Multi-objective optimization method and device for airfoil fin structure of printed circuit board heat exchanger with top gap

Abstract

The present invention belongs to the technical field related to printed circuit board manufacturing, and discloses a multi-objective optimization method and device for the airfoil fin structure of a printed circuit board heat exchanger with a top gap, comprising: S1, obtaining geometric parameters of the airfoil fin in the printed circuit board heat exchanger PCHE with a top gap, including the gap distance; S2, non-dimensionalizing the geometric parameters to obtain optimized design variables; S3, obtaining a sample set based on the optimized design variables; S4, constructing a volume heat transfer coefficient h v The first target proxy model corresponding to the drag coefficient f and the second target proxy model corresponding to the drag coefficient f; S5, maximize h v The optimization objectives are to optimize the first and second target proxy models to obtain the Pareto optimal frontier of flow and heat transfer performance. S6 uses a multi-objective decision-making method to select the variables of the compromise solution from the Pareto optimal frontier to determine the optimal optimization solution. The present invention takes top clearance into account.

Description

Technical Field

[0001] The present invention belongs to the technical field related to the manufacture of printed circuit board type heat exchangers, and more specifically, relates to a multi-objective optimization method and equipment for an airfoil fin structure of a printed circuit board type heat exchanger with a top gap. Background Art

[0002] Growing global energy demand is exacerbating global warming, air pollution, and ozone depletion, leading to an increasing demand for efficient, green energy conversion systems. The supercritical CO2 Brayton cycle offers promising energy prospects. However, due to the high pressure and high temperature operating conditions found in supercritical conditions, conventional heat exchangers struggle to effectively meet these requirements. A new type of heat exchanger, the printed circuit heat exchanger (PCHE), addresses these high-pressure, high-temperature requirements while offering enhanced safety, compactness, and efficiency. Compared to traditional machining and welding processes, the PCHE primarily utilizes chemical etching and diffusion bonding. Channels are formed by chemically etching metal plates, which are then stacked and diffusion-bonded to form a single unit. Therefore, the PCHE is capable of adapting to the extreme high-temperature and high-pressure operating conditions of the supercritical CO2 Brayton cycle.

[0003] Channel types within a PCHE are generally categorized into two types: continuous and discontinuous. Continuous channels primarily include straight, Z-shaped, and sinusoidal channels, with cross-sectional shapes typically including semicircular, rectangular, triangular, and trapezoidal. Discontinuous channels primarily include S-shaped and airfoil-shaped channels. Fins primarily improve the flow and heat transfer characteristics of the heat exchanger by increasing the heat transfer area and enhancing fluid turbulence. Airfoil-shaped fins in PCHEs exhibit superior flow and heat transfer performance compared to fins of other shapes.

[0004] The airfoil fin PCHE has different channel forms. In order to obtain the optimal geometric parameters of the airfoil fin in the PCHE channel, current existing research mainly focuses on the airfoil fin arrangement parameters (horizontal distance, vertical distance, staggered distance), and rarely studies the top gap. PCHE with different top gaps have different flow and heat transfer performance. The present invention changes the fin top gap without changing the channel height, and optimizes it together with the other three arrangement parameters. Due to limited computing resources, the more conventional method at present is to use numerical simulation and orthogonal experimental design methods to study the influence of different airfoil fin geometric parameters on heat transfer and pressure drop in the channel. However, the traditional enumeration method cannot obtain the best results within a certain parameter variation range when optimizing under preset parameters, and has great limitations, which makes it difficult to achieve the optimal design of the optimized structural configuration. Therefore, it is urgent to conduct in-depth research on the flow and heat transfer mechanism of the airfoil fin PCHE taking the fin top gap into consideration, and further optimize the airfoil fin structure to achieve the goal of high efficiency and low resistance. Summary of the Invention

[0005] In response to the above defects or improvement needs of the prior art, the present invention provides a multi-objective optimization method and equipment for the airfoil fin structure of a printed circuit board heat exchanger with a top gap, aiming to find the geometric parameters of the airfoil fin PHCE with excellent comprehensive performance.

[0006] To achieve the above objectives, according to one aspect of the present invention, a multi-objective optimization method for an airfoil fin structure of a printed circuit board heat exchanger with a top gap is provided, the method comprising the following steps:

[0007] S1, obtaining geometric parameters of the airfoil fins in the printed circuit board heat exchanger PCHE with top gap, wherein the geometric parameters include the horizontal distance L h , staggered distance L s , vertical distance L v and clearance distance L g ;

[0008] S2, non-dimensionalizing the geometric parameters of the airfoil fin to obtain optimized design variables, the optimized design variables including the horizontal number ζ h , interleaving number ζ s 、Vertical number ζ v and gap number ζ g ;

[0009] S3, performing experimental design and numerical simulation on the optimized design variables to obtain a sample set;

[0010] S4, inputting the training set in the sample set into the neural network for training to obtain the PCHE volume heat transfer coefficient h v the corresponding first target proxy model and the second target proxy model corresponding to the PCHE drag coefficient f;

[0011] S5, with ζ h ,ζ s ,ζ v and ζ g To optimize the variables, maximize h v Taking the sum and minimizing f as optimization objectives, a multi-objective optimization algorithm is used to optimize the first target proxy model and the second target proxy model to obtain the Pareto optimal frontier of flow performance and heat transfer performance;

[0012] S6, using a multi-objective decision-making method to select variables of the trade-off solution from the Pareto optimal frontier to determine the best optimization solution.

[0013] Furthermore, using the airfoil fin chord length L c and channel height L z The dimensionless geometric parameters of the airfoil fin are defined; the horizontal number is: The interleaving number is: The vertical number is The number of gaps is

[0014] Furthermore, as the airfoil fin top clearance and arrangement change, the length, width, and height of the PCHE 3D model must meet the following constraints:

[0015]

[0016] Where, L x Indicates the channel length, L y Indicates the channel width, L z Indicates the channel height, L h Indicates the horizontal distance of the airfoil, L s Indicates the staggered distance of the airfoil, L v Indicates the vertical distance of the airfoil, L g Indicates the airfoil clearance distance, L c Indicates the chord length of the airfoil, L t Represents the airfoil thickness, where i, j, k, and m are all positive integers.

[0017] Furthermore, an optimal Latin hypercube design is used to simulate sample points collected from the optimization variables in the design space to obtain a training set and a test set; the training set is used to train the neural network, and the test set is used to test the accuracy of the neural network.

[0018] Furthermore, the first target proxy model and the second target proxy model are: PSO-BP neural network.

[0019] Furthermore, the input layer of the PSO-BP neural network contains 4 neurons, namely the level number ζ h , interleaving number ζ s 、Vertical number ζ v and gap number ζ g , the output layer contains one neuron; the PSO-BP neural network is used to calculate the volume heat transfer coefficient h v and resistance coefficient f are trained separately.

[0020] Furthermore, the mean square error is used to quantitatively evaluate the prediction performance of the neural network; the process of improving the BP neural network using the improved particle swarm optimization algorithm includes: first, by optimizing the weights and learning factors of the particle swarm algorithm, an improved particle swarm algorithm is obtained; then, the initial weights and thresholds of the proxy model are encoded into particles, and the optimal initial weights and thresholds corresponding to the minimum fitness value are obtained, and finally they are assigned to the proxy model.

[0021] Furthermore, after step S5 and before step S6, the method further comprises the step of: v , minimize f, the single objective optimal solution corresponding to the PF value maximum scheme and the two compromise schemes of VIKOR and TOPSIS are simulated and verified; if the h corresponding to the five schemes v If the relative error between the predicted value of the surrogate model and the simulation result is greater than the error threshold, the number of samples in the training set is supplemented, and steps S4-S6 are repeated until the relative error meets the accuracy requirement; the variable ζ corresponding to the VIKOR and TOPSIS compromise solution that meets the accuracy requirement is h ,ζ s ,ζ v and ζ g As the optimal design parameters of the PCHE airfoil fin; wherein, the optimized printed circuit board heat exchanger with a top gap has a gap between the top of the fin and the channel wall, and the gap number satisfies 0<ζ g <0.15.

[0022] The present invention also provides a multi-objective optimization system for the airfoil fin structure of a printed circuit board type heat exchanger with a top gap. The system includes a memory and a processor. The memory stores a computer program. When the processor executes the computer program, it performs the multi-objective optimization method for the airfoil fin structure of the printed circuit board type heat exchanger with a top gap as described above.

[0023] The present invention also provides a computer-readable storage medium, which stores machine-executable instructions. When the machine-executable instructions are called and executed by a processor, the machine-executable instructions prompt the processor to implement the multi-objective optimization method for the airfoil fin structure of the printed circuit board type heat exchanger with a top gap as described above.

[0024] In general, compared with the prior art, the above technical solutions conceived by the present invention provide a multi-objective optimization method and apparatus for the airfoil fin structure of a printed circuit board heat exchanger with a top gap, which has the following beneficial effects:

[0025] 1. Designing a PCHE with a top gap can significantly reduce flow resistance while increasing the heat exchange area. It also creates a vortex structure within the channel, accelerating the mixing of hot and cold fluids and further enhancing heat transfer. When the structure has a small top gap, the PHCE has excellent thermal and hydraulic performance.

[0026] 2. The present invention adjusts the top clearance of the airfoil fin and makes the top clearance dimensionless. Combining the other three dimensionless arrangement parameters as optimization design variables, the PCHE is parameterized in three-dimensional modeling. This achieves the goal of obtaining as many airfoil geometric parameters as possible while ensuring the rationality of the heat exchanger structure. A proxy model is used to perform a large amount of optimization in the sample space, reducing the time cost while meeting the requirements of universality and overcoming the limitations of pre-given fixed parameter values.

[0027] 3. The present invention adopts the PSO-BP neural network as a proxy model and uses the PSO optimization algorithm to globally optimize the weights and thresholds of the BP neural network, replacing the traditional random assignment method, thereby making up for the shortcomings of the BP neural network algorithm. It has excellent prediction accuracy and generalization ability, and is feasible as a proxy model to predict the flow and heat transfer performance of PCHE under different airfoil fin parameters.

[0028] 4. The present invention optimizes the optimization variables through a multi-objective genetic algorithm and obtains the Pareto optimal frontier. In the actual design process, decision makers can weigh the heat transfer performance and flow characteristics based on engineering requirements and select the appropriate decision method to select the corresponding optimization solution from the Pareto optimal solution set.

[0029] 5. The present invention aims at optimizing the top clearance and geometric dimensions of the airfoil fins in PCHE, and performs multi-objective optimization based on DOE, PSO-BP neural network model, NSGA-II algorithm, VIKOR, and TOPSIS method. This optimization method can be extended to the optimization design of other types of heat exchangers. BRIEF DESCRIPTION OF THE DRAWINGS

[0030] Figure 1 1 is a flow chart of a multi-objective optimization method for an airfoil fin structure of a printed circuit board type heat exchanger with a top gap provided by one embodiment of the present invention;

[0031] Figure 2 is a schematic diagram of a PCHE geometric model of an airfoil fin with a top gap in one embodiment of the present invention;

[0032] Figure 3 is a flow chart of a PSO-BP neural network in one embodiment of the present invention;

[0033] Figure 4 The heat transfer coefficient h is given in one embodiment of the present invention. v and Pareto optimal frontier diagram of resistance coefficient f. DETAILED DESCRIPTION

[0034] In order to make the objectives, technical solutions and advantages of the present invention more clearly understood, the present invention is further described in detail below with reference to the accompanying drawings and embodiments. It should be understood that the specific embodiments described herein are merely for the purpose of explaining the present invention and are not intended to limit the present invention. In addition, the technical features involved in the various embodiments of the present invention described below may be combined with each other as long as they do not conflict with each other.

[0035] The flow and heat transfer characteristics in PCHE are related to the arrangement of channels and the top clearance of the fins. The present invention performs parametric three-dimensional modeling of the top clearance of the airfoil fin PCHE combined with three arrangement parameters by combining driving dimensions and geometric constraints. Combined with CFD, proxy models and multi-objective optimization algorithms, optimization can be achieved in a large range to achieve the goal of high efficiency and low resistance.

[0036] See also Figure 1 and Figure 2 The present invention provides a multi-objective optimization method for the airfoil fin structure of a printed circuit board heat exchanger with a top gap. The optimization method can operate under extreme operating conditions and can be used for a supercritical CO2 Brayton cycle. First, parameter design is performed based on the experimental design method. After the parameters are dimensionless, simulation is performed to obtain a training set to train the PSO-BP neural network. Subsequently, a surrogate model is used to predict the flow and heat transfer performance of the PCHE. Finally, the volume heat transfer coefficient h is used to calculate the optimal parameters. v and resistance coefficient f as the optimization objectives, the Pareto optimal frontier was obtained based on the NSGA-II algorithm, and the TOPSIS method and VIKOR method were used to select a compromise solution with excellent thermal-hydraulic performance.

[0037] The optimization method mainly comprises the following steps:

[0038] S1, obtaining geometric parameters of the airfoil fins in the printed circuit board heat exchanger PCHE with top gap, wherein the geometric parameters include the horizontal distance L h , staggered distance L s , vertical distance L v and clearance distance L g .

[0039] S2, non-dimensionalizing the geometric parameters of the airfoil fin to obtain optimized design variables, the optimized design variables including the horizontal number ζ h , interleaving number ζ s 、Vertical number ζ v and gap number ζ g .

[0040] In this embodiment, the chord length L of the airfoil fin is used. c and channel height L zThe dimensionless geometric parameters of the airfoil fin are defined; the horizontal number is: The interleaving number is: The vertical number is The number of gaps is

[0041] In another embodiment, Figure 2 As shown in the figure, due to the periodicity and symmetry of the flow, and to save computing resources, the model is simplified to a single-channel fluid domain as the numerical simulation calculation area, and 8 minimum periodic heat exchange units are considered along the flow direction. Parametric modeling is performed, and the airfoil fin used in the model is the NACA 0020 airfoil. c Take 4mm, L z Taking 1mm, the value range of the optimized design variables is shown in Table 1.

[0042] Table 1 Value ranges of optimization design variables

[0043] Design variables symbol Value range <![CDATA[Horizontal number ζ h > <![CDATA[ζ h ]]> [1.5,2.5] <![CDATA[Alternating number ζ s > <![CDATA[ζ s ]]> [0,1] <![CDATA[Vertical number ζ v > <![CDATA[ζ v ]]> [0.4,0.8] <![CDATA[Number of gaps ζ g > <![CDATA[ζ g ]]> [0.05,0.9]

[0044] S3, performing experimental design and numerical simulation on the optimized design variables in the design space to obtain a sample set.

[0045] In this embodiment, as the top clearance and arrangement of the airfoil fins change, the length, width, and height of the PCHE 3D model must meet the following constraints:

[0046]

[0047] Where, L x Indicates the channel length, L y Indicates the channel width, L z Indicates the channel height, L h Indicates the horizontal distance of the airfoil, L s Indicates the staggered distance of the airfoil, L v Indicates the vertical distance of the airfoil, L g Indicates the airfoil clearance distance, L c Indicates the chord length of the airfoil, L t Represents the airfoil thickness, where i, j, k, and m are all positive integers.

[0048] The optimal Latin hypercube design is used to simulate the sample points collected in the design space of the optimization variables to obtain a training set and a test set. The training set is used to train the neural network, and the test set is used to test the accuracy of the neural network.

[0049] In one embodiment, an optimal Latin hypercube experimental design method, based on its good space-filling and uniformity, was used to collect 200 design variable parameter combinations within the design variable space. Numerical simulations were then performed to obtain the calculated results for the Re = 10,000 operating condition, which served as the training set for the subsequent neural network model. The same method was used to collect 25 groups of sample points as the test set for the neural network model to verify its prediction accuracy.

[0050] To ensure the structural integrity of the PCHE channel along and perpendicular to the flow direction, the length, width, and height of the PCHE 3D model must meet the following constraints:

[0051]

[0052] Where, L x Indicates the channel length, L y Indicates the channel width, L z Indicates the channel height, L h Indicates the horizontal distance of the airfoil, L s Indicates the staggered distance of the airfoil, L v Indicates the vertical distance of the airfoil, L g Indicates the airfoil clearance distance, L c Indicates the chord length of the airfoil, L t Represents the airfoil thickness, where i, j, k, and m are all positive integers.

[0053] In one embodiment, the length L of the PCHE channel x and width L y With the staggered distance L s , horizontal distance L h and vertical distance L v To ensure the integrity of the channel structure along and perpendicular to the flow direction, the length, width, and height of the PCHE 3D model must meet the following constraints:

[0054]

[0055] Where, L x Indicates the channel length, L y Indicates the channel width, L z Indicates the channel height, L h Indicates the horizontal distance of the airfoil, L s Indicates the staggered distance of the airfoil, L v Indicates the vertical distance of the airfoil, L g Indicates the airfoil clearance distance, L c Indicates the chord length of the airfoil, L tRepresents the airfoil thickness, where i, j, k, and m are all positive integers.

[0056] S4, inputting the training set in the sample set into the neural network for training to obtain the PCHE volume heat transfer coefficient h v The corresponding first target proxy model and the PCHE drag coefficient f corresponding to the second target proxy model.

[0057] The first target proxy model and the second target proxy model are: PSO-BP neural network.

[0058] In one embodiment, 200 and 25 samples are taken from the sampled set as the training set and test set of the neural network respectively. In this embodiment, the BP neural network improved by the particle swarm optimization algorithm (PSO-BP) is used as the proxy model. The use of PSO to optimize the BP neural network makes up for the shortcomings of the BP neural network algorithm, enabling the BP neural network to jump out of the local extreme value, helping to accelerate the convergence process and enhance the accuracy and generalization ability of the BP neural network. The input layer contains 4 neurons, namely the level number ζ h , interleaving number ζ s 、Vertical number ζ v and gap number ζ g , due to the small number of input variables, a single hidden layer is selected and the output layer contains one neuron. PSO-BP neural network is used to calculate the volume heat transfer coefficient h v and resistance coefficient f are trained separately.

[0059] In order to quantitatively evaluate the prediction performance of the neural network, the following mean square error (MSE) is introduced to measure the prediction accuracy and generalization ability of the model.

[0060] Through the trial and comparison method, 10 BP neural networks with different network structures, with the number of hidden layer neuron nodes ranging from 3 to 12, were trained in turn. When the number of hidden layer neuron nodes was 10, the corresponding mean square error (MSE) reached the minimum value. Therefore, the 4-10-1 neural network structure was adopted.

[0061] The activation function is an important part of the BP neural network. The activation functions of the hidden layer and the output layer are selected as tansig function and purelin function respectively. purelin(x)=x.

[0062] In one embodiment, the process of improving the BP neural network using the improved particle swarm optimization algorithm (PSO) includes the following steps: first, optimizing the weights and learning factors of the particle swarm algorithm to obtain an improved particle swarm algorithm; then, encoding the initial weights and thresholds of the proxy model into particles, and obtaining the optimal initial weights and thresholds corresponding to the minimum fitness value, and finally assigning them to the proxy model.

[0063] Specifically, the iterative formulas for particle velocity and position are as follows:

[0064]

[0065] Where w is the inertia weight; c1 and c2 are the individual learning factor and the social learning factor respectively; r1 and r2 are random numbers between (0,1); k is the number of iterations; v id is the velocity of the i-th particle; P id is the local optimal position of the i-th particle, P gd is the global optimal position of the particle swarm, x id is the position of the i-th particle.

[0066] To balance global search capability and local improvement capability, this implementation adopts nonlinear inertia weighting:

[0067]

[0068] Among them, w max is the upper bound of inertia weight, w min is the lower bound of inertia weight, t is the current number of iterations, t max is the maximum number of iterations.

[0069] This implementation adopts an asynchronous learning factor, and the corresponding expression is:

[0070]

[0071] Where: c 1s , c 2s are the initial values ​​of the learning factors c1, c2, c 1e , c 2e are the termination values ​​of learning factors c1 and c2 respectively.

[0072] In one embodiment, the inertia weight w max =0.9, w min =0.3, c 1s =c 2e =2.5, c 1e =c 2s =0.5.

[0073] The PSO-BP neural network algorithm process is as follows Figure 3 As shown, the specific implementation steps are as follows:

[0074] (1) Data preprocessing: Normalize the sample data and divide it into training set and test set.

[0075] (2) Construct BP neural network structure: select the appropriate network structure, including the number of nodes in the input layer, hidden layer and output layer.

[0076] (3) Initialize the particle swarm.

[0077] (4) Calculate fitness: Calculate fitness based on mean square error (MSE).

[0078] (5) Update individual extreme values ​​and global extreme values: Compare the individual fitness values ​​of the current generation of particles in the population with the individual fitness values ​​of the previous generation and update them.

[0079] (6) Update particle velocity and position.

[0080] (7) Output the optimal solution of the particle: When the fitness value is less than the preset value or reaches the maximum evolutionary generation, the optimal initial weight and threshold are obtained.

[0081] (8) The algorithm terminates and outputs the optimal network: when the prediction error is less than the preset value or the maximum number of training times is reached, the optimized network is obtained.

[0082] The relevant parameter settings in the algorithm are described as follows: the neural network learning rate is 0.01, the maximum number of iterations is 1000, and the error accuracy is 1×10 -6 .

[0083] S5, with ζ h ,ζ s ,ζ v and ζ g To optimize the variables, maximize h v The sum and minimization of f are the optimization objectives, and a multi-objective optimization algorithm is used to optimize the first target proxy model and the second target proxy model to obtain the Pareto optimal frontier of flow performance and heat transfer performance.

[0084] The multi-objective optimization algorithm is: NSGA-Ⅱ multi-objective genetic algorithm; the multi-objective decision-making method is: multi-criteria compromise ranking method, superior and inferior solution distance method.

[0085] In one embodiment, a multi-objective optimization problem generally includes three elements: decision variables, objective functions, and constraints. Generally speaking, blindly pursuing improved heat transfer performance will inevitably increase pressure loss; conversely, simply pursuing low flow resistance will inevitably lead to deterioration of heat transfer performance. There is a contradictory relationship between the objectives. Therefore, in the design process of PCHE, the flow characteristics and heat transfer performance should be comprehensively considered. The h of the airfoil fin PCHE should be comprehensively considered. v and f are two optimization objectives, aiming to maximize h v And minimize f, the objective function is selected with h v Or f are the two neural network prediction models output, and the detailed parameter settings are listed in Table 2.

[0086] Table 2, parameter settings

[0087] parameter Population size Evolutionary Algebra Crossover probability Mutation probability Value 100 500 0.9 0.1

[0088] In another embodiment, VIKOR (Multi-Criteria Compromise Ranking) is a common multi-objective decision-making method that ranks and weighs different decision criteria to determine the best compromise solution. In VIKOR, the importance and priority of each criterion must first be clarified, and then the alternative solutions must be evaluated to ultimately determine the most suitable solution. TOPSIS (Top-Inferior Solution Distance Method) is a decision-making method for multi-objective optimization problems. Its basic idea is to evaluate and rank the alternative solutions by calculating the distance between each alternative solution and the ideal solution. In this method, the ideal solution must first be determined, and then the distance between each alternative solution and the ideal solution is calculated, and ultimately the solution with the smallest distance is selected as the optimal solution.

[0089] Supercritical CO2 is used as the working fluid for calculation, and its physical properties are obtained through the Real Gas Model in the National Institute Standard and Technology to accurately reflect the changes in the physical properties of supercritical CO2 during the flow and heat transfer process; when setting the solver, the solution type is set to 3D compressible fluid steady-state flow, pressure-based implicit solver, the turbulence model selects the SST k-ω model, the inlet Reynolds number (Re) is set to 10000, the boundary condition is set to mass flow inlet, the mass flow rate is determined by Re, and the inlet temperature is 380K; the outlet is set to pressure outlet, and the outlet pressure is 8.0MPa; symmetric boundary conditions are used on the walls on both sides of the channel, and constant wall temperature conditions are used on the upper and lower walls of the heat exchange section and the airfoil fin surface, with a wall temperature of 430K, and the upper and lower walls of the inlet and outlet sections are adiabatic boundary conditions.

[0090] S6, using a multi-objective decision-making method to select variables of the trade-off solution from the Pareto optimal frontier to determine the best optimization solution.

[0091] In another embodiment, after step S5 and before step S6, the method further comprises the step of: v , the single objective optimal solution corresponding to the scheme of minimizing f and maximizing PF value, as well as the two compromise schemes of VIKOR and TOPSIS are simulated and verified;

[0092] If the h corresponding to the five options v If the relative error between the predicted value of the proxy model and the simulation result is greater than the error threshold, the number of samples in the training set is supplemented, and steps S4-S6 are repeated until the relative error meets the accuracy requirement; the variable ζ corresponding to the compromise solution that meets the accuracy requirement is set to h ,ζ s ,ζ v and ζ g As the optimal design parameters of the PCHE airfoil fin; wherein, the optimized printed circuit board heat exchanger with a top gap has a gap between the top of the fin and the channel wall, and the gap number satisfies 0<ζ g <0.15.

[0093] Simulation data such as Figure 4 As shown in the figure, the Pareto optimal frontier obtained by combining neural network and optimization algorithm and the geometric model diagram of the compromise solution and the single-objective optimal solution when Re=10000. It can be observed that h v The two objectives of and f constrain each other, each point on the curve represents a non-dominated solution, and the set of all solutions constitutes the Pareto optimal solution set.

[0094] Table 3 lists the optimization design variables (ζ h ,ζ s ,ζ v and ζ g ) and the objective function (h v , f), where the comprehensive performance evaluation factor (PF) is defined as:

[0095] h v0 and f0 represent the structural parameters ζ h =2,ζ s =0.5,ζ v =0.6,ζ g = h under 0 v and f.

[0096] As supercritical carbon dioxide flows through the PCHE, the working fluid is heated by the high-temperature wall, causing its temperature to continue to rise. The present invention increases the heat exchange area by adding a top gap, thereby enhancing heat transfer. Furthermore, the presence of the gap creates eddies within the channel, accelerating the mixing of the hot and cold fluids and further enhancing heat transfer.

[0097] The analysis shows that the relative errors of the five schemes are all within 5%, indicating that the prediction accuracy of the neural network is feasible and meets the needs of industrial design. As can be seen from Table 3, compared with f min Compared with the TOPSIS and VIKOR schemes, although f increased by about 3 / 4, h v The improvement is more than two times. This shows that the TOPSIS scheme has a higher comprehensive performance. vmax Compared with the TOPSIS scheme and the VIKOR scheme, the h v It is only reduced by about 1 / 4, while f is significantly reduced by half, PF max Scheme and h vmax The results of the schemes are similar. The TOPSIS scheme and the VIKOR scheme show similar flow and heat transfer characteristics, which can significantly reduce the flow resistance while meeting the high heat transfer performance requirements. Through the above analysis, it can be found that f min The scheme has a large number of gaps. Although the flow resistance is small, the heat transfer capacity is also significantly reduced. Therefore, when optimizing the geometric parameters of PCHE, the comprehensive performance of PCHE with a large gap structure is not ideal, and it cannot take into account both enhanced heat transfer and reduced flow resistance. Choosing a structure with a smaller gap is beneficial to improving thermal hydraulic performance.

[0098] Table 3. Optimization design variables and corresponding values ​​of objective functions for five different types of schemes

[0099]

[0100] The present invention also provides a multi-objective optimization system for the airfoil fin structure of a printed circuit board type heat exchanger with a top gap. The system includes a memory and a processor. The memory stores a computer program. When the processor executes the computer program, it performs the multi-objective optimization method for the airfoil fin structure of the printed circuit board type heat exchanger with a top gap as described above.

[0101] The present invention also provides a computer-readable storage medium, which stores machine-executable instructions. When the machine-executable instructions are called and executed by a processor, the machine-executable instructions prompt the processor to implement the multi-objective optimization method for the airfoil fin structure of the printed circuit board type heat exchanger with a top gap as described above.

[0102] It will be easily understood by those skilled in the art that the above description is merely a preferred embodiment of the present invention and is not intended to limit the present invention. Any modifications, equivalent substitutions, and improvements made within the spirit and principles of the present invention should be included in the scope of protection of the present invention.

Claims

1. A multi-objective optimization method for the airfoil fin structure of a printed circuit board heat exchanger with a top gap, characterized in that: The method comprises the following steps: S1, obtaining geometric parameters of the airfoil fins in the printed circuit board heat exchanger PCHE with top gap, wherein the geometric parameters include the horizontal distance L h , staggered distance L s , vertical distance L v and clearance distance L g ; S2, non-dimensionalizing the geometric parameters of the airfoil fin to obtain optimized design variables, the optimized design variables including the horizontal number ζ h , interleaving number ζ s 、Vertical number ζ v and gap number ζ g ; S3, performing experimental design and numerical simulation on the optimized design variables to obtain a sample set; S4, inputting the training set in the sample set into the neural network for training to obtain the PCHE volume heat transfer coefficient h v the corresponding first target proxy model and the second target proxy model corresponding to the PCHE drag coefficient f; S5, with ζ h ,ζ s ,ζ v and ζ g To optimize the variables, maximize h v Taking the sum and minimizing f as optimization objectives, a multi-objective optimization algorithm is used to optimize the first target proxy model and the second target proxy model to obtain the Pareto optimal frontier of flow performance and heat transfer performance; S6, using a multi-objective decision-making method to select variables of the trade-off solution from the Pareto optimal frontier to determine the best optimization solution.

2. The multi-objective optimization method for the airfoil fin structure of a printed circuit board heat exchanger with a top gap according to claim 1, characterized in that: Based on the airfoil fin chord length L c and channel height L z The dimensionless geometric parameters of the airfoil fin are defined; the horizontal number is: The interleaving number is: The vertical number is The number of gaps is 3. The multi-objective optimization method for the airfoil fin structure of a printed circuit board heat exchanger with a top gap according to claim 1, characterized in that: The length, width, and height of the PCHE 3D model must meet the following constraints: Where, L x Indicates the channel length, L y Indicates the channel width, L z Indicates the channel height, L h Indicates the horizontal distance of the airfoil fin, L s Indicates the staggered distance of the airfoil fins, L v Indicates the vertical distance of the airfoil fin, L g Indicates the gap distance between airfoil fins, L c Indicates the chord length of the airfoil fin, L t Represents the thickness of the airfoil fin, i, j, k, and m are all positive integers.

4. The multi-objective optimization method for the airfoil fin structure of a printed circuit board heat exchanger with a top gap according to claim 1, characterized in that: The optimal Latin hypercube design is used to simulate the sample points collected in the design space of the optimization variables to obtain a training set and a test set; the training set is used to train the neural network, and the test set is used to test the accuracy of the neural network.

5. The multi-objective optimization method for the airfoil fin structure of a printed circuit board type heat exchanger with a top gap according to any one of claims 1 to 4, characterized in that: The first target proxy model and the second target proxy model are: PSO-BP neural network.

6. The multi-objective optimization method for the airfoil fin structure of a printed circuit board type heat exchanger with a top gap according to claim 5, characterized in that: The input layer of the PSO-BP neural network contains 4 neurons, namely the level number ζ h , interleaving number ζ s 、Vertical number ζ v and gap number ζ g , the output layer contains one neuron; the PSO-BP neural network is used to calculate the volume heat transfer coefficient h v and resistance coefficient f are trained separately.

7. The multi-objective optimization method for the airfoil fin structure of a printed circuit board type heat exchanger with a top gap according to claim 6, characterized in that: The prediction performance of the neural network was quantitatively evaluated using mean squared error; The process of improving BP neural network by using improved particle swarm optimization algorithm includes: first, optimizing the weights and learning factors of particle swarm algorithm to obtain the improved particle swarm algorithm; Then, the initial weights and thresholds of the proxy model are encoded into particles, and the optimal initial weights and thresholds corresponding to the minimum fitness value are obtained, and finally assigned to the proxy model.

8. The multi-objective optimization method for the airfoil fin structure of a printed circuit board type heat exchanger with a top gap according to any one of claims 1 to 4, characterized in that: After step S5 and before step S6, the method further comprises the following steps: v , minimize f, the single objective optimal solution corresponding to the PF value maximum scheme and the two compromise schemes of VIKOR and TOPSIS are simulated and verified; if the h corresponding to the five schemes v If the relative error between the predicted value of the surrogate model and the simulation result is greater than the error threshold, the number of samples in the training set is supplemented, and steps S4-S6 are repeated until the relative error meets the accuracy requirement; the variable ζ corresponding to the VIKOR and TOPSIS compromise solution that meets the accuracy requirement is h ,ζ s ,ζ v and ζ g As the optimal design parameters of the airfoil fin; wherein, there is a gap between the top of the fin and the channel wall of the airfoil fin structure of the optimized printed circuit board type heat exchanger with a top gap, and the gap number satisfies 0<ζ g <0.15; PF value is the value of the comprehensive performance evaluation factor.

9. A multi-objective optimization system for the airfoil fin structure of a printed circuit board heat exchanger with a top gap, characterized by: The system includes a memory and a processor, wherein the memory stores a computer program, and when the processor executes the computer program, it performs the multi-objective optimization method for the airfoil fin structure of a printed circuit board type heat exchanger with a top gap according to any one of claims 1 to 8.

10. A computer-readable storage medium, characterized in that: The computer-readable storage medium stores machine-executable instructions. When the machine-executable instructions are called and executed by the processor, the machine-executable instructions prompt the processor to implement the multi-objective optimization method for the airfoil fin structure of a printed circuit board type heat exchanger with a top gap as described in any one of claims 1 to 8.

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