Calculation method for heat storage capacity of composite phase change material based on equivalent specific heat capacity transient integral

Abstract

The invention relates to the technical field of heat energy storage and conversion, and discloses a composite phase change material heat storage capacity calculation method based on equivalent specific heat capacity transient integral, which comprises the following steps: preparing a nanoparticle reinforced composite phase change material; the material is measured through a differential scanning calorimeter, and a curve of the equivalent specific heat capacity of the material changing along with the temperature transient state is obtained; discretizing a heat reservoir filled with the material into a plurality of control volumes, and monitoring the average temperature of each volume in real time through a temperature measuring point; on the basis of the specific heat capacity curve, integration is carried out on each control volume according to the real-time temperature and the initial temperature of the control volume, then the heat storage capacity of all the control volumes is superposed, and the total heat storage capacity is obtained. According to the method, the accurate material physical property and the real system space temperature field are combined, the calculation accuracy of the heat storage capacity is improved, the instantaneous heat storage power can be dynamically calculated, and the method has very high engineering applicability.

Description

TECHNICAL FIELD

[0001] The present application relates to the technical field of thermal energy storage and conversion, in particular to a composite phase change material heat storage capacity calculation method based on equivalent specific heat capacity transient integration. BACKGROUND

[0002] At present, phase change heat storage materials (referred to as PCM) are widely used in building energy saving, solar thermal energy utilization, electronic device thermal management and other fields due to their high latent heat density, approximately constant phase change temperature and other advantages. Among them, paraffin-based materials (such as RT42) as representative organic phase change materials have good chemical stability, no corrosion, and moderate phase change temperature, becoming one of the hot materials in current research and application.

[0003] In view of the above related content, in order to improve the poor thermal conductivity of paraffin-based PCM, a common technical solution is to add high thermal conductivity fillers (such as graphene nanoplate GNP) to construct composite phase change materials. In the calculation method of heat storage capacity, the existing technology generally uses fixed latent heat value or linear simplified specific heat capacity model. These calculation methods are based on the fixed physical parameters of the material to estimate the performance.

[0004] However, the existing heat storage capacity calculation model has imperfections. Using fixed latent heat value or linear simplified specific heat capacity model, it is difficult to accurately and truly reflect the nonlinear continuous characteristics of the thermal physical parameters (such as specific heat capacity) of the phase change material changing with temperature during the heating or cooling process. For composite PCM, the introduction of nanofiller and its interface thermal resistance make the specific heat capacity of the material show more complex nonlinear change, and the traditional model is difficult to effectively fit. The deviation of this calculation model leads to the deviation of the heat storage performance evaluation results from the actual working conditions. Therefore, at the level of current calculation method, there is a lack of a heat storage capacity evaluation and calculation model that can reflect the transient change of equivalent specific heat capacity with temperature, which is difficult to accurately predict the thermal performance of composite materials in actual application scenarios.

[0005] Therefore, the present application provides a composite phase change material heat storage capacity calculation method based on equivalent specific heat capacity transient integration to solve the deficiencies in the prior art. SUMMARY

[0006] In view of the deficiencies of the prior art, the present application provides a composite phase change material heat storage capacity calculation method based on equivalent specific heat capacity transient integration, which solves the problem of inaccurate calculation results caused by ignoring the non-uniform temperature field inside the heat storage device and the coupling of sensible heat and latent heat during the phase change process in the existing traditional heat storage capacity calculation method.

[0007] To achieve the above purpose, the present application is implemented by the following technical solutions: the present application provides a composite phase change material heat storage capacity calculation method based on equivalent specific heat capacity transient integration, comprising the following steps: S1. Prepare a nanoparticle-enhanced composite phase change material, wherein the composite phase change material comprises a matrix phase change material and nanoparticles; S2. Measure the composite phase change material using a differential scanning calorimeter to obtain the curve of the equivalent specific heat capacity changing with transient temperature. S3. Arrange temperature measuring points in the heat storage device filled with the composite phase change material, and divide the heat storage area in the heat storage device into multiple control volumes. Each control volume corresponds to a temperature measuring point, and the temperature value of the temperature measuring point represents the average temperature of its corresponding control volume. S4. Based on the curve of the equivalent specific heat capacity changing with temperature transiently, for each control volume in the heat storage area, the heat storage capacity of the control volume is obtained by integral calculation according to the average temperature and initial temperature of the corresponding temperature measuring point; and the heat storage capacity of all control volumes is superimposed to obtain the total heat storage capacity of the heat storage device.

[0008] By adopting the above technical solution, this invention solves the problem that traditional heat storage calculation methods cannot accurately reflect the non-uniform temperature field and transient phase change process inside the heat storage device. Traditional methods usually rely only on the latent heat value of the material or simplified temperature changes for estimation, ignoring the coupling of sensible and latent heat during the phase change process, as well as the uneven temperature distribution inside the heat storage device caused by differences in natural convection and conduction. The technical logic adopted in this invention overcomes the above-mentioned defects: The transient curve of equivalent specific heat capacity as a function of temperature is obtained through step S2. This curve is an accurate characterization of the material's physical properties, and its integral value in the phase transition region already includes the contributions of sensible heat and latent heat. By drawing on the concept of finite element analysis in step S3, the continuous space of the thermal storage tank is discretized into multiple control volumes, and the average temperature of each volume is monitored in real time, thereby capturing the non-uniform temperature field inside. In step S4, the material property curves of S2 are combined with the real-time space temperature data of S3, and the integral calculations are performed separately for each control volume before being superimposed.

[0009] Therefore, this method can accurately and dynamically reflect the total heat storage capacity of the entire heat storage device during complex transient heat transfer processes, and the calculation results have high accuracy.

[0010] Preferably, in step S2, the sample heat flow signal is obtained by measuring the differential scanning calorimeter. ), standard sample heat flow signal ( ) and baseline drift signal ( ) Specific heat capacity of the sample to be tested ( The calculation of ) follows the following formula: ; in, Specific heat capacity of the standard sample; and The mass of the standard sample and the mass of the sample to be tested are respectively.

[0011] Preferably, in step S2, the measurement is performed under an inert atmosphere at least once with a constant heating or cooling rate, and the measurement data from the second or subsequent cycles are analyzed to eliminate the influence of thermal history.

[0012] By employing the above technical solution, using standard samples (such as sapphire) for calibration, and subtracting baseline drift signals, the accuracy and reliability of the obtained equivalent specific heat capacity transient change curve are ensured, providing a precise data foundation for subsequent integration calculations (step S4). Simultaneously, a specific thermal cycling procedure eliminates the influence of material thermal history, improving the repeatability of the measurement results.

[0013] Preferably, in step S4, the step of calculating the heat storage capacity of the control volume specifically involves: obtaining the equivalent specific heat capacity function that varies with temperature T (…). ), from the initial temperature ( The temperature reaches the termination temperature, i.e., the current temperature of the material. Integrate the results to calculate the heat storage per unit mass ( ) Then multiply the heat storage per unit mass by the material mass of the control volume. The integral calculation follows the following expression: ; in, This indicates the amount of heat stored per unit mass.

[0014] Preferably, the method further includes: repeating step S4 at different time points to obtain transient data of the total heat storage changing over time; and obtaining the instantaneous heat storage power or heat release power of the heat storage device by calculating the rate of change of the total heat storage over time.

[0015] By employing the aforementioned technical solution, this integral method scientifically incorporates all the heat absorbed by the material as it rises from its initial temperature to its current temperature. It provides a precise mathematical description of the physical process of phase change thermal storage, far superior to estimations using only latent heat or average specific heat capacity. Furthermore, by performing time differentiation on the stored heat, this method can not only calculate the total amount of stored heat but also dynamically analyze the storage rate, providing more comprehensive dynamic data for the performance evaluation and optimized design of thermal storage systems.

[0016] Preferably, in step S3, the arrangement of temperature measuring points includes: setting multiple measuring sections along the axial direction of the heat storage device, and evenly distributing multiple temperature measuring points along the radial and circumferential directions on the measuring sections.

[0017] Preferably, in step S3, the step of dividing the control volume is based on the finite element analysis method, and the thermal storage area is divided into multiple sub-regions by grid lines, the intersection of the grid lines is a node, and the temperature measuring point is the node.

[0018] By adopting the above technical solution, this three-dimensional measurement point arrangement along the axial, radial, and circumferential directions can comprehensively capture the complex three-dimensional temperature field inside the thermal storage device caused by factors such as buoyancy effect and uneven heat conduction. By using the concept of finite element analysis for spatial discretization, the temperature of each control volume can be effectively monitored, avoiding the huge errors caused by using a single measurement point to represent the overall temperature, and greatly improving the characterization accuracy of the non-uniform phase change process inside the thermal storage device.

[0019] Preferably, in step S1, the nanoparticles are at least one of graphene nanosheets, monolayer graphene, or graphite; and the matrix phase change material is a paraffin-based material.

[0020] Preferably, in step S1, the specific steps for preparing the composite phase change material include: heating and melting the matrix phase change material; adding a dispersant and mechanically stirring; adding the nanoparticles; and ultrasonically treating the mixture to break up particle agglomeration, thereby obtaining the composite phase change material.

[0021] Preferably, the matrix phase change material is RT42 paraffin, and the nanoparticles are graphene nanosheets.

[0022] By employing the above-mentioned technical solution, using melt blending supplemented with ultrasonic treatment, graphene nanosheets and other highly thermally conductive nanoparticles can be uniformly dispersed in a paraffin matrix, forming an effective heat conduction network. This improves the thermal conductivity of the composite phase change material itself, overcomes the poor thermal conductivity of the matrix phase change material, and ensures that the thermal storage system applied by this calculation method has excellent heat storage and release performance.

[0023] This invention provides a method for calculating the heat storage capacity of composite phase change materials based on the transient integral of equivalent specific heat capacity. It has the following beneficial effects: 1. This invention obtains the curve of the equivalent specific heat capacity of a material as a function of transient temperature, and integrates this curve, thereby unifying the complex coupling of sensible and latent heat in the phase change process into a single integral calculation. Simultaneously, by discretizing the thermal storage device into multiple control volumes and monitoring their temperatures individually, it overcomes the errors caused by traditional methods that rely on latent heat values ​​and average temperature estimations. This method combines accurate material properties with the real system space temperature field, resulting in highly accurate calculations of the heat storage capacity, which can truly reflect the non-uniform phase change process inside the thermal storage device.

[0024] 2. The method of this invention not only calculates the total heat storage but also possesses dynamic analysis capabilities. By repeatedly performing integral superposition calculations at different time points, transient data on the change of total heat storage over time can be obtained. Furthermore, by calculating the rate of change of total heat storage over time, the instantaneous heat storage power or heat release power of the heat storage device can be obtained. This provides crucial data support for the dynamic performance evaluation of heat storage systems and the optimization of heat charging and discharging strategies, which is unavailable through traditional static estimation methods.

[0025] 3. The temperature measurement point arrangement and control volume division method adopted in this invention draws on the concept of finite element analysis. By uniformly distributing measurement points along the axial, radial, and circumferential directions, it effectively captures the complex three-dimensional non-uniform temperature field inside the thermal storage device caused by factors such as natural convection and uneven heat transfer. This spatial discretization processing method makes this calculation method not limited to specific thermal storage device structures or idealized models, and has strong engineering applicability and universality. Attached Figure Description

[0026] Figure 1 This is a SEM image of the GNP of the present invention; Figure 2 This is a SEM image of the RT42 of the present invention; Figure 3 This is a SEM image of 1.0wt% GNP-RT of the present invention; Figure 4 The transient change of specific heat capacity of 1.0wt% GNP-RT of the present invention with temperature is shown in the figure. Figure 5 This is a technical roadmap of the present invention; Figure 6 This is a front view of the horizontally placed temperature measuring point arrangement of the topological thermal storage device of the present invention; Figure 7 This is a side view of the horizontally placed temperature measuring point arrangement of the topological thermal storage device of the present invention. Figure 8 This is a schematic diagram of the finite element volume division of the thermal storage device of the present invention; Figure 9 This is an energy analysis diagram of the topological thermal storage device of the present invention during the thermal storage process; Figure 10 This is an energy analysis diagram of the topological thermal storage device of the present invention during the heat release process. Detailed Implementation

[0027] The technical solutions in the embodiments of the present invention will be clearly and completely described below with reference to the accompanying drawings. Obviously, the described embodiments are only some embodiments of the present invention, and not all embodiments. Based on the embodiments of the present invention, all other embodiments obtained by those skilled in the art without creative effort are within the scope of protection of the present invention.

[0028] See attached document Figure 5 This invention provides a method for calculating the heat storage capacity of composite phase change materials based on the transient integral of equivalent specific heat capacity.

[0029] The implementation of this invention is based on the study of the heat transfer characteristics of a horizontally placed topological finned phase change thermal energy storage device.

[0030] The calculation method provided by this invention is characterized by including the following steps: Step (1): Prepare nanoparticle-enhanced composite phase change materials.

[0031] Composite phase change materials were prepared by melt blending, with the nanoparticles being graphene nanosheets (GNP), single-layer graphene (DGP), or graphite (GRA), and the mass fraction of the nanoparticles being 0.5-1.5 wt%.

[0032] Step (2): Measure the equivalent specific heat capacity of the composite material as a function of temperature transients using a differential scanning calorimeter (DSC).

[0033] The heat flow signal of the composite material was measured in different temperature ranges using a differential scanning calorimeter (DSC2500), and the equivalent specific heat capacity was calculated based on the specific heat capacity of the standard material. The specific calculation formula is as follows: ; In the formula: The specific heat capacity of the sample to be tested; Specific heat capacity of the standard sample; , The masses of the standard sample and the sample to be tested are respectively. , To measure the heat flux signal (μV / mg) of the sample and standard sample using sapphire crystal; The baseline drift (μV / mg) measured for a pair of empty crucibles needs to be subtracted when measuring the heat flow between the sample and the surface.

[0034] Step (3): Design and arrange the openings and temperature measuring points on the outer shell of the thermal storage tank based on the finite element analysis method, and obtain the approximate calculation method of liquid phase ratio by controlling the temperature of the volume nodes.

[0035] See attached document Figure 6 , Figure 7 and Figure 8 To perform the calculations, it is necessary to design openings and arrange temperature measuring points in the quartz glass shell of the heat storage tank. Subsequently, drawing on the finite element analysis method for numerically solving heat transfer problems, the arrangement of temperature measuring points (such as...) is determined.Figure 6 and Figure 7 As shown in T1-T24), the thermal storage area is divided into multiple sub-regions (control volume), such as... Figure 8 As shown. The intersections of the grid lines are nodes, and the temperature value of each node (measuring point) represents the average temperature of the control volume centered on that node.

[0036] Step (4): Using finite element analysis, the equivalent specific heat capacity transient curve is integrated with temperature to obtain the heat storage capacity and heat storage power of the composite phase change material.

[0037] See attached document Figure 4 This method employs a transient integration method based on the change of equivalent specific heat capacity with temperature. The curve of the sample's equivalent specific heat capacity versus temperature is obtained experimentally (as shown in step (2)). The heat absorption per unit mass of the composite material is obtained by integrating the sample's equivalent specific heat capacity curve with the temperature axis (horizontal axis), as shown in step (2). Figure 4 As shown, the expression is: ; in, It is the equivalent specific heat capacity function; , These are the phase transition initiation temperature and the phase transition termination temperature, respectively. This indicates the amount of heat stored per unit mass.

[0038] In practical implementation, the temperature measurement point (node) represents the average temperature of a single control volume. Using the above integral formula, the equivalent specific heat capacity is calculated from the initial temperature (…). The average temperature at the measuring point corresponding to the control volume ( Integrate the data to obtain the heat storage per unit mass of the control volume at this temperature.

[0039] Then, based on the material mass of the control volume, the heat storage capacity of that area is obtained. Finally, the heat storage capacity of the control volumes represented by all (e.g., 24) measuring points is superimposed to obtain the total heat storage capacity of the heat storage device.

[0040] The composite phase change material in step (1) of this invention is prepared by melt blending. This method first heats the matrix phase change material, such as paraffin-based materials (e.g., RT42), at a preset temperature (e.g., in water) until it is completely melted.

[0041] Subsequently, a dispersant is added to the molten matrix phase change material, and the dispersant is uniformly mixed in the matrix by mechanical stirring (e.g., magnetic stirring).

[0042] Then, a predetermined mass fraction of nanoparticles is added to the mixture. The nanoparticles can be graphene nanosheets (GNP), single-layer graphene (DGP), or graphite (GRA), and their mass fraction in the composite material ranges from 0.5 wt% to 1.5 wt%.

[0043] To ensure uniform dispersion of nanoparticles in the matrix and to break up any potential particle agglomeration, the mixture was treated with ultrasound.

[0044] Finally, the treated liquid composite material was sampled and cooled to complete solidification at room temperature to obtain a composite phase change material for subsequent performance analysis.

[0045] Step (2) of this invention involves obtaining the transient curve of the equivalent specific heat capacity of the composite phase change material as a function of temperature. This step is achieved by differential scanning calorimetry (DSC).

[0046] The principle of differential scanning calorimetry (DSC) is as follows: the sample and reference material (usually an empty crucible) are placed on the same heating element (e.g., a constantan pan) of the instrument. When the heater programmatically heats or cools the heating element, heat is transferred to the sample and reference material through the heating element. Due to the differences in heat capacity and thermal conductivity between the sample and reference material, they absorb or release different amounts of heat, resulting in a heat flow difference between them. This heat flow difference is monitored by thermocouples, thereby obtaining the real-time dynamic changes of thermal performance parameters such as sample heat flow and specific heat capacity with temperature.

[0047] In the specific measurement, a certain mass of the sample to be tested is first sealed in a sample crucible. Under the protection of an inert atmosphere (such as nitrogen), at least one heating and cooling cycle is performed within a set temperature variation range at a constant heating or cooling rate. To eliminate the influence of the material's own thermal potential on the measurement results, the measurement data from the second or subsequent cycles are usually used for analysis.

[0048] The equivalent specific heat capacity of the sample can be calculated using the heat flow signal obtained through measurement, according to the following formula: ; In the formula: The specific heat capacity of the sample to be tested; This refers to the specific heat capacity of a standard sample, such as sapphire. The mass of the standard sample; The mass of the sample to be tested; The heat flow signal measured on the sample is given in units of . V / mg; The heat flow signal measured from the standard sample, in units of V / mg; The baseline drift signal measured using a pair of empty crucibles, in units of V / mg, this signal needs to be subtracted when measuring the heat flow of the sample and the standard sample.

[0049] See attached document Figure 6 , Figure 7 and Figure 8 In step (3) of this invention, in order to accurately calculate the heat storage inside the thermal storage tank, it is first necessary to spatially discretize the continuous temperature field inside the thermal storage tank. This process is achieved by arranging multiple temperature measuring points at preset locations inside the thermal storage tank.

[0050] Specifically, openings are designed into the outer shell of the thermal storage tank to allow temperature sensors (such as thermocouples) to be placed inside the phase change material. The arrangement of temperature measuring points aims to comprehensively acquire the internal temperature distribution of the thermal storage tank during heat storage or release. For this purpose, the measuring points are distributed along the axial and radial directions of the thermal storage tank. For example... Figure 6 and Figure 7 The embodiment shown has multiple cross sections arranged along the axial direction, and several measuring points are evenly distributed at different positions and angles along the radial direction on each cross section.

[0051] After completing the measurement point layout, the spatial coordinate system occupied by the phase change material within the thermal storage tank is discretized, drawing on the finite element analysis approach used in numerical solutions to heat transfer problems. This method divides the thermal storage region into multiple sub-regions, i.e., control volumes, using a series of grid lines. The intersections of the grid lines are the nodes.

[0052] In this method, each temperature measuring point (e.g., attached) Figure 8 In this context, T1-T24 are considered as nodes, and the temperature values ​​measured at these nodes are used to represent the average temperature of the corresponding control volume centered on that node. In this way, the continuous temperature field of the entire thermal storage tank is simplified into a set of discrete node temperature data.

[0053] Based on this division, the percentage of each control volume relative to the total volume of the phase change material can be determined, i.e., the percentage of the measurement point volume. This discretized model forms the basis for subsequent calculations of the liquid phase ratio and heat storage capacity. By monitoring the real-time temperature of each node and combining it with its phase change temperature, the phase state (solid, liquid, or solid-liquid mixture) of each control volume can be approximately determined, thus providing a basis for calculating the total liquid phase ratio and total heat storage capacity of the entire heat storage tank.

[0054] See attached document Figure 4In step (4) of this invention, the calculation of heat storage adopts a transient integral method based on the change of equivalent specific heat capacity with temperature. The basis of this method is that the heat absorbed or released by the material within a certain temperature range can be determined by integrating its equivalent specific heat capacity within that temperature range.

[0055] Specifically, for a unit mass of composite phase change material, its temperature from the initial temperature... Change to the final temperature The heat absorbed during the process can be calculated using the following integral expression: ; in: The equivalent specific heat capacity function obtained in step (2) that varies with temperature T; The starting temperature for integration is usually the initial temperature of the material or a temperature before the phase transition begins. The temperature at which the integration ends is the current temperature of the material. This indicates the amount of heat stored per unit mass.

[0056] As attached Figure 4 As shown, the value of this integral corresponds to the equivalent specific heat capacity temperature curve. arrive The size of the area under the curve within the interval.

[0057] When applying this principle to the entire thermal storage tank, it is necessary to combine it with the finite element discretization model established in step (3). The calculation process is first performed for each independent control volume. For any control volume, the real-time temperature measured at its corresponding node (i.e., the temperature measuring point) is used as the integration termination temperature. Substituting into the above integral formula, the heat storage per unit mass of the control volume at this temperature can be calculated.

[0058] Then, by multiplying the calculated heat storage per unit mass by the mass of phase change material contained in the control volume, the total heat storage of the single control volume at the current moment can be obtained.

[0059] Finally, by summing the heat storage in all control volumes within the thermal storage tank, the total heat storage of the entire thermal storage tank at the current moment can be obtained. By repeating this calculation at different time points, transient data on the change of the total heat storage of the thermal storage tank over time can be obtained. Based on this time series data, by calculating the rate of change of the total heat storage over time, the instantaneous heat storage power or heat release power of the thermal storage tank can be further obtained.

[0060] This invention provides an experimental testing system for implementing computational methods.

[0061] The core of the experimental testing system is a topologically finned phase change thermal storage device. The outer shell of this storage device consists of a quartz glass sleeve and two end plates on either side. The glass sleeve has an outer diameter of 130 mm, an inner diameter of 124 mm (i.e., a thickness of 3 mm), and a length of 200 mm. The end plates on both sides are composed of annular quartz glass sheets with outer diameters of 130 mm and 124 mm respectively, an inner diameter of 45 mm for each, and a thickness of 3 mm for both. One side of the storage device's outer shell is welded to the end plates, while the other side is encapsulated with high-temperature resistant, waterproof, flexible silicone.

[0062] The heating system used in the thermal storage process consists primarily of a 176W electric heating element, 200mm long and 141mm wide. Made of high-temperature resistant silicone, the heating element is flexible and can be tightly fitted to the inner wall of the entire finned tube within the thermal storage unit. The heating process is controlled by a thermostat with a temperature control accuracy of ±1K.

[0063] The cooling system used for the heat release process uses a fan to deliver air into the heat storage tank at a constant flow rate, and uses a series pressure divider to regulate the air flow.

[0064] The system's data acquisition system includes temperature data acquisition and image acquisition. Temperature data acquisition is achieved through multiple K-type thermocouples, with a temperature measurement range of -60℃ to 200℃ and a measurement error of ±0.5℃ to 1℃. The sensing end of the thermocouple is fixed inside the heat storage tank, and the other end is connected to a TP700 multi-channel data acquisition instrument, which reads and records the temperature data by a computer.

[0065] The image acquisition system includes a handheld H36 infrared imager and a high-speed camera with a bracket, which are used to acquire transient temperature field distribution images of the end face of the thermal storage tank during the melting and solidification processes, and to record the phase change process.

[0066] To minimize the impact of the environment on the experiment, the entire experimental testing system was placed in an insulated chamber made of insulating foam and film.

[0067] See attached document Figure 6 , Figure 7 , Figure 8 Table 1 shows the percentage of measurement point volume according to an embodiment of the present invention.

[0068] In one specific embodiment of the present invention, the openings and temperature measuring points on the outer shell of the heat storage tank are arranged as follows: Five measuring sections are set along the axial direction of the thermal storage device, namely section A, section B, section M, section C, and section D. Section M is the central section. On section M, eight holes are evenly distributed at 45° intervals along the circumference. On the other sections A, B, C, and D, four holes are evenly distributed at 90° intervals along the radial direction.

[0069] A total of 24 K-type thermocouples (T1-T24) are arranged inside the heat storage tank through the aforementioned openings. The thermocouples (T9-T16) located at the central M section have an insertion depth of 20 mm. The thermocouples (T1-T4, T17-T20) located at sections A and B have an insertion depth of 10 mm. The thermocouples (T5-T8, T21-T24) located at sections C and D have an insertion depth of 30 mm.

[0070] Based on the spatial arrangement of the 24 temperature measuring points, the thermal storage area was divided into multiple sub-regions (control volumes) using finite element methods. Each measuring point represents the temperature of the control volume centered thereon. Based on this division, the percentage of the control volume represented by each measuring point relative to the total volume of the phase change material was calculated, as shown in Table 1.

[0071] Table 1: Volume percentage at measuring points T1-T24 See attached document Figure 9 and Figure 10 . Figure 9 and Figure 10 This is an energy analysis diagram of a topological thermal storage device using 1.0wt% GNP-RT as phase change material during the heat storage and release process, according to an embodiment of the present invention.

[0072] In one specific embodiment of the present invention, 1.0 wt% GNP-RT composite phase change material was filled into the aforementioned experimental testing system, and its thermal storage performance was analyzed using the calculation method of the present invention.

[0073] First, an approximate calculation of the liquidus fraction was performed. Based on experimental measurements, the melting phase transition range of the 1.0 wt% GNP-RT material used was 312 K to 314 K, and the solidification phase transition range was 312.5 K to 314.5 K. Based on the real-time temperatures recorded by the data acquisition instrument at each measuring point, when the temperature at a measuring point was higher than its melting point temperature, the control volume represented by that measuring point was considered to have completely melted; when the temperature at a measuring point was lower than its solidification point temperature, the liquidus fraction of that control volume was considered to be 0.

[0074] Subsequently, the heat storage capacity and heat storage power were calculated. During the heat storage process, the boundary heating temperature of the heat storage device was set to 393K. In the calculation, the transient curve of the equivalent specific heat capacity of 1.0wt%GNP-RT obtained in step (2) was first integrated from the initial temperature to the real-time temperature collected at each measuring point to obtain the heat storage capacity per unit mass of each control volume. Then, the heat storage capacity of the region was calculated based on the material mass of each control volume. Finally, the heat storage capacity of the control volumes represented by the 24 measuring points was superimposed to obtain the total heat storage capacity of the heat storage device. In particular, for the annular region without thermocouples, the average temperature of 8 measuring points at sections C and D was taken as the temperature of the annular region for calculation.

[0075] As attached Figure 9 and Figure 10 As shown, the specific calculation and analysis results are as follows: During the heat storage process, the total heat storage capacity of the heat storage device showed a continuous upward trend over time. Between 10 and 60 minutes, the material was mainly in the melting phase transition zone, and the total heat storage capacity increased from 60.64 kJ to 297.87 kJ. During this period, the heat storage power exhibited a trend of first decreasing, then increasing, and then decreasing again. This is because the melting process is slow at the beginning, accelerates in the later stages, and after the material is completely melted, the increase in heat storage capacity becomes gradual, and the heat storage power decreases accordingly.

[0076] During the heat release process, the heat release and heat release power initially vary significantly due to the influence of natural convection. After the material enters the solidification phase transition zone, within a time period of 50 to 300 minutes, the total heat release decreases from 115.73 kJ to 36.80 kJ, a decrease of 68.20%; the corresponding heat release power decreases from 187.68 W to 29.10 W, a decrease of 84.50%.

[0077] Test Example 1: Preparation, Characterization and Performance Testing of Core Composite Phase Change Material (1.0wt% GNP-RT) Reference Figure 1 , Figure 2 , Figure 3 And Tables 2 and 3. Figures 1 to 3 SEM images of GNP, RT42 and 1.0wt%GNP-RT are shown. Tables 2 and 3 list the thermal conductivity and latent heat of phase change of the composite phase change materials, respectively.

[0078] This test case mentions a core embodiment of nanoparticle-reinforced composite phase change materials, namely a composite material (1.0wt%GNP-RT) with 1.0wt% graphene nanosheets (GNP), and verifies its excellent thermal properties.

[0079] Preparation of composite phase change materials: This example demonstrates the preparation of a 1.0 wt% GNP-RT composite phase change material using a melt blending method. The specific steps are as follows: Pour 50g of solid powdered paraffin (RT42) into a 250mL beaker and place it in a 60℃ water bath to melt it completely.

[0080] Add 0.25g (0.5wt%) of SDBS dispersant and mix with RT42. Heat to 60°C using a digital display magnetic stirrer, and rotate the magnetic stir bar at 1000rpm / min for 30 minutes to ensure uniform heating and thorough mixing.

[0081] Add 0.5g (1.0wt%) of GNP.

[0082] The cells were treated with an ultrasonic cell disruptor for 60 minutes to break up the agglomeration of nanoparticles and ensure that GNP and RT42 were mixed uniformly.

[0083] Liquid composite material was dropped into a dry pot for sample encapsulation and thermophysical analysis. It was then cooled to complete solidification at room temperature to obtain the target composite phase change material 1.0wt%GNP-RT.

[0084] Microstructure (SEM) characterization: SEM analysis was performed on the 1.0 wt% GNP-RT composite phase change material to observe its microstructure. The results showed that, due to the strong bonding between GNP and RT42, the surface of 1.0 wt% GNP-RT was smoother than that of pure RT42. Within the matrix, GNP maintained a good lamellar layer structure and was uniformly dispersed in the paraffin matrix, with its edges exhibiting a certain degree of wrinkling. This wrinkled structure facilitates the interconnection of GNPs, thereby forming a continuous thermally conductive network structure within the phase change material.

[0085] Core thermophysical parameters and technical effects: The core thermophysical parameters of the 1.0wt% GNP-RT composite phase change material were measured, and the results are shown in Tables 2 and 3.

[0086] Thermal conductivity optimization: At room temperature (20°C), the thermal conductivity of pure RT42 is 0.2010 W / (m·K). After adding 1.0 wt% GNP, the thermal conductivity of the composite material 1.0 wt% GNP-RT increased to 0.3826 W / (m·K) (Table 2, item 9), which is 90.35% higher than that of pure RT42. This result demonstrates that the three-dimensional heat conduction network constructed by GNP can effectively enhance the connectivity of heat flow paths and improve the poor thermal conductivity of paraffin-based phase change materials.

[0087] Table 2: Thermophysical properties of composite phase change materials (at room temperature 20℃) Thermal storage performance and latent heat: Differential scanning calorimetry (DSC) and the equivalent specific heat capacity integral method proposed in this invention were used (see appendix). Figure 4 The latent heat of phase change of 1.0 wt% GNP-RT was measured and calculated for comparison. The results are shown in Table 3.

[0088] Table 3: Latent Heat of RT42 and Composite Phase Change Materials Where "-" indicates that it cannot be measured.

[0089] Accuracy of the calculation method: The heat storage calculation method based on the transient integral of equivalent specific heat capacity proposed in this invention was used to calculate the latent heat of 1.0 wt% GNP-RT and achieved high accuracy. Comparison of the theoretical latent heat value with the DSC experimental measurement showed a relative error of 2.30% for the melting process and 5.24% for the solidification process. This result proves that the proposed method can accurately reflect the heat storage of composite phase change materials.

[0090] Test Example 2: Detailed Description of Thermophysical Property Testing Methods This test case details the experimental methods used to characterize the thermophysical properties of composite phase change materials, including specific heat capacity measurement and thermal conductivity measurement, to support the data sources in Test Case 1 and Test Case 3.

[0091] Specific heat capacity measurement method (DSC) To obtain the curve of the specific heat capacity of the composite phase change material as a function of temperature, this invention uses a differential scanning calorimeter (DSC2500) for measurement. The specific steps are as follows: Before measurement, weigh 20-30 mg of the composite phase change material sample and place it in a sealed aluminum crucible. The test was conducted under a nitrogen atmosphere with a constant gas flow rate of 50 mL / min.

[0092] The test procedure was set as follows: first, the sample was heated from 293K (20℃) to 343K (70℃) at a heating rate of 10℃ / min; then, the sample was cooled from 343K (70℃) to 293K (20℃) at a cooling rate of 10℃ / min.

[0093] The above test will yield the results shown in the attached document. Figure 4 The transient temperature curve of the specific heat capacity during the melting and solidification process. For example, in the test of this embodiment, Peak specific heat capacity points respectively , Compared with RT42, the performance was improved by 6.28 times, 5.33 times, and 2.88 times, respectively.

[0094] Thermal conductivity measurement method (Hot Disk) Referring to Table 2, in order to measure the thermal conductivity of the composite phase change material in the solid state, this invention uses a HotDisk transient planar source thermal constant analyzer (Hot Disk TPS3500S).

[0095] The specific steps are as follows: Before measurement, the composite phase change material sample to be tested is pressed into two identical cylinders, each cylinder having a diameter of 50mm and a height of 20mm.

[0096] Measurements were performed at room temperature (20°C). A Kapton insulated sensor (model 5501) was clamped between two identical cylindrical samples. During testing, the probe's heating power was set to 100mW, and the heating time was 10s.

[0097] This method allows for the accurate measurement of the solid-state thermal conductivity of materials, and the specific measurement results are listed in Table 2.

[0098] Test Example 3: See attached document Figure 4 Tables 2 and 3. Tables 2 and 3 provide comparative data on the thermal conductivity and latent heat of phase change for different materials.

[0099] This test example aims to further demonstrate the superiority of the technical solution selected in this invention by comparing the effects of different types of carbon nanomaterials (GNP, DGP, GRA) and different mass fractions (0.5wt%, 1.0wt%, 1.5wt%) on the thermophysical properties of composite phase change materials.

[0100] Thermal conductivity comparison As shown in Table 2, the thermal conductivity of pure RT42 and composite phase change materials with different mass fractions of DGP (monolayer graphene), GRA (graphite) and GNP (graphene nanosheets) were measured at room temperature (20°C).

[0101] Analysis of the data in Table 2 shows that: All three carbon nanomaterials can improve the thermal conductivity of the RT42 matrix to varying degrees.

[0102] For DGP, GRA, and GNP, within the test range of this invention (0.5wt% to 1.5wt%), their thermal conductivity all monotonically increases with increasing mass fraction.

[0103] Taking GNP as an example, at 1.0 wt%, its thermal conductivity is 0.3826 W / (mK), which is 90.35% higher than that of pure RT42 (0.2010 W / (mK)).

[0104] When the GNP mass fraction continues to increase to 1.5 wt%, its thermal conductivity further increases to 0.4209 W / (mK).

[0105] Conclusion: Among all test groups, the 1.5wt%GNP-RT composite phase change material exhibits the best thermal conductivity.

[0106] Comparison of thermal storage performance (latent heat): As shown in Table 3, the latent heat of phase change of three materials, pure RT42, 1.0wt%GNP-RT and 1.0wt%DGP-RT, was calculated by combining the DSC experimental measurement method with the equivalent specific heat capacity integral method (theoretical value) proposed in this invention.

[0107] Analysis of the data in Table 3 shows that: Compared to pure RT42 (experimental value 197.12 J / g), the latent heat of phase change (experimental value) of composite phase change materials with added GNP, DGP, or GRA all decreased to varying degrees. This is because these carbon nanomaterials, as additives, do not undergo phase change themselves and occupy a portion of the mass, resulting in a slight reduction in the heat storage capacity per unit mass of the composite material.

[0108] Comparing the calculation method (theoretical value) of this invention with DSC (experimental value), the two show a high degree of agreement. Specifically, the relative errors of 1.0% GNP-RT are 2.30% and 5.24%, respectively; and the relative errors of 1.0% DGP-RT are 6.14% and 2.30%, respectively. This demonstrates that the calculation method proposed in this invention has universal applicability and high accuracy.

[0109] Comparison of specific heat capacity performance: See attached document Figure 4 The DSC curves can be used to obtain the peak specific heat capacity of different materials during the phase transition process.

[0110] The peak specific heat capacity of 1.0wt% GNP-RT is 60.282 kJ / (kg·K).

[0111] The peak specific heat capacity of 1.0wt% DGP-RT is 51.132 kJ / (kg·K).

[0112] Data shows that the specific heat capacity of the composite phase change material is increased by 6.28 times and 5.33 times compared with RT42, respectively, indicating that the addition of carbon materials effectively improves the heat storage capacity of the composite material.

Claims

1. A method for calculating the heat storage amount of a composite phase change material based on transient integration of equivalent specific heat capacity, characterized by, The method comprises the following steps: S1, preparing a nanoparticle-enhanced composite phase change material, which comprises a matrix phase change material and nanoparticles; S2, measuring the composite phase change material by a differential scanning calorimeter to obtain a curve of equivalent specific heat capacity transient change with temperature; S3, arranging temperature measuring points for a heat storage device filled with the composite phase change material, and dividing a heat storage area in the heat storage device into a plurality of control volumes, which correspond to the temperature measuring points one by one, and the temperature values of the temperature measuring points represent the average temperatures of the corresponding control volumes; S4, based on the curve of equivalent specific heat capacity transient change with temperature, for each control volume in the heat storage area, the heat storage amount of the control volume is obtained by integral calculation according to the average temperature and the initial temperature of the corresponding temperature measuring point, and the heat storage amounts of all control volumes are superimposed to obtain the total heat storage amount of the heat storage device.

2. The method of claim 1, wherein, In step S1, the nanoparticles are at least one of graphene nanoplatelets, single-layer graphene or graphite; and the matrix phase change material is a paraffin-based material.

3. The method of claim 1, wherein, In step S1, the specific steps for preparing the composite phase change material include: heating and melting the matrix phase change material; adding a dispersant and performing mechanical stirring; adding the nanoparticles; and ultrasonic treatment of the mixture to break the particle agglomeration, thereby obtaining the composite phase change material.

4. The method of claim 1, wherein, In step S2, the differential scanning calorimeter is used to obtain a sample heat flow signal, a standard sample heat flow signal and a baseline drift. The calculation method of the equivalent specific heat capacity of the composite phase change material is as follows: The baseline drift is subtracted from the sample heat flow signal and the standard sample heat flow signal respectively to obtain a corrected sample heat flow and a corrected standard sample heat flow; The ratio of the corrected sample heat flow to the corrected standard sample heat flow is calculated; The ratio of the mass of the standard sample to the mass of the sample to be measured is calculated; The two ratios are multiplied by the specific heat capacity of the standard sample to obtain the equivalent specific heat capacity of the composite phase change material.

5. The method of claim 4, wherein, In step S2, the measurement is performed under an inert atmosphere with a constant heating or cooling rate for at least one heating and cooling cycle, and the measurement data of the second or subsequent cycle is used for analysis to eliminate the influence of thermal history.

6. The method of claim 1, wherein, In step S3, the temperature measuring point arrangement includes: A plurality of measurement sections are arranged along the axial direction of the heat storage device, and a plurality of temperature measuring points are uniformly distributed along the radial and circumferential directions on the measurement sections.

7. The method of claim 6, wherein, In step S3, the step of dividing the control volumes is based on the finite element analysis method, and the heat storage area is divided into a plurality of sub-areas by grid lines, the intersection points of the grid lines are nodes, and the temperature measuring points are the nodes.

8. The method of claim 1, wherein, In step S4, the step of calculating the heat storage amount of the control volume is as follows: The curve of equivalent specific heat capacity transient change with temperature is integrated from the initial temperature to the average temperature of the temperature measuring point corresponding to the control volume to obtain the unit mass heat storage amount; The unit mass heat storage amount is multiplied by the material mass of the control volume.

9. The method of claim 8, wherein, The composite phase change material heat storage amount calculation method based on equivalent specific heat capacity transient integral further comprises: The S4 step is repeated at different time points to obtain transient data of the total heat storage amount changing over time; and by calculating the rate of change of the total heat storage amount over time, the instantaneous heat storage power or heat release power of the heat storage device is obtained.

10. The method of claim 2, wherein, The matrix phase change material is RT42 paraffin, and the nanoparticles are graphene nanoplatelets.

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