TPMS (Tire Pressure Monitor System)-based porous material construction method with permeability controllable in all directions

Abstract

The invention discloses a method for constructing a porous material with permeability controllable in all directions based on a TPMS (Tire Pressure Monitor System). According to the method, the porous material with permeability controllable in all directions is constructed by adopting a three-period minimal curved surface (TPMS) and based on an analytical model of permeability and anisotropy indexes in combination with a parameter adjustment method and a composite unit method. Compared with a traditional method, the model generated through the method is controllable in permeability, can be well used for designing a TPMS structure, and meanwhile has the advantages of being simple, convenient to use and the like.

Description

Technical Field

[0001] The present invention belongs to the field of materials science, and particularly relates to a method for constructing a porous material with controllable permeability anisotropy based on TPMS. Background Art

[0002] Porous materials are composed of an interconnected pore network, and have advantages such as a large specific surface area and good permeability performance, and are widely used in fields such as aerospace, machinery, medicine, and chemical engineering. Among them, graphite porous materials are widely used in the fluid field. Porous materials applied to the fluid field usually have pore sizes in the μm level, a small porosity, and a large relative density. The internal pore structure distribution of common graphite porous materials is uneven and random, which restricts their application in scenarios with high-precision requirements such as air bearings.

[0003] In order to design a porous structure model with controllable and more excellent performance, the current mainstream porous structure modeling methods mainly include the CAD method, the packing method based on topology optimization, the Voronoi method, and the TPMS method. The CAD method is limited by the constructed basic pore unit, and may not guarantee connectivity and periodicity in three-dimensional space. The packing method based on topology optimization is currently only applied to mechanical application scenarios, and the topology optimization of fluid application scenarios is very challenging. Although the Voronoi method can control the pore size, the internal structure of the constructed model is still irregular. Moreover, for the case where the model size is very large or the internal structure is very small, the Voronoi method is not applicable. In contrast, to construct a porous material model with controllable internal microstructure, the TPMS method is a better choice.

[0004] Traditional graphite porous materials often have the characteristic of permeability anisotropy, and the TPMS structure also has this problem. In this periodic structure of TPMS, the size and direction distribution of its ligaments are regular, which leads to a directional dependence of the permeability performance of the TPMS structure, and the structure has obvious strong and weak permeability directions. The anisotropy of permeability will cause different fluid flow rates through the material in different directions, and differences in pressure and wall shear stress will be generated in different regions of the material due to the differences in flow rates. In fluid application scenarios, anisotropy is a non-negligible defect. Summary of the Invention

[0005] The purpose of the present invention is to overcome the deficiencies of the prior art, and provides a method for constructing a porous material with controllable permeability anisotropy, which is based on the TPMS lattice and combines an analytical model of the permeability and anisotropy index of the TPMS structure, can be well used for various researches such as microfluidics and air bearing directions, and has the characteristics of simple method and fast use.

[0006] The object of the present invention is achieved by the following technical solutions:

[0007] A method for constructing a porous material with controllable permeability in all directions based on TPMS, comprising the following steps:

[0008] S1. Select a certain number of combinations of structural parameters to construct a TPMS porous structure sample.

[0009] S2. Use CFD to perform a flow field simulation on the TPMS structures with different structural parameters to obtain the permeability in each direction of the structure.

[0010] S3. Establish an analytical model for the permeability and permeability anisotropy index of the TPMS porous structure.

[0011] S4. Combine the analytical model and construct a porous material with controllable permeability in all directions through the structural parameter adjustment method and the composite unit method.

[0012] Furthermore, the step S1 includes the following sub-steps:

[0013] S11. Apply an implicit function that is periodic in three different directions to construct a TPMS surface. The TPMS equation is as follows:

[0014] TPMS: f(x, y, z) = C

[0015] Where C is a structural parameter that determines the geometric shape of the TPMS unit and represents the distance of the surface from the center point of the unit.

[0016] Offset the original TPMS surface by a certain distance in the positive and negative directions of the curvature Then close the two surfaces to obtain a TPMS porous structure with a wall thickness of W. Divide the structure into a pore part and a solid part through Boolean operations.

[0017] S12. For the structural parameters W and C, select a certain number of parameter combinations and use the method of step S11 to construct a TPMS porous model and establish a model sample library.

[0018] Furthermore, the step S2 includes the following sub-steps:

[0019] S21. Import the TPMS model into the flow field analysis software, set multiple groups of pressure difference boundary conditions, use the software for simulation, and then extract the flow rate data at the inlet and outlet of the model;

[0020] S22. The fluid flow of the TPMS structure satisfies Darcy's law. Calculate the permeability K of the TPMS structure using the volume flow rate at the inlet. When there are m groups of inlet and outlet flow rate data, take the logarithm of the pressure difference ΔP and the volume flow rate Q, and use the following formula to calculate the permeability:

[0021]

[0022] Wherein, A is the gas supply area (m2), η is the gas viscosity, and H is the total thickness of the structure.

[0023] S23. Change the positions of the fluid inlet and outlet of the TPMS structure, and repeat the operations in steps S21 to S22 to obtain the permeabilities in different directions of the structure.

[0024] Further, the step S3 includes the following sub-steps:

[0025] Combining Darcy's law and the Hagen-Poiseuille formula, it can be known that the permeability of the TPMS structure is proportional to the square of the wall thickness W. Considering the influence of the parameter C on the permeability, an analytical model of the permeability of the TPMS structure is proposed:

[0026] K = m·W 2 +(W - n)(C - (W - o)) 2 +p·(C - (W - o)) + q

[0027] Wherein, W is the wall thickness of the TPMS structure, C is the parameter C in the implicit equation of the TPMS, and m, n, o, p, and q are constants.

[0028] Considering the permeability differences in three directions, namely the vertical permeability Kz, the horizontal permeability Kx, and the permeability Kyz at an oblique angle of 45 degrees, the permeability anisotropy index A is defined as:

[0029]

[0030] The analytical model of the anisotropy index A is:

[0031]

[0032] Wherein, α, β, γ, δ, ε, are all constants.

[0033] Further, the step S4 includes the following sub-steps:

[0034] S41. Substitute the permeability data obtained in step S23 into the analytical models of the permeability K and the anisotropy index A in step S3 to calculate the values of each coefficient in the analytical model;

[0035] S42. If the surface of the anisotropy index A intersects with the plane A = 0, the method for constructing a material with controllable permeability in each direction by using the structural parameter adjustment method is as follows:

[0036] Solve the intersection line of the surface of the anisotropy index A and the plane A = a, where a is the specified degree of permeability anisotropy. When a = 0, all combinations of structural parameters on the intersection line satisfy isotropic permeability. Project the intersection line onto the permeability K surface to obtain the relationship between the combination of structural parameters on the intersection line and the permeability, and then the structural parameters W and C corresponding to the TPMS structure with the specified permeability and degree of anisotropy can be obtained.

[0037] S43. If the surface of the anisotropy index A and the plane A = 0 have no intersection points, the method for constructing a material with controllable permeability anisotropy using the composite structure method is as follows:

[0038] Select one structure with A > 0 and one structure with A < 0 for the anisotropy index A, and use the following formula to composite the two TPMS units to obtain a composite structure with the specified degree of permeability anisotropy.

[0039]

[0040] Among them, A1 and A2 are the permeability anisotropy indices of unit 1 and unit 2 respectively, u is the proportion of unit 1, with a value in the range of [0, 1], a is the specified degree of permeability anisotropy, f 1 and f 2 are the equations of the two TPMS units respectively.

[0041] The beneficial effects of the present invention are as follows: The present invention adopts triply periodic minimal surfaces (TPMS), based on the analytical models of permeability and anisotropy index, and combines the parameter adjustment method and the composite unit method to construct porous materials with controllable permeability anisotropy. Compared with traditional methods, the model generated by the present invention has controllable permeability performance and can be well used for the design of TPMS structures. At the same time, it also has the characteristics of simple method and fast use. Description of the Drawings

[0042] Figure 1 It is a flowchart of the method for constructing a porous material with controllable permeability anisotropy based on TPMS of the present invention.

[0043] Figure 2 It is a TPMS porous model diagram of the present invention.

[0044] Figure 3 It is a flow velocity distribution diagram of the TPMS porous structure of the present invention.

[0045] Figure 4 It is a permeability controllable model constructed by the parameter adjustment method of the present invention.

[0046] Figure 5 It is a permeability controllable model constructed by the composite unit method of the present invention. Detailed Embodiments

[0047] The present invention will be further described below in conjunction with the accompanying drawings.

[0048] As Figure 1 shown, the method for constructing a porous material with controllable permeability anisotropy based on TPMS of the present invention includes the following steps:

[0049] S1. Select a certain number of combinations of structural parameters to construct a TPMS porous structure sample; specifically, it includes the following sub-steps:

[0050] S11. Use an implicit function that has periodicity in three different directions to construct a TPMS surface. The TPMS equation is as follows:

[0051] TPMS: f(x, y, z) = C (1)

[0052] where C is a structural parameter that determines the geometric shape of the TPMS unit and represents the distance of the surface from the center point of the unit.

[0053] Offset the original TPMS surface by a certain distance in both the positive and negative directions of the curvature Then close the two surfaces to obtain a TPMS porous structure with a wall thickness of W. Divide the structure into a pore part and a solid part through Boolean operation. The constructed TPMS porous structure is as Figure 2 shown.

[0054] S12. For the structural parameters W and C, select a certain number of parameter combinations and use the method of step S11 to construct a TPMS porous model and establish a model sample library.

[0055] S2. Use CFD to perform a flow field simulation on the TPMS structures with different structural parameters to obtain the permeability in each direction of the structure; specifically, it includes the following sub-steps:

[0056] S21. Import the TPMS model into the flow field analysis software, set multiple groups of pressure difference boundary conditions, and use the software for simulation. Figure 3 This is the internal streamline diagram of the TPMS structure obtained by simulation in this example. Then extract the flow rate data at the inlet and outlet of the model;

[0057] S22. The fluid flow of the TPMS structure satisfies Darcy's law. Calculate the permeability K of the TPMS structure using the volume flow rate at the inlet. When there are m groups of inlet and outlet flow rate data, take the logarithm of the pressure difference ΔP and the volume flow rate Q, and use the following formula to calculate the structure permeability:

[0058]

[0059] In the formula, A is the air supply area (m2), η is the gas viscosity, and H is the total thickness of the structure.

[0060] S23. Change the positions of the fluid inlets and outlets of the TPMS structure, and repeat the operations in steps S21 - S22 to obtain the permeabilities in different directions of the structure.

[0061] S3. Establish an analytical model for the permeability and the permeability anisotropy index of the TPMS porous structure; specifically, it includes the following sub - steps:

[0062] Combined with Darcy's law and the Hagen - Poiseuille formula, it can be known that the permeability of the TPMS structure is proportional to the square of the wall thickness W. Considering the influence of parameter C on the permeability, an analytical model for the permeability of the TPMS structure is proposed:

[0063] K = m·W 2 +(W - n)(C-(W - o)) 2 +p·(C-(W - o))+q (3)

[0064] where W is the wall thickness of the TPMS structure, C is the parameter C in the TPMS implicit equation, and m, n, o, p, q are constants.

[0065] Considering the permeability differences in three directions, namely the permeability Kz in the vertical direction, the permeability Kx in the horizontal direction, and the permeability Kyz at a 45 - degree oblique angle, the permeability anisotropy index A is defined as:

[0066]

[0067] The analytical model for the anisotropy index A is:

[0068]

[0069] where α, β, γ, δ, ε, are all constants.

[0070] Combined with the analytical model, construct a porous material with controllable permeability in each direction through the structural parameter adjustment method and the composite unit method. Specifically, it includes the following sub - steps:

[0071] S41. Substitute the permeability data obtained in step S23 into the analytical models of the permeability K and the anisotropy index A in step S3 to calculate the values of each coefficient in the analytical model;

[0072] S42. As Figure 4 shown, if the surface of the anisotropy index A intersects with the plane A = 0, the method for constructing a material with controllable permeability in each direction using the structural parameter adjustment method is as follows:

[0073] Solve the intersection line of the surface of the anisotropy index A and the plane A = a, where a is the specified degree of permeability anisotropy. When a = 0, all combinations of structural parameters on the intersection line satisfy isotropic permeability. Project the intersection line onto the permeability K surface to obtain the relationship between the combination of structural parameters on the intersection line and the permeability, and then the structural parameters W and C corresponding to the TPMS structure with the specified permeability and degree of anisotropy can be obtained.

[0074] S43. If the surface of the anisotropy index A and the plane A = 0 have no intersection points, the method for constructing a material with controllable permeability anisotropy using the composite structure method is as follows:

[0075] As Figure 5 shown, select one structure with A > 0 and one structure with A < 0 for the anisotropy index A, and use formula (6) to composite the two TPMS units to obtain a composite structure with the specified degree of permeability anisotropy.

[0076]

[0077] where A1 and A2 are the permeability anisotropy indices of unit 1 and unit 2 respectively, u is the proportion of unit 1, with a value in the range of [0, 1], a is the specified degree of permeability anisotropy, f 1 and f 2 are the equations of the two TPMS units respectively.

[0078] Those of ordinary skill in the art will realize that the embodiments here are to help readers understand the principles of the present invention and should be understood that the protection scope of the present invention is not limited to such specific statements and embodiments. Those of ordinary skill in the art can make various other specific deformations and combinations without departing from the essence of the present invention based on these technical revelations disclosed in the present invention, and these deformations and combinations are still within the protection scope of the present invention.

Claims

1. A method for constructing a porous material with controllable permeability in all directions based on TPMS, comprising the following steps: S1. Select a certain number of structural parameter combinations to construct TPMS porous structure samples. S2. Use CFD to simulate the flow field of TPMS structures with different structural parameters to obtain the permeability of the structure in all directions. S3. Establish an analytical model for the permeability and permeability anisotropy index of TPMS porous structure. S4. Combined with the analytical model, a porous material with controllable permeability in all directions is constructed through the structural parameter adjustment method and the composite unit method.

2. A method for constructing a porous material with controllable permeability based on TPMS according to claim 1, characterized in that: The step S1 comprises the following sub-steps: S11. A TPMS surface is constructed by applying an implicit function that is periodic in three different directions. The TPMS equation is as follows: TPMS:f(x,y,z)=C Where C is the structural parameter that determines the geometric shape of the TPMS unit, representing the distance of the curved surface from the center point of the unit. Offset the original TPMS surface along the positive and negative directions of the curvature by a certain distance Then the two surfaces are closed to obtain the TPMS porous structure with a wall thickness of W. The structure is divided into a pore part and a solid part by Boolean operation. S12. For the structural parameters W and C, a certain number of parameter combinations are selected to construct a TPMS porous model using the method of step S11, and a model sample library is established.

3. A method for constructing a porous material with controllable permeability based on TPMS according to claim 1, characterized in that: The step S2 comprises the following sub-steps: S21, importing the TPMS model into the flow field analysis software, setting multiple sets of pressure difference boundary conditions, using the software for simulation, and then extracting the flow data of the model inlet and outlet; S22. The fluid flow of the TPMS structure satisfies Darcy's law, and the permeability K of the TPMS structure is calculated using the volume flow rate at the inlet. When there are m sets of inlet and outlet flow data, the pressure difference ΔP and the volume flow rate Q are taken logarithmically, and the permeability is calculated using the following formula: Where A is the gas supply area (m2), η is the gas viscosity, and H is the total thickness of the structure. S23, changing the fluid inlet and outlet positions of the TPMS structure, repeating the operations of steps S21 to S22, and obtaining the permeability of the structure in different directions.

4. A method for constructing a porous material with controllable permeability based on TPMS according to claim 1, characterized in that: The step S3 comprises the following sub-steps: Combining Darcy's law and Hagen-Poiseuille formula, it can be seen that the permeability of the TPMS structure is proportional to the square of the wall thickness W. Considering the influence of parameter C on the permeability, the permeability analytical model of the TPMS structure is proposed: K=m·W 2 +(W-n)(C-(W-o)) 2 +p·(C-(W-o))+q Wherein, W is the wall thickness of the TPMS structure, C is the parameter C in the TPMS implicit equation, and m, n, o, p, and q are constants. Considering the permeability differences in three directions, namely the vertical permeability Kz, the horizontal permeability Kx, and the 45-degree oblique permeability Kyz, the permeability anisotropy index A is defined as: The analytical model of anisotropy index A is: Among them, α, β, γ, δ, ε, are all constants.

5. A method for constructing a porous material with controllable permeability based on TPMS according to claim 1, characterized in that: The step S4 comprises the following sub-steps: S41, bringing the permeability data obtained in step S23 into the analytical model of permeability K and anisotropy index A in step S3, and calculating the values ​​of each coefficient in the analytical model; S42. If the surface of the anisotropy index A has an intersection with the plane A=0, the method of constructing a material with anisotropic controllable permeability by using the structural parameter adjustment method is as follows: Solve the intersection of the surface of anisotropy index A and plane A = a, where a is the specified degree of anisotropy of permeability. When a = 0, all combinations of structural parameters on the intersection satisfy the isotropy of permeability. Project the intersection onto the permeability K surface to obtain the relationship between the combination of structural parameters on the intersection and the permeability, and then calculate the structural parameters W and C corresponding to the TPMS structure with the specified permeability and anisotropy. S43. If the surface of the anisotropy index A has no intersection with the plane A=0, the method of constructing a material with anisotropic controllable permeability by using the composite structure method is as follows: Select one structure with anisotropy index A>0 and one structure with anisotropy index A<0, and use the following formula to compound the two TPMS units to obtain a composite structure with a specified degree of permeability anisotropy. Among them, A1 and A2 are the permeability anisotropy indexes of unit 1 and unit 2 respectively, u is the proportion of unit 1, and its value is between [0,1], a is the specified degree of permeability anisotropy, and f1 and f2 are the equations of the two TPMS units respectively.

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