Micro-channel heat sink structure design method based on multi-objective function, and heat sink

Abstract

The present invention relates to the technical field of heat sink structure design, and in particular to a micro-channel heat sink structure design method based on a multi-objective function. The method comprises the following specific steps: S1, constructing a general mathematical description of a topology optimization problem; S2, acquiring input conditions for a specific design scenario, and dividing a topology optimization design domain; S3, establishing a governing equation for a topology optimization model; S4, on the basis of an adjoint method, performing sensitivity analysis of a multi-objective function with respect to design variables; S5, solving the topology optimization model by means of a method of moving asymptotes (MMA); S6, obtaining a two-dimensional flow channel configuration of a heat sink on the basis of contour reconstruction, carrying out finite element analysis of a two-dimensional flow channel structure, and narrowing down the selection range of constraint conditions; and S7, on the basis of a two-dimensional finite element analysis result, constructing a corresponding pseudo-three-dimensional model, carrying out finite element analysis, and determining optimal constraint conditions to obtain a final topology-optimized heat sink configuration. Compared with traditional methods, the present invention can more efficiently solve the problem in respect of heat sink structure optimization under different scenarios.

Description

A microchannel heat sink structure design method based on multi-objective functions and the heat sink Technical Field

[0001] This invention relates to the field of heat sink structure design technology, and in particular to a microchannel heat sink structure design method based on multi-objective functions. Background Technology

[0002] With the rapid development of integrated circuit technology, high-performance electronic components have been widely used in various fields, such as electronic chips, electric vehicle battery packs, and spacecraft. However, the heat flux density of these high-performance electronic components is increasing, making heat dissipation a hot research topic. It is predicted that the maximum average heat flux density of high-performance electronic chips can reach 500 W / cm², with local hotspots reaching 1000 W / cm². As manufacturing processes continue to improve, the heat dissipation requirements for electronic chips continue to increase. Furthermore, once the temperature of electronic components exceeds 75°C, the probability of component failure increases exponentially with temperature. Currently, over 55% of electronic chip failures are related to insufficient heat dissipation. Heat dissipation has become one of the main bottlenecks restricting the further development of high-performance electronic chips, placing higher demands on the thermal management of high heat flux density electronic chips.

[0003] Traditional air cooling is no longer sufficient to meet the ever-increasing heat dissipation demands of electronic components. Liquid-cooled microchannel heat sinks, due to their high heat exchange efficiency, simple and stable structure, and low cost, have been widely adopted in the field of electronic chip thermal management. However, the flow and heat transfer performance of microchannel heat sinks is significantly affected by their internal structure. Current optimization design methods for internal structures largely rely on the designer's experience, which is highly subjective and fails to fully realize the heat exchange potential of the heat sink. Furthermore, as electronic components become increasingly complex, conventional heat sinks struggle to solve their heat dissipation problems, and conventional optimization design methods for specific devices suffer from long development cycles, poor heat dissipation effects, and poor temperature uniformity.

[0004] Current conventional optimization design methods are still limited by the internal flow channel topology of the radiator. Topology optimization, as an emerging structural optimization method, is less influenced by designers, has a high degree of design freedom, and can change the internal flow channel topology of the radiator during the optimization process, significantly improving the heat exchange efficiency and flow capacity of the radiator. However, because topology optimization methods are greatly affected by initial constraints, the optimal constraints under different initial boundary conditions are unclear. Three-dimensional topology optimization design is computationally expensive and time-consuming. There is an urgent need to develop a customized, high-efficiency topology optimization design method based on multi-objective functions to solve the problems of long processing time, high computational cost, and numerous 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 by proposing a microchannel heat sink structure design method based on a multi-objective function. Compared with traditional methods, the topology optimization design method of this invention can more efficiently solve the heat sink structure optimization problem in different scenarios.

[0006] The technical solution of this invention, a microchannel heat sink structure design method based on multi-objective functions, is characterized by the following specific steps:

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

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

[0009] S3. Establish the control equations of the topology optimization model. Darcy's law, which describes fluid flow in porous media, is used 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, which is composed of the weighted combination of minimizing the average temperature and minimizing the flow dissipation.

[0010] S4. 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 the material distribution with clear fluid-solid boundaries. Iterate repeatedly until the convergence condition is met, and output the material distribution of the fluid and solid.

[0012] S6. Based on the contour reconstruction, the two-dimensional flow channel configuration of the radiator is obtained. Finite element analysis of the two-dimensional flow channel structure is carried out to obtain the temperature field and velocity field distribution. The heat transfer performance is comprehensively evaluated by 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 results of the two-dimensional finite element analysis, a corresponding pseudo-three-dimensional model is constructed and finite element analysis is carried out to obtain the temperature field and velocity field distribution. The heat transfer performance is comprehensively evaluated by the average temperature, net outlet pressure difference, average heat transfer coefficient and temperature standard deviation. The optimal constraint conditions are determined to obtain the final topology-optimized radiator configuration.

[0014] Preferably, 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,

[0015] In the formula, F is the objective function that needs to be maximized or minimized in the optimization problem, and g i and h j These represent the equality constraints and inequality constraints in the research object, respectively. s(γ) is a state variable function of the design variable γ, where γ(x) is a 0-1 binary function representing the state of material presence. When γ = 0, it means that there is no material at the spatial point corresponding to position x, and when γ = 1, it means that the given material exists at that point.

[0016] Preferably, the radiator geometry in S2 includes: radiator length, width, and thickness;

[0017] Inlet and outlet boundary conditions include: fluid inlet temperature, inlet velocity, and outlet pressure;

[0018] The heat source boundary conditions are determined by the heat dissipation requirements under a specific scenario, and can be uniform heat flux boundary conditions and / or non-uniform heat flux boundary conditions.

[0019] For fluid materials, it is necessary to provide the laws governing the changes of their various physical properties with temperature, including the correlation between thermal conductivity, specific heat capacity, dynamic viscosity, and density and temperature changes.

[0020] Preferably, the interpolation function establishment process in S3 is based on the SIMP model, and to avoid the optimization problem getting trapped in local optima, the following parameterized interpolation convex function is adopted:

[0021] Where k s , ρ s and c p，s These represent the thermal conductivity, density, and specific heat capacity of a solid material, respectively; k f , ρ f and c p，f These are the thermal conductivity, density, and specific heat capacity of the fluid material, respectively.

[0022] Preferably, the multi-objective function in S3 consists of a weighted sum of minimizing the average temperature and minimizing the flow dissipation, as shown in the following equation:

[0023] Flow dissipation objective function:

[0024] Objective function for average temperature:

[0025] The function is transformed into an equivalent multi-objective function through dimensionless transformation and weighting.

[0026] Simultaneously define weighting factors:

[0027] Where w1 is the flow weight factor, w2 is the heat dissipation weight factor, and w1+w2=1.

[0028] Preferably, the sensitivity results of the objective function in S4 with respect to the design variables are as follows:

[0029] Sensitivity results of the flow dissipation function Φ with respect to the design variable γ:

[0030] Sensitivity results of the mean temperature function Γ with respect to the design variables:

[0031] Preferably, the filtering method in S5 is used to address grid dependency in the topology optimization process. It employs a filtering scheme independent of the grid, expressed by the following formula:

[0032] Density filtering is performed using the Helmholtz equation, as shown in the following expression:

[0033] Where r is the set filtering radius, and γ is the design variable before filtering. These are the design variables after filtration; manufacturing constraints are added during the filtration process, and the minimum filtration radius is the minimum flow channel size. This size is not greater than the precision of the processing method, thereby ensuring manufacturability and shortening the heat sink design cycle.

[0034] Preferably, in S5, the projection technology uses hyperbolic tangent projection as shown in the following formula to project the filtered design variables, and adopts a continuous projection strategy, thereby obtaining a clear flow channel topology optimization structure.

[0035] in, These are the projected design variables, where β is the projection slope and γ is the projection slope. β It is the projection point.

[0036] Finite element analysis in S6 is conducted using commercial CFD software.

[0037] Preferably, the pseudo-3D model in S7 can be obtained by stretching the two-dimensional topology optimization flow channel configuration.

[0038] A microchannel heat sink structure is designed using the aforementioned multi-objective function-based microchannel heat sink structure design method.

[0039] Compared with the prior art, the present invention has the following beneficial technical effects:

[0040] This invention employs a porous media assumption to simulate the distinction between the internal solid and fluid domains, and introduces volume forces based on Brinkman dynamics. Permeability is used to represent the material's permeability to the fluid under different design variables. Based on the SIMP model, interpolation functions for different physical property parameters are constructed. A multi-objective function composed of a weighted average temperature minimization and flow dissipation minimization is built, and the sensitivity of the objective function to design variables is solved using the adjoint method. The optimization model is solved using the MMA method, and density filtering is performed using the Helmholtz equation. Hyperbolic tangent projection is then used to project the filtered design variables, obtaining the fluid-solid material distribution under different constraints. Based on the material distribution, a two-dimensional topology-optimized flow channel is obtained through contour extraction, and flow and heat transfer simulations are conducted to obtain the Pareto optimal design curve. Based on this curve, further pseudo-three-dimensional flow and heat transfer simulations are performed. Finally, by comprehensively comparing the average temperature, inlet and outlet pressure difference, temperature standard deviation, and average heat transfer coefficient, the optimal initial constraints are selected, ultimately obtaining the topology-optimized design model of the microchannel radiator. This method, based on two-dimensional and pseudo-three-dimensional simulation results, greatly reduces the huge computational cost of three-dimensional topology optimization design while ensuring the reliability of the results, and effectively shortens the topology optimization design cycle of microchannel heat sinks. Attached Figure Description

[0041] Figure 1 is a flowchart of the topology optimization design method based on multi-objective functions of the present invention;

[0042] Figure 2 shows the Pareto optimal design curve obtained by the method of the present invention;

[0043] Figure 3 is a schematic diagram of the topology-optimized liquid-cooled microchannel heat sink structure in an embodiment of the present invention; Figure 3(a) is a pseudo-three-dimensional model of the topology-optimized heat sink, and Figure 3(b) is the temperature distribution under a uniform heat source;

[0044] Figure 4 shows physical images of topology-optimized heat sinks with different structures;

[0045] Figure 5(a) shows the flow path installation diagram of the topology-optimized heatsink for model TO-U-50;

[0046] Figure 5(b) shows the flow channel packaging diagram of the topology-optimized heat sink of model TO-U-50;

[0047] Figure 6(a) shows q = 30 W / cm 2 Comparison of average temperature of heat sink flow heat dissipation at different Reynolds numbers (Re);

[0048] Figure 6(b) shows q = 30 W / cm 2 Comparison of inlet and outlet pressure differences for heat sink flow at different Reynolds numbers Re. Detailed Implementation

[0049] Example 1

[0050] As shown in Figure 1, the proposed topology optimization design method for liquid-cooled radiators based on multi-objective functions, as illustrated in Figure 1, includes the following steps:

[0051] Step 1: Determine the input conditions for the heat sink in this application scenario, including its length, width, and thickness. Based on the projections of the heat sink's length and width, form a topology optimization design domain, including the heat source distribution and size. In this embodiment, a uniform heat source distribution with a size of 100 W / cm² is adopted. 2 The heat dissipation length, width, and thickness are 30mm, 24mm, and 3mm, respectively, and the solid material is copper and the working fluid is water.

[0052] Step 2: Begin the operation according to the process shown in Figure 1, and set the initial constraints of the topology optimization model. In this embodiment, the constraint is set as volume fraction. and weighting factor w, where The volume fraction of the fluid in the entire radiator;

[0053] The multi-objective function is shown in the following equation:

[0054] Step 3: Based on the established forced convection conjugate heat transfer control equations, initialize the physical field using finite element analysis and solve for it. The control equations are shown below:

[0055] And based on the SIMP model, interpolation functions with different parameters are constructed:

[0056] The change of γ from 0 to 1 is represented by the Brinkman equation as the material transitioning from a solid to a fluid.

[0057] The sensitivity results of the objective function with respect to the design variables were obtained based on the finite element analysis results:

[0058] Step 4: Solve the current design variables using the MMA algorithm based on the sensitivity results. 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. A continuous projection strategy is used to ensure the convergence of the optimization problem.

[0059] The Helmholtz equation can be expressed as:

[0060] Where r is the set filtering radius, and γ is the design variable before filtering. These are the filtered design variables.

[0061] The hyperbolic tangent projection method is expressed as:

[0062] in, These are the projected design variables, where β is the projection slope and γ is the projection slope. β It is the projection point

[0063] A single calculation is completed, with a maximum of 400 iterations, until the tolerance is less than 10. -6 The calculation ends. If the conditions are not met, the physical field is recalculated to obtain the sensitivity result. The process is repeated until the tolerance is less than the set value. At this point, the material distribution is derived, and the topology optimization solution is completed.

[0064] Step 5: The material distribution is transformed into a two-dimensional flow channel configuration by contour extraction. Since the flow conjugate heat transfer model in the topology optimization model has been simplified, finite element analysis is performed again based on the two-dimensional results. The flow heat transfer characteristics of the two-dimensional topology optimization heat dissipation channel under different working conditions are compared. The Pareto optimal design curves with different initial constraints are obtained as shown in Figure 2, which narrows the range of constraint selection.

[0065] Step Six: The two-dimensional topology-optimized heat dissipation channels are encapsulated through post-processing such as stretching to form a pseudo-three-dimensional heat sink model as shown in Figure 3(a). The main internal flow channel is shaped like a leaf vein, and the flow channel branches are similar to capillaries and are distributed throughout the heat sink, which effectively enhances fluid disturbance and strengthens the heat transfer effect. The heat transfer characteristics of the heat sink within the range of optimal constraint conditions obtained from the two-dimensional simulation are compared. This is mainly done 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 temperature cloud map shown in Figure 3(b) to select the optimal constraint conditions. Finally, the topology-optimized heat sink model is output.

[0066] The pressure difference between the inlet and outlet is defined as: Δp = p in -p out

[0067] The standard deviation of temperature is defined as:

[0068] The average heat transfer coefficient is defined as:

[0069] Comparative verification of the flow heat dissipation performance of topology-optimized liquid-cooled microchannel radiators:

[0070] A traditional flat microchannel heat sink was designed while ensuring a consistent volume fraction.

[0071] The flow and heat transfer simulation under the same operating conditions was carried out using the numerical simulation model from step six. The specific operating conditions were set as follows: inlet temperature 20℃, inlet flow velocity 0.8m / s, and applied uniform heat source of 50W / cm².2 .

[0072] The specific simulation results are shown in Table 1:

[0073] Table 1 Comparison of Traditional Radiators and Topology-Optimized Radiators

[0074] After optimizing the radiator structure using the method of the present invention, the average temperature is reduced by 6.5℃, the flow capacity is increased by 22.3%, the heat exchange capacity is increased by 52.4%, and the temperature uniformity is improved by 24.1%. This shows that the radiator designed by the topology optimization method proposed in this invention is significantly better than the traditional flat microchannel radiator in all aspects.

[0075] According to the multi-objective function-based topology optimization design method for single-phase liquid-cooled heat sinks proposed in this invention, after designing and outputting the topology-optimized heat sink model, topology-optimized heat sinks with different structures are fabricated. Figure 4 shows physical images of the topology-optimized heat sinks with different structures. In the model names TO-U-20, TO-U-50, and TO-U-70, TO represents topology, U represents uniform heat source, and 20 / 50 / 70 represent the weighting factors of topology optimization. Figure 5(a) shows the flow channel installation diagram of the topology-optimized heat sink model TO-U-50; Figure 5(b) shows the flow channel packaging diagram of the topology-optimized heat sink model TO-U-50.

[0076] Figure 6(a) shows the heat flux density q = 30 W / cm². 2 A comparison of the average temperature of heat dissipation from each radiator at different Reynolds numbers Re; Figure 6(b) shows the heat flux density q = 30 W / cm². 2 The comparison of the pressure difference between the inlet and outlet of each radiator under different Reynolds numbers Re is shown in Figures 6(a) and 6(b). Based on the results shown in Figures 6(a) and 6(b), the topology-optimized radiator of model TO-U-50 has the best overall performance, with heat dissipation performance close to that of Y-70 and exhibiting the lowest pressure drop.

[0077] The embodiments of the present invention have been described in detail above with reference to the accompanying drawings. However, 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 heat sink structure design method based on multi-objective functions, characterized in that, The specific steps include the following: S1. Construct a general mathematical description of the topology optimization problem; S2. Obtain the input conditions under the specific design scenario, including but not limited to: radiator geometry, inlet and outlet boundary conditions, heat source boundary conditions, solid material and fluid working medium, and divide the topology optimization design domain. S3. Establish the control equations of the topology optimization model. Darcy's law, which describes fluid flow in porous media, is used 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, which is composed of the weighted combination of minimizing the average temperature and minimizing the flow dissipation. S4. 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 the material distribution with clear fluid-solid boundaries. Iterate repeatedly until the convergence condition is met, and output the material distribution of the fluid and solid. S6. Based on the contour reconstruction, the two-dimensional flow channel configuration of the radiator is obtained. Finite element analysis of the two-dimensional flow channel structure is carried out to obtain the temperature field and velocity field distribution. The heat transfer performance is comprehensively evaluated by 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 results of the two-dimensional finite element analysis, a corresponding pseudo-three-dimensional model is constructed and finite element analysis is carried out to obtain the temperature field and velocity field distribution. The heat transfer performance is comprehensively evaluated by the average temperature, net outlet pressure difference, average heat transfer coefficient and temperature standard deviation. The optimal constraint conditions are determined to obtain the final topology-optimized radiator configuration.

2. The microchannel heat sink structure design method based on multi-objective functions 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, In the formula, F is the objective function that needs to be maximized or minimized in the optimization problem, and g i and h j These represent the equality constraints and inequality constraints in the research object, respectively. s(γ) is a state variable function of the design variable γ, where γ(x) is a 0-1 binary function representing the state of material presence. When γ = 0, it means that there is no material at the spatial point corresponding to position x, and when γ = 1, it means that the given material exists at that point.

3. The microchannel heat sink structure design method based on multi-objective functions according to claim 1, characterized in that, The radiator geometry in S2 includes: 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 under a specific scenario, and can be uniform heat flux boundary conditions and / or non-uniform heat flux boundary conditions. For fluid materials, it is necessary to provide the laws governing the changes of their various physical properties with temperature, including the correlation between thermal conductivity, specific heat capacity, dynamic viscosity, and density and temperature changes.

4. The microchannel heat sink structure design method based on multi-objective functions according to claim 1, characterized in that, The interpolation function in S3 is based on the SIMP model, and to avoid the optimization problem getting trapped in local optima, a parameterized interpolation convex function as shown below is used: Where k s , ρ s and c p，s These represent the thermal conductivity, density, and specific heat capacity of a solid material, respectively; k f , ρ f and c p，f These are the thermal conductivity, density, and specific heat capacity of the fluid material, respectively.

5. The microchannel heat sink structure design method based on multi-objective functions according to claim 1, characterized in that, In S3, the multi-objective function is composed of a weighted sum of minimizing the average temperature and minimizing the flow dissipation, as shown in the following equation: Flow dissipation objective function: Objective function for average temperature: The function is transformed into an equivalent multi-objective function through dimensionless transformation and weighting. Simultaneously define weighting factors: Where w1 is the flow weight factor, w2 is the heat dissipation weight factor, and w1+w2=1.

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

7. The microchannel heat sink structure design method based on multi-objective functions according to claim 1, characterized in that, The filtering method in S5 is used to solve the grid dependency in the topology optimization process. It adopts a filtering scheme independent of the grid, expressed by the following formula: Density filtering is performed using the Helmholtz equation, as shown in the following expression: Where r is the set filtering radius, and γ is the design variable before filtering. These are the design variables after filtration. Manufacturing constraints are added during the filtration process, and the minimum filtration radius is the minimum flow channel size. This size is no greater than the precision of the processing method, thereby ensuring manufacturability and shortening the heat sink design cycle.

8. The microchannel heat sink structure design method based on a multi-objective function according to claim 1, characterized in that, In S5, the projection technology uses hyperbolic tangent projection as shown in the following formula to project the filtered design variables. A continuous projection strategy is adopted to obtain a clear channel topology optimization structure. in, These are the projected design variables, where β is the projection slope and γ is the projection slope. β It is the projection point.

9. The microchannel heat sink structure design method based on multi-objective functions according to claim 1, characterized in that, In S7, the pseudo-3D model can be obtained by stretching the two-dimensional topology optimization flow channel configuration.

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

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