A simulation method for lung-simulating groove blood vessel fin phase change heat storage system enhanced by nanofluid

Abstract

This invention relates to the field of phase change heat storage technology, specifically to a simulation method for a phase change heat storage system using nanofluid-enhanced pulmonary groove vessel fins. First, a three-dimensional physical model of the pulmonary groove vessel fin-enhanced phase change heat storage system is established. The three-dimensional model is then simulated and analyzed. The simulation results are compared with experimental results, and the simulation model parameters are adjusted to improve the accuracy of the simulation results. Using the optimized simulation analysis platform, different nanofluids are selected to enhance the heat transfer of the heat transfer fluid (HTF). The effects of nanoparticle volume fraction, nanoparticle type, HTF temperature, and initial velocity on the liquid phase distribution, temperature distribution, melting characteristics, and kinetic energy consumption of the TES are analyzed. Finally, by optimizing the kinetic energy, TES heat storage capacity, and melting time using a three-objective approach, the objective function and optimal value are obtained, providing a reference for multi-objective optimization of TES using nanofluids as the working fluid.

Description

Technical Field

[0001] This invention relates to the field of phase change heat storage technology, and in particular to a simulation method for a phase change heat storage system using nanofluid-enhanced simulated lung groove vascular fins. Background Technology

[0002] With the intensification of climate change and the proposal of "dual carbon" targets, the development and utilization of clean energy has become an urgent task. Solar energy, as an inexhaustible and clean energy source, has received increasing attention. However, the intermittent nature of solar energy leads to insufficient stability, becoming one of the key factors limiting its large-scale application. Therefore, how to effectively store solar energy to ensure a continuous and stable energy supply has become a research hotspot in this field.

[0003] Phase change energy storage technology utilizes the latent heat absorbed and released by phase change materials (PCMs) during phase change processes to store and utilize energy, providing a new approach to solving the intermittent nature of solar energy. PCMs can absorb or release large amounts of heat during melting or solidification with minimal temperature change, thus enabling efficient energy storage and release. Phase change energy storage technology shows great application potential in various fields, such as solar energy, building energy conservation, industrial waste heat recovery, and battery thermal management systems. Among these, the shell-and-tube latent heat system is currently one of the research hotspots in phase change energy storage technology. This system typically consists of two layers of pipes, with the middle layer filled with PCM and the outer layer used for heat transfer. By controlling the flow of fluid within the pipes, heating and cooling of the PCM can be achieved, thereby realizing energy storage and release.

[0004] Figure 1 This demonstration showcases the application of a shell-and-tube phase change thermal energy storage (TES) system in a seawater desalination system. This system utilizes daytime solar energy to store heat in a phase change material (PCM) and releases it when needed, achieving efficient use of clean energy. The shell-and-tube system employs fluid heat exchange within the inner tube, with the PCM storing heat between the inner and outer tubes, forming a highly efficient heat storage and release mechanism. The accumulator consists of multiple vertical latent heat units.

[0005] In the field of tube-type phase change thermal storage (TES), many researchers have drawn inspiration from the excellent heat transfer properties of biological structures in nature, applying them to the fin design of TES. Biomimetic structures offer significant advantages in enhancing heat transfer and can effectively improve thermal energy storage efficiency. Furthermore, existing nanoparticles are widely used to enhance the thermal storage performance of PCMs (Polymerized Chlorinated Flow Meters), but there is currently no systematic analysis of the combination of nanoparticles and high-temperature ductile heat transfer (HTF). Most studies focus on combining nanoparticles with PCMs. In addition, few researchers have conducted multi-objective optimization designs for the kinetic energy of nanofluids in relation to the heat storage capacity and storage time of TES. In summary, there is currently no systematic analysis of the interaction between the kinetic energy loss of nanofluids and the increase in thermal conductivity caused by excessively high nanoparticle volume fraction. Moreover, the use of nanofluids in heat exchange involves a complex competitive game between initial velocity, temperature, and nanoparticle volume fraction, affecting both the initial kinetic energy and heat storage capacity of the TES flow. Therefore, existing technologies lack a simulation method for using nanofluids to enhance the pulmonary duct fin-based phase change thermal storage system, providing an accurate basis for multi-objective optimization of TES rotation. Summary of the Invention

[0006] The purpose of this invention is to provide a simulation method for a phase change heat storage system using nanofluid-enhanced pulmonary groove vascular fins. This addresses the current lack of systematic research analyzing the interaction between the kinetic energy loss of nanofluids and the increase in thermal conductivity caused by excessively high nanoparticle volume fraction. Furthermore, the use of nanofluids in heat exchange involves a complex competitive relationship between initial velocity, temperature, and nanoparticle volume fraction, which affects both the initial kinetic energy and heat storage capacity of the TES flow. Therefore, the existing technology lacks a simulation method for a phase change heat storage system based on nanofluids and enhanced with nanofluid-enhanced pulmonary groove vascular fins, thus failing to provide an accurate basis for multi-objective optimization of TES rotation.

[0007] To achieve the above objectives, this invention provides a simulation method for a phase change heat storage system using nanofluid-enhanced simulated lung groove vascular fins, comprising the following steps:

[0008] S1: Establish a physical model of the cross-section of the simulated pulmonary groove vascular fin phase change heat storage and enhanced heat transfer system, and perform three-dimensional simulation on the physical model to obtain the three-dimensional model of the simulated pulmonary groove vascular fin phase change heat storage and enhanced heat transfer system.

[0009] S2: A three-dimensional simulation analysis of the cross-section of the simulated pulmonary groove vascular fin phase change heat storage and enhanced heat transfer system is performed to simulate the melting and solidification process of PCM and analyze the heat transfer performance and energy storage efficiency of the system.

[0010] S3: Obtain experimental results by setting up experimental equipment or via the Internet;

[0011] S4: Compare the simulation results with the experimental results, adjust the parameters of the simulation model, improve the accuracy of the simulation results, and obtain the optimized simulation analysis platform for the simulated lung groove vascular fin phase change heat storage and enhanced heat transfer system.

[0012] S5: Using the optimized simulation analysis platform of the simulated lung groove vascular fin phase change heat storage enhanced heat transfer system, the effects of nanoparticle volume fraction, nanoparticle type, heat transfer fluid temperature and initial velocity on TES liquid phase distribution, temperature distribution, melting characteristics and kinetic energy consumption are analyzed, providing guidance for the optimized design of latent heat system.

[0013] In step S1, the pulmonary alveolar vascular fin phase change heat storage and enhanced heat transfer system consists of multiple sleeve units. Each unit includes an inner tube and an outer tube. The inner tube diameter Ф1 is 8 mm and the outer tube diameter Ф2 is 35 mm. The fin structure of the solar phase change heat storage system based on pulmonary alveolar vascular fins imitates the structure of pulmonary alveolar artery vessels. The fins adopt a fractal structure design. The length of the left branch adopts a 5-level fractal and the right branch adopts a 4-level fractal. The length of the left branch adopts the Fibonacci sequence decreasing from 5 mm, 3 mm, 2 mm and 1 mm. The branch width is L and the bifurcation angles are θ and α.

[0014] In step S1, before establishing the physical model, the enthalpy porosity method is used to simulate the melting process of PCM in TES, and the governing equations are as follows:

[0015] Energy equation:

[0016]

[0017] In the formula, ρ is the density of PCM, and H is the enthalpy of PCM material. Here, k is the thermal conductivity, and k is the vector differential operator.

[0018] Continuity equation:

[0019]

[0020] In the formula, It is a velocity vector;

[0021] Momentum equation:

[0022]

[0023] In the formula, t is time; ρ is density; p is pressure; μ is dynamic viscosity; ξ is the coefficient of thermal expansion; T ref For reference temperature, source term The damping term of Darcy's law can be expressed as:

[0024]

[0025] The liquid phase rate at different stages is expressed as follows:

[0026]

[0027] Where is T solid Solid temperature, T liquid It is the liquid phase temperature of the PCM;

[0028] Total enthalpy consists of sensible enthalpy and latent enthalpy:

[0029]

[0030] ΔH=λL

[0031] H=λL+h

[0032] Where ΔH is the latent enthalpy and h is the sensible enthalpy;

[0033] In step S1, the physical model established involves the physical properties of the nanofluid. These properties are calculated using classical formulas for nanoparticle mixtures, and the equations are shown below:

[0034] The density and specific heat of nanofluids are shown in the following formulas:

[0035] ρ nf =(1-φ ns )ρ f +φ ns ρ ns

[0036] (ρc p ) nf =(1-φ ns )(ρc p ) f +φ ns (ρc p ) ns

[0037] The effective dynamic viscosity of nanofluids is shown by the Brinkman equation:

[0038]

[0039] The thermal conductivity of nanofluids is shown by the Brinkman equation:

[0040]

[0041] Where B is the Boltzmann constant (B = 1.3807 × 10⁻²³ J / K), and γ represents a variable indicating the volume fraction of nanoparticles, expressed as:

[0042] γ=8.4407(100φns ) -1.07304 (0.01<φ ns <0.1)

[0043] The empirical function f(T,φ) is shown below:

[0044]

[0045] The heat storage rate of a phase change material melting during endothermic reaction is expressed as:

[0046]

[0047] The heat storage density of a phase change material when it melts during heat absorption is expressed as:

[0048]

[0049] In step S1, during the two-dimensional simulation of the physical model, the temperature of the heat transfer fluid is simplified to the pipe wall temperature. At the initialization time t=0, the PCM temperature is 293K, and it is in a solidified state. When t>0, the HTF temperature is set to 363K to melt the PCM.

[0050]

[0051] The fins and PCM are coupled by boundary conditions, satisfying Fourier's law of thermal conductivity, as shown below:

[0052]

[0053] In step S1, the specific content of performing two-dimensional simulation of the physical model includes: using MESH software to mesh the latent heat system and using the computational fluid dynamics software ANSYS Fluent to perform numerical calculations.

[0054] In step S1, when meshing the latent heat system using MESH software, an unstructured mesh consisting of a mixture of triangles and quadrilaterals is used. During the numerical calculation using the computational fluid dynamics software ANSYS Fluent, the Solidification / Melting model in Fluent is selected for solution. The PISO algorithm is used to handle the coupling problem between the pressure field and the velocity field, and the PRESTO! algorithm is used for pressure correction.

[0055] In step S3, the specific steps for obtaining experimental results by setting up the experimental setup are as follows:

[0056] An experimental setup was constructed to enhance heat transfer by phase change heat storage using a finned pulmonary groove vessel. Appropriate PCM and nanoparticles were selected, nanofluids were prepared and injected into the system, and the parameters of the heat source and cooling system were adjusted to simulate different operating conditions. The melting and solidification processes of the PCM were recorded, and experimental results were obtained.

[0057] This invention discloses a simulation method for a latent heat storage system using nanofluid-enhanced pulmonary groove vessel finned phase change heat storage. First, a physical model of the cross-section of the pulmonary groove vessel finned phase change heat storage system is established, and a two-dimensional simulation is performed on the physical model to obtain a two-dimensional model of the cross-section of the pulmonary groove vessel finned phase change heat storage system. The two-dimensional model is then simulated to analyze the melting and solidification process of the PCM (Polymerized Polymer), analyze the system's heat transfer performance and energy storage efficiency, and obtain experimental results. The simulation results are compared with the experimental results, and the parameters of the simulation model are adjusted to improve the accuracy of the simulation results, resulting in an optimized simulation analysis platform. This optimized platform can analyze the effects of nanoparticle volume fraction, rotational speed, fin material, and heat transfer fluid (HTF) temperature on the liquid phase distribution, temperature distribution, melting characteristics, and kinetic energy consumption of the latent heat system, providing a reference for multi-objective optimization of the latent heat system's rotation. Attached Figure Description

[0058] To more clearly illustrate the technical solutions in the embodiments of the present invention or the prior art, the drawings used in the description of the embodiments or the prior art will be briefly introduced below. Obviously, the drawings described below are only some embodiments of the present invention. For those skilled in the art, other drawings can be obtained based on these drawings without creative effort.

[0059] Figure 1 This is a schematic diagram illustrating the application scenario of the existing shell-and-tube phase change thermal storage system (TES) provided by this invention in building envelope heating.

[0060] Figure 2 This is a flowchart of the simulation method of the present invention using nanofluid-enhanced simulated lung groove vascular fin phase change heat storage system.

[0061] Figure 3 This is a schematic diagram of the specific structure of the shell-and-tube phase change thermal storage system (TES) provided by the present invention.

[0062] Figure 4 These are verification diagrams for four different grid numbers provided by this invention.

[0063] Figure 5 This is a schematic diagram of the fitting results of the experiment and simulation of PCM melting and solidification provided by the present invention.

[0064] Figure 6These are liquid phase cloud maps and temperature cloud map analysis diagrams of nanoparticle mixtures with different volume fractions provided by this invention.

[0065] Figure 7 This is a data analysis diagram of the mixture of nanoparticles with different volume fractions provided by the present invention.

[0066] Figure 8 This is a temperature cloud map analysis diagram of TES with different nanoparticle volume fractions provided by the present invention.

[0067] Figure 9 This is an analysis chart of the melting characteristics of TES with different nanoparticle volume fractions provided by the present invention.

[0068] Figure 10 This is an analysis diagram of the melting characteristics of TES under different fluid velocities provided by the present invention.

[0069] Figure 11 This is an analysis chart of the melting characteristics of TES at different HTF initial temperatures provided by the present invention.

[0070] Figure 12 This is an analysis diagram of the influence of various response surfaces on the melting time of TES provided by the present invention.

[0071] Figure 13 This is an analysis diagram of the influence of various response surfaces on the heat storage capacity of TES provided by the present invention.

[0072] Figure 14 This is an analysis diagram of the impact of various response surfaces on the kinetic energy loss of the TES provided by the present invention.

[0073] Figure 15 This is the Pareto front curve obtained by multi-objective optimization provided by the present invention. Detailed Implementation

[0074] Embodiments of the present invention are described in detail below, examples of which are illustrated in the accompanying drawings, wherein the same or similar reference numerals denote the same or similar elements or elements having the same or similar functions throughout. The embodiments described below with reference to the accompanying drawings are exemplary and intended to explain the present invention, and should not be construed as limiting the present invention.

[0075] Please see Figures 1 to 15 This invention provides a simulation method for a phase change heat storage system using nanofluid-enhanced simulated lung groove vascular fins, comprising the following steps:

[0076] S1: Establish a physical model of the cross-section of the simulated pulmonary groove vascular fin phase change heat storage and enhanced heat transfer system, and perform three-dimensional simulation on the physical model to obtain the three-dimensional model of the simulated pulmonary groove vascular fin phase change heat storage and enhanced heat transfer system.

[0077] S2: A three-dimensional simulation analysis of the cross-section of the simulated pulmonary groove vascular fin phase change heat storage and enhanced heat transfer system is performed to simulate the melting and solidification process of PCM and analyze the heat transfer performance and energy storage efficiency of the system.

[0078] S3: Obtain experimental results by setting up experimental equipment or via the Internet;

[0079] S4: Compare the simulation results with the experimental results, adjust the parameters of the simulation model, improve the accuracy of the simulation results, and obtain the optimized simulation analysis platform for the simulated lung groove vascular fin phase change heat storage and enhanced heat transfer system.

[0080] S5: Using the optimized simulation analysis platform of the simulated lung groove vascular fin phase change heat storage enhanced heat transfer system, the effects of nanoparticle volume fraction, nanoparticle type, heat transfer fluid (HTF) temperature and initial velocity on TES liquid phase distribution, temperature distribution, melting characteristics and kinetic energy consumption are analyzed, providing guidance for the optimized design of latent heat system.

[0081] In this embodiment, a physical model of the cross-section of the simulated pulmonary duct fin phase change heat storage and enhanced heat transfer system is first established, and a three-dimensional simulation is performed on the physical model to obtain a three-dimensional model of the simulated pulmonary duct fin phase change heat storage and enhanced heat transfer system. The three-dimensional model is then simulated and analyzed to simulate the melting and solidification process of PCM, analyze the heat transfer performance and energy storage efficiency of the system, and obtain experimental results. The simulation results are compared with the experimental results, and the parameters of the simulation model are adjusted to improve the accuracy of the simulation results, resulting in an optimized simulation analysis platform. Through the optimized simulation analysis platform, the effects of nanoparticle volume fraction, rotation speed, fin material, and heat transfer fluid (HTF) temperature on the liquid phase distribution, temperature distribution, melting characteristics, and kinetic energy consumption of the latent heat system can be analyzed, providing a certain reference for the multi-objective optimization of the latent heat system rotation.

[0082] in, Figure 3The specific structure of the shell-and-tube phase change thermal energy storage system (TES) is shown. In step S1, the solar phase change thermal energy storage system based on pulmonary artery-shaped fins consists of multiple shell-and-tube units. Each unit includes an inner tube and an outer tube. The inner tube diameter Ф1 is 8 mm, and the outer tube diameter Ф2 is 35 mm. The fin structure of the solar phase change thermal energy storage system based on pulmonary artery-shaped fins mimics the structure of the pulmonary artery. The fins adopt a fractal structure design, with the left branch length using a 5-level fractal and the right branch using a 4-level fractal. The length of the left branch uses a Fibonacci sequence. The Nachice sequence decreases from 5mm, 3mm, 2mm, to 1mm, with a branch width of L and bifurcation angles of θ and α. According to existing research, the bifurcation structure exhibits optimal energy loss characteristics and heat dissipation when θ is 31.6° and α is 43.4°. Therefore, this optimal angle is used for all bifurcation angles in this technical solution. The phase change materials involved in the solar phase change thermal storage system based on pulmonary groove vascular fins in this technical solution are paraffin wax and nanoparticles. The physical properties of PCM and nanoparticles are shown in Table 1 below.

[0083] Table 1. Physical properties of PCM and nanoparticles

[0084] Physical properties Nanoparticles PCM Main ingredients <![CDATA[Al2O3]]> RT55 <![CDATA[Density / kg / m 3 > 3970 770 Specific heat / J / (kg·K) 680 2000 Thermal conductivity / W / (m·K) 70.2 Thermal conductivity (K⁻¹) 16.3 <![CDATA[4.5×10 -4 ]]> Latent heat / kJ / (kg) —— 170 Dynamic viscosity / kg / (m·s) —— <![CDATA[3.408×10 -4 ]]> Solid phase temperature / K —— 324 Liquid phase temperature / K —— 330

[0085] The structural parameters of the fins in the pulmonary alveolar artery model are shown in Table 2 below:

[0086] Table 2. Structural parameters of the fins in the pulmonary artery model

[0087] Classification Length H / mm Width L / mm bifurcation angle θ bifurcation angle α 1 2 1 31.6° 43.4° 2 5 0.8 31.6° 43.4° 3 3 0.6 31.6° 43.4° 4 2 0.4 31.6° 43.4° 5 1 0.4 31.6° 43.4°

[0088] Furthermore, since the phase transition process of PCM is relatively complex, it exhibits a porous structure during melting. Therefore, in step S1, before establishing the physical model, the enthalpy porosity method is used to calculate the phase transition process of PCM in the TES unit, and the following assumptions are made: (1) Liquid PCM is laminar and incompressible; (2) The thermal properties of PCM remain constant within the operating temperature range, and the density adopts the Boussinesq assumption, which can be simplified to constant during cooling; (3) Heat loss between TES and the external environment is ignored, and it is assumed that the thermal conductivity of the coupling wall is the same as that of copper, and the thickness of the coupling wall is temporarily not considered; (4) Viscous dissipation coefficient is ignored. Based on the above assumptions, the enthalpy porosity method is used to simulate the melting process of PCM in TES. The governing equations are as follows:

[0089] Energy equation:

[0090]

[0091] In the formula, ρ is the density of PCM, and H is the enthalpy of PCM material. Here, k is the thermal conductivity, and k is the vector differential operator.

[0092] Continuity equation:

[0093]

[0094] In the formula, It is a velocity vector;

[0095] Momentum equation:

[0096]

[0097] In the formula, t is time; ρ is density; p is pressure; μ is dynamic viscosity; ξ is the coefficient of thermal expansion; T ref For reference temperature, source term The damping term of Darcy's law can be expressed as:

[0098]

[0099] The liquid phase rate at different stages is expressed as follows:

[0100]

[0101] Where is T solid Solid temperature, T liquid It is the liquid phase temperature of the PCM;

[0102] Total enthalpy consists of sensible enthalpy and latent enthalpy:

[0103]

[0104] ΔH=λL

[0105] H=λL+h

[0106] Where ΔH is the latent enthalpy and h is the sensible enthalpy.

[0107] Rotational kinetic energy is calculated using the classical kinetic energy formula:

[0108] The moment of inertia of the ring is:

[0109] I = m·(r1) 2 +r2 2 ) / 2

[0110] The formula for calculating the kinetic energy of a ring rotating around its center is:

[0111] KE=(1 / 2)·I·ω 2

[0112] Where m is the mass of the annular sleeve, r1 is the inner radius, and r2 is the outer radius.

[0113] In step S1, the established physical model includes the physical properties of the nanofluid. These properties are calculated using classical formulas for nanoparticle mixtures, and the resulting equations are shown below:

[0114] The density and specific heat of nanofluids are shown in the following formulas:

[0115] ρ nf =(1-φ ns )ρ f +φ ns ρ ns

[0116] (ρc p ) nf =(1-φ ns )(ρc p ) f +φ ns (ρc p ) ns

[0117] The effective dynamic viscosity of nanofluids is shown by the Brinkman equation:

[0118]

[0119] The thermal conductivity of nanofluids is shown by the Brinkman equation:

[0120]

[0121] Where B is the Boltzmann constant (B = 1.3807 × 10⁻²³ J / K), and γ represents a variable indicating the volume fraction of nanoparticles, expressed as:

[0122] γ=8.4407(100φ ns ) -1.07304 (0.01<φ ns <0.1)

[0123] The empirical function f(T,φ) is shown below:

[0124]

[0125] The heat storage rate of a phase change material melting during endothermic reaction is expressed as:

[0126]

[0127] The heat storage density of a phase change material when it melts during heat absorption is expressed as:

[0128]

[0129] Furthermore, in step S1, the specific content of the two-dimensional simulation of the physical model includes: meshing the latent heat system using MESH software, performing numerical calculations using the computational fluid dynamics software ANSYS Fluent, and using an unstructured mesh combining triangles and quadrilaterals when meshing the latent heat system using MESH software. During the numerical calculations using ANSYS Fluent, the Solidification / Melting model in Fluent software is selected for solution, and the PISO algorithm is used to handle the coupling problem between the pressure and velocity fields. The PRESTO! algorithm is used for pressure correction, where the relaxation factors for momentum, pressure, energy, and liquid phase velocity are set to 0.7, 0.2, 1.0, and 0.9, respectively. The relative residuals of the energy and momentum equations are set to be less than 10. -6 The relative residual of the continuity equation is set to be less than 10. -4 .

[0130] Furthermore, when using MESH software to mesh a latent heat system, such as... Figure 4 As shown,

[0131] Appropriate mesh refinement was applied around the interface between the fins and the PCM, and the HTF fluid domain was divided using a boundary layer mesh. Mesh independence verification was performed. Figure 4 (a) shows the simulation results using four different grid numbers: 1,512,283, 2,2954, 3,217,101, and 5,256,142. The results show that the variation in the average PCM temperature gradually decreases as the grid number increases. When the grid number increases from 3217,101 to 5,256,142, the average PCM temperature only increases from 327.3314 to 327.3426 after 300 seconds, a relative change of only 0.0034%. Figure 4 The PCM average temperature in (a) shows that the curves for grid numbers of 327,101 and 5,256,142 basically overlap, with very little difference. This indicates that further increasing the grid number has a negligible impact on the heat transfer analysis results. Therefore, this technical solution selects a grid number of 3,217,101 as the final computational grid number. Figure 4 (b) Presents simulation results using four different time steps: 0.005s, 0.01s, 0.05s, and 0.1s. The results show that the relative error of the PCM average temperature over 50 seconds is almost negligible between time steps of 0.01s and 0.05s. Zooming in reveals that the maximum temperature difference between 0.05s and 0.01s is only about 0.01K. To conserve computational resources, this paper selects a time step of 0.05s for subsequent calculations.

[0132] Furthermore, in order to verify the accuracy of numerical simulation and improve work efficiency, this technical solution directly uses experimental data from existing technologies to compare and analyze numerical simulation results (the experimental data from Soltanl et al. are used here). The experimental data is used to verify that the algorithm model and relaxation factor parameters of this technical solution are reasonable. Figure 5 The comparison and analysis between numerical simulation results and experimental data are presented. The trends of the PCM liquid phase fraction and PCM average temperature curves show a high degree of agreement between the numerical simulation results and experimental data. The maximum deviation in PCM liquid phase fraction is only 2.92%, and the maximum deviation in PCM average temperature is only 0.91%. This indicates that the numerical model of this technical solution has high accuracy and can provide reliable theoretical support for subsequent research.

[0133] Furthermore, the cross-verification between simulation results and experimental results shows that:

[0134] 1. Analysis of research on modification with different nanoparticles;

[0135] To enhance heat transfer in PCM (Polymerized Carbon Methane), many researchers have mixed nanoparticles with PCM; however, few have studied the mixing of nanoparticles with HTF (Heat Transfer Fluid) to achieve the same effect. This section focuses on four nanoparticles—Al2O3, CuO, TiO2, and Cu—at a volume fraction of 5%. These nanoparticles possess advantages such as high thermal conductivity, non-toxicity, and non-corrosiveness, making them widely used in academic and industrial fields. A latent heat transfer system with lung-like vascular fins, using pure water as the heat transfer medium, was selected as a control group. Figure 6The image shows the liquid phase contour plot of TES from 100s to 550s. It is clear that the heat transfer effect of HTF containing nanoparticles is significantly higher than that of HTF using pure water as the working fluid, indicating that nanoparticles have a significant advantage in improving the thermal conductivity of HTF. Furthermore, a horizontal comparison of different nanoparticles reveals that Cu has the best heat transfer effect, which is directly proportional to the thermal conductivity of the nanoparticles. In terms of thermal conductivity, Cu > CuO > Al2O3 > TiO2. Therefore, the melting rate of PCM also follows this order. In addition, the contour plot shows that the upper half of the PCM melts faster than the lower half. This is due to two reasons: First, the HTF flows from top to bottom, so the temperature of the HTF in the upper region is higher than that in the lower region. According to Fourier's law of thermal conductivity, a smaller temperature difference leads to a smaller heat transfer. Second, natural convection occurs during the melting process of PCM, causing the heat flow to rise, resulting in faster melting in the upper half. Finally, we found that, in general, the cross-sectional melting of the PCM is achieved by the HTF transferring heat in all directions through the pulmonary groove vascular fins. These fins can effectively transfer heat to various dead zones, and there are not many branch fins occupying the volume of the PCM. Therefore, this fin shape is a good heat transfer shape, which is not only beneficial for heat dissipation from the human body, but also for heat storage in the TES.

[0136] in, Figure 7 (a) and Figure 7 (b) demonstrates the effect of different nanoparticles on the PCM melting process. The results show that adding 5% volume fraction Cu significantly improves the heat transfer performance of PCM, resulting in a significantly increased melting rate and average temperature. At 500 seconds, the average temperature of the 5% Cu group was approximately 12 K higher than that of the pure PCM group. This phenomenon is mainly attributed to the increased thermal conductivity of PCM due to the addition of nanoparticles. Furthermore, as the volume fraction of nanoparticles increases, the thermal conductivity of the mixed HTF also increases, thereby accelerating heat transfer and improving the heat transfer effect. Figure 7 (a) It can be observed that the average temperature of the PCM hardly changes between 50s and 300s, forming a straight line. This indicates that the PCM is storing latent heat during this period, exhibiting a typical phase change effect. Figure 7 (c) shows that Al2O3 and TiO2 are almost similar in terms of heat storage rate and heat storage density, which is also due to their similar thermal conductivity. This data further demonstrates that the heat transfer effect of TES is positively correlated with the thermal conductivity of nanoparticles. Compared with pure PCM, the addition of 5% volume fraction nanoparticles increased the heat storage density by 58.14 kJ / kg and the heat storage rate by 0.04 kJ / s, demonstrating a certain degree of heat transfer enhancement. However, it should be noted that the addition of nanoparticles increases the HTF mass, leading to an increase in the required kinetic energy, which will be addressed in subsequent optimization processes.

[0137] 2. The effect of different nanoparticle volume fractions on TES heat transfer;

[0138] The volume fraction of nanoparticles directly affects the thermal conductivity of the HTF, thus influencing the melting of the PCM. The initial operating conditions for this section are an HTF temperature of 263 K and a melting rate of 0.1 m / s. Figure 8 The figure shows the effect of different nanoparticle volume fractions on the temperature contour plot of the TES. It is clearly visible from the figure that a 5% volume fraction of nanoparticles mixed with the HTF exhibits the best heat transfer performance. At 550 s, most of the PCM has melted. From the side view, it can be seen that the volume of the solid PCM in the blue region decreases progressively with increasing volume fraction. The addition of nanoparticles increases the thermal conductivity and also increases the mass of the HTF, leading to a corresponding increase in the required kinetic energy. Furthermore, from... Figure 9 The data provides a more intuitive view of the rapid increase in both the average temperature and liquidus fraction of the PCM, which occurs at a volume fraction of 5%. Furthermore, it can be observed that the difference is not significant before 300 seconds, and after 300 seconds, the temperature does not change significantly. This is mainly because 300 seconds ago, the PCM was undergoing a phase transition process, during which the temperature itself changed very little, while the liquidus fraction changed considerably. This is because the liquidus fraction is more sensitive than temperature, especially during the PCM melting process. Figure 9 (c) It can be observed that, compared to 1% nanoparticles, 5% Cu nanoparticles result in a 10K increase in heat storage temperature, a 19.94% increase in heat storage capacity, an 11.74% decrease in melting time, a 19.84% increase in heat storage density, and a 20.14% increase in heat storage rate. The heat storage capacity, heat storage density, and heat storage rate are calculated over a 500-second period. This timeframe was chosen because the PCM in all cases melted by 500 seconds, making this a scientifically sound decision. In conclusion, increasing the volume fraction of nanoparticles significantly improves the heat storage performance of TES.

[0139] 3. The effect of different nanofluid velocities on TES heat transfer;

[0140] In phase change energy storage systems, the initial velocity of nanofluids has a significant impact on heat storage performance. Newton's law of cooling shows that a higher flow velocity results in a higher convective heat transfer coefficient and a more pronounced heat transfer effect. Figure 10 (a) and (b) show the heat transfer characteristics of the PCM average temperature and liquid phase fraction under different initial velocities. It can be seen that for every 0.05 m / s increase in initial velocity, both the PCM average temperature and liquid phase fraction increase, but the rate of increase decreases. This indicates that the flow rate should not be blindly increased; otherwise, sacrificing too much kinetic energy will not significantly improve the TES heat storage effect, resulting in extremely low cost-effectiveness. Therefore, further analysis will be conducted later in conjunction with kinetic energy. Figure 10 (c) It can be observed that with an initial velocity of 0.25 m / s compared to 0.05 m / s, the average temperature of the PCM increases by 17 K, the heat storage capacity increases by 28.34%, the melting time decreases by 7.73%, the heat storage density increases by 28.35%, and the heat storage rate increases by 28.26%. Interestingly, when the velocity exceeds 0.15 m / s, the curves for heat storage density and heat storage rate become nearly flat, indicating that velocities exceeding 0.15 m / s do not significantly improve heat transfer performance but consume excessive kinetic energy.

[0141] 4. The effect of HTF temperature on TES heat transfer;

[0142] The heat transfer temperature (HTF) significantly affects the heat storage performance of the thermally conductive solar energy system (TES). According to Fourier's law of thermal conductivity, the greater the temperature difference between the HTF and the thermally conductive polymer (PCM), the higher the heat flux density and the higher the heat transfer efficiency. However, the HTF temperature is influenced by solar radiation; excessively high HTF temperatures place higher demands on solar energy utilization efficiency and weather conditions, while excessively low HTF temperatures lead to slow heat storage in the PCM. Therefore, studying the impact of HTF temperature on TES heat transfer is crucial. This study selected an HTF temperature range of 353 K to 373 K. Figure 11 (a) and (b) show that the liquid phase fraction and average temperature of the PCM both increase significantly with increasing HTF temperature. This is because the higher temperature difference promotes heat transfer efficiency, allowing the fin temperature and wall temperature to be rapidly transferred to the PCM, thereby achieving a temperature rise of the phase change material in a shorter time. Figure 11 (c) shows that all heat transfer parameters of the TES reach their maximum values ​​when the HTF temperature is 373K. Compared with an HTF temperature of 353K, the heat storage capacity increases by 90.58%, the average PCM temperature increases by 12.76%, the complete melting time decreases by 56.43%, the heat storage density increases by 90.65%, and the heat storage rate increases by 90.56%. Therefore, the HTF temperature has the greatest impact on the performance of the TES. Thus, to achieve the best heat storage effect, higher requirements are placed on the solar collector, requiring the heat transfer fluid to be heated to 373K, which is the vapor-liquid phase transition point of water. This allows for maximum utilization of heat for seawater desalination and achieves more energy-efficient energy utilization.

[0143] 5. Multi-objective optimization of nanoflow in TES;

[0144] This technical solution employs Response Surface Methodology (RSM) to conduct multi-objective optimization analysis of the TES, aiming to determine the optimal combination of factors to optimize TES performance. RSM is a statistical method used to study the influence of multiple factors on one or more response variables. Specifically, this technical solution uses Box-Behnken design (BBD) for variable design, and the influencing factor parameters are shown in Table 4.

[0145] Table 4. Design parameters for BBD impact factor

[0146]

[0147] The response surface plot output by RSM is used for analysis, and the response surface regression equation and optimal solution are fitted.

[0148] in, Figure 12 (a), (b) and (c) represent the influence of each response on the TES melting time. Figure 12 (d) is a comparative analysis of the RSM predicted values ​​and the actual values ​​obtained from the numerical model. From Figure 12 (d) It can be seen that the RSM predicted value and the actual value fit perfectly, which shows that the response surface methodology design was successful. Figure 11 The red area represents a long melting time, while the blue area represents a short melting time. It's clear that the blue area is mainly concentrated in the range of initial temperature (368K to 373K), initial velocity (0.15m / s to 0.25m / s), and nanofluid volume fraction (4% to 5%). Furthermore, the study found that initial temperature has a significantly greater impact on TES melting time than initial velocity and nanoparticle volume fraction. This is mainly because, according to Fourier's law of thermal conductivity, temperature difference has a direct impact on heat transfer, while HTF velocity and nanoparticles only improve the heat transfer coefficient; therefore, HTF temperature has a greater influence. The specific target equation corresponding to the melting time is shown in the following formula:

[0149] Complete melting time=163368+8625.5A-868.07B-268.2C-26AB+16.25AC+0.7125BC+1825A 2 +1.1575B 2 -0.5C 2

[0150] Figure 13 (a), (b) and (c) represent the impact analysis of each response surface on the heat storage capacity of the TES. Figure 13 (d) is a comparative analysis of the RSM predicted values ​​and the actual values ​​obtained from the numerical model. From Figure 12 (d) It can be seen that the RSM predicted value and the actual value fit perfectly, which shows that the response surface methodology design was successful. Figure 13 The red area represents a large amount of heat storage, while the blue area represents a small amount. It is evident that the red area is mainly concentrated in the range of initial temperature 368K to 373K, initial velocity 0.15m / s to 0.25m / s, and nanofluid volume fraction between 4% and 5%. The fitted heat storage target equation is shown in the following formula:

[0151] Heat storage capacity=-419.60046+71.68017A+2.08374B+1.90938C-0.111669AB-1.09696AC-0.003356BC-61.73895A 2 -0.002525B 2 -0.064964C 2

[0152] Figure 14 (a), (b) and (c) represent the impact analysis of each response surface on the energy consumption of TES. Figure 13 (d) is a comparative analysis of the RSM predicted values ​​and the actual values ​​obtained from the numerical model. From Figure 14 (d) It can be seen that the RSM predicted value and the actual value fit perfectly, which shows that the response surface methodology design was successful. Figure 14 The red area represents areas with higher kinetic energy consumption, while the blue area represents areas with lower kinetic energy consumption. It's clear that the blue areas are mainly concentrated in the ranges with lower initial velocities and smaller nanoparticle volume fractions. This is primarily because the kinetic energy formula shows a positive correlation between HTF velocity and density, thus requiring both to be as low as possible. This creates a competition between heat storage and melting time. Furthermore, it can be observed that kinetic energy is almost unrelated to the initial HTF temperature; therefore, when considering kinetic energy consumption, the initial HTF temperature does not need to be considered excessively. The fitted objective equation for kinetic energy consumption is shown in the following formula:

[0153] Kinetic energy=0.485836-5.50375A-0.000908B-0.107062C+0.000000000000000276335AB+1.83625AC-0.00000000000000000543489BC+95.1375A 2 +0.00000125B 2 -0.000031C 2

[0154] Furthermore, this scheme employs a non-dominated sorting genetic algorithm (NSGA-II) for multi-objective optimization. The objective equation of RSM is used for optimization, yielding... Figure 15The Pareto front is shown. Based on three given decision variables: initial velocity (0.05-0.25 m / s), initial temperature (353-373 K), and volume fraction (1-5%), a Pareto curve was obtained with heat storage, melting time, and kinetic energy as objective functions. Since the objectives are to achieve maximum heat storage, minimum melting time, and minimum kinetic energy, there is a clear competition among the three objective functions. As melting time increases, the kinetic energy decreases. As heat storage increases, the kinetic energy increases. Therefore, point O was found on the Pareto curve, and the value of the objective function corresponding to this point was taken as the optimal solution for multi-objective optimization. At point O, the values ​​of heat storage, melting time, and kinetic energy are 10.33 kJ, 492.19 K, and 2.25 mJ, respectively, corresponding to initial velocity, initial temperature, and volume fraction values ​​of 0.15 m / s, 373.00 K, and 4.41%, respectively. Table 4 lists the basic parameter settings of the optimization algorithm. The fitted data were input into Fluent software for calculation and verification. It was found that the error in heat storage was only 0.031% and the melting time was 0.019%, indicating that the optimization results were reasonable.

[0155] The conclusions are as follows:

[0156] (1) By comparing the heat transfer of different nanoparticles, it was found that in terms of heat transfer effect, Cu>CuO>Al2O3>TiO2. In addition, compared with nanoparticles of different volume fractions, 5% Cu nanoparticles, compared with 1% nanoparticles, have a 10K higher heat storage temperature, a 19.94% higher heat storage capacity, an 11.74% lower melting time, a 19.84% higher heat storage density, and a 20.14% higher heat storage rate. A higher volume fraction is more conducive to heat transfer, but it also increases the HTF density, which is not conducive to flow.

[0157] (2) Studies under HTF conditions revealed that compared to an initial velocity of 0.05 m / s, an initial velocity of 0.25 m / s increased the average PCM temperature by 17 K, increased heat storage by 28.34%, decreased melting time by 7.73%, increased heat storage density by 28.35%, and increased heat storage rate by 28.26%. Interestingly, above 0.15 m / s, the heat storage density and rate curves became nearly flat, indicating that velocities above 0.15 m / s did not significantly improve heat transfer performance but consumed excessive kinetic energy. Furthermore, heating the HTF to 373 K was recommended; higher temperatures were more beneficial for heat transfer.

[0158] (3) The TES was optimized according to the response surface methodology to obtain the objective equations for heat storage, melting time and kinetic energy consumption. The study found that the initial temperature of HTF had a greater impact on TES than the initial velocity of HTF and the volume fraction of nanoparticles in terms of heat storage and melting time. However, the initial velocity of HTF had a greater impact on kinetic energy consumption than the volume fraction of nanoparticles and the initial velocity of HTF.

[0159] (4) Multi-objective optimization was performed using the Non-dominated sorting genetic algorithm II (NSGA-II), and the optimal parameter combination was determined: the melting time and kinetic energy were 10.33 kJ, 492.19 K and 2.25 mJ, respectively, and the corresponding initial velocity, initial temperature and volume fraction were 0.15 m / s, 373.00 K and 4.41%, respectively.

[0160] In summary, the verification results provide important theoretical reference for the simulation optimization design of a phase change heat storage system using nanofluid-enhanced simulated lung groove vascular fins.

[0161] The above description discloses only one preferred embodiment of the present invention, and should not be construed as limiting the scope of the present invention. Those skilled in the art will understand that all or part of the processes of the above embodiments can be implemented, and equivalent changes made in accordance with the claims of the present invention are still within the scope of the invention.

Claims

1. A simulation method for a nano-fluid enhanced lung-simulating channel blood vessel fin phase change heat storage system, characterized in that, Includes the following steps: S1: Establish a physical model of the cross-section of the simulated pulmonary groove vascular fin phase change heat storage and enhanced heat transfer system, and perform three-dimensional simulation on the physical model to obtain the three-dimensional model of the simulated pulmonary groove vascular fin phase change heat storage and enhanced heat transfer system. S2: Simulate and analyze the three-dimensional model of the cross-section of the simulated lung groove vascular fin phase change heat storage and enhanced heat transfer system, simulate the melting and solidification process of PCM, and analyze the heat transfer performance and energy storage efficiency of the system. S3: Obtain experimental results by setting up experimental equipment or via the Internet; S4: Compare the simulation results with the experimental results, adjust the parameters of the simulation model, improve the accuracy of the simulation results, and obtain the optimized simulation analysis platform for the simulated lung groove vascular fin phase change heat storage and enhanced heat transfer system. S5: Using the optimized simulation analysis platform of the simulated lung groove vascular fin phase change heat storage and enhanced heat transfer system, the effects of nanoparticle volume fraction, nanoparticle type, heat transfer fluid temperature and initial velocity on TES liquid phase distribution, temperature distribution, melting characteristics and kinetic energy consumption are analyzed to provide guidance for the optimized design of latent heat system. In step S1, the pulmonary alveolar vascular fin phase change heat storage and enhanced heat transfer system consists of multiple sleeve units. Each unit includes an inner tube and an outer tube. The inner tube diameter Ф1 is 8 mm and the outer tube diameter Ф2 is 35 mm. The fin structure of the solar phase change heat storage system based on pulmonary alveolar vascular fins imitates the structure of pulmonary alveolar artery vessels. The fins adopt a fractal structure design. The length of the left branch adopts a 5-level fractal and the right branch adopts a 4-level fractal. The length of the left branch adopts the Fibonacci sequence decreasing from 5 mm, 3 mm, 2 mm and 1 mm. The branch width is L and the bifurcation angles are θ and α, where θ is 31.6° and α is 43.4°. In step S1, before establishing the physical model, the enthalpy porosity method is used to calculate the PCM phase transition process in the TES unit.

2. The simulation method for a phase change heat storage system using nanofluid-enhanced simulated lung groove vascular fins as described in claim 1, characterized in that, In step S1, the enthalpy porosity method is used to calculate the PCM phase transition process in the TES unit. Simultaneously, the physical model established involves the physical properties of the nanofluid. These properties are calculated using classical formulas for nanoparticle mixtures, and their equations are shown below: The density and specific heat of nanofluids are shown in the following formulas: ； ； The effective dynamic viscosity of nanofluids is shown by the Brinkman equation: ； The thermal conductivity of nanofluids is shown by the Brinkman equation: ； where B is the Boltzmann constant (B = 1.3807 x 10"23J / K), A variable representing the volume fraction of nanoparticles is represented as: (0.01< <0.1)； empirical function As shown below: ； The heat storage rate of a phase change material melting during endothermic reaction is expressed as: ； The heat storage density of a phase change material when it melts during heat absorption is expressed as: ； In step S1, before establishing the physical model, the enthalpy porosity method is used to simulate the melting process of PCM in TES. The governing equations are as follows: Energy equation: ； In the formula, ρ is the density of PCM, H is the enthalpy of PCM material, ∇ is the vector differential operator, and k is the thermal conductivity. Continuity equation: ； In the formula, is the velocity vector; Momentum equation: ； where t is time; p is density; p is pressure; is the dynamic viscosity; is the thermal expansion coefficient; is the reference temperature, source term is the Darcy's law damping term ； The liquid phase rate at different stages is expressed as follows: ； wherein is solidus temperature, is the PCM liquidus temperature; Total enthalpy consists of sensible enthalpy and latent enthalpy: ； ； ；； wherein, is the latent enthalpy, h is the sensible enthalpy value; Meanwhile, the enthalpy porosity method was used to simulate the melting process of PCM in TES, and the objective equation corresponding to the specific melting time is shown in the following formula: ； The fitted target equation for heat storage is shown in the following formula: ； The fitted objective equation for kinetic energy consumption is shown in the following formula: 。 3. The simulation method for a phase change heat storage system using nanofluid-enhanced simulated lung groove vascular fins as described in claim 2, characterized in that, In step S1, during the three-dimensional simulation of the physical model, the temperature of the heat transfer fluid is simplified to the pipe wall temperature. At the initialization time t=0, the PCM temperature is 293K, and it is in a solidified state. When t>0, the HTF temperature is set to 363K to melt the PCM. ； The fins and PCM are coupled by boundary conditions, satisfying Fourier's law of thermal conductivity, as shown below: 。 4. The simulation method for a phase change heat storage system using nanofluid-enhanced simulated lung groove vascular fins as described in claim 3, characterized in that, In step S1, the specific content of the three-dimensional simulation of the physical model includes: using MESH software to mesh the latent heat system and using the computational fluid dynamics software ANSYS Fluent to perform numerical calculations.

5. The simulation method for a phase change heat storage system using nanofluid-enhanced simulated lung groove vascular fins as described in claim 4, characterized in that, In step S1, when meshing the latent heat system using MESH software, an unstructured mesh consisting of a mixture of triangles and quadrilaterals is used. During the numerical calculation using the computational fluid dynamics software ANSYS Fluent, the Solidification / Melting model in Fluent software is selected for solution, and the PISO algorithm is used to handle the coupling problem between the pressure field and the velocity field, while the PRESTO! algorithm is used for pressure correction.

6. The simulation method for a phase change heat storage system using nanofluid-enhanced simulated lung groove vascular fins as described in claim 5, characterized in that, In step S3, the specific steps for obtaining experimental results by setting up the experimental setup are as follows: An experimental setup was constructed to enhance heat transfer by phase change heat storage using a finned pulmonary groove vessel. Appropriate PCM and nanoparticles were selected, nanofluids were prepared and injected into the system, and the parameters of the heat source and cooling system were adjusted to simulate different operating conditions. The melting and solidification processes of the PCM were recorded, and experimental results were obtained.

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