Tube bundle structure thermal coupling multi-objective topological optimization method considering gap heat conduction

Abstract

The invention discloses a tube bundle structure thermal coupling multi-objective topological optimization method considering gap heat conduction. According to the method, firstly, two matrix models are subjected to topological optimization with mechanical flexibility and heat dissipation weakness as optimization targets, and then the two matrix models are combined into a coupling model for topological optimization; an objective function during topological optimization of the coupling model is formed by carrying out linear weighted aggregation on mechanical compliance and heat dissipation weakness after normalization processing, then adjusting weight factors of the mechanical compliance and the heat dissipation weakness in the objective function, and generating Pareto leading edges of a multi-objective optimal solution set under different weight factors; and screening an optimal solution from the Pareto frontier, carrying out thermal coupling simulation on the tube bundle model reconstructed by using the screened optimal solution, then adjusting the constraint volume fraction, and repeating the steps until the optimal tube bundle model is obtained. According to the invention, collaborative optimization of rigidity, heat dissipation and weight reduction of the tube bundle structure can be realized.

Description

Technical Field

[0001] This invention belongs to the field of nuclear reactor structure optimization technology, specifically relating to a multi-objective topology optimization method for tube bundle structures that considers gap heat conduction. Background Technology

[0002] The heat pipe cooled reactor adopts a structural design in which fuel rods and heat pipes are arranged alternately in a solid matrix. It utilizes the capillary action of the heat pipes and the phase change characteristics of the working fluid to efficiently remove the heat of fission. It eliminates the need for pumps and pipelines in traditional liquid cooling systems and has the advantages of passive safety, compact structure and small size. It has broad application prospects in fields such as deep space exploration, deep-sea submersible navigation and power supply in remote areas.

[0003] As one of the main mobile energy supply equipment in extreme environments such as deep space exploration, deep-sea submersion, and remote area operations, lightweighting is a key performance indicator for heat pipe cooled reactors. Existing research on lightweighting of heat pipe cooled reactors mainly focuses on optimizing fuel enrichment, heat pipe layout and size optimization, and designing radiators using lightweight, high-strength materials (such as Nb-Ti alloys and HOPG). It also combines surrogate models and genetic algorithms to optimize the heat dissipation structure to reduce weight. However, the substrate, as the main heat transfer medium and load-bearing structure, has not received sufficient attention. How to balance stiffness, thermal conductivity, and lightweighting has become a core challenge. Moreover, the thermal expansion between heat pipes, fuel rods, and cladding leads to complex coordinated deformation. Assembly gaps between components introduce additional thermal resistance, and these gaps dynamically change with thermal expansion and creep, affecting heat transfer efficiency. The heat transfer behavior of gap filling materials also increases modeling complexity. These factors make it extremely difficult to accurately predict the stress distribution and heat transfer path of the reactor core. Summary of the Invention

[0004] The purpose of this invention is to overcome the shortcomings of the prior art and propose a multi-objective topology optimization method for tube bundle structures that considers gap heat conduction.

[0005] To achieve the above objectives, the present invention adopts the following technical solution:

[0006] This invention considers a multi-objective topology optimization method for thermo-mechanical coupling of tube bundle structures based on gap heat conduction, as detailed below:

[0007] Step S1: Establish a core model of the heat pipe cooled reactor, perform thermo-mechanical coupled finite element analysis on the core model, and obtain surface pressure data and surface heat source data of each heat pipe hole wall and each fuel rod hole wall.

[0008] Step S2: Establish two matrix models of the reactor core. Set mechanical loads and heat source loads for the two matrix models respectively, so that the stress distribution of one matrix model and the temperature distribution of the other matrix model are consistent with the stress distribution and temperature distribution of the reactor core model. Set displacement boundary conditions and temperature boundary conditions for the two matrix models respectively. Then, perform topology optimization on the two matrix models with mechanical compliance and heat dissipation weakness as optimization objectives respectively.

[0009] Step S3: Merge the two matrix models with mechanical load and displacement boundary conditions and heat source load and temperature boundary conditions into a coupled model. Taking mechanical compliance and heat dissipation weakness as optimization objectives, normalize the two optimization objectives and aggregate them into a multi-objective function expression through linear weighting. Perform topology optimization on the coupled model. Then, repeatedly adjust the weight factor values ​​of the two optimization objectives and perform topology optimization on the coupled model based on the multi-objective function after adjusting the weight factor values ​​of the two optimization objectives. Solve the multi-objective problem and obtain the Pareto front of the set of optimal solutions for the multi-objective problem under different weight factors.

[0010] Step S4: Select the optimal solution in the Pareto front based on the ideal point method, thereby selecting the optimal matrix.

[0011] Step S5: Establish an optimized core model using the optimized matrix model corresponding to the optimal solution obtained in step S4, and perform thermo-mechanical coupled finite element analysis on the optimized core model to determine whether the optimized core model meets the design requirements.

[0012] Step S6: Update the constraint volume fraction based on the judgment result of step S5, and repeat steps S2 to S5 using the updated constraint volume fraction.

[0013] Step S7: Update the constraint volume fraction based on the results of the two previous judgments and the corresponding performance change curvature, and repeat steps S2 to S5 using the updated constraint volume fraction; wherein, the performance change curvature is the ratio of the change value of the objective function value that comprehensively considers mechanical compliance and heat dissipation weakness corresponding to the results of the two previous judgments to the change value of the corresponding constraint volume fraction.

[0014] Step S8: Repeat step S7 until the judgment result is that the optimized core model meets the design requirements and the number of consecutive preset times of performance change curvature is less than the curvature threshold. At this time, the last optimized core model is the optimal core model.

[0015] Preferably, the specific process of step S1 is as follows:

[0016] Step S11: Establish the reactor core model;

[0017] Step S12: Set the material properties of the core model;

[0018] Step S13: Mesh the core model;

[0019] Step S14: Set the displacement boundary conditions for the core model;

[0020] Step S15: Set the temperature boundary conditions for the core model;

[0021] Step S16: Automatically set the gap behavior of the core model through the contact module of the finite element software, and define the mechanical contact properties of the core model contact interface.

[0022] Step S17: Select the Coupled Temp-Displacement solver to solve the core thermo-coupling problem. Use the UMAT subroutine to simulate the core deformation behavior of the core model and output the surface pressure data of the walls of each heat pipe hole and each fuel rod hole. Use the GAPCON subroutine to simulate the core heat transfer behavior of the core model and output the surface heat source data of the walls of each heat pipe hole and each fuel rod hole.

[0023] Preferably, the specific process of step S2 is as follows:

[0024] Step S21: Establish two matrix models with consistent geometry, material, and mesh information, denoted as Loadcase1 model and Loadcase2 model;

[0025] Step S22: Extract the surface pressure data of each heat pipe hole wall and each fuel rod hole wall, as well as the surface heat source data of each heat pipe hole wall and each fuel rod hole wall from the result file of the thermo-coupled finite element analysis of the core model in step S1. Apply the extracted surface pressure data to the same position in the Loadcase1 model and the surface heat source data to the same position in the Loadcase2 model. Set displacement boundary conditions and temperature boundary conditions for the Loadcase1 model and the Loadcase2 model, respectively.

[0026] Step S23: Input the constraint volume fraction and minimum filtering radius. For the Loadcase1 model and Loadcase2 model obtained from step S22, with mechanical compliance and heat dissipation weakness as optimization objectives respectively, run the topology optimization Python program to solve them. Obtain the elastic strain energy and nodal displacement of each element's Gaussian integration point and node in the Loadcase1 model, and the nodal temperature and nodal heat flux of each element's Gaussian integration point and node in the Loadcase2 model. Calculate the sensitivity value of each element in the Loadcase1 model with mechanical compliance as the optimization objective and the sensitivity value of each element in the Loadcase2 model with heat dissipation weakness as the optimization objective. After filtering and bidirectional progressive structural optimization analysis, obtain the updated information of the design variable, i.e., the relative density of each element, and update the material distribution in the Loadcase1 and Loadcase2 models.

[0027] More preferably, the sensitivity value of each unit is the relative density of the objective function with respect to the design variables. The partial derivatives of are given by two objective functions, one optimizing mechanical compliance and the other optimizing heat dissipation weakness.

[0028]

[0029]

[0030] In the formula, The objective function is mechanical compliance; It is the global mechanical force vector; It is a global displacement vector; It is the global stiffness matrix; Let e ​​be the displacement vector of the node of the element. The element's equivalent stiffness matrix; It is the relative density of all units The vector formed; It is the total number of units; The objective function is the heat dissipation weakness; It is the global heat source load vector; It is the global node temperature vector; For the overall heat conduction matrix; It is the temperature vector of the e-th unit node; The unit is the equivalent thermal conductivity stiffness matrix;

[0031] Element equivalent stiffness matrix and the unit equivalent thermal conduction stiffness matrix In a linear manner with relative density Link:

[0032]

[0033]

[0034] In the formula, It is a punishment index. and Here are the element stiffness matrix and element thermal conductivity stiffness matrix of the initial structure. Let be the relative density of the e-th unit, with candidate values ​​of 1 and 2. ;

[0035] The formulas for calculating the sensitivity values ​​of each unit with mechanical compliance as the optimization objective and the sensitivity values ​​of each unit with heat dissipation weakness as the optimization objective are as follows:

[0036]

[0037]

[0038] In the formula, Let be the sensitivity value of the e-th unit, with mechanical compliance as the optimization objective. Let be the sensitivity value of the e-th unit with heat dissipation weakness as the optimization objective.

[0039] More preferably, the specific process of step S3 is as follows:

[0040] Step S31: Using the direct coupling analysis technique of thermal and mechanical physical fields, merge the Loadcase1 model and Loadcase2 model obtained in step S22 into a coupled model;

[0041] Step S32: Taking mechanical compliance and heat dissipation weakness as optimization objectives, a multi-objective function is established. The element sensitivity values ​​based on mechanical compliance and heat dissipation weakness are multiplied by weighting factors to achieve linear weighted aggregation and obtain the element sensitivity values ​​of the coupled model. After filtering and bidirectional progressive structural optimization analysis, the updated information of the design variables, i.e., the relative density of each element, is obtained and used to update the material distribution in the coupled model. The topology optimization Python program is then used to solve the coupled model.

[0042] More preferably, the specific process of step S32 is as follows:

[0043] (1) The expression for the multi-objective optimization problem is as follows:

[0044]

[0045] In the formula, A multi-objective function that comprehensively considers mechanical compliance and heat dissipation weakness; and These are the weighting factors for mechanical compliance and heat dissipation weakness, respectively. and These are the optimal values ​​for mechanical compliance and heat dissipation weakness, respectively. and These represent the initial mechanical compliance and heat dissipation weakness of the coupled model, respectively. This represents the total volume of the coupled model; It is the unit volume; To constrain volume fraction;

[0046] (2) and Multiply by weighting factors respectively , By combining normalization processing with linear weighted aggregation, the sensitivity values ​​of each unit under multi-objective optimization are obtained.

[0047]

[0048] (3) Numerical processing of the sensitivity of each unit under multi-objective optimization:

[0049] ① Spatial filtering is performed on the sensitivity values ​​of each unit under multi-objective optimization:

[0050]

[0051]

[0052] In the formula, To optimize the sensitivity value of the e-th cell in a multi-target system after spatial filtering; For the e-th unit and the The distance between units; This is the weighting function used to average the original sensitivity values; Minimum filter radius; For the first Weighting factors for the original sensitivity values ​​of each unit; For the first The original sensitivity values ​​of each unit;

[0053] ②Historical information averaging: The sensitivity values ​​of each unit in the current iteration, after spatial filtering, are averaged with the corresponding unit sensitivity values ​​in the previous iteration, after spatial filtering.

[0054]

[0055] In the formula, This represents the sensitivity value of the e-th unit after spatial filtering during the k-th iteration. This is the sensitivity value of the e-th unit after spatial filtering during the (k-1)-th iteration;

[0056] (4) The relative density of the cells is updated iteratively by using a bidirectional progressive structure optimization method;

[0057] (5) Adjust the two weighting factors and The value is repeated from step (1) to step (4).

[0058] (6) Repeat step (5) to obtain the Pareto front of the multi-objective optimal solution set under different weight factors.

[0059] More preferably, the specific process of step S4 is as follows:

[0060] Step S41: The optimal results of the two matrix models obtained in step S2 are weighted by the weight factors of the two optimization objectives and constructed into a virtual Utopian point.

[0061] Step S42: Select the non-dominated solution with the shortest Euclidean distance to the Utopia point from the Pareto front weighted results obtained in step S3 as the optimal solution.

[0062] Preferably, the specific process of step S5 is as follows:

[0063] The optimized matrix model corresponding to the optimal solution obtained in step S4 is assembled with the cladding and fuel rods to establish an optimized core model. A thermo-coupled finite element analysis is then performed using the optimized core model to obtain temperature field contour maps, stress field contour maps, displacement field contour maps, heat flux density contour maps, and strain energy density contour maps of the optimized core model. Based on the temperature field contour maps, it is determined whether the temperature range of the optimized matrix model is within the preset temperature range and whether the maximum temperature gradient value of the optimized matrix model is less than the preset temperature gradient value. Based on the stress field contour maps, it is determined whether the maximum stress of the optimized matrix model is lower than the ultimate strength of the matrix material. Based on the displacement field contour maps, it is determined whether the maximum displacement of the optimized matrix model is within the preset displacement range and whether the maximum displacement is within the preset displacement range. Based on the heat flux density contour maps... The algorithm determines whether the heat flux density gradient value of the optimized matrix model is less than the preset heat flux density gradient value. It calculates the Pearson correlation coefficient between strain energy density and stress intensity on the optimized matrix model based on the strain energy density cloud map and stress field cloud map, and determines whether the Pearson correlation coefficient is greater than the preset coefficient value. If the optimized matrix model's temperature range is within the preset temperature range, the maximum temperature gradient value is less than the preset temperature gradient value, the maximum stress is lower than the ultimate strength of the matrix material, the maximum displacement is within the preset displacement range, the maximum heat flux density gradient value is less than the preset heat flux density gradient value, and the calculated Pearson correlation coefficient is greater than the preset value, then the optimized core model meets the design requirements; otherwise, the optimized core model does not meet the design requirements.

[0064] Preferably, the specific process of step S6 is as follows: if the optimized core model meets the design requirements, the constraint volume fraction is reduced by a preset value of one; if the optimized core model does not meet the design requirements, the constraint volume fraction is increased by a preset value of one; and then steps S2 to S5 are repeated using the updated constraint volume fraction.

[0065] Preferably, the specific process of step S7 is as follows: when the previous judgment result is that the optimized core model meets the design requirements, and the current judgment result is consistent with the previous judgment result, if the curvature of the performance change of the current optimized core model relative to the previous optimized core model is less than the curvature threshold, the preset value 1 is not updated, but the constraint volume fraction is updated to reduce the current constraint volume fraction by the preset value 1; otherwise, the preset value 1 is updated to make the current preset value 1 half of the previous preset value 1, and the constraint volume fraction is updated to reduce the current constraint volume fraction by the updated preset value 1. When the current judgment result is inconsistent with the previous judgment result, the preset value 1 is updated to make the current constraint volume fraction half of the previous preset value 1. Set the value to half of the previous preset value, and update the constraint volume fraction so that the current constraint volume fraction increases by the updated preset value. If the previous judgment result is that the optimized core model does not meet the design requirements, and the current judgment result is consistent with the previous judgment result, do not update the preset value, but update the constraint volume fraction so that the current constraint volume fraction increases by the preset value. If the current judgment result is inconsistent with the previous judgment result, update the preset value to half of the previous preset value, and update the constraint volume fraction so that the current constraint volume fraction decreases by the updated preset value. Then repeat steps S2 to S5 using the updated constraint volume fraction.

[0066] The present invention has the following beneficial effects:

[0067] This invention simultaneously considers structural mechanical and thermal properties to achieve topology optimization of a heat pipe-cooled reactor core. The optimized core structure exhibits superior heat transfer and stiffness performance. Specifically, this invention first performs topology optimization on two base models, with mechanical compliance and heat dissipation weakness as optimization objectives, respectively. Both base models are subjected to mechanical loads and displacement boundary conditions, as well as heat source loads and temperature boundary conditions, obtained from finite element analysis of the core model. This ensures that the two base models accurately match the stress and temperature fields of the actual reactor core. Next, the two base models are merged into a coupled model, and topology optimization is performed. The objective function of the coupled model in topology optimization integrates mechanical compliance and heat dissipation weakness. These are normalized and then linearly weighted to achieve topology optimization under thermo-mechanical coupling, considering the influence of material distribution on structural stiffness and thermal performance, thus realizing topology optimization of the base structure. Topology optimization is performed, taking into account structural mechanical and thermal performance. Further, by adjusting the weighting factors of mechanical compliance and heat dissipation weakness in the objective function, a series of Pareto fronts with different trade-offs between mechanical and thermal performance are generated. An optimal solution is selected from the Pareto fronts using the ideal point method. The matrix model obtained from the optimal solution selected from the Pareto fronts is then reconstructed into a core model, and thermo-mechanical coupling simulation is performed. Based on the simulation results, it is determined whether the reconstructed core model meets the design requirements. Based on the judgment results and the curvature of performance changes, the constraint volume fraction is adjusted. The above steps are repeated until the judgment result indicates that the reconstructed core model meets the design requirements, and the number of consecutive curvature changes is less than the curvature threshold. At this point, the last reconstructed core model is the optimal core model. While meeting the design requirements, "lightweight maximization" is achieved, thereby realizing the synergistic optimization of core stiffness, heat dissipation, and weight reduction. Attached Figure Description

[0068] Figure 1 This is a flowchart of the present invention.

[0069] Figure 2 This is a 1 / 12 division diagram of a classic hexagonal honeycomb.

[0070] Figure 3 The physical quantity distribution cloud map is obtained by performing thermo-coupled finite element analysis on the core model of the classic hexagonal honeycomb before optimization.

[0071] Figure 4 The physical quantity distribution cloud map is obtained by thermo-coupled finite element analysis of the core model of the classic hexagonal honeycomb after optimization by this invention. Detailed Implementation

[0072] The present invention will now be further described with reference to the accompanying drawings.

[0073] like Figure 1 As shown, the present invention provides a multi-objective topology optimization method for thermo-mechanical coupling of tube bundle structures considering gap heat conduction, as detailed below:

[0074] Step S1: Establish a core model of the heat pipe-cooled reactor, and perform thermo-mechanical coupled finite element analysis on the core model to obtain the core deformation behavior and heat transfer behavior. The specific process is as follows:

[0075] Step S11: Taking a heat pipe-cooled reactor with a classic hexagonal honeycomb layout as the research object, in the finite element software ABAQUS, the core of the heat pipe-cooled reactor is divided into 1 / 12 equal parts (e.g., Figure 2 The core model is established using the cell shown as a representative cell. The core includes fuel rods, cladding, and substrate. Multiple heat pipe hole groups are concentrically arranged on the substrate. Each heat pipe hole group consists of multiple heat pipe holes arranged in a regular hexagonal pattern. A heat pipe hole is also opened at the center of the substrate. Except for the heat pipe holes of the outermost heat pipe hole group, the fuel rod holes opened in the substrate form a regular hexagonal distribution around each of the remaining heat pipe holes. Each heat pipe hole and each fuel rod hole is provided with a cladding, and each cladding located in each fuel rod hole is provided with a fuel rod.

[0076] Step S12: Set the material properties of the reactor core model: Set the material properties of the fuel rods to uranium dioxide (UO2), the density of uranium dioxide to 10.52 t / m³, and the material properties of the cladding and the substrate to SS316 stainless steel.

[0077] Step S13: Mesh the core model: Use a 4-node generalized plane strain element CPEG4T to mesh the core model, with an average mesh size of 0.4 mm.

[0078] Step S14: Set the displacement boundary conditions of the core model: In order to characterize the thermo-mechanical coupling response of the complete core structure, set the boundary conditions of the two sides of the core model (the surfaces in the core model along the radial direction of the complete core structure) as symmetrical boundary conditions, and set the boundary conditions of the lower edge surface (the surface in the core model along the circumferential direction of the complete core structure) as fixed boundary conditions.

[0079] Step S15: Set the temperature boundary conditions of the core model: Set the convective heat transfer coefficient of the inner surface of the cladding to 10mW / mm² / K, the volume heat flux (heat flux per unit volume) of the fuel rods to 10W / mm³, set the lower edge surface and both sides as adiabatic boundary conditions, set the initial temperature of the fuel rods, cladding and substrate to 948K, and set the core power density to 10W / cm³.

[0080] Step S16: Automatically set the gap behavior (gap between cladding and fuel rods, heat pipe holes and fuel rod holes) of the core model through the contact module of the finite element software ABAQUS, and define the mechanical contact properties of the core model contact interface; wherein, the mechanical contact properties include normal hard contact and tangential frictionless contact.

[0081] Step S17: Select the Coupled Temp-Displacement solver to solve the core thermo-coupling problem, set the analysis duration (5 years in this embodiment), and assume that the core model structure is within the small deformation assumption range. Use the UMAT subroutine to simulate the core deformation behavior and output the surface pressure data of each heat pipe hole wall and each fuel rod hole wall. Use the GAPCON subroutine to simulate the core heat transfer behavior and output the surface heat source data of each heat pipe hole wall and each fuel rod hole wall.

[0082] The reactor core operates under harsh conditions of high temperature and high radiation for extended periods. Its deformation behavior is influenced by multiple factors, including elastic deformation, thermal expansion, creep, and swelling that may be caused by fission products. The total strain rate of the reactor core is...

[0083]

[0084] In the formula, The total strain rate of the reactor core. It is the total elastic strain rate of all materials in the reactor core (the sum of the elastic strain rates of each material, which is determined by the material properties). It is the total thermal expansion strain rate of all materials in the reactor core (the sum of the thermal expansion strain rates of all materials, which is determined by the material properties). The total creep strain rate of all materials in the reactor core. This represents the total swelling strain rate of all materials in the reactor core.

[0085] creep strain rate of fuel rods for

[0086]

[0087] In the formula, The fuel rod material burnup rate, For the equivalent Mises stress of the fuel rod material, Let be the ideal gas constant. For fuel rod temperature, This is the percentage of fuel density (actual fuel density / theoretical maximum density). The average grain size of the fuel rod material. For fuel rod material constants, , , These are the activation energies for dislocation slip, diffusion creep, and grain boundary sliding in the fuel rod material, and the fuel rod material constants. and fuel rod material activation energy , , Obtained through calibration experiments and curve fitting;

[0088] Total swelling strain rate of fuel rods Solid fission swelling strain rate and gas fission swelling strain rate The sum of the two yields the solid fission swelling strain rate of the fuel rod. and gas fission swelling strain rate They are respectively

[0089]

[0090]

[0091] The cladding made of SS316 stainless steel does not undergo a fission reaction with the substrate. Considering only creep behavior, the creep strain rate of the cladding or substrate is...

[0092]

[0093] In the formula, It is time. The equivalent Mises stress of the cladding or matrix material, parameter , , , , and The results were obtained through calibration experiments and curve fitting.

[0094] In the finite element software Abaqus, the Fourier heat conduction governing equation is used to describe the main heat transfer modes of solid heat conduction, and its expression is:

[0095]

[0096] In the formula, For the thermal conductivity of the material, For the temperature field, This refers to the heat source power density (i.e., the volumetric heat flux of the fuel rod). For material density, Specific heat capacity of the material;

[0097] The heat transferred through the gap surface is determined by the temperature of each material surface and the equivalent gap heat transfer coefficient. The gap heat transfer model is as follows:

[0098]

[0099] In the formula, For interstitial heat flux, The equivalent gap heat transfer coefficient is... and The surface temperature on both sides of the gap;

[0100] in, The heat transfer mechanism within the gap is determined by three main components: heat conduction of the gas within the gap, radiative heat transfer between the surfaces on both sides of the gap, and contact heat conduction at the possible closing points of the gap.

[0101]

[0102] In the formula, Let be the heat transfer coefficient of the gas within the gap. The contact heat transfer coefficient between the two surfaces when the gap is closed. The radiative heat transfer coefficient is the coefficient between the two surfaces of the gap.

[0103] The temperature of the gas near the gap is not equal to the solid surface temperature, which is related to the size of the gap and the roughness of the surfaces on both sides of the gap. This temperature discontinuity is called temperature jump. The calculation model for the heat transfer coefficient of the gas in the gap is as follows:

[0104]

[0105] In the formula, For the thermal conductivity of gases, The gap width, This is the roughness coefficient (obtained through calibration experiments). and These are the surface roughnesses on both sides of the gap, This represents the total jump distance of the gas relative to each other within the gap.

[0106] In the interstitial gas heat conduction model, the gas is assumed to be a non-flowing solid for analysis, neglecting the convective heat transfer that may occur under heating conditions. The thermal conductivity of the gas varies with temperature, gas composition, and reactor operating conditions. For a mixture of He, Xe, and Kr, the thermal conductivity is [missing value].

[0107]

[0108] In the formula, It is the mole fraction of each gas. , and The thermal conductivity of each gas;

[0109] The total jump distance of the gas relative to the gap is

[0110]

[0111] In the formula, This is the adjustment coefficient for the components of the mixed gas. The thermal conductivity of the mixed gas, i.e. = , The temperature of the mixed gas. The pressure of the mixed gas. This represents the number of different types of gas molecules contained in the gas mixture. For the first mole fraction of the gas For the first The relative molecular mass of a gas.

[0112] When local contact may occur on the gap surfaces, the contact area plays a crucial role in heat transfer. However, since the contact surfaces are not perfectly smooth but have a certain surface roughness, only some points in the contact area are actually pressed together, and a certain air gap also exists. Therefore, the thermal conductivity is related to the contact pressure. When the gap is closed, the contact heat transfer coefficient of the two sides is...

[0113]

[0114] In the formula, The contact constant between the gas inside the gap and the surfaces on both sides of the gap is obtained through calibration experiments. and These are the thermal conductivity of the surface materials on both sides of the gap. This refers to the contact pressure between the gas inside the gap and the surfaces on both sides of the gap. The average gas film thickness, and , The value is the Meiss hardness of the softer material on the surface of the gap.

[0115] The radiation heat transfer coefficient between the two surfaces of the gap is

[0116]

[0117]

[0118] In the formula, This is the Stephan-Boltzman constant. The radiation function is related to the emissivity of the surfaces on both sides of the gap. and These are the emissivity of the surface materials on both sides of the gap.

[0119] Step S2: Establish two matrix models, and set mechanical loads and displacement boundary conditions, as well as heat source loads and temperature boundary conditions for the two matrix models respectively. Then, perform topology optimization with mechanical compliance and heat dissipation weakness as optimization objectives respectively. The specific process is as follows:

[0120] Step S21: In the ABAQUS / CAE environment, establish two base models with consistent geometry, material and mesh information. One base model is used to set mechanical loads and displacement boundary conditions, denoted as Loadcase1 model, and the other base model is used to set heat source loads and temperature boundary conditions, denoted as Loadcase2 model.

[0121] Step S22: Extract the surface pressure data (mechanical load) of each heat pipe hole wall and each fuel rod hole wall, as well as the surface heat source data (heat source load) of each heat pipe hole wall and each fuel rod hole wall from the result file after performing thermo-coupling finite element analysis on the core model in step S1. Apply the extracted surface pressure data to the same position in the Loadcase1 model and the surface heat source data to the same position in the Loadcase2 model, so that the stress distribution of the Loadcase1 model and the temperature distribution of the Loadcase2 model are consistent with the stress distribution and temperature distribution of the core model, respectively. Set displacement boundary conditions and temperature boundary conditions for the Loadcase1 model and the Loadcase2 model, respectively.

[0122] Step S23: Input the constraint volume fraction and minimum filter radius. For the Loadcase1 and Loadcase2 models obtained in step S22, run the topology optimization Python program to solve them, with mechanical compliance and heat dissipation weakness as optimization objectives respectively. This yields two result files with the .odb extension, representing the topology optimization results with mechanical compliance and heat dissipation weakness as optimization objectives, respectively. The Loadcase1 model is solved using the General static analysis step, while the Loadcase2 model is solved using the Heat dissipation analysis step. The transfer analysis step is used to solve the problem. During the solution process, the Loadcase1 model and Loadcase2 model are traversed respectively to obtain the elastic strain energy and nodal displacement of each element's Gaussian integration point and node in the Loadcase1 model, and the nodal temperature and nodal heat flux of each element's Gaussian integration point and node in the Loadcase2 model. The sensitivity values ​​of each element in the Loadcase1 model with mechanical compliance as the optimization objective and the sensitivity values ​​of each element in the Loadcase2 model with heat dissipation weakness as the optimization objective are calculated respectively. After filtering and bidirectional progressive structural optimization analysis, the updated information of the design variable, namely the relative density of each element, is obtained and used to update the material distribution in the Loadcase1 model and Loadcase2 model.

[0123] Among these, high sensitivity values ​​indicate high contribution and are therefore retained, while low sensitivity values ​​are deleted. The sensitivity value of each unit is the objective function (mechanical compliance or heat dissipation weakness) relative to the design variable, namely, relative density. The partial derivatives reflect the degree of influence of retaining or removing element materials on structural performance, determining the direction and magnitude of design variable updates. The mechanical compliance objective function aims to maximize structural stiffness to minimize deformation under mechanical loads, while the heat dissipation weakness objective function aims to maximize the structure's heat dissipation performance to minimize the average temperature within the design domain. The two objective functions, with mechanical compliance and heat dissipation weakness as optimization objectives respectively, are...

[0124]

[0125]

[0126] In the formula, Let be the objective function for mechanical compliance. Mechanical compliance reflects the ease with which a structure deforms when subjected to mechanical loads. The smaller the mechanical compliance, the greater the stiffness of the structure and the stronger its ability to resist deformation. It is the global mechanical force vector; It is a global displacement vector; It is the global stiffness matrix; Let e ​​be the displacement vector of the node of the element. The element's equivalent stiffness matrix; It is the relative density of all units The vector formed; It is the total number of units; The objective function is the heat dissipation weakness, which reflects the heat dissipation performance of the structure. The smaller the heat dissipation weakness, the higher the heat dissipation efficiency of the structure, and the more conducive it is to heat transfer and dissipation. It is the global heat source load vector; It is the global node temperature vector; For the overall heat conduction matrix; It is the temperature vector of the e-th unit node; The unit is the equivalent thermal conductivity stiffness matrix;

[0127] Element equivalent stiffness matrix and the unit equivalent thermal conduction stiffness matrix Directly related to relative density in a linear manner Link:

[0128]

[0129]

[0130] In the formula, It is a punishment index. and Here are the element stiffness matrix and element thermal conductivity stiffness matrix of the initial structure. Let be the relative density (design variable) of the e-th element, with candidate values ​​of 1 (indicating the presence of a solid) and . (0.001 indicates that material has been removed).

[0131] The formulas for calculating the sensitivity values ​​of each unit with mechanical compliance as the optimization objective and the sensitivity values ​​of each unit with heat dissipation weakness as the optimization objective are as follows:

[0132]

[0133]

[0134] In the formula, Let be the sensitivity value of the e-th unit, with mechanical compliance as the optimization objective. Let be the sensitivity value of the e-th unit with heat dissipation weakness as the optimization objective, where This represents the elastic strain energy of the e-th element. It represents the vector composed of the heat flow of all Gaussian integral points in the e-th unit.

[0135] Step S3: Combine the Loadcase1 and Loadcase2 models obtained in step S22 into a coupled model. Ensure that the stress and temperature distributions of the coupled model are consistent with those of the Loadcase1 and Loadcase2 models, respectively. Considering mechanical compliance and heat dissipation weakness as optimization objectives, normalize the two optimization objectives (mechanical compliance and heat dissipation weakness) and then aggregate them into a multi-objective function expression through linear weighting. Perform topology optimization on the coupled model. Then, repeatedly adjust the weight factor values ​​of the two optimization objectives and perform topology optimization on the coupled model based on the multi-objective function after adjusting the weight factor values ​​of the two optimization objectives. Solve the multi-objective problem and obtain the Pareto front of the set of optimal solutions for the multi-objective problem under different weight factors. The specific process is as follows:

[0136] Step S31: Using the direct coupling analysis technique of thermal and mechanical physical fields provided in ABAQUS, namely the CoupledTemp-Displacement analysis step, the Loadcase1 model and Loadcase2 model obtained in step S22 are merged into a coupled model to achieve direct thermo-mechanical coupling.

[0137] Step S32: Taking mechanical compliance and heat dissipation weakness as optimization objectives, a multi-objective function is established. The element sensitivity values ​​based on mechanical compliance and heat dissipation weakness are multiplied by weighting factors to achieve linear weighted aggregation and obtain the element sensitivity values ​​of the coupled model. After filtering and bidirectional progressive structural optimization analysis, the updated information of the design variables, i.e., the relative density of each element, is obtained and used to update the material distribution in the coupled model. The topology optimization Python program is then run to solve the coupled model. The specific process is as follows:

[0138] (1) Constructing a multi-objective problem expression: After normalizing the two optimization objectives (mechanical compliance and heat dissipation weakness), they are aggregated into a multi-objective function expression through linear weighting. The expression is obtained by adjusting the weight factors of the two optimization objectives. and This allows for a trade-off between two optimization objectives, thereby obtaining the Pareto front of the multi-objective optimal solution set under different weighting factors. The multi-objective optimization problem is expressed as follows:

[0139]

[0140] In the formula, A multi-objective function that comprehensively considers mechanical compliance and heat dissipation weakness; and These are the weighting factors for mechanical compliance and heat dissipation weakness, respectively. and These are the optimal values ​​of the objective functions with mechanical compliance and heat dissipation weakness as optimization objectives, respectively. That is, after the Loadcase1 model and Loadcase2 model obtained in step S22 are run for topology optimization, the minimum values ​​of mechanical compliance and heat dissipation compliance that can be achieved under the constraints of volume fraction and minimum filter radius. and These represent the mechanical compliance and heat dissipation weakness of the initial coupled model (without topology optimization); This represents the total volume of the coupled model; It is the unit volume; To constrain the volume fraction; where, equation The static equilibrium of the coupled model structure was constrained, and the equations were... The thermal conduction steady-state equilibrium of the coupled model structure was constrained.

[0141] (2) Establish the calculation formula for the sensitivity value of each unit under multi-objective optimization: and Multiply by weighting factors respectively , By combining normalization processing with linear weighted aggregation, the sensitivity values ​​of each unit under multi-objective optimization are obtained.

[0142]

[0143] (3) To avoid grid dependency and checkerboard pattern, the sensitivity values ​​of each element under multi-objective optimization are processed as follows:

[0144] ① Spatial filtering is performed on the sensitivity values ​​of each unit under multi-objective optimization:

[0145]

[0146]

[0147] In the formula, To optimize the sensitivity value of the e-th cell in a multi-target system after spatial filtering; For the e-th unit and the The distance between units; This is the weighting function used to average the raw (unspatial filtered) sensitivity values; Minimum filter radius; For the first Weighting factors for the original sensitivity values ​​of each unit; For the first The original sensitivity value of each unit.

[0148] ② Historical information averaging: The sensitivity values ​​of each unit in the current iteration, after spatial filtering, are averaged with the corresponding unit sensitivity values ​​in the previous iteration, after spatial filtering, to improve convergence.

[0149]

[0150] In the formula, This represents the sensitivity value of the e-th unit after spatial filtering during the k-th iteration. It represents the sensitivity value of the e-th unit after spatial filtering during the (k-1)-th iteration.

[0151] (4) Two-way progressive structural optimization (BESO) is adopted to iteratively update the relative density of elements using a bisection method. Starting from a structural design that has not undergone topology optimization, the structural volume is reduced iteratively by updating the element states:

[0152] a. Initialize the sensitivity threshold range: Calculate and process the sensitivity values ​​of all current elements under multi-objective optimization, and set the minimum and maximum sensitivity values ​​among all current elements under multi-objective optimization as the upper and lower limits of the sensitivity threshold range, respectively denoted as... and ;

[0153] b. Calculate the candidate sensitivity threshold: The candidate sensitivity threshold is...

[0154]

[0155] c. Unit state update: If the unit sensitivity value Let the relative density of the unit be... (Retain material), if unit sensitivity value Let the relative density of the unit be... (Remove materials);

[0156] d. Volume check and sensitivity threshold adjustment: Calculate the target volume fraction of the updated coupled model. and with constraint volume fraction In comparison, if This indicates that the current sensitivity threshold is too low and needs to be increased and updated. ,like This indicates that the current sensitivity threshold is too high and needs to be lowered and updated. ;

[0157] e. Cyclic Convergence: Repeat steps b to d until the relative error between the upper and lower limits of the sensitivity threshold satisfies the convergence condition. and the final determined threshold Used for calculating the relative density of elements in the current iteration, thereby ensuring precise control of material volume during topology optimization. To achieve convergence tolerance, take ;

[0158] f. Calculate the target volume fraction for the next iteration. : Target volume fraction in the next iteration Based on the target volume fraction at the current iteration and an evolution ratio Determined, that is

[0159]

[0160] g. Repeat steps a through f until... .

[0161] (5) Adjust the two weighting factors and The value is repeated from step (1) to step (4).

[0162] (6) Repeat step (5) to obtain the Pareto front of the multi-objective optimal solution set under different weight factors.

[0163] Step S4: Based on the ideal point method, the optimal solution that balances stiffness and heat dissipation is selected, thereby selecting the optimal substrate, as detailed below:

[0164] Step S41: Obtain the optimal result of the Loadcase1 model obtained in step S2. The optimal result of the Loadcase2 model Constructed as a virtual utopian point ;

[0165] Step S42: Select the non-dominated solution with the shortest Euclidean distance to the Utopia point from the Pareto front weighted results obtained in step S3. To find the optimal solution, the optimal matrix is ​​selected; where the Euclidean distance between each non-dominated solution in the Pareto front and the utopia point is...

[0166]

[0167] Step S5: Establish an optimized core model using the optimized matrix model corresponding to the optimal solution obtained in step S4, and determine whether the optimized core model meets the design requirements through thermo-coupled finite element analysis. The specific process is as follows:

[0168] The optimized matrix model corresponding to the optimal solution obtained in step S4 is assembled with the cladding and fuel rods to establish an optimized core model. A thermo-coupled finite element analysis is then performed using the optimized core model to obtain temperature field contour maps, stress field contour maps, displacement field contour maps, heat flux density contour maps, and strain energy density contour maps. Based on the temperature field contour maps, it is determined whether the temperature range of the optimized matrix model is within a preset temperature range, and whether the maximum temperature gradient value of the optimized matrix model is less than the preset temperature gradient value (used to determine whether heat is effectively transferred from the fuel rods to the matrix and whether there are local hot spots on the matrix). Based on the stress field contour maps, it is determined whether the maximum stress of the optimized matrix model is lower than the ultimate strength of the matrix material. Based on the displacement field contour maps, it is determined whether the maximum displacement of the optimized matrix model is within a preset displacement range. Based on the heat flux density contour maps, it is determined whether the heat flux density gradient value of the optimized matrix model is... The Pearson correlation coefficient between strain energy density and stress intensity on the optimized matrix model is calculated based on the strain energy density cloud map and stress field cloud map. The coefficient is then checked to see if it is greater than the preset value. A Pearson correlation coefficient closer to 1 indicates a higher consistency between the strain energy distribution and the stress path, resulting in better structural force transmission efficiency. If the optimized matrix model's temperature range is within the preset temperature range, the maximum temperature gradient is less than the preset temperature gradient, the maximum stress is lower than the ultimate strength of the matrix material, the maximum displacement is within the preset displacement range, the maximum heat flux density gradient is less than the preset heat flux density gradient, and the calculated Pearson correlation coefficient is greater than the preset value, then the optimized core model meets the design requirements. Otherwise, the optimized core model does not meet the design requirements.

[0169] Step S6: If the optimized core model meets the design requirements, decrease the constraint volume fraction by a preset value of 1. If the optimized core model does not meet the design requirements, increase the constraint volume fraction by a preset value of 1. Then, repeat steps S2 to S5 using the updated constraint volume fraction.

[0170] Step S7: When the previous judgment result indicates that the optimized core model meets the design requirements, and the current judgment result is consistent with the previous judgment result, if the curvature of the performance change of the current optimized core model relative to the previous optimized core model is less than the curvature threshold, the preset value 1 is not updated, but the constraint volume fraction is updated to reduce the current constraint volume fraction by the preset value 1. Otherwise, the preset value 1 is updated to half of the previous preset value 1, and the constraint volume fraction is updated to reduce the current constraint volume fraction by the updated preset value 1. When the current judgment result is inconsistent with the previous judgment result, the preset value 1 is updated to half of the previous preset value 1. The current constraint volume fraction is increased by the updated preset value 1. If the previous judgment result is that the optimized core model does not meet the design requirements, and the current judgment result is consistent with the previous judgment result, the current constraint volume fraction is increased by the updated preset value 1 instead of the preset value 1. If the current judgment result is inconsistent with the previous judgment result, the current preset value 1 is updated to half of the previous preset value 1, and the current constraint volume fraction is decreased by the updated preset value 1. Then, steps S2 to S5 are repeated using the updated constraint volume fraction. Among them, the performance change curvature is the ratio of the change in the objective function value that comprehensively considers mechanical compliance and heat dissipation weakness corresponding to the two judgment results to the change in the corresponding constraint volume fraction value. (When the previous judgment result is that the optimized core model meets the design requirements, and the current judgment result is consistent with the previous judgment result, it means that the core model has been further optimized. At this time, the performance change curvature is greater than 0. Therefore, the curvature threshold should also be set to a value greater than 0. If the performance change curvature is too large, it means that the constraint volume fraction decreases too quickly. When approaching the optimal core model, it is easy to deviate too much from the optimal core model, resulting in repeated oscillations and optimization near the optimal core model, which affects the optimization efficiency.)

[0171] Step S8: Repeat step S7 until the judgment result is that the optimized core model meets the design requirements and the calculated performance change curvature is less than the curvature threshold for a continuous preset number of times. At this time, the corresponding optimized core model is the optimal core model, which achieves "maximum lightweighting" while meeting the design requirements.

[0172] in, Figure 3The physical quantity distribution contour map is obtained from the thermo-coupled finite element analysis of the core model before optimization. Figure 4 The physical quantity distribution contour map obtained after thermo-coupled finite element analysis of the optimized reactor core model. Figure 3 (a) and (b) are the temperature field contour maps of the core model before optimization and the 1 / 6 matrix model, respectively. Figure 4 (a) and (b) are the temperature field cloud maps of the optimized core model and the 1 / 6 matrix model, respectively. The overall temperature trend of the optimized core model is basically consistent with that of the unoptimized core model: the temperature gradually decreases from the center to the periphery in a circumferential radial diffusion pattern. In local areas, a relatively complete heat transfer path is maintained between the heat pipe holes and the fuel rods, and the temperature distribution is uniform. The heat is effectively dispersed and conducted, which reflects the success of multi-objective optimization in maintaining heat dissipation efficiency. Figure 3 (c) and Figure 4 (c) shows the stress field cloud map of the 1 / 6 matrix model before optimization and the stress field cloud map of the 1 / 6 matrix model after optimization. On both the matrix models before and after optimization, the high stress areas are concentrated near the fuel rod holes. The overall stress distribution on the optimized matrix model is relatively uniform. Although the maximum stress has increased, it is still far below the ultimate strength of the matrix material. Figure 3 (d) and Figure 4 The figures in (d) are displacement field cloud diagrams of the 1 / 6 matrix model before and after optimization, respectively. The displacement trend of the matrix model after optimization is basically consistent with that of the matrix model before optimization, indicating that the matrix model after optimization retains the main bearing path of the matrix model before optimization. Although the maximum displacement increases to 0.0079mm, it is still within the small deformation range, indicating that while the structural volume is significantly reduced, its stiffness is still effectively maintained, and it has good resistance to deformation, which can effectively cope with external loads in the actual working environment. Figure 3 (e) and Figure 4 In the middle (e), the heat flux density cloud maps of the 1 / 6 matrix model before optimization and the 1 / 6 matrix model after optimization are respectively. Compared with the matrix model before optimization, the optimized matrix model has a more uniform heat flux density distribution, which enables the heat to be effectively dispersed and conducted. Figure 3 (f) and Figure 4Figure (f) shows the strain energy density cloud diagrams of the 1 / 6 matrix model before and after optimization, respectively. Compared with the matrix model before optimization, the optimized matrix model has a more uniform strain energy density distribution and a higher consistency between the strain energy distribution and the stress path, indicating that the optimized matrix model has better force transmission efficiency. In summary, this optimal design demonstrates a good balance between heat dissipation performance and structural stiffness in thermo-mechanical coupling analysis. In particular, it still strictly guarantees efficient heat dissipation capacity under the premise of a significant reduction in structural volume. Although the maximum displacement increases slightly, the overall structure still has excellent mechanical properties.

Claims

1. A multi-objective topology optimization method for thermo-mechanical coupling of tube bundle structures considering gap heat conduction, characterized in that: Specifically as follows: Step S1: Establish a core model of the heat pipe cooled reactor, perform thermo-mechanical coupled finite element analysis on the core model, and obtain surface pressure data and surface heat source data of each heat pipe hole wall and each fuel rod hole wall. Step S2: Establish two matrix models of the reactor core. Set mechanical loads and heat source loads for the two matrix models respectively, so that the stress distribution of one matrix model and the temperature distribution of the other matrix model are consistent with the stress distribution and temperature distribution of the reactor core model. Set displacement boundary conditions and temperature boundary conditions for the two matrix models respectively. Then, perform topology optimization on the two matrix models with mechanical compliance and heat dissipation weakness as optimization objectives respectively. Step S3: Merge the two matrix models with mechanical load and displacement boundary conditions and heat source load and temperature boundary conditions into a coupled model. Take mechanical compliance and heat dissipation weakness as optimization objectives. After normalization, the two optimization objectives are aggregated into a multi-objective function expression through linear weighting and topology optimization of the coupled model. Then, the weight factor values ​​of the two optimization objectives are repeatedly adjusted, and the coupled model is topologically optimized based on the multi-objective function after the weight factor values ​​of the two optimization objectives are adjusted to solve the multi-objective problem and obtain the Pareto front of the set of optimal solutions of the multi-objective under different weight factors. Step S4: Select the optimal solution in the Pareto front based on the ideal point method, thereby selecting the optimal matrix; Step S5: Establish an optimized core model using the optimized matrix model corresponding to the optimal solution obtained in step S4, and perform thermo-mechanical coupled finite element analysis on the optimized core model to determine whether the optimized core model meets the design requirements. Step S6: Update the constraint volume fraction based on the judgment result of step S5, and repeat steps S2 to S5 using the updated constraint volume fraction. Step S7: Update the constraint volume fraction based on the judgment results of the two previous judgments and the corresponding performance change curvature, and repeat steps S2 to S5 using the updated constraint volume fraction; wherein, the performance change curvature is the ratio of the change value of the objective function value that comprehensively considers mechanical compliance and heat dissipation weakness corresponding to the two previous judgments to the corresponding change value of the constraint volume fraction. Step S8: Repeat step S7 until the judgment result is that the optimized core model meets the design requirements and the number of consecutive preset times of performance change curvature is less than the curvature threshold. At this time, the last optimized core model is the optimal core model.

2. The multi-objective topology optimization method for tube bundle structures considering gap heat conduction according to claim 1, characterized in that: The specific process of step S1 is as follows: Step S11: Establish the core model; Step S12: Set the material properties of the core model; Step S13: Mesh the core model; Step S14: Set the displacement boundary conditions for the core model; Step S15: Set the temperature boundary conditions for the core model; Step S16: Automatically set the gap behavior of the core model through the contact module of the finite element software, and define the mechanical contact properties of the core model contact interface. Step S17: Select the Coupled Temp-Displacement solver to solve the core thermo-coupling problem. Use the UMAT subroutine to simulate the core deformation behavior of the core model and output the surface pressure data of the walls of each heat pipe hole and each fuel rod hole. Use the GAPCON subroutine to simulate the core heat transfer behavior of the core model and output the surface heat source data of the walls of each heat pipe hole and each fuel rod hole.

3. The multi-objective topology optimization method for thermo-mechanical coupling of tube bundle structures considering gap heat conduction as described in claim 1, characterized in that: The specific process of step S2 is as follows: Step S21: Establish two matrix models with consistent geometry, material, and mesh information, denoted as Loadcase1 model and Loadcase2 model; Step S22: Extract the surface pressure data of each heat pipe hole wall and each fuel rod hole wall, as well as the surface heat source data of each heat pipe hole wall and each fuel rod hole wall from the result file of the thermo-coupled finite element analysis of the core model in step S1. Apply the extracted surface pressure data to the same position in the Loadcase1 model and the surface heat source data to the same position in the Loadcase2 model. Set displacement boundary conditions and temperature boundary conditions for the Loadcase1 model and the Loadcase2 model, respectively. Step S23: Input the constraint volume fraction and minimum filtering radius. For the Loadcase1 model and Loadcase2 model obtained from step S22, with mechanical compliance and heat dissipation weakness as optimization objectives respectively, run the topology optimization Python program to solve them. Obtain the elastic strain energy and nodal displacement of each element's Gaussian integration point and node in the Loadcase1 model, and the nodal temperature and nodal heat flux of each element's Gaussian integration point and node in the Loadcase2 model. Calculate the sensitivity value of each element in the Loadcase1 model with mechanical compliance as the optimization objective and the sensitivity value of each element in the Loadcase2 model with heat dissipation weakness as the optimization objective. After filtering and bidirectional progressive structural optimization analysis, obtain the updated information of the design variable, i.e., the relative density of each element, and update the material distribution in the Loadcase1 and Loadcase2 models.

4. The multi-objective topology optimization method for tube bundle structures considering gap heat conduction according to claim 3, characterized in that: The sensitivity value of each unit is the relative density of the objective function with respect to the design variables. The partial derivatives of are given by two objective functions, one optimizing mechanical compliance and the other optimizing heat dissipation weakness. In the formula, The objective function is mechanical compliance; It is the global mechanical force vector; It is a global displacement vector; It is the global stiffness matrix; Let e ​​be the displacement vector of the node of the element. The element's equivalent stiffness matrix; It is the relative density of all units The vector formed; It is the total number of units; The objective function is the heat dissipation weakness; It is the global heat source load vector; It is the global node temperature vector; For the overall heat conduction matrix; It is the temperature vector of the e-th unit node; The unit is the equivalent thermal conductivity stiffness matrix; Element equivalent stiffness matrix and the unit equivalent thermal conduction stiffness matrix In a linear manner with relative density Link: In the formula, It is a punishment index. and Here are the element stiffness matrix and element thermal conductivity stiffness matrix of the initial structure. Let be the relative density of the e-th unit, with candidate values ​​of 1 and 2. ; The formulas for calculating the sensitivity values ​​of each unit with mechanical compliance as the optimization objective and the sensitivity values ​​of each unit with heat dissipation weakness as the optimization objective are as follows: In the formula, Let be the sensitivity value of the e-th unit, with mechanical compliance as the optimization objective. Let be the sensitivity value of the e-th unit with heat dissipation weakness as the optimization objective.

5. The multi-objective topology optimization method for thermo-mechanical coupling of tube bundle structures considering gap heat conduction as described in claim 3, characterized in that: The specific process of step S3 is as follows: Step S31: Using the direct coupling analysis technique of thermal and mechanical physical fields, merge the Loadcase1 model and Loadcase2 model obtained in step S22 into a coupled model; Step S32: Taking mechanical compliance and heat dissipation weakness as optimization objectives, a multi-objective function is established. The element sensitivity values ​​based on mechanical compliance and heat dissipation weakness are multiplied by weighting factors to achieve linear weighted aggregation and obtain the element sensitivity values ​​of the coupled model. After filtering and bidirectional progressive structural optimization analysis, the updated information of the design variables, i.e., the relative density of each element, is obtained and used to update the material distribution in the coupled model. The topology optimization Python program is then used to solve the coupled model.

6. The multi-objective topology optimization method for thermo-mechanical coupling of tube bundle structures considering gap heat conduction according to claim 5, characterized in that: The specific process of step S32 is as follows: (1) The expression for the multi-objective optimization problem is as follows: In the formula, A multi-objective function that comprehensively considers mechanical compliance and heat dissipation weakness; and These are the weighting factors for mechanical compliance and heat dissipation weakness, respectively. and These are the optimal values ​​for mechanical compliance and heat dissipation weakness, respectively. and These represent the initial mechanical compliance and heat dissipation weakness of the coupled model, respectively. This represents the total volume of the coupled model; It is the unit volume; To constrain volume fraction; (2) and Multiply by weighting factors respectively , By combining normalization processing with linear weighted aggregation, the sensitivity values ​​of each unit under multi-objective optimization are obtained. (3) Numerical processing of the sensitivity of each unit under multi-objective optimization: ① Spatial filtering is performed on the sensitivity values ​​of each unit under multi-objective optimization: In the formula, To optimize the sensitivity value of the e-th cell in a multi-target system after spatial filtering; For the e-th unit and the The distance between units; This is the weighting function used to average the original sensitivity values; Minimum filter radius; For the first Weighting factors for the original sensitivity values ​​of each unit; For the first The original sensitivity values ​​of each unit; ②Historical information averaging: The sensitivity values ​​of each unit in the current iteration, after spatial filtering, are averaged with the corresponding unit sensitivity values ​​in the previous iteration, after spatial filtering. In the formula, This represents the sensitivity value of the e-th unit after spatial filtering during the k-th iteration. This is the sensitivity value of the e-th unit after spatial filtering during the (k-1)-th iteration; (4) The relative density of the cells is updated iteratively by using a bidirectional progressive structure optimization method; (5) Adjust the two weighting factors and The value is repeated from step (1) to step (4). (6) Repeat step (5) to obtain the Pareto front of the multi-objective optimal solution set under different weight factors.

7. The multi-objective topology optimization method for tube bundle structures considering gap heat conduction according to claim 4, characterized in that: The specific process of step S4 is as follows: Step S41: The optimal results of the two matrix models obtained in step S2 are weighted by the weight factors of the two optimization objectives and constructed into a virtual Utopian point. Step S42: Select the non-dominated solution with the shortest Euclidean distance to the Utopia point from the Pareto front weighted results obtained in step S3 as the optimal solution.

8. The multi-objective topology optimization method for thermo-mechanical coupling of tube bundle structures considering gap heat conduction according to claim 1, characterized in that: The specific process of step S5 is as follows: The optimized matrix model corresponding to the optimal solution obtained in step S4 is assembled with the cladding and fuel rods to establish an optimized core model. A thermo-coupled finite element analysis is then performed using the optimized core model to obtain temperature field contour maps, stress field contour maps, displacement field contour maps, heat flux density contour maps, and strain energy density contour maps of the optimized core model. Based on the temperature field contour maps, it is determined whether the temperature range of the optimized matrix model is within the preset temperature range and whether the maximum temperature gradient value of the optimized matrix model is less than the preset temperature gradient value. Based on the stress field contour maps, it is determined whether the maximum stress of the optimized matrix model is lower than the ultimate strength of the matrix material. Based on the displacement field contour maps, it is determined whether the maximum displacement of the optimized matrix model is within the preset displacement range and whether the maximum displacement is within the preset displacement range. Based on the heat flux density contour maps... The algorithm determines whether the heat flux density gradient value of the optimized matrix model is less than the preset heat flux density gradient value. It calculates the Pearson correlation coefficient between strain energy density and stress intensity on the optimized matrix model based on the strain energy density cloud map and stress field cloud map, and determines whether the Pearson correlation coefficient is greater than the preset coefficient value. If the optimized matrix model's temperature range is within the preset temperature range, the maximum temperature gradient value is less than the preset temperature gradient value, the maximum stress is lower than the ultimate strength of the matrix material, the maximum displacement is within the preset displacement range, the maximum heat flux density gradient value is less than the preset heat flux density gradient value, and the calculated Pearson correlation coefficient is greater than the preset value, then the optimized core model meets the design requirements; otherwise, the optimized core model does not meet the design requirements.

9. The multi-objective topology optimization method for tube bundle structures considering gap heat conduction according to claim 1, characterized in that: The specific process of step S6 is as follows: If the optimized core model meets the design requirements, the constraint volume fraction is reduced by a preset value of 1. If the optimized core model does not meet the design requirements, the constraint volume fraction is increased by a preset value of 1. Then, steps S2 to S5 are repeated using the updated constraint volume fraction.

10. The multi-objective topology optimization method for thermo-mechanical coupling of tube bundle structures considering gap heat conduction according to claim 1, characterized in that: The specific process of step S7 is as follows: If the previous judgment result indicated that the optimized core model met the design requirements, and the current judgment result is consistent with the previous judgment result, then if the curvature of the performance change of the current optimized core model relative to the previous optimized core model is less than the curvature threshold, the preset value 1 is not updated; instead, the constraint volume fraction is updated, reducing the current constraint volume fraction from the preset value 1. Otherwise, the preset value 1 is updated, making the current preset value 1 half of the previous preset value 1, and the constraint volume fraction is updated, reducing the current constraint volume fraction from the updated preset value 1. If the current judgment result is inconsistent with the previous judgment result, the preset value 1 is updated, making the current preset value 1 equal to the previous preset value 1. The current constraint volume fraction is increased by half of the previous preset value 1. If the previous judgment result is that the optimized core model does not meet the design requirements, and the current judgment result is consistent with the previous judgment result, the current constraint volume fraction is increased by the previous preset value 1 instead of the previous preset value 1. If the current judgment result is inconsistent with the previous judgment result, the current preset value 1 is increased by half of the previous preset value 1, and the current constraint volume fraction is decreased by the previous preset value 1. Then, steps S2 to S5 are repeated using the updated constraint volume fraction.

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