Composite heat sink design method based on multi-material topology optimization

Abstract

The application discloses a composite radiator design method based on multi-material topology optimization, which comprises the following steps: establishing the geometric size of a two-dimensional design domain of a radiator and the position of an inlet and an outlet of a flow channel; determining the boundary conditions of the radiator and the physical properties of the materials used; introducing material pseudo-density gamma as a design variable, and constructing an ordered interpolation model of the physical properties of different materials; establishing a multi-material topology optimization model with the maximum heat transfer and the minimum flow dissipation under the volume fraction constraint as the optimization target; based on the finite element analysis method, the design variable is updated through an optimization algorithm to obtain the optimized topology shape of the two-dimensional radiator; and a three-dimensional composite radiator geometric model is established according to the optimization result, and the performance of the three-dimensional composite radiator geometric model is analyzed and verified. The method can obtain an efficient heat dissipation path according to specific cooling requirements, and optimizes the distribution position of different heat-conducting materials in the radiator, so that the cooling performance is greatly improved, and a cost-effective thermal management scheme is provided.

Description

Technical Field

[0001] This invention belongs to the field of electronic equipment technology, specifically relating to a composite heat sink design method based on multi-material topology optimization. Background Technology

[0002] In recent years, the increasingly smaller transistor sizes and higher chip integration densities in electronic devices have driven rapid advancements in device performance, but this has also led to a significant increase in heat flux. Furthermore, the heat flux generated from localized hot spots within a device can rise to eight times the average heat flux, as illustrated in the literature: "Ansari D, Kim KY. Hotspot thermal management using a microchannel-pinfin hybrid heat sink[J]. International Journal of Thermal Sciences, 2018, 134: 27-39." Failure to dissipate heat in a timely manner can cause overheating and malfunctions, resulting in serious damage. Ensuring effective heat dissipation is a prerequisite for maintaining the performance and reliability of electronic devices. Therefore, proper thermal management is becoming increasingly important, and the development of new, efficient heat dissipation systems is urgently needed.

[0003] Liquid-cooled heat sinks remove heat generated by electronic components through forced convection heat exchange caused by liquid flowing through internal channels, ensuring that electronic devices operate at safe temperatures. Heat sinks are widely popular due to their high heat transfer efficiency, small installation space requirements, and high reliability. Heat sinks can be made from a variety of materials, including aluminum alloys, copper, and others. Copper has excellent thermal conductivity, making it an ideal heat dissipation material; however, it is relatively heavy and expensive. Aluminum heat sinks have lower thermal conductivity but offer a lighter solution. Furthermore, due to the significant difference in heat generated at the core of electronic devices compared to other background areas, traditional single-material cooling techniques cannot maintain uniform temperature conditions on the device surface. Designing the heat sink structure based on the core area may lead to increased pump power for the background areas. Therefore, composite cold plates made of copper and aluminum offer a cost-effective, high-performance, and lightweight thermal management solution that meets a wide range of application needs.

[0004] Traditional heat sink design often relies on empirical methods, which may lead to suboptimal thermal performance and uncertain design cycles, as illustrated in the literature: "Dbouk TA review about the engineering design of optimal heat transfer systems using topology optimization[J]. Applied Thermal Engineering, 2017, 112: 841-854." The structure of the flow channels is crucial to the heat transfer performance of the heat sink. Previous conjugate heat transfer topology optimization methods can find the most effective new cooling channel design structure for the heat sink. However, multi-material topology optimization methods often focus on static structural optimization problems, with relatively little research on the material distribution of the heat sink. Therefore, multi-material topology optimization is used to design composite heat sinks, optimizing the flow heat dissipation path and the positional distribution of the two materials within the heat sink, providing a more efficient cooling solution for electronic devices. Summary of the Invention

[0005] The purpose of this invention is to provide a composite heat sink design method based on multi-material topology optimization. This method can obtain an efficient heat dissipation path according to specific cooling requirements and optimize the distribution of different thermally conductive materials in the heat sink, thereby greatly improving cooling performance while providing a cost-effective thermal management solution.

[0006] The technical solution adopted in this invention is:

[0007] The composite radiator design method based on multi-material topology optimization includes: establishing the geometric dimensions of the two-dimensional design domain and the inlet and outlet positions of the flow channels; determining the boundary conditions of the radiator and the physical properties of the materials used; introducing the material pseudo-density γ as a design variable to construct an ordered interpolation model of the physical properties of different materials; establishing a multi-material topology optimization model with the optimization objectives of maximum heat transfer and minimum flow dissipation under volume fraction constraints; solving the conjugate heat transfer multiphysics field based on the finite element analysis method, updating the design variables through optimization algorithms, and obtaining the optimized topology shape of the two-dimensional radiator; establishing a three-dimensional composite radiator geometric model based on the optimization results, and analyzing and verifying its performance.

[0008] The invention is further characterized by:

[0009] The composite heat sink design method based on multi-material topology optimization is implemented according to the following steps:

[0010] Step 1: Determine the geometric dimensions of the topology optimization two-dimensional design domain and the inlet / outlet distribution of the fluid based on the configuration of the electronic equipment;

[0011] Step 2: Determine the fluid and thermal properties parameters of different solid materials, as well as the boundary conditions of the inlet, outlet, and wall of the flow channel;

[0012] Step 3: Construct an ordered interpolation function for the physical properties of multiple materials characterized by a single design variable, and establish an expression for the damping coefficient in the flow control equation that distinguishes between fluid and solid states.

[0013] Step 4: Based on actual engineering needs, and taking the linear combination of the maximum heat transfer of the radiator and the flow power dissipation as the optimization objective, establish a mathematical model for multi-material topology optimization.

[0014] Step 5: Based on the finite element analysis method, solve the conjugate heat transfer multiphysics field, update the design variables through optimization algorithm, and obtain the optimized topology of the two-dimensional heat sink.

[0015] Step 6: Based on the topological boundary of the two-dimensional optimization results obtained in Step 5, construct the geometric model of the three-dimensional composite heat sink, and then determine the entire flow channel configuration and the distribution of multiple materials in the entire heat sink.

[0016] It also includes the following two steps:

[0017] Step 7: Determine the thermal boundary conditions of the three-dimensional composite heat sink obtained in Step 6, and discretize the structure according to the solution requirements, and perform finite element method solution analysis.

[0018] Step 8: Analyze the temperature performance indicators of the heat source surface and the flow performance indicators of the channel to determine the effect of the optimized structure.

[0019] In step 1, the geometric dimensions of the determined two-dimensional design domain are length L and width W; the locations of the entrances and exits are distributed as follows: on the center line of the design domain, on the diagonal line of the design domain, or staggered at the four corners of the design domain, with a characteristic length of D for each.

[0020] Step 2 identifies two solid materials: copper and aluminum 6061, with densities ρ1 and ρ2, constant-pressure heat capacities c1 and c2, and thermal conductivity k1 and k2, respectively; the fluid cooling medium is water, with a density ρ3, constant-pressure heat capacity c3, and thermal conductivity k3; the defined boundary conditions include the inlet flow velocity U. in Inlet temperature T in Export pressure P out The adiabatic boundary conditions of the external wall and the heat source Q based on the distribution of the solid material.

[0021] The ordered interpolation function in step 3 is as follows:

[0022] The physical properties of multiple materials are characterized using the pseudo-density γ as a single design variable, where γ=0 represents the copper material, γ=0.5 represents aluminum 6061, and γ=1 represents the cooling working medium water; according to the ordering of material properties: ρ1>ρ2>ρ3, k1>k2>k3 and c1<c2<c3, and based on the ordered and penalized solid isotropic material method, a material ordered interpolation function related to γ is constructed, with the expression as follows:

[0023]

[0024] In Equation (1), E denotes the physical property parameter of the material, including density, constant-pressure heat capacity and thermal conductivity; when the subscript i is equal to 1, 2 and 3, it respectively represents copper, aluminum 6061 and water; p denotes the penalty parameter for the interpolation function.

[0025] The specific expression of the damping coefficient in Step 3 is as follows:

[0026] The damping coefficient α(γ) is a quantity related to γ, which distinguishes the fluid and solid states through the value of the damping coefficient. When the damping coefficient reaches the maximum value, it characterizes a solid material, and when the value of the damping coefficient is close to zero, it characterizes a fluid material, and its interpolation expression is as follows:

[0027]

[0028] In Equation (2),

[0029] In Equation (2) and Equation (3), α max is the maximum inverse permeability, Da is the Darcy number, e is the natural constant, s is the control parameter for adjusting the convexity of the interpolation curve, and b denotes the intermediate transition point that controls the interpolation curve from the maximum value to the minimum value.

[0030] Step 4 is specifically as follows:

[0031] Step 4.1: Taking the linear combination of maximum heat transfer and minimum flow power dissipation as the optimization objective J, and performing normalization processing on them respectively, the expression is as follows:

[0032]

[0033] In Equation (4),

[0034] In Equation (4) and Equation (5), J Q is the heat transfer quantity, J f is the flow dissipation power, the subscript 0 denotes the initial value of the optimization objective, T Q is the ideal temperature of the heat source, h is the heat generation coefficient, T is the temperature in the design domain, Ω is the design domain, μ is the hydrodynamic viscosity, and u is the scalar of the fluid flow velocity;

[0035] Step 4.2: Introduce the optimization objective into the mathematical model of topology optimization and establish corresponding constraints, including flow control equations, heat transfer control equations, average volume constraints determined by limiting material costs, and the constraint range of design variables, as expressed below:

[0036]

[0037] In equation (6), Here, u is the gradient operator, P is the velocity vector, and V is the pressure vector. total Indicates the total volume of the design domain. This indicates an average volume constraint.

[0038] Step 5 specifically involves:

[0039] The value of the objective function in step 4 is obtained by solving the finite element method. The sensitivity of the objective function in step 4 to the design variables is calculated by applying the adjoint method. Then, the optimization direction of the design variables that have a significant impact on the hydrothermal performance is found. The moving asymptote algorithm is used to update the design variables. This process is repeated until the iteration stopping condition is met.

[0040] The stopping condition for the moving asymptote algorithm is: given a maximum number of iterations of 500, and specifying the tolerance of the objective function as the convergence condition: |J k+1 -J k |≤10 -6 , where k represents the number of iterations. The calculation terminates when the optimization reaches the maximum number of iterations or meets the convergence condition, and the two-dimensional optimization result is obtained.

[0041] Step 6 specifically involves:

[0042] Extract the topological boundary of the two-dimensional optimized structure obtained in step 5, import it into the modeling software to establish a three-dimensional composite heat sink model. The normal section of the three-dimensional model is consistent with the two-dimensional optimization result. The determined internal dimensions of the model are length L, width W and height H, the external dimensions are length L1, width W1 and height H1, and the inlet and outlet feature length is D.

[0043] The beneficial effects of this invention are:

[0044] (1) Compared with uniform material heat sinks, the method of the present invention uses heat sinks made of copper and aluminum. By utilizing the properties of the materials themselves, the problem of uneven temperature of core hot spots in electronic devices can be effectively solved. It has the advantage of simultaneously taking into account both high thermal conductivity and low cost.

[0045] (2) Compared with traditional design methods, the method of this invention applies topology optimization to the design of composite radiator structures, which greatly eliminates the interference of human factors and can automatically find the flow heat dissipation path based on the optimization objectives in actual engineering, thereby increasing the design freedom of the flow channel structure. In addition, the method of this invention improves the convective heat transfer capacity and efficiency of the radiator by changing the flow mode of the cooling medium;

[0046] (3) The method of this invention is based on the ordered SIMP interpolation method. It uses a single design variable to characterize two solid materials and one fluid material, reducing the number of variables and the influence of unstable factors in the design, and realizing a conjugate heat transfer process of multi-material topology optimization. By optimizing the distribution and shape of the two solid materials in the radiator with a given target and heat source, the thermal conductivity of different materials can be better utilized, thereby further improving the temperature uniformity and heat transfer efficiency of the entire radiator, which has certain guiding significance for the development of new high-efficiency radiators. Attached Figure Description

[0047] Figure 1 This is a flowchart of the method of the present invention;

[0048] Figure 2 This is a schematic diagram of a two-dimensional model of multi-material topology optimization obtained in Embodiment 1 of the present invention;

[0049] Figure 3 This is a three-dimensional composite radiator model and dimension diagram with the inlet and outlet on the center line obtained in Embodiment 1 of the present invention;

[0050] Figure 4 This is the temperature distribution on the upper surface of the three-dimensional composite heat sink obtained in Embodiment 1 of the present invention;

[0051] Figure 5 The traditional design features a three-dimensional uniform heatsink surface temperature distribution.

[0052] Figure 6 This is a three-dimensional composite radiator cross-sectional flow channel velocity vector diagram obtained in Embodiment 1 of the present invention;

[0053] Figure 7 This is a comparison chart of the average temperature of the method in Embodiment 1 of the present invention and the traditional design method under different heat source heat flux densities;

[0054] Figure 8 This is a three-dimensional composite heat sink model and size diagram with the inlet and outlet on the diagonal obtained in Embodiment 2 of the present invention;

[0055] Figure 9 This is a three-dimensional composite heat sink model and size diagram with the inlet and outlet staggered at the four corners, obtained in Embodiment 3 of the present invention.

[0056] In the diagram, 1. Copper, 2. Aluminum 6061, 3. Cooling medium water. Detailed Description of the Embodiments

[0057] The present invention is described in detail below with reference to the accompanying drawings and specific embodiments.

[0058] As shown in Figure 1 the figure, the design method of the composite heat sink based on multi-material topology optimization of the present invention is specifically implemented according to the following steps:

[0059] Step 1: According to the configuration status of the electronic equipment, determine the geometric dimensions of the two-dimensional topology optimization design as length L and width W, and determine the position distribution of the inlets and outlets. The position distribution of the inlets and outlets determined by the present invention can be: on the center line of the design domain, on the diagonal of the design domain, or staggered at the four corners of the design domain, with a characteristic length of D in all cases;

[0060] Step 2: In order to analyze the physical phenomena in the actual system, determine the flow and thermal property parameters of the fluid and different solid materials, as well as the boundary conditions of the flow channel inlets, outlets and wall surfaces;

[0061] The determined multi-solid materials include copper and aluminum 6061, with densities of ρ1 and ρ2 respectively, constant-pressure heat capacities of c1 and c2 respectively, and thermal conductivities of k1 and k2 respectively; the determined fluid cooling working medium is water, with a density of ρ3, a constant-pressure heat capacity of c3, and a thermal conductivity of k3; the determined boundary conditions include the inlet flow velocity U

[0033] , the inlet temperature T in , the outlet pressure P out , the adiabatic boundary condition of the outer wall surface, and the heat generation source Q based on the distribution of the solid materials;

[0062] Step 3: In order to make the design variables represent different materials, construct an ordered interpolation function for the physical properties of multi-materials characterized by a single design variable, and establish the damping coefficient expression in the flow control equation for distinguishing the fluid and solid states;

[0063] The specific ordered interpolation function is as follows:

[0064] The pseudo-density γ is used as a single design variable to characterize the physical properties of multiple materials, where γ=0 represents the copper material; γ=0.5 represents aluminum 6061; γ=1 represents the cooling working medium water. According to the ordering of material properties: ρ1>ρ2>ρ3, k1>k2>k3 and c1<c2<c3, and based on the ordered penalized Solid Isotropic Material with Penalization (SIMP) method, a material interpolation function related to γ is constructed, and the expression is:

[0065]

[0066] In equation (1), E represents the physical property parameters of the material, including density, constant pressure heat capacity and thermal conductivity; the subscripts i equal to 1, 2 and 3 represent copper, aluminum 6061 and water respectively; p represents the penalty parameter of the interpolation function.

[0067] The specific expression for the damping coefficient is as follows:

[0068] The damping coefficient α(γ) is a quantity related to γ. The value of the damping coefficient distinguishes between fluid and solid states. When the damping coefficient reaches its maximum, it represents a solid material; when the value of the damping coefficient approaches zero, it represents a fluid material. Its interpolation expression is:

[0069]

[0070] In equation (2),

[0071] In equations (2) and (3), α max For maximum reverse osmosis, Da is the Darcy number, e is the natural constant, s is the control parameter for adjusting the convexity of the interpolation curve, and b represents the intermediate transition point of the interpolation curve from the maximum value to the minimum value.

[0072] Step 4: Based on actual engineering needs, and taking the linear combination of the radiator's maximum heat transfer and flow power dissipation as the optimization objective, establish a mathematical model for multi-material topology optimization. The specific steps are as follows:

[0073] Step 4.1: Taking the linear combination of maximum heat transfer and minimum flow power dissipation as the optimization objective J, in order to reduce the difference between the two objective orders of magnitude, they are normalized respectively, and the expression is:

[0074]

[0075] In equation (4),

[0076] In equations (4) and (5), J Q For heat transfer, J f T represents the flow dissipation power, with the subscript 0 indicating the initial value of the optimization objective. Q Where is the ideal temperature of the heat source, h is the coefficient of heating, T is the temperature within the design domain, Ω is the design domain, μ is the fluid dynamic viscosity, and u is the scalar of the fluid flow velocity.

[0077] Step 4.2: Introduce the optimization objective into the mathematical model of topology optimization and establish corresponding constraints, including flow control equations, heat transfer control equations, average volume constraints determined by limiting material costs, and the constraint range of design variables, as expressed below:

[0078]

[0079] In equation (6), Here, u is the gradient operator, P is the velocity vector, and V is the pressure vector. total Indicates the total volume of the design domain. Indicates average volume constraint;

[0080] Step 5: Based on the finite element analysis method, solve the conjugate heat transfer multiphysics field, update the design variables through optimization algorithms, and obtain the optimized topology of the two-dimensional heat sink. The specific steps are as follows:

[0081] The value of the objective function in step 4 is obtained by solving the finite element method. The sensitivity of the objective function in step 4 to the design variables is calculated by applying the adjoint method. Then, the optimization direction of the design variables that have a significant impact on the hydrothermal performance is found. The moving asymptote algorithm (MMA) is used to update the design variables. This process is repeated until the iteration stopping condition is met.

[0082] The stopping condition for the moving asymptote algorithm is: given a maximum number of iterations of 500, and specifying the tolerance of the objective function as the convergence condition: |J k+1 -J k |≤10 -6 , where k represents the number of iterations. The calculation terminates when the optimization reaches the maximum number of iterations or meets the convergence condition, yielding the two-dimensional optimization result.

[0083] Step 6: Extract the topological boundary of the two-dimensional optimized structure obtained in Step 5, import it into the modeling software CreoParametric, smooth the topological boundary, establish a three-dimensional composite heat sink model, and then determine the entire flow channel configuration and the distribution of copper and aluminum 6061 materials in the entire heat sink. The topological structure of the normal section of the three-dimensional model should be consistent with the two-dimensional optimization results. The determined internal dimensions of the model are length L, width W and height H, the external dimensions are length L1, width W1 and height H1, and the inlet and outlet feature length is D.

[0084] Step 7: Determine the thermal boundary conditions of the three-dimensional composite heat sink obtained in Step 6, and discretize the structure according to the solution requirements, and perform finite element method solution analysis. The specific steps are as follows:

[0085] Step 7.1: Determine the heat flow boundary conditions of the three-dimensional composite radiator, including: the location of the heat source and the heat flux density Q, and the inlet velocity U. in Inlet temperature T in Export pressure P out Insulating boundary with the external wall;

[0086] Step 7.2: Based on the geometric dimensions and physical field requirements of the radiator, the size and discretization form of the mesh are determined by the mesh independence test. The mesh generation unit adopts unstructured tetrahedral elements to adapt to the geometrically irregular computational domain, and a thin boundary layer mesh is generated on the wetted perimeter surface to accurately capture the fluid near the wall.

[0087] Step 7.3: Perform finite element analysis using the commercial software Comsol Multiphysics.

[0088] Step 8: Analyze the temperature performance indicators of the heat source surface and the flow performance indicators of the channel to determine the effect of the optimized structure.

[0089] The surface temperature performance index is expressed as follows:

[0090]

[0091]

[0092] In equations (7) and (8), RMST represents the root mean square temperature;

[0093] The expression for the flow friction coefficient of the flow channel is as follows:

[0094]

[0095] In equation (9), ΔP represents the pressure drop at the inlet and outlet of the flow channel, l represents the length of the flow channel, and U avg It represents the average velocity of the fluid.

[0096] Example 1

[0097] 1. Simulation model parameter settings:

[0098] This embodiment uses the optimized two-dimensional model of the heat sink obtained by the method of the present invention, as shown below. Figure 2 As shown, the structure of the three-dimensional composite heat sink obtained based on the two-dimensional topology is as follows: Figure 3 As shown, its internal dimensions are 100mm × 100mm × 7mm, its external dimensions are 104mm × 104mm × 11mm, its shell thickness is 2mm, the flow channel inlet and outlet are distributed on the center line of the radiator, the characteristic length of the flow channel inlet and outlet is 10mm, and the heat source heat flux density is set to 20000W / m. 2 The inlet flow velocity is 0.03 m / s, the inlet temperature is 293.15 K, the ambient temperature is 293.15 K, the outlet pressure is 0 Pa, and the external walls are adiabatic boundary conditions. The densities of copper, aluminum 6061, and water are 8960 kg / m³. 3 2700kg / m 3and 998kg / m 3 The thermal conductivity values ​​are 400 W / (m·K), 155 W / (m·K) and 0.6 W / (m·K), respectively.

[0099] Figure 3 In the diagram, label 1 represents copper, label 2 represents aluminum, and label 3 represents water. It can be seen that the distribution of these three materials exhibits an irregular shape. Overall, after entering from the inlet, the fluid first splits into three main channels, then each branch further subdivides into smaller branches, and finally all the branches converge and flow out at the outlet. Copper material 1 is widely distributed around the channels, increasing the heat transfer rate through its high thermal conductivity, thereby thinning the thermal boundary layer formed at the fluid-solid interface. Aluminum material 2 is distributed in areas with lower heat dissipation requirements, either surrounded by copper material 1 or distributed at the four corners of the radiator, increasing the economic efficiency of the materials.

[0100] 2. Comparison of Simulation Content and Results

[0101] Mesh analysis and finite element method (FEM) solutions were performed in Comsol Multiphysics. Table 1 shows the performance comparison between the composite radiator with inlets and outlets on the centerline and the traditional radiator, both based on multi-material topology optimization. The results in Table 1 show significant improvements in temperature and flow performance indicators. The average temperature of the heat source decreased by 7.41 K, the root mean square temperature decreased by 1.99 K, and the flow friction coefficient decreased by 0.74. This indicates that the optimized radiator has improved cooling performance and further reduced the required pump power, thus playing a positive role in energy conservation.

[0102] Table 1. Performance comparison between composite radiators with inlets and outlets at the centerline and traditional radiators using multi-material topology optimization design.

[0103] Topology optimization structure 321.06 3.98 0.74 Traditional design structure 328.47 5.97 1.48

[0104] like Figure 4 The figure shows the temperature distribution on the upper surface of the three-dimensional composite heat sink after optimization using the method of the present invention. Figure 5 This image shows the surface temperature distribution of a three-dimensional uniformly distributed radiator designed using a traditional method. It can be seen that the heat source temperature gradually increases along the flow direction of the cooling medium in both designs, with the high-temperature hotspots mainly concentrated on the outlet side. This is because the fluid absorbs a large amount of heat generated by the heat source as it moves towards the outlet, leading to a temperature rise. Compared to the temperature distribution of the traditional design, the optimized heat source exhibits a smaller high-temperature region and a more uniform temperature gradient. The maximum temperature is reduced by 10.3 K, and the heat generation of the heat source is effectively controlled.

[0105] like Figure 6The diagram shows the velocity vector of the cross-section of the three-dimensional composite radiator optimized using the method of this invention. It can be seen that the optimized flow velocity is evenly distributed across all branches, reducing unnecessary flow separation in the channel. Furthermore, there are almost no stagnant fluid areas at the corners of the optimized channel, making fluid mixing easier. Therefore, the radiator system experiences less energy loss and higher heat dissipation efficiency.

[0106] To further illustrate the effects of the present invention, the heat flux density of the heat source is increased from 5000 W / m³. 2 ~60000W / m 2 The following temperature will be described in further detail. Figure 7 This is a comparison of the average temperature of the present invention and a traditional design under different heat source heat flux densities. From Figure 7 As can be seen, the average temperature increases linearly with heat flux density. The optimized temperature curve is generally below the traditional design temperature curve, and the slope of the curve is greater. This indicates that the optimized heat sink of this invention provides a greater improvement in performance under high heat flux density conditions.

[0107] Example 2

[0108] 1. Simulation model parameter settings:

[0109] The structure of the optimized three-dimensional composite heat sink using the method of the present invention in this embodiment is as follows: Figure 8 As shown, its internal dimensions are 100mm × 100mm × 7mm, its external dimensions are 104mm × 104mm × 11mm, its shell thickness is 2mm, the flow channel inlet and outlet are distributed on the diagonal of the heat sink, the characteristic length of the flow channel inlet and outlet is 10mm, and the heat source heat flux density is set to 20000W / m. 2 The inlet flow velocity is 0.03 m / s, the inlet temperature is 293.15 K, the ambient temperature is 293.15 K, the outlet pressure is 0 Pa, and the external walls are adiabatic boundary conditions. The densities of copper, aluminum 6061, and water are 8960 kg / m³. 3 2700kg / m 3 and 998kg / m 3 The thermal conductivity coefficients are 400 W / (m·K), 155 W / (m·K), and 0.6 W / (m·K), respectively. It can be seen that after the fluid enters from the inlet, it first splits into two main channels, then differentiates into small branches, and finally converges to the outlet and flows out. Both copper material 1 and aluminum material 2 exhibit irregular distribution shapes.

[0110] 2. Comparison of Simulation Content and Results

[0111] Mesh analysis and finite element method (FEM) solutions for the multiphysics field were performed in Comsol Multiphysics. Table 2 shows the performance comparison between the composite radiator with diagonal inlets and outlets, designed using multimaterial topology optimization, and a traditional radiator. The results in Table 2 show that the average temperature of the heat source decreased by 6.55 K, the root mean square temperature decreased by 1.59 K, and the flow friction coefficient decreased by 0.6.

[0112] Table 2. Performance Comparison of Composite Radiators with Diagonal Inlet / Outlet Design and Traditional Radiators

[0113] Topology optimization structure 322.19 4.13 0.59 Traditional design structure 328.74 5.72 1.19

[0114] Example 3

[0115] 1. Simulation model parameter settings:

[0116] The structure of the optimized three-dimensional composite heat sink using the method of the present invention in this embodiment is as follows: Figure 9 As shown, its internal dimensions are 100mm × 100mm × 7mm, its external dimensions are 104mm × 104mm × 11mm, and its shell thickness is 2mm. The flow channel inlets and outlets are staggered at the four corners of the radiator, with a characteristic length of 10mm for each inlet and outlet. The heat source heat flux density is set to 20000W / m³. 2 The inlet flow velocity is 0.03 m / s, the inlet temperature is 293.15 K, the ambient temperature is 293.15 K, the outlet pressure is 0 Pa, and the external walls are adiabatic boundary conditions. The densities of copper, aluminum 6061, and water are 8960 kg / m³. 3 2700kg / m 3 and 998kg / m 3 The thermal conductivity coefficients are 400 W / (m·K), 155 W / (m·K), and 0.6 W / (m·K), respectively. It can be seen that after the fluid enters from the inlet, it first forms a main channel, then differentiates into small branches, and finally converges to the outlet and flows out. Both copper material 1 and aluminum material 2 exhibit irregular distribution shapes.

[0117] 2. Comparison of Simulation Content and Results

[0118] Mesh analysis and finite element method (FEM) solutions were performed in Comsol Multiphysics. Table 3 shows the performance comparison between a composite radiator with staggered inlets and outlets at the four corners of the radiator and a traditional radiator, based on multi-material topology optimization design. The results in Table 3 show that the average temperature of the heat source decreased by 8.14 K, the root mean square temperature decreased by 2.67 K, and the flow friction coefficient decreased by 0.1.

[0119] Table 3. Performance comparison between composite radiators with staggered inlets and outlets at the four corners of the radiator and traditional radiators using multi-material topology optimization design.

[0120] Topology optimization structure 313.03 1.96 0.33 Traditional design structure 321.17 4.63 0.43

Claims

1. A composite heat sink design method based on multi-material topology optimization, characterized in that, The specific steps are as follows: Step 1: Based on the configuration of the electronic equipment, determine the geometric dimensions of the topology optimization two-dimensional design domain and the inlet and outlet distribution of the flow channels; Step 2: Determine the fluid and thermal properties parameters of different solid materials, as well as the boundary conditions of the inlet, outlet, and wall of the flow channel; Step 3: Construct an ordered interpolation function for the physical properties of multiple materials characterized by a single design variable, and establish an expression for the damping coefficient in the flow control equation that distinguishes between fluid and solid states. Step 4: Based on actual engineering needs, and taking the linear combination of the maximum heat transfer and minimum flow power dissipation of the radiator as the optimization objective, establish a mathematical model for multi-material topology optimization. Step 5: Based on the finite element analysis method, solve the conjugate heat transfer multiphysics field, update the design variables through optimization algorithm, and obtain the optimized topology of the two-dimensional heat sink. Step 6: Based on the topological boundary of the optimized topology of the two-dimensional heat sink obtained in Step 5, construct the geometric model of the three-dimensional composite heat sink, and then determine the entire flow channel configuration and the distribution of multiple materials in the entire heat sink. In step 1, the geometric dimensions of the determined two-dimensional design domain are length L and width W; the locations of the entrances and exits are distributed as follows: on the center line of the design domain, on the diagonal line of the design domain, or staggered at the four corners of the design domain, and the characteristic length of the entrances and exits is D. The different solid materials identified in step 2 include copper and aluminum 6061, with densities of respectively. ρ 1 and ρ 2. The constant pressure heat capacities are respectively c 1 and c 2. The thermal conductivity is respectively k 1 and k 2; The cooling fluid is water, with a density of ρ 3. Constant pressure heat capacity is c 3. Thermal conductivity is k 3; The defined boundary conditions include the inlet flow velocity. U in Inlet temperature T in Export pressure P out Insulating boundary conditions of the external wall and heat sources based on the distribution of solid materials. Q ; The ordered interpolation function in step 3 is as follows: Through pseudo-density γ When used as a single design variable to characterize the physical properties of multiple materials, when Representing copper materials, when Representing aluminum 6061, when Represents cooling medium water; ordered according to material properties: ρ 1> ρ 2> ρ 3. k 1> k 2> k 3 and c 1< c 2< c 3. Based on the method of ordered, penalized solid isotropic materials, a method is constructed that is similar to... γ The relevant material ordered interpolation function is expressed as follows: （1） In equation (1), E These are physical property parameters of a material, including density, constant-pressure heat capacity, and thermal conductivity. p This represents the penalty parameter applied to the interpolation function.

2. The composite heat sink design method based on multi-material topology optimization according to claim 1, characterized in that, It also includes the following two steps: Step 7: Determine the thermal boundary conditions of the three-dimensional composite heat sink obtained in Step 6, and discretize the structure according to the solution requirements, and perform finite element method solution analysis. Step 8: Analyze the temperature performance indicators of the heat source surface and the flow performance indicators of the channel to determine the effect of the optimized structure.

3. The composite heat sink design method based on multi-material topology optimization according to claim 1, characterized in that, The specific expression for the damping coefficient in step 3 is as follows: Damping coefficient Is with γ The relevant quantity, the value of the damping coefficient, distinguishes between fluid and solid states. When the damping coefficient reaches its maximum, it represents a solid material; when the damping coefficient is close to zero, it represents a fluid material. The interpolation expression is as follows: （2） In equation (2), (3) In equations (2) and (3), The maximum reverse osmosis rate is given by Da, where Da is the Darcy number. e It is a natural constant. s To adjust the control parameters for the convexity of the interpolation curve, b This indicates the intermediate transition point of the control interpolation curve from its maximum to its minimum value. This refers to the fluid dynamic viscosity.

4. The composite heat sink design method based on multi-material topology optimization according to claim 1, characterized in that, Step 5 specifically involves: The value of the optimization objective in step 4 is obtained by solving the finite element method. The sensitivity of the optimization objective in step 4 to the design variables is calculated by applying the adjoint method. Then, the optimization direction of the design variables that have a significant impact on the hydrothermal performance is found. The moving asymptote algorithm is used to update the design variables. This process is repeated until the iteration stopping condition is met. The stopping condition for the moving asymptote algorithm is: given a maximum number of iterations of 500, and specifying the tolerance of the optimization objective as the convergence condition. ,in, k This represents the number of iteration steps. The calculation terminates when the optimization reaches the maximum number of iteration steps or the convergence condition is met, thus obtaining the optimized topology of the two-dimensional heat sink.

5. The composite heat sink design method based on multi-material topology optimization according to claim 1, characterized in that, Step 6 specifically involves: Extract the topological boundary of the optimized topology of the two-dimensional radiator obtained in step 5, import it into the modeling software to establish a three-dimensional composite radiator model. The normal section of the three-dimensional model is consistent with the optimized topology of the two-dimensional radiator. The determined internal dimensions of the model are length L, width W and height H, the external dimensions are length L1, width W1 and height H1, and the inlet and outlet feature length is D.

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