Heat conduction structure based on topological optimization and design method thereof

Abstract

The invention provides a heat conduction structure based on topological optimization and a design method thereof, and belongs to the technical field of energy and heat storage. In order to solve the problems that an existing solid heat storage material is low in heat conductivity coefficient and a conventional fin is high in cost, the heat conduction fin of an irregular radial branch structure is designed through topological optimization of a density method. The fins are fixed to the outer wall of the heat exchange pipeline, and the overall effective heat conductivity coefficient is increased by one order of magnitude through the heat conduction channels optimized in a targeted mode while it is guaranteed that the volume fraction of the high-heat-conductivity material does not exceed 10%. The heat charging and discharging power is greatly improved, the material cost is reduced, and the solid heat storage device is suitable for a large-scale solid heat storage device.

Description

Technical Field

[0001] This invention relates to the field of energy storage and heat transfer enhancement technology, and in particular to a topology-optimized heat conduction structure and its design method. Background Technology

[0002] The development and utilization of renewable energy are becoming increasingly important. However, renewable energy sources such as wind and solar power exhibit significant intermittency and volatility, leading to a mismatch between supply and demand over time. Energy storage technology, as a key means of solving this problem, has received widespread attention.

[0003] Among various energy storage technologies, thermal storage technology (especially sensible thermal storage) occupies an important position due to its low cost, long lifespan, and scalability potential. Solid thermal storage materials (such as concrete and magnesia bricks) have advantages such as mature technology, abundant raw materials, and simple structure. However, solid thermal storage materials are typically porous media with low intrinsic thermal conductivity. This thermal property defect severely limits the heat charge / discharge rate (power) of the thermal storage system, resulting in low efficiency when facing rapid response demands.

[0004] To address the aforementioned issues, existing technologies typically employ the addition of heat-conducting fins made of highly thermally conductive materials (such as aluminum alloys or copper) to the outer wall of heat exchange pipes. This increases the heat exchange area and shortens the heat conduction path. Currently used heat-conducting fins mostly adopt regular geometric shapes, such as spiral, square, triangular, or fan blade shapes.

[0005] However, in the process of realizing this invention, the applicant discovered that the heat-conducting fins in the prior art have the following main defects:

[0006] First, the rib shapes are mostly designed based on engineering experience without targeted optimization, which results in the material's thermal conductivity potential not being fully realized and the overall effective thermal conductivity being only slightly improved.

[0007] Secondly, to achieve the desired heat conduction effect, traditional fins often require a large volume ratio (high volume fraction), which means that a large amount of expensive metal materials (such as aluminum alloys) are needed. For large-scale thermal storage systems, this will significantly increase the initial investment cost of the system, which is not conducive to commercialization.

[0008] Therefore, there is an urgent need for a heat-conducting structure that can significantly improve the thermal conductivity of solid thermal storage materials while strictly controlling the amount of high thermal conductivity materials used and reducing costs. Summary of the Invention

[0009] This invention provides a topology-optimized thermal conductive structure and its design method. Existing thermal conductive fins often use regular geometric shapes that have not been verified and optimized. This results in limited improvement on the overall thermal conductivity of the thermal storage system despite the high cost of thermally conductive materials, failing to balance high performance and low cost.

[0010] The core technology of this invention is to design a thermally conductive fin structure with irregular radial branching characteristics through density-based topology optimization technology. While strictly controlling the volume fraction of high thermal conductivity material to within 10%, it achieves an order-of-magnitude increase in the effective thermal conductivity of the heat storage medium.

[0011] In a first aspect, the present invention provides a topology-optimized heat conduction structure, comprising: Heat exchange pipes, whose interiors are used to circulate heat exchange working fluid; and Several heat-conducting fins are arranged at intervals along the axial direction of the heat exchange pipe and fixedly connected to the outer wall of the heat exchange pipe. The heat-conducting fins are made of high thermal conductivity material, and their geometry is an irregular branching structure generated based on density method topology optimization. The irregular branching structure extends radially outward from the heat exchange pipe as the center, forming multiple main heat paths and secondary heat conduction paths formed by the branching of the main heat paths, so as to minimize the average temperature of the heat storage area under a limited material volume fraction.

[0012] Furthermore, each heat-conducting fin is a three-dimensional geometric structure, which is formed by stretching a planar shape generated by two-dimensional topology optimization along the axial direction of the heat exchange pipe. The thickness of the thermal fins and the spacing between adjacent thermal fins remain consistent throughout the thermal conductive structure.

[0013] Furthermore, the volume fraction of the thermally conductive fins in the heat storage unit of the solid heat storage device does not exceed 10%, and the thermal conductivity of the thermally conductive fins is at least 100 times that of the heat storage material in the solid heat storage device.

[0014] Furthermore, the heat-conducting fins and the heat exchange pipes are fixedly connected by fasteners, and a flexible high thermal conductivity pad is provided between the contact surfaces of the heat-conducting fins and the heat exchange pipes. The flexible high thermal conductivity pad is used to fill the contact gaps to enhance heat transfer.

[0015] Furthermore, the outer contour of the heat-conducting fins is adapted to the geometric boundary of the heat storage unit, which is a square or a regular hexagon, so that multiple heat exchange pipes and their corresponding heat-conducting structures can be arranged in a close array in the heat storage device.

[0016] Secondly, the present invention provides a design method for a topology-optimized heat-conducting structure as described above, comprising the following steps: S1. Establish the geometric model: Determine the outer contour of the thermal storage unit and the central pipe area, and define the design domain; S2. Set up the topology optimization density model: Introduce control variables and perform filtering and projection processing on the control variables to obtain the physical density variables; S3. Set up a solid heat transfer model: Based on the physical density variable, use a material interpolation model to interpolate between the thermal conductivity of the heat storage material and the thermal conductivity of the fin material, and construct a steady-state heat transfer equation that includes the internal heat source. S4. Set up the research configuration: take minimizing the average temperature within the design domain as the objective function, take the volume fraction of high thermal conductivity material as the constraint, and use the moving asymptote algorithm to iteratively solve the objective function; S5. Generate Structure: Extract the region in the solution result where the physical density variable is greater than the preset threshold, obtain the two-dimensional rib shape, and stretch it into a three-dimensional solid structure.

[0017] Furthermore, in step S2, the filtration process employs a Helmholtz partial differential equation filter, which eliminates the checkerboard effect by controlling the filtration radius; The projection process uses a hyperbolic tangent projection function, which maps the filtered variables to either 0 or 1 by adjusting the projection slope, in order to obtain clear structural boundaries.

[0018] Furthermore, in step S3, the material interpolation model adopts the solid isotropic material penalty model; in the steady-state heat transfer equation, the thermal conductivity is a function of the physical density variable. When the physical density variable approaches 0, the thermal conductivity approaches the low thermal conductivity of the heat storage material; when the physical density variable approaches 1, the thermal conductivity approaches the high thermal conductivity of the fin material.

[0019] Furthermore, in step S3, the boundary conditions set include: the outer boundary of the design domain is an adiabatic boundary, and the inner boundary of the central pipe region is a constant temperature boundary.

[0020] Furthermore, in step S4, the constraint conditions are set as follows: the lower limit of the volume fraction of high thermal conductivity material is 0.05 and the upper limit is 0.1; in step S5, the preset threshold is 0.5, and the extracted two-dimensional rib shape is used for metal casting or die casting molding process.

[0021] The main contributions and innovations of this invention are as follows: 1. Extremely high thermal conductivity enhancement efficiency (high cost-effectiveness): The finned structure generated by the topology optimization algorithm in this invention can form the optimal heat conduction path. Experimental data shows that, at the same volume fraction, the thermal conductivity of this structure is improved by more than 25% to 30% compared with traditional rectangular fins; compared with low thermal conductivity thermal storage materials without fins, the overall effective thermal conductivity is improved by more than 10 times (an order of magnitude).

[0022] 2. Significant cost advantages: Thanks to the precise control of material distribution through topology optimization, this invention can strictly control the volume fraction of high thermal conductivity materials (such as aluminum alloys) to 10% or even lower (e.g., 5%) while ensuring high performance. In large-scale thermal storage applications, this can greatly reduce the amount of expensive metal materials used, significantly reducing system costs.

[0023] 3. Excellent anisotropic thermal conductivity: The optimized fins exhibit a radiating shape from the central channel outwards, constructing a targeted radial rapid heat conduction pathway. Compared to isotropic materials formed by simply mixing high thermal conductivity particles, the structure of this invention can more effectively transfer heat along the axial and radial depths, significantly improving the charging and discharging heat power.

[0024] 4. Good engineering robustness: Data shows that even in extreme cases where material properties deteriorate during processing (e.g., the thermal conductivity of the fins themselves decreases), this topology-optimized structure can still maintain a high effective thermal conductivity, demonstrating strong engineering adaptability and reliability.

[0025] 5. Advanced design method: The topology optimization method based on steady-state heat transfer equation (such as SIMP interpolation combined with MMA algorithm) adopted in this invention significantly reduces the optimization parameters and computational resource consumption compared with transient method, has better convergence, and can obtain high-precision optimal structural design in a short time.

[0026] Details of one or more embodiments of the present invention are set forth in the following drawings and description, so that other features, objects and advantages of the invention will be more readily understood. Attached Figure Description

[0027] The accompanying drawings, which are included to provide a further understanding of the invention and form part of this invention, illustrate exemplary embodiments of the invention and are used to explain the invention, but do not constitute an undue limitation of the invention. In the drawings: Figure 1 This is a front view of a topology-optimized heat-conducting structure according to an embodiment of the present invention; Figure 2 This is a side view of a topology-optimized heat-conducting structure according to an embodiment of the present invention; Figure 3 This is a flowchart of topology optimization according to an embodiment of the present invention; Figure 4 This is a comparison diagram of the thermal conductivity of different fins according to an embodiment of the present invention; Figure 5 This is a diagram showing the results of two-dimensional planar topology optimization according to an embodiment of the present invention. Figure 6 This is a graph of the objective function with different iteration numbers according to an embodiment of the present invention.

[0028] In the diagram, 1 is the heat exchange pipe; 2 is the heat-conducting fin. Detailed Implementation

[0029] Exemplary embodiments will now be described in detail, examples of which are illustrated in the accompanying drawings. When the following description relates to the drawings, unless otherwise indicated, the same numerals in different drawings denote the same or similar elements. The embodiments described in the following exemplary embodiments do not represent all embodiments consistent with one or more embodiments of this specification. Rather, they are merely examples of apparatuses and methods consistent with some aspects of one or more embodiments of this specification as detailed in the appended claims.

[0030] It should be noted that the steps of the corresponding methods are not necessarily performed in the order shown and described in this specification in other embodiments. In some other embodiments, the methods may include more or fewer steps than described in this specification. Furthermore, a single step described in this specification may be broken down into multiple steps in other embodiments; and multiple steps described in this specification may be combined into a single step in other embodiments.

[0031] Example 1: Thermal Conductive Structure Based on Topology Optimization like Figure 1 and Figure 2 As shown, this embodiment provides a topology-optimized heat-conducting structure for a solid thermal storage device. The structure mainly includes a heat exchange pipe 1 and several heat-conducting fins 2 fixed to the outer wall of the heat exchange pipe 1.

[0032] Specifically, the heat exchange pipe 1 serves as a fluid channel, through which a heat exchange medium (such as water, steam, or heat transfer oil) flows. It is typically made of a high-temperature, high-pressure resistant metal tube. The heat-conducting fins 2 are arranged in an array at intervals along the axial direction of the heat exchange pipe 1. In this embodiment, the thickness of the heat-conducting fins 2 and the spacing between adjacent fins 2 remain consistent throughout the entire heat-conducting structure to facilitate processing and control of the material volume fraction. The thickness of the heat-conducting fins 2 can range from 2-70 mm, preferably 20 mm.

[0033] To reduce costs and ensure thermal conductivity, the heat-conducting fins 2 are made of a high thermal conductivity material, preferably aluminum alloy 1060 or 6061, and are integrally formed by casting or die casting. The heat exchange pipe 1 is surrounded by a solid heat storage material (such as concrete), and the heat-conducting fins 2 are encased in the solid heat storage material.

[0034] The core of this embodiment lies in the geometry of the heat-conducting fin 2. Unlike traditional rectangular, circular, or spiral fins, the shape of the heat-conducting fin 2 in this embodiment is an irregular branched structure generated based on density-based topology optimization. For example... Figure 2 and Figure 5 As shown, the structure extends radially outward from the central heat exchange pipe 1 as the origin, forming multiple primary heat conduction paths. These primary heat conduction paths further branch into secondary heat conduction paths during their extension, resembling a tree-like or root-like structure. This irregular structure constitutes a targeted and rapid heat conduction pathway, capable of quickly transferring heat from the central pipe wall to the surrounding deep heat storage material, or rapidly converging heat from the surrounding area to the center.

[0035] To minimize the contact thermal resistance between the heat-conducting fins 2 and the heat exchange pipe 1, the heat-conducting fins 2 are fastened to the heat exchange pipe 1 using fasteners (such as bolts). Furthermore, a flexible, highly thermally conductive pad is placed between the contact surfaces of the heat-conducting fins 2 and the heat exchange pipe 1; in this embodiment, graphite paper is preferably used. Graphite paper has a certain degree of compressive resilience, which can effectively fill the microscopic gaps between the metal contact surfaces, significantly enhancing the heat transfer effect.

[0036] In practical large-scale thermal storage devices, there are typically hundreds or thousands of thermal storage units. In this embodiment, the outer contour design of the heat-conducting fin 2 is adapted to the geometric boundaries of the thermal storage units. For example, when the pipes in the thermal storage device are arranged in a square array, the outer contour of the heat-conducting fin 2 is a square; when the pipes are arranged in an equilateral triangle, the outer contour can be a regular hexagon. Taking a square arrangement as an example, the side length of the square corresponds to the pipe spacing (e.g., 320 mm), and the diameter of the central circular hole corresponds to the outer diameter of the pipe (e.g., 20 mm). Through this design, multiple heat-conducting structures can be seamlessly spliced ​​together, maximizing the use of space.

[0037] Example 2: Design Method of Thermal Conductive Structure Based on Topology Optimization This embodiment details the design method of the aforementioned heat-conducting structure. This method is based on variable density topology optimization theory and is solved using computer software (such as COMSOL Multiphysics). Figure 3 As shown, the design process includes the following steps: S1. Establishing a geometric model The design domain is determined based on actual engineering requirements. A square or regular hexagon is set as the outer contour, with a circular hole cut out in the center to serve as the central pipe area. In this embodiment, the side length of the square design domain is set to 320mm, and the diameter of the central circular hole is 20mm.

[0038] S2. Set up the topology optimization density model To obtain clear structural boundaries and avoid the checkerboard effect, this step constructs a density model that includes filtering and projection: 1. Introduce control variables: Let... These are the original control variables corrected by the optimization procedure. .

[0039] 2. Helmholtz Filter: This filter applies a filter to the original control variables to obtain the filtered variables. The equation is as follows:

[0040] in, It is the filtration radius. It is a Laplacian operator.

[0041] 3. Hyperbolic Tangent Projection: To eliminate intermediate density grayscale cells, the filtered variables are projected to obtain the projected variables. The equation is as follows:

[0042] in, It is the projection slope, which controls the steepness of the projection; It is the projection point (threshold).

[0043] 4. SIMP Interpolation: Apply solid isotropic material penalty (SIMP) interpolation to the projected variables to obtain the final physical density variable (the variable after SIMP interpolation). :

[0044] in, It is the SIMP penalty index, usually taken as 3 to penalize intermediate density.

[0045] S3. Set up the solid heat transfer model The steady-state heat transfer physical field is constructed, and its governing equations are as follows:

[0046]

[0047] in, For density, For constant pressure heat capacity, Let Q be the velocity field (this is static in this case, so this term can be ignored), and Q be the internal heat source. Let k be the heat flux, k be the thermal conductivity, and T be the temperature. For temperature gradient.

[0048] In this model, the thermal conductivity k is a variable related to the physical density. The function of the thermal conductivity of the heat storage material Thermal conductivity of fin materials Interpolate between them:

[0049] In this embodiment, the following settings are provided: (Representing concrete) (e.g., representing aluminum alloy).

[0050] Set boundary conditions: Design the outer boundary: set it as an adiabatic boundary condition (simulating periodic symmetric or isolated elements).

[0051] Inner boundary of the central pipe: set to constant temperature boundary conditions, for example, T=300℃.

[0052] Heat source: A uniform internal heat source is set throughout the entire design domain, for example... (The equivalent heat source that simulates the exothermic or endothermic process).

[0053] S4. Setting up research configuration and solving. The Moving Asymptote (MMA) optimization algorithm is adopted, the solver is set to a steady-state MUMPS solver, and the automatic nonlinear Newton method is used.

[0054] Objective function: Minimize the regional average temperature, i.e. , where A is the area of ​​the region. This means that, given a heat source, the faster the heat dissipates (the better the thermal conductivity), the lower the average temperature.

[0055] Constraints: Limit the volume fraction of high thermal conductivity materials.

[0056]

[0057] In this embodiment, the lower limit of volume fraction upper limit (i.e., 5% to 10%).

[0058] Iteration parameters: Set the maximum number of iterations to 500, tolerance .

[0059] Figure 6 The convergence curve of the objective function (average temperature) during the iteration process is shown. It can be seen that the objective function tends to stabilize after about 100 iterations, which proves that the proposed method has good convergence and high computational efficiency.

[0060] S5, Generation Structure After the solution is completed, extract the physical density variable. The area, obtained as Figure 5 The shape of the two-dimensional ribs shown. Figure 5 This demonstrates the shape evolution process from 10 iterations to 500 iterations, ultimately forming a clear tree-like branching structure. Stretching this two-dimensional shape along the axial direction yields... Figure 2 The three-dimensional thermally conductive fins shown.

[0061] Example 3: Performance Comparison and Analysis To verify the effectiveness of the embodiments of the present invention, the above-mentioned heat-conducting structure based on topology optimization design (5% volume fraction) was compared with the structure without ribs, the conventional rectangular rib structure with 5% volume fraction, and the uniform mixed material with 5% volume fraction. Figure 4 The comparison results at the two-dimensional level are shown: Finless: Effective thermal conductivity is only 2 W / (m·K).

[0062] Uniformly mixed (5%): effective thermal conductivity is approximately 12.46 W / (m·K).

[0063] Rectangular fins (5%): effective thermal conductivity is 22.1 W / (m·K).

[0064] Topology-optimized fins (this invention, 5%): effective thermal conductivity reaches 28.1 W / (m·K).

[0065] The results show that, with the same amount of material, the topology-optimized structure of the present invention improves thermal conductivity by about 27% compared to conventional rectangular fins, and by more than 10 times compared to the case without fins.

[0066] If this volume fraction is increased to around 10%, the results are shown in Table 1 below: Table 1

[0067] When a slightly larger amount of material is allowed (about 10-11%), the present invention can further unlock its performance potential, achieving a high thermal conductivity of 46.8, and has a performance advantage of about 30% compared to conventional fins with the same amount.

[0068] The superior performance of this invention is due to the optimized structure's three-dimensional anisotropic thermal conductivity. Heat tends to be rapidly transported radially along the highly thermally conductive aluminum alloy skeleton, rather than slowly diffused in the low thermal conductivity concrete.

[0069] In addition, Table 2 presents the robustness analysis: Table 2

[0070] Even under extreme conditions (assuming that actual processing causes the thermal conductivity of the rib itself to drop from 200 to 150 W / (m·K)), the effective thermal conductivity of the present invention remains at 23 W / (m·K), which is still better than that of the undegraded conventional rectangular rib (22.1 W / (m·K)), proving that the structure has extremely strong engineering stability and fault tolerance.

[0071] In summary, the thermally conductive structure designed by the present invention through topology optimization can achieve an order-of-magnitude improvement in the overall thermal conductivity of the thermal storage device with a very small amount of high thermal conductivity material (<10%), thus solving the contradiction between cost and performance in large-scale thermal storage systems.

[0072] Those skilled in the art should understand that the technical features of the above embodiments can be combined in any way. For the sake of brevity, not all possible combinations of the technical features in the above embodiments have been described. However, as long as there is no contradiction in the combination of these technical features, they should be considered to be within the scope of this specification.

[0073] The above embodiments are merely illustrative of several implementations of the present invention, and their descriptions are relatively specific and detailed, but they should not be construed as limiting the scope of the present invention. It should be noted that those skilled in the art can make various modifications and improvements without departing from the concept of the present invention, and these all fall within the protection scope of the present invention. Therefore, the protection scope of the present invention should be determined by the appended claims.

Claims

1. A heat-conducting structure based on topology optimization, characterized in that, include: Heat exchange pipes, which are used to circulate heat exchange working fluid; as well as A plurality of heat-conducting fins are arranged at intervals along the axial direction of the heat exchange pipe and fixedly connected to the outer wall of the heat exchange pipe. The heat-conducting fins are made of a high thermal conductivity material, and their geometry is an irregular branch structure generated based on density-based topology optimization. The irregular branch structure extends radially outward from the heat exchange pipe as the center, forming multiple main heat paths and secondary heat conduction paths formed by the branching of the main heat paths, so as to minimize the average temperature of the heat storage area under a limited material volume fraction.

2. The topology-optimized heat conduction structure as described in claim 1, characterized in that, Each of the heat-conducting fins is a three-dimensional geometric structure, which is formed by stretching a planar shape generated by two-dimensional topology optimization along the axial direction of the heat exchange pipe. The thickness of the heat-conducting fins and the spacing between adjacent heat-conducting fins remain consistent throughout the heat-conducting structure.

3. The topology-optimized heat conduction structure as described in claim 1, characterized in that, The volume fraction of the thermally conductive fins in the thermal storage unit of the solid thermal storage device does not exceed 10%, and the thermal conductivity of the thermally conductive fins is at least 100 times that of the thermal conductivity of the thermal storage material in the solid thermal storage device.

4. The heat conduction structure based on topology optimization as described in claim 1, characterized in that, The heat-conducting fins are fixedly connected to the heat exchange pipe by fasteners, and a flexible high thermal conductivity pad is provided between the contact surfaces of the heat-conducting fins and the heat exchange pipe. The flexible high thermal conductivity pad is used to fill the contact gap to enhance heat transfer.

5. A topology-optimized heat conduction structure as described in claim 1, characterized in that, The outer contour of the heat-conducting fins is adapted to the geometric boundary of the heat storage unit, which is a square or a regular hexagon, so that the multiple heat exchange pipes and their corresponding heat-conducting structures can be arranged in a close array in the heat storage device.

6. A design method for a topology-optimized thermal conductive structure as described in any one of claims 1-5, characterized in that, Includes the following steps: S1. Establish the geometric model: Determine the outer contour of the thermal storage unit and the central pipe area, and define the design domain; S2. Set up the topology optimization density model: Introduce control variables and perform filtering and projection processing on the control variables to obtain the physical density variables; S3. Set up a solid heat transfer model: Based on the physical density variable, use a material interpolation model to interpolate between the thermal conductivity of the heat storage material and the thermal conductivity of the fin material to construct a steady-state heat transfer equation that includes the internal heat source. S4. Set up the research configuration: take minimizing the average temperature within the design domain as the objective function, take the volume fraction of high thermal conductivity material as the constraint, and use the moving asymptote algorithm to iteratively solve the objective function; S5. Generate Structure: Extract the region in the solution result where the physical density variable is greater than the preset threshold, obtain the two-dimensional rib shape, and stretch it into a three-dimensional solid structure.

7. The design method as described in claim 6, characterized in that, In step S2, the filtration process employs a Helmholtz partial differential equation filter, which eliminates the checkerboard effect by controlling the filtration radius; The projection processing uses a hyperbolic tangent projection function, which maps the filtered variables to the two poles of 0 or 1 by adjusting the projection slope, so as to obtain clear structural boundaries.

8. The design method as described in claim 6, characterized in that, In step S3, the material interpolation model adopts the solid isotropic material penalty model; in the steady-state heat transfer equation, the thermal conductivity is a function of the physical density variable. When the physical density variable approaches 0, the thermal conductivity approaches the low thermal conductivity of the heat storage material; when the physical density variable approaches 1, the thermal conductivity approaches the high thermal conductivity of the fin material.

9. The design method as described in claim 6, characterized in that, In step S3, the boundary conditions set include: The outer boundary of the design domain is an adiabatic boundary, and the inner boundary of the central pipe region is a constant temperature boundary.

10. The design method as described in claim 6, characterized in that, In step S4, the constraint condition is set as follows: The volume fraction of the high thermal conductivity material has a lower limit of 0.05 and an upper limit of 0.1; in step S5, the preset threshold is 0.5, and the extracted two-dimensional rib shape is used for metal casting or die casting molding process.

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