Method and structure for optimizing porosity of porous media for sweat cooling with length of coupling phase region characteristics

Abstract

The present application relates to the technical field of porous medium sweating cooling structure optimization, and provides a porous medium sweating cooling porosity optimization design method and structure coupled with phase region length characteristics, a two-dimensional sweating cooling flow and heat transfer model is established based on a modified thermal non-equilibrium two-phase mixture model, and the influence of solid thermal conductivity, porosity and spherical particle diameter on phase region length evolution is analyzed according to a phase region length evolution formula; solid thermal conductivity, porosity and spherical particle diameter are taken as design variables, solid skeleton outlet temperature and pressure drop are taken as objective functions, and the optimal design variable combination of the solid skeleton outlet temperature and pressure drop and the corresponding average porosity are obtained by using a multi-objective optimization method; the multi-objective optimization method and the phase region length design model coupled with porosity are used, the porosity of the liquid phase region and the gas phase region is taken as a design variable, the solid skeleton outlet temperature and the pressure drop are taken as objective functions, the optimal porosity distribution combination of the three phase regions is obtained, and the matching of the porosity distribution and the flow and heat transfer characteristics of each phase region is realized.

Description

Technical Field

[0001] This invention relates to the field of porous media sweating cooling structure optimization technology, and in particular to a porous media sweating cooling porosity optimization design method and structure with coupled phase region length characteristics. Background Technology

[0002] With the rapid development of hypersonic flight technology, the next generation of aircraft is evolving towards higher flight performance and reusability. As a key power unit for hypersonic aircraft, the ramjet engine's combustion chamber is subjected to both aerodynamic heating and combustion heat release during operation, operating in a harsh environment of high temperature and high heat flux density. This places higher demands on combustion chamber thermal protection technology. Currently, traditional passive thermal protection methods such as heat insulation and heat sinks mainly rely on the high-temperature resistance and heat capacity of the materials themselves. However, limited by the temperature resistance and heat storage capacity of the materials, they can no longer meet the increasingly stringent thermal protection requirements of modern hypersonic aircraft. Therefore, active thermal protection technology, with its high cooling efficiency, long-term operational stability, and flexible structural design, has gradually gained attention and become an important solution to address the extreme thermal environment problems of hypersonic aircraft.

[0003] Active thermal protection technologies mainly include convection cooling, thin-film cooling, and sweating cooling. Among them, sweating cooling effectively utilizes the latent heat of phase change of the coolant, thus providing better cooling performance. The basic principle of sweating cooling is to inject liquid coolant into a porous medium, absorbing heat from the porous matrix through internal convection heat transfer and latent heat of phase change. Simultaneously, the discharged coolant forms a protective film layer on the heated surface, enhancing the thermal resistance between the main flow and the solid wall, thereby reducing the wall's thermal load. During sweating cooling, the porous medium typically forms three regions: a liquid phase region, a two-phase region, and a gas phase region. The liquid and gas phase regions primarily exchange heat through convection between the coolant and the solid framework, while the heat in the two-phase region is mainly absorbed by the latent heat of vaporization of the coolant.

[0004] Liquid sweating cooling is a complex coupled process involving heat conduction, convective heat transfer, latent heat of phase change, and flow resistance, with different phase regions exhibiting varying thermo-hydraulic performance requirements. However, traditional methods of uniform porosity distribution or simple control based on overall structural parameters are insufficient to meet the differentiated needs of each phase region, thus hindering the synergistic reduction of pressure loss and solid skeleton outlet temperature. Therefore, there is an urgent need to design a structural optimization method based on the coupling of phase region length characteristics and porosity, matching the porosity distribution with the performance requirements of different phase regions to obtain porous flat plate structures with superior overall performance. Summary of the Invention

[0005] To address the aforementioned technical problems, this invention provides a method for optimizing the porosity design of porous media with coupled phase region length characteristics, the method comprising: S1. A two-dimensional sweating cooling flow heat transfer model was established based on the modified thermal nonequilibrium two-phase mixing model (LTNE-TPMM). The effects of solid thermal conductivity, porosity and spherical particle diameter on the evolution of phase region length were analyzed according to the phase region length evolution formula. The coupling mechanism between heat conduction, heat convection, latent heat of phase change and flow resistance during sweating cooling was explored. S2 uses solid thermal conductivity, porosity, and spherical particle diameter as design variables, and solid skeleton outlet temperature and pressure drop as objective functions. It uses Gaussian process regression, NSGA-II genetic algorithm, and multi-criteria decision method to perform multi-objective optimization, and obtains the optimal combination of design variables and the corresponding average porosity for synergistically reducing the outlet temperature and pressure drop of the solid skeleton. S3. Using Gaussian process regression, NSGA-II genetic algorithm, multi-criteria decision method and porosity coupled phase region length design model from step S2, the porosity of the liquid and gas phase regions is used as design variables. The porosity of the two phase regions is determined by the inverse solution of the average porosity constraint. The optimal porosity distribution combination of the three phase regions is obtained with the outlet temperature and pressure drop of the solid skeleton as the objective function, so as to achieve the matching of porosity distribution with the flow and heat transfer characteristics of each phase region.

[0006] Furthermore, in step S1, the two-dimensional sweating cooling flow heat transfer model includes a continuity equation, a momentum equation, and a fluid-solid dual-energy equation, which are used to describe the coolant flow, fluid-solid heat transfer, and phase change process, and the boundaries of the liquid phase region, two-phase region, and gas phase region are determined by the liquid phase saturation. Among them, the continuity equation is:

[0007] In the formula, ρ is Mixing density; u is the mixing Darcy velocity; For divergence operators; Momentum equation:

[0008] In the formula, K For penetration rate; ν ( s ) represents the kinematic viscosity of the fluid mixture; This is the pressure gradient vector; Fluid energy equation:

[0009] In the formula, c p，l This represents the isobaric heat capacity of the liquid phase. TM for Fluid correction temperature; The effective thermal diffusivity on the fluid side; q sf For heat source items; Correcting the temperature gradient for the fluid; Solid energy equation:

[0010] In the formula, The effective thermal conductivity of the solid framework; For solid temperature gradient.

[0011] Furthermore, in step S1, the phase region length evolution formula includes: Formula for the evolution of liquid phase length:

[0012] In the formula, L lp Indicates the length of the liquid phase region; c p，l This represents the isobaric heat capacity of the liquid phase, expressed in J / (kg·K). T in This indicates the coolant inlet temperature, expressed in Kelvin (K). m in Indicates inlet mass flow rate, in kg / s; T sat This represents the saturation temperature, expressed in Kelvin (K). h sl It represents the convective heat transfer coefficient between solid and liquid, with units of W / (m²·K); ΔT sl This represents the solid-liquid temperature difference, expressed in Kelvin (K). A c This represents the cross-sectional area, with the unit being m². A sf Specific surface area, unit is m² - ¹; Subscript m This represents the average value; Evolution formula for the length of the two-phase region:

[0013] In the formula, L tp Indicates the length of the two-phase region; H fg Latent heat is expressed in J / kg; q boil This indicates the boiling term, with units of W / m³. q v,conv This represents the steam convection term, with units of W / m³. χ This indicates the proportion of coolant capable of carrying latent heat in the two-phase region; when a gas phase region is present... χ =1; when it does not exist, 0 < χ <1; Formula for the evolution of gas phase length:

[0014] In the formula, L vp Indicates the length of the gas phase region; q This indicates the outlet heat flux, expressed in W / m³. 2 ; h sv This represents the convective heat transfer coefficient between solid and gas, with units of W / (m²·K). ΔT sv This represents the temperature difference between solid and air, expressed in Kelvin (K).

[0015] Furthermore, the specific steps of step S2 are as follows: Operating conditions and the ranges for solid thermal conductivity, porosity, and spherical particle diameter were defined. A surrogate model was established using Gaussian process regression, and validation data was randomly generated using Latin hypercube sampling to evaluate the accuracy of the surrogate model. The NSGA-II genetic algorithm was used for multi-objective optimization, with population size, maximum number of iterations, crossover probability, and mutation probability set to obtain a Pareto solution set that satisfies the optimization objectives. Finally, a multi-criteria decision-making method combining Shannon entropy weighting and TOPSIS was employed. Objective weights were determined based on the dispersion of the solid skeleton outlet temperature and pressure drop. The Pareto solutions were then comprehensively ranked by calculating their relative proximity to the ideal solution to determine the optimal solution in terms of overall performance.

[0016] Furthermore, the porosity-coupled phase region length design model in step S3 is as follows:

[0017] In the formula, The average porosity; ε lp Porosity of the liquid phase region; ε tp The porosity of the two-phase region; ε vp Porosity of the gas phase region; L The total length of the porous medium.

[0018] Another aspect of the present invention provides a porous plate structure with porosity coupled to the length of each phase region. The porous medium sweating cooling structure is sintered from isotropic and uniform metal spherical particles, with a coolant inlet at the lower end and a coolant outlet and a high-temperature heat flow application wall at the upper end. The porous medium sweating cooling structure is divided into a liquid phase region, a two-phase region, and a gas phase region along the thickness direction according to the length of each phase region. Under the condition of constant average porosity, each phase region is configured with a different porosity, which is solved by the above-mentioned optimization design method.

[0019] The present invention has the following beneficial effects: This invention, combining a proposed phase region length evolution formula, analyzes the influence of solid thermal conductivity, porosity, and spherical particles on phase region length evolution, solid skeleton outlet temperature, and pressure loss, revealing the coupling mechanism among heat conduction, convective heat transfer, latent heat of phase change, and flow resistance within each phase region. Based on this, multi-objective optimization of solid thermal conductivity, porosity, and spherical particle diameter is performed, achieving a synergistic reduction in solid skeleton outlet temperature and pressure loss, and determining the average porosity. Furthermore, utilizing the proposed phase region length-coupled porosity model and multi-objective optimization method, while maintaining a constant average porosity, the porosity distribution is matched to the thermal-hydraulic performance requirements of different phase regions, thereby further reducing the solid skeleton outlet temperature and pressure loss. Through the optimization design method of this invention, a porous plate structure with a phase region length-coupled porosity distribution and superior overall thermal-hydraulic performance can be obtained. Attached Figure Description

[0020] Figure 1 This is a flowchart of the optimized design in the embodiment.

[0021] Figure 2 This is a flowchart illustrating the solution process for the solid and fluid energy equations, continuity equations, and momentum equations in the embodiment.

[0022] Figure 3 This is a diagram showing the evolution of phase region length of the porous plate structure under different solid thermal conductivity in the embodiments.

[0023] Figure 4 This is a diagram showing the evolution of phase region length in the porous flat plate structure under different porosities in the embodiment.

[0024] Figure 5 This is a diagram showing the evolution of phase region length in the porous plate structure under different spherical particle diameters in the embodiments.

[0025] Figure 6 This is a comparison diagram of the outlet temperature and pressure drop of the porous flat plate solid skeleton under different solid thermal conductivity in the embodiment.

[0026] Figure 7This is a comparison diagram of the outlet temperature and pressure drop of the porous flat plate solid skeleton under different porosities in the embodiment.

[0027] Figure 8 This is a comparison diagram of the outlet temperature and pressure drop of the porous flat plate solid skeleton under different spherical particle diameters in the embodiment.

[0028] Figure 9 The figure shows the solid skeleton outlet temperature predicted by the proxy model in the embodiment and the numerical simulation results.

[0029] Figure 10 The graph shows the pressure drop predicted by the proxy model and the numerical simulation results in the embodiment.

[0030] Figure 11 This is the Pareto solution set graph obtained from the multi-objective optimization in the embodiment.

[0031] Figure 12 This is a schematic diagram of the optimized porous flat plate structure obtained in this embodiment. Detailed Implementation

[0032] The technical solution of the present invention will be further described in detail below with reference to specific embodiments. However, these embodiments are not intended to limit the present invention. Any similar structures and similar variations of the present invention should be included in the protection scope of the present invention. The commas in the present invention all indicate the relationship between and. The English letters in the present invention are case-sensitive.

[0033] like Figure 1 As shown, this embodiment provides a method for optimizing the porosity of porous media with coupled phase region length characteristics during sweating cooling. The method includes: S1. A two-dimensional sweating cooling flow heat transfer model was established based on the modified thermal nonequilibrium two-phase mixing model (LTNE-TPMM). This model describes the coolant flow, fluid-solid heat transfer, and phase change process through the continuity equation, momentum equation, and fluid-solid dual energy equation. The liquid phase saturation is used to determine the boundaries of the liquid phase region, two-phase region, and gas phase region. Based on the phase region length evolution formula, the effects of solid thermal conductivity, porosity, and spherical particle diameter on the phase region length evolution were analyzed to explore the coupling mechanism between heat conduction, heat convection, latent heat of phase change, and flow resistance during sweating cooling. Specifically, the constitutive equations of the modified thermally nonequilibrium two-phase mixing model (LTNE-TPMM) shown in Table 1 are written into Fluent using user-defined functions (UDFs) to solve the solid and fluid energy equations, while the continuity and momentum equations are solved using Fluent's built-in solver. The continuity equation is as follows:

[0034] In the formula, ρ isMixing density; u is the mixing Darcy velocity; For divergence operators; Momentum equation:

[0035] In the formula, K For penetration rate; ν ( s ) represents the kinematic viscosity of the fluid mixture; This is the pressure gradient vector; Fluid energy equation:

[0036] In the formula, c p，l This represents the isobaric heat capacity of the liquid phase. T M for Fluid phase temperature; The effective thermal diffusivity on the fluid side; q sf For heat source items; For the fluid temperature gradient; Solid energy equation:

[0037] In the formula, The effective thermal conductivity of the solid framework; For solid temperature gradient.

[0038] like Figure 2 As shown, the final convergent solution is obtained through initialization and iterative updates of the solution parameters, specifically: Step 1, Construct a physical model: For the sweating and cooling process of porous media, establish a fluid-solid thermal non-equilibrium two-phase physical model, and determine the structural parameters of the porous plate, the physical properties of the porous medium and coolant, and the boundary conditions, etc. Step 2, Mesh Generation and UDF Import: Discretize the computational mesh of the established physical model and import the completed UDF code. Embed the constitutive equations of the LTNE-TPMM model in Table 1 into Fluent to provide program support for solving the custom energy equations in the future. Step 3, Solve parameter initialization: Set material property parameters, boundary conditions, porous media parameters, etc. in Fluent, and initialize fluid temperature, solid skeleton temperature, liquid phase saturation and related auxiliary variables through UDF to complete the setting of the initial conditions of the calculation field; Step 4, First round of solution parameter update: Update the flow and heat transfer state parameters of the iteration step based on the initialization results, and start the iterative loop calculation; Step 5, Solve the flow control equations: Call the Fluent built-in solver to solve the continuity equation and momentum equation to obtain the velocity field and pressure field of the coolant inside the porous medium in the current iteration step; Step 6, Solve the two-phase energy equations: Based on the imported UDF, load the LTNE-TPMM constitutive equations, solve the energy equations for the fluid phase and the solid phase respectively, and update the temperature field information of the two phases; Step 7, Secondary solution parameter update: Based on the solution results of the flow field and temperature field, update the relevant solution parameters again; Step 8, Convergence Judgment: Check all residuals and monitor whether the physical quantities meet the preset convergence criteria. If convergence is not achieved, the updated solution parameters are sent back to Step 4, and the entire loop of iterative update, equation solving, parameter refresh, and convergence judgment is repeated. If the convergence requirements are met, the iteration is terminated, and the numerical calculation process ends.

[0039] Table 1

[0040] In the initial model, the dimensions of the two-dimensional porous plate were 40 mm × 100 mm, with the coolant inlet at the bottom of the plate, an inlet temperature of 300 K, and an inlet mass flux of 0.15 kg / (m³). 2 The top of the plate is the coolant outlet and the heat flow wall; the outlet pressure is 0 Pa, and the heat flow rate is 5 × 10⁻⁶. 5 W / m 2 The left and right walls of the plate are both adiabatic boundary conditions; the coolant is water; the solid porous skeleton is sintered from metal spherical particles with a thermal conductivity of 50 W / (m·K), a porosity of 0.4, and a diameter of 400 μm for the spherical particles.

[0041] When the sweating cooling system is in steady state, energy balance is achieved in the liquid phase region. The heat required for the coolant to rise from the inlet temperature to the saturation temperature is equal to the convective heat transfer between the solid skeleton and the coolant. The fluid-solid convective heat transfer that varies along the liquid phase region can be equated to the average heat transfer per unit length. Therefore:

[0042] The simplified formula for the evolution of the liquid phase region length is as follows:

[0043] In the formula, L lp Indicates the length of the liquid phase region; c p，l This represents the isobaric heat capacity of the liquid phase, expressed in J / (kg·K). T in This indicates the coolant inlet temperature, expressed in Kelvin (K).m in Indicates inlet mass flow rate, in kg / s; T sat This represents the saturation temperature, expressed in Kelvin (K). h sl It represents the convective heat transfer coefficient between solid and liquid, with units of W / (m²·K); ΔT sl This represents the solid-liquid temperature difference, expressed in Kelvin (K). A c This represents the cross-sectional area, with the unit being m². A sf Specific surface area, unit is m² - ¹; Subscript m This represents the average value; When energy equilibrium is reached in the two-phase region, the energy required for complete vaporization of the coolant is equal to the sum of boiling heat transfer and convective heat transfer between the solid skeleton and the gaseous coolant. Therefore:

[0044] The simplified formula for the evolution of the two-phase region length is as follows:

[0045] In the formula, L tp Indicates the length of the two-phase region; H fg Latent heat is expressed in J / kg; q boil This indicates the boiling term, with units of W / m³. q v,conv This represents the steam convection term, with units of W / m³. χ This indicates the proportion of coolant capable of carrying latent heat in the two-phase region; when a gas phase region is present... χ =1; when it does not exist, 0 < χ <1; When energy equilibrium is reached in the gas phase region, the total heat flow is:

[0046] Therefore, the heat acting on the gas phase region:

[0047] This heat is equal to the convective heat transfer between the solid skeleton and the superheated steam, therefore:

[0048] The simplified formula for the evolution of the gas phase region length is as follows:

[0049] In the formula,L vp Indicates the length of the gas phase region; q This indicates the outlet heat flux, expressed in W / m³. 2 ; h sv This represents the convective heat transfer coefficient between solid and gas, with units of W / (m²·K). ΔT sv This represents the temperature difference between solid and air, expressed in Kelvin (K).

[0050] With the length, width, and boundary conditions of the porous plate remaining constant, different solid thermal conductivity, porosity, and spherical particle diameters were set. Numerical simulations were used to obtain the phase region length, solid skeleton outlet temperature, and pressure drop, yielding results such as... Figures 3-8 The result. From Figure 3 As can be seen, as the thermal conductivity of the solid increases, the length of the liquid phase region decreases, while the lengths of the two-phase and gas phase regions increase. This is because the increased thermal conductivity of the solid enhances the axial heat conduction capacity within the porous medium, increasing the temperature difference between the solid skeleton and the coolant in the liquid phase region. This leads to an increase in the average convective heat transfer per unit length, and according to the formula for calculating the liquid phase region length, the liquid phase region length shortens accordingly. Simultaneously, the enhanced axial heat conduction capacity improves the heat distribution within the porous medium, reducing heat accumulation in the outlet region. This weakens the fluid-solid heat transfer in the two-phase and gas phase regions, and according to the formulas for calculating the lengths of the two-phase and gas phase regions, their lengths increase accordingly. Therefore, the thermal conductivity of the solid skeleton primarily affects the length changes of each phase region by adjusting the axial heat distribution within the porous medium.

[0051] from Figure 4 It can be seen that as porosity increases, the lengths of both the liquid and gas phase regions shorten, while the length of the two-phase region increases. According to the calculation formulas for effective thermal conductivity and specific surface area in Table 1, increased porosity simultaneously reduces both the effective thermal conductivity and specific surface area of ​​the solid skeleton. When the effect of decreased specific surface area dominates, it increases the solid-liquid temperature difference and enhances the average convective heat transfer per unit length. According to the formula for calculating the liquid phase length, the liquid phase length shortens accordingly. In the two-phase region, increased porosity enhances capillary transport within the porous medium, increasing enthalpy transfer capacity and reducing the average heat transfer per unit length. According to the formula for calculating the two-phase region length, the two-phase region length increases accordingly. In the gas phase region, the combined effect of lower effective thermal conductivity and specific surface area increases the fluid-solid temperature difference, thereby enhancing the average convective heat transfer per unit length. According to the formula for calculating the gas phase length, the gas phase length shortens accordingly. Therefore, porosity primarily affects the evolution of the single-phase region length by altering axial heat conduction and solid-liquid convection heat transfer, and influences the evolution of the two-phase region length by regulating capillary transport. Figure 5It is evident that as the diameter of the spherical particles increases, the lengths of both the liquid and gas phase regions shorten, while the length of the two-phase region increases. According to the calculation formulas for convective heat transfer coefficient and specific surface area in Table 1, increasing the diameter of the spherical particles simultaneously reduces both the convective heat transfer coefficient and specific surface area within the single-phase region. This combined effect weakens heat transfer at the fluid-solid interface, raising the temperature of the solid skeleton, thereby increasing the solid-liquid temperature difference and enhancing the average convective heat transfer per unit length. Based on the calculation formulas for the lengths of the liquid and gas phase regions, the lengths of these regions shorten accordingly. In the two-phase region, increasing the diameter of the spherical particles enhances capillary transport within the porous medium, reducing the average heat transfer per unit length. Based on the calculation formula for the length of the two-phase region, the length of the two-phase region increases accordingly. Therefore, the diameter of the spherical particles primarily affects the evolution of the single-phase region length by altering the fluid-solid convective heat transfer within the single-phase region, and influences the evolution of the two-phase region length by adjusting capillary transport characteristics.

[0052] from Figures 6-8 As can be seen, with the increase of solid thermal conductivity, the outlet temperature of the solid skeleton decreases but the pressure drop increases. With the increase of porosity and spherical particle diameter, the outlet temperature of the solid skeleton increases but the pressure drop decreases. This shows that it is difficult to achieve a synergistic reduction in the outlet temperature and pressure drop of the solid skeleton by changing only a single structural parameter.

[0053] S2 uses solid thermal conductivity, porosity, and spherical particle diameter as design variables, and solid skeleton outlet temperature and pressure drop as objective functions. It uses Gaussian process regression, NSGA-II genetic algorithm, and multi-criteria decision method to perform multi-objective optimization, and obtains the optimal combination of design variables and the corresponding average porosity for synergistically reducing the outlet temperature and pressure drop of the structural solid skeleton. Specifically, the inlet mass flux is selected to be 0.15 kg / (m²·s), and the outlet heat flux is selected to be 1×10⁻⁶. 6 The operating conditions are W / m² and coolant inlet temperature of 300 K, and the solid thermal conductivity is considered... k s = 40 W / (m·K), porosity ε =0.40, diameter of spherical particles d p =400 μm is used as the initial design variable. Based on the initial design variable, the range of values ​​for solid thermal conductivity, porosity, and spherical particle diameter are reasonably set: k s =20~100 W / (m·K), ε =0.25~0.70、 d p=300~750 μm. In the multi-objective optimization process, 55 sets of sample data were obtained based on orthogonal experiments and single-factor analysis. A surrogate model was established using the Gaussian process regression method, and 30 sets of validation data were randomly generated using the Latin hypercube sampling method to evaluate the accuracy of the surrogate model. The surrogate model describes the nonlinear mapping relationship between the design variables and the objective function using the Matérn 3 / 2 kernel function. Based on this, the NSGA-II genetic algorithm was used to carry out multi-objective optimization, with a population size of 200, a maximum number of iterations of 150, a crossover probability of 0.9, and a mutation probability of 0.1, to obtain the Pareto solution set that satisfies the optimization objective. Finally, a multi-criteria decision-making method combining Shannon entropy weight method and TOPSIS was used to determine the objective weights based on the dispersion of the solid skeleton outlet temperature and pressure drop indicators. The Pareto solutions were comprehensively ranked by calculating the relative closeness between the Pareto solutions and the ideal solutions to determine the solution with the best overall performance.

[0054] like Figure 9 and Figure 10 As shown, the outlet temperature and pressure drop of the solid skeleton predicted by the surrogate model are in high agreement with the numerical simulation results, and its coefficient of determination R0 is also consistent. 2 The values ​​were 0.9963 and 0.9995 respectively, which verifies the accuracy of the surrogate model. Figure 11 The Pareto solution set obtained from multi-objective optimization is used to determine the optimal combination of structural parameters for overall performance through a multi-criteria decision-making method: solid thermal conductivity. k s =100 W / (m·K), porosity ε =0.33, diameter of spherical particles d p =740 μm. At this point, the weights corresponding to the solid skeleton outlet temperature and pressure drop are 0.71 and 0.29, respectively. Further numerical verification of the optimization results shows that the error in the solid skeleton outlet temperature between the prediction model and the numerical simulation is only 0.102%, and the error in the pressure drop is 2.698%, indicating that the optimization results have high reliability. Compared with the initial structure, the optimized solid skeleton outlet temperature and pressure drop are reduced by 30.76% and 13.29%, respectively, effectively solving the problem of the difficulty in synergistically reducing the solid skeleton outlet temperature and pressure drop, and greatly improving the thermal-hydraulic performance of the porous plate. Based on the optimal combination of structural parameters, the average porosity of this structure is determined to be 0.33.

[0055] S3. Using Gaussian process regression, NSGA-II genetic algorithm, multi-criteria decision-making method and porosity coupled phase region length design model from step S2, the porosity of the liquid and gas phase regions is used as design variables. The porosity of the two phase regions is determined by the inverse solution of the average porosity constraint. The optimal porosity distribution combination of the three phase regions is obtained with the outlet temperature and pressure drop of the solid skeleton as the objective function, so as to achieve the matching of porosity distribution with the flow and heat transfer characteristics of each phase region. The porosity-coupled phase region length design model combines a multi-objective optimization algorithm to match porosity distribution with phase region requirements, thereby achieving a further synergistic reduction in outlet temperature and pressure drop of porous solid skeleton structures. As can be seen from step S1, sweating cooling is a complex coupled process involving heat conduction, convective heat transfer, latent heat of phase change, and flow resistance, and different phase regions have different thermal-hydraulic performance requirements.

[0056] The porosity-coupled phase region length design model is as follows:

[0057] The average porosity is 0.33. L =100 mm, length of liquid phase region L lp Length of two-phase region L tp and gas phase length L vp All were obtained through calculation. By using the porosity of the liquid phase and gas phase as known variables in the solution, the porosity of the two-phase region can be obtained:

[0058] The above model is then embedded into the LTNE-TPMM model via a UDF for subsequent calculations. Specifically, the range of variables is first defined, including the porosity in the liquid phase region. ε lp =0.25~0.40, porosity in the gas phase region ε vp =0.25~0.40, and the porosity of the two-phase region is determined as an intermediate variable through a porosity-coupled phase region length design model. Thirty sets of validation data were randomly generated using the Latin hypercube sampling method to evaluate the accuracy of the surrogate model, and the coefficient of determination R0 was determined between the solid skeleton outlet temperature and pressure drop predicted by the surrogate model and the numerical simulation results. 2The values ​​were 0.9999 and 0.9946 respectively, verifying the accuracy of the surrogate model. Based on a fully orthogonal experiment, 16 sets of sample data were obtained. A Gaussian process regression method was used to establish the surrogate model, and 30 sets of validation data were randomly generated using the Latin hypercube sampling method to evaluate the accuracy of the surrogate model. The surrogate model uses a Matérn 3 / 2 kernel function to describe the nonlinear mapping relationship between the design variables and the objective function. Based on this, the NSGA-II genetic algorithm was used for multi-objective optimization, with a population size of 200, a maximum number of iterations of 150, a crossover probability of 0.9, and a mutation probability of 0.1, to obtain a Pareto solution set that satisfies the optimization objective. Finally, a multi-criteria decision-making method combining Shannon entropy weight method and TOPSIS was used. Objective weights were determined based on the dispersion of the solid skeleton outlet temperature and pressure drop indicators. The Pareto solutions were comprehensively ranked by calculating the relative closeness between the Pareto solutions and the ideal solutions, and the optimal porosity distribution combination was determined as follows: liquid phase porosity... ε lp =0.26, porosity in the two-phase region ε tp =0.39, porosity in the vapor phase ε vp =0.30. Further numerical verification of the optimization results showed that the error in outlet temperature of the solid skeleton between the prediction model and the numerical simulation was only 0.03%, and the error in pressure drop was 0.41%, indicating that the optimization results have high reliability. Compared with the initial structure, the optimized model reduced the outlet temperature and pressure drop of the solid skeleton by 1.19% and 5.29%, respectively, achieving a match between the thermal-hydraulic performance requirements of the porosity distribution in the same phase region, and further realizing a synergistic reduction in the outlet temperature and pressure drop of the porous flat plate structure solid skeleton.

[0059] Based on the above optimized structure, this embodiment yields a porous plate structure with porosity coupled to the phase region length, which exhibits better overall performance. For example... Figure 12 As shown, the sweating cooling plate structure is sintered from isotropic and uniform metal spherical particles. The lower end is the coolant inlet, and the upper end is the coolant outlet and the wall surface for applying high-temperature heat flow. Under stable operating conditions, the porous plate structure is filled with coolant. The porous plate is divided into three parts along its thickness direction according to the length of each phase region: a liquid phase region, a two-phase region, and a gas phase region. Furthermore, under the condition of constant average porosity, each part is configured with different porosities to match the thermo-hydraulic performance requirements of each phase region.

[0060] The sintered metal spherical particles of the porous media sweating cooling plate have a thermal conductivity of 20~100 W / (m·K), preferably 100 W / (m·K). The diameter of the sintered metal spherical particles is 300~750 μm, preferably 740 μm. The average porosity is 0.25~0.70, preferably 0.33. The porosity of the liquid phase region is 0.25~0.40, preferably 0.26. The porosity of the two-phase region is 0.25~0.40, preferably 0.39. The porosity of the vapor phase region is 0.25~0.40, preferably 0.30. The porous medium evaporation cooling plate has excellent thermal and hydraulic properties.

[0061] Although preferred embodiments of this application have been described, those skilled in the art, upon learning the basic inventive concept, can make other changes and modifications to these embodiments. Therefore, the appended claims are intended to be interpreted as including the preferred embodiments as well as all changes and modifications falling within the scope of this application.

Claims

1. A method for optimizing the porosity of porous media undergoing sweating cooling based on coupled phase region length characteristics, characterized in that, The method includes: S1. A two-dimensional sweating cooling flow heat transfer model was established based on the modified thermal non-equilibrium two-phase mixing model. The effects of solid thermal conductivity, porosity and spherical particle diameter on the evolution of phase region length were analyzed according to the phase region length evolution formula. The coupling mechanism between heat conduction, heat convection, latent heat of phase change and flow resistance during sweating cooling was explored. S2 uses solid thermal conductivity, porosity, and spherical particle diameter as design variables, and solid skeleton outlet temperature and pressure drop as objective functions. It uses Gaussian process regression, NSGA-II genetic algorithm, and multi-criteria decision method to perform multi-objective optimization, and obtains the optimal combination of design variables and the corresponding average porosity for synergistically reducing the outlet temperature and pressure drop of the solid skeleton. S3. Using Gaussian process regression, NSGA-II genetic algorithm, multi-criteria decision method and porosity coupled phase region length design model from step S2, the porosity of the liquid phase region and gas phase region are used as design variables. The porosity of the two phase regions is determined according to the inverse solution of the average porosity constraint. The optimal porosity distribution combination of the three phase regions is obtained with the outlet temperature and pressure drop of the solid skeleton as the objective function.

2. The porous medium sweating cooling porosity optimization design method according to claim 1, characterized in that, In step S1, the two-dimensional sweating cooling flow heat transfer model includes a continuity equation, a momentum equation, and a fluid-solid dual-energy equation, which are used to describe the coolant flow, fluid-solid heat transfer, and phase change process, and the boundaries of the liquid phase region, two-phase region, and gas phase region are determined by the liquid phase saturation. Among them, the continuity equation is: In the formula, ρ U is the mixing density; u is the mixing Darcy velocity; For divergence operators; Momentum equation: In the formula, K For penetration rate; ν ( s ) represents the kinematic viscosity of the fluid mixture; This is the pressure gradient vector; Fluid energy equation: In the formula, c p，l This represents the isobaric heat capacity of the liquid phase. T M for Fluid correction temperature; The effective thermal diffusivity on the fluid side; q sf For heat source items; Correcting the temperature gradient for the fluid; Solid energy equation: In the formula, The effective thermal conductivity of the solid framework; For solid temperature gradient.

3. The porous medium sweating cooling porosity optimization design method according to claim 1, characterized in that, In step S1, the phase region length evolution formula includes: Formula for the evolution of liquid phase length: In the formula, L lp Indicates the length of the liquid phase region; c p，l This represents the isobaric heat capacity of the liquid phase, expressed in J / (kg·K). T in This indicates the coolant inlet temperature, expressed in Kelvin (K). m in Indicates inlet mass flow rate, in kg / s; T sat This represents the saturation temperature, expressed in Kelvin (K). h sl It represents the convective heat transfer coefficient between solid and liquid, with units of W / (m²·K); ΔT sl This represents the solid-liquid temperature difference, expressed in Kelvin (K). A c This represents the cross-sectional area, with the unit being m². A sf Specific surface area, unit is m² - ¹; Subscript m This represents the average value; Evolution formula for the length of the two-phase region: In the formula, L tp Indicates the length of the two-phase region; H fg Latent heat is expressed in J / kg; q boil This indicates the boiling term, with units of W / m³. q v,conv This represents the steam convection term, with units of W / m³. χ This indicates the proportion of coolant capable of carrying latent heat in the two-phase region; when a gas phase region is present... χ =1; when it does not exist, 0 < χ <1; Formula for the evolution of gas phase length: In the formula, L vp Indicates the length of the gas phase region; q This indicates the outlet heat flux, expressed in W / m³. 2 ; h sv This represents the convective heat transfer coefficient between solid and gas, with units of W / (m²·K). ΔT sv This represents the temperature difference between solid and air, expressed in Kelvin (K).

4. The porous medium sweating cooling porosity optimization design method according to claim 1, characterized in that, The specific steps of step S2 are as follows: Operating conditions and the ranges for solid thermal conductivity, porosity, and spherical particle diameter were defined. A surrogate model was established using Gaussian process regression, and validation data was randomly generated using Latin hypercube sampling to evaluate the accuracy of the surrogate model. The NSGA-II genetic algorithm was used for multi-objective optimization, with population size, maximum number of iterations, crossover probability, and mutation probability set to obtain a Pareto solution set that satisfies the optimization objectives. Finally, a multi-criteria decision-making method combining Shannon entropy weighting and TOPSIS was employed. Objective weights were determined based on the dispersion of the solid skeleton outlet temperature and pressure drop. The Pareto solutions were then comprehensively ranked by calculating their relative proximity to the ideal solution to determine the optimal solution in terms of overall performance.

5. The porous medium sweating cooling porosity optimization design method according to claim 1, characterized in that, The porosity-coupled phase region length design model in step S3 is as follows: In the formula, The average porosity; ε lp Porosity of the liquid phase region; ε tp The porosity of the two-phase region; ε vp Porosity of the gas phase region; L The total length of the porous medium.

6. A porous medium sweating cooling structure, characterized in that, The porous medium sweating cooling structure is sintered from isotropic and uniform metal spherical particles, with a coolant inlet at the lower end and a coolant outlet and high-temperature heat flow application wall at the upper end. The porous medium sweating cooling structure is divided into liquid phase region, two-phase region and gas phase region along the thickness direction according to the length of each phase region. Under the condition of constant average porosity, each phase region is configured with a different porosity, which is solved by the optimization design method described in any one of claims 1-5.

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