A heat pipe type heat exchanger fin parameter optimization method

Abstract

This invention discloses a method for optimizing fin parameters in a heat pipe heat exchanger, including: establishing a physical model of the heat pipe heat exchanger; setting several different fin parameters to obtain several experimental groups corresponding to different fin parameters; performing simulations on each experimental group to obtain the exhaust gas outlet temperature corresponding to different experimental groups; performing regression analysis to obtain a polynomial response model between fin parameters and exhaust gas outlet temperature; establishing a material cost model; using exhaust gas outlet temperature and fin material cost as objective functions, solving the polynomial response model and material cost model through several multi-objective optimization algorithms to obtain the optimal solution set corresponding to different multi-objective optimization algorithms; deciding on the optimal solution; and using the fin parameters corresponding to the optimal solution as the optimization result. This invention addresses the problems of algorithmic bias and low design reliability in existing heat pipe heat exchanger fin parameter design methods, thereby improving the robustness and reliability of the design results.

Description

Technical Field

[0001] This invention relates to the field of heat exchanger design, and more specifically to a method for optimizing the fin parameters of a heat pipe heat exchanger. Background Technology

[0002] With the escalating global energy crisis and increasingly stringent environmental protection requirements, industrial waste heat recovery has become a crucial means of energy conservation and emission reduction. Heat pipe heat exchangers, due to their high heat transfer efficiency and structural flexibility, are widely used in waste heat recovery systems for flue gas in industries such as chemical, power, and metallurgy. As one of the core structures of a heat pipe heat exchanger, the geometric parameters (such as spacing, thickness, and height) of the fins directly affect heat exchange efficiency and material costs.

[0003] Existing design approaches for heat pipe heat exchanger fin parameters have at least the following drawbacks:

[0004] 1. Using a single optimization algorithm for optimization may result in different algorithms converging in different local regions due to differences in their mechanisms, leading to "algorithm bias" in the optimization results. This makes it difficult to guarantee the global optimum, and the reliability of the obtained optimal solution is low.

[0005] 2. Limited evaluation dimensions. Optimization objectives are usually limited to heat exchange performance, ignoring actual production costs and the impact of manufacturing tolerances and operational fluctuations on fin performance.

[0006] 3. The decision-making process is simple. Existing evaluation methods are based only on the original optimization objective, failing to comprehensively measure the performance of candidate solutions across multiple dimensions, and the decision weights are fixed, making it impossible to flexibly adjust them according to actual engineering needs.

[0007] Therefore, it is necessary to improve the existing design methods for heat pipe heat exchanger fin parameters. Summary of the Invention

[0008] This invention provides a method for optimizing the fin parameters of a heat pipe heat exchanger, which solves the problems of algorithm bias and low design reliability in the existing heat pipe heat exchanger fin parameter design methods, thereby improving the robustness and reliability of the design results.

[0009] This invention is achieved through the following technical solution:

[0010] A method for optimizing the fin parameters of a heat pipe heat exchanger includes the following steps:

[0011] S1. Establish a physical model of the heat pipe heat exchanger; the heat pipe heat exchanger includes fins;

[0012] S2. Set several different fin parameters, substitute the different fin parameters into the physical model, and obtain several experimental groups corresponding to different fin parameters.

[0013] S3. Set boundary conditions, determine the turbulence model, and use the turbulence model to simulate each experimental group to obtain the exhaust gas outlet temperature corresponding to different experimental groups.

[0014] S4. Based on the fin parameters and exhaust gas outlet temperature of different experimental groups, regression analysis was performed to obtain a polynomial response model between fin parameters and exhaust gas outlet temperature.

[0015] S5. Establish a material cost model based on fin parameters;

[0016] S6. Using exhaust gas outlet temperature and fin material cost as objective functions, solve the polynomial response model and the material cost model using several different multi-objective optimization algorithms to obtain the optimal solution set corresponding to several different multi-objective optimization algorithms;

[0017] S7. Based on the aforementioned optimal solution set, determine the optimal solution;

[0018] S8. The fin parameters corresponding to the optimal solution are used as the optimization result.

[0019] To address the problems of algorithmic bias and low design reliability in existing heat pipe heat exchanger fin parameter design methods, this invention proposes a method for optimizing heat pipe heat exchanger fin parameters. This method first establishes a physical model of the heat pipe heat exchanger including fins. Then, several different fin parameters are designed and substituted into the physical model to obtain several experimental groups for later use. Next, necessary preparations for simulation are performed, such as setting boundary conditions and determining the turbulence model. Numerical simulations are conducted on different experimental groups to obtain the corresponding exhaust gas outlet temperatures. Then, based on the fin parameters and corresponding exhaust gas outlet temperatures of different experimental groups, polynomial regression is performed to obtain the polynomial response model between the fin parameters and the exhaust gas outlet temperature; thus, the relationship function between the fin parameters and the exhaust gas outlet temperature is established. Next, a material cost model is established. This material cost model can be designed based on the raw material costs under the current time and operating conditions, without specific limitations; thus, the relationship function between different fin parameters and material costs is obtained. Finally, multi-objective optimization is performed. This application uses exhaust gas outlet temperature and fin material cost as objective functions, and employs different multi-objective optimization algorithms to solve them. Each multi-objective optimization algorithm yields an optimal solution, therefore, N different multi-objective optimization algorithms will yield N optimal solutions. The set of N optimal solutions is the optimal solution set in this application. Finally, this application performs a secondary decision based on the optimal solution set to obtain the final optimal solution, and its corresponding fin parameters can be used as the optimization result.

[0020] As can be seen, this application can run a variety of multi-objective optimization algorithms with different mechanisms according to specific needs, and then obtain the best-performing solution based on the idea of ​​quadratic decision-making. This effectively avoids the local optima and algorithm bias problems that may be caused by the use of a single algorithm in existing technologies, and makes the final selected solution robust and reliable across algorithms. This significantly improves the accuracy and reliability of the design results and provides designers with a clear and interpretable basis for decision-making.

[0021] In other words, this application does not rely on the search preferences of a specific algorithm, but rather reflects the consensus under different optimization paths. For example, a certain design scheme may be optimal under a certain optimization algorithm, but may perform poorly under the perspective of other optimization algorithms. The optimal solution determined by this application has cross-algorithm robustness, and its performance remains excellent under various optimization logics, greatly improving the credibility of the optimal solution.

[0022] Furthermore, in step S2: the fin parameters include at least two of the following: fin spacing, fin thickness, fin length, fin bottom height, and fin top height. Those skilled in the art should understand that the fin thickness and fin length refer to the dimensions of a single fin, the fin spacing refers to the dimensions of adjacent fins, and the fin bottom height and fin top height refer to the height of the fin relative to the heat pipe heat exchanger body.

[0023] Furthermore, in step S3: the turbulence model is a Realizable k-ε model; the simulation is a steady-state heat transfer simulation. The Realizable k-ε model, by introducing achievable constraints and a more reasonable dissipation rate equation, significantly improves the accuracy of predicting complex flows while maintaining the computational efficiency of the k-ε model. In this application, it can more effectively balance reliability and economy. In addition, this scheme uses steady-state heat transfer simulation, which can quickly predict the limiting temperature or heat flux distribution, improving design efficiency.

[0024] Furthermore, in step S4: the coefficient of determination of the polynomial response model is made to be no less than 0.95 to ensure the accuracy of the prediction of the exhaust gas outlet temperature. It is easy to understand that if the coefficient of determination of the polynomial response model is less than 0.95, the regression analysis is repeated until the requirement of a coefficient of determination of no less than 0.95 is met. The specific regression analysis method can be any existing polynomial regression algorithm, and no specific limitation is made here.

[0025] Furthermore, in step S6: the multi-objective optimization algorithm includes the NSGA-II algorithm, the MOPSO algorithm, and the MOEA / D algorithm. This scheme specifies three multi-objective optimization algorithms; in addition, other multi-objective optimization algorithms can be added according to specific working conditions.

[0026] Furthermore, step S7 specifically includes:

[0027] S701. Remove duplicate solutions from the optimal solution set to obtain a candidate solution pool;

[0028] S702. Determine several evaluation indicators;

[0029] S703. Based on the evaluation index, obtain the comprehensive quality index of each solution in the candidate solution pool;

[0030] S704 outputs the solution with the highest overall quality index, and uses its corresponding fin parameters as the optimization result.

[0031] This scheme calculates the comprehensive quality index of each solution in the candidate solution pool using several evaluation indicators, overcoming the problems of single evaluation dimensions and one-sided decision results in existing technologies, and significantly improving the accuracy and reliability of the design results.

[0032] Furthermore, the evaluation indicators include exhaust gas outlet temperature, material cost, and robustness score. This scheme explicitly defines three evaluation indicators. In addition, other evaluation indicators can be added according to specific operating conditions to make the evaluation results more comprehensive and multi-dimensional.

[0033] Furthermore, step S703 specifically includes:

[0034] S7031. Obtain the evaluation index corresponding to the current solution and normalize each evaluation index;

[0035] S7032. Based on the normalized evaluation index, draw a plot in the polar coordinate system and connect the lines sequentially to obtain a closed region, and calculate the area of ​​the closed region.

[0036] S7033. Calculate the grey relational degree of the current solution relative to the remaining solutions in the candidate solution pool;

[0037] S7034. Based on the area of ​​the closed region and the gray relational degree, the comprehensive quality index of the current solution is obtained.

[0038] This scheme constructs a multi-dimensional evaluation index system, which integrates different evaluation indicators into a geometric measurement to intuitively reflect the balance of each candidate solution across various dimensions; the larger the area of ​​the closed region, the better the overall performance of the current solution. Furthermore, this scheme also considers the grey relational degree of each candidate solution relative to other candidate solutions based on the grey relational degree method. Finally, a comprehensive evaluation is conducted based on the area of ​​the closed region and the grey relational degree, which helps improve the balance and reliability of the optimization results.

[0039] Furthermore, in step S7031: each evaluation index is positively or negatively normalized so that the normalization result of all evaluation indices satisfies the condition that the larger the value, the better the performance. That is, for positive evaluation indices, a positive normalization algorithm is used; for negative evaluation indices, a negative normalization algorithm is used.

[0040] Furthermore, in step S7034, the overall quality index (CQI) of the current solution is obtained using the following formula: i =α×S i +β×γ i Among them, CQI i S represents the overall quality index of the i-th solution in the candidate solution pool; i γ represents the area of ​​the closed region of the i-th solution in the candidate solution pool; i α represents the grey relational degree of the i-th solution in the candidate solution pool; α is the area weight coefficient; β is the relational degree weight coefficient.

[0041] This scheme does not impose specific limitations on the values ​​of the weighting coefficients α and β, which can be flexibly adjusted according to actual working conditions or needs. This reflects the different levels of emphasis on performance balance and algorithm consensus, and truly realizes the leap from "theoretically optimal" to "engineering applicable" in fin design.

[0042] Compared with the prior art, the present invention has at least the following advantages and beneficial effects:

[0043] 1. This invention provides a method for optimizing fin parameters of a heat pipe heat exchanger. It can run multiple multi-objective optimization algorithms with different mechanisms according to specific needs, and then obtain the solution with the best performance based on the idea of ​​secondary decision-making. This effectively avoids the local optima and algorithm bias problems that may be caused by the use of a single algorithm in the prior art. It makes the final selected solution robust and reliable across algorithms, thereby significantly improving the accuracy and reliability of the design results and providing designers with a clear and interpretable decision basis.

[0044] 2. The present invention provides a method for optimizing the fin parameters of a heat pipe heat exchanger. By calculating the comprehensive quality index of each solution in the candidate solution pool through several evaluation indicators, it overcomes the problems of single evaluation dimensions and one-sided decision results in the prior art, and significantly improves the accuracy and reliability of the design results.

[0045] 3. The present invention provides a method for optimizing the fin parameters of a heat pipe heat exchanger. By constructing a multi-dimensional evaluation index system, different evaluation indices are comprehensively measured geometrically to intuitively reflect the balance of each candidate solution in each dimension.

[0046] 4. The present invention provides a method for optimizing the fin parameters of a heat pipe heat exchanger. It considers the degree of grey relational relationship between each candidate solution and other candidate solutions, and finally conducts a comprehensive evaluation based on the area of ​​the closed region and the degree of grey relational relationship, which is conducive to improving the balance and reliability of the optimization results.

[0047] 5. The present invention provides a method for optimizing the fin parameters of a heat pipe heat exchanger. The coefficient weights can be flexibly adjusted according to actual working conditions or requirements, thereby reflecting different levels of emphasis on performance balance and algorithm consensus, and truly realizing the leap from "theoretical optimal" to "engineering applicability" in fin design. Attached Figure Description

[0048] The accompanying drawings, which are included to provide a further understanding of embodiments of the invention and form part of this application, do not constitute a limitation thereof. In the drawings:

[0049] Figure 1 This is a schematic diagram of the overall process of a specific embodiment of the present invention;

[0050] Figure 2 This is a flowchart illustrating the process of determining the optimal solution in a specific embodiment of the present invention. Detailed Implementation

[0051] To make the objectives, technical solutions, and advantages of the present invention clearer, the present invention will be further described in detail below with reference to the embodiments and accompanying drawings. The illustrative embodiments and descriptions of the present invention are only used to explain the present invention and are not intended to limit the present invention.

[0052] Example 1:

[0053] A method for optimizing fin parameters in a heat pipe heat exchanger; please refer to [reference needed]. Figure 1 This includes the following steps:

[0054] S1. Establish a physical model of the heat pipe heat exchanger; the heat pipe heat exchanger includes fins.

[0055] S2. Set several different fin parameters, substitute the different fin parameters into the physical model, and obtain several experimental groups corresponding to different fin parameters.

[0056] In this embodiment, the fin parameters include at least two of the following: fin spacing, fin thickness, fin length, fin bottom height, and fin top height.

[0057] S3. Set boundary conditions, determine the turbulence model, and simulate each experimental group using the turbulence model to obtain the exhaust gas outlet temperature corresponding to different experimental groups.

[0058] In this embodiment, the turbulence model is preferably a Realizable k-ε model; the simulation method is preferably steady-state heat transfer simulation.

[0059] S4. Based on the fin parameters and exhaust gas outlet temperature of different experimental groups, regression analysis was performed to obtain a polynomial response model between the fin parameters and the exhaust gas outlet temperature.

[0060] In this embodiment, the polynomial response model is obtained using the least squares method.

[0061] In this embodiment, the polynomial response model is also verified, such that the determination coefficient of the polynomial response model is greater than or equal to 0.95.

[0062] S5. Based on fin parameters, establish a material cost model.

[0063] In this embodiment, the fin volume can be calculated based on the fin parameters, the volume can be converted into mass based on the material density, and then a material cost model can be established by combining the local and current raw material costs.

[0064] S6. Using exhaust gas outlet temperature and fin material cost as objective functions, solve the polynomial response model and the material cost model using several different multi-objective optimization algorithms to obtain Pareto front solutions corresponding to several different multi-objective optimization algorithms. Establish a set to obtain the optimal solution set.

[0065] In this embodiment, the various multi-objective optimization algorithms include: NSGA-II algorithm, MOPSO algorithm, and MOEA / D algorithm.

[0066] S7. Determine the optimal solution from the set of optimal solutions;

[0067] S8. The fin parameters corresponding to the optimal solution are used as the optimization result.

[0068] Example 2:

[0069] A method for optimizing fin parameters of a heat pipe heat exchanger, based on Example 1, please refer to... Figure 2 In this embodiment, the optimal solution is determined from the optimal solution set using the following method:

[0070] S701. Remove duplicate solutions from the optimal solution set to obtain a candidate solution pool.

[0071] S702. Determine several evaluation indicators.

[0072] The evaluation indicators determined in this embodiment include exhaust gas outlet temperature, material cost, and robustness score.

[0073] S703. Based on the evaluation index, obtain the comprehensive quality index of each solution in the candidate solution pool. The specific process is as follows:

[0074] Obtain the evaluation index corresponding to the current solution, and normalize each evaluation index so that the larger the normalization result of all evaluation indices, the better the performance. Specifically, for positive evaluation indices, a positive normalization algorithm is used; for negative evaluation indices, a negative normalization algorithm is used.

[0075] Based on the normalized evaluation indicators, a radar chart is obtained by plotting the data in a polar coordinate system and connecting the lines sequentially. The area S of the closed region formed by the radar chart is then calculated. i .

[0076] Calculate the grey relational degree γ of the current solution relative to the remaining solutions in the candidate solution pool. i .

[0077] Preferably, the grey relational degree of the current solution relative to the other solutions in the candidate solution pool is calculated by averaging. For example, for a total of 1-4 candidate solutions, for candidate solution 1, the grey relational degrees from candidate solution 1 to candidate solution 2, candidate solution 3, and candidate solution 4 are calculated respectively, and then the average value is taken.

[0078] Finally, based on the area of ​​the closed region and the gray relational degree, the comprehensive quality index of the current solution is obtained:

[0079] CQI i =α×S i +β×γ i Among them, CQI i S represents the overall quality index of the i-th solution in the candidate solution pool; i γ represents the area of ​​the closed region of the i-th solution in the candidate solution pool; i α represents the grey relational degree of the i-th solution in the candidate solution pool; α is the area weight coefficient; β is the relational degree weight coefficient.

[0080] S704, Press CQI i The candidate solution pool is sorted from high to low values, and the top-ranked solutions are output for designers to refer to, thus providing designers with clear and interpretable decision-making basis.

[0081] Of course, the top-ranked solution can also be directly output as the final design scheme.

[0082] Furthermore, this embodiment not only outputs the optimal design scheme but also provides radar charts for each candidate solution across various evaluation metrics, intuitively demonstrating the balanced performance of each design scheme in multiple dimensions such as heat exchange performance, cost, and robustness. This "visualized decision-making" enables engineering designers to clearly understand why a solution was selected and in what aspects it has advantages, providing a scientific and transparent basis for subsequent structural design and manufacturing processes.

[0083] Example 3:

[0084] This embodiment verifies the effectiveness of the method of this application through specific experiments.

[0085] For a known heat pipe heat exchanger, the design process of its fin parameters was simulated. The optimal solution obtained by the method in Example 2 (denoted as Scheme A) was compared with the traditional optimal solutions obtained by using a single NSGA-II and MOGA algorithm and weighted summation based on fixed weights (heat transfer performance: cost = 0.5:0.5) (denoted as Schemes B and C, respectively). The results of the comparison experiment are shown in Table 1.

[0086] Table 1 Comparative Experimental Results

[0087]

[0088] In Table 1, the “Experimental Data” column shows the results obtained using the fin parameters of the existing heat pipe heat exchanger. The corresponding exhaust gas outlet temperature is obtained from numerical simulation experiments, and the corresponding material cost is calculated using the fin size parameters.

[0089] It should be noted that the material cost in this embodiment is dimensionless, that is, it is a relative cost calculated assuming the unit price of the material is 1. Its essence is to characterize the amount of material used.

[0090] As shown in Table 1, the method of this application achieves a near-optimal balance in both the exhaust gas outlet temperature and material cost, two key indicators: its exhaust gas outlet temperature is only 0.02℃ higher than the NSGA-II algorithm, while its cost is 17.26℃ lower; simultaneously, its cost is only 23.37℃ higher than the MOGA algorithm, while its exhaust gas outlet temperature is 0.29℃ lower. In contrast, it is evident that a single multi-objective optimization algorithm, lacking a global perspective and exhibiting biases and differences, may not be able to objectively and absolutely approximate the best frontier across countless solution sets for the two objectives represented by the functions. Therefore, this application demonstrates that it can utilize a comprehensive evaluation index to select the solution closest to the ideal compromise from a global perspective, thereby achieving a better balance between two conflicting objectives, with an overall performance significantly superior to any single algorithm.

[0091] The specific embodiments described above further illustrate the purpose, technical solution, and beneficial effects of the present invention. It should be understood that the above description is only a specific embodiment of the present invention and is not intended to limit the scope of protection of the present invention. Any modifications, equivalent substitutions, improvements, etc., made within the spirit and principles of the present invention should be included within the scope of protection of the present invention.

[0092] It should be noted that, in this document, terms such as “comprising,” “including,” or any other variations thereof are intended to cover non-exclusive inclusion, such that a process, method, article, or apparatus that comprises a list of elements includes not only those elements but also other elements not expressly listed, or elements inherent to such process, method, article, or apparatus.

Claims

1. A method for optimizing fin parameters of a heat pipe heat exchanger, characterized in that, Includes the following steps: S1. Establish a physical model of the heat pipe heat exchanger; the heat pipe heat exchanger includes fins; S2. Set several different fin parameters, substitute the different fin parameters into the physical model, and obtain several experimental groups corresponding to different fin parameters. S3. Set boundary conditions, determine the turbulence model, and use the turbulence model to simulate each experimental group to obtain the exhaust gas outlet temperature corresponding to different experimental groups. S4. Based on the fin parameters and exhaust gas outlet temperature of different experimental groups, regression analysis was performed to obtain a polynomial response model between fin parameters and exhaust gas outlet temperature. S5. Establish a material cost model based on fin parameters; S6. Using exhaust gas outlet temperature and fin material cost as objective functions, solve the polynomial response model and the material cost model using several different multi-objective optimization algorithms to obtain the optimal solution set corresponding to several different multi-objective optimization algorithms; S7. Based on the aforementioned optimal solution set, determine the optimal solution; S8. The fin parameters corresponding to the optimal solution are used as the optimization result.

2. The method for optimizing fin parameters of a heat pipe heat exchanger according to claim 1, characterized in that, In step S2: the fin parameters include at least two of the following: fin spacing, fin thickness, fin length, fin bottom height, and fin top height.

3. The method for optimizing fin parameters of a heat pipe heat exchanger according to claim 1, characterized in that, In step S3: the turbulence model is a Realizable k-ε model; the simulation is a steady-state heat transfer simulation.

4. The method for optimizing fin parameters of a heat pipe heat exchanger according to claim 1, characterized in that, In step S4: the determination coefficient of the polynomial response model is not less than 0.

95.

5. The method for optimizing fin parameters of a heat pipe heat exchanger according to claim 1, characterized in that, In step S6: the multi-objective optimization algorithm includes the NSGA-II algorithm, the MOPSO algorithm, and the MOEA / D algorithm.

6. The method for optimizing fin parameters of a heat pipe heat exchanger according to claim 1, characterized in that, Step S7 specifically includes: S701. Remove duplicate solutions from the optimal solution set to obtain a candidate solution pool; S702. Determine several evaluation indicators; S703. Based on the evaluation index, obtain the comprehensive quality index of each solution in the candidate solution pool; S704 outputs the solution with the highest overall quality index, and uses its corresponding fin parameters as the optimization result.

7. The method for optimizing fin parameters of a heat pipe heat exchanger according to claim 6, characterized in that, The evaluation metrics include exhaust gas outlet temperature, material cost, and robustness score.

8. The method for optimizing fin parameters of a heat pipe heat exchanger according to claim 6, characterized in that, Step S703 specifically includes: S7031. Obtain the evaluation index corresponding to the current solution and normalize each evaluation index; S7032. Based on the normalized evaluation index, draw a plot in the polar coordinate system and connect the lines sequentially to obtain a closed region, and calculate the area of ​​the closed region. S7033. Calculate the grey relational degree of the current solution relative to the remaining solutions in the candidate solution pool; S7034. Based on the area of ​​the closed region and the gray relational degree, the comprehensive quality index of the current solution is obtained.

9. The method for optimizing fin parameters of a heat pipe heat exchanger according to claim 8, characterized in that, In step S7031: each evaluation index is positively or negatively normalized so that the normalization result of all evaluation indices satisfies the condition that the larger the value, the better the performance.

10. The method for optimizing fin parameters of a heat pipe heat exchanger according to claim 8, characterized in that, In step S7034, the overall quality index (CQI) of the current solution is obtained using the following formula: i =α×S i +β×γ i Among them, CQI i S represents the overall quality index of the i-th solution in the candidate solution pool; i γ represents the area of ​​the closed region of the i-th solution in the candidate solution pool; i α represents the grey relational degree of the i-th solution in the candidate solution pool; α is the area weight coefficient; β is the relational degree weight coefficient.

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