Design method of micro-channel heat sink based on embedded profiled material and micro-channel heat sink obtained

Abstract

This invention relates to the field of radiator structure design technology, and provides a microchannel radiator design method based on embedded irregular materials and the obtained microchannel radiator, including: constructing a general mathematical description of the topology optimization problem; obtaining input conditions and dividing the topology optimization design domain; establishing the control equations of the topology optimization model, constructing a dual objective function, and performing sensitivity analysis of the multi-objective function with respect to design variables; solving the topology optimization model, and using filtering methods and projection techniques to obtain material distribution with clear fluid-structure boundaries; obtaining the two-dimensional flow channel configuration of the radiator, performing finite element analysis to obtain the temperature field and velocity field distribution, comprehensively evaluating the heat transfer performance, and determining the two-dimensional flow channel configuration; based on the two-dimensional flow channel configuration, constructing the corresponding three-dimensional model and performing finite element analysis to obtain the temperature field and velocity field distribution, evaluating the heat transfer performance using the PEC criterion, verifying the effectiveness of the method in three dimensions, and obtaining the final topology-optimized radiator configuration.

Description

Technical Field

[0001] This invention relates to the field of radiator structure design technology, and in particular to a microchannel radiator design method based on embedded irregular materials and the obtained microchannel radiator. Background Technology

[0002] In the field of ultra-precision manufacturing, thermal deformation of core components such as high-speed spindles and ball screws is a key factor leading to a decrease in machining accuracy, with thermal errors accounting for as much as 40% to 70% of the total error. Currently, this is mainly addressed through two technical approaches: thermal error compensation and active cooling. While thermal error compensation technology can provide post-processing correction, it cannot fundamentally solve the imbalance between heat generation and dissipation. Therefore, developing efficient active cooling systems is the fundamental way to control thermal deformation and ensure accuracy.

[0003] The performance of traditional cooling systems (such as air cooling and liquid cooling) directly determines the temperature field stability of components. However, these systems mostly rely on empirically designed fixed flow channels (such as spiral and straight channels), which have problems such as low heat dissipation efficiency and easy formation of local hot spots, making it difficult to meet the stringent requirements of temperature field uniformity in precision manufacturing.

[0004] Topology optimization technology automatically optimizes the flow channel layout by "distributing materials on demand," providing an effective solution to overcome the limitations of traditional cooling designs. Related research has applied this technology to various structural designs, including cold plates, water jackets, and radiators, significantly improving heat dissipation uniformity and efficiency. For example, using topology optimization in cold plate and water jacket designs improves the uniformity of temperature field distribution; novel heat dissipation structures such as spiderweb and leaf vein designs have also demonstrated superior heat dissipation performance in experiments. Furthermore, this technology has been extended to emerging fields such as lithium battery thermal management and 3D-printed integrated heat sinks, showcasing its wide applicability and good results in complex thermal management scenarios.

[0005] Although topology optimization has shown significant advantages in cooling channel design, current methods still have obvious limitations: Firstly, existing optimizations are mostly limited to the solid domain of a single material, failing to synergistically utilize the differences in properties between high and low thermal conductivity materials to achieve active guidance and blockage of heat flow paths; Secondly, the lack of a conjugate heat transfer topology optimization framework that can simultaneously optimize heat transfer paths in the solid and fluid domains of multiple materials results in limited design freedom and insufficient thermal control capabilities.

[0006] Therefore, there is an urgent need to develop a collaborative optimization method that integrates multi-material layout and flow channel topology to solve the problem of insufficient collaborative design of heterogeneous materials and cooling channels in complex thermal management scenarios. Summary of the Invention

[0007] The purpose of this invention is to address the problems existing in the background technology by proposing a design method for microchannel heat sinks based on embedded irregular materials and the resulting microchannel heat sink. The design method adopts a conjugate heat transfer multi-solid topology optimization method. Compared with traditional methods, the topology optimization design method of this invention can improve the thermal regulation performance of cooling channels, providing theoretical support and design methods for the development of high-performance composite cold plates.

[0008] To achieve the above objectives, the technical solution adopted by the present invention is as follows: In a first aspect, the present invention provides a microchannel heat sink design method based on embedded irregular materials, comprising the following specific steps: Step S1: Construct a general mathematical description of the topology optimization problem; Step S2: Obtain input conditions, including: radiator geometry, inlet and outlet boundary conditions, heat source boundary conditions, solid materials and fluid materials, and divide the topology optimization design domain; Step 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 materials to the fluid. An interpolation function is selected, and a dual objective function containing weighting factors is constructed. The dual objective function is composed of a weighted average of maximizing the total heat generation of the heat source and minimizing flow dissipation. Step S4: Perform sensitivity analysis of the multi-objective function with respect to the design variables based on the adjoint method; Step S5: Solve the topology optimization model using the SNOPT algorithm, and obtain the material distribution with clear fluid-solid boundaries using filtering methods and projection techniques. Iterate repeatedly until the convergence condition is met, and output the material distribution of the fluid and solid. Step S6: Obtain the two-dimensional flow channel configuration of the radiator based on the contour reconstruction, conduct finite element analysis of the two-dimensional flow channel structure, obtain the temperature field and velocity field distribution, and comprehensively evaluate the heat transfer performance by using the highest temperature, average temperature, inlet and outlet pressure difference, and root mean square temperature to determine the two-dimensional flow channel configuration. Step S7: Based on the two-dimensional flow channel configuration, construct the corresponding three-dimensional model and conduct finite element analysis to obtain the temperature field and velocity field distribution. Evaluate the heat transfer performance comprehensively using the average temperature, root mean square temperature, friction coefficient, average Nusselt number and performance evaluation criterion PEC, verify the effectiveness of the method in three dimensions, and obtain the final topology-optimized radiator configuration.

[0009] As a further technical solution, in S1 above, the mathematical model for topology optimization is as follows:

[0010]

[0011]

[0012]

[0013]

[0014]

[0015] In the formula, γ1 is the pseudo density value of the matrix domain; γ2 is the pseudo density value of the embedding domain; For J th The weighting coefficient of '; For J f The weighting coefficient of '; The overall thermal target for the design domain; Ω1 represents the total resistance target of the design domain; Ω2 represents the matrix domain; V1 represents the embedded domain; V2 represents the total volume of the matrix domain; V1* represents the upper bound of the volume fraction constraint of the matrix domain; V2* represents the upper bound of the volume fraction constraint of the embedded domain.

[0016] As a further technical solution, the geometric dimensions of the heat sink in step S2 include: heat sink length, width and thickness; Inlet and outlet boundary conditions include: fluid inlet temperature, inlet flow rate, 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 both solid and 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.

[0017] As a further technical solution, the interpolation function establishment process in step 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:

[0018]

[0019]

[0020]

[0021]

[0022]

[0023]

[0024]

[0025] Where: k1, C p1 ρ1 and α1 represent the thermal conductivity, specific heat capacity at constant pressure, density, and reverse osmosis in the matrix domain, respectively, while k2 and C p2 ρ² and α² represent the thermal conductivity, specific heat capacity at constant pressure, density, and reverse osmosis in the embedded domain, respectively, and k s1 , ρ s1 and C ps1 These are the thermal conductivity, density, and specific heat capacity at constant pressure of the first solid material, respectively; k s2 , ρ s2 and C ps2 These are the thermal conductivity, density, and specific heat capacity at constant pressure of the second solid material, respectively; k f , ρ f and c pf α represents the thermal conductivity, density, and specific heat capacity at constant pressure of the fluid material, respectively; μ represents the dynamic viscosity of the fluid; Da represents the Darcy number; and q represents the interpolation parameter for the variation trend of the adjustment function α1. ' represents the feature length.

[0026] As a further technical solution, the specific construction process of the dual objective function in step S3 is as follows: The heat source heat output of the matrix domain and the embedded domain is obtained, and the heat targets of the matrix domain and the embedded domain are added together to obtain the total heat target; The total potential energy of the matrix domain and the embedded domain is obtained, and the flow resistance targets of the matrix domain and the embedded domain are added together to obtain the total flow resistance target. After regularizing the total heat target and the total drag target, the targets are combined using weighting coefficients to construct a multi-objective function.

[0027] As a further technical solution, the filtering method in step S5 is used to solve the grid dependency in the topology optimization process, and density filtering is performed using the Helmholtz equation.

[0028] As a further technical solution, manufacturing constraints are added during the filtration process. The minimum filtration radius is the minimum flow channel size, which is less than or equal to the precision of the processing method, thereby ensuring manufacturability and shortening the heat sink design cycle.

[0029] As a further technical solution, in step S5, the projection technology uses hyperbolic tangent projection to project the filtered design variables and adopts a continuous projection strategy, thereby obtaining a clear channel topology optimization structure.

[0030] As a further technical solution, the three-dimensional model in step S7 is obtained by stretching the two-dimensional topology optimization flow channel configuration.

[0031] Secondly, the present invention also provides a microchannel heat sink structure, which is designed using the microchannel heat sink design method based on embedded irregular materials.

[0032] Compared with the prior art, the present invention has the following beneficial technical effects: This invention employs a porous medium assumption to simulate the distinction between the internal solid and fluid domains. Darcy's law, used to describe fluid flow in porous media, is used to represent the permeability of different design variables to the fluid. Material interpolation formulas are applied to each design variable to represent low- and high-thermal-conductivity materials, extending single-solid material optimization to multi-solid material optimization. A multi-objective function is constructed, consisting of a weighted average of maximizing the total heat generation of the heat source and minimizing flow dissipation. The sensitivity of the objective function to the design variables is solved using the adjoint method. The optimization model is solved using the SNOPT method (sequential quadratic programming), and filtering and projection processing are performed to obtain the fluid-solid material distribution. The two-dimensional flow channel configuration of the radiator was obtained by contour reconstruction extraction. Flow heat transfer simulation was carried out, and the heat transfer performance was comprehensively evaluated by the highest temperature, average temperature, inlet and outlet pressure difference, and root mean square temperature to determine the two-dimensional flow channel configuration. Based on the two-dimensional flow channel configuration, the corresponding three-dimensional model was constructed and finite element analysis was carried out to obtain the temperature field distribution. The heat transfer performance was comprehensively evaluated by the average temperature, root mean square temperature, friction coefficient, average Nusselt number, and performance evaluation criterion PEC, which verified the effectiveness of the method in three dimensions and obtained the final topology-optimized radiator configuration.

[0033] This method effectively optimizes the distribution of flow channels and dual-solid materials with different thermal conductivity, while simultaneously improving the thermal regulation performance of cooling channels by considering multiple objectives and constraints. This provides theoretical support and design methods for the development of high-performance composite material cold plate microchannel radiators. Furthermore, the composite material cold plate microchannel radiators designed using this method are relatively simple to fabricate and have lower costs. Attached Figure Description

[0034] Figure 1 This is a flowchart of the multi-solid topology optimization design method for conjugate heat transfer based on embedded heterogeneous materials, as described in this invention. Figure 2 These are description diagrams of the topology-optimized radiator size, design domain layout, inlet / outlet and boundary conditions of the present invention; wherein, (a) is a description diagram of ACP; and (b) is a description diagram of BCP. Figure 3 The diagrams show the flow channel shapes of traditional topology optimization and the topology optimization method of this invention at different Reynolds numbers; where (a), (b), and (c) are flow channel shapes of traditional topology optimization at Reynolds numbers of 100, 150, and 200, respectively; and (d), (e), and (f) are flow channel shapes of the topology optimization method of this invention at Reynolds numbers of 100, 150, and 200, respectively. Figure 4 These are the performance values ​​of the two models (ACP and BCP) of this invention at different Reynolds numbers, where (a) is the highest temperature T. max (b) represents the average temperature T. avg (c) represents the root mean square temperature T. σ (d) represents the pressure drop ΔP; Figure 5 These are the temperature and velocity field contour maps of the two models (ACP and BCP) of this invention at a Reynolds number of 200; where (a) and (b) are the velocity field contour maps of ACP and BCP, respectively; and (c) and (d) are the temperature field contour maps of ACP and BCP, respectively. Figure 6 These are graphs showing the changes in flow channels with the number of iterations during the topology optimization process of the two models (ACP and BCP) of this invention; where (a) is the ACP model and (b) is the BCP model. Figure 7 These are three-dimensional simulation models of the three models (ACP, BCP, and ARP) of this invention; where (a) is the ACP model; (b) is the BCP model; and (c) is the ARP model. Figure 8 These are the temperature fields after three-dimensional simulation of the three models (ACP, BCP, and ARP) of this invention, where (a), (b), and (c) are the temperature field cloud maps corresponding to the ACP, BCP, and ARP models, respectively. Figure 9 The three models of this invention (ACP, BCP, and ARP) are compared under different heat flux densities (q). a The performance curves are shown below, where (a) represents the average temperature T. avg With heat flux density q a The curve showing the change of temperature, (b) is the root mean square temperature T. σ With heat flux density q a The curve showing the change of friction coefficient f with heat flux density q is shown in (c). a The curve showing the change in the average Nusselt number (d) is shown. avg Curve showing the variation of heat flux density qa; Figure 10 This is the histogram distribution of the performance evaluation criteria (PEC) for the three models (ACP, BCP, and ARP) of this invention. Detailed Implementation

[0035] It should be noted that the following detailed description is illustrative and intended to provide further explanation of the invention. Unless otherwise specified, all technical and scientific terms used in this invention have the same meaning as commonly understood by one of ordinary skill in the art to which this invention pertains.

[0036] It should be noted that the terminology used herein is for the purpose of describing particular embodiments only and is not intended to limit the scope of exemplary embodiments according to the invention. As used herein, unless otherwise expressly indicated by the invention, the singular form is also intended to include the plural form. Furthermore, it should be understood that when the terms "comprising" and / or "including" are used in this specification, they indicate the presence of features, steps, operations, devices, components, and / or combinations thereof. As described in the background section, existing topology optimization techniques are mostly limited to single-material solid domains, failing to synergistically utilize the differences in properties between high and low thermal conductivity materials to actively guide and block heat flow paths. Furthermore, they lack a conjugate heat transfer topology optimization framework capable of simultaneously optimizing heat transfer paths within multi-material solid and fluid domains, resulting in limited design freedom and insufficient thermal control capabilities. Therefore, this embodiment proposes a microchannel heat sink design method based on embedded heterogeneous materials and the resulting microchannel heat sink. This method is a collaborative optimization approach that integrates multi-material layout and channel topology to address the challenge of insufficient collaborative design between heterogeneous materials and cooling channels in complex thermal management scenarios.

[0037] Definition: The ACP (All-Homogeneous Cooling Plate) model refers to a fully homogeneous cold plate model. The BCP (Boundary Composite Plate) model refers to the boundary composite cold plate model. The ARP (Arrayed Rectangular-channel Plate) model refers to an arrayed rectangular channel cold plate model. Example 1 This embodiment proposes a method for designing a liquid-cooled radiator structure based on conjugate heat transfer multi-solid topology optimization using embedded heterogeneous materials, comprising the following steps: Step 1: Construct a general mathematical model to describe the topology optimization problem. The mathematical model is as follows:

[0038]

[0039]

[0040]

[0041]

[0042]

[0043]

[0044] In this embodiment, the initial constraint condition of the topology optimization model is set, that is, the aforementioned constraint condition is the volume fraction. , and weighting factors , γ1 and γ2 are the pseudo-density values ​​of the matrix domain and the embedding domain, respectively. , J th 'and J f The weighting coefficient of '; and Ω1 and Ω2 represent the total thermal target and total drag target of the design domain, respectively; Ω1 and Ω2 represent the matrix domain and the embedded domain, respectively, which together constitute the design domain; V1 and V2 represent the total volume of the matrix domain and the total volume of the embedded domain, respectively; V1* and V2* represent the upper bound of the volume fraction constraint of the matrix domain and the upper bound of the volume fraction constraint of the embedded domain, respectively. Step 2: Determine the input conditions for the heat sink in this application scenario, including the heat sink's length, width, and thickness, and based on... The projections of the heat dissipation length and width form the topology optimization design domain, and the distribution and size of the heat sources are shown in Table 1. Table 1: Relevant Parameters of the Radiator

[0045] In this embodiment, the heat source adopts a uniform heat source distribution, and the length, width, and thickness of the heat dissipation plate are 120mm, 100mm, and 14mm, respectively. Figure 2 Where Lx is the length of the heat dissipation plate; Ly is the width of the heat dissipation plate; and L is the inlet and outlet widths. A conventional single-material topology-optimized cold plate is set as a control group, such as... Figure 2 As shown in (a) above. Composite cold-rolled steel sheets require clearly defined matrix domain Ω1 and embedded domain Ω2, as... Figure 2 As shown in (b); the two solid materials are 6061 aluminum alloy and copper, and the fluid material is water; and at the inlet boundary, the fluid velocity is equal to the given inlet velocity and the fluid temperature is equal to the given inlet temperature. Step 3: Establish the governing 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. An interpolation function is selected, and a dual objective function containing weighting factors is constructed. The dual objective function is composed of a weighted average of maximizing the total heat generation of the heat source and minimizing flow dissipation. The control equations in this embodiment are as follows:

[0046]

[0047] in, Here, ρ is the gradient operator, u is the velocity field, P is the pressure, and ρ is the pressure field. f μ and μ represent fluid density and dynamic viscosity, respectively; F is the volume force, used to simulate the frictional resistance effect of fluid flow in porous media.

[0048]

[0049]

[0050] Where T is the local temperature, T Q As an idealized heat source with a constant temperature, θ is the heat production coefficient used to adjust T. Q The proportional relationship between the temperature difference and the local temperature T, where Q is the heat generated per unit volume; and interpolation functions with different parameters are constructed based on the SIMP model:

[0051]

[0052]

[0053]

[0054] Among them, k1 and C p1 ρ1 and α1 represent the thermal conductivity, specific heat capacity at constant pressure, density and reverse permeability in the matrix domain, respectively; s1 and s2 represent two solid materials, respectively; γ1 is the pseudo density value of the matrix domain; Da is the Darcy number; and q is the interpolation parameter for adjusting the trend of the function α1.

[0055]

[0056]

[0057]

[0058]

[0059] Among them, k2 and C p2 ρ2 and α2 represent the thermal conductivity, specific heat capacity at constant pressure, density and reverse osmosis in the embedded domain, respectively; γ2 is the pseudo density value of the embedded domain; and q is the interpolation parameter for adjusting the trend of the α2 function. ' represents the feature length; The changes of γ1 and γ2 from 0 to 1 are represented by the Brinkman equation as the transition of the material from a solid to a fluid; where k s1 ρ s1 and C ps1 These are the thermal conductivity, density, and specific heat capacity at constant pressure of the first solid material, respectively; k s2 ρs2 and C ps2 These are the thermal conductivity, density, and specific heat capacity at constant pressure of the second solid material, respectively; k f ρ f and c pf These are the thermal conductivity, density, and specific heat capacity at constant pressure of the fluid material, respectively.

[0060] The multi-objective function is composed of a weighted average of maximizing the total heat generated by the heat source and minimizing flow dissipation, as shown in the following equation:

[0061]

[0062]

[0063] In the formula J th1 and J th2 The heat generation of the matrix domain and the embedded domain are respectively defined. By adding the heat targets of the matrix domain and the embedded domain, the total heat target J can be synthesized. th ;

[0064]

[0065]

[0066] In the formula J f1 and J f2 Let J be the total potential energy of the matrix domain and the embedded domain, respectively. By adding the flow resistance targets of the matrix domain and the embedded domain, the total flow resistance target J can be synthesized. f ; For the total heat target J th With total resistance target J f Perform regularization as follows:

[0067]

[0068] In the formula, J th,max and J th,min The total heat target J is respectively th The maximum and minimum values ​​of J f,max and J f,min The total flow resistance target J is respectively f The maximum and minimum values; The target J is weighted by the weighting coefficients. th 'and J f Combine them to construct a multi-objective function ,as follows:

[0069] Where ω1 and ω2 are J th 'Item and J f The weight coefficient of the item, and and The sum is 1.

[0070] Step 4: Perform sensitivity analysis of the multi-objective function with respect to the design variables based on the adjoint method; First, for each independent performance objective, an adjoint equation is constructed and solved based on its corresponding finite element governing equations to obtain its respective adjoint variable field. Then, using these adjoint fields, the derivatives of the current physical field and the element stiffness matrix with respect to the design variables, the sensitivity distribution of each performance objective relative to all design variables is calculated in parallel. Finally, these independent sensitivity information are combined into a complete gradient matrix, accurately quantifying the impact of modifying arbitrary local materials in the design on various global performance indicators, thus providing core data-driven basis for subsequent multi-objective trade-offs and decisions. This method, by reusing the overall stiffness matrix decomposition, ensures extremely high computational efficiency and is a key technology for handling complex multi-objective optimization problems in engineering.

[0071] Step 5: Based on the sensitivity results, use the SNOPT algorithm to find the improvement points for the current design variables. During the solution process, density filtering is performed using the Helmholtz equation, and the hyperbolic tangent projection method is used to analyze the filtered design variables. The quantities are projected, and a continuous projection strategy is used to ensure the convergence of the optimization problem.

[0072] The Helmholtz equation can be expressed as:

[0073]

[0074] Where, γ c γ is an unfiltered design variable. f To obtain the filtered solution by solving the partial differential equation, R min This is the length parameter of the filter radius. These parameters are defined as γ in the matrix domain. c1 ,γ f1 and R min1 In the embedding domain, they are respectively defined as γ c2 ,γ f2 and R min2 That is: γ c1 ,γ f1 and R min1These represent the unfiltered design variables in the matrix domain, the filtered solution obtained by solving partial differential equations in the matrix domain, and the filtered solution obtained by solving partial differential equations in the matrix domain, respectively. The hyperbolic tangent projection method is expressed as:

[0075]

[0076] Where γ is the projected design variable, β is the projection slope, and γ β These are the projection points; γ1, β1, γ β1 These represent the design variables, projection slope, and projection point of the matrix domain, respectively, γ2, β2, and γ. β2 These are the design variables, projection slope, and projection point of the embedded domain, respectively.

[0077] The maximum number of iterations in a single calculation is 200, 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.

[0078] Step Six: The material distribution is transformed into a two-dimensional flow channel configuration using the contour extraction method. Since the flow conjugate heat transfer model was simplified in the topology optimization model, a new finite element analysis is performed based on the two-dimensional results. The temperature field and velocity field are as follows: Figure 5 As shown. The heat transfer performance was comprehensively evaluated using the highest temperature, average temperature, inlet and outlet pressure difference, and root mean square temperature, and the two-dimensional flow channel configuration was determined, as shown. Figure 3 and Figure 4 As shown, the heat dissipation flow channel with a Reynolds number of 200 was ultimately selected; Figure 6 This demonstrates the changes in the flow channel during the optimization process; Step 7: Two-dimensional topology optimization heat dissipation channels are formed through post-processing and encapsulation, such as stretching, as shown in the attached figure. Figure 7 The three-dimensional heat dissipation cold plate models shown in (a) and (b) are used as a reference to establish a rectangular parallel flow channel cold plate. Figure 7 (c) in the figure; where Z represents the thickness of the heat dissipation plate; further, finite element analysis is performed to obtain the temperature field distribution, such as Figure 8 As shown; Figure 8 In this context, T represents temperature; T max Indicates the highest temperature; Furthermore, through average temperature Root mean square temperature Friction coefficient f, mean Nusselt number Nu avg The performance evaluation criteria of PEC comprehensively evaluate the heat transfer performance, such as Figure 9 and Figure 10The effectiveness of the method in three dimensions was verified, and the final topology-optimized heatsink configuration was obtained.

[0079] The average temperature is defined as:

[0080] Where: T is the fluid (or solid) temperature at any point in space within the computational domain Ω; Ω is the computational domain; The average temperature characterizes the overall hotness or coldness of the entire computational region and is a spatially weighted average of the temperature field.

[0081] The root mean square temperature is defined as:

[0082] The root mean square (RMS) temperature is used to measure the uniformity of temperature distribution within the computational domain. The smaller the value, the more uniform the temperature distribution; the larger the value, the more pronounced the unevenness of heating and cooling.

[0083] The friction coefficient f is defined as:

[0084] Where ΔP represents the pressure drop within the channel, W is the length of the channel from the inlet to the outlet, and D... h It is the hydraulic diameter of the channel, ρ f U represents the fluid density. avg It is the average velocity of the fluid region, and it is calculated as follows:

[0085] Average velocity characterizes the overall speed of fluid flow throughout the channel.

[0086] The average Nusselt number is Nu avg Defined as:

[0087] Mean Nusselt number avg Characterizes the intensity of convective heat transfer; the larger the value, the more intense the heat exchange between the fluid and the wall; where k f h is the thermal conductivity of the fluid. avg The average heat transfer coefficient is calculated using the following formula:

[0088] Average heat transfer coefficient It is a core indicator for measuring heat exchange capacity, representing the amount of heat exchanged per unit heat exchange area and per unit temperature difference; where Q w Indicates the heat applied to the heated surface; A eff Indicates the effective heat transfer area; T wall and T fThese are the average wall temperature and the average fluid temperature, respectively. The performance evaluation criterion PEC is defined as follows:

[0089] Performance evaluation criteria are the core judgment for heat exchanger optimization, comprehensively evaluating the "heat exchange benefits - resistance costs" of enhancing the heat exchange structure. Among them, Nu... avg,0 f0 and f0 are Nu avg And the reference value of f.

[0090] Comparative verification of the flow heat dissipation performance of topology-optimized liquid-cooled microchannel radiators: The three-dimensional model was used to conduct flow and heat transfer simulations under the same operating conditions, specifically: inlet temperature 20℃, inlet velocity 0.02m / s, and a uniform surface heat source of 20000 W / m². 2 .

[0091] The specific simulation results are shown in Table 2. Figure 8 , Figure 9 and Figure 10 As shown: Table 2: Performance parameters of the 3D model under the same working conditions

[0092] After optimizing the radiator structure using the method of this invention, the BCP type cold plate T avg and T σ Compared to ARP, the values ​​decreased by 17.37K (5.07%) and 6.73K (45.6%) respectively, for BCP type cold-rolled steel plate T. avg and T max The decreases of 1.44K (0.42%) and 1.91K (0.57%) compared to ACP indicate that the heat sink designed by the topology optimization method proposed in this invention is significantly better than the rectangular parallel microchannel heat sink in all aspects, and is also better than the traditional topology-optimized microchannel heat sink in all aspects.

[0093] This embodiment uses the porous medium assumption to simulate the distinction between the internal solid and fluid domains, and introduces volume forces based on the Brinkman equation. The distribution of the solid and fluid regions is determined by the permeability. Based on the SIMP (Solid Isotropic Material Penalty Method) model, interpolation functions for different physical property parameters are constructed. A multi-objective function is constructed, which is a weighted combination of maximizing the total heat generation of the heat source and minimizing the flow dissipation. The sensitivity of the objective function with respect to the design variables is solved by the adjoint method. The optimization model is solved by the SNOPT (Sequential Quadratic Programming) method. 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.

[0094] Two-dimensional topology-optimized flow channels are obtained by contour extraction based on material distribution. Flow heat transfer simulation is carried out, and heat transfer performance is comprehensively evaluated by the highest temperature, average temperature, inlet and outlet pressure difference, and root mean square temperature to determine the two-dimensional flow channel configuration. Based on the two-dimensional flow channel configuration, the corresponding three-dimensional model is constructed and finite element analysis is carried out to obtain the temperature field distribution. The heat transfer performance is comprehensively evaluated by the average temperature, root mean square temperature, friction coefficient f, average Nusselt number Nu, and performance evaluation criterion PEC, which verifies the effectiveness of the method in three dimensions and obtains the final topology-optimized radiator configuration.

[0095] This method effectively optimizes the distribution of flow channels and dual-solid materials with different thermal conductivity, while simultaneously improving the thermal regulation performance of cooling channels by considering multiple objectives and constraints. This provides theoretical support and design methods for the development of high-performance composite material cold plate microchannel radiators. Furthermore, the composite material cold plate microchannel radiators designed using this method are relatively simple to fabricate and have lower costs.

[0096] The core of this method lies in characterizing various material properties through multiple design variables. Therefore, all topology optimization methods based on this principle should be included within the scope of protection of this invention.

[0097] Example 2 This embodiment provides a microchannel heat sink structure, which is designed using the microchannel heat sink design method based on embedded irregular materials described in Embodiment 1.

[0098] The embodiments of the present invention have been described in detail above with reference to the accompanying drawings and tables. 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.

[0099] The above description is merely a preferred embodiment of the present invention and is not intended to limit the invention. Various modifications and variations can be made to the present invention by those skilled in the art. Any modifications, equivalent substitutions, improvements, etc., made within the spirit and principles of the present invention should be included within the scope of protection of the present invention.

Claims

1. A microchannel heat sink design method based on embedded irregular materials, characterized in that, Includes the following steps: Step S1: Construct a general mathematical model description of the topology optimization problem; Step S2: Obtain input conditions, including: radiator geometry, inlet and outlet boundary conditions, heat source boundary conditions, solid materials and fluid materials, and divide the topology optimization design domain; Step 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 materials to the fluid. An interpolation function is selected, and a dual objective function containing weighting factors is constructed. The dual objective function is composed of a weighted average of maximizing the total heat generation of the heat source and minimizing flow dissipation. Step S4: Perform sensitivity analysis of the multi-objective function with respect to the design variables based on the adjoint method; Step S5: Solve the topology optimization model using the SNOPT algorithm, 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. Step 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 highest temperature, average temperature, inlet and outlet pressure difference and root mean square temperature to determine the two-dimensional flow channel configuration. Step S7: Based on the two-dimensional flow channel configuration, construct the corresponding three-dimensional model and conduct finite element analysis to obtain the temperature field and velocity field distribution. Evaluate the heat transfer performance comprehensively using the average temperature, root mean square temperature, friction coefficient, average Nusselt number and performance evaluation criterion PEC, verify the effectiveness of the method in three dimensions, and obtain the final topology-optimized radiator configuration.

2. The microchannel heat sink design method based on embedded irregular materials as described in claim 1, characterized in that, In step S1, the mathematical model is as follows: In the formula, γ1 is the pseudo density value of the matrix domain; γ2 is the pseudo density value of the embedding domain; For J th The weighting coefficient of '; For J f The weighting coefficient of '; The overall thermal target for the design domain; Ω1 represents the total resistance target of the design domain; Ω2 represents the matrix domain; V1 represents the embedded domain; V2 represents the total volume of the matrix domain; V1* represents the upper bound of the volume fraction constraint of the matrix domain; V2* represents the upper bound of the volume fraction constraint of the embedded domain.

3. The microchannel heat sink design method based on embedded irregular materials as described in claim 1, characterized in that, The geometric dimensions of the heat sink in step S2 include: the length, width, and thickness of the heat sink; 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 the given scenario, and are either uniform heat flow boundary conditions or non-uniform heat flow boundary conditions. For both solid and 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 design method based on embedded irregular materials as described in claim 1, characterized in that, The interpolation function establishment process in step 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 used: Where: k1, C p1 ρ1 and α1 represent the thermal conductivity, specific heat capacity at constant pressure, density, and reverse osmosis in the matrix domain, respectively, while k2 and C p2 ρ² and α² represent the thermal conductivity, specific heat capacity at constant pressure, density, and reverse osmosis in the embedded domain, respectively, and k s1 , ρ s1 and C ps1 These are the thermal conductivity, density, and specific heat capacity at constant pressure of the first solid material, respectively; k s2 , ρ s2 and C ps2 These are the thermal conductivity, density, and specific heat capacity at constant pressure of the second solid material, respectively; k f , ρ f and c pf α represents the thermal conductivity, density, and specific heat capacity at constant pressure of the fluid material, respectively; μ represents the dynamic viscosity of the fluid; Da represents the Darcy number; and q represents the interpolation parameter for the variation trend of the adjustment function α1. ' represents the feature length; γ1 represents the pseudo-density value of the matrix domain; γ2 represents the pseudo-density value of the embedding domain.

5. The microchannel heat sink design method based on embedded irregular materials as described in claim 1, characterized in that, The specific construction process of the dual objective function in step S3 is as follows: The heat source heat output of the matrix domain and the embedded domain is obtained, and the heat targets of the matrix domain and the embedded domain are added together to obtain the total heat target; The total potential energy of the matrix domain and the embedded domain is obtained, and the flow resistance targets of the matrix domain and the embedded domain are added together to obtain the total flow resistance target. After regularizing the total heat target and the total drag target, the targets are combined using weighting coefficients to construct a bi-objective function.

6. The microchannel heat sink design method based on embedded irregular materials as described in claim 1, characterized in that, The filtering method in step S5 is used to solve the grid dependency problem in the topology optimization process, and density filtering is performed using the Helmholtz equation.

7. The microchannel heat sink design method based on embedded irregular materials as described in claim 6, characterized in that, Manufacturing constraints are added during the filtration process, and the minimum filtration radius is the minimum flow channel size. The minimum flow channel size is less than or equal to the precision of the processing method.

8. The microchannel heat sink design method based on embedded irregular materials as described in claim 1, characterized in that, In step S5, the projection technique uses hyperbolic tangent projection to project the filtered design variables. By adopting a continuous projection strategy, a clear flow channel topology optimization structure can be obtained.

9. The microchannel heat sink design method based on embedded irregular materials as described in claim 1, characterized in that, In step S7, the three-dimensional model is obtained by stretching the two-dimensional topology optimization flow channel configuration.

10. A microchannel heat sink structure, characterized in that, The design is carried out using the microchannel heat sink design method based on embedded irregular materials as described in any one of claims 1-9.

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