A thermal amplification super device and a multi-scale topological optimization design and preparation method thereof

Abstract

The present application belongs to the technical field of thermal metamaterial design, and discloses a thermal amplification super device and a multiscale topological optimization design and preparation method thereof, which comprises the following steps: (1) at a macro scale, based on the shape and amplification factor of a thermal amplification device to be optimized, a thermal conduction tensor required in the thermal amplification super device is calculated by using a region transformation thermal method; (2) at a micro scale, a microstructure topological optimization model with a set thermal conduction tensor is established, and then a corresponding microstructure configuration is topologically optimized based on the microstructure topological optimization model and the thermal conduction tensor required in the thermal amplification super device. The thermal amplification super device designed by the present application has a specific structure by using cross-scale topological optimization amplification design, and has high design freedom.

Description

Technical Field

[0001] This invention belongs to the technical field of thermal metamaterial design, and more specifically, relates to a thermally amplified metadevice and its multi-scale topology optimization design and fabrication method. Background Technology

[0002] Thermal metamaterials are a new type of artificially designed structural material with extraordinary thermal properties not found in conventional materials, offering significant advantages in controlling heat flow. In recent years, with the development of transformation thermal and scattering cancellation methods, a series of powerful thermal metadevices have been designed based on thermal metamaterials, such as thermal cloaks, thermal concentrators, thermal spinners, thermal camouflage, thermal diodes, and thermal amplification devices.

[0003] Generally speaking, thermal amplification devices guide heat flow by designing special material structures, enabling line heat sources to generate a larger uniform temperature field through thermal amplification materials. The structural configuration of traditional thermal amplification devices is the same as that of thermal stealth devices, which means that thermal amplification devices can be designed by recombining the background material and internal structure of thermal stealth devices. Therefore, thermal amplification devices evolved from thermal stealth devices have an inherent defect: when the background material is changed, the thermal function of thermal amplification devices will be lost. Summary of the Invention

[0004] To address the above-mentioned deficiencies or improvement needs of existing technologies, this invention provides a thermal amplification superdevice and its multi-scale topology optimization design and fabrication method. It adopts cross-scale topology optimization design of the thermal amplification superdevice structure and fabricates the thermal superdevice based on additive manufacturing technology.

[0005] To achieve the above objectives, according to one aspect of the present invention, a multi-scale topology optimization design method for thermal amplification superdevices is provided, the method mainly comprising the following steps:

[0006] (1) On a macroscopic scale, based on the shape and amplification factor of the thermal amplification device to be optimized, the required thermal conduction tensor inside the thermal amplification device is calculated by the region transformation thermal method.

[0007] (2) At the microscale, a microstructure topology optimization model with a set thermal conductivity tensor is established, and then the corresponding microstructure configuration is designed based on the microstructure topology optimization model and the thermal conductivity tensor required inside the thermal amplification device.

[0008] Furthermore, the relationship between the heat conduction tensor in the virtual space and the transformed space satisfies the following equation:

[0009]

[0010]

[0011]

[0012] Among them κ o κ and κ′ are the heat conduction tensors in the virtual space and the transformed space, respectively. T and T′ are the temperature distributions in the virtual space and the transformed space, respectively. J is the Jacobian transformation matrix from the virtual space to the transformed space.

[0013] Furthermore, the region transformation thermal method transforms the design region by dividing it into triangles. The thermal conductivity tensor between triangle ΔABD in the virtual space and the triangular region ΔA'B'E' in the transformed space has the following relationship:

[0014]

[0015] Among them, (x A ,y A ), (x B ,y B ), (x C ,y C ), (x′ A′ ,y′ A′ ), (x′ B′ ,y′ B′ ) and (x′ E′ ,y′ E′ ) are the vertex coordinates of triangles ΔABD and ΔA'B'E', respectively.

[0016] Furthermore, the mathematical expression for the microstructure topology optimization model is:

[0017] Find: ρ1, ρ2, ... ρ N

[0018]

[0019]

[0020]

[0021]

[0022]

[0023] Where V is the total volume of the microstructure, N is the total number of finite elements, and ρ e It is a design variable; κ(ρ) e The thermal conductivity of each unit is represented by ), which is determined by material 1, material 2, and the penalty coefficient p. It is a unit heat conduction matrix; It is the temperature vector at each unit node, calculated by applying a test heat flux to each unit, T e The vector represents the local temperature field, calculated by applying a test heat flux to the entire microstructure. T is the global temperature vector of the microstructure, and N is the shape function in the finite element analysis. C is the objective function of the topology optimization model, and G is the constraint function of the topology optimization model, determined by f(.). f(.) is a continuous function used to balance the homogenization heat conduction tensor. and target heat conduction tensor The error of each component, ε is a positive number.

[0024] Furthermore, based on the vertex coordinates of the triangle, the Jacobian matrix is ​​calculated using the following formula.

[0025]

[0026] Where (x) A ,y A ),(x B ,y B ),(x C ,y C ),(x′ A′ ,y′ A′ ),(x′ B′ ,y′ B′ ) and (x′ E′ ,y′ E′ ) are the coordinates of the vertices of triangles ΔABD and ΔA'B'E', respectively;

[0027] Then, substituting the Jacobian matrix into the following formula, the required heat conduction tensor can be calculated:

[0028]

[0029] The present invention also provides a method for fabricating a thermal amplification super-device. The method uses the multi-scale topology optimization design method for thermal amplification super-devices described above to design the microstructure configuration of the thermal amplification super-device, and then uses additive manufacturing to fabricate the thermal amplification device. The thermal amplification device is a background-independent thermal amplification device.

[0030] Furthermore, the substrate of the thermally magnified metamaterial printed by additive manufacturing technology uses polydimethylsiloxane as the filler material.

[0031] Furthermore, the background material for the thermal amplification device was selected with a thermal conductivity of 13 W / m². -1 K -1 A 5mm thick solid silicone sheet.

[0032] Furthermore, the thermal conductivity of the filler between the background material and the metamaterial is 13 W / m². -1 K -1 Semi-solid thermal grease.

[0033] The present invention also provides a thermal amplification super device, which is prepared by the thermal amplification super device preparation method described above.

[0034] In summary, compared with the prior art, the thermal amplification super-device and its multi-scale topology optimization design and fabrication method provided by this invention mainly have the following advantages:

[0035] Beneficial effects:

[0036] 1. The thermal amplification super-device designed in this invention adopts a cross-scale topology optimization amplification design for its specific structure, which has a high degree of design freedom.

[0037] 2. The thermal amplification device designed in this invention can overcome the dependence of traditional thermal amplification devices on background materials and can maintain the thermal amplification function under any background material.

[0038] 3. The thermal amplification super-device designed in this invention can be reliably and precisely fabricated based on additive manufacturing technology.

[0039] 4. The substrate of the thermal amplification super-device designed in this invention can be made of high thermal conductivity materials such as aluminum alloy and pure copper, which increases the flexibility of the design.

[0040] 5. The thermal amplification superdevice designed in this invention can be filled with liquid organic polymers such as polydimethylsiloxane and then cured, eliminating contact thermal resistance and providing convenience for the realization of metamaterial multi-scale structures.

[0041] 6. The design method proposed in this invention can be used to design two-dimensional and three-dimensional thermal amplification super devices, and the fabricated super devices are applicable to both steady-state and transient conditions, and have universality. Attached Figure Description

[0042] Figure 1 This is a flowchart illustrating a multi-scale topology optimization design method for a thermally amplified super-device provided by the present invention;

[0043] Figure 2 'a' in the text is Figure 1 Schematic diagram related to the multi-scale topology optimization design of thermally amplified metamaterials in the image; b and c are thermally amplified metamaterials under different backgrounds;

[0044] Figure 3 In the figure, 'a' represents the simulation results of the thermal double amplifier device in a continuous medium under pure material conditions; 'b', 'c', and 'd' represent the simulation results of the thermal double amplifier device in a continuous medium under different background materials.

[0045] Figure 4 In the figure, 'a' represents the simulation results of the thermal triple amplifier device in a continuous medium under pure material conditions; 'b', 'c', and 'd' represent the simulation results of the thermal triple amplifier device in a continuous medium under different background materials.

[0046] Figure 5 In the figure, 'a' represents the simulation results of the thermal double amplifier device in a continuous medium under a multi-scale structure; 'b', 'c', and 'd' represent the simulation results of the thermal double amplifier device in a continuous medium under different background materials.

[0047] Figure 6 In the figure, 'a' represents the simulation results of the thermal triple amplifier device in a continuous medium under a multi-scale structure; 'b', 'c', and 'd' represent the simulation results of the thermal triple amplifier device in a continuous medium under different background materials.

[0048] Figure 7 In the diagram, a, b, and c represent the experimental schematic, the 3D printed substrate, and the experimental temperature field results, respectively. Detailed Implementation

[0049] To make the objectives, technical solutions, and advantages of this invention clearer, the invention will be further described in detail below with reference to the accompanying drawings and embodiments. It should be understood that the specific embodiments described herein are merely illustrative and not intended to limit the invention. Furthermore, the technical features involved in the various embodiments of this invention described below can be combined with each other as long as they do not conflict with each other.

[0050] Please see Figure 1 This invention provides a multi-scale topology optimization design method for thermal amplification superdevices, the method mainly including the following steps:

[0051] Step 1: On a macroscopic scale, based on the shape and amplification factor of the thermal amplification device to be optimized, the required thermal conductivity tensor inside the thermal amplification device is calculated using the region transformation thermal method.

[0052] The relationship between the heat conduction tensor in virtual space and transformed space satisfies the following equation:

[0053]

[0054]

[0055]

[0056] Among them κ o κ and κ′ are the heat conduction tensors in the virtual space and the transformed space, respectively. T and T′ are the temperature distributions in the virtual space and the transformed space, respectively. J is the Jacobian transformation matrix from the virtual space to the transformed space.

[0057] The region transformation thermal method transforms the design region by dividing it into triangles. The thermal conductivity tensor between triangle ΔABD in the virtual space and the triangular region ΔA'B'E' in the transformed space has the following relationship:

[0058]

[0059] Among them, (x A ,y A ), (x B ,y B ), (x C ,y C ), (x′ A′ ,y′ A′ ), (x′ B′ ,y′ B′ ) and (x′ E′ ,y′ E ′) are the coordinates of the vertices of the triangle.

[0060] Step 2: At the microscale, establish a microstructure topology optimization model with a set thermal conductivity tensor, and then design the corresponding microstructure configuration based on the microstructure topology optimization model and the thermal conductivity tensor required inside the thermal amplification super device.

[0061] The mathematical expression for the microstructure topology optimization model is:

[0062] Find: ρ1, ρ2, ... ρ N

[0063]

[0064]

[0065]

[0066]

[0067]

[0068] Where V is the total volume of the microstructure, N is the total number of finite elements, and ρ e It is a design variable; κ(ρ) e The thermal conductivity of each unit is represented by ), which is determined by material 1, material 2, and the penalty coefficient p. It is a unit heat conduction matrix; It is the temperature vector at each unit node, calculated by applying a test heat flux to each unit, T eThe vector represents the local temperature field, calculated by applying a test heat flux to the entire microstructure. T is the global temperature vector of the microstructure, and N is the shape function in the finite element analysis. C is the objective function of the topology optimization model, and G is the constraint function of the topology optimization model, determined by f(.). f(.) is a continuous function used to balance the homogenization heat conduction tensor. and target heat conduction tensor The error of each component, ε, is a very small positive number.

[0069] This invention also provides a method for fabricating a thermal amplification super-device. The method employs the multi-scale topology optimization design method described above to design the microstructure configuration of the thermal amplification super-device, and then uses additive manufacturing to fabricate the thermal amplification device. The thermal amplification device is a background-independent thermal amplification device. Specifically, the thermal amplification super-material substrate printed using additive manufacturing technology is used as a filler material to fabricate the thermal amplification super-device.

[0070] The present invention also provides a thermal amplification super device, which is prepared by the thermal amplification super device preparation method described above.

[0071] To verify the feasibility of the multi-scale topology optimization design and fabrication method for a background material-independent thermal amplification superdevice proposed in this invention, numerical simulations and experimental verifications were conducted on typical thermal amplification superdevices. The main steps included:

[0072] Step 1: (1) On a macroscopic scale, based on the shape and amplification factor of the thermal amplification device, the required thermal conductivity tensor inside the thermal amplification device is calculated using the region transformation thermal method.

[0073] For simplicity without loss of generality, consider a two-dimensional case. Figure 2 This diagram illustrates the transformation of the thermal amplification superdevice design region, where the thermal amplification factor is determined by the ratio of A'B' to E'F'. To achieve the thermal amplification effect, the design region is divided into two triangular sub-regions, and ΔABD and ΔBCD in the virtual space are mapped to ΔA'B'E' and ΔB'F'E' in the transformation space, respectively. Based on the vertex coordinates of the triangles, the Jacobian matrix can be calculated using the following formula.

[0074]

[0075] Where (x) A ,y A ),(x B ,y B ),(x C ,y C ),(x′ A′ ,y′A′ ),(x′ B′ ,y′ B′ ) and (x′ E′ ,y′ E′ ) are the coordinates of the vertices of the triangle.

[0076] Then, substituting the Jacobian matrix into the following formula, the required heat conduction tensor can be calculated:

[0077]

[0078] Based on the above formulas, given the corresponding coordinate points, the required thermal conduction tensor distributions for each region of the thermal double-amplification and triple-amplification superdevices are shown in Tables 1 and 2.

[0079] Table 1 Design parameters of thermal double-amplification superdevice

[0080]

[0081] Table 2 Design parameters for thermal triple-amplification superdevice

[0082]

[0083] Step 2: At the microscale, establish a microstructure topology optimization model with a specific thermal conductivity tensor, and design the corresponding microstructure configuration based on the required thermal conductivity tensor topology optimization.

[0084] In this embodiment, the constructed microstructure topology optimization design model is as follows:

[0085]

[0086] Where V represents the total volume of the microstructure, N represents the total number of finite elements, and ρ e Represents design variables; κ(ρ) e The thermal conductivity of each unit is represented by ), which is determined by material 1, material 2, and the penalty coefficient p. It is a unit heat conduction matrix; It is the temperature vector at each element node, calculated by applying a test heat flux to each element, T e The vector represents the local temperature field, calculated by applying a test heat flux to the entire microstructure. T is the global temperature vector of the microstructure, and N is the shape function in the finite element analysis. C is the objective function of the topology optimization model, and G is the constraint function of the topology optimization model, determined by f(.). f(.) is a continuous function used to balance the homogenization heat conduction tensor. and target heat conduction tensor The error of each component, ε, is a very small positive number.

[0087] Step 3: The substrate for thermal amplification metamaterials was fabricated using 3D printing technology. Using polydimethylsiloxane as the filler material, thermal amplification metadevices were prepared. The functionality of the thermal amplification metadevices was tested through continuous medium simulation, equivalent medium simulation, and thermal experiments, verifying the feasibility of the design of this invention.

[0088] First, based on the required thermal conductivity tensor, a continuous medium simulation was conducted in COMSOL Multiphysics software. In the continuous medium simulation, the temperatures of the left and right boundaries were set to 363K and 273K, respectively, and the other boundaries were set to be thermally insulated. Figure 3 and Figure 4 The simulation results of the thermal amplification device in continuous media under different background materials are presented. The simulation results show that the thermal amplification device can maintain good amplification function regardless of the background material.

[0089] Then, using the thermal conductivity tensors calculated in Tables 1 and 2 as the target thermal conductivity tensors, topology optimization design was performed based on the aforementioned topology optimization model. Copper and polydimethylsiloxane were selected as the materials for optimization, with the microstructure size set to 5mm × 5mm and the finite element mesh divided into 200 × 200 sections. After obtaining the optimal microstructures for each region, the microstructures were periodically arrayed, and then the arrayed microstructures were trimmed and assembled, ultimately resulting in thermally doubled and tripled metamaterial structures, as shown below. Figure 5 and 6 As shown in the figure. After obtaining the thermally amplified metamaterial structure, an equivalent medium simulation was then performed in COMSOL Multiphysics software. The boundary conditions for the equivalent medium simulation were kept the same as those for the continuous medium simulation. After simulation calculation, the final steady-state simulation results are as follows. Figure 5 and Figure 6 As shown in the figure, it can be seen that the results of the equivalent medium simulation are similar to those of the continuous medium simulation.

[0090] Finally, the thermally amplified metamaterial device was fabricated and thermal experiments were conducted. In this invention, the designed multi-scale structure was longitudinally stretched to a thickness of 5 mm, its STL model was derived, and a thermally amplified metamaterial substrate was additively fabricated, such as... Figure 7 As shown in b. After printing the thermal amplification metamaterial substrate, it was placed in a container made of acrylic sheet. Polydimethylsiloxane was poured into the container, and after vacuum degassing, uniform heating, and trimming of excess material, the thermal amplification metamaterial used in the experiment was completed. Next, the thermal amplification device was fabricated. The background material selected for the device was a material with a thermal conductivity of 13 W / m². -1 K -1 A 5mm thick solid silicone sheet is used; this silicone is relatively soft and can be easily cut into various shapes with a knife. To reduce contact thermal resistance, a material with a thermal conductivity of 13 W / m² is filled between the background silicone and the metamaterial.-1 K -1 The semi-solid thermal conductive grease is then used, thus completing the fabrication of the entire thermal amplification super device.

[0091] The fabrication process of the thermal amplification device was briefly described above. Following this, experimental testing of the device's performance was conducted. In the experiment, the entire thermal amplification device was embedded in an insulating foam to reduce the influence of air convection. The heat source and cold source were respectively heated by a heating element and cooled by a cooler at both ends of the thermal amplification device. The temperature was controlled by thermocouples and maintained at the same temperature as the simulation boundary. The temperature field of the entire thermal amplification device was recorded by a thermal infrared camera fixed above the device, such as... Figure 7 As shown in 'a'. In the experiment, to ensure that the thermal emissivity of the entire thermal amplification device was the same, a layer of black, 0.1 mm thick PVC tape was covered over the entire device surface. The experiment began when the heat source and cold source were operating. When the temperature distribution of the entire thermal amplification device remained essentially unchanged, the temperature field at this time was recorded as shown in 'a'. Figure 7 As shown in c in the figure. The temperature distribution shows that the experimentally obtained temperature field is basically similar to the simulated temperature field, indicating that the thermal amplification device exhibits thermal amplification functionality.

[0092] Those skilled in the art will readily understand that the above description is merely a preferred embodiment of the present invention and is not intended to limit the present invention. Any modifications, equivalent substitutions, and improvements made within the spirit and principles of the present invention should be included within the scope of protection of the present invention.

Claims

1. A multi-scale topology optimization design method for thermal amplification superdevices, characterized in that, The method includes the following steps: (1) On a macroscopic scale, based on the shape and amplification factor of the thermal amplification device to be optimized, the required thermal conduction tensor inside the thermal amplification device is calculated using the region transformation thermal method; (2) At the microscale, a microstructure topology optimization model with a set thermal conductivity tensor is established, and then the corresponding microstructure configuration is designed based on the microstructure topology optimization model and the thermal conductivity tensor required inside the thermal amplification device. The region transformation thermal method transforms the design region by dividing it into triangles. The thermal conductivity tensor between triangle ΔABD in the virtual space and the triangular region ΔA'B'E' in the transformed space has the following relationship: in, , , , , and These are the coordinates of the vertices of triangles ΔABD and ΔA'B'E', respectively. The mathematical expression for the microstructure topology optimization model is: in V It is the overall volume of the microstructure. N It is the total number of finite elements. These are design variables; The thermal conductivity of each unit is represented by material 1, material 2, and a penalty coefficient. p Decide; It is a unit heat conduction matrix; It is the temperature vector at each unit node, calculated by applying a test heat flux to each unit. The vector represents the local temperature field, which is calculated by applying a test heat flux to the entire microstructure. T is the global temperature vector of the microstructure, and N is the shape function in the finite element analysis. C This is the objective function of the topology optimization model. G These are the constraint functions of the topology optimization model, derived from... Decide; It is a continuous function used to balance the homogenization of the heat conduction tensor. and target heat conduction tensor The error of each component, It is a positive number.

2. The multi-scale topology optimization design method for thermal amplification superdevices as described in claim 1, characterized in that: The relationship between the heat conduction tensor in virtual space and transformed space satisfies the following equation: in and These are the heat conduction tensors in virtual space and transformation space, respectively. and Let be the temperature distributions in the virtual space and the transformed space, respectively, and J be the Jacobian transformation matrix from the virtual space to the transformed space.

3. The multi-scale topology optimization design method for thermal amplification superdevices as described in claim 2, characterized in that: The Jacobian matrix can be calculated using the following formula based on the vertex coordinates of the triangle. : in , , , , and These are the coordinates of the vertices of triangles ΔABD and ΔA'B'E', respectively. Then, substituting the Jacobian matrix into the following formula, the required heat conduction tensor can be calculated: 。 4. A method for fabricating a thermally amplified super-device, characterized in that: The preparation method uses the multi-scale topology optimization design method of thermal amplification super-devices according to any one of claims 1-3 to design the microstructure configuration of the thermal amplification super-device, and then uses additive manufacturing to prepare the thermal amplification device, wherein the thermal amplification device is a background-independent thermal amplification device.

5. The method for fabricating the thermal amplification super-device as described in claim 4, characterized in that: The substrate of the thermally magnified metamaterial was printed using additive manufacturing technology, with polydimethylsiloxane as the filler material.

6. The method for fabricating the thermal amplification super-device as described in claim 5, characterized in that: The background material for the thermal amplification device has a thermal conductivity of 13 W / m. -1 K -1 A 5mm thick solid silicone sheet.

7. The method for fabricating the thermal amplification super-device as described in claim 6, characterized in that: The thermal conductivity of the filler between the background material and the metamaterial is 13 W / m. -1 K -1 Semi-solid thermal grease.

8. A thermal amplification device, characterized in that: The thermal amplification super-device is prepared using the preparation method of the thermal amplification super-device according to any one of claims 4-7.

Images