A heat dissipation structure design method and system based on topology optimization

Abstract

The application belongs to the technical field of structural topology optimization, and discloses a heat dissipation structure design method based on topology optimization, which comprises the following steps: defining a three-dimensional design domain and boundary conditions of the heat dissipation structure, converting the three-dimensional design domain into a two-dimensional model, and establishing a load uncertainty model according to the distribution of the boundary conditions and the temperature of a heat source; performing robust topology optimization on the two-dimensional model according to the load uncertainty model to obtain a two-dimensional flow channel topology structure; mapping the two-dimensional flow channel topology structure into a three-dimensional flow channel structure; based on the iteration principle of Menger sponge, constructing fractal lattices with different volume fractions, and embedding the constructed fractal lattices into the three-dimensional flow channel structure after the fractal lattices are endowed with material properties, to obtain an optimized heat dissipation structure. The application further discloses a heat dissipation structure design system based on topology optimization. The method and the system realize efficient design and performance optimization of a heat transport channel by integrating pseudo-three-dimensional modeling, fractal lattice structure and an efficient sampling strategy.

Description

TECHNICAL FIELD

[0001] The present application belongs to the technical field of structural topology optimization, and particularly relates to a heat dissipation structure design method and system based on topology optimization. BACKGROUND

[0002] Topology optimization is a design method that seeks the optimal distribution of materials within a design domain, aiming to optimize certain performance of a structure under given boundary conditions and constraints. In mathematical form, topology optimization is usually expressed as a high-dimensional constrained optimization problem, with design variables derived from finite element discretization of the design region, and an objective function used to maximize or minimize a specific physical response.

[0003] Currently, the mainstream topology optimization methods mainly include density-based methods (such as SIMP method), level set methods, and phase field methods, etc. In the past few decades, topology optimization has been widely studied and applied in structural design and multidisciplinary engineering problems, covering areas such as minimum structural compliance, heat dissipation performance enhancement, conjugate heat transfer, and fluid dynamics optimization. With the development of additive manufacturing technology, topology optimization has shown significant advantages in the preparation of complex and precise heat dissipation structures. For example, the profiled cooling channels designed based on topology optimization have higher thermal efficiency, more uniform temperature distribution, and shorter cooling period compared to traditional straight channels.

[0004] Although topology optimization is a powerful design tool, its application in three-dimensional models still faces significant challenges, including high computational complexity and convergence difficulties caused by the exponential increase in design variables. To alleviate these bottlenecks, existing research has proposed strategies such as hybrid two-dimensional-three-dimensional modeling frameworks and density method with accompanying variable solutions. However, such methods still have obvious limitations in computational efficiency and adaptability to variable conditions (such as load uncertainty).

[0005] To address uncertainty (such as load fluctuations), robust topology optimization methods have gradually developed, which convert probabilistic problems into deterministic multi-condition optimization problems through sampling approximation or polynomial chaos expansion. Representative methods include structure compliance minimization under uncertain loads and failure safety design considering random damage. On the other hand, multi-scale topology optimization supports collaborative design at macro and micro scales by relaxing the intermediate density penalty mechanism, and commonly used microstructure units include parameterized lattices and free-topology microstructures.

[0006] However, most existing robust and multi-scale topology optimization methods are still computationally expensive when dealing with three-dimensional heat management problems, and are sensitive to uncertainty factors such as temperature fluctuations of heat sources, with poor robustness.

[0007] In the prior art, the design of heat transfer channels mainly relies on traditional empirical formulas or simple geometric configurations, such as straight-line channels or spiral channels. Although the rise of advanced technologies such as additive manufacturing provides new process paths for the formation of complex structures, the corresponding design methods have not been fundamentally improved, and their limitations are increasingly evident, as follows:

[0008] (1) High computational complexity and poor optimization convergence: Three-dimensional topology optimization problems involve a large number of design variables, which can easily cause "computational explosion" problems, making it difficult for the optimization process to converge and inefficient. Traditional numerical methods such as the density method or the level set method have high computational costs when dealing with complex three-dimensional models, making it difficult to perform efficient iterative optimization, and thus unable to meet the needs of engineering practical scenarios such as turbine blade cooling jackets.

[0009] (2) Lack of robustness to variable operating conditions: Existing topology optimization methods are mostly based on deterministic load conditions, ignoring the widespread existence of load uncertainty in actual engineering (such as fluctuations in heat source temperature, mechanical vibration, and assembly errors). This assumption makes the final design overly sensitive to parameter changes, and can easily lead to performance degradation or even failure when deviating from the design operating conditions. For example, in the case of uncertain heat source temperature, the original design can cause local overheating, thermal stress concentration, or even structural damage.

[0010] (3) Bottleneck in improving heat transfer performance: Traditional serpentine or spiral channel layouts cannot fully utilize the advantages of multi-scale structures in increasing specific surface area and promoting fluid mixing, and their thermal efficiency is significantly lower than that of natural porous structures with high porosity, excellent energy absorption, and anisotropic heat transfer characteristics, which cannot realize the potential benefits of thermal efficiency improvement.

[0011] (4) Lack of multi-scale collaborative design capability: Current methods cannot seamlessly integrate micro-fractal lattice structures with macro-topological morphology, which can easily cause interface discontinuity, stress concentration, and other problems, while significantly increasing the complexity of modeling and calculation. In addition, when considering uncertainty optimization, traditional Monte Carlo simulation methods have low sampling efficiency and are prone to random walk difficulties, which cannot effectively reduce the system's sensitivity to uncertain parameters.

[0012] (5) Insufficient manufacturing feasibility and verification effectiveness: Existing topology optimization designs often do not fully consider the technical constraints of additive manufacturing (such as minimum feature size, support structure, and warping deformation), making it difficult to actually form some optimization results. At the same time, there is a lack of an efficient so-called "pseudo-three-dimensional" modeling method to bridge the gap between two-dimensional optimization and three-dimensional verification, resulting in low efficiency and poor reliability in the conversion process from design to experimental verification.

[0013] In summary, the existing heat transport channel design method has significant defects in calculation efficiency, robustness, multi-scale integration and manufacturing verification, which limits its reliable application in high heat flow density heat dissipation scenarios such as turbine blades. SUMMARY

[0014] The purpose of the present application is to provide a heat dissipation structure design method and system based on topology optimization, which realizes efficient design and performance optimization of heat transport channels by integrating pseudo-three-dimensional modeling, fractal lattice structure and efficient sampling strategy, and overcomes the defects of dependence on traditional experience and insufficient performance under uncertain conditions in existing heat dissipation structure design.

[0015] To achieve the above purpose, the technical scheme adopted by the present application is as follows:

[0016] A heat dissipation structure design method based on topology optimization, the method comprising the following steps:

[0017] (1) defining the three-dimensional design domain and boundary conditions of the heat dissipation structure, converting the three-dimensional design domain into a two-dimensional model, and establishing a load uncertainty model according to the boundary conditions and the distribution of heat source temperature;

[0018] (2) performing robust topology optimization on the two-dimensional model according to the load uncertainty model to obtain a two-dimensional flow channel topology structure;

[0019] (3) mapping the two-dimensional flow channel topology structure to a three-dimensional flow channel structure;

[0020] (4) based on the Menger sponge iteration principle, constructing fractal lattices with different volume fractions, and embedding the constructed fractal lattices with material properties into the three-dimensional flow channel structure to obtain an optimized heat dissipation structure.

[0021] In step (1), the specific method for converting the three-dimensional design domain into a two-dimensional model is as follows: a dimension reduction model is established with flow channel height distribution as the design variable, based on the assumption of incompressible fully developed laminar flow, the velocity is assumed to be parabolic along the height direction and the temperature is assumed to be a fourth-order polynomial distribution; an equivalent density, in-plane scaled pressure field and viscous drag coefficient are introduced to construct a local resistance model, wherein the resistance term decreases with increasing flow channel height; the velocity and temperature profile functions are substituted into the energy conservation equation to derive the two-dimensional heat transfer control equation, wherein the flow channel height is determined by linear interpolation between the preset minimum and maximum values, and the minimum filtering radius is determined by the gradient extremum of the height field, thereby completing the dimension reduction from three-dimensional problem to two-dimensional optimization problem.

[0022] Step (1) specifically comprises: determining the design space of the heat dissipation structure, including the fluid inlet, outlet position and heat source distribution area; mapping the three-dimensional design domain into a two-dimensional equivalent model through a dimension reduction method; establishing a probability distribution model of heat source temperature and other parameters to describe the random fluctuation characteristics and provide input conditions for subsequent robust optimization.

[0023] In step (1), the method for establishing the load uncertainty model according to the distribution of the boundary conditions and the heat source temperature is:

[0024] (1-1) Establishing a load model according to the boundary conditions;

[0025] (1-2) Defining the distribution of the heat source temperature, including the mean value, standard deviation and truncation interval;

[0026] (1-3) Integrating the distribution of the heat source temperature into the load model to obtain the load uncertainty model.

[0027] In step (1-2), the truncated normal distribution is used to simulate the variability of the heat source temperature to represent the temperature fluctuation range in actual operation; the load uncertainty model obtained in step (1-3) provides input for subsequent scenario sampling, ensuring that the model can reflect the true uncertainty source.

[0028] Further, the robust topology optimization process of step (2) comprises: constructing an optimization model with the weighted combination of the mean value and variance of the thermal performance index as the objective function; setting the volume fraction and pressure drop constraint conditions; using a mixed Hamilton Monte Carlo and progressive sampling strategy to handle parameter uncertainty; performing sensitivity analysis through the adjoint method, and combining filtering technology and continuation strategy to ensure numerical stability and convergence efficiency of the optimization process.

[0029] Step (2) comprises the following sub-steps:

[0030] (2-1) Constructing a mean-variance robust objective function containing volume constraints and pressure drop constraints for the generated two-dimensional model;

[0031] (2-2) Using a mixed strategy combining Hamilton Monte Carlo and progressive sampling to extract a number of temperature samples from the distribution of the heat source temperature of the load uncertainty model for use, and determining effective temperature samples;

[0032] (2-3) Calculating the mean value and variance of the robust objective function based on the effective temperature samples, obtaining the gradient information of the objective function with respect to the design variables through adjoint sensitivity analysis, updating the design variables using a gradient-based optimization algorithm, and iterating until convergence to obtain a two-dimensional flow passage topology structure that meets the robustness requirements.

[0033] The objective function in step (2-1) is expressed as:

[0034] ;

[0035] wherein, is the mean of the objective function, is the variance of the objective function, is defined as the mean of the base objective function F under the sampling scenario, where the base objective function is expressed as:

[0036] ;

[0037] wherein,

[0038] ,

[0039] ;

[0040] and represent the weight factor of the objective function, represents the design domain, T Q represents the preset heat source temperature, Q vd represents the fluid viscous dissipation, , , and are preset constants for dimensionless processing of the objective function.

[0041] wherein, is a trade-off coefficient for balancing the performance mean and robustness; the base objective function quantifies the expected performance and variability under uncertainty by aggregating the performance values of the sampling scenarios, ensuring that the optimization result is robust to heat source fluctuations.

[0042] Step (2-2) includes the following sub-steps:

[0043] (2-2-1) Initialize the sampling process, extract initial samples from the uncertainty model, and use the momentum mechanism of Hamilton Monte Carlo to realize efficient exploration of the parameter space;

[0044] (2-2-2) Divide the key interval according to the sensitivity information and local variance of historical iterations, increase the sample density in the high variance area, and gradually expand the total sample number, wherein the sample number of the progressive sampling strategy is expressed as , t is the current iteration number;

[0045] (2-2-3) By integrating multiple rounds of sampling data, the mean and variance of the objective function are calculated to monitor the stability of the optimization process, and the sampling is terminated when the change rate is lower than the set threshold, wherein the termination condition is expressed as the average target change rate and the variance being less than the threshold, which reduces unnecessary sampling calculations by monitoring the performance stability in the optimization iteration.

[0046] Step (2-3) includes the following sub-steps:

[0047] (2-3-1) Adopt a material property interpolation method to approach the design variable to a 0-1 distribution, wherein the material property interpolation function is expressed as , and are solid and fluid properties, is a design variable, is a penalty function factor; the formula punishes the intermediate density value based on the SIMP method, ensuring that the optimization converges to a clear solid-fluid configuration;

[0048] (2-3-2) Solve the fluid control equation and the energy equation, calculate the accompanying sensitivity to update the design variable, and iterate to convergence to obtain a two-dimensional channel skeleton;

[0049] (2-3-3) After each update of the design variable, perform a feasibility check of the volume constraint and the pressure drop constraint, and project the design that violates the constraint for correction;

[0050] (2-3-4) Use Heaviside projection filtering technology to ensure the minimum feature size, and gradually increase the projection sharpness combined with the continuation strategy to promote the formation of a clear and manufacturable topology structure;

[0051] (2-3-5) Set the convergence criteria, when the relative change of the objective function is less than the set threshold and all constraints are satisfied, terminate the iteration process, and output the final two-dimensional flow channel topology structure.

[0052] In step (3), the center line extraction is performed on the two-dimensional model, the redundant branches are removed through graph structure pruning, and then the path smoothing is realized through spline fitting. The smoothed path is mapped to a three-dimensional flow channel structure. In the mapping process, the minimum wall thickness, curvature limitation and inlet and outlet connectivity are ensured.

[0053] Further, the two-dimensional to three-dimensional mapping process of step (3) specifically includes: extracting the flow channel skeleton structure from the optimized two-dimensional topology result; obtaining the channel center path by using the center line extraction algorithm; pruning redundant branches and retaining the main flow path by using graph theory algorithm; generating a smooth three-dimensional path through spline curve fitting technology, and performing geometric transformation along the third dimension direction to form a three-dimensional flow channel structure that satisfies the minimum wall thickness and curvature constraints.

[0054] Further, the fractal lattice construction and integration process of step (4) comprises: generating a multi-scale fractal lattice based on the Menger sponge iteration principle; establishing a proxy model of the equivalent performance of the lattice through single-cell conjugate heat transfer simulation; embedding the fractal lattice into the three-dimensional flow channel wall surface according to the macroscopic channel layout; performing macro-micro consistency correction to ensure the performance matching of the multi-scale design; and finally verifying the comprehensive performance of the heat dissipation structure through full-order conjugate heat transfer simulation.

[0055] In step (4), the method for constructing fractal lattices with different volume fractions is:

[0056] (4-1) Construct a lattice family based on the Menger sponge iteration principle, and form a self-similar porous structure by removing the central region step by step;

[0057] (4-2) Adjust the iteration depth and strut thickness parameters of the lattice to generate lattice variants with different volume fractions to adapt to the needs of different fluid regions;

[0058] (4-3) Assign material properties to the solid region and fluid region of the lattice variant, respectively, and use structural symmetry to simplify numerical simulation.

[0059] In step (4-2), the volume fraction is controlled by the iteration depth and strut thickness to realize independent regulation of the surface area-volume ratio and hydraulic resistance, and to realize parameterized Menger sponge lattice. For example, the present application constructs three types of lattice structures, and the volume fraction of the solid material is 22%, 55% and 74% respectively, and the volume fraction of the corresponding fluid region is 78%, 45% and 26% respectively, and the average volume fraction of the three is about 50%.

[0060] In step (4-3), the equivalent properties of the micro-lattice are obtained by homogenization method based on asymptotic expansion or volume averaging to ensure the physical consistency of the macro-micro model.

[0061] The present application also provides a heat dissipation structure design system based on topology optimization, which comprises:

[0062] A two-dimensional model construction module defines the three-dimensional design domain and boundary conditions of the heat dissipation structure, converts the three-dimensional design domain into a two-dimensional model, and establishes a load uncertainty model according to the boundary conditions and the distribution of heat source temperature;

[0063] A robust topology optimization module performs robust topology optimization on the two-dimensional model according to the load uncertainty model to obtain a two-dimensional flow channel topology structure, and maps the two-dimensional flow channel topology structure to a three-dimensional flow channel structure;

[0064] The fractal lattice integrated module is based on the iteration principle of Menger sponge, constructs fractal lattices with different volume fractions, and embeds the fractal lattices with material properties into a three-dimensional flow channel structure to obtain an optimized heat dissipation structure.

[0065] The specific implementation of each module has been discussed in the design method, and will not be repeated here.

[0066] Compared with the prior art, the beneficial effects of the present application are:

[0067] The present application can greatly improve the heat transfer efficiency and system stability under the condition of ensuring the design robustness and manufacturability, and is not limited by a single scale or deterministic loading. The present application realizes seamless integration of macroscopic layout and microscopic wall configuration by adding a multi-scale fractal lattice homogenization module, forms a two-way information transmission mechanism, and significantly improves the thermal efficiency under the same volume fraction and pressure drop budget conditions, significantly reduces the response variability, effectively alleviates the crack risk caused by thermal-mechanical stress gradient, and improves the cooling uniformity, especially for complex structural components such as turbine blades. By introducing a robust topology optimization algorithm, combining the mean-variance objective function and using Hamilton Monte Carlo and progressive sampling strategies to efficiently explore high-dimensional parameter space, the calculation cost is greatly reduced compared to the full Monte Carlo method, and the optimization process converges faster, achieving lower temperature fluctuations under thermal uncertainty, reducing the average temperature of turbine blades, reducing response variability, significantly enhancing robustness to operating variability, extending equipment service life and reducing maintenance costs. By using pseudo-three-dimensional mapping and lattice instantiation post-processing, the computational resource demand is significantly reduced, while preserving the dominant thermal fluid behavior, avoiding performance drift and non-physical interpretation, and improving design space exploration efficiency and innovation. The present application is superior to existing products in terms of thermal efficiency, robustness and computational efficiency, especially suitable for high-temperature complex systems such as aircraft engines, and can achieve shorter cooling time, more uniform temperature distribution and lower total life cycle cost. BRIEF DESCRIPTION OF DRAWINGS

[0068] Figure 1 A flowchart of a heat dissipation structure design method based on topology optimization provided for the embodiment;

[0069] Figure 2 A typical turbine blade structure provided for the embodiment;

[0070] Figure 3 A simplified two-dimensional model of a turbine blade structure provided for Example 1 and Comparative Example 1;

[0071] Figure 4 A robust topology optimization flow channel structure in Example 1;

[0072] Figure 5 The deterministic topology optimization flow channel structure in Comparative Example 1;

[0073] Figure 6 Three different types of lattice structures constructed for Example 1;

[0074] Figure 7 The fractal lattice fluid heat transfer performance verification scene in Example 1;

[0075] Figure 8 The fractal lattice fluid region temperature distribution in Example 1;

[0076] Figure 9 The lattice mapping rule diagram in Example 1 and Comparative Example 1;

[0077] Figure 10 The flow channel design scheme comparison in Example 1, Comparative Example 1 and Comparative Example 2;

[0078] Figure 11 The fluid region temperature distribution graph when the heat source temperature is 80℃ in Example 1, Comparative Example 1 and Comparative Example 2;

[0079] Figure 12 The performance comparison of the flow channel design scheme in Example 1, Comparative Example 1 and Comparative Example 2 under different heat source temperatures. DETAILED DESCRIPTION

[0080] Turbine blades are key components of an aero-engine, and their thermal management design has an important influence on the overall performance. Based on the method proposed in the present application, the turbine blade cooling channel is designed and optimized. First, deterministic topology optimization is carried out on a pseudo-three-dimensional model, and further robust topology optimization is implemented under thermal uncertainty conditions. Finally, the optimization results are mapped to a multi-scale fractal lattice structure, and its thermal performance is verified by numerical simulation.

[0081] Example 1

[0082] The heat dissipation structure design method based on topology optimization provided in the present embodiment is as shown in Figure 1 , and the specific process is as follows:

[0083] S1, define the three-dimensional design domain and boundary conditions of the heat dissipation structure, convert the three-dimensional design domain into a two-dimensional model, and establish a load uncertainty model according to the boundary conditions and the distribution of heat source temperature.

[0084] In a turbine fan engine, the design of turbine blades is crucial. In order to achieve effective heat dissipation, the blades are usually equipped with complex cooling channels, among which serpentine channel design is particularly common, such as Figure 2The illustrated. This type of channel design forces the cooling fluid to follow a serpentine path through the hottest parts of the blade, helping to maintain the blade within a safe operating temperature range and ensuring the performance and reliability of the engine.

[0085] However, the traditional serpentine channel layout largely relies on engineering experience, and there is still room for improvement in terms of thermal flow synergy efficiency and handling of uncertain thermal loads. To further improve cooling performance and design reliability, topology optimization technology is introduced into this field. This method automatically generates the optimal material distribution form through mathematical modeling and optimization algorithms, breaking through the limitations of experience and providing innovative configurations with higher thermodynamic performance. Accordingly, the present invention considers applying topology optimization to the design of turbine blade cooling channels to achieve better heat dissipation performance and robustness.

[0086] Based on the dimensionality reduction model, a two-dimensional equivalent model of a turbine blade is constructed as shown in Figure 3 The model consists of a large square design domain with a side length of 200 mm and two small square inlet and outlet areas with a side length of 25 mm. In the reduced model, the temperature of the upper and lower surfaces of the channel is set to 50℃. The fluid inlet velocity is distributed in a parabolic manner, with the maximum velocity set to 0.01 m / s. The inlet temperature follows a polynomial distribution, with the minimum temperature set to 20℃. The outlet pressure is set to 0 Pa, and liquid water is chosen as the heat transfer medium. Setting the outlet pressure to 0 Pa helps simplify the numerical calculation: since the flow is driven by the pressure gradient rather than the absolute pressure value, this setting avoids redundant calculations caused by handling large absolute pressures, thereby improving computational efficiency while ensuring physical accuracy.

[0087] S2, according to the load uncertainty model, the two-dimensional model is robustly topologically optimized, and the two-dimensional flow channel topology structure is obtained.

[0088] To ensure that the designed turbine blade cooling channel maintains excellent cooling performance under various heat source temperature conditions, the present invention performs numerical experiments based on the COMSOL Multiphysics and MATLAB interface. The experiment focuses on the optimization process under heat source temperature uncertainty, using a progressive sampling strategy to efficiently handle variable load conditions, thereby ensuring the robustness of the design to uncertainty.

[0089] The optimization problem is based on the reduced model shown in (b) in Figure 3 The variable load condition is a surface heat source, with its temperature value as a variable parameter, varying between 60℃ and 100℃, as shown in Figure 3The design domain in (b) and (c) is a square region of 80 mm x 80 mm, discretized into a 60 x 60 grid. The boundary conditions are set as: inlet velocity of 0.01 m / s, inlet temperature of 20 °C, and outlet pressure of 0 Pa. To introduce robustness consideration, the heat source temperature is assumed to be uncertain, following a truncated normal distribution with mean of 80 °C, standard deviation of 5 °C, and truncation interval of [60 °C, 100 °C]. The optimization objective is to minimize the following robust objective function:

[0090] ;

[0091] where and denote the mean and variance of the objective function, respectively. The weight coefficient is initially set as 0.2 to prioritize the mean performance, and can be adjusted later to balance the mean and variance requirements. The volume upper bound is set as 0.5, and the initial density is set as 0.5, with the initial value of each iteration step following the optimization result of the previous iteration step.

[0092] The optimization employs an iterative framework based on MATLAB, with a total of 100 iterations. The sampling strategy is based on the progressive sampling method, with the number of samples in each iteration being , where denotes the current iteration number. This strategy uses fewer samples in the early optimization stage to quickly explore the design trend, and gradually increases the number of samples in the later stage to improve the accuracy of robustness evaluation. The specific steps are as follows:

[0093] (a) Extract temperature samples from the truncated normal distribution, and combine the Hamiltonian Monte Carlo method to improve sampling efficiency and sample representativeness. The resulting samples are screened to determine the effective temperature sample set for robustness analysis.

[0094] (b) Use the material property interpolation model based on the SIMP method to control the intermediate density with a penalty factor and promote the design variables to converge to a 0-1 distribution. The equivalent material properties of the solid and fluid regions are calculated as follows:

[0095] ;

[0096] and are the solid and fluid properties, is the design variable, is the penalty function factor.

[0097] For each temperature sample, update the model parameters, solve the Navier-Stokes equation and heat transfer equation, calculate the accompanying sensitivity and update the design variables to obtain the corresponding objective function value. After each update of the design variables, perform feasibility checks for volume constraints and pressure drop constraints, and perform projection correction on design results that do not meet the constraints. The Heaviside projection filtering technique is used to ensure the minimum feature size, and the continuation strategy is used to gradually increase the projection sharpness, so as to obtain a clear solid-fluid boundary.

[0098] (c) Calculate the mean value of the objective function based on the effective samples and variance , and then derive the robust objective function value , and monitor the average density change to ensure that the volume fraction constraint meets the upper limit requirement of 0.5;

[0099] (d) iterate until 100 times, or terminate iteration when the objective function change rate is less than the convergence condition.

[0100] The resulting robust topology optimization flow channel structure is shown in Figure 4 .

[0101] S3, map the two-dimensional flow channel topology structure to a three-dimensional flow channel structure.

[0102] The skeletonization algorithm is used to extract the two-dimensional channel centerline, ensuring that the path is continuous and farthest from the boundary. Check the wall thickness by distance transformation, and if it is below the set threshold, adjust the skeleton structure. At the same time, use the path search algorithm to connect the breakpoints, and finally output the parameterized two-dimensional centerline in the form of point sequence or spline curve.

[0103] Convert the centerline to a graph structure, and apply a graph theory algorithm to prune redundant branches, including short branches and loops, and preferentially retain the main flow path. The curvature limit and minimum wall thickness requirements must be met during the process, and the connectivity from the inlet to the outlet must be verified. Finally, output the simplified main channel path graph structure.

[0104] Fit the pruned path to a smooth spline curve, and control the points to make the curvature not exceed the set upper limit. Extrude or bend the two-dimensional spline along the third dimension to generate a three-dimensional parameterized path, and verify the uniformity of the wall thickness and the continuity of the path endpoints.

[0105] S4, based on the Menger sponge iteration principle, construct a fractal lattice with different volume fractions, and embed the constructed fractal lattice with material properties into the three-dimensional flow channel structure to obtain the optimized heat dissipation structure.

[0106] Menger sponge is a generalization of Cantor set and Sierpinski carpet in three-dimensional space. Each surface of Menger sponge presents the geometric structure of Sierpinski carpet, and intersects with any diagonal of the original cube to form a Cantor set. As a closed set, the structure is also a compact set according to Heine-Borel theorem, and has the characteristics of being uncountable and having a Lebesgue measure of 0. From the perspective of topological dimension, the topological dimension of Menger sponge is 1, belonging to the category of general curves. It should be particularly noted that although the structure has a finite volume, its surface area is infinite.

[0107] The construction process of Menger sponge includes the following steps: (a) taking a cube as the starting unit; (b) dividing each face of the cube into 9 equal small squares, and then dividing the entire cube into 27 identical small cubes; (c) removing the small cube at the center of each face and the small cube at the center of the entire large cube, leaving the remaining 20 small cubes; (d) recursively performing steps (a) to (c) on each of the remaining small cubes. Repeat the process infinitely to form the Menger sponge structure.

[0108] Based on the above Menger sponge configuration, three different types of lattice structures are constructed, with solid material volume fractions of 22%, 55% and 74% (corresponding fluid region volume fractions of 78%, 45% and 26%) respectively, and an average volume fraction of about 50% as shown in Figure 6 .

[0109] Since the lattice structure has complete symmetry in three-dimensional space, only the inlet-outlet condition in a single dimension needs to be considered for simulation analysis during fluid heat transfer performance verification. The solid region material is selected as structural steel, with a density of 7850 kg / m 3 , a thermal conductivity of 44 W / m•K, and a specific heat capacity of 460 J / kg•K. The fluid region material is selected as liquid water, with a density of 1000 kg / m 3 , a thermal conductivity of 0.6 W / m•K, a specific heat capacity of 4200 J / kg•K, and a dynamic viscosity of 0.001 Pa•s.

[0110] The lattice structure is placed in a flow field environment with consistent size and boundary conditions, and multi-physical field coupling simulation analysis is carried out, as shown in Figure 7 . The cube region containing the lattice is set by customizing the material properties, so that the microscopic lattice structure is equivalent to a material model with macroscopic uniform properties.

[0111] The temperature distribution of the fluid region of the constructed lattice and the multi-field coupling simulation results are shown in Figure 8 . The approximate material properties of lattice I in the macroscopic dimension are determined as follows: density of 2360 kg / m 3It has a thermal conductivity of 9.28 W / m•K and a specific heat capacity of 3452 J / kg•K. Approximate material properties of Lattice II in the macroscopic dimension: density of 4400 kg / m³. 3 It has a thermal conductivity of 22.3 W / m•K and a specific heat capacity of 2330 J / kg•K. Approximate material properties of Lattice III in the macroscopic dimension: density of 6440 kg / m³. 3 Its thermal conductivity is 35.32 W / m•K and its specific heat capacity is 1280 J / kg•K.

[0112] S5. Result Comparison and Verification

[0113] Since the blade cross-sectional shape is approximately... Figure 2 The sector shown cannot be directly generated from its internal three-dimensional flow channel topology through simple stacking of two-dimensional optimization results. Therefore, the irregular design domain is discretized into 60... A 60 square cell grid is used, and the fractal lattice type is assigned to it based on the weighted value of the design variables of each cell.

[0114] Robust multi-scale design is based on Figure 4 Robust topology optimization results obtained under uncertain heat source conditions. Both designs are stretched along the blade height direction to construct pseudo-3D models, and the following lattice mapping rules are uniformly applied: design variable values ​​in the interval [0, 1 / 3] correspond to lattice I, [1 / 3, 2 / 3] correspond to lattice II, and [2 / 3, 1] correspond to lattice III, as shown below. Figure 9 As shown in (a) above. The final generated three-dimensional multi-scale heat dissipation channel structure is as follows. Figure 10 As shown in (a) above, the model's appearance is as follows Figure 10 As shown in (d) in the figure.

[0115] Comparative Example 1

[0116] The method used in Example 1 differs from that in Example 1 in that:

[0117] The two-dimensional model constructed in step (1) is under constant load conditions, such as Figure 3 As shown in (a), the temperature of its heat source remains constant.

[0118] In step (2): The design goal is to maximize heat transfer performance while ensuring smooth flow within the channel. Heat transfer efficiency can be characterized by the change in heat flux density at the inlet and outlet. Given that the inlet temperature is constant, the heat transfer performance can be simplified to the outlet temperature, and is positively correlated with it. Flow performance is represented by the pressure drop between the inlet and outlet of the channel. Since the outlet pressure is set to zero, the flow performance can be simplified to the inlet pressure value, and is negatively correlated with it. Based on the above principles, a convective heat transfer topology optimization problem for a square heat exchanger is established:

[0119] ;

[0120] wherein, represents the outlet boundary, represents the inlet boundary, represents the upper limit of pressure drop, which is usually determined by scaling the pressure drop of the reference design. In the topology optimization process of the present case, the pressure drop constraint is crucial. Without the pressure drop limit, the channel height will be continuously reduced to maximize the outlet temperature, which is not feasible in practice. The pressure drop constraint ensures the continuity of the channel, thus making the design practically feasible.

[0121] The solid material in the design domain is selected as structural steel, and the corresponding density is 7850 kg / m 3 , the thermal conductivity is 44 W / m•K, and the specific heat capacity is 460 J / kg•K; the liquid material is liquid water, and the corresponding density is 1000 kg / m 3 , the thermal conductivity is 0.6 W / m•K, the specific heat capacity is 4200 J / kg•K, and the dynamic viscosity is 0.001 Pa•s. The design domain is uniformly divided by a 60 60 grid, and there are 61 61=3721 design variables in total, each of which represents the density of the current node for controlling the distribution of solid-liquid materials. The objective function is composed of two parts of heat transfer performance and flow performance , which are set to be dimensionless through a ratio relationship, as shown in the following formula:

[0122] ;

[0123] wherein, and represent the weight factors of the objective function, both of which are 0.5, represents the design domain, T Q represents the preset heat source temperature, Q vd represents the fluid viscosity dissipation, , , and are preset constants for the dimensionless processing of the objective function. The physical property parameters of the porous medium material in the design domain are calculated according to formula (2).

[0124] The values thereof are related to the density corresponding to the design variable. The upper threshold of the material volume fraction is set to 0.5, that is, the fluid phase distribution area cannot exceed 50% of the total volume of the design domain. The results of the deterministic topology optimization flow channel structure are shown in Figure 5 .

[0125] In step (3): deterministic multiscale design is based on Figure 5 The resulting two-dimensional flow channel topology is discretized into elements and then subjected to lattice mapping (e.g., Figure 9 As shown in (b)), the final generated three-dimensional multi-scale heat dissipation channel structure is as follows: Figure 10 As shown in (b) above, the model's appearance is as follows Figure 10 As shown in (d) in the figure.

[0126] Comparative Example 2

[0127] The difference between this comparative example and Example 1 is that:

[0128] This comparative example uses a traditional serpentine water jacket structure, rather than a water jacket structure obtained through robust topology optimization. The serpentine water jacket is arranged in a regular curved channel along the flow direction, with the channel width and bend spacing remaining constant, and no optimization design was performed for temperature field distribution and operating condition disturbances.

[0129] The upper limit threshold for material volume fraction is set at 0.5, meaning the proportion of the fluid phase distribution area to the total volume of the design domain does not exceed 50%. The serpentine flow channel structure is as follows: Figure 10 As shown in (c) above, the model's appearance is as follows Figure 10 As shown in (d) in the figure.

[0130] Performance testing and characterization

[0131] Subsequent thermal performance evaluations employed the homogenized material properties derived for the three lattice types. To enhance the reliability of the multi-scale channel heat dissipation performance, a comparative analysis was conducted with that of a traditional serpentine flow channel. To ensure fairness, the solid-liquid volume ratio for all three flow channels was controlled at 50%, meaning the material proportions were identical.

[0132] Since the original topology flow channel is a two-dimensional design, the simulation verification of heat dissipation performance requires adjustment of the loading conditions: the inlet temperature is maintained at 20℃, the outlet pressure is set to 0, and the boundary heat source is set to different sample temperatures to simulate uncertainty. All flow channels are verified under the same heat source temperature conditions.

[0133] Figure 11 This shows the temperature distribution in the fluid region when the heat source temperature is 80℃. Figure 11 (a) in the example is a robust multi-scale topology optimization channel (Example 1). Figure 11 (b) in the figure represents a deterministic multi-scale topology optimization channel (Comparative Example 1). Figure 11 (c) The serpentine channel (Comparative Example 2). For multi-scale channels, corresponding equivalent material properties are assigned to each partitioned region based on the fluid heat transfer performance of each lattice. The overall average temperature values ​​of the three designs at different heat source temperatures are shown in Table 1.

[0134] Table 1 Overall average temperature values ​​under different heat source temperatures

[0135]

[0136] Under different heat source temperatures, the average blade temperature shows a monotonically increasing trend with increasing heat source temperature, a phenomenon consistent with physical expectations. Figure 12 As shown in (a) above. By comparing the average blade temperature and the temperature distribution in the flow channel region, it can be seen that, while maintaining a similar turbine blade material volume fraction, the multi-scale design significantly improves heat dissipation performance. Overall, deterministic topology optimization can achieve an average cooling effect of approximately 16.3% to 18.9%, while robust topology optimization further increases the cooling effect to 19.5% to 23.2%, demonstrating superior cooling performance. Especially under high-temperature heat source conditions, the temperature control advantage of robust multi-scale topology optimization design is more prominent. At the same time, this design exhibits smaller temperature fluctuations under different heat source conditions, such as... Figure 12 As shown in box plot (b) in the figure, its superior robustness and applicability under high heat load conditions are highlighted.

Claims

1. A method for designing a heat dissipation structure based on topology optimization, characterized by, The method comprises the following steps: (1) defining a three-dimensional design domain and boundary conditions of the heat dissipation structure, converting the three-dimensional design domain into a two-dimensional model, and establishing a load uncertainty model according to the boundary conditions and the distribution of heat source temperature; (2) performing robustness topology optimization on the two-dimensional model according to the load uncertainty model to obtain a two-dimensional flow channel topology structure; (3) mapping the two-dimensional flow channel topology structure into a three-dimensional flow channel structure; (4) based on the Menger sponge iteration principle, constructing fractal lattices with different volume fractions, and embedding the constructed fractal lattices with material properties into the three-dimensional flow channel structure to obtain an optimized heat dissipation structure; In step (3), the center line of the two-dimensional model is extracted, the redundant branches are removed through graph structure pruning, and then the path is smoothed through spline fitting, and the smoothed path is mapped into a three-dimensional flow channel structure.

2. The design method of a heat dissipation structure based on topology optimization according to claim 1, characterized in that, In step (1), the specific method of converting the three-dimensional design domain into a two-dimensional model is: a dimension reduction model is established with the flow channel height distribution as the design variable, based on the assumption of incompressible fully developed laminar flow, the velocity is assumed to be parabolic along the height direction and the temperature is assumed to be a fourth-order polynomial distribution; an equivalent density, in-plane scale pressure field and viscous resistance coefficient are introduced to construct a local resistance model, wherein the resistance term decreases with the increase of the flow channel height; the velocity and temperature profile functions are substituted into the energy conservation equation to derive the two-dimensional heat transfer control equation, wherein the flow channel height is determined by linear interpolation between the preset minimum value and maximum value, and the minimum filtering radius is determined by the gradient extremum of the height field, thereby completing the dimension reduction from three-dimensional problem to two-dimensional optimization problem.

3. The topology optimization-based heat dissipation structure design method according to claim 1, characterized by, In step (1), the method for establishing a load uncertainty model according to the boundary conditions and the distribution of heat source temperature is: (1-1) establishing a load model according to the boundary conditions; (1-2) defining the distribution of heat source temperature, including mean value, standard deviation and truncation interval; (1-3) integrating the distribution of heat source temperature into the load model to obtain the load uncertainty model.

4. The topology optimization-based heat dissipation structure design method according to claim 1, characterized by, Step (2) comprises the following sub-steps: (2-1) constructing a mean-variance robust objective function containing volume constraints and pressure drop constraints for the generated two-dimensional model; (2-2) a hybrid strategy combining Hamilton Monte Carlo and progressive sampling is used to extract a plurality of temperature samples from the distribution of heat source temperature of the load uncertainty model for use, and effective temperature samples are determined; (2-3) calculating the mean and variance of the robust objective function based on the effective temperature samples, obtaining the gradient information of the objective function with respect to the design variables through adjoint sensitivity analysis, updating the design variables by using a gradient-based optimization algorithm, and iterating until convergence to obtain a two-dimensional flow channel topology structure that meets the robustness requirements.

5. The topology optimization-based heat dissipation structure design method according to claim 4, characterized by, The objective function in step (2-1) is expressed as: ； wherein, is the mean of the objective function, is the variance of the objective function, Based on the aggregated computation of the sampled scenarios, define the mean of the base objective function F under the sampled scenarios, where the base objective function is expressed as: ； In the formula: ； ； and weight factor representing the objective function, design domain, T Q preset heat source temperature, Q vd fluid viscous dissipation, , , , preset constant for dimensionless processing of the objective function, weight coefficient, design variable.

6. The topology optimization-based heat dissipation structure design method according to claim 4, characterized by, Step (2-2) comprises the following sub-steps: (2-2-1) initializing the sampling process, extracting initial samples from the uncertainty model, and realizing efficient exploration of the parameter space by using the momentum mechanism of Hamilton Monte Carlo; (2-2-2) According to the sensitivity information of historical iterations and the local variance, the key interval is divided, the sample density is increased in the high variance area, and the total sample number is gradually expanded, wherein the sample number of the progressive sampling strategy is expressed as , t is the current iteration number; (2-2-3) Calculate the mean and variance of the objective function by integrating multiple rounds of sampling data, monitor the stability of the optimization process, and terminate sampling when the change rate is lower than the set threshold, where the termination condition is that the average target change rate and variance are less than the threshold.

7. The design method of a heat dissipation structure based on topology optimization according to claim 4, characterized in that, Step (2-3) includes the following sub-steps: (2-3-1) Adopting material property interpolation method to make design variables approach to 0-1 distribution, wherein the material property interpolation function is expressed as , and are solid and fluid properties respectively, is a design variable, is a penalty function factor; (2-3-2) Solve the fluid control equation and energy equation, calculate the accompanying sensitivity to update the design variables, and iterate to convergence to obtain the two-dimensional channel skeleton; (2-3-3) After each update of the design variable, perform feasibility checking of the volume constraint and pressure drop constraint, and project the design that violates the constraint for correction; (2-3-4) Use Heaviside projection filtering technology to ensure the minimum feature size, and gradually increase the projection sharpness combined with the continuation strategy to promote the formation of clear and manufacturable topological structure; (2-3-5) Set the convergence criterion, when the relative change of the objective function is less than the set threshold and all constraints are satisfied, terminate the iteration process, and output the final two-dimensional flow channel topological structure.

8. The topology optimization-based thermal structure design method of claim 1, wherein, In step (4), the method for constructing fractal lattices with different volume fractions is: (4-1) Construct a lattice family based on the Menger sponge iteration principle, and form a self-similar porous structure by removing the center region step by step; (4-2) Adjust the iteration depth and strut thickness parameters of the lattice to generate lattice variants with different volume fractions; (4-3) Assign material properties to the solid and fluid regions of the lattice variants, and use structural symmetry to simplify numerical simulation.

9. A heat dissipation structure design system based on topology optimization, characterized in that, The system comprises: A two-dimensional model construction module defines the three-dimensional design domain and boundary conditions of the heat dissipation structure, converts the three-dimensional design domain into a two-dimensional model, and establishes a load uncertainty model according to the distribution of boundary conditions and heat source temperature; A robust topology optimization module performs robust topology optimization on the two-dimensional model according to the load uncertainty model to obtain a two-dimensional flow channel topological structure, and maps the two-dimensional flow channel topological structure to a three-dimensional flow channel structure: extracts the center line of the two-dimensional model, removes redundant branches through graph pruning, and then realizes path smoothing through spline fitting, and maps the smoothed path to a three-dimensional flow channel structure; A fractal lattice integration module constructs fractal lattices with different volume fractions based on the Menger sponge iteration principle, and embeds the constructed fractal lattices into the three-dimensional flow channel structure after assigning material properties to obtain an optimized heat dissipation structure.

Images