Design method and device of gradient multi-hole anti-bending heat pipe based on TPMS

Abstract

The application discloses a design method and device for a gradient porous anti-bending heat pipe based on a TPMS, and the method comprises the following steps: constructing a skeleton type wick basic structure according to a structure equation of a three-period minimum surface, performing coordinate system conversion to adapt to the geometric characteristics of the heat pipe to obtain a conformal structure, and correcting the distortion of the conformal structure; dividing the conformal structure into a plurality of micro square lattices, constructing a quadratic polynomial regression model based on the equation parameters of the structure equation of each micro square lattice and the porosity, determining the target porosity of each region of the heat pipe, determining the equation parameters by using the quadratic polynomial regression model, assigning the equation parameters to the TPMS capillary structure of the corresponding region of the heat pipe, realizing accurate regulation and control of the porosity, and obtaining the anti-bending heat pipe. The method solves the problem that the capillary structure of the existing heat pipe cannot balance among low cost, anti-bending, no direction limitation and high heat transfer performance, and thus it is difficult to meet the demand of high-end electronic equipment on the conformal adaptation, flexible installation and long-term stability of the heat pipe.

Description

Technical Field

[0001] This application relates to the field of thermal management technology, and in particular to a design method and apparatus for a gradient porous anti-bending heat pipe based on TPMS. Background Technology

[0002] With the rapid evolution of technologies such as artificial intelligence and high-performance computing, the computing power demand of electronic devices continues to explode, and the power density of chips and modules is constantly increasing. Heat dissipation has become a key factor restricting the performance and reliability of electronic devices. As a highly efficient two-phase heat transfer element, heat pipes can quickly remove heat from the heat source, ensuring that electronic devices operate in a stable temperature environment. They are widely used in high-end electronic manufacturing and are of great significance for enhancing the core competitiveness of the electronics industry.

[0003] Currently, the capillary structures of mainstream heat pipes are mainly divided into powder-sintered heat pipes and grooved heat pipes. Powder-sintered heat pipes provide capillary force by sintering metal powder into a porous sintered layer on the inner wall of the pipe, exhibiting good heat transfer stability. However, the manufacturing process is complex and technically demanding, resulting in high manufacturing costs. Furthermore, parameter control during the sintering process is difficult, leading to relatively high thermal resistance. Grooved heat pipes, on the other hand, form axial grooves in the inner wall through machining to serve as capillary channels. They offer advantages such as low cost and simple manufacturing processes. However, their capillary force is strictly limited by the direction of the grooves, exhibiting strong directional dependence. In addition, this type of grooved structure is prone to deformation when bent, leading to a sharp decline in heat transfer performance and making it difficult to adapt to the bending installation requirements in complex layouts.

[0004] Furthermore, neither of the aforementioned structures addresses the differentiated optimization of the condensation and evaporation sections of the heat pipe. The condensation section has insufficient specific surface area, while the evaporation section exhibits high resistance to vapor escape, thus limiting overall heat transfer efficiency. Moreover, existing technologies fail to achieve a balance between low cost, bend resistance, unrestricted directional operation, and high heat transfer performance, making it difficult to meet the requirements of high-end electronic devices for conformal heat pipe design, flexible installation, and long-term stability. Summary of the Invention

[0005] This application provides a design method and apparatus for a gradient porous, bend-resistant heat pipe based on TPMS, which solves the problem that the capillary structure of existing heat pipes cannot achieve a balance between low cost, bend resistance, no directional restrictions, and high heat transfer performance, thus making it difficult to meet the requirements of high-end electronic devices for heat pipes that are adaptable to different shapes, flexible in installation, and long-term stable.

[0006] In a first aspect, embodiments of this application provide a design method for a gradient porous, bend-resistant heat pipe based on TPMS, including:

[0007] Based on the target working conditions, a three-period minimum surface is selected, and a skeleton-type liquid absorption core basic structure is constructed according to its structural equation.

[0008] The coordinate system of the skeleton-type liquid wick basic structure is transformed to adapt to the geometric characteristics of the heat pipe, resulting in a conformal structure. The distortion correction of the conformal structure is achieved by modifying the structural equation.

[0009] The conformal structure is divided into multiple tiny square lattices. Based on the equation parameters and porosity of the structural equation of each tiny square lattice, a quadratic polynomial regression model is constructed to predict the relationship between the equation parameters and porosity.

[0010] The target porosity of each region of the heat pipe is determined using the Laplace-Young equation, and the equation parameters are determined using the quadratic polynomial regression model based on the target porosity.

[0011] By assigning equation parameters to the TPMS capillary structure of the corresponding region of the heat pipe, precise control of porosity can be achieved, resulting in a bend-resistant heat pipe.

[0012] In conjunction with the first aspect, in one possible implementation, the structural equation is as follows:

[0013] ;

[0014] In the formula, Representing the structural equation, Represents the three-dimensional coordinates of a point in three-dimensional space. L , a and c The equation parameters represent the structural equations. L , a For coefficients, c For constant terms, This represents the characteristic function of the surface.

[0015] In conjunction with the first aspect, in one possible implementation, the skeleton-type absorbent core basic structure is as follows:

[0016] ;

[0017] In the formula, This indicates the basic structure of the skeleton-type absorbent core. This represents the threshold for determining structure generation. This represents the structural equations after mapping to the polar coordinate system.

[0018] In conjunction with the first aspect, in one possible implementation, the coordinate system transformation of the skeleton-type wicking base structure to adapt to the geometric features of the heat pipe, resulting in a conformal structure, and the distortion correction of the conformal structure by modifying the structural equation, includes:

[0019] The structural equations are transformed to map the skeleton-type absorbent core basic structure in the rectangular coordinate system to the polar coordinate system;

[0020] Using the centerline of the heat pipe bend as the bending path, a mapping relationship from the polar coordinate system to the global three-dimensional spatial coordinate system is established using the Frenet-Serret frame to ensure that the capillary channel is tangentially aligned with the fluid flow direction, thus obtaining a conformal structure.

[0021] Construct the Jacobian matrix of the basic structure of the skeleton-type liquid absorber in polar coordinates, which maps to the bending path of the heat pipe;

[0022] The compensation factor is determined by solving the Jacobian matrix to correct the constant terms of the structural equations;

[0023] Based on the Gauss-Bonnet theorem, the surface curvature of the skeleton-type liquid-absorbing core basic structure is extracted, a regularized level set functional equation containing curvature extremum penalty terms is constructed, and the coefficients of the structural equation are modified again to achieve distortion correction of the conformal structure.

[0024] In conjunction with the first aspect, in one possible implementation, the construction of a quadratic polynomial regression model for predicting the relationship between the equation parameters and porosity based on the structural equations of each micro square lattice includes:

[0025] The volume fraction, spatial position, and corresponding equation parameters of each tiny square lattice in the TPMS unit cell of the framework-type liquid absorption core structure were obtained.

[0026] Based on multiple tiny square lattices, the Box-Behnken response surface design method is used, with the equation parameters of the structural equation as independent variables and the porosity and volume fraction of the conformal structure as dependent variables. A quadratic polynomial regression model is constructed through a quadratic polynomial function to predict the relationship between the equation parameters and porosity.

[0027] In conjunction with the first aspect, in one possible implementation, the step of determining the target porosity of each region of the heat pipe using the Laplace-Young equation, and determining the equation parameters using the quadratic polynomial regression model based on the target porosity, includes:

[0028] The relationship between capillary pressure and pore structure is quantified using the Laplace-Young equation to determine the target porosity of each region of the heat pipe.

[0029] Based on the target porosity, the equation parameters are solved using the quadratic polynomial regression model.

[0030] Based on the parameters of the equation, the porosity is adjusted to change linearly along the z-axis so that the porosity gradually increases from the evaporation section to the condensation section;

[0031] Based on the parameters of the equation, the radial porosity of the condensing section, the wall-side porosity, and the radial porosity of the evaporation section are determined. The radial porosity of the condensing section, the wall-side porosity, and the radial porosity of the evaporation section are adjusted respectively to improve the condensation and evaporation efficiency of the heat pipe.

[0032] Multiple channels are uniformly added along the steam chamber side of the evaporation section, and each channel corresponds one-to-one with the TPMS cell in the conformal structure to reduce the resistance to steam escape.

[0033] In conjunction with the first aspect, in one possible implementation, the relationship between capillary pressure and pore structure is quantified using the Laplace-Young equation, as follows:

[0034] ;

[0035] In the formula, Indicates capillary pressure. Indicates the surface tension of a liquid working fluid. Indicates the contact angle formed by the working fluid and the wicking material. Indicates the effective capillary diameter of the pores.

[0036] Secondly, embodiments of this application provide a design device for a gradient porous anti-bending heat pipe based on TPMS, comprising:

[0037] The basic construction module is used to select a three-period minimum surface according to the target working condition and construct a skeleton-type liquid absorption core basic structure according to its structural equation.

[0038] The geometric adaptation module is used to perform coordinate system transformation on the skeleton-type liquid absorber basic structure to adapt to the geometric features of the heat pipe, thereby obtaining a conformal structure. The distortion correction of the conformal structure is achieved by modifying the structural equation.

[0039] A simplification module is used to divide the conformal structure into multiple micro square lattices, and based on the equation parameters and porosity of the structural equation of each micro square lattice, a quadratic polynomial regression model is constructed to predict the relationship between the equation parameters and porosity.

[0040] The solution module is used to determine the target porosity of each region of the heat pipe using the Laplace-Young equation, and to determine the equation parameters using the quadratic polynomial regression model based on the target porosity.

[0041] The gradient optimization module is used to assign equation parameters to the TPMS capillary structure of the corresponding region of the heat pipe, so as to achieve precise control of porosity and obtain a bend-resistant heat pipe.

[0042] Thirdly, embodiments of this application provide an apparatus comprising: a processor; a memory for storing processor-executable instructions; wherein, when the processor executes the executable instructions, it implements the method as described in the first aspect or any possible implementation of the first aspect.

[0043] Fourthly, embodiments of this application provide a non-volatile computer-readable storage medium, the non-volatile computer-readable storage medium including storage for storing a computer program or instructions that, when executed, cause the method described in the first aspect or any possible implementation of the first aspect to be implemented.

[0044] One or more technical solutions provided in the embodiments of this application have at least the following technical effects or advantages:

[0045] This application embodiment constructs a skeleton-type wicking core basic structure, which can form a continuous three-dimensional network of capillary channels, effectively eliminating the directional dependence of grooved heat pipes and ensuring uniform distribution of capillary force in all directions. This improves the heat transfer stability of the heat pipe under complex operating conditions. Through coordinate system transformation and structural equation correction, the skeleton-type wicking core basic structure and the geometric features of the heat pipe are precisely matched, especially in the bending region. By correcting the distortion of the conformal structure, the integrity of the capillary channels and the smoothness of fluid flow under bending conditions are ensured, significantly enhancing the bending resistance of the heat pipe. By constructing a quadratic polynomial regression model, a quantitative mapping relationship between equation parameters and porosity is established, enabling precise gradient control in different regions. Thus, while ensuring low cost and bending resistance, the overall heat transfer performance of the heat pipe is greatly improved, meeting the comprehensive requirements of high-end electronic devices for conformal heat pipe design, flexible installation, and long-term stability. It effectively solves the problem that the capillary structure of existing heat pipes cannot achieve a balance between low cost, bending resistance, no directional restriction and high heat transfer performance, thus making it difficult to meet the requirements of high-end electronic devices for heat pipes that are adaptable to shape, flexible in installation and long-term stable. Attached Figure Description

[0046] To more clearly illustrate the technical solutions of the embodiments of this application, the drawings used in the description of the embodiments of this application or the prior art will be briefly introduced below. Obviously, the drawings described below are some embodiments of the present invention. For those skilled in the art, other drawings can be obtained based on these drawings without creative effort.

[0047] Figure 1 A flowchart illustrating the design method of a TPMS-based gradient porous anti-bending heat pipe provided in this application embodiment;

[0048] Figure 2 This is a schematic diagram of the basic structure of the skeleton-type liquid absorption core according to an embodiment of the present invention;

[0049] Figure 3 This is a schematic diagram of the basic structure of the skeleton-type liquid absorption core in the rectangular coordinate system according to an embodiment of the present invention;

[0050] Figure 4 This is a schematic diagram of the basic structure of the skeleton-type liquid absorption core in polar coordinates according to an embodiment of the present invention;

[0051] Figure 5 This is a partial schematic diagram of the conformal structure according to an embodiment of the present invention;

[0052] Figure 6 This is a schematic diagram of an anti-bending heat pipe according to an embodiment of the present invention;

[0053] Figure 7 This is a schematic diagram of the design device for a TPMS-based gradient porous anti-bending heat pipe provided in an embodiment of this application. Detailed Implementation

[0054] The technical solutions of the embodiments of this application will be clearly and completely described below with reference to the accompanying drawings. Obviously, the described embodiments are only some, not all, of the embodiments of this invention. All other embodiments obtained by those skilled in the art based on the embodiments of this invention without creative effort are within the scope of protection of this invention.

[0055] The following description of some technologies involved in the embodiments of this application is provided to aid understanding and should be considered merely exemplary. Therefore, those skilled in the art should recognize that various changes and modifications can be made to the embodiments described herein without departing from the scope and spirit of this application. Similarly, for clarity and brevity, some descriptions of well-known functions and structures are omitted in the following description.

[0056] Figure 1 This is a flowchart of a design method for a TPMS-based gradient porous flexural heat pipe according to an embodiment of this application, including steps 101 to 105. Figure 1 This is merely one execution order shown in the embodiments of this application and does not represent the only execution order of the TPMS-based gradient porous flexural heat pipe design method. Where the final result can be achieved, Figure 1 The steps shown can be performed in parallel or in reverse order.

[0057] Step 101: Select a three-period minimum surface based on the target operating conditions, and construct a skeleton-type liquid-absorbing core basic structure according to its structural equation. In this embodiment, a three-period minimum surface is selected, which has high connectivity, uniform pore distribution, and excellent self-support. It can naturally form continuous capillary channels, which is suitable for the core requirements of "smooth mass transfer + stable structure" of the liquid-absorbing core. The skeleton-type liquid-absorbing core basic structure is constructed according to the structural equation of the three-period minimum surface, which not only ensures the structural stability to resist bending stress, but also maintains high pore connectivity to provide channels for the flow of working fluid, ensuring the adaptability of the structure and the suitability for capillary mass transfer requirements.

[0058] For example, the structure of a Tri-Period Minimal Surface (TPMS) includes: Diamond surface, Gyroid surface, Schwarz P surface, F-RD surface (a type of face-centered cubic / rhombohedral distorted TPMS), I-WP surface (body-centered cubic symmetric TPMS with channels arranged in a wavy parallel pattern), GD surface (a composite surface formed by mixing / splicing Gyroid and Diamond topologies within the same unit), Scherk3 surface, Neovius surface, Dprime surface (a topological deformation / low-symmetry variant of the Diamond surface, maintaining bicontinuity but with reduced symmetry), and Split surface. The following are some of the following surface structures: P (split P surface / split unit cell surface), Lidinoid surface, FKS (a class of face-centered cubic symmetric three-period minimal surfaces), Double Gyroid surface, Double SD surface (double SD surface / double rhombic dodecahedron surface, SD usually refers to diamond rhombic dodecahedron), first surface, second surface, third surface, fourth surface, fifth surface, sixth surface, and seventh surface.

[0059] For example, this embodiment uses a Diamond-type Skeletal-TPMS (skeleton-type three-period minimal surface) as the basic structure of the skeleton-type liquid absorber to prepare a circular, bend-resistant heat pipe adapted for heat dissipation of AI server chips. The heat pipe has an inner diameter of 8 mm and a length of 210 mm, and needs to be able to bend 90° for installation.

[0060] First, a hexahedral unit cell is constructed based on the Diamond-type TPMS implicit functional equation (i.e., structural equation), such as... Figure 2 As shown. This TPMS unit cell, as the basic physical unit of the absorbent core structure, possesses high connectivity and excellent self-support. The Cartesian coordinate equation of the Diamond-type TPMS in this embodiment is:

[0061] ,

[0062] In the formula, x , y , z Let be the three-dimensional coordinates of a point in three-dimensional space, where sin is the trigonometric sine function and cos is the trigonometric cosine function. L , a and c For equation parameters, c The constant term (i.e., the offset coefficient) directly changes the offset thickness of the skeleton reference plane, thereby controlling the wall thickness of the skeleton-type absorbent core base structure. The wall thickness determines the mechanical strength of the skeleton-type absorbent core base structure and is crucial for ensuring the absorbent core resists bending stress. Simultaneously, it can be adjusted... L The size of the TPMS unit cell is adjusted to regulate the pore size and overall connectivity of the skeletal core structure. Pore size directly affects the diameter of the capillary channels, while connectivity determines the smoothness of the working fluid flow. By adjusting the parameters of the above equations, the porosity of the skeletal core structure is controlled between 30% and 40%, meeting the requirements for both structural strength and mass transfer. The skeletal core structure in Cartesian coordinates is shown below. Figure 3 As shown.

[0063] The structural equation for the basic structure of the skeleton-type absorbent core is as follows:

[0064] ,

[0065] In the formula, Representing the structural equation, Represents the three-dimensional coordinates of a point in three-dimensional space. L , a and c The equation parameters represent the structural equations. L , a For coefficients, c For constant terms, This represents the characteristic function of the surface.

[0066] Skeleton-type absorbent core basic structure (such as) Figure 2 As shown below:

[0067] ,

[0068] In the formula, This indicates the basic structure of the skeleton-type absorbent core. This represents the threshold for determining structure generation. This represents the structural equations after mapping to the polar coordinate system.

[0069] This embodiment employs a Skeletal-type structure construction method. The surface where the structural equation equals 0 is taken as the skeleton reference plane. Thickness offset is performed along the surface normal to form a closed solid structure (i.e., a skeleton-type absorbent core base structure). The solid volume of the skeleton-type absorbent core base structure... Total volume of a single cell The ratio satisfies the porosity The formula is as follows:

[0070] ,

[0071] In the formula, This indicates the volume corresponding to the basic structure of the skeleton-type absorbent core. This represents the volume corresponding to the regional unit cell.

[0072] Step 102: Transform the coordinate system of the skeleton-type wicking base structure to adapt to the geometric characteristics of the heat pipe, obtaining a conformal structure. Correct the distortion of the conformal structure by revising the structural equation. In this embodiment, the structural equation is transformed to map the skeleton-type wicking base structure in the Cartesian coordinate system to the polar coordinate system. Using the centerline of the heat pipe bend as the bending path, a mapping relationship from the polar coordinate system to the global three-dimensional spatial coordinate system is established using the Frenet-Serret frame to ensure that the capillary channel is tangentially aligned with the fluid flow direction, thus obtaining the conformal structure. A Jacobian matrix is ​​constructed to map the skeleton-type wicking base structure to the bending path of the heat pipe in the polar coordinate system. The compensation factor is determined by solving the Jacobian matrix to correct the constant terms of the structural equation. Based on the Gauss-Bonnet theorem, the surface curvature of the skeleton-type wicking base structure is extracted, and a regularized level set functional equation containing curvature extremum penalty terms is constructed. The coefficients of the structural equation are then corrected again to achieve distortion correction of the conformal structure.

[0073] Specifically, in response to the geometric characteristics of circular heat pipes and the requirement for uniform circumferential heat transfer, this application adopts two strategies: polar coordinate systematization and path conformalization, to achieve precise adaptation between the capillary structure and the geometry of the heat pipe, resulting in a conformal structure.

[0074] Structural polarization involves transforming the structural equations of the aforementioned skeleton-type wicking core structure using coordinate mapping, converting the rectangular coordinate system to a polar coordinate system. This coordinate mapping transformation ensures that the TPMS cells of the skeleton-type wicking core structure are periodically and uniformly distributed along the circumference of the heat pipe, achieving geometric conformal fit between the capillary structure and the inner wall of the heat pipe, and eliminating the flow dead zone generated by traditional rectangular coordinate filling.

[0075] Furthermore, the framework-type wicking structure is constructed based on a cubic unit cell in a Cartesian coordinate system. If it is directly filled into a heat pipe with a circular wall, cut-out defects will occur at the boundary. Therefore, in order to achieve geometric adaptation between the unit cell structure and the wall of the circular heat pipe, a coordinate system mapping transformation is required.

[0076] For example, to adapt to the inner wall of a circular heat pipe and eliminate the flow dead zone caused by traditional rectangular coordinate filling, the structural equation of the skeleton-type wicking core basic structure undergoes a first coordinate transformation, changing from a rectangular coordinate system to a polar coordinate system (structure as shown in the figure). Figure 3 As shown), taking the axial direction of the heat pipe as the z-axis as an example, the transformation equation is as follows:

[0077] ,

[0078] In the formula, Represents the polar radius in polar coordinates. Indicates the rotation angle, representing the torsion angle of the basic structure of the skeleton-type absorbent core. Represents the polar angle in polar coordinates. This indicates the offset diameter of the basic structure of the skeleton-type liquid absorption core. This indicates the length of the basic structure of the skeleton-type absorbent core. , , This indicates the axial, radial, and spanwise coordinates of the skeleton-type absorbent core base structure. , , This represents the x, y, and z coordinates of the skeleton-type wicking core structure in the polar coordinate system. The first coordinate transformation ensures that the skeleton-type wicking core structure is evenly distributed along the circumference of the heat pipe, guaranteeing consistent circumferential heat transfer and reducing the resistance to recirculation of the working fluid.

[0079] Path conformalization introduces the Frenet-Serret frame. ,in, It is the axial centerline of the heat pipe. It is the principal normal vector. This is the secondary normal vector. Integrating the annular cross-section of the heat pipe along its axial centerline ensures that the capillary channel remains tangentially aligned with the fluid flow direction, eliminating the geometric cutoff and flow dead zones caused by traditional rectangular coordinate filling. This method ensures that the capillary channel maintains topological continuity and axial accessibility in complex spatial paths, eliminates flow dead zones or localized congestion that may occur at bends during working fluid recirculation, significantly improves the mass transfer efficiency and heat transfer uniformity of the heat pipe in complex layouts, and can adapt to the conformal design requirements of various irregularly shaped heat pipes.

[0080] Furthermore, after completing the first coordinate transformation in the above-mentioned structural polar coordinate transformation (structure as follows) Figure 4 As shown in the figure, attention needs to be paid to the bending requirements of the heat pipe in three-dimensional space. If the axial nonlinear bending is directly performed, structural interference is likely to occur at the bend. Therefore, it is necessary to further introduce a differential geometric frame and sweep along the three-dimensional path to ensure the continuity of the capillary channel at the bend, as detailed below.

[0081] To achieve precise conformal shaping of the skeletal heat pipe's wicking structure within complex three-dimensional spatial paths, this application employs a second coordinate transformation driven by the axial centerline. The axial centerline of the heat pipe is defined as a three-dimensional spatial curve. And establish a local Frenet-Serret frame at each point on the three-dimensional curve. The TPMS unit points of the skeleton-type absorbent core basic structure after the first coordinate transformation are mapped to the global three-dimensional space coordinate system, and the mapping relationship is as follows:

[0082] ,

[0083] In the formula, This represents the three-dimensional position vector of any point on the surface of the skeleton-type liquid-absorbing core basic structure. Indicates the axial centerline of the heat pipe (in terms of axial arc length). (This is a parameter), representing the reference axis of the suction core. Indicates the axial centerline exist The unit normal vector at that location, Indicates the axial centerline exist The unit binormal vector at that location, This indicates the axial arc length of the corresponding heat pipe. and This represents the normal and subnormal coordinates within the corresponding cross section, where , , Represents the polar radius in polar coordinates. This represents the polar angle in polar coordinates.

[0084] Furthermore, in response to the high-dimensional mapping distortion and porosity deviation caused by the extremely high local bending curvature of the heat pipe, this application can also adopt a dynamic compensation and topological morphology regularization approach boundary control strategy based on the Jacobian matrix to correct the distortion of the conformal structure.

[0085] Specifically, by calculating the mapping transformation relationship from the polar coordinate system to the global three-dimensional spatial coordinate system, the Jacobian matrix is ​​determined, a compensation factor is introduced, and the constant terms in the structural equation are dynamically corrected to eliminate the negative impact of local geometric distortion caused by bending on porosity. This ensures that the deviation between the local porosity of the bending region and the design value is strictly controlled within a specific threshold (such as ±1%), thus ensuring the continuous distribution of capillary pressure.

[0086] For example, to eliminate the negative impact of local geometric distortion caused by bending on porosity, a Jacobian matrix is ​​introduced for distortion correction. This is achieved by calculating the Jacobian matrix of the transformation between the aforementioned coordinate systems. Dynamically correct the constant term in the structural equations c The values ​​are as follows:

[0087] ,

[0088] In the formula, This indicates the corrected parameter item. This represents the constant term before the correction. Describes the Jacobian determinant of a Jacobian matrix. This represents the compensation factor determined based on the mapping relationship before and after coordinate transformation and the Jacobian matrix.

[0089] Furthermore, during the 3D spatial path conformal mapping based on the Frenet-Serret frame, the sharp increase in local bending curvature of the heat pipe easily leads to the Jacobian determinant of the inner mapping region approaching the critical threshold or even exhibiting singularities. This, in turn, induces self-intersection and topological dimensionality reduction deformation of the TPMS cell walls, generating non-manifold edges and disrupting the continuous accessibility of capillary channels. To address this issue, this application proposes a topological morphological regularization boundary approximation control strategy based on the Gauss-Bonnet theorem.

[0090] By extracting the average curvature and Gaussian curvature of the conformal structure surface, a regularized level set functional equation containing curvature extremum penalty terms is constructed. During the three-dimensional path sweep iteration, the phase field evolution equation corresponding to the variation of this energy functional is solved, and the coefficients of the locally polarized equation are corrected by second-order derivative perturbation. This eliminates the hidden dangers of mesh tearing and overlap under high spatial curvature from the geometric bottom layer, ensuring that the solid-liquid two-phase interface in the bending extremum region maintains the minimal surface topological manifold domain characteristics without singularities.

[0091] For example, by introducing the average surface curvature of the skeleton-type wicking core base structure H With Gaussian curvature K Construct a regularized level set functional equation that includes a curvature extremum penalty term:

[0092] ,

[0093] In the formula, Let represent the functional equation for the regularized level set. Represents the computational domain. This represents the average curvature of the structural surface. Indicates the target mean curvature. The gradient of the level set function is represented. The implicit level set function (i.e., structural equation) of the basic structure of the skeleton-type liquid absorption core. For the Dirac function, and As the curvature penalty weighting factor, For Gaussian curvature, This represents the critical Gaussian curvature threshold, the critical safety line that leads to topological distortion (channel blockage or mesh self-intersection).

[0094] During the 3D path sweep iteration, the coefficients of the equation parameters after the second coordinate transformation are obtained by solving the phase field evolution equation corresponding to the regularized level set functional equation. L , a The second derivative perturbation correction is performed. This mechanism not only eliminates the hidden dangers of mesh tearing and self-overlapping under high spatial curvature at the geometric level, but also ensures that the solid-liquid two-phase interface in the bending extreme region maintains the intrinsic physical properties of the minimum surface. This provides a singularity-free topological manifold domain guarantee for the continuous distribution of capillary force, and keeps the deviation of the local porosity in the bending region from the design value within ±1%, ensuring the continuity of capillary pressure.

[0095] Step 103: The conformal structure is divided into multiple micro square lattices. Based on the equation parameters and porosity of the structural equation of each micro square lattice, a quadratic polynomial regression model is constructed to predict the relationship between the equation parameters and porosity. In this embodiment, the volume fraction, spatial position, and corresponding equation parameters of each micro square lattice in the TPMS unit cell of the framework-type absorbent core structure are obtained. Based on multiple micro square lattices, using the Box-Behnken response surface design method, with the equation parameters of the structural equation as independent variables and the porosity and volume fraction of the conformal structure as dependent variables, a quadratic polynomial regression model is constructed through a quadratic polynomial function to predict the relationship between the equation parameters and porosity.

[0096] Specifically, after the two coordinate transformations in step 102, the TPMS unit cell in the conformal structure undergoes complex geometric deformation, making it difficult to directly calculate its structural parameters using traditional analytical formulas. To quickly obtain the deformed structural parameters, this application proposes a simplified similarity calculation strategy (such as...). Figure 5 As shown, the four corner points of a partial structure of the skeleton-type absorbent core base structure are illustrated, namely the upper left corner point 1, the upper right corner point 2, the lower right corner point 3, and the lower left corner point 4. Figure 5The deformation of the local structure before and after two coordinate transformations is shown by the changes in the positions of the four corner points and the shape of the quadrilateral formed by the four corner points.

[0097] The conformal structure is divided into several tiny square lattices along the radial, circumferential, and axial directions. Each tiny square lattice is equivalent to a TPMS unit in the original rectangular coordinate system, and the proportion of each tiny square lattice in the TPMS unit cell is recorded.

[0098] Based on the Box-Behnken response surface design method, the equation parameters are selected ( L , a , c Using the independent variable as the independent variable and structural parameters (porosity, specific surface area, etc.) as the dependent variable, multiple experimental schemes were designed, and a quadratic polynomial regression model was constructed using a quadratic polynomial function. The statistical coefficient of the quadratic polynomial regression model is close to 1, which can accurately predict the quantitative relationship between the equation parameters and porosity. The differentiated heat transfer requirements of different regions of the heat pipe are inversely mapped to specific TPMS solution control parameters, thereby realizing a closed loop from performance requirements to structural design.

[0099] Step 104: Determine the target porosity of each region of the heat pipe using the Laplace-Young equation, and determine the equation parameters using a quadratic polynomial regression model based on the target porosity. In this embodiment, the relationship between capillary pressure and pore structure is quantified using the Laplace-Young equation (a standard term in the field of thermal management / capillary mechanics) to determine the target porosity of each region of the heat pipe; the equation parameters are solved using a quadratic polynomial regression model based on the target porosity; the porosity is adjusted linearly along the z-axis based on the equation parameters to gradually increase porosity from the evaporation section to the condensation section; the radial porosity of the condensation section, the wall-side porosity, and the radial porosity of the evaporation section are determined based on the equation parameters, and the radial porosity of the condensation section, the wall-side porosity, and the evaporation section are adjusted respectively to improve the condensation and evaporation efficiency of the heat pipe; multiple channels are uniformly added along the vapor chamber side of the evaporation section, each channel corresponding one-to-one with the TPMS cell in the conformal structure to reduce vapor escape resistance.

[0100] In this embodiment, the relationship between the quantified capillary pressure and the pore structure is as follows:

[0101] ,

[0102] In the formula, Indicates capillary pressure. Indicates the surface tension of a liquid working fluid. Indicates the contact angle formed by the working fluid and the wicking material. This represents the effective capillary pore size. From the above formula, it can be seen that... The smaller the value, the greater the capillary pressure difference and the stronger the capillary driving force. Based on this, adjustments can be made... Implement gradient porosity design (i.e. determine the target porosity) to accurately match the differentiated mass transfer requirements of the condensation and evaporation sections.

[0103] Specifically, the axial gradient equation for porosity is:

[0104] ,

[0105] In the formula, This represents the porosity at the z-axis of the heat pipe. This indicates the initial porosity of the evaporation section. Denotes the gradient coefficients, and >0, so that the porosity gradually changes from low to high from the evaporator section to the condenser section of the heat pipe, corresponding to The force gradually increases from small to large, ensuring that the capillary force in the evaporation section is always greater than that in the condensation section, forming a stable axial driving force that drives the condensate to flow back from the condensation section to the evaporation section, thus accelerating the liquid film suction efficiency.

[0106] For example, using the porosity gradient equation This allows the porosity to gradually change from 30% to 65% from the evaporation section to the condensation section, while ensuring... The force is gradually increased throughout the process to ensure that the capillary driving force in the evaporation section is greater than the sum of gravity, steam resistance, and liquid flow resistance.

[0107] To address the mass transfer requirements of the condensation section, a radial gradient structure with low porosity on the steam side and high porosity on the wall side was designed. To achieve a gradual increase in porosity, the radial gradient equation for the porosity in the condensation section is:

[0108] ,

[0109] In the formula, Indicates the radial direction of the heat pipe condenser section Porosity at that location Porosity on the wall side The radial gradient coefficient, and >0, Let be the inner radius of the heat pipe. This design causes the porosity of the heat pipe wall to increase from the vapor chamber side. The design utilizes the high capillary force on the wall side to generate radial traction, rapidly drawing the liquid condensed from the steam on the inner surface of the core to the interior (near the tube wall), completing the liquid transfer. Simultaneously, the large pore structure on the inner side reduces steam discharge resistance and accelerates steam diffusion. This design allows the liquid near the steam chamber side (…) Approaching The porosity is small. Smaller, increasing specific surface area to accelerate steam condensation; near the wall side ( Porosity close to 0 is high. Larger diameter increases permeability, facilitating rapid flow of condensate into the axial channel and achieving synergistic effects of efficient condensation and rapid drainage.

[0110] For example, the porosity radial gradient equation of the condensation section is used to set the porosity on the wall side. Set the radial gradient coefficient of the condensation section to 50%, so that the section closer to the steam chamber side ( The porosity of the 8mm diameter decreased to 40%, near the wall side ( The porosity of the steam side is kept at 65% (=0), achieving a gradient distribution of low porosity on the steam side and high porosity on the wall side, increasing the condensation specific surface area while improving the drainage permeability.

[0111] To address the mass transfer requirements of the evaporation section, a radial gradient structure opposite to that of the condensation section is designed. Simultaneously, directional channels for bubble escape are added. The radial gradient equation for porosity in the evaporation section is:

[0112] ,

[0113] In the formula, Indicates the radial direction of the heat pipe evaporation section Porosity at that location Indicates the porosity on the wall side. This represents the radial gradient coefficient of the evaporation section, and >0, This is the inner radius of the heat pipe. This design makes the side closest to the wall ( Approaching The porosity is small. Smaller size enhances capillary suction capability, rapidly transporting the liquid film to the evaporation interface; closer to the vapor chamber side ( Porosity close to 0 is high. Larger, reducing steam flow resistance.

[0114] For example, the radial gradient design uses the radial gradient equation of the evaporation section to set the porosity on the wall side. Set the radial gradient coefficient of the evaporation section to 30%, so that the side closer to the steam chamber ( The porosity of the 8mm diameter increased to 40%, near the wall side ( The porosity of the wall is maintained at 30% (=0), which enhances the capillary suction capacity of the wall surface.

[0115] In this embodiment, in the conformal structure of the evaporation section, multiple bubble escape channels are uniformly opened along the steam chamber side. Each TPMS cell corresponds to a directional bubble escape hole (i.e., channel). The channel diameter is set to 0.8 mm, the channel spacing is 2 mm, and the channel direction is consistent with the steam rising direction, further reducing the steam escape resistance and preventing steam from lingering in the evaporation section.

[0116] The gradient design is calculated under ideal paths, but when the solid body bends, the congestion of space can cause the local porosity to deviate from the design value. To compensate for the performance loss caused by this physical deformation, specific parameter corrections are required for the bending region. For the 90° bend requirement of the heat pipe, the bending curve equation (i.e., the Jacobian matrix and the regularized level set functional equation) is integrated into the conformal design equation (that is, the mathematical equation of the precise spatial conformal of the skeleton-type wicking base structure in polar coordinates along the axial centerline of the heat pipe, constructed based on the transformation relationship between the Frenet-Serret frame and the coordinate system). Essentially, it uses the actual bending geometric characteristics of the heat pipe as constraints to dynamically correct and optimize the conformal design equation. This enables the basic mapping equation, which originally only achieved conformal fitting of the structure, to have the ability to compensate for geometric distortion and correct the topological shape in the bending region. Ultimately, the conformal structure generated by the mapping not only fits the bending shape of the heat pipe, but also maintains the design porosity and complete topological characteristics in the bending region, fundamentally ensuring the heat transfer and bending resistance performance of the heat pipe after bending. This application also corrects the effective capillary diameter at bends using a response surface model. Ensure capillary pressure in key bending areas Greater than the flow resistance of the working fluid, such as Figure 6 As shown.

[0117] This application constructs a quantitative control model based on the Laplace-Young equation. The axial gradient ensures a dynamic balance between the strong capillary driving force in the evaporation section and the low reflux resistance in the condensation section, accelerating liquid film suction. The radial gradient in the condensation section increases the specific surface area through the low porosity on the vapor side, accelerating vapor condensation, while the high porosity on the wall side enhances liquid permeability. The reverse radial gradient in the evaporation section strengthens capillary suction on the wall, and, in conjunction with the bubble escape channels, significantly reduces vapor escape resistance. Compared to traditional uniform pore or simple gradient structures, this application effectively avoids problems such as working fluid reflux blockage, localized drying, and vapor retention, adapting to the heat dissipation requirements of high power density chips. The heat transfer stability and efficiency are significantly superior to existing technologies.

[0118] Step 105: Assign equation parameters to the TPMS capillary structure of the corresponding region of the heat pipe to achieve precise control of porosity and obtain a bend-resistant heat pipe. In this embodiment, the equation parameters determined in step 104 for different positions in the axial evaporation section, condensation section, and radial direction ( L , a , c(etc.), by assigning TPMS capillary unit cells to the corresponding regions in the conformal structure through a parameterized mapping algorithm.

[0119] Specifically, for the axial direction, along the z-axis of the heat pipe's centerline, according to the axial porosity gradient equation... The corresponding parameter values ​​are used to update the equation parameters of the conformal structure's structural equation segment by segment; for the radial direction, the radial porosity equations are applied to the condensation and evaporation sections respectively. and Adjusting different radial directions The equation parameters of the structural equations at the location were adjusted to ensure a smooth transition of the radial gradient. Subsequently, the topological continuity of the conformal structure after adjusting the equation parameters was verified using finite element analysis software to ensure that there was no overlap or breakage in the structure of each region, and that the deviation of the porosity distribution from the design value was controlled within ±1%.

[0120] Furthermore, this application also allows for the integrated fabrication of heat pipes using additive manufacturing processes. Leveraging the excellent self-supporting properties of the TPMS structure, a simultaneous "wick-shell" molding scheme is designed, eliminating the need for additional support structures. Materials such as aluminum alloy, stainless steel, titanium alloy, mold steel, or nickel-based high-temperature alloys are selected to meet the heat transfer and structural strength requirements of the heat pipe. Selective laser melting (SLM) and other 3D printing technologies are employed to achieve integrated molding of the wick and outer shell. An ultrasonic cleaning process is designed to remove powder residue, followed by vacuum sealing and injection of the working fluid, ensuring the molding quality and heat transfer stability of the heat pipe.

[0121] Compared to sintered heat pipes, the ordered TPMS structure allows for precise control of porosity and permeability through the equation parameters of the structural equation, solving the problem of high thermal resistance in sintered heat pipes without requiring complex sintering processes. Compared to grooved heat pipes, the TPMS structure naturally forms continuous, non-directional capillary channels without capillary force direction constraints. Furthermore, through conformal design that couples the Laplace-Young formula with the curve equation, the structure at the bending point is adaptively optimized without fracture or deformation. This solves the core pain points of traditional grooved heat pipes, such as easy channel damage and a sharp drop in heat transfer efficiency after bending, achieving a unified performance of "high-efficiency heat transfer + bending resistance + non-directional constraints".

[0122] While this application provides the method operation steps as described in the embodiments or flowcharts, more or fewer operation steps may be included based on conventional or non-inventive labor. The order of steps listed in this embodiment is merely one possible execution order among many and does not represent the only execution order. In actual device or client product execution, the methods shown in this embodiment or the accompanying drawings can be executed sequentially or in parallel (e.g., in a parallel processor or multi-threaded processing environment).

[0123] like Figure 7As shown in the figure, this application embodiment also provides a design device 700 for a gradient porous anti-bending heat pipe based on TPMS. The device includes: a basic construction module 701, a geometry adaptation module 702, a simplification module 703, a solution module 704, and a gradient optimization module 705, as detailed below.

[0124] The basic construction module 701 is used to select a three-period minimum surface according to the target working condition and construct a skeleton-type liquid absorption core basic structure according to its structural equation.

[0125] The geometry adaptation module 702 is used to perform coordinate system transformation on the skeleton-type liquid wick basic structure to adapt to the geometric characteristics of the heat pipe, thereby obtaining a conformal structure. The distortion correction of the conformal structure is achieved by modifying the structural equation.

[0126] The simplification module 703 is used to divide the conformal structure into multiple tiny square lattices. Based on the equation parameters and porosity of the structural equation of each tiny square lattice, a quadratic polynomial regression model is constructed to predict the relationship between the equation parameters and porosity.

[0127] The solver module 704 is used to determine the target porosity of each region of the heat pipe using the Laplace-Young equation, and to determine the equation parameters using a quadratic polynomial regression model based on the target porosity.

[0128] The gradient optimization module 705 is used to assign equation parameters to the TPMS capillary structure of the corresponding region of the heat pipe in order to achieve precise control of porosity and obtain a bend-resistant heat pipe.

[0129] Some modules in the apparatus described in this application can be described in the general context of computer-executable instructions that are executed by a computer, such as program modules. Generally, program modules include routines, programs, objects, components, data structures, classes, etc., that perform a specific task or implement a specific abstract data type. This application can also be practiced in distributed computing environments where tasks are performed by remote processing devices connected via a communication network. In distributed computing environments, program modules can reside in local and remote computer storage media, including storage devices.

[0130] The apparatus or module described in the above embodiments can be implemented by a computer chip or physical entity, or by a product with a certain function. For ease of description, the above apparatus is described by dividing it into various modules according to their functions. When implementing the embodiments of this application, the functions of each module can be implemented in one or more software and / or hardware. Of course, a module that implements a certain function can also be implemented by combining multiple sub-modules or sub-units.

[0131] The methods, apparatus, or modules described in this application can be implemented in a computer-readable program code manner. The controller can be implemented in any suitable manner, such as a microprocessor or processor and a computer-readable medium storing computer-readable program code (e.g., software or firmware) executable by the (micro)processor, logic gates, switches, application-specific integrated circuits (ASICs), programmable logic controllers, and embedded microcontrollers. Examples of controllers include, but are not limited to, the following microcontrollers: ARC 625D, Atmel AT91SAM, Microchip PIC18F26K20, and Silicon Labs C8051F320. A memory controller can also be implemented as part of the control logic of a memory. Those skilled in the art will also recognize that, in addition to implementing the controller in purely computer-readable program code manner, the same functionality can be achieved by logically programming the method steps to make the controller take the form of logic gates, switches, application-specific integrated circuits, programmable logic controllers, and embedded microcontrollers. Therefore, such a controller can be considered a hardware component, and the means included within it for implementing various functions can also be considered as structures within the hardware component. Alternatively, the device used to implement various functions can be viewed as either a software module that implements the method or a structure within a hardware component.

[0132] This application also provides an apparatus, the apparatus comprising: a processor; a memory for storing processor-executable instructions; wherein, when the processor executes the executable instructions, it implements the method described in this application.

[0133] This application also provides a non-volatile computer-readable storage medium storing a computer program or instructions thereon, which, when executed, enables the method described in this application embodiment to be implemented.

[0134] Furthermore, in the various embodiments of the present invention, each functional module can be integrated into a processing module, or each module can exist independently, or two or more modules can be integrated into a single module.

[0135] The aforementioned storage media include, but are not limited to, Random Access Memory (RAM), Read-Only Memory (ROM), Cache, Hard Disk Drive (HDD), or Memory Card. The memory can be used to store computer program instructions.

[0136] As can be seen from the above description of the embodiments, those skilled in the art can clearly understand that this application can be implemented by means of software plus necessary hardware. Based on this understanding, the technical solution of this application, in essence, or the part that contributes to the prior art, can be embodied in the form of a software product, or it can be embodied in the process of data migration. The computer software product can be stored in a storage medium, such as ROM / RAM, magnetic disk, optical disk, etc., and includes several instructions to cause a computer device (which may be a personal computer, mobile terminal, server, or network device, etc.) to execute the methods described in various embodiments or some parts of the embodiments of this application.

[0137] The various embodiments described in this specification are presented in a progressive manner. Similar or identical parts between embodiments can be referred to interchangeably. Each embodiment focuses on its differences from other embodiments. All or part of this application can be used in numerous general-purpose or special-purpose computer system environments or configurations. Examples include: personal computers, server computers, handheld or portable devices, tablet devices, mobile communication terminals, multiprocessor systems, microprocessor-based systems, programmable electronic devices, network PCs, minicomputers, mainframe computers, and distributed computing environments including any of the above systems or devices, etc.

[0138] The above embodiments are only used to illustrate the technical solutions of this application, and are not intended to limit this application. Although this application has been described in detail with reference to the foregoing embodiments, those skilled in the art should understand that modifications can still be made to the technical solutions described in the foregoing embodiments, or equivalent substitutions can be made to some or all of the technical features therein. Such modifications or substitutions do not cause the essence of the corresponding technical solutions to deviate from the scope of the technical solutions of this application.

Claims

1. A design method for a gradient porous, bend-resistant heat pipe based on TPMS, characterized in that, include: Based on the target working conditions, a three-period minimum surface is selected, and a skeleton-type liquid absorption core basic structure is constructed according to its structural equation. The coordinate system of the skeleton-type wicking core base structure is transformed to adapt to the geometric characteristics of the heat pipe, resulting in a conformal structure. Distortion correction of the conformal structure is achieved by modifying the structural equations, including: transforming the structural equations to map the skeleton-type wicking core base structure from the Cartesian coordinate system to the polar coordinate system; establishing a mapping relationship from the polar coordinate system to the global three-dimensional spatial coordinate system using the centerline of the heat pipe bend as the bending path, ensuring that the capillary channel is tangentially aligned with the fluid flow direction, thus obtaining the conformal structure; constructing the Jacobian matrix mapping the skeleton-type wicking core base structure to the bending path of the heat pipe in the polar coordinate system; determining the compensation factor by solving the Jacobian matrix to correct the constant terms of the structural equations; extracting the surface curvature of the skeleton-type wicking core base structure based on the Gauss-Bonnet theorem, constructing a regularized level set functional equation containing curvature extremum penalty terms, and further correcting the coefficients of the structural equations to achieve distortion correction of the conformal structure. The conformal structure is divided into multiple micro square lattices. Based on the equation parameters and porosity of the structural equation of each micro square lattice, a quadratic polynomial regression model is constructed to predict the relationship between the equation parameters and porosity. This includes: obtaining the volume fraction, spatial position, and corresponding equation parameters of each micro square lattice in the TPMS unit cell of the skeletal liquid core basic structure; and constructing a quadratic polynomial regression model based on multiple micro square lattices using the Box-Behnken response surface design method, with the equation parameters of the structural equation as independent variables and the porosity and volume fraction of the conformal structure as dependent variables, to predict the relationship between the equation parameters and porosity. The target porosity of each region of the heat pipe is determined using the Laplace-Young equation, and the equation parameters are determined using the quadratic polynomial regression model based on the target porosity. By assigning equation parameters to the TPMS capillary structure of the corresponding region of the heat pipe, precise control of porosity can be achieved, resulting in a bend-resistant heat pipe.

2. The method according to claim 1, characterized in that, The structural equation is as follows: ； In the formula, Representing the structural equation, Represents the three-dimensional coordinates of a point in three-dimensional space. L , a and c The equation parameters represent the structural equations. L , a For coefficients, c For constant terms, This represents the characteristic function of the surface.

3. The method according to claim 1, characterized in that, The basic structure of the skeleton-type liquid absorption core is as follows: ； In the formula, This indicates the basic structure of the skeleton-type absorbent core. This represents the threshold for determining structure generation. This represents the structural equations after mapping to the polar coordinate system.

4. The method according to claim 1, characterized in that, The process of determining the target porosity of each region of the heat pipe using the Laplace-Young equation, and determining the equation parameters using the quadratic polynomial regression model based on the target porosity, includes: The relationship between capillary pressure and pore structure is quantified using the Laplace-Young equation to determine the target porosity of each region of the heat pipe. Based on the target porosity, the equation parameters are solved using the quadratic polynomial regression model. Based on the parameters of the equation, the porosity is adjusted to change linearly along the z-axis so that the porosity gradually increases from the evaporation section to the condensation section; Based on the parameters of the equation, the radial porosity of the condensing section, the wall-side porosity, and the radial porosity of the evaporation section are determined. The radial porosity of the condensing section, the wall-side porosity, and the radial porosity of the evaporation section are adjusted respectively to improve the condensation and evaporation efficiency of the heat pipe. Multiple channels are uniformly added along the steam chamber side of the evaporation section, and each channel corresponds one-to-one with the TPMS cell in the conformal structure to reduce the resistance to steam escape.

5. The method according to claim 4, characterized in that, The relationship between capillary pressure and pore structure is quantified using the Laplace-Young equation as follows: ； In the formula, Indicates capillary pressure. Indicates the surface tension of a liquid working fluid. Indicates the contact angle formed between the working fluid and the wicking material. Indicates the effective capillary diameter of the pores.

6. A design apparatus for a TPMS-based gradient porous flexural heat pipe for implementing the method described in any one of claims 1-5, characterized in that, include: The basic construction module is used to select a three-period minimum surface according to the target working condition and construct a skeleton-type liquid absorption core basic structure according to its structural equation. A geometric adaptation module is used to perform coordinate system transformation on the skeleton-type wicking base structure to adapt to the geometric characteristics of the heat pipe, resulting in a conformal structure. The module corrects distortion of the conformal structure by modifying the structural equations. This includes: transforming the structural equations to map the skeleton-type wicking base structure from a Cartesian coordinate system to a polar coordinate system; establishing a mapping relationship from the polar coordinate system to the global three-dimensional coordinate system using the centerline of the heat pipe bend as the bending path, ensuring that the capillary channel is tangentially aligned with the fluid flow direction, thus obtaining the conformal structure; constructing a Jacobian matrix mapping the skeleton-type wicking base structure to the bending path of the heat pipe in the polar coordinate system; determining a compensation factor by solving the Jacobian matrix to correct the constant terms of the structural equations; extracting the surface curvature of the skeleton-type wicking base structure based on the Gauss-Bonnet theorem, constructing a regularized level set functional equation containing curvature extremum penalty terms, and further correcting the coefficients of the structural equations to achieve distortion correction of the conformal structure. A simplified module is used to divide the conformal structure into multiple micro square lattices. Based on the equation parameters and porosity of the structural equation of each micro square lattice, a quadratic polynomial regression model is constructed to predict the relationship between the equation parameters and porosity. This includes: obtaining the volume fraction, spatial position, and corresponding equation parameters of each micro square lattice in the TPMS unit cell of the skeletal liquid-absorbing core basic structure; and constructing a quadratic polynomial regression model based on multiple micro square lattices using the Box-Behnken response surface design method, with the equation parameters of the structural equation as independent variables and the porosity and volume fraction of the conformal structure as dependent variables, through a quadratic polynomial function to predict the relationship between the equation parameters and porosity. The solution module is used to determine the target porosity of each region of the heat pipe using the Laplace-Young equation, and to determine the equation parameters using the quadratic polynomial regression model based on the target porosity. The gradient optimization module is used to assign equation parameters to the TPMS capillary structure of the corresponding region of the heat pipe, so as to achieve precise control of porosity and obtain a bend-resistant heat pipe.

7. An apparatus for performing a TPMS-based design method for gradient porous flexural heat pipes, characterized in that, include: processor; Memory used to store processor-executable instructions; When the processor executes the executable instructions, it implements the method as described in any one of claims 1 to 5.

8. A non-volatile computer-readable storage medium, characterized in that, Includes storage of computer programs or instructions that, when executed, cause the method as described in any one of claims 1 to 5 to be implemented.

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