A multi-objective optimization design method for sodium-air heat exchanger based on sensitivity driving

Abstract

The application discloses a sodium-air heat exchanger multi-objective optimization design method based on sensitivity driving, and the method establishes a comprehensive performance model of heat transfer, pressure drop, volume, mass and cost, determines the importance classification of design parameters by combining sensitivity analysis, and constructs a population initialization and adaptive mutation strategy accordingly, so as to guide a multi-objective evolutionary optimization process. In the optimization process, the constraint dominance rule is adopted to process the power window, the pressure drop limit and the geometric and strength constraints, and finally a high feasible rate and a uniformly distributed Pareto solution set are obtained. The application can significantly improve the optimization efficiency and the proportion of feasible solutions, and improve the engineering applicability and decision support capability of the optimization results.

Description

Technical Field

[0001] This application belongs to the field of engineering design and optimization, and in particular relates to a sensitivity-driven multi-objective optimization design method for sodium-air heat exchangers. Background Technology

[0002] The sodium-air heat exchanger is a core component of sodium-cooled fast reactors, enabling passive residual heat removal and ensuring inherent safety. It safely releases reactor decay heat into the environment through the sodium-air heat exchange channel, which is of great significance for improving reactor safety, simplifying system structure, and enhancing self-sustaining cooling capacity under accident conditions.

[0003] To improve air-side heat transfer performance, sodium-air heat exchangers typically employ finned tube heat exchangers. Traditional sodium-air heat exchanger design relies on engineers' experience, manual consultation, and repeated manual calculations. The core challenge lies in: (1) Multidisciplinary coupling and strong target conflict: The design needs to take into account multiple disciplines such as heat transfer, fluid flow, structural strength and manufacturing cost, resulting in numerous design variables (such as fin height, fin spacing, pipe diameter, and arrangement). However, there are strong contradictions between core objectives (such as pressure drop, volume and cost), making it difficult to optimize them simultaneously using traditional methods.

[0004] (2) Low design efficiency: Traditional methods require a lot of iterative calculations and lack systematic design space exploration, resulting in long design cycles and low efficiency.

[0005] (3) Complex engineering constraints: The actual design needs to meet strict engineering constraints, such as specific heat exchange power windows, pressure drop limits and strict geometric and strength feasibility. These constraints further reduce the design space and increase the difficulty of finding a feasible solution. Summary of the Invention

[0006] The purpose of this application is to overcome the problems of existing technologies by disclosing a sensitivity-driven multi-objective optimization design method for sodium-air heat exchangers. This application deeply integrates sensitivity analysis with multi-objective optimization algorithms to achieve intelligent guidance of design variables, thereby significantly improving optimization efficiency and solution quality. This application unifies the handling of multi-source engineering constraints and provides engineering-oriented decision support, realizing automated end-to-end design from parameter input to feasible engineering solutions.

[0007] The objective of this application is achieved through the following technical solution: A sensitivity-driven multi-objective optimization design method for sodium-air heat exchangers, comprising: S1: Parametric model construction of engineering indicators, definition of design parameters, establishment of integrated thermal-structural-cost calculation model and encapsulation into a unified simulation interface; S2: Sensitivity analysis and parameter importance assessment. A multi-level sensitivity analysis method is used to analyze the design parameters. After eliminating insensitive parameters, the remaining parameters are analyzed in detail to generate the sensitivity weight and importance level of each design parameter to the optimization objective. S3: Sensitivity-driven multi-objective optimization. Based on sensitivity weights, hierarchical sampling is used to initialize the population. Objective functions and constraints are set. Adaptive mutation strategy and constraint dominance selection are used for optimization iteration until the intelligent early stopping condition is met. S4: Engineering decision support and solution recommendation. The Pareto solution set obtained by optimization is sorted and optimized, and a multi-criteria decision method is used for comprehensive evaluation to identify robust solutions and classify and recommend solutions.

[0008] According to a preferred embodiment, the sodium-air heat exchanger has a finned tube structure, with the fins being open-toothed spiral fins and the tube bundle being a serpentine tube. In step S1, the design parameters include the outer diameter of the tube, fin height, length of a single tube, tube spacing ratio, fin spacing, fin thickness, number of tube rows, number of tubes per row, number of folds in the serpentine tube, and operating parameters including inlet and outlet temperatures and design pressure.

[0009] According to a preferred embodiment, the thermal-structural-cost calculation model includes a thermodynamic calculation module. The thermodynamic calculation module is configured to calculate the heat transfer power, logarithmic mean temperature difference, and overall heat transfer coefficient based on the principles of heat transfer and considering the thermodynamic characteristics of the sodium flow inside the tube and the air flow outside the tube, using the ε-NTU method.

[0010] According to a preferred embodiment, the thermal-structural-cost calculation model includes a fluid dynamics calculation module, which is configured to calculate the fluid pressure drop on the air and sodium sides based on fluid dynamics and in-tube / out-tube flow resistance models, taking into account the influence of fin and heat exchange tube geometry parameters on fluid resistance, and using empirical formulas or simplified CFD models.

[0011] According to a preferred embodiment, the thermal-structural-cost calculation model includes a structural strength calculation module, which is configured to calculate the minimum wall thickness of pressure-bearing components, including heat exchange tubes, tube sheets, and shells, based on design pressure, temperature, and material properties, and output the volume and weight of the design scheme.

[0012] According to a preferred embodiment, the thermal-structural-cost calculation model includes a manufacturing cost calculation module, which is used to calculate material costs and labor costs. The material costs take into account the differentiated unit prices of standard and non-standard pipes, and the labor costs are estimated according to the process flow based on the complexity and size of the heat exchanger.

[0013] According to a preferred embodiment, in step S2, the optimization objectives include heat transfer power, sodium-side pressure drop, air-side pressure drop, volume, and cost, with corresponding weights of 0.3, 0.2, 0.2, 0.15, and 0.15, respectively. Furthermore, the multi-level sensitivity analysis method includes: firstly, using the Morris method to perform preliminary global sensitivity analysis, eliminating non-sensitive parameters, then using the FAST method to analyze the remaining parameters, and finally using the Sobol method to perform sensitivity analysis on the pre-selected key parameters.

[0014] According to a preferred embodiment, in step S3, the constraints include heat transfer power, air-side pressure drop, sodium-side pressure drop, equipment volume, manufacturing cost, and engineering feasibility. In the adaptive mutation strategy, parameters greater than the preset sensitivity threshold are adjusted to a value less than the preset variable asynchronous length to accelerate local convergence, while parameters less than the preset sensitivity threshold are adjusted to a value greater than the preset mutation rate to enhance global exploration capability. Furthermore, the mutation rate and variable asynchronous length adaptively decrease with the number of generations.

[0015] According to a preferred embodiment, in step S3, the sorting of constraint dominance selection includes: prioritizing the retention of feasible solutions that satisfy all constraints; for infeasible solutions, sorting them according to the sum of constraint violation degrees, with individuals having lower violation degrees given priority; for individuals at the same non-dominated level, prioritizing individuals with larger parameter space weighted distances. In step S3, the intelligent early stopping condition is that the size of the Pareto set no longer increases within several consecutive generations, or the standard deviation of the diversity of the Pareto solution set approaches zero.

[0016] According to a preferred embodiment, in step S4, the multi-criteria decision-making method includes TOPSIS, weighted and / or AHP, which normalizes the target value of the scheme and calculates a comprehensive score by combining the decision weights; the recommended scheme types include balanced, economical, efficient and compact.

[0017] The aforementioned main solution and its various further alternative solutions can be freely combined to form multiple solutions, all of which are solutions that can be adopted and are claimed in this application. Those skilled in the art, after understanding the solution of this application, will realize that there are many combinations based on the prior art and common general knowledge, all of which are technical solutions to be protected in this application, and will not be exhaustively listed here.

[0018] The beneficial effects of this application are: (1) More comprehensive multi-objective consideration: Traditional heat exchanger optimization methods are often limited to two core conflicting objectives: heat transfer performance (such as heat exchange capacity or heat flux density) and fluid pressure drop. This application, building upon this, incorporates volume (compactness) and cost as equally important optimization objectives, forming a four-objective optimization system (heat exchange power, pressure drop, volume, and cost) that is more valuable for engineering applications and commercially competitive. This comprehensive consideration helps designers find a better balance between performance, size, and economy.

[0019] (2) Sensitivity-Driven Optimization Strategy: Existing optimization methods typically employ random or uniform population initialization, lacking consideration of the importance of design variables. Before performing multi-objective optimization, this application first conducts multi-level sensitivity analysis on the design parameters to obtain the importance weight and rank of each parameter to the objective function. This sensitivity information is then used to intelligently guide the optimization process, specifically in the following ways: Focused population initialization: For key parameters identified as having a significant impact on the core objective, a more concentrated normal or Beta distribution is used for stratified sampling, so that the initial population is concentrated in the central interval where optimal solutions are more likely to be generated; while for parameters with a smaller impact, uniform or Latin hypercube sampling is used to ensure a broad exploration of the design space.

[0020] Adaptive Mutation Strategy: In the mutation operation of genetic algorithms, the mutation rate and variation length of parameters are dynamically correlated with their sensitivity weights. For critical parameters, a smaller variation length is used for fine-tuning to accelerate local convergence; for low-sensitivity parameters, a larger mutation rate is maintained to enhance global exploration capabilities. This strategy adaptively decays with each generation (evolutionary progress) throughout the evolutionary process, achieving a balance between global exploration and local optimization.

[0021] (3) Integration and Domination of Multi-Source Engineering Constraints: Traditional optimization methods often employ simple penalty function methods when dealing with complex engineering constraints, which may lead to the optimization algorithm getting stuck in infeasible regions or having low convergence efficiency. This application integrates various engineering constraints, including but not limited to power windows, upper limits of air and sodium side pressure drops, geometric rationality, and strength verification results, into a unified optimization framework. By introducing the concept of "constraint domination," this method prioritizes feasible solutions that satisfy all constraints in the non-dominated sorting; among infeasible solutions, it sorts them according to the sum of constraint violation degrees, thereby enabling the optimization algorithm to quickly and effectively approximate and search the boundary of the feasible design region.

[0022] (4) End-to-end closed-loop and engineering decision support: This application not only finds a set of Pareto optimal solutions, but more importantly, transforms these solutions into feasible engineering solutions. This method utilizes multi-criteria decision making (MCDM) methods (such as TOPSIS, weighted sum, AHP, etc.) to comprehensively score and rank the Pareto solution set, and can incorporate engineers' preferences and risk assessments. By performing perturbation analysis on the decision weights, this method can evaluate the robustness and stability of the recommended solutions, ultimately outputting various types of recommended solutions, such as balanced, economical, efficient, and compact solutions, along with their decision confidence levels. This provides strong quantitative evidence for engineering review and decision-making, achieving an end-to-end closed loop from parameter input to engineering solution output. Attached Figure Description

[0023] Figure 1 This is a flowchart illustrating the multi-objective optimization design method for the sodium-air heat exchanger proposed in this application; Figure 2 and Figure 3 This is a schematic diagram of the sodium-air heat exchanger of this application; Figure 4 This is a schematic diagram of the convergence history curve of multi-objective optimization. Detailed Implementation

[0024] The following specific examples illustrate the implementation of this application. Those skilled in the art can easily understand other advantages and effects of this application from the content disclosed in this specification. This application can also be implemented or applied through other different specific embodiments, and various details in this specification can also be modified or changed based on different viewpoints and applications without departing from the spirit of this application. It should be noted that, unless otherwise specified, the following embodiments and features in the embodiments can be combined with each other.

[0025] It should be noted that similar labels and letters in the following figures indicate similar items. Therefore, once an item is defined in one figure, it does not need to be further defined and explained in subsequent figures.

[0026] In the description of this application, it should be noted that the terms "center," "upper," "lower," "left," "right," "vertical," "horizontal," "inner," and "outer," etc., indicate the orientation or positional relationship based on the orientation or positional relationship shown in the accompanying drawings, or the orientation or positional relationship commonly used when the product of this application is in use. They are only for the convenience of describing this application and simplifying the description, and do not indicate or imply that the device or element referred to must have a specific orientation, or be constructed and operated in a specific orientation, and therefore should not be construed as a limitation on this application. In addition, the terms "first," "second," and "third," etc., are only used to distinguish descriptions and should not be construed as indicating or implying relative importance.

[0027] Furthermore, terms such as "horizontal," "vertical," and "sag" do not imply that components must be absolutely horizontal or suspended, but rather that they can be slightly tilted. For example, "horizontal" simply means that its direction is more horizontal relative to "vertical," and does not mean that the structure must be completely horizontal, but can be slightly tilted.

[0028] In the description of this application, it should also be noted that, unless otherwise expressly specified and limited, the terms "set up," "install," "connect," and "link" should be interpreted broadly. For example, they can refer to a fixed connection, a detachable connection, or an integral connection; they can refer to a mechanical connection or an electrical connection; they can refer to a direct connection or an indirect connection through an intermediate medium; and they can refer to the internal connection of two components. Those skilled in the art can understand the specific meaning of the above terms in this application based on the specific circumstances.

[0029] Furthermore, it should be noted that unless otherwise specified in this application, the specific structures, connections, positions, power sources, etc. involved are all things that a person skilled in the art can know without creative effort based on the prior art.

[0030] refer to Figure 1 As shown, this application discloses a sensitivity-driven multi-objective optimization design method for sodium-air heat exchangers, which includes the following steps.

[0031] Step 1: Constructing a parametric model for engineering indicators 1. Define design parameters: Determine the design variables that affect the performance of the finned tube heat exchanger, including but not limited to geometric parameters such as tube outer diameter, fin height, single tube length, tube spacing ratio, fin spacing, fin thickness, number of tube rows, number of tubes per row, and number of folds in the serpentine tube, as well as operating parameters such as inlet and outlet temperatures and design pressure.

[0032] 2. Establish a performance and strength calculation model: Construct an integrated thermal-structural-cost calculation model. This model can calculate the corresponding heat exchanger performance indicators (such as heat exchange power, heat flux density, air-side and sodium-side pressure drop), structural strength indicators (such as tube / shell wall thickness), and manufacturing costs based on all input design parameters. Specifically, it includes the following modules.

[0033] (1) Thermodynamic Calculation Module: Based on the principles of heat transfer, this module calculates the heat transfer power, logarithmic mean temperature difference, and overall heat transfer coefficient of the heat exchanger under given operating conditions. This module will simultaneously consider the thermodynamic characteristics of the sodium flow inside the tube and the air flow outside the tube, and use the ε-NTU method to perform accurate calculations of the heat transfer performance.

[0034] (2) Fluid Dynamics Calculation Module: Based on fluid dynamics and the in-pipe / out-of-pipe flow resistance model, this module calculates the fluid pressure drop on the air and sodium sides. It considers the influence of the geometric parameters of the fins and heat exchange tubes on the fluid resistance and predicts the flow resistance using empirical formulas or simplified CFD models.

[0035] (3) Structural strength calculation module: Strictly follow engineering specifications (such as ASME or GB150), calculate the minimum wall thickness of key pressure-bearing components such as heat exchange tubes, tube sheets, and shells based on the heat exchanger design pressure, temperature and material properties, and ensure the structural safety of the design scheme, while outputting the calculated volume and weight of the design scheme.

[0036] (4) Manufacturing cost calculation module: Construct a comprehensive cost model, including material cost and labor cost. Material cost will take into account the differentiated unit price of standard and non-standard pipes to reflect the actual situation of market supply and manufacturing cost; labor cost will be estimated according to the complexity and size of the heat exchanger and the process flow (such as fin stamping, tube bundle assembly, shell welding, etc.).

[0037] 3. Establish a simulation interface: Encapsulate the above calculation model into a unified simulation interface to ensure that any set of design parameters can output a complete set of engineering indicators and perform geometric and strength rationality checks.

[0038] Step 2: Sensitivity Analysis and Parameter Importance Assessment 1. Coarse sensitivity analysis: Within the domain of the design parameters, the Morris method is first used to perform a preliminary global sensitivity analysis on all design parameters in order to quickly identify parameters that are not important or do not affect the results.

[0039] 2. Precise analysis of parameters after screening: After removing the unimportant parameters identified in step 1, the remaining set of key parameters is further sensitively analyzed using the FAST method to obtain the main effects of the parameters and their interaction effects with other parameters.

[0040] 3. High-precision verification: Finally, for the most important parameters, the computationally intensive Sobol method is used to perform high-precision sensitivity analysis to obtain accurate main effect and total effect indices, which serve as the final basis for guiding subsequent optimization.

[0041] 4. Generate sensitivity weights: Based on the results of multi-stage sensitivity analysis, generate the sensitivity weight and importance level of each design parameter to the core optimization objective, and use it as parameter management data for subsequent steps.

[0042] Step 3: Sensitivity-Driven Multi-Objective Optimization 1. Initialize the population: Before the algorithm runs, the initial population of the optimization algorithm is initialized by stratified sampling based on the sensitivity weights generated in step 2.

[0043] (1) High sensitivity parameter: Use normal or Beta distribution to sample within a preset central interval to improve the quality of the initial solution.

[0044] (2) Low sensitivity parameters: Uniform or Latin hypercube sampling is used to ensure population diversity and broad exploration of the design space.

[0045] 2. Define the objective function and constraints: (1) Objective function: Set four objectives to be minimized: air-side pressure drop, sodium-side pressure drop, volume, and cost.

[0046] (2) Constraints: Set hard constraints, including but not limited to: 1) Minimum heat exchange power; 2) Maximum allowable pressure drop across both sides; 3) Maximum allowable volume; 4) Maximum allowable cost; 5) Physical constraints: Ensure that all geometric parameters are within a reasonable range and can be physically arranged, and that all calculated pipe / shell wall thicknesses meet the strength verification requirements.

[0047] 3. Perform adaptive genetic operations: During the optimization iteration process, an adaptive mutation strategy is adopted. The mutation rate and variation length of the parameters are dynamically related to their sensitivity weights. For highly sensitive parameters, a smaller variation length is used for fine-tuning to accelerate local convergence; for low-sensitive parameters, a larger mutation rate is maintained to enhance global exploration capabilities.

[0048] 4. Implementing constrained dominance selection: During the non-dominated ranking and environmental selection stages, the constrained dominance principle is used to screen the population.

[0049] (1) Sorting principle: Prioritize retaining feasible solutions that satisfy all constraints and place them before infeasible solutions.

[0050] (2) Infeasible solution sorting: For infeasible solutions, sort them according to the sum of their constraint violation degrees, with the individual with the smaller violation degree taking priority.

[0051] (3) Maintaining diversity: For individuals at the same non-dominated level, while ensuring the number of feasible solutions, individuals with large weighted distance in parameter space are preferred to ensure the diversity of solutions.

[0052] 5. Intelligent early stopping: The optimization process will continue to iterate until the preset intelligent early stopping conditions are met, such as: the size of the Pareto set no longer increases within several consecutive generations, or the standard deviation of the diversity of the Pareto solution set approaches zero.

[0053] Step 4: Engineering Decision Support and Solution Recommendation 1. Pareto solution set preparation: Select the final Pareto solution set obtained from optimization, remove the dominant solutions and non-engineering feasible solutions, and generate the final set of solutions to be evaluated.

[0054] 2. Multi-criteria decision analysis: (1) Target matrix normalization: The target values ​​(such as pressure drop, volume, cost) of each scheme in the scheme set are normalized to eliminate the influence of different dimensions and make their value range uniform in the [0,1] interval.

[0055] (2) Decision weight setting: Engineers set corresponding decision weights for different objectives (such as economy, compactness, performance) according to actual needs. For example, the cost weight can be set high for economical design.

[0056] (3) Comprehensive score calculation: The multi-criteria decision-making (MCDM) method is adopted to calculate the comprehensive score of each scheme based on the normalized objective matrix and decision weights. For example, the TOPSIS method calculates the relative merits of each scheme by measuring the distance between each scheme and the ideal optimal solution (positive ideal solution) and the ideal worst solution (negative ideal solution).

[0057] 3. Robustness assessment and solution selection: (1) Weight perturbation analysis: By perturbing the decision weights within a small range, the multi-criteria decision analysis is repeatedly performed. The sensitivity of the analysis results is then assessed to evaluate the stability of the recommended scheme.

[0058] (2) Robust solution identification: Identify solutions that perform well under various weight combinations as “robust solutions” to provide additional reference for decision-making.

[0059] (3) Category recommendation: Based on the preset typical engineering preferences (such as "economic", "efficient", "compact" and "balanced"), the corresponding set of recommended solutions is automatically selected from the Pareto set and its key indicators are displayed.

[0060] 4. Output and Decision Support: Outputs the final recommended solution, its overall score, and the score difference with other alternatives (as decision confidence level), and provides a set of key parameters for the solution. Additionally, it can sort the solutions by score to help decision-makers quickly select the optimal solution.

[0061] Example 1. Case Background and Design Task Design objective: Design a finned tube sodium-air heat exchanger for a reactor cooling system, with a heat exchange capacity of not less than 30MW (safety margin 1.2).

[0062] The fin type is a toothed spiral fin; its schematic diagram and parameter description can be found in [link to schematic diagram]. Figure 2 andFigure 3 According to the reference standard GB / T47030-2013, the tube bundle form is a serpentine tube. Figure 2 and Figure 3 In the diagram, D represents the outer diameter of the fin (mm), h represents the fin height (mm), fin pitch (mm), d represents the tube diameter (mm), h1 represents the height from the root of the toothed fin to the outer diameter of the tube (mm), t represents the fin pitch (mm), N represents the number of fins, e represents the tube wall thickness (mm), s represents the fin thickness (mm), and D1 represents the mid-circle diameter of the fin (mm) (D1=d+h, when the fin is not toothed; D1=d+h1, when the fin is toothed).

[0063] Operating limits: Air-side pressure drop limit: 100 Pa; Sodium-side pressure drop limit: 1000 Pa; Cost limit: 5 million; Structural limits: Heat transfer tube arrangement, fin arrangement, etc. must meet geometric rationality requirements.

[0064] Operating conditions: Sodium side inlet temperature: 500℃; Sodium side outlet temperature: 300℃; Sodium side design temperature: 550℃; Sodium side design pressure: 1MPa; Air side inlet temperature: 30℃; Air side outlet temperature: 350℃; Air side design temperature: 400℃; Air side design pressure: 0.1MPa.

[0065] Material selection: The heat exchange tubes, fins, and shell are all made of 316L steel; the material cost is set at 20,000 yuan / ton. If the heat transfer tubes are non-standard, the price will increase by 50%.

[0066] 2. Design parameters Geometric parameters: tube outer diameter, fin height, single tube length, tube spacing ratio, fin spacing, fin thickness, number of tube rows, number of tubes per row, number of folds in the serpentine tube.

[0067] 3. Sensitivity Analysis Analysis methods: Multilevel sensitivity analysis was performed sequentially using Morris, FAST, and Sobol methods.

[0068] The weightings for heat transfer power, sodium-side pressure drop, air-side pressure drop, volume, and cost are 0.3, 0.2, 0.2, 0.15, and 0.15, respectively.

[0069] Results: The analysis results of each method are shown in the table below.

[0070]

[0071] The final analysis results show that the parameters most important to the target are, in order of importance: Highly sensitive parameter: tube spacing ratio; Highly sensitive parameters: outer diameter of the tube, fin height, number of tube rows; Low to medium sensitivity parameters: number of tubes per row, tube length, number of bends in the serpentine tube; Low-sensitivity parameters: fin spacing and fin thickness.

[0072] 4. Optimization process Algorithm: An improved algorithm based on NSGA-II is adopted.

[0073] The optimized parameter range and sensitivity weights are shown in the table below:

[0074] Population initialization: Based on the sensitivity results, parameters with a sensitivity weight greater than 0.8 are sampled using a more concentrated normal distribution, while other parameters are sampled using a uniform distribution.

[0075] Mutation strategy: During the iteration process, parameters with a sensitivity weight greater than or equal to 1 are mutated with a small step size, parameters with a sensitivity greater than or equal to 0.8 are mutated with a medium step size, and the remaining parameters are mutated with a large step size.

[0076] Algorithm parameters: Population size 100, maximum number of optimizations 100 generations.

[0077] 5. Optimization Results Pareto solution set: After 17 iterations, a Pareto solution set containing 100 non-dominated solutions is obtained. The convergence process is as follows: Figure 4 As shown.

[0078] The first 10 solutions are shown in the table below:

[0079] 6. Decision support and solution recommendation The decision weights are set as follows [air-side pressure drop, sodium-side pressure drop, volume, cost]: Cost focus: [0.2, 0.2, 0.2, 0.4]; Prioritize performance: [0.4, 0.4, 0.1, 0.1]; Balanced solution: [0.25, 0.25, 0.25, 0.25].

[0080] After scoring each proposal, the three recommended design schemes are as follows: ① Cost-optimal solution: Pareto front number: 1; air pressure drop: 84.1 Pa; sodium pressure drop: 66.8 Pa; equipment volume: 29.653 m³; manufacturing cost: 1,301,774 yuan.

[0081] Recommendation reason: Lowest cost, only 1,301,774 yuan. Although the pressure drop is 84 Pa for air and 67 Pa for sodium, it is economical. Suitable for projects with limited budgets.

[0082] ②Optimal performance solution: Pareto front number: 11; air pressure drop: 24.1 Pa; sodium pressure drop: 16.2 Pa; equipment volume: 52.852 m³; manufacturing cost: 4,411,432 yuan.

[0083] Recommended because: It offers the best pressure drop performance, 24 Pa on the air side and 16 Pa on the sodium side. Although the cost is 4,411,432 yuan, it boasts the highest operating efficiency and is suitable for applications with demanding performance requirements.

[0084] ③ Balanced solution: Pareto front number: 3; air pressure drop: 95.4 Pa; sodium pressure drop: 71.0 Pa; equipment volume: 25.249 m³; manufacturing cost: 1,344,677 yuan.

[0085] Recommendation reason: Balanced performance across all indicators with no obvious weaknesses. Air pressure drop 95Pa, sodium pressure drop 71Pa, volume 25.25m³, cost 1,344,677 yuan. Suitable for most engineering applications.

[0086] Decision sensitivity analysis By applying small-scale perturbations to the decision weights, the multi-criteria decision analysis is repeatedly performed. The sensitivity of the analysis results is then assessed to evaluate the stability of the recommended scheme.

[0087] Decision stability: 0.979; Number of robust solutions: 3.

[0088] Stability under different weight configurations: Cost-focused: 0.972; Performance-focused: 0.981; Balanced consideration: 0.979.

[0089] The above description is merely a preferred embodiment of this application and is not intended to limit this application. Any modifications, equivalent substitutions, and improvements made within the spirit and principles of this application should be included within the protection scope of this application.

Claims

1. A sensitivity-driven multi-objective optimization design method for sodium-air heat exchangers, characterized in that, The multi-objective optimization design method for the sodium-air heat exchanger includes: S1: Parametric model construction of engineering indicators, definition of design parameters, establishment of integrated thermal-structural-cost calculation model and encapsulation into a unified simulation interface; S2: Sensitivity analysis and parameter importance assessment. A multi-level sensitivity analysis method is used to analyze the design parameters. After eliminating insensitive parameters, the remaining parameters are analyzed in detail to generate the sensitivity weight and importance level of each design parameter to the optimization objective. S3: Sensitivity-driven multi-objective optimization. Based on sensitivity weights, hierarchical sampling is used to initialize the population. Objective functions and constraints are set. Adaptive mutation strategy and constraint dominance selection are used for optimization iteration until the intelligent early stopping condition is met. S4: Engineering decision support and solution recommendation. The Pareto solution set obtained by optimization is sorted and optimized, and a multi-criteria decision method is used for comprehensive evaluation to identify robust solutions and classify and recommend solutions.

2. The multi-objective optimization design method for sodium-air heat exchangers as described in claim 1, characterized in that, The sodium-air heat exchanger has a finned tube structure, with fins in the form of open-tooth spiral fins and tube bundles in the form of serpentine tubes. In step S1, the design parameters include the outer diameter of the tube, fin height, length of a single tube, tube spacing ratio, fin spacing, fin thickness, number of tube rows, number of tubes per row, number of folds in the serpentine tube, and operating parameters including inlet and outlet temperatures and design pressure.

3. The multi-objective optimization design method for sodium-air heat exchangers as described in claim 2, characterized in that, The thermal-structural-cost calculation model includes a thermodynamic calculation module. The thermodynamic calculation module is configured to calculate the heat transfer power, logarithmic mean temperature difference, and overall heat transfer coefficient based on the principles of heat transfer and considering the thermodynamic characteristics of the sodium flow inside the tube and the air flow outside the tube, using the ε-NTU method.

4. The multi-objective optimization design method for sodium-air heat exchangers as described in claim 2, characterized in that, The thermal-structural-cost calculation model includes a fluid dynamics calculation module, which is configured to be based on fluid dynamics and in-tube / out-tube flow resistance models, taking into account the influence of fin and heat exchange tube geometric parameters on fluid resistance, and calculating the fluid pressure drop on the air and sodium sides through empirical formulas or simplified CFD models.

5. The multi-objective optimization design method for sodium-air heat exchangers as described in claim 2, characterized in that, The thermal-structural-cost calculation model includes a structural strength calculation module, which is configured to calculate the minimum wall thickness of pressure-bearing components, including heat exchange tubes, tube sheets, and shells, based on design pressure, temperature, and material properties, and output the volume and weight of the design scheme.

6. The multi-objective optimization design method for sodium-air heat exchangers as described in claim 2, characterized in that, The thermal-structural-cost calculation model includes a manufacturing cost calculation module, which is used to calculate material costs and labor costs. The material costs take into account the differentiated unit prices of standard and non-standard pipes, and the labor costs are estimated according to the process flow based on the complexity and size of the heat exchanger.

7. The multi-objective optimization design method for sodium-air heat exchangers as described in claim 2, characterized in that, In step S2, the optimization objectives include heat transfer power, sodium-side pressure drop, air-side pressure drop, volume, and cost, with corresponding weights of 0.3, 0.2, 0.2, 0.15, and 0.15, respectively. Furthermore, the multi-level sensitivity analysis method includes: firstly, using the Morris method to perform preliminary global sensitivity analysis, eliminating non-sensitive parameters, then using the FAST method to analyze the remaining parameters, and finally using the Sobol method to perform sensitivity analysis on the pre-selected key parameters.

8. The multi-objective optimization design method for sodium-air heat exchangers as described in claim 7, characterized in that, In step S3, the constraints include heat transfer power, air-side pressure drop, sodium-side pressure drop, equipment volume, manufacturing cost, and engineering feasibility. In the adaptive mutation strategy, parameters greater than the preset sensitivity threshold are adjusted to a value less than the preset variable asynchronous length to accelerate local convergence, while parameters less than the preset sensitivity threshold are adjusted to a value greater than the preset mutation rate to enhance global exploration capability. Furthermore, the mutation rate and variable asynchronous length adaptively decrease with the number of generations.

9. The multi-objective optimization design method for sodium-air heat exchangers as described in claim 8, characterized in that, In step S3, the ordering of constraint dominance selection includes: prioritizing the retention of feasible solutions that satisfy all constraints; for infeasible solutions, sorting them according to the sum of constraint violation degrees, with individuals having lower violation degrees given priority; for individuals at the same non-dominated level, prioritizing individuals with larger weighted distances in the parameter space. In step S3, the intelligent early stopping condition is that the size of the Pareto set no longer increases within several consecutive generations, or the standard deviation of the diversity of the Pareto solution set approaches zero.

10. The multi-objective optimization design method for sodium-air heat exchangers as described in claim 1, characterized in that, In step S4, the multi-criteria decision-making methods include TOPSIS, weighted and / or AHP. The target values ​​of the schemes are normalized and the comprehensive score is calculated by combining the decision weights. The recommended scheme types include balanced, economical, efficient and compact.

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