Non-uniform TPMS dot matrix phase change heat sink design method based on topological optimization density mapping

Abstract

The invention discloses a design method of a non-uniform TPMS dot matrix phase change heat sink based on topological optimization density mapping. The non-uniform TPMS dot matrix phase change heat sink is formed by compounding a non-uniform hole framework based on a three-period minimal curved surface and a phase change material filled in the framework. The porosity of the three-period minimum curved surface units of the non-uniform hole framework in the horizontal direction and the vertical direction is obtained through a heat sink topological optimization density mapping method. The invention further discloses the heat sink topological optimization density mapping method. According to the method, a topological optimization and density mapping design method is adopted, so that the TPMS heat sink skeleton is re-optimized in a three-dimensional space, and the heat transfer performance of the phase change heat sink is remarkably improved.

Description

Technical Field

[0001] This invention relates to the field of phase change thermal energy storage technology, and in particular to a design method for a non-uniform TPMS lattice phase change heat sink based on topology optimization density mapping. Background Technology

[0002] With the rapid development of modern electronic components towards higher integration and power density, power semiconductor devices are increasingly widely used in modern electronic systems. This has led to the problem of extremely high localized heat flux density, which has become a key bottleneck restricting equipment performance and reliability. Traditional active cooling methods such as air cooling and liquid cooling are difficult to apply in space-constrained or passive operating conditions. Phase change thermal storage technology, with its high latent heat density and isothermal heat storage characteristics of phase change materials, provides an ideal passive thermal management solution for intermittent high thermal shock. However, the inherently low thermal conductivity of common organic phase change materials severely restricts rapid heat transport, resulting in sluggish thermal response within the phase change heat sink and an inability to promptly remove heat from the heat source. To solve this problem, introducing a high thermal conductivity metal framework into a PCMs matrix to form a composite material has become the mainstream technical approach. Among them, the three-period minimal surface (TPMS) structure, with its zero average curvature, high specific surface area, and fully interconnected porosity, is considered a highly promising enhanced heat transfer framework.

[0003] However, existing technologies still have shortcomings in dealing with the typical localized high heat flux conditions of electronic devices. Traditional TPMS skeleton designs are mostly limited to uniform porosity or simple linear gradient distribution. This homogenized design cannot match the thermal load characteristics of local heat sources at the bottom, resulting in excessive diffusion thermal resistance in the heat source area and thus heat accumulation. Summary of the Invention

[0004] Purpose of the invention: To overcome the shortcomings of the prior art, this invention provides a design method for a non-uniform TPMS lattice phase change heat sink based on topology optimization density mapping. This method takes a given design domain, constraints, and initial conditions as inputs, and performs topology optimization with minimum thermal compliance as the optimization objective. It iterates the calculation of the structure in the given design domain to obtain a reasonable material density field model. Then, using the density mapping method, it maps the relative density of the heat sink topology to the surface offset of the three-period minimum surface to design a TPMS mapped lattice phase change heat sink structure.

[0005] Technical solution: The present invention provides a design method for a non-uniform TPMS lattice phase change heat sink based on topology optimization density mapping. The non-uniform TPMS lattice phase change heat sink is composed of a non-uniform porous skeleton based on a three-period minimal surface and a phase change material filled in the skeleton. The porosity of the three-period minimal surface units in both the horizontal and vertical directions of the non-uniform pore skeleton is obtained by the heat sink topology optimization density mapping method. The heat sink topology optimization density mapping method includes the following steps: S1. Input the expressions for the heat sink topology optimization model and the three-period minimum surface TPMS, as well as the corresponding design domain boundary and initial parameters; S2. The density mapping mesh of the design domain of the heat sink topology optimization model is generated using the variable density method to obtain the heat sink topology optimization density field structure. S3. Extract the relative density distribution of material distribution within the unit region based on the topology optimization density field; S4. Establish a mapping relationship between the surface offset of the three-period minimum surface and the relative density in the unit region obtained in S3, and construct the three-period minimum surface in the design domain to obtain the TPMS mapping lattice phase change heat sink structure. S5. Perform surface mesh generation on the TPMS mapped lattice phase change heat sink structure and perform preprocessing operations on the model to obtain the model file of the TPMS mapped lattice phase change heat sink structure with re-meshed surface mesh. S6. Import the model file into the simulation software and perform finite element mesh generation; S7. Set boundary conditions in the simulation software and perform simulation calculations and analyses to complete the optimized design of the TPMS mapping lattice phase change heat sink structure.

[0006] Furthermore, the skeleton is made of stainless steel, copper alloy, aluminum alloy, ceramic or resin; the phase change material is hexadecylamine or inorganic salt phase change material.

[0007] Furthermore, the governing equation of the level set of the three-period minimal surface is F(X, Y, Z) = C, where X, Y, and Z are the lengths of the three directions in the Cartesian coordinate system, and C is the surface offset.

[0008] Furthermore, the three-period minimum surfaces include Primitive configuration, Gyroid configuration, and Diamond configuration.

[0009] Furthermore, the governing equations corresponding to the three-period minimum surface are: Primitive configuration: ; Gyroid configuration: ; Diamond configuration: ; Where k = 2π / L.

[0010] Furthermore, the heat sink topology optimization model in S1 is as follows: ; ; in, C t For thermal flexibility, Γ q For the boundary conditions of the second kind, where constant heat flux density acts, To satisfy the temperature field of the homogeneous equation, γ For artificial density fields, k Thermal conductivity, T For temperature field, h The convective heat transfer coefficient is... T ∞ For ambient temperature, |▽ γ | represents the gradient modulus of the pseudo-density field. Q As the heat source, Ω represents the optimized design domain. ρ e To optimize the pseudo-density of the material within the design area, Φ, representing the upper limit of the volume fraction of the heat sink structure, is set to 0.2.

[0011] Furthermore, the boundary range of the design domain in S1 is .

[0012] Furthermore, in S3, the design domain is discretized into multiple unit sub-regions, and the relative density of each unit sub-region is calculated separately.

[0013] Furthermore, S4 establishes a mapping relationship between the surface bias and the relative density within the unit region in the three-period minimal surface control equation, mapping the topology-optimized density field to the surface bias value of the three-period minimal surface unit, and constructing the TPMS mapped lattice phase change heat sink structure.

[0014] Furthermore, in S7, the model is imported into simulation software to conduct simulation experiments on the heat transfer characteristics of the phase change heat sink. By giving boundary conditions, initial values ​​and constraints, the complete melting time of the structural phase change material is obtained.

[0015] Beneficial Effects: Compared with existing technologies, the significant advantages of this invention are: by employing topology optimization and density mapping design methods, the TPMS heat sink framework is re-optimized in three-dimensional space, significantly improving the heat transfer performance of the phase change heat sink. Firstly, regarding reducing diffusion thermal resistance, this invention addresses the condition of localized high heat flux density at the bottom of electronic devices by constructing a dense, highly thermally conductive channel in the heat source contact area, effectively solving the transmission bottleneck at the heat inlet. The non-uniform TPMS lattice phase change heat sink structure of this invention can reduce diffusion thermal resistance and effectively increase the thermal conductivity; thanks to the rapid heat transport through the low thermal resistance channels, this structure accelerates the melting rate of the phase change material, greatly improving the response speed and heat storage efficiency of the phase change heat sink in the face of transient high thermal shock. Attached Figure Description

[0016] Figure 1 (a) is a schematic diagram of the overall structure of the non-uniform TPMS lattice phase change heat sink based on topology optimization density mapping in the embodiment; (b) is a schematic diagram of a 1 / 4 local structure of the non-uniform TPMS lattice phase change heat sink based on topology optimization density mapping. Figure 2 This is a diagram illustrating the iterative process of topology optimization in the fixed design domain in the embodiment. Figure 3 (a) is a schematic diagram of the TPMS uniform lattice heat sink structure in Comparative Example 1; (b) is a schematic diagram of the TPMS gradient lattice heat sink structure in Comparative Example 2. Figure 4 This is a comparison chart of the effective thermal conductivity and diffusion thermal resistance results of the present invention with those of Comparative Examples 1 and 2. Figure 5 This is a comparison chart of the melting rates of the phase change materials of the present invention with those of Comparative Examples 1 and 2. Figure 6 This is a comparison chart of the thermal storage power of the present invention with that of Comparative Examples 1 and 2. Detailed Implementation

[0017] The technical solution of the present invention will be further described below with reference to the accompanying drawings and embodiments.

[0018] like Figure 1 As shown, the non-uniform TPMS lattice phase change heat sink is composed of a non-uniform porous framework based on a three-period minimal surface and a phase change material filling the framework. The porosity of the three-period minimal surface units in both the horizontal and vertical directions of the non-uniform porous framework is obtained by the heat sink topology optimization density mapping method. The framework material is stainless steel, copper alloy, aluminum alloy, ceramic, or resin; the phase change material is hexadecylamine or an inorganic salt phase change material. The governing equation of the level set of the three-period minimal surface is F(X, Y, Z) = C, where X, Y, and Z are the lengths in the three directions in the Cartesian coordinate system, and C is the surface offset. The three-period minimal surface includes Primitive, Gyroid, or Diamond configurations.

[0019] The corresponding governing equations are: Primitive configuration: ; Gyroid configuration: ; Diamond configuration: ; Where k = 2π / L.

[0020] A three-dimensional topology optimization model considering convective heat transfer is constructed, as follows: ; ; in, C t For thermal flexibility, Γ q For the boundary conditions of the second kind, where constant heat flux density acts, To satisfy the temperature field of the homogeneous equation, γ For artificial density fields, k Thermal conductivity, T For temperature field, h The convective heat transfer coefficient is... T ∞ For ambient temperature, |▽ γ | represents the gradient modulus of the pseudo-density field. Q As the heat source, Ω represents the optimized design domain. ρ e To optimize the pseudo-density of the material within the design area, Φ, representing the upper limit of the volume fraction of the heat sink structure, is set to 0.2.

[0021] In the finite element analysis software, a design domain of cube shape is established, and the boundary range of the design domain is... A constant heat flux density was applied at the bottom center of the design domain, and the initial temperature field of the model was set to 293.15 K.

[0022] Topology optimization iterative calculations were performed based on the variable density method. The objective function of the optimization model was set to minimize thermal compliance, and the constraint condition was set to ensure that the volume fraction of solid material did not exceed 20%. During the iteration process, a Helmholtz filter and a hyperbolic tangent projection function were introduced to suppress the checkerboard effect and ensure boundary clarity. Figure 2 As shown, after about 80 iterative calculations, the objective function converges, and the optimal density field structure of the heat sink topology in the design domain is finally obtained.

[0023] A quantitative mapping relationship is established between the surface bias of a three-period minimum surface and the relative density of the elements. In this embodiment, the three-period minimum surface selected is of the Primitive configuration, and its geometric governing equations are: ; To achieve density mapping in the heat sink topology optimization structure, the relative density ρ of the unit cell under different C values ​​was calculated using a numerical integration method. r Value. By fitting the calculated data to a formula, the mapping relationship is obtained: .

[0024] Using density mapping technology, the topology-optimized design domain is discretized into multiple cell sub-regions, and the relative density of each cell sub-region is calculated, that is, the volume ratio of the topology in each cell region.

[0025] Substituting the relative density values ​​of each unit region obtained from the statistics into the mapping relationship, the surface offset C value of the three-period minimum surface corresponding to the spatial location is calculated, and the TPMS mapping lattice heat sink structure is generated using modeling software.

[0026] The TPMS-mapped lattice phase change heat sink structure was meshed, and the model preprocessing was performed to obtain the model file of the TPMS-mapped lattice phase change heat sink structure with re-meshed surface mesh. The model file was imported into the simulation software for finite element mesh generation, and the heat transfer characteristics of the phase change heat sink were simulated. By giving boundary conditions, initial values ​​and constraints, the complete melting time of the phase change material of the structure was obtained, and the optimized design of the TPMS-mapped lattice phase change heat sink structure was completed.

[0027] A non-uniform TPMS-mapped lattice heat sink prototype was prepared using 316L stainless steel powder as the framework material and integrally formed using selective laser melting technology. The porosity of the framework was 80%. Hexadecylamine was used as the phase change material. After the framework was printed, it was cleaned and heat-treated, and then the phase change material was filled into the heat sink framework using a vacuum impregnation process to form a TPMS lattice phase change heat sink. The thermophysical parameters of the materials used are shown in Table 1.

[0028] Table 1. Material thermophysical properties

[0029] like Figure 3 As shown, this embodiment introduces two comparative examples: Comparative Example 1 is a TPMS uniform lattice structure with uniform porosity distribution, and Comparative Example 2 is a gradient lattice structure with porosity linearly varying along the axial direction. The porosity of the framework of the three structures remains consistent. Thermal storage performance tests were conducted. A ceramic electric heating element with constant heat flux was used to heat the bottom of the TPMS lattice phase change heat sink, and thermocouples were used to record the temperature distribution within the phase change heat sink. Simultaneously, the heat transfer characteristics of the phase change heat sink were simulated.

[0030] Figure 4 This diagram compares the effective thermal conductivity and diffusion thermal resistance of the TPMS mapped lattice phase change heat sink in this embodiment with those of Comparative Examples 1 and 2. The comparison shows that the non-uniform TPMS mapped lattice structure described in this invention has significant advantages in heat transfer performance, possessing not only the highest effective thermal conductivity but also lower diffusion thermal resistance than Comparative Examples 1 and 2. Figure 5 This is a comparison chart of the melting rates of the TPMS mapped lattice phase change heat sink in Example 1 with the phase change materials in Comparative Examples 1 and 2. The comparison shows that the non-uniform TPMS mapped lattice structure described in this invention has a shorter complete melting time and higher heat storage efficiency compared to the uniform TPMS lattice structure. Figure 6This is a comparison chart showing the thermal storage power of the TPMS mapped lattice phase change heat sink in Example 1 with that of Comparative Examples 1 and 2, measured experimentally. Analysis of the results shows that the average thermal storage power of the non-uniform TPMS mapped lattice structure described in this invention is superior to that of the uniform TPMS lattice structure and the TPMS gradient lattice structure. This structure can rapidly transfer more heat from the heat source surface to the interior of the heat sink per unit time, thereby significantly improving the heat absorption efficiency in dealing with transient thermal shocks in high-power electronic devices. These excellent characteristics of high thermal conductivity, low diffusion thermal resistance, and fast thermal storage rate demonstrate the reliability of this invention and promote the application of phase change heat sinks in the thermal management of electronic devices.

Claims

1. A design method for a non-uniform TPMS lattice phase change heat sink based on topology optimization density mapping, characterized in that: The non-uniform TPMS lattice phase change heat sink is composed of a non-uniform porous skeleton based on a three-period minimal surface and a phase change material filled in the skeleton. The porosity of the three-period minimal surface units in both the horizontal and vertical directions of the non-uniform pore skeleton is obtained by the heat sink topology optimization density mapping method. The heat sink topology optimization density mapping method includes the following steps: S1. Input the expressions for the heat sink topology optimization model and the three-period minimum surface TPMS, as well as the corresponding design domain boundary and initial parameters; S2. The density mapping mesh of the design domain of the heat sink topology optimization model is generated using the variable density method to obtain the heat sink topology optimization density field structure. S3. Extract the relative density distribution of material distribution within the unit region based on the topology optimization density field; S4. Establish a mapping relationship between the surface offset of the three-period minimum surface and the relative density in the unit region obtained in S3, and construct the three-period minimum surface in the design domain to obtain the TPMS mapping lattice phase change heat sink structure. S5. Perform surface mesh generation on the TPMS mapped lattice phase change heat sink structure and perform preprocessing operations on the model to obtain the model file of the TPMS mapped lattice phase change heat sink structure with re-meshed surface mesh. S6. Import the model file into the simulation software and perform finite element mesh generation; S7. Set boundary conditions in the simulation software and perform simulation calculations and analyses to complete the optimized design of the TPMS mapping lattice phase change heat sink structure.

2. The design method for non-uniform TPMS lattice phase change heat sink based on topology optimization density mapping according to claim 1, characterized in that: The skeleton is made of stainless steel, copper alloy, aluminum alloy, ceramic or resin; the phase change material is hexadecylamine or inorganic salt phase change material.

3. The design method for non-uniform TPMS lattice phase change heat sink based on topology optimization density mapping according to claim 1, characterized in that: The governing equation for the level set of the three-period minimal surface is F(X, Y, Z) = C, where X, Y, and Z are the lengths of the three directions in the Cartesian coordinate system, and C is the surface offset.

4. The design method for non-uniform TPMS lattice phase change heat sink based on topology optimization density mapping according to claim 1, characterized in that: The three-period minimal surfaces include Primitive, Gyroid, and Diamond configurations.

5. The design method for non-uniform TPMS lattice phase change heat sink based on topology optimization density mapping according to claim 4, characterized in that, The governing equations corresponding to the three-period minimum surface are: Primitive configuration: ； Gyroid configuration: ； Diamond configuration: ； Where k = 2π / L.

6. The design method for non-uniform TPMS lattice phase change heat sink based on topology optimization density mapping according to claim 1, characterized in that, The heat sink topology optimization model in S1 is as follows: ； ； in, C t For thermal flexibility, Γ q For the boundary conditions of the second kind, where constant heat flux density acts, To satisfy the temperature field of the homogeneous equation, γ For artificial density fields, k Thermal conductivity, T For temperature field, h The convective heat transfer coefficient is... T ∞ For ambient temperature, |▽ γ | represents the gradient modulus of the pseudo-density field. Q As the heat source, Ω represents the optimized design domain. ρ e To optimize the pseudo-density of the material within the design area, Φ, representing the upper limit of the volume fraction of the heat sink structure, is set to 0.

2.

7. The design method for non-uniform TPMS lattice phase change heat sink based on topology optimization density mapping according to claim 6, characterized in that, The boundary range of the design domain in S1 is .

8. The design method for non-uniform TPMS lattice phase change heat sink based on topology optimization density mapping according to claim 1, characterized in that, In S3, the design domain is discretized into multiple cell sub-regions, and the relative density of each cell sub-region is calculated.

9. The design method for non-uniform TPMS lattice phase change heat sink based on topology optimization density mapping according to claim 1, characterized in that, S4 establishes the mapping relationship between the surface bias and the relative density within the unit region in the three-period minimal surface control equation, maps the topology-optimized density field to the surface bias value of the three-period minimal surface unit, and constructs the TPMS mapped lattice phase change heat sink structure.

10. The design method for non-uniform TPMS lattice phase change heat sink based on topology optimization density mapping according to claim 1, characterized in that, In S7, the model is imported into the simulation software to conduct a simulation experiment on the heat transfer characteristics of the phase change heat sink. By giving boundary conditions, initial values ​​and constraints, the complete melting time of the structural phase change material is obtained.

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