Liquid metal microfluidic channel heat spreader optimization method

Abstract

The application relates to a liquid metal micro-channel radiator optimization method, which comprises the following steps: determining basic parameters of radiator optimization; determining a micro-channel inlet boundary condition, establishing a two-dimensional liquid metal micro-channel radiator model; establishing a topological optimization objective function and constraint condition according to a heat control index requirement; defining a material interpolation function of the inverse permeability coefficient of a porous medium, the thermal conductivity coefficient of a material and the specific heat coefficient of the material; iteratively calculating the two-dimensional liquid metal micro-channel radiator model to obtain an optimized radiator flow channel configuration; constructing a three-dimensional model of the liquid metal radiator flow channel; comparing a radiator three-dimensional finite element model analysis result with a heat dissipation index and a flow index to determine whether the working requirement is met; and when the working requirement is met, the most effective liquid metal micro-channel radiator with the corresponding heat dissipation capacity is obtained. The application can reduce the power consumption of an external driving system and obtain the corresponding optimal liquid metal micro-channel radiator structure.

Description

Technical Field

[0001] This invention relates to the field of heat transfer and heat dissipation technology, and in particular to an optimization method for liquid metal microchannel heat sinks. Background Technology

[0002] With the development of high-density electronic devices and microelectromechanical systems (MEMS), the integration level of electronic circuits and the capacity of various high-power electronic devices are constantly increasing. One of the major problems facing the electronics industry is that the excessively high heat flux density in electronic devices leads to excessively high operating temperatures. However, high temperatures are a major cause of reduced equipment reliability and significantly shortened lifespan. Therefore, liquid cooling systems have been extensively studied due to their heat dissipation potential.

[0003] Traditional liquid cooling channel structures, such as straight channels, fractal channels, S-shaped channels, and spiral channels, have high flow resistance, resulting in low heat dissipation efficiency and failing to meet the ever-increasing heat dissipation demands. To ensure the performance and cycle life of high-power and highly integrated electronic devices, it is essential to develop optimal, compact, and efficient liquid cooling systems. This makes microchannel heat sinks the best choice.

[0004] Microchannel heat sinks are highly compact cooling devices with channel feature sizes ranging from 1 micrometer to 1 millimeter. They possess an extremely high heat transfer area (the ratio of heat transfer area to volume), achieving high heat dissipation levels even under low coolant flow conditions and exhibiting excellent performance in device thermal management. Compared to traditional heat sinks, microchannel heat sinks offer advantages such as strong cooling capacity, leak resistance, high integration, compact structure, quiet operation, diverse patterns, and ease of manufacturing. They are highly efficient heat dissipation devices with broad application prospects in fields involving high heat flux densities, such as solar cells, fuel cells, and computer data centers.

[0005] The main methods to enhance heat dissipation in microchannels:

[0006] The first approach involves altering the geometry of the microchannels, a key factor influencing heat dissipation. The geometry of the microchannels can improve heat dissipation by reducing boundary layer thickness, promoting fluid mixing, and increasing the fluid velocity gradient at the hot surface. However, designing the structure of liquid-cooled radiators with high heat flux is currently a complex and time-consuming task. Experience-based design is limited by the designer's experience and existing structures, requiring a lengthy trial-and-error process, increasing R&D costs and extending the development cycle. In contrast, topology optimization techniques offer advantages over traditional design methods, including independence from the initial structure, high design freedom, flexibility, and more targeted design.

[0007] The second method involves changing the cooling medium. The heat dissipation capacity between the cooling medium and the heat source depends on the thermal conductivity, viscosity, density, and flow rate of the cooling medium. By improving the performance of the coolant, a higher convective heat dissipation coefficient can be obtained, thereby enhancing the heat dissipation performance of the microchannel radiator.

[0008] Currently, liquid cooling devices using water as the cooling medium have significantly higher heat dissipation capabilities than traditional heat dissipation technologies. However, water is a coolant with low thermal conductivity, limiting the heat dissipation capacity of liquid cooling devices. Compared to water, liquid metals have higher thermal conductivity and excellent fluidity, thus possessing extremely high heat transfer capabilities. Furthermore, liquid metals have stable physicochemical properties and low melting points, making them very suitable as a long-term, effective working fluid. Therefore, liquid metals have significant advantages as coolants in the field of high-power device heat dissipation.

[0009] However, the existing heat dissipation systems for high-power devices are insufficient to achieve their original performance, resulting in reduced performance. The heat dissipation system requires a high-power external drive system to enable the high-power devices to operate normally, which leads to huge energy consumption and prohibitive costs. Summary of the Invention

[0010] In view of this, it is necessary to provide an optimization method for liquid metal microchannel heat sinks, which can obtain the optimal liquid metal microchannel heat sink structure under the appropriate power consumption of the external drive system.

[0011] This invention provides an optimization method for liquid metal microchannel heat sinks, comprising the following steps: S1. Determining the basic parameters for heat sink optimization based on requirements; S2. Determining the microchannel inlet boundary conditions and establishing a two-dimensional liquid metal microchannel heat sink model based on the output characteristics of the external drive system; S3. Establishing a topology optimization objective function to maximize heat dissipation capacity based on thermal control requirements, while using material usage and heat sink pressure drop as constraints; S4. Utilizing material interpolation methods to optimize the reverse permeability coefficient of the porous medium, the thermal conductivity coefficient of the material, and the specific heat of the material. S5. Define the material interpolation function for the coefficients; S6. Discretize the design region based on finite element analysis, and iteratively calculate the two-dimensional liquid metal microchannel radiator model to redistribute the material of the radiator and obtain the optimized radiator flow channel configuration; S7. Construct a three-dimensional model of the liquid metal radiator flow channel based on the optimized radiator flow channel configuration; S8. Compare the analysis results of the three-dimensional finite element model of the radiator with the heat dissipation index and flow index to determine whether it meets the working requirements; S9. When the working requirements are met, obtain the liquid metal microchannel radiator with the most effective heat dissipation capacity.

[0012] Preferably, the method further includes: when the working requirements are not met, proceeding to step S9 and then returning to step S1; step S9 includes: adjusting the Reynolds number, Peckley number and pressure drop constraint.

[0013] Preferably, the basic parameters include: heat source, radiator boundary conditions, heat dissipation index, flow index, material, radiator size, inlet and outlet quantity and distribution pattern.

[0014] Preferably, step S2 includes:

[0015] In the process of constructing a liquid metal microchannel heat sink, the two-dimensional liquid metal microchannel heat sink model is configured as follows:

[0016] Assuming the liquid metal is incompressible, and its flow state within the microchannel is single-phase laminar flow, then the corresponding incompressible Navier-Stokes equations are:

[0017]

[0018] Where: ρ is the density of the liquid metal, and μ is the dynamic viscosity of the liquid metal; during the optimization process, the density value of each discrete unit varies in [0,1], where 0 represents solid and 1 represents fluid. Therefore, the design domain contains both fluid and solid phases, exhibiting the characteristics of a porous medium.

[0019] Preferably, step S3 includes:

[0020] In the structural topology optimization process, design variables are correlated with material physical properties, and the interpolation function for liquid metal and heat sink material is defined as follows:

[0021]

[0022] Where: α min For a value close to or equal to 0, α max Let q be a sufficiently large number to ensure that the velocity is zero in the solid domain, and let c be the convexity control coefficient of the interpolation function. f For the specific heat of a liquid at constant pressure, c s It is the specific heat at constant pressure of a solid. These are the design variables after projection.

[0023] Preferably, step S3 further includes:

[0024] In the two-dimensional liquid metal microchannel radiator model, Equation (8) is used as the objective function. In order to ensure good flow conditions and flow channel continuity within the microchannel, the pressure drop of the radiator is used as a constraint condition, as shown in Equation (9):

[0025]

[0026] Preferably, step S4 includes:

[0027] The filtering of design variables is achieved using Helmholtz partial differential equations, namely:

[0028]

[0029] Where γ is a design variable, γ∈[0,1]; Here, r represents the filtered design variable; r is the filtering radius.

[0030] By reducing the area of ​​grayscale units through hyperbolic tangent projection, a clear topology of the heat sink flow channel is obtained, improving the manufacturability and practicality of the structure; the projection equation is expressed as:

[0031]

[0032] In the formula, ξ∈[0,1] is the threshold, which is usually set to 0.5; β is the projection slope.

[0033] Preferably, step S5 includes:

[0034] Step S51: Preset initial design variables;

[0035] Step S52: Perform filtering, projection, and other operations on the initial design variables to achieve regularization.

[0036] Step S53: Solve the flow and energy equations using the finite element method to obtain the current flow field and temperature field information;

[0037] Step S54: Solve for the adjoint sensitivity of the objective function using the adjoint sensitivity method;

[0038] Step S55: Based on the accompanying sensitivity, update the design variables using the moving asymptote method, filter the projection of the design variables at the fluid-structure boundary, and redistribute the material.

[0039] Step S56: Determine whether the design variables have converged: If they have converged, proceed to step S57; if they have not converged, return to step S52.

[0040] Step S57: Extract the two-dimensional liquid metal microchannel heat sink model structure obtained by topology optimization, and extrude it to obtain a three-dimensional model.

[0041] Preferably, step S6 includes:

[0042] The two-dimensional topology of the liquid metal radiator flow channel is stretched to obtain the corresponding three-dimensional model. A three-dimensional non-isothermal flow finite element model is constructed based on the boundary conditions. The heat transfer performance of the radiator is analyzed by analyzing the temperature field distribution and flow field distribution of the radiator.

[0043] This invention can achieve an optimal liquid metal microchannel heat sink structure with appropriate power consumption of the external drive system, thereby reducing energy consumption and lowering costs. Attached Figure Description

[0044] Figure 1 This is a flowchart of the optimization method for liquid metal microchannel heat sink of the present invention;

[0045] Figure 2 This is a schematic diagram of a two-dimensional liquid metal microchannel heat sink model provided in an embodiment of the present invention;

[0046] Figure 3 This is a flowchart of topology optimization for a two-dimensional liquid metal microchannel heat sink model provided in an embodiment of the present invention;

[0047] Figure 4 A schematic diagram illustrating the iterative process of one of the liquid metal microchannel heat sinks obtained through topology optimization according to an embodiment of the present invention;

[0048] Figure 5 This is a schematic diagram of a three-dimensional heat sink model provided in an embodiment of the present invention, wherein: (a) is an xy-plane view of the center of the three-dimensional heat sink model in an embodiment of the present invention; (b) is a perspective view of the three-dimensional heat sink model in an embodiment of the present invention;

[0049] Figure 6 This is a schematic diagram of the surface temperature distribution of a three-dimensional heat sink model provided in an embodiment of the present invention. Detailed Implementation

[0050] The present invention will now be described in further detail with reference to the accompanying drawings and specific embodiments.

[0051] See Figure 1 The diagram shown is a flowchart of a preferred embodiment of the liquid metal microchannel heat sink optimization method of the present invention.

[0052] Step S1: Determine the basic parameters for radiator optimization based on requirements. Specifically:

[0053] The basic parameters include: heat source, radiator boundary conditions, heat dissipation index, flow index, material, radiator size, number and distribution of inlet and outlet, etc.

[0054] Step S2: Based on the output characteristics of the external drive system, determine the inlet boundary conditions of the microchannel and establish a two-dimensional liquid metal microchannel heat sink model. Please refer to [link / reference]. Figure 2 The boundary conditions include: inlet flow velocity and inlet temperature; the inlet flow velocity is the steady inlet velocity of liquid metal flowing into the radiator.

[0055] Specifically:

[0056] In the process of constructing the liquid metal microchannel heat sink, the two-dimensional liquid metal microchannel heat sink model is set as follows:

[0057] The boiling point of liquid metal is much higher than its melting point, resulting in completely single-phase flow in the radiator, eliminating the need to consider phase transitions. Assuming the liquid metal is incompressible, its flow within the microchannel is a single-phase laminar flow, corresponding to the incompressible Navier-Stokes equations:

[0058]

[0059] Where: ρ is the density of the liquid metal, and μ is the dynamic viscosity of the liquid metal; during the optimization process, the density value of each discrete unit varies in [0,1], where 0 represents solid and 1 represents fluid. Therefore, the design domain contains both fluid and solid phases, exhibiting the characteristics of a porous medium.

[0060] To analyze fluid flow in porous media, it is necessary to ensure that the velocities in the solid domain and solid boundary are zero. Therefore, the flow control equations need to be improved using the Brinkman penalty model. A drag term is added to the momentum equation to simulate the frictional resistance f = -αu experienced by the fluid flow in the porous media, where α is the material flow resistance coefficient. This establishes the flow control equations that simultaneously describe the fluid and solid domains:

[0061]

[0062] Assume that natural convection and radiation are neglected in the steady-state heat transfer process. Heat transfer in the radiator relies on heat conduction and convection mechanisms. Furthermore, the material properties of the liquid metal are considered independent of temperature. The energy equations for both solid materials and liquid metals are defined as follows:

[0063]

[0064] Where: k s It is the thermal conductivity of a solid material, k. f It is the thermal conductivity of liquid metal, c p is the specific heat capacity of the liquid, and Q is the heat source distribution applied to the solid domain. The conjugate heat transfer problem is reflected in the convection term (dominated by the fluid velocity vector) and the diffusion term (driven by the effective thermal conductivity). However, the microchannel structure in the design domain can only be determined after topology optimization, so equation (3) is unified into the following form:

[0065]

[0066] Step S3: Based on the thermal control requirements, establish the objective function and constraints. That is:

[0067] Based on the thermal control requirements of high-power devices, a topology optimization objective function for maximizing heat dissipation capacity is established, with material usage and heat sink voltage drop as constraints. Specifically:

[0068] In the process of structural topology optimization, it is necessary to associate design variables with material physical properties. Therefore, the interpolation function for liquid metal and heat sink material is defined as follows:

[0069]

[0070] Where: α min For a value close to or equal to 0, α max Let q be a sufficiently large number to ensure that the velocity is zero in the solid domain, and let c be the convexity control coefficient of the interpolation function. f For the specific heat of a liquid at constant pressure, c s It is the specific heat at constant pressure of a solid. These are the design variables after projection.

[0071] In the two-dimensional liquid metal microchannel radiator model, Equation (8) is used as the objective function. In order to ensure good flow conditions and flow channel continuity within the microchannel, the pressure drop of the radiator is used as a constraint condition, as shown in Equation (9):

[0072]

[0073] Step S4: Using material interpolation methods, define material interpolation functions for the reverse permeability coefficient of the porous medium, the thermal conductivity coefficient of the material, and the specific heat coefficient of the material. Specifically:

[0074] During topology optimization, problems such as checkerboard structures formed by alternating distributions of solid materials and voids, unclear boundaries, and mesh dependency may arise. These issues can affect the numerical stability and convergence of topology optimization calculations. To avoid mesh dependency and checkerboard problems and improve the reliability of the solution, this embodiment performs density filtering on the design variables. The filtered variables are then used in the topology optimization solution process, resulting in more stable values ​​and a more continuous boundary structure.

[0075] The filtering of design variables is achieved using Helmholtz partial differential equations, namely:

[0076]

[0077] Where γ is a design variable γ∈[0,1]; is the design variable after filtering; r is the filtering radius. To make the result independent of the grid, the filtering radius is set to a constant and is greater than the size of the smallest grid cell.

[0078] The density filtering described above effectively solves the mesh dependency and checkerboard problems, but it leads to the generation of gray-scale cells. Gray-scale cells are density cells with a material density between 0 and 1, resulting in unclear boundaries. Such a result lacks practical significance in actual manufacturing and is therefore unsuitable for processing. Hyperbolic tangent projection can reduce the area of ​​gray-scale cells, obtaining a clearer heatsink channel topology and improving the manufacturability and practicality of the structure. The projection equation is expressed as:

[0079]

[0080] In the formula, ξ∈[0,1] is the threshold, which is generally set to 0.5; β is the projection slope, which is the main parameter controlling the projection process. The initial value of the projection slope β is set to 1, and it is doubled after a fixed number of iterations until the preset maximum value of 1024 is reached.

[0081] Step S5 involves discretizing the design region based on finite element analysis and iteratively calculating the two-dimensional liquid metal microchannel heat sink model. This redistributes the material of the heat sink, resulting in an optimized heat sink channel configuration. In other words:

[0082] By selecting a filtering method, projection mode, and optimization solver, the design region is discretized based on finite element analysis. Using design variable sensitivity information, iterative optimization calculations are performed on the two-dimensional liquid metal microchannel radiator model. The calculation ends when the termination condition is met, yielding the two-dimensional topology of the liquid metal radiator channel. Specifically:

[0083] Please see Figure 3 The topology optimization process in this embodiment includes:

[0084] Step S51: Preset initial design variables;

[0085] Step S52: Perform filtering, projection, and other operations on the initial design variables to achieve regularization.

[0086] Step S53: Solve the flow and energy equations using the finite element method to obtain the current flow field and temperature field information;

[0087] Step S54: Solve for the adjoint sensitivity of the objective function using the adjoint sensitivity method;

[0088] Step S55: Based on the accompanying sensitivity, update the design variables using the moving asymptote method, filter the projection of the design variables at the fluid-structure boundary, and redistribute the material.

[0089] Step S56: Determine whether the design variables have converged. If converged, proceed to step S57; if not, return to step S52.

[0090] Step S57: Extract the two-dimensional liquid metal microchannel heat sink model structure obtained by topology optimization, and extrude it to obtain a three-dimensional model.

[0091] Based on the above scheme, the following embodiments perform topology optimization on the heat flux density of the heat source. The operating conditions include: all heat sources Q are distributed and the value is 50 W / cm². 2 The design domain size is 25mm × 25mm, the Reynolds number is 553, the Peckley number is 29.4, the material volume constraint is 0.5 times the design domain volume, and the flow resistance constraint is 0.02 times the flow resistance of the structure corresponding to the initial design variables. Figure 4 The diagram illustrates the iterative process of a liquid metal microchannel heatsink obtained through topology optimization. As the projection slope increases, the fluid-structure boundary becomes increasingly clear. Finally, the structure obtained through topology optimization is extracted, and the resulting two-dimensional structure is stretched into a three-dimensional model to obtain the heatsink configuration. Figure 5 As shown.

[0092] Step S6: Based on the optimized radiator flow channel configuration, construct a three-dimensional model of the liquid metal radiator flow channel and simulate its temperature change under heat source conditions. Please refer to [link to relevant documentation]. Figure 6 . That is:

[0093] The two-dimensional topology of the liquid metal radiator flow channel is stretched to obtain the corresponding three-dimensional model. A three-dimensional non-isothermal flow finite element model is constructed based on the boundary conditions. The heat transfer performance of the radiator is analyzed by analyzing the temperature field distribution and flow field distribution of the radiator.

[0094] Step S7: Compare the analysis results of the 3D finite element model of the radiator with the heat dissipation index and flow index to determine whether the working requirements are met. If they are met, proceed to step S8; if they are not met, proceed to step S9 and then return to step S1.

[0095] Step S8: Obtain the liquid metal microchannel radiator with the most effective heat dissipation capacity.

[0096] Step S9: Adjust the Reynolds number, Peckley number, and pressure drop constraint.

[0097] Although the present invention has been described with reference to the present preferred embodiments, those skilled in the art should understand that the above preferred embodiments are only used to illustrate the present invention and are not intended to limit the scope of protection of the present invention. Any modifications, equivalent substitutions, improvements, etc., 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 method for optimizing a liquid metal microchannel heat sink, characterized in that, The method includes the following steps: S1. Determine the basic parameters for radiator optimization based on requirements; S2. Based on the output characteristics of the external drive system, determine the inlet boundary conditions of the microchannel and establish a two-dimensional liquid metal microchannel heat sink model; S3. Based on the thermal control requirements, establish a topology optimization objective function to maximize heat dissipation capacity, while taking the amount of material used and the pressure drop of the heat sink as constraints. S4. Using material interpolation methods, define material interpolation functions for the reverse permeability coefficient of porous media, the thermal conductivity coefficient of materials, and the specific heat coefficient of materials; S5. Based on finite element analysis, the design region is discretized, and the two-dimensional liquid metal microchannel heat sink model is iteratively calculated to redistribute the heat sink material and obtain an optimized heat sink channel configuration. S6. Based on the optimized radiator flow channel configuration, construct a three-dimensional model of the liquid metal radiator flow channel; S7. Compare the analysis results of the three-dimensional finite element model of the radiator with the heat dissipation index and flow index to determine whether the working requirements are met. S8. A liquid metal microchannel radiator that achieves the most effective heat dissipation capacity when meeting operational requirements; wherein: Step S3 includes: In the structural topology optimization process, design variables are correlated with material physical properties, and the interpolation function for liquid metal and heat sink material is defined as follows: （5） （6） （7） in: It is a value close to or equal to 0. It should be a sufficiently large number to ensure that the velocity is zero in the solid domain. These are the convexity control coefficients of the interpolation function. For the specific heat of a liquid at constant pressure, It is the specific heat at constant pressure of a solid. These are the design variables after projection.

2. The method for optimizing a liquid metal microchannel heat sink as described in claim 1, characterized in that, The method further includes: when the working requirements are not met, proceeding to step S9, and then returning to step S1; step S9 includes: Adjust the Reynolds number, Peckley number, and pressure drop constraints.

3. The method for optimizing liquid metal microchannel heat sinks as described in claim 2, characterized in that, The basic parameters include: heat source, radiator boundary conditions, heat dissipation index, flow index, material, radiator size, inlet and outlet quantity and distribution method.

4. The method for optimizing a liquid metal microchannel heat sink as described in claim 3, characterized in that, Step S2 includes: In the process of constructing a liquid metal microchannel heat sink, the two-dimensional liquid metal microchannel heat sink model is configured as follows: Assuming the liquid metal is incompressible, and its flow state within the microchannel is single-phase laminar flow, then the corresponding incompressible Navier-Stokes equations are: （1） in: It is the density of liquid metal. It is the dynamic viscosity of liquid metal; during the optimization process, the density value of each discrete unit varies in [0,1], where 0 represents solid and 1 represents fluid. Therefore, the design domain contains both fluid and solid phases, exhibiting the characteristics of a porous medium.

5. The method for optimizing a liquid metal microchannel heat sink as described in claim 4, characterized in that, Step S3 further includes: In the two-dimensional liquid metal microchannel radiator model, Equation (8) is used as the objective function. In order to ensure good flow state and flow channel continuity in the microchannel, the pressure drop of the radiator is used as the constraint condition, as shown in Equation (9): （8） 。 6. The method for optimizing a liquid metal microchannel heat sink as described in claim 5, characterized in that, Step S4 includes: The filtering of design variables is achieved using Helmholtz partial differential equations, namely: （10） （11） in, For design variables, ; These are the filtered design variables; The filter radius; By reducing the area of ​​grayscale units through hyperbolic tangent projection, a clear topology of the heat sink flow channel is obtained, improving the manufacturability and practicality of the structure; the projection equation is expressed as: （12） In the formula, This is a threshold value, typically set to 0.

5. It is the projection slope.

7. The method for optimizing a liquid metal microchannel heat sink as described in claim 6, characterized in that, Step S5 includes: Step S51: Preset initial design variables; Step S52: Perform filtering, projection, and other operations on the initial design variables to achieve regularization. Step S53: Solve the flow and energy equations using the finite element method to obtain the current flow field and temperature field information; Step S54: Solve for the adjoint sensitivity of the objective function using the adjoint sensitivity method; Step S55: Based on the accompanying sensitivity, update the design variables using the moving asymptote method, filter the projection of the design variables at the fluid-structure boundary, and redistribute the material. Step S56: Determine if the design variables have converged: If they have converged, proceed to step S57; if they have not converged, return to step S52. Step S57: Extract the two-dimensional liquid metal microchannel heat sink model structure obtained by topology optimization, and extrude it to obtain a three-dimensional model.

8. The method for optimizing a liquid metal microchannel heat sink as described in claim 7, characterized in that, Step S6 includes: The two-dimensional topology of the liquid metal radiator flow channel is stretched to obtain the corresponding three-dimensional model. A three-dimensional non-isothermal flow finite element model is constructed based on the boundary conditions. The heat transfer performance of the radiator is analyzed by analyzing the temperature field distribution and flow field distribution of the radiator.

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