Optimization method of liquid metal micro-channel radiator

Abstract

The invention relates to a method for optimizing a liquid metal micro-channel radiator. The method comprises the following steps: determining basic parameters for optimizing the radiator; determining boundary conditions of a micro-channel inlet, and establishing a two-dimensional liquid metal micro-channel radiator model; establishing a topological optimization objective function and constraint conditions according to thermal control index requirements; carrying out material interpolation function definition on the reverse permeability coefficient of the porous medium, the heat conduction coefficient of the material and the specific heat coefficient of the material; carrying out iterative calculation on the two-dimensional liquid metal micro-channel radiator model to obtain an optimized radiator channel configuration; constructing a three-dimensional model of the liquid metal radiator flow channel; comparing an analysis result of the three-dimensional finite element model of the radiator with a heat dissipation index and a flow index, and judging whether a working requirement is met or not; and when the working requirements are met, the liquid metal micro-channel radiator with the most effective corresponding heat dissipation capability is obtained. According to the invention, the power consumption of an external driving system can be reduced, and the corresponding optimal liquid metal micro-channel radiator structure can be obtained.

Description

Technical Field

[0001] The invention relates to the technical field of heat transfer and heat dissipation, and in particular to a method for optimizing a liquid metal microchannel radiator. Background Art

[0002] With the development of high-density electronic devices and micro-electromechanical systems, the integration of electronic circuits and the capacity of various high-power electronic devices are constantly increasing. One of the huge problems facing the development of the electronics industry is that the excessive heat flux density in electronic devices makes the device operating temperature too high. However, high temperature is the main reason for the reduction of equipment reliability and greatly shortened life. Therefore, liquid cooling systems have been widely 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 unable to meet the growing demand for heat dissipation. In order to ensure the performance and cycle life of high-power and highly integrated electronic devices, it is necessary to develop an optimal, compact and efficient liquid cooling system for the equipment. This makes microchannel heat sinks the best choice.

[0004] The microchannel heat sink is a highly compact cooling device with a characteristic channel size between 1 micron and 1 millimeter. It has an ultra-high heat transfer specific area (ratio of heat transfer area to volume), can achieve a high level of heat dissipation under low coolant flow working conditions, and has excellent performance in device thermal management. Compared with traditional heat sinks, microchannel heat sinks have the advantages of strong cooling capacity, anti-leakage, high integration, compact structure, quiet operation, diverse patterns, and easy manufacturing. It is an efficient heat dissipation device with broad application prospects in fields involving high heat flux density, such as solar cells, fuel cells, and computer data centers.

[0005] The main methods to enhance microchannel heat dissipation:

[0006] The first is to change the geometric configuration of the microchannel. The geometric configuration of the microchannel is a key factor affecting the heat dissipation capacity. The geometric structure of the microchannel can improve the heat dissipation mechanism by reducing the thickness of the boundary layer, promoting fluid mixing, and increasing the fluid velocity gradient at the hot surface. However, at present, the structural design of liquid-cooled radiators with high heat flux density is a complex and time-consuming task. Empirical design is limited by the designer's design experience and existing structures. It requires a long trial and error process, which increases the R&D cost and lengthens the R&D cycle. Compared with traditional design methods, topology optimization technology has the advantages of not relying on the initial structure, high design freedom, strong flexibility, and more obvious targeting.

[0007] The second is to change 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 convection heat dissipation coefficient can be obtained, thereby enhancing the heat dissipation performance of the microchannel radiator.

[0008] At present, the heat dissipation capacity of liquid cooling devices using water as the cooling medium is much higher than that of traditional heat dissipation technology. However, water is a coolant with low thermal conductivity, which limits the heat dissipation capacity of liquid cooling devices. Compared with water, liquid metal has higher thermal conductivity and good fluidity, so it has extremely high heat transfer capacity; in addition, the physical and chemical properties of liquid metal are stable and the melting point is low, making it very suitable as a long-term and effective operating fluid. Therefore, liquid metal has great advantages as a coolant in the field of heat dissipation of high-power devices.

[0009] However, the existing heat dissipation system of high-power devices is not sufficient to exert their original working performance, resulting in reduced working performance. The heat dissipation system requires a very powerful external drive system to enable the high-power devices to work normally, resulting in huge energy consumption and unbearable costs. Summary of the invention

[0010] In view of this, it is necessary to provide a liquid metal microfluidic channel heat sink optimization method, which can obtain the best liquid metal microfluidic channel heat sink structure under the power consumption of an appropriate external driving system.

[0011] The present invention provides a liquid metal microfluidic channel heat sink optimization method, which includes the following steps: S1. Determine the basic parameters of heat sink optimization according to the requirements; S2. Determine the microfluidic channel inlet boundary conditions according to the output characteristics of the external drive system, and establish a two-dimensional liquid metal microfluidic channel heat sink model; S3. According to the thermal control index requirements, establish a topology optimization objective function for maximizing the heat dissipation capacity, and use the material usage and the pressure drop of the heat sink as constraints; S4. Use the material interpolation method to calculate the reverse permeability coefficient of the porous medium, the thermal conductivity coefficient of the material, and the specific heat of the material. The material interpolation function is defined based on the coefficients; S5. The design area is discretized based on finite element analysis, and the two-dimensional liquid metal microfluidic channel heat sink model is iteratively calculated to redistribute the material of the heat sink and obtain an optimized heat sink flow channel configuration; S6. According to the optimized heat sink flow channel configuration, a three-dimensional model of the liquid metal heat sink flow channel is constructed; S7. The analysis results of the three-dimensional finite element model of the heat sink are compared with the heat dissipation index and flow index to determine whether the working requirements are met; S8. When the working requirements are met, a liquid metal microfluidic channel heat sink with the most effective corresponding heat dissipation capacity is obtained.

[0012] Preferably, the method further comprises: when the working requirements are not met, entering step S9, and then returning to step S1; said step S9 comprises: adjusting the Reynolds number, the Peclet number and the 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 method.

[0014] Preferably, it is characterized in that the step S2 comprises:

[0015] In the process of building a liquid metal microfluidic heat sink, the two-dimensional liquid metal microfluidic heat sink model is set up:

[0016] Assuming that the liquid metal is incompressible and the flow state in the microchannel is single-phase laminar flow, the corresponding incompressible Navier-Stokes equation is:

[0017]

[0018] Where: ρ is the density of liquid metal, μ is the dynamic viscosity of liquid metal; during the optimization process, the density value of each discrete unit changes in [0,1], 0 represents solid, and 1 represents fluid, so the design domain contains both fluid and solid phases, showing the characteristics of porous media.

[0019] Preferably, the step S3 comprises:

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

[0021]

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

[0023] Preferably, the step S3 further includes:

[0024] In the two-dimensional liquid metal microfluidic heat sink model, equation (8) is used as the objective function. In order to ensure a good flow state and flow continuity in the microchannel, the pressure drop of the heat sink is used as a constraint condition. The constraint condition is shown in equation (9):

[0025]

[0026] Preferably, the step S4 comprises:

[0027] The Helmholtz partial differential equation is used to realize the filtering of the design variables, namely:

[0028]

[0029] Among them, γ is the design variable, γ∈[0,1]; is the design variable after filtering; r is the filter radius;

[0030] The area of ​​the grayscale unit is reduced by hyperbolic tangent projection to obtain a clear heat sink flow channel topology and improve the manufacturability and practicality of the structure; the projection equation is expressed as:

[0031]

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

[0033] Preferably, the step S5 comprises:

[0034] Step S51: presetting initial design variables;

[0035] Step S52: filtering, projecting, and other operations are performed on the initial design variables to perform regularization processing;

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

[0037] Step S54: using the adjoint sensitivity method to solve the adjoint sensitivity of the objective function;

[0038] Step S55: updating the design variables according to the adjoint sensitivity and the moving asymptote method, filtering and projecting the design variables at the fluid-solid boundary, and redistributing the materials;

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

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

[0041] Preferably, step S6 comprises:

[0042] The two-dimensional topological structure 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 according to the boundary conditions. The heat transfer performance of the radiator is analyzed through the temperature field distribution and flow field distribution of the radiator.

[0043] The present invention can obtain an optimal liquid metal microchannel radiator structure under the power consumption of an appropriate external driving system, thereby reducing energy consumption and lowering costs. BRIEF DESCRIPTION OF THE DRAWINGS

[0044] Figure 1 It is a flow chart of the liquid metal micro-channel heat sink optimization method of the present invention;

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

[0046] Figure 3 A flowchart of topological optimization of a two-dimensional liquid metal microchannel heat sink model provided by an embodiment of the present invention;

[0047] Figure 4 A schematic diagram of an iterative process of a liquid metal microchannel heat sink obtained by topology optimization according to an embodiment of the present invention;

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

[0049] Figure 6 It is a schematic diagram of the surface temperature distribution of the three-dimensional radiator model provided by an embodiment of the present invention. DETAILED DESCRIPTION

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

[0051] See also Figure 1 , which is an operation flow chart of a preferred embodiment of the liquid metal microchannel heat sink optimization method of the present invention.

[0052] Step S1, determining basic parameters for heat sink optimization according to requirements. Specifically:

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

[0054] Step S2, according to the output characteristics of the external driving system, determine the boundary conditions of the microchannel inlet and establish a two-dimensional liquid metal microchannel heat sink model, see Figure 2 The boundary conditions include: inlet flow rate and inlet temperature; the inlet flow rate is the steady inlet velocity of the liquid metal flowing into the radiator.

[0055] Specifically:

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

[0057] The boiling point of liquid metal is much higher than its melting point. It is in a completely single-phase flow in the heat sink, and there is no need to consider the phase change problem. Assuming that the liquid metal is incompressible and the flow state in the microchannel is a single-phase laminar flow, the corresponding incompressible Navier-Stokes equation is:

[0058]

[0059] Where: ρ is the density of liquid metal, μ is the dynamic viscosity of liquid metal; during the optimization process, the density value of each discrete unit changes in [0,1], 0 represents solid, and 1 represents fluid, so the design domain contains both fluid and solid phases, showing the characteristics of porous media.

[0060] In order to analyze the flow of fluid in porous media, it is necessary to ensure that the velocity of the solid domain and the solid boundary is 0. Therefore, it is necessary to improve the flow control equation using the Brinkman penalty model. The resistance term is set in the momentum equation to simulate the friction resistance f = -αu of the fluid flow in the porous medium, where α is the material flow resistance coefficient. Thus, the flow control equation that describes both the fluid domain and the solid domain is established:

[0061]

[0062] Assume that the steady-state heat transfer process ignores natural convection and radiation. Heat transfer in the radiator depends on heat conduction and convection mechanisms. The material properties of the liquid metal are considered to be independent of temperature. The energy equation in the solid material and liquid metal is defined as follows:

[0063]

[0064] Where: k s is the thermal conductivity of the solid material, k f is the thermal conductivity of liquid metal, c p is the constant 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, establish the objective function and constraint conditions according to the thermal control index requirements. That is:

[0067] According to the thermal control index requirements of high-power devices, a topology optimization objective function for maximizing heat dissipation capacity is established, while the material usage and the heat sink pressure drop are used as constraints. Specifically:

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

[0069]

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

[0071] In the two-dimensional liquid metal microfluidic heat sink model, equation (8) is used as the objective function. In order to ensure a good flow state and flow continuity in the microchannel, the pressure drop of the heat sink is used as a constraint condition. The constraint condition is shown in equation (9):

[0072]

[0073] Step S4, using the material interpolation method, define the material interpolation function 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 the topology optimization process, problems such as checkerboard structures formed by alternating distribution of solid materials and holes, unclear boundaries, and mesh dependency may occur, which will affect the numerical stability and convergence of the topology optimization calculation. In order to avoid mesh dependency and checkerboard problems and improve the reliability of the solution, this embodiment performs density filtering on the design variables and uses the filtered variables to participate in the topology optimization solution process, thereby obtaining more stable values ​​and more continuous boundary structures.

[0075] The Helmholtz partial differential equation is used to realize the filtering of the design variables, namely:

[0076]

[0077] Among them, γ is the design variable γ∈[0,1]; is the design variable after filtering; r is the filter radius. In order to make the result independent of the grid, the filter radius is set to a constant that is larger than the size of the smallest grid unit.

[0078] The above density filtering can solve the grid dependency and checkerboard problems well, but it will lead to the generation of gray units. Gray units are density units with material density between 0-1, which leads to unclear boundaries. Such results lack practical significance in actual processing and manufacturing and cannot be processed. The hyperbolic tangent projection method can reduce the area of ​​gray units, obtain a clear heat sink flow channel topology, and improve the manufacturability and practicality of the structure. The projection equation is expressed as:

[0079]

[0080] Where ξ∈[0,1] is the threshold, which is generally set to 0.5; β is the projection slope, which is the main parameter for regulating the projection process. The initial value of the projection slope β is set to 1, and it is doubled after each fixed number of iterations until it reaches the preset maximum value of 1024.

[0081] Step S5, discretize the design area based on finite element analysis, iterate the calculation of the two-dimensional liquid metal microchannel heat sink model, redistribute the heat sink material, and obtain the optimized heat sink flow channel configuration. That is:

[0082] Select filtering method, projection mode and optimization solver, discretize the design area based on finite element analysis, use the sensitivity information of design variables to optimize the iterative calculation of the two-dimensional liquid metal microfluidic heat sink model, and end the calculation when the termination condition is met to obtain the two-dimensional topological structure of the liquid metal heat sink flow channel. Specifically:

[0083] See also Figure 3 , the topology optimization process of this embodiment includes:

[0084] Step S51: presetting initial design variables;

[0085] Step S52: filtering, projecting, and other operations are performed on the initial design variables to perform regularization processing;

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

[0087] Step S54: using the adjoint sensitivity method to solve the adjoint sensitivity of the objective function;

[0088] Step S55: updating the design variables according to the adjoint sensitivity and the moving asymptote method, filtering and projecting the design variables at the fluid-solid boundary, and redistributing the materials;

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

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

[0091] Based on the above scheme, the following embodiment performs topological optimization on the heat flux density of the heat source. The working conditions include: the heat source Q is distributed and the value is 50W / cm 2 , the design domain size is 25mm×25mm, the Reynolds number is 553, the Peclet 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 As shown in the figure, the iterative process of a liquid metal microfluidic heat sink obtained through topology optimization is shown. As the projection slope increases, the fluid-solid boundary structure becomes clearer. Finally, the structure obtained by topology optimization is extracted, and the obtained two-dimensional structure is stretched into a three-dimensional model to obtain the heat sink configuration. Figure 5 shown.

[0092] Step S6: construct a three-dimensional model of the liquid metal radiator flow channel according to the optimized radiator flow channel configuration to simulate its temperature change under the condition of heat source, see Figure 6 . That is:

[0093] The two-dimensional topological structure 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 according to the boundary conditions. The heat transfer performance of the radiator is analyzed through 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 the flow index to determine whether the working requirements are met. If so, proceed to step S8; if not, proceed to step S9, and then return to step S1.

[0095] Step S8, obtaining a liquid metal microchannel heat sink with the most effective heat dissipation capacity.

[0096] Step S9, adjusting the Reynolds number, Peclet number and pressure drop constraint.

[0097] Although the present invention has been described with reference to the current preferred embodiments, those skilled in the art should understand that the above-mentioned preferred embodiments are only used to illustrate the present invention and are not used to limit the scope of protection of the present invention. Any modifications, equivalent substitutions, improvements, etc. made within the spirit and principle of the present invention should be included in the scope of protection of the present invention.

Claims

1. A liquid metal microchannel heat sink optimization method, characterized in that: The method comprises the following steps: S1. Determine the basic parameters of radiator optimization according to demand; S2. According to the output characteristics of the external driving system, the boundary conditions of the microchannel inlet are determined, and a two-dimensional liquid metal microchannel heat sink model is established; S3. According to the thermal control index requirements, establish the topology optimization objective function for maximizing the heat dissipation capacity, while taking the material usage and the pressure drop of the heat sink as constraints; S4. Using the material interpolation method, define the material interpolation function for the reverse permeability coefficient of the porous medium, the thermal conductivity coefficient of the material, and the specific heat coefficient of the material; S5. Discretize the design area based on finite element analysis, iteratively calculate the two-dimensional liquid metal microfluidic channel heat sink model, redistribute the heat sink material, and obtain the optimized heat sink flow channel configuration; S6. constructing a three-dimensional model of the liquid metal radiator flow channel according to the optimized radiator flow channel configuration; S7. Compare the analysis results of the 3D finite element model of the radiator with the heat dissipation index and the flow index to determine whether the working requirements are met; S8. When the working requirements are met, a liquid metal microfluidic heat sink with the most effective heat dissipation capacity is obtained.

2. The liquid metal microchannel heat sink optimization method according to claim 1, characterized in that: The method further includes: when the working requirements are not met, entering step S9, and then returning to step S1; the step S9 includes: Adjust the Reynolds number, Péclet number, and pressure drop constraints.

3. The liquid metal microchannel heat sink optimization method according to 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 liquid metal microchannel heat sink optimization method according to claim 3, characterized in that: The step S2 comprises: In the process of building a liquid metal microfluidic heat sink, the two-dimensional liquid metal microfluidic heat sink model is set up: Assuming that the liquid metal is incompressible and the flow state in the microchannel is single-phase laminar flow, the corresponding incompressible Navier-Stokes equation is: Where: ρ is the density of liquid metal, μ is the dynamic viscosity of liquid metal; during the optimization process, the density value of each discrete unit changes in [0,1], 0 represents solid, and 1 represents fluid, so the design domain contains both fluid and solid phases, showing the characteristics of porous media.

5. The liquid metal microchannel heat sink optimization method according to claim 4, characterized in that: The step S3 comprises: In the process of structural topology optimization, the design variables are associated with the physical properties of the material, and the interpolation function of the liquid metal and heat sink material is defined as: Where: α min is a value close to or equal to 0, α max is a sufficiently large number to ensure that the velocity is zero in the solid domain, q is the convexity control coefficient of the interpolation function, and c f is the specific heat of liquid at constant pressure, c s is the specific heat of the solid at constant pressure, is the design variable after projection.

6. The liquid metal microchannel heat sink optimization method according to claim 5, characterized in that: The step S3 further comprises: In the two-dimensional liquid metal microfluidic heat sink model, equation (8) is used as the objective function. In order to ensure a good flow state and flow continuity in the microchannel, the pressure drop of the heat sink is used as a constraint condition. The constraint condition is shown in equation (9): J=∫ Ω T 2 dV (8) 7. The liquid metal microchannel heat sink optimization method according to claim 6, characterized in that: The step S4 comprises: The Helmholtz partial differential equation is used to realize the filtering of the design variables, namely: Among them, γ is the design variable, γ∈[0,1; is the design variable after filtering; r is the filter radius; The area of ​​the grayscale unit is reduced by hyperbolic tangent projection to obtain a clear heat sink flow channel topology and improve the manufacturability and practicality of the structure; the projection equation is expressed as: Where ξ∈[0,1] is the threshold, which is generally set to 0.5; β is the projection slope.

8. The liquid metal microchannel heat sink optimization method according to claim 7, characterized in that: The step S5 comprises: Step S51: presetting initial design variables; Step S52: filtering, projecting, and other operations are performed on the initial design variables to perform regularization processing; Step S53: using the finite element method to solve the flow and energy equations to obtain current flow field and temperature field information; Step S54: using the adjoint sensitivity method to solve the adjoint sensitivity of the objective function; Step S55: updating the design variables according to the adjoint sensitivity and the moving asymptote method, filtering and projecting the design variables at the fluid-solid boundary, and redistributing the materials; Step S56: Determine whether the design variables have converged: if converged, proceed to step S57; if not, return to step S52. Step S57: extracting the two-dimensional liquid metal microchannel heat sink model structure obtained by topology optimization, and stretching it to obtain a three-dimensional model.

9. The liquid metal microchannel heat sink optimization method according to claim 8, characterized in that: The step S6 comprises: The two-dimensional topological structure 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 according to the boundary conditions. The heat transfer performance of the radiator is analyzed through the temperature field distribution and flow field distribution of the radiator.

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