A microchannel radiator structure design method based on multi-objective function and radiator

Abstract

The present invention relates to the technical field of radiator structure design, and relates to a microchannel radiator structure design method based on a multi-objective function, which includes the following specific steps: S1, constructing a general mathematical description of a topology optimization problem; S2, obtaining input conditions under a specific design scenario and dividing the topology optimization design domain; S3, establishing the control equation of a topology optimization model; S4, performing sensitivity analysis of the multi-objective function with respect to design variables based on an adjoint method; S5, solving the topology optimization model by an MMA moving asymptote method; S6, obtaining a two-dimensional flow channel configuration of the radiator based on contour reconstruction, conducting finite element analysis of the two-dimensional flow channel structure, and narrowing the selection range of constraint conditions; S7, constructing a corresponding pseudo-three-dimensional model based on the two-dimensional finite element analysis results and conducting finite element analysis to determine the optimal constraint conditions and obtain the final topology optimized radiator configuration. Compared with traditional methods, the present invention can more efficiently solve radiator structure optimization problems in different scenarios.

Description

Technical Field

[0001] The present invention relates to the technical field of radiator structure design, in particular to a microchannel radiator structure design method based on multi-objective functions. Background Art

[0002] With the rapid development of integrated technology, high-performance electronic components have been widely used in various fields, such as electronic chips, electric vehicle power battery packs, and spacecraft. The heat flux density of high-performance electronic components is getting higher and higher, and their heat dissipation problem has become a hot topic of current research. According to predictions, the maximum average heat flux density of high-performance electronic chips can reach 500W / cm2, and the heat flux density of local hot spots will reach 1000W / cm2. With the continuous improvement of process technology, the heat dissipation required by electronic chips continues to increase. At the same time, after the temperature of electronic components exceeds 75°C, the probability of component failure increases exponentially with the increase in temperature. Currently, more than 55% of electronic chip failures are related to insufficient heat dissipation. The heat dissipation problem has become one of the main bottlenecks restricting the further development of high-performance electronic chips, and has put forward higher requirements for the thermal management of high-heat flux density electronic chips.

[0003] Currently, traditional air-cooling is no longer able to meet the growing heat dissipation needs of electronic components. Liquid-cooled microchannel radiators, however, have been widely used in electronic chip thermal management due to their high heat transfer efficiency, simple and stable structure, and low cost. The flow and heat transfer performance of microchannel radiators is significantly affected by their internal structure. Current optimization design methods for internal structures mostly rely on the designer's experience, which is significantly influenced by their subjective experience and cannot fully realize the radiator's heat transfer potential. Furthermore, as electronic components become increasingly complex, conventional radiators struggle to solve their heat dissipation problems. Conventional optimization design methods for specific devices suffer from long cycle times, poor heat dissipation, and poor temperature uniformity.

[0004] Currently, conventional optimization design methods are still limited by the topological configuration of the flow channels within the radiator. Topological optimization, as an emerging structural optimization method, is less affected by the designer, has a high degree of design freedom, and can change the topological configuration of the flow channels within the radiator during the optimization process, significantly improving the radiator's heat transfer efficiency and flow capacity. However, since topological optimization methods are significantly affected by initial constraints, the optimal constraints for different initial boundary conditions are unclear, and the three-dimensional topological optimization design is computationally expensive and time-consuming. There is an urgent need to develop a customized, efficient topological optimization design method based on multiple objective functions to address the long time-consuming, high computational cost, and high number of iterations in the topology optimization process of microchannel radiator structures. Summary of the Invention

[0005] The purpose of this invention is to address the problems existing in the background technology and propose a microchannel radiator structure design method based on multi-objective functions. Compared with traditional methods, the topology optimization design method of the present invention can more efficiently solve the radiator structure optimization problem in different scenarios.

[0006] The technical solution of the present invention is a microchannel radiator structure design method based on a multi-objective function, characterized by comprising the following specific steps:

[0007] S1. Construct a general mathematical description of the topology optimization problem;

[0008] S2. Obtain input conditions for a specific design scenario, including but not limited to: radiator geometry, inlet and outlet boundary conditions, heat source boundary conditions, solid material, and fluid, and divide the topology optimization design domain;

[0009] S3. Establish the governing equations of the topology optimization model. Use Darcy's law, which describes fluid flow in porous media, to represent the permeability of different design variables to the fluid. Select an appropriate interpolation function and construct a multi-objective function with weighting factors, consisting of weighted minimization of average temperature and minimization of flow dissipation.

[0010] S4. Conduct sensitivity analysis of multi-objective functions with respect to design variables based on the adjoint method;

[0011] S5. Solve the topology optimization model using the MMA moving asymptote method, and use filtering and projection techniques to obtain a material distribution with a clear fluid-solid boundary. Repeat the iterative solution until the convergence condition is met, and output the material distribution of the fluid and solid.

[0012] S6. Based on the contour reconstruction, the 2D flow channel configuration of the radiator is obtained. Finite element analysis of the 2D flow channel structure is performed to obtain the temperature field and velocity field distribution. The heat transfer performance is comprehensively evaluated through the average temperature, inlet and outlet pressure difference, average heat transfer coefficient, and temperature standard deviation to narrow the range of constraint conditions.

[0013] S7. Based on the two-dimensional finite element analysis results, a corresponding pseudo-three-dimensional model is constructed and finite element analysis is performed to obtain the temperature field and velocity field distribution. The heat transfer performance is comprehensively evaluated through the average temperature, net outlet pressure difference, average heat transfer coefficient and temperature standard deviation, the optimal constraint conditions are determined, and the final topology optimized radiator configuration is obtained.

[0014] Preferably, in S1, the topology optimization mathematical model is as follows:

[0015]

[0016] subjectto:

[0017] g(y,s(y))=0,i=1,,n

[0018] hj(y,s(y))≤0,j=1,...,m,

[0019]

[0020] Where F is the objective function that needs to be maximized or minimized in the optimization problem, gi and h j They represent the equality constraints and inequality constraints in the research object respectively. s(γ) is the state variable function of the design variable γ, where γ(x) is a 0-1 binary function representing the state of material existence. When γ = 0, it means that there is no material at the spatial point corresponding to the x position, and γ = 1 indicates that the given material exists at that point.

[0021] Preferably, the geometric dimensions of the radiator in S2 include: radiator length, width and thickness;

[0022] Inlet and outlet boundary conditions include: fluid inlet temperature, inlet velocity, and outlet pressure;

[0023] The heat source boundary conditions are determined by the heat dissipation requirements in a specific scenario and can be uniform heat flow boundary conditions and / or non-uniform heat flow boundary conditions;

[0024] The fluid material needs to provide the law of how its different physical parameters change with temperature, including the correlation between thermal conductivity, specific heat capacity, dynamic viscosity and density and temperature changes.

[0025] Preferably, the interpolation function establishment process in S3 is based on the SIMP model, and in order to avoid the optimization problem falling into a local optimal solution, a parameterized interpolation convex function as shown below is adopted:

[0026]

[0027]

[0028]

[0029]

[0030] where k s , ρ s and c p，s are the thermal conductivity, density and specific heat capacity of the solid material respectively; k f , ρ f and c p，f are the thermal conductivity, density and specific heat capacity of the fluid material, respectively.

[0031] Preferably, the multi-objective function in S3 is composed of weighted minimization of average temperature and minimization of flow dissipation, as shown in the following formula:

[0032] Flow dissipation objective function:

[0033]

[0034] Average temperature objective function:

[0035]

[0036] Transformed into equivalent multi-objective function through dimensionless and weighted processing

[0037]

[0038] Also define the weight factor:

[0039]

[0040] Wherein w1 is the flow weight factor, w2 is the heat dissipation weight factor, and w1+w2=1.

[0041] Preferably, the sensitivity of the objective function in S4 to the design variables is as follows:

[0042] Sensitivity results of the flow dissipation function Φ with respect to the design variable γ:

[0043]

[0044] Sensitivity results of the average temperature function Γ with respect to the design variables:

[0045]

[0046] Preferably, the filtering method in S5 is used to solve the mesh dependency in the topology optimization process, using a filtering scheme independent of the mesh, which is expressed by the following formula:

[0047]

[0048] The Helmholtz equation is used for density filtering, and the expression is as follows:

[0049]

[0050] Where r is the set filter radius, γ is the design variable before filtering, It is the design variable after filtration; manufacturing restrictions are added during the filtration process, and the set minimum filtration radius is the minimum flow channel size, which is no greater than the accuracy of the processing method, thereby ensuring machinability and shortening the radiator design cycle.

[0051] Preferably, the projection technology in S5 uses the hyperbolic tangent projection shown in the following formula to project the filtered design variables, and adopts a continuous projection strategy, so as to obtain a clear flow channel topology optimization structure;

[0052]

[0053] in, is the projected design variable, β is the projected slope, γ β is the projection point.

[0054] Finite element analysis in S6 is performed based on commercial CFD software.

[0055] Preferably, the pseudo three-dimensional model in S7 is obtained by stretching the two-dimensional topology optimized flow channel configuration.

[0056] A microchannel radiator structure is designed using the above-mentioned microchannel radiator structure design method based on multi-objective function.

[0057] Compared with the prior art, the present invention has the following beneficial technical effects:

[0058] The present invention uses the porous medium hypothesis to simulate the internal solid and fluid domain distinction, and introduces volume force based on Brinkman. The permeability is used to represent the degree of material permeability to the fluid when different design variables are present. Based on the SIMP model, interpolation functions of different physical parameters are constructed, and a multi-objective function consisting of weighted average temperature minimization and flow dissipation minimization is constructed. The sensitivity of the objective function to the design variables is solved by the adjoint method. The optimization model is solved by the MMA method, and the Helmholtz equation is used for density filtering and hyperbolic tangent projection is used to project the filtered design variables to obtain the fluid-solid material distribution under different constraint conditions. Based on the material distribution, contour extraction is performed to obtain a two-dimensional topological optimized flow channel, and flow heat transfer simulation is carried out to obtain the Pareto optimal design curve. Based on this curve, pseudo-three-dimensional model flow heat transfer simulation is further carried out. Finally, the optimal initial constraint conditions are selected by comprehensively comparing the average temperature, inlet and outlet pressure difference, temperature standard deviation and average heat transfer coefficient, and the topological optimization design model of the microchannel radiator is finally obtained. This method is based on two-dimensional and pseudo-three-dimensional simulation results. While ensuring the reliability of the results, it greatly reduces the huge computational cost brought by three-dimensional topology optimization design and effectively shortens the topology optimization design cycle of the microchannel radiator. BRIEF DESCRIPTION OF THE DRAWINGS

[0059] Figure 1 It is a flow chart of the topology optimization design method based on multi-objective functions of the present invention;

[0060] Figure 2 is the Pareto optimal design curve obtained by the method of the present invention;

[0061] Figure 3 is a schematic diagram of a topology optimized liquid-cooled microchannel radiator structure according to an embodiment of the present invention; Figure 3 (a) is a pseudo 3D model of the topology optimized heat sink. Figure 3 (b) is the temperature distribution under uniform heat source. DETAILED DESCRIPTION

[0062] Example 1

[0063] like Figure 1 As shown in the figure, the present invention proposes a liquid cooling radiator structure topology optimization design method based on multi-objective function, the main core process Figure 1 As shown, the specific steps include:

[0064] Step 1: Determine the input conditions of the heat sink in this application scenario, including the length, width, and thickness of the heat sink, and form a topology optimization design domain based on the projection of the heat sink length and width, as well as the heat source distribution and size. In this embodiment, the heat source adopts a uniform heat source distribution with a size of 100W / cm 2 , the heat dissipation length, width and thickness are 30mm, 24mm and 3mm respectively, the solid material is copper and the fluid medium is water;

[0065] Step 2: Corresponding to the Figure 1 The process starts with setting the initial constraints of the topology optimization model. In this implementation, the constraints are set to volume fraction. and weight factor w, where is the volume fraction of the fluid in the entire radiator;

[0066] The multi-objective function is shown as follows:

[0067]

[0068]

[0069]

[0070] Step 3: Initialize the physical field and solve the established forced convection heat transfer control equation based on finite element analysis. The control equation is as follows:

[0071]

[0072]

[0073]

[0074] And construct interpolation functions with different parameters based on the SIMP model:

[0075]

[0076]

[0077]

[0078]

[0079] The change of γ from 0 to 1 is represented by the Brinkman equation as the material transition from solid to fluid.

[0080] Based on the finite element analysis results, the sensitivity results of the objective function with respect to the design variables are obtained:

[0081]

[0082]

[0083] Step 4: Solve the sensitivity results using the MMA algorithm to obtain the improvement points of the current design variables. During the solution process, density filtering is performed using the Helmholtz equation, and the filtered design variables are projected using the hyperbolic tangent projection method. In order to ensure the convergence of the optimization problem, a continuous projection strategy is adopted.

[0084] The Helmholtz equation is expressed as:

[0085]

[0086] Where r is the set filter radius, γ is the design variable before filtering, is the filtered design variable.

[0087] The hyperbolic tangent projection method is expressed as:

[0088]

[0089] in, is the projected design variable, β is the projected slope, γ β is the projection point

[0090] The calculation is completed in a single pass, with a maximum number of iterations of 400, until the tolerance is less than 10 -6 End the calculation. If the result is not satisfied, recalculate the physical field to obtain the sensitivity result and iterate repeatedly until the tolerance is less than the set value. At this time, the material distribution is derived and the topology optimization solution is completed.

[0091] Step 5: The material distribution is converted into a two-dimensional flow channel configuration by the contour extraction method. Since the flow conjugate heat transfer model is simplified in the topology optimization model, the finite element analysis is performed again based on the two-dimensional results, and the flow and heat transfer characteristics of the two-dimensional topology optimization heat dissipation flow channel under different working conditions are compared. The following results are obtained: Figure 2 The Pareto optimal design curves for different initial constraints are shown to narrow the range of constraint selection.

[0092] Step 6: The two-dimensional topology optimized heat dissipation channel is packaged through post-processing such as stretching to form the following Figure 3 (a) shows a pseudo-three-dimensional radiator model. The main flow channel is leaf-vein-shaped, and the branched flow channel is similar to capillaries and is distributed throughout the radiator, which effectively enhances the fluid disturbance and strengthens the heat transfer effect. The flow and heat transfer characteristics of the radiator within the optimal constraint condition selection range obtained by two-dimensional simulation are compared. The results are mainly obtained by comprehensively comparing the average temperature of the heat source surface, the inlet and outlet pressure difference, the temperature standard deviation and the average heat transfer coefficient, and combining the following Figure 3 (b) The temperature cloud map selects the optimal constraint conditions and finally outputs the topology optimized radiator model.

[0093] The inlet and outlet pressure difference is defined as:

[0094] Ap=PinnPout

[0095] The temperature standard deviation is defined as:

[0096]

[0097] The average heat transfer coefficient is defined as:

[0098]

[0099] Comparative verification of flow heat dissipation performance of topology optimized liquid-cooled microchannel radiator:

[0100] A traditional flat microchannel heat sink was designed and the volume fraction was kept consistent;

[0101] The numerical simulation model in step 6 is used to carry out flow and heat transfer simulation under the same working conditions. The specific working conditions are set as: inlet temperature 20℃, inlet flow velocity 0.8m / s, and applied uniform heat source of 50W / cm 2 .

[0102] The specific simulation results are shown in Table 1:

[0103] Table 1 Comparison between traditional radiator and topology optimized radiator

[0104] Evaluation indicators Traditional radiator Topology optimized heat sink promote / % <![CDATA[Average temperature Tav g / K]]> 58.23 51.75 11％ Inlet and outlet pressure difference Δp / Pa 764.03 593.10 22.3％ <![CDATA[Average heat transfer coefficient hav g / W·m- 2 ·K- 1 > 5582.72 8506.33 52.4％ <![CDATA[Standard deviation of temperature T δ / K]]> 9.07 6.89 24.1％

[0105] After optimizing the radiator structure using the method of the present invention, its average temperature decreased by 6.5°C, its flow capacity increased by 22.3%, its heat exchange capacity increased by 52.4%, and its temperature uniformity increased by 24.1%, indicating that the radiator designed using the topology optimization method proposed in the present invention is significantly superior to the traditional flat microchannel radiator in all aspects.

[0106] The embodiments of the present invention are described in detail above with reference to the accompanying drawings, but the present invention is not limited thereto. Various changes can be made within the scope of knowledge possessed by those skilled in the art without departing from the spirit of the present invention.

Claims

1. A microchannel radiator structure design method based on multi-objective function, characterized in that: The specific steps include: S1. Construct a general mathematical description of the topology optimization problem; S2. Obtain input conditions for a specific design scenario, including but not limited to: radiator geometry, inlet and outlet boundary conditions, heat source boundary conditions, solid material, and fluid, and divide the topology optimization design domain; S3. Establish the governing equations of the topology optimization model. Use Darcy's law, which describes fluid flow in porous media, to represent the permeability of different design variables to the fluid. Select an appropriate interpolation function and construct a multi-objective function with weighting factors, consisting of weighted minimization of average temperature and minimization of flow dissipation. S4. Conduct sensitivity analysis of multi-objective functions with respect to design variables based on the adjoint method; S5. Solve the topology optimization model using the MMA moving asymptote method, and use filtering and projection techniques to obtain a material distribution with a clear fluid-solid boundary. Repeat the iterative solution until the convergence condition is met, and output the material distribution of the fluid and solid. S6. Based on the contour reconstruction, the 2D flow channel configuration of the radiator is obtained. Finite element analysis of the 2D flow channel structure is performed to obtain the temperature field and velocity field distribution. The heat transfer performance is comprehensively evaluated through the average temperature, inlet and outlet pressure difference, average heat transfer coefficient, and temperature standard deviation to narrow the range of constraint conditions. S7. Based on the two-dimensional finite element analysis results, a corresponding pseudo-three-dimensional model is constructed and finite element analysis is performed to obtain the temperature field and velocity field distribution. The heat transfer performance is comprehensively evaluated through the average temperature, net outlet pressure difference, average heat transfer coefficient and temperature standard deviation, the optimal constraint conditions are determined, and the final topology optimized radiator configuration is obtained.

2. The microchannel radiator structure design method based on multi-objective function according to claim 1, characterized in that: In S1, the topology optimization mathematical model is as follows: subject to: g i (γ,s(γ))=0,i=1,...,n, h j (γ,s(γ))≤0,j=1,...,m, Where F is the objective function that needs to take the maximum or minimum value in the optimization problem, g i and h j They represent the equality constraints and inequality constraints in the research object respectively. s(γ) is the state variable function of the design variable γ, where γ(x) is a 0-1 binary function representing the state of material existence. When γ = 0, it means that there is no material at the spatial point corresponding to the x position, and γ = 1 indicates that the given material exists at that point.

3. The microchannel radiator structure design method based on multi-objective function according to claim 1, characterized in that: The geometric dimensions of the radiator in S2 include: radiator length, width and thickness; Inlet and outlet boundary conditions include: fluid inlet temperature, inlet velocity, and outlet pressure; The heat source boundary conditions are determined by the heat dissipation requirements in a specific scenario and can be uniform heat flow boundary conditions and / or non-uniform heat flow boundary conditions; The fluid material needs to provide the law of how its different physical parameters change with temperature, including the correlation between thermal conductivity, specific heat capacity, dynamic viscosity and density and temperature changes.

4. The microchannel radiator structure design method based on multi-objective function according to claim 1, characterized in that: The interpolation function establishment process in S3 is based on the SIMP model, and in order to avoid the optimization problem falling into a local optimal solution, a parameterized interpolation convex function is used as shown below: where k s ,ρ s and c p，s are the thermal conductivity, density and specific heat capacity of the solid material respectively; k f ,ρ f and c p，f are the thermal conductivity, density and specific heat capacity of the fluid material, respectively.

5. The microchannel radiator structure design method based on multi-objective function according to claim 1, characterized in that: The multi-objective function in S3 consists of weighted minimization of average temperature and minimization of flow dissipation, as shown in the following formula: Flow dissipation objective function: Average temperature objective function: Transformed into an equivalent multi-objective function through dimensionless and weighted processing Also define the weight factor: Wherein w1 is the flow weight factor, w2 is the heat dissipation weight factor, and w1+w2=1.

6. The microchannel radiator structure design method based on multi-objective function according to claim 1, characterized in that: The sensitivity results of the objective function in S4 with respect to the design variables are as follows: Sensitivity results of the flow dissipation function Φ with respect to the design variable γ: Sensitivity results of the average temperature function Γ with respect to the design variables:

7. The microchannel radiator structure design method based on multi-objective function according to claim 1, characterized in that: The filtering method in S5 is used to solve the mesh dependency in the topology optimization process. It adopts a filtering scheme independent of the mesh and is expressed by the following formula: The Helmholtz equation is used for density filtering, and the expression is as follows: Where r is the set filter radius, γ is the design variable before filtering, It is the design variable after filtration. Manufacturing restrictions are added during the filtration process. The set minimum filtration radius is the minimum flow channel size, which is no larger than the accuracy of the processing method, thereby ensuring machinability and shortening the radiator design cycle.

8. The microchannel radiator structure design method based on multi-objective function according to claim 1, characterized in that: The projection technology in S5 uses the hyperbolic tangent projection shown in the following formula to project the filtered design variables and adopts a continuous projection strategy to obtain a clear flow channel topology optimization structure; in, is the projected design variable, β is the projected slope, γ β is the projection point.

9. The microchannel radiator structure design method based on multi-objective function according to claim 1, characterized in that: The pseudo three-dimensional model in S7 can be obtained by stretching the two-dimensional topology optimized flow channel configuration.

10. A microchannel radiator structure, characterized in that: The design is performed using the microchannel radiator structure design method based on multi-objective functions as described in any one of claims 1 to 9.

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