efficient and practical accumulator.
1 Introduction to Accumulators
As shown in Figure 1, the phase change accumulator with multi-channel parallel flow flat tube and compact fin is mainly composed of four parts: heat storage box, multi-channel parallel flow flat tube, compact fin and phase change material.
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 | 图1 蓄热器结构图Fig. 1 Structure diagram of thermal storage device |
As the core heat transfer element of the heat accumulator, the specific structure of the multi-channel parallel flow flat tube is shown in Figure 2. There are 21 independent microchannels inside the multi-channel parallel flow flat tube, and the tiny fins are evenly distributed on the upper and lower sides of each microchannel. These tiny fins increase the heat transfer area with the heat-carrying fluid and also intensify the internal disturbances. The cross-sectional dimensions of the microchannel are 5 mm × 5 mm, the inner wall thickness is 0.5 mm, and the outer wall thickness is 1 mm. The thickness of the tiny fins is 0.35 mm, the height is 0.75 mm, and the fin spacing is 0.31 mm. The vertical compact fins are bent from a 0.25 mm thick aluminum sheet and are evenly attached to the middle of the height of the multi-channel flat tube in the middle of the 460 mm range. The structural parameters of the multi-channel parallel flow flattened tube and the compact fin are shown in Table 1, and the fin structure is shown in Figure 3.
The regenerator is made of transparent polycarbonate sheet and has dimensions of 130 mm× 80 mm × 460 mm. In the experiment, water was used as the heat-carrying fluid and lauric acid was filled with the regenerator as the phase change material, and the liquid-phase filling rate was 82.5%, and the physical parameters of lauric acid are shown in Table 2. All surfaces in contact with the outside world are insulated with 50 mm thick polystyrene insulation board with a thermal conductivity of 0.034 W/(m∙ K)).
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| | 图2 多通道平行流扁管结构图Fig. 2 Structure of multi-channel parallel flow flat tube |
| | 表1 多通道平行流扁管和紧凑式翅片的结构参数Table 1 Structure parameters of multi-channel parallel flow flat tube and compact fin |
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| | 图3 紧凑式翅片结构图Fig. 3 Structure of compact fin |
| | 表2 月桂酸物性参数Table 2 Properties of lauric acid |
2 Test systems and research methods
2.1 Experimental system and measurement point layout
The experimental system is mainly composed of three parts: multi-channel parallel flow flat tube-compact fin phase change accumulator, cold and hot fluid exchange circulation system and data acquisition system. The cold and hot fluid exchange circulation system mainly includes a constant temperature water bath, a flow meter, a shut-off valve and a pipeline, a constant temperature water bath control system controls the inlet temperature of the heat-carrying fluid, and a flowmeter adjusts the circulating flow of the heat-carrying fluid. The data acquisition system consists of a data acquisition instrument, a thermocouple, and a computer. The parameters of the measuring instrument and test element are shown in Table 3, and the principle of the experimental system is shown in Figure 4.
| | 表3 测量设备参数Table 3 Parameters of the testing equipment |
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| | 图4 实验系统原理图Fig. 4 Schematic diagram of the experimental system |
The thermostatic water bath provides the experimental setup with constant temperature water as a cold/heat source, and the flow rate of the thermostatic water is controlled by a flow meter. The temperature of each measuring point is measured by a thermocouple, and the specific distribution of the measuring points is shown in Figure 5. The data logger collects the electrical signal of each thermocouple and converts it into a temperature signal. The system is mainly composed of two circulating circuits: heat storage and heat release. In the process of heat storage, the valves V1, V2, V5 and V7 are opened when the hot water is in and out, and the valves V1, V4, V3 and V7 are opened when the hot water is in and out. During the exothermic process, the valves V8, V2, V5 and V6 are opened when the cold water enters and exits, and the valves V8, V4, V3 and V6 open when the cold water enters and exits.
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| | 图5 实验测点布置图Fig. 5 Measuring position of thermocouples |
2.2 Experimental conditions
Table 4 lists the different experimental conditions under which the heat storage/release performance of the accumulator was tested. The initial temperature of the PCM is set at 25 β °C and 60 β °C under the regenerative and exothermic conditions, respectively. When the temperature of each measuring point in the box is almost unchanged for a long period of time, the experiment is ended.
| | 表4 实验工况Table 4 Experimental conditions |
2.3 Data Processing
The heat transfer effect of the device was evaluated by analyzing the average temperature, heat storage/release power, specific power and average effectiveness of the phase change materials under different working conditions.
(1) The average temperature of phase change materials
T=∑i=517Ti13=∑=51713 (1)
where: Ti(i = 5, 6...... 16, 17) is the temperature of each measurement point, °C.
(2) Heat storage power/heat release power
P=Mwatercp,water|Tin−Tout|=water,water|in−out| (2)
式中：Mwater为水的质量流量, kg/s; cp, water为水的比热容, kJ/(kg∙ K)。
(3) Heat storage specific power/heat release specific power
p=Mwatercp,water|Tin−Tout|mPCM=water,water|in−out|PCM (3)
where: Tin and Tout are the inlet and outlet temperatures of water, °C, respectively; mPCM is the mass of phase change material, kg.
(4) Average effectiveness
For the heat transfer fluid in the tube, the effectiveness is defined as the ratio of the actual heat transfer of the heat exchanger to the theoretical maximum heat transfer, which is used to reflect the heat utilization efficiency in the heat carrying fluid. In the thermal process of phase transition, the effectiveness evaluation of the device mainly focuses on the phase transition period [14], so the effectiveness analysis is selected to be set in the phase transition period, and the expressions of instantaneous effectiveness and average effectiveness are as follows:
ε=Tin−ToutTin−TPCM=in−outin−PCM (4)
ε¯¯¯=∫t0εdtt¯=∫0d (5)
where: TPCM is the average temperature of the phase change material during the phase transition period, °C.
2.4 Error Analysis
The accuracy of the experimental measuring instrument has a decisive influence on the error of the experimental results, and the dependent variables of the experimental results are represented by y, x1, x2, x3...... xn is denoted as n independent independent variables, then:
y=xα11xα22xα33⋯⋯xαnn=112233⋯⋯ (6)
The uncertainty of the experimental result y can be defined as:
Δy=[∑i=1n(∂y∂xiΔxi)2]12Δ=[∑=1(∂∂Δ)2]12 (7)
where ∆ y is the uncertainty of the experimental result y; ∆ xi is the uncertainty of the independent variable xi.
The accuracy of the experimental equipment is shown in Table 3. Based on the above error propagation formula and the accuracy of each device in the experiment, the relative error of the results can be obtained as shown in Table 5.
| | 表5 结果相对误差Table 5 Relative error of results |
3 Experimental results and analysis
3.1 Influence of heat-carrying fluid injection mode
Figure 6 shows the changes of the inlet and outlet temperatures and temperature differences of the heat-carrying fluid under the two injection modes of bottom-in, top-out and top-in, bottom-out and bottom-out injection modes in the process of heat storage/heat release, the inlet temperature of the heat-carrying fluid is 60β °C and 25β °C, respectively, and the injection flow rate is 100 L/h.
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| | 图6 蓄热（a）和放热（b）时不同注入方式下载热流体进出口温度和温差Fig. 6 Inlet and outlet temperature and temperature difference of different injection methods under heat charge (a) and heat discharge (b) |
As can be seen from Fig. 6(a), a larger temperature difference between the inlet and outlet of the heat-carrying fluid can be obtained by the bottom-in-top and top-out injection method in the heat storage process, which is about 0.8β °C higher than that of the up-inlet and bottom-out temperature difference, that is, the heat transfer from the heat-carrying fluid to the PCM is more and the heat exchange is more sufficient. This is due to the fact that natural convection plays an important role in the heat storage process, and the injection mode of bottom in and out makes the flow direction of the heat-carrying fluid in the device consistent with the natural convection direction, so as to strengthen the natural convection and make the heat exchange more sufficient. As shown in Fig. 6(b), the heat transfer is not affected by different injection methods during the exothermic process, and the temperature curves of the inlet/outlet of the thermal fluid are basically the same under the two working conditions, that is, the heat emitted by the phase change material is basically the same. This is due to the gradual solidification of phase change materials during the exothermic process, and the heat transfer is mainly heat conduction, and the influence of natural convection is relatively small. Moreover, the change of injection method will not affect the thermal conductivity of the PCM. In summary, the heat-carrying fluid injection method is selected from bottom in and top out.
3.2 Temperature Distribution
Fig. 7 shows the temperature trend of each measurement point in the vertical direction of the PCM under the two working conditions of heat storage and heat release, and the change trend shows a consistent three-stage rule: in the first stage, the heat transfer between the PCM and the heat-carrying fluid is carried out in the form of sensible heat exchange, the temperature rises/falls rapidly, and the slope of the temperature curve is large; In the second stage, the phase change material reaches the phase change temperature and starts the phase transformation, and the heat exchange mechanism becomes latent heat, the temperature is basically the same, and the slope of the curve is very small. In the third stage, most of the phase change materials complete the phase change, the heat exchange mechanism changes to sensible heat exchange again, and the slope of the temperature curve increases again, but the temperature difference between the phase change materials and the heat-carrying fluid is smaller than that of the first stage, so the temperature change rate is smaller than that of the first stage. The temperature of the PCM rises rapidly/decreases to close to the temperature of the heat-carrying fluid.
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| | 图7 蓄热（a）和放热（b）时竖直高度方向相变材料温度变化Fig. 7 Temperature change of phase change material in the vertical height direction under heat charge (a) and heat discharge (b) |
Fig. 7(a) shows that the temperature of the measuring point in the vertical height direction of the box during heat storage is T9> T5> T6> T8> T7. As the phase change material melts into a liquid state, its density is small and the temperature is high, and it converges to the highest point of the box under the action of natural convection, so the temperature of T9 is the highest. In addition, the temperature of T5 at the bottom of the box is also relatively high, which is due to the fact that the heat-carrying fluid flows from the bottom of the flat tube and flows out from the top. However, the measuring point T7 located in the middle of the box is less affected by natural convection than T9 and T8, and the heat exchange sequence with the heat-carrying fluid is after T5 and T6, so its temperature is the lowest. It can be seen that the natural convection and the heat exchange sequence of heat-carrying fluids and phase change materials have a significant effect on the temperature in the vertical height direction during heat storage.
The temperature change in the height direction of the box under the exothermic condition is shown in Figure 7(b). With the continuous heat release, the volume of the phase change material gradually decreases after changing from liquid state to solid state, and the temperature of the measuring point T9 at the top of the box decreases rapidly after the phase transformation is completed, and the temperature change rate of the measuring point T5 at the bottom of the box is also faster.
Fig. 8 shows the variation of fin height direction temperature with time under the two conditions of heat storage and heat release. It can be seen in the figure that the heat transfer effect of the measuring point at the bottom of the fin is better than that of the measuring point at the top of the fin, regardless of the open and closed area of the fin, which is manifested by the higher temperature under the heat storage condition (T11> T7> T10, T13> T12), lower temperature (T11< T7< T10, T13< T12). This is due to the fact that the bottom of the fin is attached to the outer wall of the flat tube, the temperature is higher, the temperature difference with the phase change material is larger, and the heat is more favorable to heat exchange, and more heat is gained or lost from the heat-carrying fluid in the flat tube. In addition, taking the heat storage condition as an example, the temperature of the measurement point in the closed area with the same fin height is higher than that in the open area, i.e., T13> T11, T12> T10. This is due to the fact that the phase change material in the closed area of the fin is better wrapped, and the heat exchange conditions are better.
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| | 图8 蓄热（a）和放热（b）时翅片高度方向相变材料温度变化Fig. 8 Temperature change of phase change material in the fin height direction under heat charge (a) and heat discharge (b) |
3.3 Effect of heat-carrying fluid flow
Figure 9 shows the variation curves of the average temperature of the phase change material with different fluid flow rates at the inlet temperatures of 60 β °C and 25 β °C under the heat storage/release conditions. The injection flow rates were adjusted to 80, 100 and 120 L/h respectively (corresponding Reynolds numbers 415, 519 and 633, respectively).
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| | 图9 蓄热（a）和放热（b）时不同体积流量下相变材料温度变化Fig. 9 Temperature change of phase change material at different volume flow under heat charge (a) and heat discharge (b) |
As can be seen in the figure, with the increasing inlet flow, the phase transition time is gradually shortened, and the time required for heat storage is 25.1, 20.7 and 19.8 min, and the time for heat release is 18.9, 17.5 and 16.7 min, respectively. This is due to the increase in the fluidity of the heat-carrying fluid, the convective heat transfer resistance between the heat-carrying fluid and the wall of the flat tube, the enhancement of the natural convection in the device, and the increase in the rate of heat absorption/release of the phase change material. However, the overall difference caused by the change of the flow rate of the heat-carrying fluid is not significant, especially when the flow rate is 100 L/h and 120 L/h, the curves basically overlap, the flow rate increases by 20 L/h, and the completion time of phase change in the heat storage and heat release processes is only shortened by 4.3% and 4.6%, respectively, indicating that when the flow rate reaches 100 L/h, the increase of the flow rate has little effect on the heat exchange.
This is because, on the one hand, although the larger the flow rate, the smaller the heat transfer thermal resistance, the larger the flow rate, the less sufficient the heat transfer between the heat-carrying fluid and the phase change material, and the thermal resistance is mainly concentrated on the phase change material side, and the increase of the flow rate has little effect. On the other hand, the increase of flow rate leads to an increase in flow resistance, pressure loss and energy consumption. Therefore, in practical engineering applications, under the premise of ensuring a short phase change time, a small flow rate should be selected as much as possible. Taking the three working conditions in this section as examples, the injection flow rate of 100 L/h is the optimal working condition among the three working conditions from the aspects of energy saving and heat storage/release performance.
3.4 Effect of inlet temperature of heat-carrying fluid
In the process of heat storage/heat release in the accumulator, the temperature difference between the heat-carrying fluid and the phase change material is the driving force for heat transfer. Therefore, the inlet temperature of the heat-carrying fluid can have a significant impact on the heat storage/release performance of the accumulator under the condition that other conditions are equal.
Fig. 10(a) shows the effect of the fluid inlet temperature on the average temperature of the phase change material when the volume flow rate of the heat-carrying fluid is 100 L/h during the heat storage process, and the fluid temperatures are 50, 55, 60, and 65β °C, respectively. It can be seen that the temperature of the PCM increases continuously in the first 20 min until it reaches the phase change temperature, and the difference is not obvious at the inlet temperature of different heat-carrying fluids. After 20 min, the phase change materials completed the phase transformation at different inlet temperatures, and the temperature increased rapidly again, and the curves were significantly different. In addition, the completion time of heat storage is significantly shortened with the increase of fluid inlet temperature, and when the inlet temperature is 50β °C, it takes 52 min for the phase change material in the box to complete the phase change. When the inlet temperature rises to 65β °C, the phase change material in the box needs to be completely melted in 20 min, that is, the inlet temperature is increased by 15β °C, and the time required to complete the phase change is shortened by 61.5%.
Therefore, the increase in the inlet temperature significantly enhances the heat transfer process inside the regenerator. When the temperature reaches its phase transition point, the PCM absorbs latent heat but the temperature remains unchanged, and the increase of the inlet temperature of the heat-carrying fluid has little effect on the thermal conductivity of the PCM, so the difference between the curves in the first half is not significant. In the second half of the PCM, most of the PCM melts into liquid, the heat transfer capacity of the PCM side is improved, and the higher the inlet temperature of the heat-carrying fluid, the higher the fin temperature, the larger the temperature difference between the PCM and the PCM, the greater the corresponding heat flux, and the more intense the heat exchange. At the same time, because the higher the fluid temperature, the greater the temperature difference in the direction of the fin height, and the natural convection is more significant under the large temperature difference, which is conducive to heat exchange.
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| | 图10 蓄热（a）和放热（b）时不同流体入口温度下相变材料温度变化Fig. 10 Temperature change of phase change material at different fluid inlet temperatures under heat charge (a) and heat discharge (b) |
Fig. 10(b) shows the effect of fluid inlet temperature on the average temperature of the PCM when the volume flow rate of the heat-carrying fluid is 100 L/h during the exothermic process. The inlet temperatures of the fluids were 20, 25, 30 and 35 β °C, respectively. It can be seen that the trend of each curve is about the same in the first 15 min, but after 15 min, the fluid inlet temperature decreases from 35β °C to 25β °C, and the phase change completion time is shortened from 35 min to 13 min, which is shortened by 62.9%. The first half of the PCM is mainly the liquid phase, and the sensible heat is released from the PCM, and its temperature drops rapidly to the initial phase change point. Therefore, the influence of inlet temperature is not obvious, and the temperature change curve is almost the same. The second half mainly relies on heat conduction and heat transfer, and cold fluids with lower temperatures can increase the temperature difference, accelerate the release of heat, and shorten the heat release time.
Figure 11 shows the variation of the specific power of the accumulator at different inlet temperatures of the heat-carrying fluids in the heat storage/release process. It can be seen that the specific power of heat storage/heat release gradually decreases with time, and the change of the overall specific power can be roughly divided into two stages. In the first stage (30 min before the heat storage condition and 25 min before the heat release condition), the specific power under the heat storage/release condition decreases significantly, which is due to the continuous decrease of the temperature difference between the heat carrier fluid and the phase change material, which leads to the gradual decrease of the heat exchange between the two and the decrease of the temperature difference between the inlet and outlet of the heat carrying fluid. Taking the heat storage condition as an example, the higher the inlet temperature of the heat-carrying fluid, the greater the specific power, and the average heat storage specific power increases from 64.79 W/kg to 92.71 W/kg when the inlet temperature increases from 50 β °C to 65 β °C, an increase of 43.1%.
After the phase change is completed, the phase change material enters the second stage, in which the temperature of the phase change material increases slowly, and the natural convection inside the box gradually stabilizes, and the specific power is relatively stable at about 20 W/kg. It can be seen from the figure that the relationship between the specific power of the second stage under different inlet temperatures is opposite to that of the first stage, because the higher the inlet temperature of the downloaded heat fluid in the heat storage condition, the shorter the time required to complete the heat storage, and after the heat exchange is completed, the specific power gradually stabilizes, while the heat carrier fluid with low inlet temperature still continues to carry out heat exchange with the phase change material, and the specific power exceeds the high inlet temperature. The reasons for the power change under the heat-release condition are the same as above.
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| | 图11 蓄热（a）和放热（b）时不同流体入口温度下比功率变化Fig. 11 Changes in the specific power at different fluid inlet temperatures under heat charge (a) and heat discharge (b) |
3.5 Heat storage and release performance of the accumulator under small temperature difference
Small temperature difference heat storage/release can not only meet the needs of more practical applications, but also increase the utilization efficiency of low temperature heat energy and improve the heat utilization quality of the heat accumulator. The injection flow rate was kept at 100 L/h, and the effects of lower hot fluid inlet temperature and higher cold fluid inlet temperature on the heat storage/release performance of the accumulator were investigated on the basis of section 3.4.
Fig. 12 shows the variation curves of the average temperature of the phase change material with time at the inlet temperature of different heat-carrying fluids under the conditions of heat storage and heat release. The smaller the temperature difference between the inlet temperature of the heat-carrying fluid and the phase transition temperature of the phase change material, the longer the "plateau" period of the phase transformation, that is, the longer the time to complete the phase transformation. This is due to the fact that the smaller the temperature difference, the slower the rate of energy exchange between the two. When the inlet temperature is 45β °C, the slope of the temperature curve of the PCM starts to increase again at about 270 min. When the inlet temperature is 41β °C, the phase change material can complete the phase transformation in about 75 min. That is, the minimum heat storage/heat release temperature difference of the accumulator is 2β °C.
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| | 图12 小温差工况蓄热（a）和放热（b）时不同流体入口温度下相变材料温度变化Fig. 12 Temperature change of phase change material at different fluid inlet temperatures during heat charge (a) and heat discharge (b) under small temperature difference condition |
Figure 13 shows the phase transition completion time, average specific power, and average availability as a function of the inlet temperature of the heat-carrying fluid for small temperature difference storage/heat release. As can be seen in the figure, with the decrease of the heat exchange temperature difference, the heat exchange driving force decreases, the heat exchange between the heat-carrying fluid and the phase change material decreases, and the temperature difference between the inlet and outlet of the heat-carrying fluid decreases, resulting in the continuous extension of the phase change completion time, and the average specific power and average effectiveness are significantly reduced.
When the inlet temperature of the heat-carrying fluid reaches 60β °C, the inlet temperature continues to increase, the phase transformation completion time changes slightly, and the increase of the average heat storage specific power and average effectiveness is also greatly reduced. From 60 °C to 65 °C, the phase change completion time is shortened by 25.6%, the average effective power is increased by 6.7%, and the average heat storage specific power is increased by only 1.9%. After the inlet temperature of the heat-carrying fluid reaches 25β °C, the inlet temperature of the heat-carrying fluid continues to decrease during heat release, which is similar to that of heat storage. At the same time, at the minimum heat storage temperature of 45β °C, the specific power is 25.18 W/kg, and the average effectiveness can reach 0.195 2. The maximum heat storage temperature in the experimental conditions was 65 β °C, and the average effectiveness was 0.249 2. From 45 β °C to 65 β °C, the temperature increased by 20 β °C, and the effectiveness increased by only 27.6%.
During the exothermic process, the minimum exothermic temperature was 41β °C and the specific power was 20.23 W/kg. From the minimum exothermic temperature difference of 2β °C to 23β °C, the heat exchange temperature difference increased by 21 β °C, and the average effectiveness increased from 0.173 1 to 0.272 3, which was only 1.5 times that of the former. SONG et al. [15] proposed a shell-and-tube heat storage device with vertical rectangular fins, using lauric acid with a phase change temperature of 42 ~ 48β °C as the phase change material, and calculated that the average heat storage specific power was 23.8 W/kg when the heat storage temperature difference was 10β °C.
When the difference between the temperature of the heat-carrying fluid and the phase change temperature of the phase change material in the accumulator in this study is 2β °C, the average heat storage/release ratio power can still reach more than 20 W/kg. It can be seen that the proposed heat accumulator can still maintain good heat storage/release performance under small temperature difference, and has the advantages of "small temperature difference and high power". In addition, compared with the above average availability data, it can be seen that the inlet temperature of the heat-carrying fluid has a more significant effect on the exothermic process. This is due to the presence of solid phase change materials during heat release, which leads to heat transfer mainly in the form of heat conduction, and the heat exchange temperature difference is the main driving force. In the process of heat storage, natural convection and heat conduction exist at the same time, and the effect of natural convection is more significant, and the influence of heat exchange temperature difference is relatively small.
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| | 图13 蓄热（a）和放热（b）流体不同入口温度下相变完成时间-平均蓄热比功率-有效性变化图Fig. 13 Phase transition completion time-average heat storage specific power-efficiency change diagram at different inlet temperatures of fluid under heat charge (a) and heat discharge (b) |
4 Conclusion
In this paper, a heat accumulator combining multi-channel parallel flow flattened tubes and compact fins was designed, and its heat storage/release performance under different conditions was experimentally studied, and the following conclusions were drawn:
(1) The difference caused by the heat-carrying fluid injection mode is only obvious in the heat storage process, and the temperature difference between the inlet and outlet of the heat-carrying fluid is about 0.8β °C higher than that of the up-in-out and bottom-out mode.
(2) The flow direction of the heat-carrying fluid and natural convection have a significant effect on the vertical temperature distribution of the PCM. Phase change materials close to the bottom of the fin are more susceptible to phase change. Due to the complete envelopment of the fins, the PCM in the closed region of the fins has a faster rate of heat accumulation/release.
(3) The larger the flow rate of the heat-carrying fluid, the faster the heat exchange rate, and the effect of continuing to increase when it is increased to 100 L/h is not obvious. Considering the energy saving and heat storage/heat release performance, the injection flow rate of 100 L/h is the best choice.
(4) Compared with other variables, the inlet temperature of the heat-carrying fluid has a more significant effect on the heat storage/release performance of the accumulator. During heat storage, the inlet temperature of the heat-carrying fluid increased from 50β °C to 65β °C, the time required to complete the phase change was shortened by 61.5%, and the average heat storage specific power increased from 64.79 W/kg to 92.71 W/kg, an increase of 43.1%. During exothermics, the inlet temperature decreases from 35 °C to 25 β °C, and the time to complete the phase change is shortened from 35 min to 13 min. The minimum heat storage/heat release temperature difference of the accumulator is about 2β °C, and the average heat storage specific power is 25.18 W/kg and 20.23 W/kg when the minimum temperature difference is the average heat extraction specific power.
bibliography
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