Tree-shaped cold plate channel free-form surface modeling and optimization design method

Abstract

The application discloses a tree-shaped cold plate channel free-form surface modeling and optimization design method, which comprises the determination of the cold plate entrance and exit position, geometric size and physical boundary parameters; based on the determined tree-shaped flow channel skeleton, further tree-shaped structure features are provided; the same branch is processed in segments, the branch layer inter-topology relationship construction and branch layer internal free modeling two processes are distinguished, and a more natural and flexible tree-shaped modeling framework is provided; cubic B-spline function and Bernstein function are adopted to characterize the channel mode, the elliptical cross section shape and size and channel torsion; the parameters for controlling the geometric features are taken as the design variables; the non-dominated sorting genetic algorithm II (NSGA-II) is adopted to optimize the tree-shaped flow channel distribution, and the design variables are normalized to improve the optimization stability. The application takes the minimum average temperature and the minimum temperature root mean square of the specified plane as the target, and improves the heat dissipation performance by optimizing the structural distribution of the tree-shaped channel radiator.

Description

Technical Field

[0001] This invention belongs to the field of electronic equipment technology, specifically relating to a method for free-form surface modeling and optimization design of tree-shaped cold plate channels. Background Technology

[0002] Thermal management has been widely applied in various engineering applications, such as electric and hybrid electric vehicles, electronic chips, robots, wearable devices, and motors. Currently, with the continuous emergence of miniaturization, high integration, and high energy density requirements, the importance of thermal management is constantly increasing, even becoming a core design element. Conjugate heat transfer, as an efficient cooling strategy, is commonly used in thermal management design, including liquid cooling and air cooling. However, structural design plays a crucial role in the three processes of heat generation, heat transfer, and heat dissipation, forming the foundation for subsequent designs. In recent decades, research on improving the cooling performance of radiators by providing various geometric structures has been extensively developed. Tree-like structures are ubiquitous in nature, such as plant roots, leaves, respiratory systems, and river networks; these structures can be considered optimal solutions and structures resulting from long-term natural selection and evolution. Therefore, many researchers have conducted studies on the flow and heat transfer performance of tree-like structures in various applications, such as cold plates, finned radiators, and heat exchangers. Interestingly, many studies have found that structures obtained through topology optimization design (conceptual design methods) possess tree-like structures, further demonstrating the advantages of this structure in improving heat transfer performance. In the fine design of tree-like structures, most research focuses on T-type, Y-type, or hybrid TY-type tree channels to improve the heat transfer performance of radiators. The tree-like features studied mainly include branch angles, branch lengths, branch layers, number of branches, and corresponding cross-sectional shapes and dimensions. However, it is worth reflecting on the fact that, with the increasing demands of thermal management, these fixed forms limit further exploration of the potential of tree-like structures to improve cooling performance.

[0003] The existing technology has the following drawbacks:

[0004] 1. Existing tree-like channel design and analysis only focus on two-dimensional configurations, and then obtain three-dimensional configurations through simple stretching.

[0005] 2. Its design process relies heavily on the designer's experience and inspiration, the entire design process is time-consuming, and whether the obtained design is optimal usually requires a long period of discussion and optimization.

[0006] 3. Most designs are limited to tree-like branch angles, branch lengths, number of branches, and branch levels, involving limited geometric features. This weakens the potential of the geometry to enhance heat transfer performance, and the resulting designs are conventional with limited heat exchange efficiency.

[0007] 4. Corresponding geometric features are usually set to fixed values. Although some designs have optimized the geometric features, fixed forms and sizes are not conducive to further exploring the heat transfer law and improving the performance of the tree structure.

[0008] 5. Due to limitations in design methodology, traditional tree-shaped flow channels have always tended to design square channels, with other cross-sectional forms rarely being considered.

[0009] 6. Traditional tree-like structure designs typically do not incorporate longitudinal and transverse waves to improve the heat transfer performance of the cold plate. Summary of the Invention

[0010] The purpose of this invention is to provide a method for free-form surface modeling and optimization design of tree-shaped cold plate channels. This method removes the constraints of geometric structure and dimensions on heat transfer performance, and aims to achieve the minimum average temperature and root mean square minimum temperature on a specified plane. By optimizing the layout of the tree-shaped flow channel cold plate structure, it further improves heat dissipation performance.

[0011] The technical solution adopted in this invention is: a method for modeling and optimizing the free-form surface of a tree-shaped cold plate channel, comprising the following steps:

[0012] (1) Determine the surface heat flux density of the power devices, the external dimensions of the cold plate, and the inlet and outlet positions of the flow channels based on the configuration of the electronic equipment on site;

[0013] (2) Based on the determined heat flux density and external dimensions, determine the geometric dimensions of the inlet and outlet of the flow channel, the heat transfer properties, the flow properties, and the material properties of the heat dissipation system;

[0014] (3) Based on the determined cold plate dimensions, construct a tree-like flow channel skeleton by parameterizing the rotation and translation matrices;

[0015] (4) Based on the determined skeleton, determine the basic topological relationships between the branch layers;

[0016] (5) Based on the determined branch layer topology, the length of each branch is divided into three parts, and each length is further normalized.

[0017] (6) Based on the normalized branch parts, construct the geometric and topological relationships between and within the branch layers in each branch, including channel patterns, channel cross sections and channel torsion.

[0018] (7) Based on the determined tree-like flow channel model, further parameterize and construct the connection between the tree-like flow channel and the parallel flow channel;

[0019] (8) Based on engineering requirements, construct the design variables of the optimization framework, including the control coefficients of the cubic B-spline function characterizing the channel mode; the control coefficients of the Bernstein function characterizing the channel cross section and channel torsion; and the control parameters of the tree-like geometric feature variables; construct the objective function of the optimization framework, and use minimizing the average temperature and root mean square temperature of the upper and lower surfaces of the cold plate as indicators for optimizing the overall performance and temperature distribution uniformity of the cold plate.

[0020] (9) Based on the shape optimization model, apply boundary conditions to establish a finite element model of the cold plate with tree-like and parallel channels;

[0021] (10) Based on the finite element model of the cold plate, the objective function is optimized by non-dominated sorting genetic algorithm II to obtain the temperature distribution of the cold plate and the surface of the power device.

[0022] The technical solution adopted in this invention is also characterized by:

[0023] Furthermore, in steps (1) and (2), the external dimensions of the cold plate include length L, width W, and height H; the inlet / outlet geometric parameters include inlet diameter D. in and D out The heat transfer properties include the inlet fluid problem T. in The thermal boundary of the external wall and the distance from the heat source Q; the flow property parameters include the inlet flow velocity U. in and export pressure P out The heat dissipation system is made of solid aluminum 6061-T6 and liquid transport medium water, and its properties include: solid thermal conductivity k s Fluid thermal conductivity k f Specific heat capacity of fluid at constant pressure C p And fluid density ρ.

[0024] Furthermore, in step (3), a tree-like flow channel skeleton is constructed by parameterizing the rotation and translation matrices. The fitting is performed in the XOY plane, where Z is the height direction; the rotation and translation matrices are given by formula (1):

[0025]

[0026] Where t and θ are the parameter variables for constructing the tree-like skeleton and subsequent modeling; in the first term, X(t, θ), Y(t, θ), and Z(t, θ) are the spatial positions of the corresponding geometric features in the full coordinate system. Geometric features include points, lines, and surfaces; a point is represented by no parameter variable, a line by one parameter variable, and a surface by two parameter variables; the second and third terms are the spatial parameters of the geometric features in the fourth term, x(t, θ), y(t, θ), and z(t, θ), rotated to the full coordinate system in the local coordinate system. The second term is the rotation around the Z-axis. It is its rotation amount, the third item is the rotation about the Y-axis. The first term is the rotation amount; the fifth term is the translation amount from local to global. When constructing the tree-like skeleton, since the operation is performed in the XOY plane, the third term needs to be removed, and since the skeleton is a line feature, only t is retained as a parameter variable.

[0027] Furthermore, in step (4), the basic topological relationships between the branch layers are determined according to formula (2):

[0028]

[0029] Where m represents the m-th branch layer of the tree-like flow channel, P m This indicates the Pth branch within that branch layer. m One branch; and Representing the m-th branch layer and P-th branch layer respectively m The channel diameter of the branch is related to the Pth branch of the (m+1)th branch layer. m+1 The diameter of the channel for each branch; and Representing the m-th branch layer and P-th branch layer respectively m The terminal cutoff distance of each branch and the Pth branch of the (m+1)th branch level m+1 The truncation distance at the beginning of each branch; Represents the Pth branch of the m-th branch layer. m The bifurcation angle of each branch at its end is...

[0030] Furthermore, in step (5), the length of each branch is divided into three parts, and each length is further normalized, as expressed in formula (3):

[0031]

[0032] Where w is the new parameter variable replaced by the normalized variable; t a t b and t c These represent the variable expressions for segment 1, segment 2, and segment 3 after the new parameter variable replaces the original parameter variable t; t1 and t2 are the positions of two nodes that divide a branch length into three parts.

[0033] Furthermore, in step (6), the geometric and topological relationships between and within each branch layer are constructed respectively; wherein, the relationships between branch layers are constructed within segment 1 and segment 3, and the geometric features within a branch layer are constructed within segment 2, as follows:

[0034] (6a) Construct segment 1 according to formula (4):

[0035] here

[0036] Among them, segment 1 uses new parameter variables. Replace the original parameter variable t with the surface features of the first section of the tree-like flow channel; Represents the Pth branch of m branch layers. m The branch length of each branch; t a (θ) is an intermediate variable;

[0037] (6b) Construct segment 3 according to formula (5):

[0038] here

[0039] Among them, segment 3 uses new parameter variables. Replace the original parameter variable t to establish the surface features of the end portion of the tree-like flow channel; t c (θ) is an intermediate variable;

[0040] (6c) Within the branch layer of segment 2, the geometric features of channel pattern, channel cross section, and channel torsion can be established, and their parameters are expressed by formulas (6), (7), and (8):

[0041]

[0042] Where d(t) represents the initial point located on the tree skeleton. The normal distance to the final centerline point (x0(t), y0(t), z0(t) = C0) is represented by a cubic B-spline function, which has a total of P+1 control points; at the same time, since it operates in the XOY plane, C0 is half the value of the given H.

[0043]

[0044] The elliptical channel section is constructed, with two geometric features: the major axis a(t) and the minor axis b(t), both characterized by Bernstein functions; the corresponding control coefficients are a0, b ... and b0, respectively. j and b j And the maximum power value is n;

[0045]

[0046] The channel torsion is still characterized by the Bernstein function; the corresponding control coefficient is φ. j And the maximum power value is q.

[0047] Furthermore, in step (7), the connection between the tree-like flow channel and the parallel flow channel is further parameterized and constructed, and its expression is formula (9):

[0048]

[0049] here

[0050]

[0051] The coordinates of the endpoint of the last tree branch are respectively and It is the radius of the auxiliary circle connecting the tree-like channels and the parallel channels. It is the ratio of the radius of the auxiliary circle to the radius of the last branch channel; It is a unified parameter to avoid inconsistencies in expressions due to different symbols. This is to avoid excessively small negative values; the final connecting arc is formed by... Characterization.

[0052] Furthermore, in step (8), a shape optimization framework is established as shown in formula (10):

[0053]

[0054] Wherein, ω is a normalized vector group composed of design variables, including control coefficients for tree-like geometric features (branch angle, number of branches, branch layer, number of branches); control coefficients for cubic B-spline functions characterizing channel patterns; and control coefficients for Bernstein functions characterizing channel cross-sections and channel torsion. To determine the average temperature of the surface, RMST is the root mean square temperature of the surface, Ω is the integration domain, T is the temperature field in that domain, dΩ represents the differentiation with respect to the specified surface, and ∫ is the integral sign.

[0055] Furthermore, in step (9), an unstructured tetrahedral mesh is used to establish a finite element model.

[0056] Furthermore, in step (10), the Non-Dominated Sorting Genetic Algorithm II (NSGA-II) is used, with the corresponding population size P and iteration number G set, and the relevant convergence criteria set as shown in formula (11):

[0057]

[0058] This formula indicates that the iteration will terminate if the last six iterations remain unchanged; p max This represents the maximum population size; the subscripts p and gen represent the population size and the current iteration number, respectively.

[0059] The beneficial effects of this invention are:

[0060] 1. The method proposed in this invention can effectively perform free modeling of three-dimensional tree structure models, including tree features (branch angle, branch level, branch length, number of branches), channel patterns, elliptical cross-sectional shape and size, and channel twisting, etc.

[0061] 2. The method proposed in this invention uses cubic B-spline functions and Bernstein functions as geometric features representing the tree structure. This is mainly because: cubic B-spline functions can be accessed through specific points and have continuous first derivatives, which is beneficial for constructing boundary-sensitive geometric features, such as preventing adjacent channels from colliding during optimization. Bernstein functions can control the overall trend of the formed Bézier curve with only a few points, which is beneficial for constructing a compact, simple optimization system that does not require redundant design variables.

[0062] 3. In the method proposed in this invention, an entire tree-like branch is divided into three segments, and the parameter variables representing the segments are redefined. This process helps to distinguish between the construction of topological relationships between branch layers and the free modeling within branch layers, enabling a more natural and flexible design process to be explored while satisfying the tree-like topological relationships.

[0063] 4. The method proposed in this invention provides a modeling system for tree-like structures, which can largely explore tree-like structures that satisfy the heat transfer structure law through optimization techniques, thereby obtaining radiators that are more conducive to heat transfer. The optimized radiator has a more reliable temperature distribution, which is beneficial to engineering practice.

[0064] 5. The method proposed in this invention, combined with computer-aided analysis, further proposes an optimization framework to explore the impact of high geometrical degrees of freedom on the heat transfer performance of cold plates with tree-like channels.

[0065] 6. The method proposed in this invention reduces the influence of the designer's experience and inspiration on the final structural layout, thereby improving the robustness of the design method.

[0066] 7. The modeling framework proposed in this invention can provide a parameterized interface for arbitrary cross-sectional shapes and sizes, enabling research and discussion on different cross-sections.

[0067] 8. The method proposed in this invention, through modeling and optimization, introduces longitudinal and transverse waves in the direction of fluid flow, which helps to break the flow and heat transfer boundary layer and effectively improves heat transfer performance.

[0068] 9. The design obtained by the method proposed in this invention conforms to the structural laws of heat transfer. Attached Figure Description

[0069] Figure 1 This is a flowchart of the optimized design method for the tree-shaped flow channel conjugate heat transfer radiator of the present invention;

[0070] Figure 2 This is a schematic diagram of the three-dimensional conjugate heat transfer radiator structure in this invention;

[0071] Figure 3 This is a temperature distribution diagram of the upper surface of the heat sink before optimization by the method of the present invention;

[0072] Figure 4 This is a temperature distribution diagram of the upper surface of the optimal heat sink structure after optimization by the method of this invention;

[0073] Figure 5 This is a diagram showing the heat sink flow channel configuration and temperature distribution before optimization using the method of this invention;

[0074] Figure 6 Figure 1 shows the optimal heat sink flow channel configuration and temperature distribution after optimization by the method of this invention.

[0075] Figure 7 Figure 2 shows the optimal heat sink flow channel configuration and temperature distribution after optimization by the method of this invention.

[0076] Figure 8 The goal of this invention is to minimize the average surface temperature and the Pareto front plot of the root mean square temperature. Detailed Implementation

[0077] The present invention will be further described below with reference to the accompanying drawings and specific embodiments.

[0078] like Figure 1 As shown, the method for modeling and optimizing the free-form surface of a tree-shaped cold plate channel involves the following specific steps:

[0079] Step 1: Determine the surface heat flux density of the power device and the basic external dimensions of the cold plate, as well as the inlet and outlet positions of the flow channels;

[0080] Based on the configuration of the electronic equipment on site, determine the surface heat flux density Q of the power devices; the external dimensions of the heat sink: length L, width W, height H; and the location of the inlet and outlet, such as... Figure 2 As shown;

[0081] Step 2: Determine the physical boundary parameters and corresponding physical property parameters of the cold plate;

[0082] Based on the determined heat flux density and cold plate dimensions, the inlet and outlet geometric parameters, including the inlet diameter D, are determined. in and D out Heat transfer properties include inlet fluid T. in The thermal boundary of the external wall and the distance from the heat source Q; flow property parameters include the inlet velocity U. in and export pressure P outThe heat dissipation system materials include solid aluminum 6061-T6 and liquid transport medium water, whose properties include: solid thermal conductivity kJ / L. s Fluid thermal conductivity k f Specific heat capacity of fluid at constant pressure C p and fluid density ρ;

[0083] Step 3: Determine the framework of the tree-like flow channel;

[0084] A tree-like flow channel skeleton is constructed by parameterizing rotation and translation matrices. Each branch only considers the spatial positions of its first and last ends. Starting from the first branch, other branches with topological relationships are derived layer by layer based on their spatial positions. The fitting is performed in the XOY plane, where Z is the height direction. The rotation and translation matrices are given by formula (1):

[0085]

[0086] Where t is the parameter variable for constructing the tree-like skeleton; X(t), Y(t), and Z(t) in the first term are the spatial positions of the corresponding skeleton geometric features in the global coordinate system; the second term is the spatial parameter of rotating the spatial positions x(t), y(t), and z(t) of the skeleton's beginning and end points in the local coordinate system (the third term) to the global coordinate system, where the second term is the rotation around the Z-axis. The first term is its rotation; the fourth term is the translation from local to global.

[0087] Step 4: Determine the basic topological relationships between branch layers according to formula (2):

[0088]

[0089] Where m represents the m-th branch layer of the tree-like flow channel, P m This indicates the Pth branch within that branch layer. m One branch; and Representing the m-th branch layer and P-th branch layer respectively m The channel diameter of the branch is related to the Pth branch of the (m+1)th branch layer. m+1 The diameter of the channel for each branch; and Representing the m-th branch layer and P-th branch layer respectively m The terminal cutoff distance of each branch and the Pth branch of the (m+1)th branch level m+1 The truncation distance at the beginning of each branch; Represents the Pth branch of the m-th branch layer. m The bifurcation angle of each branch at its end is...

[0090] Step 5: Divide the length of each branch into three parts, and further normalize each length, as expressed in formula (3):

[0091]

[0092] Where w is the new parameter variable replaced by the normalized variable; t a t b and t c These represent the variable expressions for segment 1, segment 2, and segment 3 after the new parameter variable replaces the original parameter variable t; t1 and t2 are the positions of two nodes that divide a branch length into three parts.

[0093] Step 6: Construct the geometric and topological relationships between and within branch layers;

[0094] (6a) Construct segment 1 according to formula (4):

[0095] here

[0096] Among them, segment 1 uses new parameter variables. Replace the original parameter variable t with the surface features of the first section of the tree-like flow channel; Represents the Pth branch of m branch layers. m The branch length of each branch; t a (θ) is an intermediate variable;

[0097] (6b) Construct segment 3 according to formula (5):

[0098] here

[0099] Among them, segment 3 uses new parameter variables. Replace the original parameter variable t to establish the surface features of the end portion of the tree-like flow channel; t c (θ) is an intermediate variable;

[0100] (6c) Within the branch layer of segment 2, the geometric features of channel pattern, channel cross section, and channel torsion can be established, and their parameters are expressed by formulas (6), (7), and (8):

[0101]

[0102] Where d(t) represents the initial point located on the tree skeleton. The normal distance to the final centerline point (x0(t), y0(t), z0(t) = C0) is represented by a cubic B-spline function, which has a total of P+1 control points; at the same time, since it operates in the XOY plane, C0 is half the value of the given H.

[0103]

[0104] The elliptical channel section is constructed, with two geometric features: the major axis a(t) and the minor axis b(t), both characterized by Bernstein functions; the corresponding control coefficients are a0, b ... and b0, respectively. j and b j And the maximum power value is n;

[0105]

[0106] The channel torsion is still characterized by the Bernstein function; the corresponding control coefficient is φ. j And the maximum power value is q;

[0107] Step 7, construct the connection between the tree-like flow channel and the parallel flow channel; the construction expression is formula (9):

[0108]

[0109] here

[0110]

[0111] The coordinates of the endpoint of the last tree branch are respectively and It is the radius of the auxiliary circle connecting the tree-like channels and the parallel channels. It is the ratio of the radius of the auxiliary circle to the radius of the last branch channel; It is a unified parameter to avoid inconsistencies in expressions due to different symbols. This is to avoid excessively small negative values; the final connecting arc is formed by... Characterization;

[0112] Step 8: Establish shape optimization criteria;

[0113] The shape optimization framework is established as shown in formula (10):

[0114]

[0115] Wherein, ω is a normalized vector group composed of design variables, including control coefficients for tree-like geometric features (branch angle, number of branches, branch layer, number of branches); control coefficients for cubic B-spline functions characterizing channel patterns; and control coefficients for Bernstein functions characterizing channel cross-sections and channel torsion. To determine the average temperature of the surface, RMST is the root mean square temperature of the surface, Ω is the integration domain, T is the temperature field in the domain, dΩ represents the differentiation with respect to the specified surface, and ∫ is the integral sign.

[0116] Step 9: Based on the shape optimization model, apply boundary conditions to establish a finite element model of the cold plate with tree-like and parallel channels;

[0117] Step 10: Based on the finite element model of the cold plate, the non-dominated sorting genetic algorithm II (NSGA-II) is used to optimize the objective number to obtain the improved temperature distribution of the specified surface of the cold plate (the surface where the power devices are placed).

[0118] The Non-Dominated Sorting Genetic Algorithm II (NSGA-II) is adopted, with the corresponding population size P and iteration number G set, and the relevant convergence criterion set as shown in formula (11):

[0119]

[0120] This formula indicates that the iteration will terminate if the last six iterations remain unchanged; p max This represents the maximum population size; the subscripts p and gen represent the population size and the current iteration number, respectively.

[0121] The advantages of this invention are further illustrated by the following simulation examples:

[0122] 1. Simulation parameters

[0123] like Figure 2 As shown, the three-dimensional dimensions of the cold plate are 140mm*200mm*14mm, and the distance from the heat source is Q=8.33W / cm². 2 The diameter of both the entrance and exit is D. in =D out =6mm, inlet temperature is T in =20℃, inlet flow rate is U in =0.16697m / s, outlet pressure is P out =0 Pa. The solid material is aluminum 6061-T6, and the liquid working fluid is water.

[0124] 2. Simulation Content and Results

[0125] like Figure 3 and 4Table 1 shows the temperature distribution on the upper surface of the cold plate before and after optimization, with the corresponding average temperature and root mean square temperature data. The results show that the overall thermal performance and temperature uniformity of the cold plate are better than the initial cold plate's temperature distribution, with reductions of 5.79℃ (9.00%) and 1.88℃ (21.49%), respectively. Furthermore, in the initial temperature distribution, the temperature gradually worsens from the inlet to the outlet. This is because the generated heat is not dissipated from the system in time as the fluid flows, leading to an increasing fluid temperature and weakening the heat transfer capacity in the latter half. In the optimized structure, the tree-like flow channels in the front half exhibit a converging configuration, allowing the fluid to quickly enter the latter half of the system, enhancing the heat transfer capacity there. Of course, the heat dissipation performance of the front half of the cold plate system is relatively weakened, thus exhibiting good temperature uniformity.

[0126] Figure 5 To optimize the flow path and temperature distribution of the front radiator, Figure 6 and Figure 7 This paper presents two perspectives on the optimized flow channel trajectory and temperature distribution of the radiator structure. From the initial upper surface temperature distribution, it can be seen that the temperature distribution around the heat source, ranked from best to worst, is: closest to the inlet > both sides of the inlet > closest to the outlet > both sides of the outlet. However, the optimized channel structure is positioned as far away from the heat source near the inlet as possible, while simultaneously being as close as possible to the heat source near the outlet. This indicates that the optimization criteria weaken the areas with better initial temperature distribution and strengthen the areas with poorer initial temperature distribution, thus improving temperature uniformity. Furthermore, it can be observed that the hydraulic diameter of the tree-like channels near the inlet and outlet increases. This is beneficial for storing more cooler fluid at the inlet and for increasing the convective heat transfer area at the outlet, both contributing to enhanced heat transfer performance. Figure 5 As shown in Figure 7, the optimized central channel can swing vertically as much as possible. This demonstrates both the effectiveness of the proposed method and that the change in channel pattern is the main factor promoting improved heat transfer performance. Simultaneously, the change in channel torsion is clearly observed, which facilitates the generation of secondary flow. The presence of longitudinal waves makes the flow boundary layer easier to break, reducing the velocity distribution among fluids and consequently reducing the temperature distribution, thus enhancing heat transfer capacity. This is also a major factor contributing to the improved heat transfer performance. Changes in the channel's hydraulic diameter can lead to the generation of transverse waves. This process helps compress the flow boundary layer thickness, resulting in more heat being transferred outside the cold plate system. Figure 8 Given the target, the optimal structure is obtained by setting the Pareto front plot of the minimum surface average temperature and the root mean square temperature to 0.5:0.5.

[0127] Table 1 Comparison of radiator surface performance before and after optimization.

[0128]

[0129]

[0130] Scheme 1 represents the result of preprocessing before shape optimization, while Scheme 2 represents the result of the optimal tree structure after shape optimization. Δ represents the data difference between Scheme 1 and Scheme 2. From the data and temperature distribution, the optimized temperature distribution is better, and the heat dissipation performance is further improved.

Claims

1. A method for free-form surface modeling and optimization design of tree-shaped cold plate channels, characterized in that, Includes the following steps: (1) Determine the surface heat flux density of the power devices, the external dimensions of the cold plate, and the inlet and outlet positions of the flow channels based on the configuration of the electronic equipment on site; (2) Based on the determined heat flux density and external dimensions, determine the geometric dimensions of the inlet and outlet of the flow channel, the heat transfer properties, the flow properties, and the material properties of the heat dissipation system; (3) Based on the determined cold plate dimensions, construct a tree-like flow channel skeleton by parameterizing the rotation and translation matrices; (4) Based on the determined tree-like flow channel skeleton, determine the basic topological relationships between the branch layers; (5) Based on the determined branch layer topology, the length of each branch is divided into three parts, and each length is normalized. (6) Based on the normalized branch parts, construct the geometric and topological relationships between and within the branch layers in each branch, including channel patterns, channel cross sections and channel torsion. In step (6), the geometric features of the channel mode are expressed by the parameters of formula (6): （6） Where d(t) represents the initial point located on the tree-like flow channel skeleton. The normal distance to the final centerline point (x0(t), y0(t), z0(t) = C0) is represented by a cubic B-spline function, which has P+1 control points. Since the operation is in the XOY plane, C0 is half the value of the given H. The cold plate's external dimensions include height H. t is a parameter variable used for constructing the tree-like flow channel skeleton and modeling. The elliptical channel section is constructed, with its two geometric features being the major axis a(t) and the minor axis b(t), both characterized by Bernstein functions; the geometric features of the channel torsion are expressed by the formula (8): （8） The channel torsion is characterized by the Bernstein function; the corresponding control coefficient is φ. j And the maximum power value is q; (7) Based on the determined tree-like flow channel model, construct the connection between the tree-like flow channel and the parallel flow channel in a parameterized manner; (8) Based on engineering requirements, construct the design variables of the optimization framework, including the control coefficients of the cubic B-spline function characterizing the channel mode; the control coefficients of the Bernstein function characterizing the channel cross section and channel torsion; and the control parameters of the tree-like geometric feature variables; construct the objective function of the optimization framework, and use minimizing the average temperature and root mean square temperature of the upper and lower surfaces of the cold plate as indicators for optimizing the overall performance and temperature distribution uniformity of the cold plate. (9) Based on the shape optimization model, apply boundary conditions to establish a finite element model of the cold plate with tree-like and parallel channels; (10) Based on the finite element model of the cold plate, the objective function is optimized by non-dominated sorting genetic algorithm II to obtain the temperature distribution of the cold plate and the surface of the power device.

2. The method for free-form surface modeling and optimization design of tree-shaped cold plate channels according to claim 1, characterized in that, In step (4), the basic topological relationships between branch layers are determined according to formula (2): Where m represents the m-th branch layer of the tree-like flow channel, P m This indicates the Pth branch within that branch layer. m One branch; and Representing the m-th branch layer and P-th branch layer respectively m The channel diameter of the branch is related to the Pth branch of the (m+1)th branch layer. m+1 The diameter of the channel for each branch; and Representing the m-th branch layer and P-th branch layer respectively m The terminal cutoff distance of each branch and the Pth branch of the (m+1)th branch level m+1 The truncation distance at the beginning of each branch; Represents the Pth branch of the m-th branch layer. m The bifurcation angle of each branch at its end is... .

3. The method for free-form surface modeling and optimization design of tree-shaped cold plate channels according to claim 2, characterized in that, In step (9), an unstructured tetrahedral mesh is used to establish a finite element model.

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