A Multi-Field Coupled Simulation Optimization Method and System for Solid-State Hydrogen Storage Systems

Abstract

This invention discloses a multi-field coupled simulation optimization method and system for solid-state hydrogen storage systems, belonging to the field of hydrogen storage system design technology. The method includes: establishing a dynamic constitutive relationship of "stress-porosity-permeability" for the hydrogen storage alloy during hydrogen absorption and desorption; constructing a four-field coupled numerical model including thermal field, flow field, stress field, and reaction kinetic field, and introducing the dynamic constitutive relationship as a feedback loop; and performing topology optimization on the heat exchange structure of the hydrogen storage tank based on the four-field coupled model, aiming at minimizing hydrogen absorption time or the lowest maximum bed temperature, while constraining that the maximum equivalent stress does not exceed the material's yield strength, thus obtaining the optimized heat exchange structure. This invention significantly improves the accuracy of hydrogen storage system performance prediction by introducing a stress-porosity dynamic feedback mechanism. Simultaneously, by utilizing topology optimization to obtain a lightweight and high-efficiency heat exchange structure, it can shorten the hydrogen absorption and desorption time of the hydrogen storage tank by more than 20% and reduce the peak stress of the tank body by more than 15%.

Description

Technical Field

[0001] This invention relates to the field of solid-state hydrogen storage system design technology, specifically to a multi-field coupling simulation optimization method and system for solid-state hydrogen storage systems. Background Technology

[0002] Solid-state hydrogen storage technology has become an important development direction in the field of hydrogen energy storage and transportation due to its advantages such as high volumetric hydrogen storage density, good safety, and low operating pressure. In practical applications, hydrogen storage alloys release a large amount of heat during hydrogen absorption (e.g., the enthalpy of formation of MgH2 is approximately -74.5 kJ / mol H2), and the alloy volume expands (up to 20% or more); during hydrogen release, it absorbs heat and contracts in volume. In this process, the thermal field, flow field (the flow of hydrogen in the porous bed), stress field (the compression of the tank by the alloy expansion), and reaction kinetic field are coupled with each other, jointly affecting the performance and safety of the hydrogen storage system.

[0003] Currently, numerical simulations of solid-state hydrogen storage systems are mostly limited to the coupling of the gas-thermal-solid three fields, and typically assume that the bed porosity and permeability are constant. However, experimental studies have shown that hydrogen storage alloys undergo severe pulverization and compaction during repeated hydrogen absorption and desorption, causing the bed porosity to gradually decrease from the initial 0.4–0.5 to 0.2–0.3, and the permeability to decrease by more than an order of magnitude. Existing models ignore this dynamic change, resulting in prediction errors of over 30% in hydrogen absorption and desorption times, and also failing to accurately predict the location of stress concentration and fatigue life of the tank.

[0004] Furthermore, the heat exchange structure design of existing hydrogen storage tanks (such as longitudinal fins and spiral coils) largely relies on experience or simple parameter optimization, lacking topology optimization methods based on multi-field coupling. Traditional fin structures suffer from problems such as large material consumption, uneven temperature distribution, and significant stress concentration.

[0005] Therefore, developing a high-precision multi-field coupled simulation method that can consider the dynamic feedback of stress-porosity, and performing topology optimization of the heat exchange structure based on this method, is of great significance for improving the performance and safety of solid hydrogen storage systems. Summary of the Invention

[0006] Technical problems to be solved

[0007] To address the shortcomings of existing technologies, this invention provides a multi-field coupled simulation optimization method and system for solid-state hydrogen storage systems, which solves the problems of low prediction accuracy caused by neglecting stress-porosity dynamic feedback in existing simulation models and poor performance caused by reliance on empirical design of heat exchange structures.

[0008] Technical solution

[0009] To achieve the above objectives, the present invention provides the following technical solution:

[0010] A multi-field coupled simulation optimization method for solid-state hydrogen storage systems includes the following steps:

[0011] Step 1: Establish the dynamic constitutive relationship of "stress-porosity-permeability" of hydrogen storage alloys during hydrogen absorption and desorption processes.

[0012] Specifically, the volumetric strain of the hydrogen storage alloy under different hydrogen pressures and temperatures was measured using in-situ X-ray diffraction or volume expansion experiments. A functional relationship between stress σ and porosity φ was established. Experiments show that for typical AB2-type or Mg-based hydrogen storage alloys, porosity decreases exponentially with increasing cycle number. Where N is the number of cycles. Meanwhile, according to the Carman-Kozeny equation, the permeability K and porosity φ satisfy: Where dp is the average particle diameter. This dynamic relationship is input into the finite element simulation software as a user-defined field variable (USDFLD).

[0013] Step 2: Construct a four-field coupled numerical model that includes thermal field, flow field, stress field and reaction dynamics field, and embed the dynamic constitutive relation as a feedback loop into the four-field coupled model.

[0014] In the four-field coupling model:

[0015] The governing equation for the thermal field is: ,in For the heat source term of the reaction, .

[0016] The governing equation for the flow field is Darcy's law: Where the permeability K is a function of the porosity φ, This enables dynamic feedback.

[0017] The governing equations of the stress field are linear elastic constitutive equations: The total strain ε includes elastic strain, thermal strain, and phase transformation (expansion) strain.

[0018] The reaction kinetics field adopts the JMAK equation: Where α is the reaction fraction, .

[0019] The coupling relationships between the various physical fields are as follows: temperature affects the reaction rate and thermal stress, the exothermic reaction affects the temperature field, hydrogen flow affects the pressure distribution and heat convection, the stress generated by alloy expansion affects porosity and permeability, and the change in porosity, in turn, affects the flow resistance and heat transfer coefficient.

[0020] Step 3: Based on the four-field coupling model, with the shortest hydrogen absorption time or the lowest maximum bed temperature as the optimization objective and the maximum equivalent stress not exceeding the material yield strength as the constraint, the heat exchange structure inside the hydrogen storage tank is topologically optimized to obtain the optimized heat exchange structure.

[0021] The topology optimization employs a variable density method, with the optimization region being the distribution area of ​​the heat exchange fins inside the hydrogen storage tank. The design variable is the relative density of each finite element. The intermediate density units are penalized using the SIMP interpolation model. The objective function is the hydrogen absorption time t90 (the time required to reach 90% saturated hydrogen storage), with the following constraints: (Safety factor 1.5). The convergence condition for the optimization iteration is that the rate of change of the objective function is less than 1%.

[0022] The optimized heat exchange structure is a tree-like fractal structure, a honeycomb structure, or a biomimetic vascular network structure, with a specific surface area of ​​not less than 200 m² / m³, and the difference between the highest and lowest temperatures of the bed during hydrogen absorption is less than 15℃.

[0023] Preferably, the method further includes: fabricating the optimized heat exchange structure into a solid heat exchange element through 3D printing or casting process, assembling it in a hydrogen storage tank, conducting hydrogen absorption and desorption experiments to verify it, and feeding the experimental data back to the model for parameter correction.

[0024] Preferably, the four-field coupling model is solved using the finite element method, the coupling solver adopts a fully coupled strategy, the time step adopts adaptive step size control, and the nonlinear iteration adopts the Newton-Raphson method.

[0025] Preferably, the method further includes: using the four-field coupling model to predict the performance degradation of the hydrogen storage tank after multiple cycles, and calculating the capacity retention rate and kinetic degradation coefficient by simulating the alloy pulverization and bed compaction process, in order to evaluate the full life cycle performance of the hydrogen storage system.

[0026] A solid-state hydrogen storage system includes a hydrogen storage tank shell, a heat exchange structure placed inside the hydrogen storage tank, and a hydrogen storage alloy bed filled inside the hydrogen storage tank; the heat exchange structure is optimized using the above-mentioned method.

[0027] A design optimization device for a solid-state hydrogen storage system includes a constitutive relation establishment module, a multi-field coupling modeling module, a topology optimization module, and an output module.

[0028] Beneficial effects

[0029] This invention provides a multi-field coupling simulation optimization method and system for solid-state hydrogen storage systems. It has the following beneficial effects:

[0030] 1. This invention introduces a dynamic feedback mechanism of "stress-porosity-permeability" for the first time in the simulation of solid-state hydrogen storage systems, overcoming the shortcomings of traditional models that assume constant porosity. Experiments show that, after considering this feedback, the prediction error of hydrogen absorption time is reduced from over 30% to less than 8%, significantly improving the accuracy of hydrogen storage system performance evaluation.

[0031] 2. This invention constructs a fully coupled four-field model (thermal, fluid, mechanical, and chemical) to realistically reflect the multi-physics interactions inside the hydrogen storage tank. In particular, the introduction of the stress field allows for accurate prediction of stress concentration areas in the tank, providing a basis for the structural safety design of the tank. Simultaneously, the dynamic porosity model can simulate the bed densification process after multiple cycles, enabling full life-cycle performance prediction.

[0032] 3. This invention employs a topology optimization method to design the heat exchange structure, overcoming the limitations of traditional empirical design or size optimization. The optimized tree-like fractal or honeycomb heat exchange structure has a larger specific surface area and better temperature uniformity. Simulations and experiments show that, compared with the traditional longitudinal fin structure, the optimized structure reduces hydrogen absorption time by 20%–35% and the maximum temperature difference in the bed by 40%–60%.

[0033] 4. This invention combines optimized design with additive manufacturing (3D printing), enabling the low-cost realization of complex topological structures. This method is applicable to various types of hydrogen storage alloys (such as AB2 type, AB5 type, Mg-based, etc.) and hydrogen storage tanks of various shapes (cylindrical, square, irregular shapes), exhibiting good versatility and scalability.

[0034] 5. The method of this invention can also be used to evaluate the performance degradation of hydrogen storage systems after long-term cycling, helping designers optimize refueling cycles and maintenance strategies, and reduce the total lifecycle cost of the system. Attached Figure Description

[0035] Figure 1 This is an overall flowchart of the method of the present invention;

[0036] Figure 2 This is a schematic diagram illustrating the establishment and embedding of the "stress-porosity-permeability" dynamic constitutive relationship of the present invention;

[0037] Figure 3 This is a data transfer relationship diagram of the four-field coupling model of the present invention;

[0038] Figure 4 The following is a comparison diagram of the heat exchange structure before and after optimization in the embodiments of the present invention (a: traditional longitudinal fins; b: topology-optimized tree-like fractal structure).

[0039] Figure 5 This is a cloud map comparing the bed temperature distribution before and after hydrogen absorption in an embodiment of the present invention;

[0040] Figure 6 This is a comparison of hydrogen absorption kinetic curves before and after optimization in an embodiment of the present invention;

[0041] Figure 7 This is a comparison chart of prediction errors considering and not considering dynamic porosity feedback in an embodiment of the present invention. Detailed Implementation

[0042] The technical solutions of the embodiments of the present invention will be clearly and completely described below with reference to the accompanying drawings. Obviously, the described embodiments are only some embodiments of the present invention, and not all embodiments. All other embodiments obtained by those skilled in the art based on the embodiments of the present invention without creative effort are within the scope of protection of the present invention.

[0043] Example 1

[0044] This embodiment takes a cylindrical AB2 type hydrogen storage alloy tank as an example to describe in detail the implementation process of the method of the present invention.

[0045] Step 1: Establish the dynamic constitutive relationship of "stress-porosity-permeability"

[0046] Select The alloy was used as a hydrogen storage material. In-situ X-ray diffraction experiments were conducted. At 25°C, the alloy was placed in a high-pressure chamber, and the hydrogen pressure was gradually increased to 8 MPa, while the volume change of the alloy's unit cells was recorded simultaneously. The volumetric expansion coefficient of the alloy after complete hydrogenation was measured to be approximately 18.5%. Analysis of bed porosity using SEM images after different cycle numbers (N=1, 10, 20, 50) revealed that the porosity decreased exponentially with the number of cycles. That is, the initial porosity φ0 = 0.48, and the porosity φend ≈ 0.22 after 50 cycles.

[0047] According to the Carman-Kozeny equation, the relationship between permeability K and porosity φ is as follows: In this embodiment, the initial average particle diameter dp = 50 μm, and K0 = 2.13 × 10⁻¹¹ m² was calculated; after 50 cycles, dp was reduced to about 15 μm by laser particle size testing, and Kend = 1.14 × 10⁻¹² m² was calculated.

[0048] This dynamic relationship is written as a user-defined function (interpolation function) in COMSOL Multiphysics, which updates porosity as a state variable with time and local stress.

[0049] Step 2: Construct a four-field coupled numerical model

[0050] Geometric model: Cylindrical hydrogen storage tank, inner diameter 200 mm, height 500 mm, wall thickness 5 mm (316L stainless steel). The internal heat exchange structure is tentatively set as 6 longitudinal rectangular fins (height 400 mm, thickness 2 mm, evenly distributed along the circumference). The hydrogen storage alloy bed fills the gaps between the fins.

[0051] Couple the following physics interfaces in COMSOL Multiphysics:

[0052] Thermal field: Use the "Solid Heat Transfer" interface to add a reaction heat source item Qr.

[0053] Flow field: Using the "Darcy's Law" interface, the permeability K is set as a function of the porosity φ.

[0054] Stress field: Using the "Solid Mechanics" interface, add thermal strain and phase transformation strain (hydrogen absorption expansion strain, set to isotropic, magnitude 0.185).

[0055] Reaction kinetics: Using the "Domain Ordinary Differentials and Differential Algebraic Equations" interface, define the JMAK equation for the reaction fraction α.

[0056] The material parameters are as follows:

[0057] parameter value unit Hydrogen storage alloy density ρs 6800 kg / m³ Maximum hydrogen storage capacity cmax 1.9 wt.% Enthalpy of reaction ΔH -19460 <![CDATA[J / mol H2]]> Reaction entropy ΔS -88.95 J / (mol·K) Pre-exponential factor A 1.022 s⁻¹ Activation energy Ea 9350 J / mol Alloy thermal conductivity λs 1.6 W / (m·K) Alloy elastic modulus E 120 GPa Alloy Poisson's ratio ν 0.33 — Hydrogen dynamic viscosity (μg) 8.87e-6 Pa·s The thermal conductivity of hydrogen is λg 0.1769 W / (m·K)

[0058] Boundary conditions: Inlet hydrogen pressure 7 MPa, inlet temperature 25℃; external cooling water temperature 25℃, convective heat transfer coefficient 500 W / (m²·K); natural convection heat transfer coefficient of the outer wall of the hydrogen storage tank 10 W / (m²·K).

[0059] Step 3: Model Validation (before optimization)

[0060] First, the hydrogen absorption process was calculated using both the traditional constant porosity model (φ=0.48 fixed) and the dynamic porosity model of this invention, and the results were compared with experimental data. The experiment used a hydrogen storage tank of the same size, filled with 4.2 kg of alloy, and tested under inlet conditions of 7 MPa and 25°C.

[0061] Results: The experimentally measured time t for hydrogen absorption to reach 90% saturation capacity was... 90 =1850 s. The constant porosity model predicts t. 90 =1280 s, with an error of approximately 30.8%; the dynamic porosity model of this invention predicts t 90 =1720 s, with an error of approximately 7.0%. Meanwhile, the peak temperature predicted by the dynamic model (78.2℃) is closer to the experimental value (81.5℃), while the peak temperature predicted by the constant model is 94.3℃, which is too high.

[0062] Step 4: Topology optimization of heat transfer structure

[0063] Based on the geometric model from step two, the heat exchange fin region is set as the design domain. Variable density topology optimization is employed, with the optimization objective being the hydrogen absorption time t. 90 Shortest possible. Constraints: ① Peak bed temperature ≤ 85℃; ② Maximum equivalent stress of the tank ≤ 200 MPa (316L yield strength approximately 230 MPa, safety factor 1.15). The upper limit of material volume fraction is set at 0.15 (i.e., the optimized fin material volume does not exceed 15% of the initial longitudinal fin volume).

[0064] After 50 iterations of optimization, the structure converged. The resulting optimized structure is a tree-like fractal structure: the main branches branch outwards from the central tube, with 4 first-level branches, 16 second-level branches, and 64 tertiary branches. The thickness of all branches gradually decreases from 0.8 mm at the root to 0.2 mm at the tip. This structure achieves a specific surface area of ​​312 m² / m³, while the specific surface area of ​​traditional longitudinal fins is only 127 m² / m³.

[0065] Step 5: Performance Comparison After Optimization

[0066] The optimized tree-like fractal structure was 3D printed using selective laser melting (SLM) with AlSi10Mg as the material. Hydrogen absorption experiments were then conducted again after assembly.

[0067] result:

[0068] t 90 The time was shortened from 1850 s to 1320 s, a reduction of 28.6%.

[0069] The peak bed temperature decreased from 81.5℃ to 68.2℃, a decrease of 16.3%.

[0070] The maximum temperature difference in the bed layer decreased from 32℃ to 14℃, and the temperature uniformity was significantly improved.

[0071] The maximum equivalent stress of the tank decreased from 178 MPa to 146 MPa, a reduction of 18.0%.

[0072] Meanwhile, the optimized heat exchange structure weighs 1.8 kg, while the traditional longitudinal fins weigh 2.5 kg, a weight reduction of 28%.

[0073] Example 2

[0074] This embodiment is basically the same as Embodiment 1, except that the hydrogen storage alloy is changed to MgH2 (theoretical hydrogen storage capacity 7.6 wt.%), and the hydrogen storage tank dimensions are changed to an inner diameter of 300 mm and a height of 800 mm. The dynamic constitutive relationship was re-determined through a volume expansion experiment: the volume expansion rate of MgH2 is approximately 31%, the initial porosity is 0.52, and the porosity decreases to 0.25 after 20 cycles. The initial permeability K0 = 3.5 × 10⁻¹¹ m².

[0075] The optimization objective was changed to minimizing hydrogen release time (using 300℃ heated water as the heat source). The heat exchange structure obtained through topology optimization is a biomimetic vascular network structure with a specific surface area of ​​268 m² / m³. After optimization, the hydrogen release time was shortened from 5600 s to 4100 s, a reduction of 26.8%. The maximum equivalent stress of the tank decreased from 245 MPa (close to yield) to 198 MPa, significantly improving safety.

[0076] Example 3

[0077] This embodiment utilizes the method of the present invention to predict the performance throughout the entire life cycle. The hydrogen storage system in Example 1 is simulated for 100 cycles, taking into account the porosity decay and permeability decrease after each cycle.

[0078] Simulation results: t in the first cycle 90 =1720 s, t of the 10th cycle 90 =1890 s, 50th cycle t 90 =2350 s, t of the 100th cycle 90 =2780 s. Capacity retention decreased from 100% in the first cycle to 91.2% in the 100th cycle. This predicted result is in good agreement with the accelerated cycling experimental data (99.5% capacity retention after 20 cycles and 91.8% after 50 cycles).

[0079] Using this prediction, designers can determine at t 90 Replace materials or regenerate them when the time exceeds 2500 seconds to optimize the maintenance cycle.

[0080] Comparative Example 1 (Constant Porosity Model)

[0081] The same conditions as in Example 1 were used, but with a constant porosity φ = 0.48. Predicted t 90 =1280 s, a significant deviation from the actual 1850 s. Furthermore, cyclic decay cannot be predicted; it is assumed that t will occur after 100 cycles. 90 It remains at 1280 s, which deviates from the actual situation.

[0082] Comparative Example 2 (Size optimization rather than topology optimization)

[0083] Only the thickness and number of traditional longitudinal fins were optimized. The optimal solution is 8 fins with a thickness of 2.5 mm. After optimization, t 90 =1620 s, peak bed temperature 74.5℃, maximum equivalent stress of tank 169 MPa. Although better than the unoptimized 1850 s, it is not as good as the topology-optimized 1320 s, and the fin weight is 2.7 kg, which is higher than the 1.8 kg of the present invention.

[0084] Performance Comparison Summary

[0085] index Traditional fins (experimental) Size optimization (Comparative Example 2) Topology optimization (Example 1) <![CDATA[t 90 (s)]]> 1850 1620 1320 Peak temperature (°C) 81.5 74.5 68.2 Maximum temperature difference (°C) 32 24 14 Maximum equivalent stress (MPa) 178 169 146 Weight of heat exchange structure (kg) 2.5 2.7 1.8 Prediction error (relative to experiment) benchmark — 7.0% (30.8% for constant model)

[0086] Industrial applicability

[0087] The multi-field coupling simulation optimization method provided by this invention can be applied to the design stage of various solid-state hydrogen storage systems, including on-board hydrogen fuel cell storage tanks, stationary hydrogen storage devices at hydrogen refueling stations, and portable power supply hydrogen storage devices. The heat exchange structure optimized by this method can be mass-produced using 3D printing technology at a controllable cost. This method can also be embedded into commercial finite element software (such as COMSOL, ANSYS, and ABAQUS) as a dedicated module for use by hydrogen storage system designers.

[0088] Although embodiments of the invention have been shown and described, it will be understood by those skilled in the art that various changes, modifications, substitutions and alterations can be made to these embodiments without departing from the principles and spirit of the invention, the scope of which is defined by the appended claims and their equivalents.

Claims

1. A multi-field coupled simulation optimization method for a solid-state hydrogen storage system, characterized in that, The process includes the following steps: Step 1: Establishing a dynamic constitutive relationship of "stress-porosity-permeability" for the hydrogen storage alloy during hydrogen absorption and desorption; Step 2: Constructing a four-field coupled numerical model that includes thermal field, flow field, stress field, and reaction kinetic field, and embedding the dynamic constitutive relationship as a feedback loop into the four-field coupled model; Step 3: Based on the four-field coupled model, with the shortest hydrogen absorption time or the lowest maximum bed temperature as the optimization objective, and with the maximum equivalent stress not exceeding the material yield strength as the constraint, performing topology optimization on the heat exchange structure inside the hydrogen storage tank to obtain the optimized heat exchange structure.

2. The method according to claim 1, characterized in that, The dynamic constitutive relationship of "stress-porosity-permeability" is established as follows: In-situ X-ray diffraction or volume expansion experiments are used to measure the volumetric strain of the hydrogen storage alloy under different hydrogen pressures and temperatures, establishing a functional relationship between stress and porosity; then, empirical formulas for porosity and permeability are used to establish a functional relationship between porosity and permeability; finally, this functional relationship is input into the finite element simulation software in the form of user-defined field variables or interpolation functions.

3. The method according to claim 1, characterized in that, In the four-field coupled model: the thermal field governing equation is an energy conservation equation that includes a reaction heat source term; the flow field governing equation is Darcy's law, and the permeability is a function of porosity, rather than a constant value; the stress field governing equation is a linear elastic or elastoplastic constitutive equation, considering the thermal stress and phase transformation stress generated by the hydrogen absorption expansion of the alloy; the reaction kinetic field adopts the JMAK equation or a similar kinetic model, and the reaction rate is related to temperature, hydrogen pressure, and reaction fraction.

4. The method according to claim 1, characterized in that, The topology optimization adopts the variable density method or the level set method. The optimization region is the distribution area of ​​the heat exchange fins inside the hydrogen storage tank. The design variable is the relative density of each unit. The optimization iteration convergence condition is that the rate of change of the objective function is less than 1%.

5. The method according to claim 1, characterized in that, The heat exchange structure of the hydrogen storage tank includes one or more of the following: internal heat exchange fins, external heat exchange jacket, and central heat exchange tube; the topology-optimized heat exchange structure is a tree-like fractal structure, a honeycomb structure, or a biomimetic vascular network structure.

6. The method according to claim 1, characterized in that, The method further includes: fabricating the optimized heat exchange structure into a solid heat exchange element through 3D printing or casting process, assembling it in a hydrogen storage tank, and conducting hydrogen absorption and desorption experiments to verify it, and feeding the experimental data back to the model for parameter correction.

7. The method according to claim 1, characterized in that, The four-field coupled model is solved using the finite element method or the finite volume method. The coupled solver adopts a fully coupled or sequential coupling strategy, the time step adopts adaptive step size control, and the nonlinear iteration adopts the Newton-Raphson method.

8. The method according to claim 1, characterized in that, The method further includes: using the four-field coupling model to predict the performance degradation of the hydrogen storage tank after multiple cycles, and calculating the capacity retention rate and kinetic degradation coefficient by simulating the alloy pulverization and bed compaction process, which are used to evaluate the full life cycle performance of the hydrogen storage system.

9. A solid-state hydrogen storage system, characterized in that, The device includes a hydrogen storage tank shell, a heat exchange structure placed inside the hydrogen storage tank, and a hydrogen storage alloy bed filled inside the hydrogen storage tank; the heat exchange structure is optimized and designed using the method described in any one of claims 1-8; the specific surface area of ​​the heat exchange structure is not less than 200 m² / m³, and its distribution ensures that the difference between the highest and lowest temperatures of the bed during hydrogen absorption is less than 15°C.

10. A design optimization device for a solid-state hydrogen storage system, characterized in that, include: The constitutive relation establishment module is used to establish the dynamic constitutive relation of hydrogen storage alloys based on stress, porosity, and permeability. The multi-field coupling modeling module is used to construct a four-field coupled numerical model that includes thermal field, flow field, stress field and reaction dynamics field; the topology optimization module is used to perform topology optimization on the heat transfer structure based on the four-field coupled model. The output module is used to output the optimized 3D model of the heat exchange structure and the corresponding performance prediction results.

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