A dual-scale simulation method for a TPMS porous radiator

Abstract

The application discloses a double-scale simulation method for a TPMS porous radiator, and belongs to the technical field of energy system thermal management and high-performance chip heat dissipation. The method comprises the following steps: extracting a representative unit body of the TPMS radiator to perform pore-scale simulation, obtaining inherent permeability, Forscheimer coefficient and fluid-solid heat transfer coefficient by simulating the fluid-solid conjugate heat transfer process of the representative unit body, and obtaining solid and fluid effective thermal conductivities by simulating the pure heat conduction process of the representative unit body; and substituting the equivalent model parameters into a porous medium equivalent model to perform full-size macro-scale simulation on the radiator by using the porous medium equivalent model. The application avoids the complex geometric modeling and body grid division process in the CFD numerical simulation of the fluid-solid conjugate heat transfer process of the TPMS porous structure, breaks through the limitation of the number of TPMS porous structure units and the complexity of the shape that can be simulated by the traditional CFD method, and significantly reduces the calculation cost.

Description

Technical Field

[0001] This invention relates to the fields of thermal management of energy systems, thermal management of aerospace engineering, and heat dissipation technology of high-performance chips, and in particular to a two-scale simulation method for TPMS porous heat sinks. Background Technology

[0002] As high-power electronic devices and aerospace systems evolve towards higher parameters and longer lifespans, heat dissipation has become a key bottleneck restricting performance improvements. Traditional heat dissipation structures such as fins, heat pipes, and metal foams have long dominated industrial applications due to their mature technology and high reliability. However, their inherent geometric topologies are relatively simple and fixed, making it difficult to achieve further breakthroughs in heat transfer performance within limited spaces.

[0003] Triple Periodic Minimal Surfaces (TPMS) have been widely studied and applied in radiators and heat exchangers due to their excellent thermal performance and design flexibility. The overall structure of TPMS can be precisely controlled by implicit functions, and its smooth surface and highly interconnected pores provide an efficient and reliable solution for the geometric design of porous heat exchange components. A complete TPMS radiator or heat exchanger typically consists of a large number of TPMS units.

[0004] However, existing direct simulation methods for simulating TPMS heat sinks have the following shortcomings: First, the geometric modeling is complex. The geometric modeling of TPMS porous structures is technically complex. Some tiny edges and faces in the geometric model may cause mesh problems such as free edges, self-intersecting edges, multiple connections, and negative volumes.

[0005] Second, body-fit mesh generation is difficult. Generating a high-quality body-fit mesh may take more time than the actual CFD numerical solution. When the number of TPMS structural elements is large or the geometry is too complex, body-fit mesh generation is difficult.

[0006] Third, the computational cost is high. The required number of computational fluid dynamics (CFD) meshes is very large, the mesh generation process is complex, the computational cost is high, and the geometric preprocessing is cumbersome.

[0007] Fourth, the simulable scale is limited. Traditional CFD methods are severely limited in the number and shape complexity of TPMS porous structural units that can be simulated.

[0008] Therefore, there is an urgent need to develop a method that can efficiently and accurately simulate the heat transfer and flow characteristics of TPMS porous heat sinks in order to overcome the shortcomings of the existing technologies. Summary of the Invention

[0009] This invention aims to propose a dual-scale simulation method for TPMS porous heat sinks, which solves the problems of complex geometric modeling of TPMS porous structures, difficulty in body mesh generation, and limitations in the number and shape complexity of TPMS porous structure elements that can be simulated in the prior art.

[0010] This invention proposes a two-scale simulation method for TPMS porous heat sinks, including the following steps: S1, extracting representative unit cells of the TPMS heat sink, and obtaining the inherent permeability by simulating the fluid-structure conjugate heat transfer process of the representative unit cells. Fochheimer coefficient Fluid-structure heat transfer coefficient The effective thermal conductivity of the solid is obtained by simulating the pure heat conduction process of the representative unit. and fluid effective thermal conductivity S2, The inherent permeability obtained in step S1 Fochheimer coefficient Fluid-structure heat transfer coefficient Solid effective thermal conductivity and fluid effective thermal conductivity Substituting into the porous medium equivalent model, the TPMS heat sink is simulated at a full-size macroscale using the porous medium equivalent model.

[0011] Furthermore, in step S1, the governing equations used in the fluid-structure conjugate heat transfer process of the representative unit include: mass conservation equation: ; Momentum conservation equation: ; Energy conservation equation: ; in, For fluid density, For fluid velocity vector, For pressure, For fluid dynamic viscosity, The specific heat capacity at constant pressure of the fluid. For fluid temperature, Fluid thermal conductivity ， This is the volumetric heat source term.

[0012] Furthermore, in step S1, the fluid-structure conjugate heat transfer process of the representative unit is provided with periodic flow boundary conditions, and the same heat flow as the full-size TPMS radiator is provided at the bottom.

[0013] Further, in step S2, the formula for calculating the coolant mass flow rate of the representative unit is: ; in, This refers to the total mass flow rate of the coolant in a full-size TPMS radiator. For full-size TPMS heatsinks Length in the direction, denoted as the length of the representative unit in the x-direction.

[0014] Further, in step S2, the formula for calculating the inlet temperature of the representative unit is: ; ; ; in, REV reference fluid temperature, and These are the average temperatures of the coolant inlet and outlet of a full-size TPMS radiator, respectively. This represents the temperature rise of the REV reference fluid.

[0015] Further, in step S2, the inherent permeability And Fochheimer coefficient The following formula is used to fit the relationship between the pressure gradient and the velocity to determine: ; in, For the pressure drop of REV, For Darcy speed, The characteristic length of the representative unit.

[0016] Further, in step S2, the fluid-structure heat transfer coefficient The calculation formula is: ; in, The heat flux density at the bottom of the radiator. The volume of a representative unit. The mass-weighted average temperature of the fluid within a representative unit. The average temperature of the solid surface at the bottom of the representative unit is denoted as .

[0017] Further, in step S2, the effective thermal conductivity of the solid... and fluid effective thermal conductivity The calculation formulas are as follows: ; in, The cross-sectional area of ​​a representative unit cell. For heat flow vectors, The outward normal unit vector, and These are the thermal side surfaces of the fluid domain and the solid domain, respectively. , These represent the hot and cold side temperatures of the solid domain, respectively. , These represent the hot and cold side temperatures of the fluid domain, respectively.

[0018] Furthermore, in step S2, the flow model of the porous medium equivalent model adopts the Darcy-Lapwood-Forchheimer-Brinkman model, and the heat transfer model adopts the local thermal non-equilibrium model.

[0019] Further, in step S2, the governing equations of the porous medium equivalent model include: Continuity equation: ; Momentum equation: ; Fluid and solid energy equations: ; in, The porosity of a representative unit cell For solid density, The specific heat capacity at constant pressure of a solid. For solid temperature, and These are the volumetric heat source terms for the fluid domain and the solid domain, respectively.

[0020] The dual-scale simulation method for TPMS porous heat sinks of the present invention has the following advantages: This invention avoids complex geometric modeling and body-fitting mesh generation. By extracting representative unit cells to obtain equivalent parameters through pore-scale simulation, and then using an equivalent model of porous media for full-scale macroscopic simulation, it completely avoids the complex geometric modeling and body-fitting mesh generation process in CFD numerical simulation of fluid-solid conjugate heat transfer processes in TPMS porous structures.

[0021] Breaking through simulation scale limitations. This invention overcomes the limitations of traditional CFD methods in the number and shape complexity of porous TPMS structural units that can be simulated, enabling efficient simulation of TPMS heat sinks with arbitrary number of units and arbitrary complex shapes.

[0022] Significantly reduces computational costs. Compared to performing fine-mesh CFD simulations directly on full-size TPMS heat sinks, the dual-scale simulation method used in this invention greatly reduces the number of computational grids, significantly lowering computational costs and time.

[0023] This invention facilitates batch simulation and topology customization. It provides a new method for batch numerical simulation of laminar flow-solid conjugate heat transfer processes in porous TPMS structures with different morphologies, and helps to achieve efficient topology customization of porous TPMS structures for enhanced heat transfer. Attached Figure Description

[0024] The accompanying drawings are provided to further illustrate the invention and form part of the specification. They are used in conjunction with embodiments of the invention to explain the invention and do not constitute a limitation thereof. In the drawings: Figure 1 The diagram shown is a schematic of the original computational model of the full-size Gyroid-type TPMS heat sink in this invention.

[0025] Figure 2 The diagram shown is a representative unit of the Gyroid-type TPMS heat sink in this invention. Figure 2 (a) is the calculation model for the fluid-structure conjugate heat transfer process. Figure 2 (b) is the calculation model for a pure heat conduction process.

[0026] Figure 3 The diagram shows a simplified two-dimensional model for macroscopic simulation of the porous media equivalent model in this invention. Detailed Implementation

[0027] The technical solutions of the present invention will be clearly and completely described below with reference to the accompanying drawings of the embodiments of the present invention. Obviously, the described embodiments are only some embodiments of the present invention, and not all embodiments.

[0028] Example 1: This example uses a full-size Gyroid-type TPMS heat sink as an example to illustrate the dual-scale simulation method for TPMS multi-hole heat sinks provided by the present invention.

[0029] like Figure 1 As shown, in the original calculation model of the full-size Gyroid-type TPMS radiator, the heat flow enters the calculation domain from the bottom of the radiator, and the cooling medium enters from the mass flow inlet and flows out from the pressure outlet, carrying away the heat.

[0030] I. Extract representative unit cells for pore-scale simulation First, a representative unit cell (REV) of the heatsink is extracted for pore-scale simulation. For example... Figure 2 As shown, where Figure 2(a) The calculation is a fluid-solid conjugate heat transfer process with periodic flow boundary conditions set. The same heat flux as the full-size radiator is set at the bottom to obtain the inherent permeability. Fochheimer coefficient and fluid-structure heat transfer coefficient Figure 2 (b) The calculation is for the pure heat conduction process, used to obtain the effective thermal conductivity of the solid. and fluid effective thermal conductivity .

[0031] The governing equations used in the fluid-structure conjugate heat transfer process of a representative unit are shown in equations (1) to (3).

[0032] II. Calculation of Equivalent Model Parameters Coolant mass flow rate of this representative unit The result is obtained according to formula (7), where This refers to the total mass flow rate of the coolant in a full-size TPMS radiator.

[0033] Representative unit inlet temperature Calculated from equations (8) to (10), where The reference fluid temperature is the temperature of the representative unit cell. and These are the average temperatures of the coolant inlet and outlet of a full-size TPMS radiator, respectively. The temperature rise value is the reference fluid value of the representative unit.

[0034] equivalent parameters And Fochheimer coefficient The relationship between pressure gradient and velocity is determined by fitting equation (11), where The pressure drop of a representative unit. This refers to Darcy's speed.

[0035] parameter It is calculated from equation (12), where The volume of a representative unit. The mass-weighted average temperature of the fluid within a representative unit. The average temperature of the solid surface at the bottom of the representative unit is denoted as . and The values ​​are calculated from equations (13) and (14), respectively, where The cross-sectional area of ​​a representative unit cell. and These are the heat flux vector and the outward normal unit vector, respectively. and These are the thermal side surfaces of the fluid domain and the solid domain, respectively.

[0036] III. Conduct full-scale macroscopic simulation Substituting the above equivalent model parameters into the porous medium equivalent model, the porous medium equivalent model is used to perform a full-scale macroscopic simulation of the heat sink. For example... Figure 3 As shown, the macroscopic simulation uses a simplified two-dimensional model, with the inlet and outlet lengths remaining consistent with the original calculation model. The coolant flows in from the mass flow inlet, passes through the porous medium, is heated by the volumetric heat source, carries away heat, and flows out from the pressure outlet.

[0037] The flow model adopted is the Darcy-Lapwood-Forchheimer-Brinkman model, and the heat transfer model adopts the Local Thermal Nonequilibrium (LTNE) model. The governing equations are shown in equations (4) to (6).

[0038] By following the steps above, a two-scale simulation of a full-size Gyroid-type TPMS heatsink can be completed efficiently and accurately.

[0039] Example 2: The difference between this example and Example 1 is that the TPMS heat sink is a type D (Diamond type) TPMS structure.

[0040] Representative units of the D-type TPMS heat sink were extracted for pore-scale simulation, using the same method as in Example 1. Although D-type TPMS and Gyroid-type TPMS have different topological morphologies and different geometric structures of their representative units, the methods for extracting equivalent parameters and macroscopic-scale simulation are completely identical.

[0041] Specifically, for the D-type TPMS heat sink, the following steps are performed sequentially: extract representative unit cells → perform pore-scale fluid-structure conjugate heat transfer simulation to obtain... Pore-scale pure thermal conductivity simulation was performed to obtain and The equivalent parameters were substituted into the equivalent model of the porous medium for full-scale macroscopic simulation.

[0042] Example 3: The difference between this example and Example 1 is that the TPMS heat sink is a P-type (Primitive) TPMS structure.

[0043] A representative unit cell of the P-type TPMS heat sink was extracted for pore-scale simulation, using the same method as in Example 1. The P-type TPMS also exhibits the characteristics of a three-period minimum surface, and the extraction of its equivalent parameters and the macroscopic-scale simulation method are universal.

[0044] This embodiment demonstrates that the dual-scale simulation method provided by the present invention has universality for porous TPMS structures with different morphologies and can be widely applied to the simulation of heat sinks with various TPMS morphologies such as Gyroid, D, P, and I-WP.

[0045] Example 4: The difference between this example and Example 1 is that the macroscopic scale simulation uses a three-dimensional model instead of a two-dimensional simplified model.

[0046] For applications with complex geometries or requiring three-dimensional temperature and flow field distributions, a three-dimensional porous medium equivalent model can be directly used for full-scale macroscopic simulation. The governing equations are the same as those for the two-dimensional model, only requiring expansion in the spatial dimension. Three-dimensional macroscopic simulation provides more complete flow and heat transfer information and is suitable for engineering applications with higher simulation accuracy requirements.

[0047] Therefore, the dual-scale simulation method for TPMS porous heat sinks provided by this invention avoids complex geometric modeling and body-fitting mesh generation. This invention obtains equivalent parameters by extracting representative unit cells for pore-scale simulation, and then uses a porous medium equivalent model for full-scale macroscopic simulation, completely avoiding the complex geometric modeling and body-fitting mesh generation process in CFD numerical simulation of the fluid-solid conjugate heat transfer process of TPMS porous structures.

[0048] Breaking through simulation scale limitations. This invention overcomes the limitations of traditional CFD methods in simulating the number of porous TPMS structural elements and the complexity of their shapes, enabling efficient simulation of TPMS heat sinks with arbitrary element counts and complex shapes. Significantly reducing computational costs. Compared to directly performing fine-mesh CFD simulations of full-size TPMS heat sinks, the dual-scale simulation method employed in this invention significantly reduces the number of computational grids, thereby significantly reducing computational costs and time. Facilitating batch simulations and topology customization. This invention provides a new method for batch numerical simulation of laminar flow-solid conjugate heat transfer processes in porous TPMS structures with different morphologies, facilitating efficient topology customization of porous TPMS structures with enhanced heat transfer.

[0049] The above description is only a preferred embodiment of the present invention, but the scope of protection of the present invention is not limited thereto. Any equivalent substitutions or modifications made by those skilled in the art within the scope of the technology disclosed in the present invention, based on the technical solution and inventive concept of the present invention, should be covered within the scope of protection of the present invention.

Claims

1. A dual-scale simulation method for TPMS porous heat sinks, characterized in that, Including the following steps: S1. Extract representative units of the TPMS heat sink and obtain the inherent permeability by simulating the fluid-structure conjugate heat transfer process of the representative units. Fochheimer coefficient Fluid-structure heat transfer coefficient The effective thermal conductivity of the solid is obtained by simulating the pure heat conduction process of the representative unit. and fluid effective thermal conductivity ; S2, the inherent permeability obtained in step S1 Fochheimer coefficient Fluid-structure heat transfer coefficient Solid effective thermal conductivity and fluid effective thermal conductivity Substituting into the porous medium equivalent model, the TPMS heat sink is simulated at a full-size macroscale using the porous medium equivalent model.

2. The dual-scale simulation method for TPMS porous heat sinks according to claim 1, characterized in that, In step S1, the governing equations used in the fluid-structure conjugate heat transfer process of the representative unit include: mass conservation equation: ; Momentum conservation equation: ; Energy conservation equation: ; in, For fluid density, For fluid velocity vector, For pressure, For fluid dynamic viscosity, The specific heat capacity at constant pressure of the fluid. For fluid temperature, For fluid thermal conductivity, This is the volumetric heat source term.

3. The dual-scale simulation method for TPMS porous heat sinks according to claim 1, characterized in that, In step S1, the fluid-structure conjugate heat transfer process of the representative unit is provided with periodic flow boundary conditions, and the same heat flow as the full-size TPMS radiator is provided at the bottom.

4. The dual-scale simulation method for TPMS porous heat sinks according to claim 1, characterized in that, In step S2, the formula for calculating the coolant mass flow rate of the representative unit is: ; in, This refers to the total mass flow rate of the coolant in a full-size TPMS radiator. For full-size TPMS heatsinks Length in the direction, As a representative unit in Length in the direction.

5. The dual-scale simulation method for TPMS porous heat sinks according to claim 4, characterized in that, In step S2, the formula for calculating the inlet temperature of the representative unit is: ; ; ; in, REV reference fluid temperature, and These are the average temperatures of the coolant inlet and outlet of a full-size TPMS radiator, respectively. This represents the temperature rise of the REV reference fluid.

6. The dual-scale simulation method for TPMS porous heat sinks according to claim 5, characterized in that, In step S2, the inherent permeability And Fochheimer coefficient The following formula is used to fit the relationship between the pressure gradient and the velocity to determine: ; in, For the pressure drop of REV, For Darcy speed, The characteristic length of the representative unit.

7. The dual-scale simulation method for TPMS porous heat sinks according to claim 6, characterized in that, In step S2, the fluid-solid heat transfer coefficient The calculation formula is: ; in, The heat flux density at the bottom of the radiator. The volume of a representative unit. The mass-weighted average temperature of the fluid within a representative unit. The average temperature of the solid surface at the bottom of the representative unit is denoted as .

8. The dual-scale simulation method for TPMS porous heat sinks according to claim 7, characterized in that, In step S2, the effective thermal conductivity of the solid and fluid effective thermal conductivity The calculation formulas are as follows: ; in, The cross-sectional area of ​​a representative unit cell. For heat flux vectors, The outward normal unit vector, and These are the thermal side surfaces of the fluid domain and the solid domain, respectively. , These represent the hot and cold side temperatures of the solid domain, respectively. , These represent the hot and cold side temperatures of the fluid domain, respectively.

9. The dual-scale simulation method for TPMS porous heat sinks according to claim 8, characterized in that, In step S2, the flow model of the porous medium equivalent model adopts the Darcy-Lapwood-Forchheimer-Brinkman model, and the heat transfer model adopts the local thermal non-equilibrium model.

10. The dual-scale simulation method for TPMS porous heat sinks according to claim 9, characterized in that, The governing equations of the porous media equivalent model in step two include: Continuity equation: ; Momentum equation: ; Fluid and solid energy equations: ; in, The porosity of a representative unit cell For solid density, The specific heat capacity at constant pressure of a solid. For solid temperature, and These are the volumetric heat source terms for the fluid domain and the solid domain, respectively.

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