Pin-Fin structure topological optimization design method based on variable density method

Abstract

The invention discloses a Pin-Fin structure topological optimization design method based on a variable density method, and belongs to the technical field of liquid cooling structure design, and the method specifically comprises the steps: judging whether the inlet flow velocity of a design unit is determined, if yes, calculating an inlet Reynolds number and drawing a Pareto leading edge, and if not, calculating a Pareto leading edge; calculating the minimum value and the value range of the heat exchange amount objective function and the fluid total potential energy objective function, and selecting an operation condition point meeting the heat sink performance requirement; if the inlet flow velocity is uncertain, a target value is set, an inlet Reynolds number and the inlet flow velocity are calculated, a Pareto front edge is drawn, and operation condition points are marked; determining the weight according to the distribution of the operating condition points on the Pareto front, constructing a total objective function of topological optimization, and implementing topological optimization, including density interpolation and establishment of a fluid flow and heat transfer control equation, to obtain a two-dimensional optimization result; and reconstructing the two-dimensional result into a three-dimensional model, carrying out analogue simulation, comparing a simulation result with a two-dimensional optimization result, and screening a topological structure meeting optimization design requirements.

Description

Technical Field

[0001] The present invention relates to the technical field of liquid cooling structure design, and in particular to a Pin-Fin structure topology optimization design method based on a variable density method. Background Art

[0002] In modern thermal management systems, the Pin-Fin structure of heat dissipation elements is widely used in various heat exchange devices and electronic cooling systems due to its efficient heat dissipation performance. The design optimization of Pin-Fin is the key to improving its heat dissipation efficiency and reducing flow resistance. Traditional Pin-Fin design methods mainly rely on empirical formulas and trial and error methods, which are often time-consuming and difficult to achieve optimal design. In recent years, topology optimization technology has been introduced into Pin-Fin design. Through mathematical modeling and algorithm iteration, the optimal material distribution is automatically found, thereby improving performance and reducing material usage.

[0003] Although existing research has provided a variety of solutions for the topology optimization of Pin-Fin, there is still room for further improvement. In particular, how to improve the calculation efficiency and the manufacturability of the results while ensuring the optimization accuracy in practical applications is still a problem to be solved. Therefore, the present invention proposes a Pin-Fin structure topology optimization design method based on the variable density method. Summary of the invention

[0004] The purpose of the present invention is to provide a Pin-Fin structure topology optimization design method based on a variable density method to solve the following technical problems: In practical applications, how to improve the computational efficiency and the manufacturability of the results while ensuring the optimization accuracy.

[0005] The purpose of the present invention can be achieved by the following technical solutions: The Pin-Fin structure topology optimization design method based on the variable density method includes the following steps: Determine whether the inlet flow rate of the design unit is determined. When the inlet flow rate is determined, calculate the inlet Reynolds number according to the inlet flow rate and the target size, and draw the Pareto front under the inlet Reynolds number according to the fitting equation; Based on the Pareto front curve, the heat transfer objective function J under the inlet Reynolds number is calculated respectively. t and the total potential energy objective function J f The minimum value of the inlet Reynolds number is obtained. t And the objective function J f The value range of ; select the operating point that meets the set heat sink performance requirements on the Pareto front; When the inlet flow rate is uncertain, the objective function J is set t And the objective function Jf The target value of J is selected to meet the set operating condition point; t and J f Substitute the target value into the fitting equation to calculate the inlet Reynolds number, calculate the inlet flow velocity based on the inlet Reynolds number, draw the corresponding Pareto front, and mark the operating point; According to the distribution of the operating condition points on the Pareto frontier, the objective function J is determined. t And the objective function J f The weights ω1 and ω2 are used to construct the model according to the inlet Reynolds number and the weights ω1 and ω2, respectively, to form the total objective function J of topology optimization, and to implement topology optimization, including interpolating the density of solid materials and establishing the control equations of fluid flow and heat transfer, to obtain the two-dimensional optimization results of topology optimization; The two-dimensional optimization result is reconstructed into a three-dimensional model, the three-dimensional model is simulated, the simulation result is compared with the two-dimensional optimization result, and the topological structure that meets the optimization design requirements is screened.

[0006] As a further solution of the present invention: the heat exchange objective function formula is J t =ST average ,ST average represents the average temperature of the solid and fluid domains in the design unit; The objective function formula of the total potential energy of the fluid is: ; Where u represents the fluid velocity, α is the reflectivity of the porous medium, T is the local temperature in the domain, γ represents the material density design variable with a value range of [0,1], and μ represents the fluid viscosity.

[0007] As a further solution of the present invention: the process of interpolating the density of solid materials in the topology optimization is: The RAMP interpolation function model is used to interpolate the physical properties of solid materials. The interpolation function is: ; In the formula, K s Represents the thermal conductivity of the solid, K f represents the thermal conductivity of the fluid, q is the penalty factor of the interpolation function, and multiple iterations are performed until the material density design variable approaches 0 or 1.

[0008] As a further solution of the present invention: when the design domain is divided into multiple non-overlapping regions, density filtering is performed by solving the Helmholtz partial differential equation: ; The solution obtained by solving the partial differential equation is the design variable after filtering, r is the length parameter of the filter radius rfilter; Project the design variables. All material density design variables exceeding the threshold η are projected to 1, and those below the threshold η are projected to 0. The physical density obtained by projection is The smooth function expression controlled by the projection parameter β: ; Where e represents a natural constant, γ i represents any material density design variable; The expression can be simplified by using the hyperbolic tangent function tanh as follows: ; in, is the design variable after projection, γ β is the projection point.

[0009] As a further solution of the present invention: the process of establishing the control equation of fluid flow in the topology optimization is: The conservation of momentum of the fluid is expressed according to the following formula: ; Where f is the dimensionless volume force, which is proportional to the velocity u, ρ is the fluid density, and p represents the pressure. In the fluid domain, α is 0, and in the solid domain, α is infinite. The RAMP interpolation function model is used to interpolate α, and the formula is:

[0010] α s represents the reflectivity of the solid porous medium, α f Represents the porous medium reflectivity of the fluid; The integrated fluid flow control equation is: .

[0011] As a further solution of the present invention: the process of establishing the heat transfer control equation in the topology optimization is: The equation for heat transfer from a heat source in a solid domain is: , the equation for heat transfer from a heat source in a fluid domain is , C p is the constant pressure specific heat capacity of the fluid; T is the local temperature in each domain; Q is the heat generated by the heat source per unit volume; The integrated solid-fluid heat transfer control equation is: .

[0012] As a further solution of the present invention: the total objective function J of topology optimization is: The heat exchange objective function J t and the total potential energy objective function J f Normalize it and get J' t and J' f , then the total objective function J = ω1J' t +ω2J' f .

[0013] Beneficial effects of the present invention: The present invention solves the contradiction between enhancing heat transfer performance and reducing flow resistance by establishing mass conservation equations and momentum conservation equations considering incompressible flow and laminar flow, as well as heat transfer control equations in solid and fluid domains, and optimizing the maximization of heat transfer and minimization of total potential energy of the fluid simultaneously through a dual objective function weighted method. The weight coefficient is introduced to flexibly adjust the relative importance of different objectives to meet different design requirements. The RAMP interpolation function model is used to interpolate the physical properties of solid materials, ensuring the sudden change of the material density design variable from 0 to 1 and defining a clear fluid-solid boundary. Through nonlinear interpolation processing, the non-existence of solutions that may be caused by discrete 0-1 problems is avoided, the practicality of the design is improved, and density filtering is realized by using Helmholtz-type partial differential equations, which is suitable for complex model design domains and simplifies the complexity in parallel calculations. Combined with the projection method, the consistency of design sensitivity is maintained, the generation of intermediate density is suppressed, the results are more practical, and the topological design method of the Pin-Fin structure is optimized. BRIEF DESCRIPTION OF THE DRAWINGS

[0014] The present invention will be further described below in conjunction with the accompanying drawings.

[0015] Figure 1 It is a schematic diagram of the process of dual-objective topology optimization of the present invention; Figure 2 It is a schematic diagram of the solution process of the material density design variable of the present invention. DETAILED DESCRIPTION

[0016] The following will be combined with the drawings in the embodiments of the present invention to clearly and completely describe the technical solutions in the embodiments of the present invention. Obviously, the described embodiments are only part of the embodiments of the present invention, not all of the embodiments. Based on the embodiments of the present invention, all other embodiments obtained by ordinary technicians in this field without creative work are within the scope of protection of the present invention.

[0017] See also Figure 1-Figure 2 As shown, the present invention is a Pin-Fin structure topology optimization design method based on a variable density method, comprising the following steps: First, determine whether the inlet flow rate of the design unit is determined. In one case, when the inlet flow rate is determined, the inlet Reynolds number is calculated according to the inlet flow rate and the target size, and the Pareto front under the inlet Reynolds number is drawn according to the fitting equation; Based on the Pareto front curve, the heat transfer objective function J under the inlet Reynolds number is calculated respectively. t and the total potential energy objective function J f The minimum value of the inlet Reynolds number is obtained, and the objective function Jt and the objective function J under the inlet Reynolds number are obtained. f The value range of the heat sink is based on the requirements for heat sink performance in practical applications (a typical trade-off requirement is to ensure that J t and J f The objective function of flow and the objective function of heat transfer are weighed, and then the operating point after the trade-off is determined on the Pareto front calculated in the above steps.

[0018] Another case is when the inlet flow rate is uncertain, but the objective function J is clearly optimized. t and J f The value of , then set the objective function J t And the objective function J f The target value of J is selected to meet the set operating condition point; t and J f Substitute the target value into the fitting equation to calculate the inlet Reynolds number, calculate the inlet flow velocity based on the inlet Reynolds number, draw the corresponding Pareto front, and mark the operating point; In both cases, the objective function is determined based on the distribution of the operating points on the Pareto front. Jt And the objective function J f The weights ω1 and ω2 are used to construct the model according to the inlet Reynolds number and the weights ω1 and ω2, respectively, to form the total objective function J of topology optimization, and to implement topology optimization, including interpolating the density of solid materials and establishing the control equations of fluid flow and heat transfer, to obtain the two-dimensional optimization results of topology optimization; The two-dimensional optimization result is reconstructed into a three-dimensional model, the three-dimensional model is simulated, the simulation result is compared with the two-dimensional optimization result, it is judged whether the structure meets the optimization design requirements, and the topological structure that meets the optimization design requirements is selected.

[0019] 1: Basic conditions to be considered in topology optimization: The basic cases considered are: (A) the fluid flow is incompressible laminar flow; (B) the viscous dissipation of the fluid is not considered; (C) the heat dissipation consists of heat conduction and heat convection; (D) the effect of gravity on fluid flow is ignored; (E) the material properties are independent of temperature.

[0020] The original intention of topology optimization is to solve the distribution problem of two discontinuous materials in space, which can be expressed as a discrete 0-1 problem. However, the discrete 0-1 problem may lead to the phenomenon that the solution does not exist, which is why the variable density topology optimization relaxes the design variables to 0 to 1. However, this may result in a large transition area between [0,1], making the boundary between the flow and the solid unclear and difficult to apply in practice. Good topology optimization should make the design variables have a very sudden change from 0 (solid) to 1 (fluid), thereby defining a clear boundary between the fluid and the solid. In order to achieve this goal, the physical properties of the solid and the fluid should be appropriately penalized. The method adopted by the present invention is to use a nonlinear interpolation function model (in the form of RAMP) for the physical parameters of the material.

[0021] ; Where s is the state variable of the corresponding physical quantity, G1 is the constraint function of the fluid volume fraction, V f is the fluid volume fraction, and f is the volume force.

[0022] 2. Basic equations of conjugate heat transfer to be considered during topology optimization: (1) Adding a resistance term to the momentum equation represents the resistance encountered by the fluid when it flows through the design domain; (2) The material density in the design domain is represented by the design variable γ. When the design variable is equal to 1, it means that the design unit is filled with fluid material. When the design variable is equal to 0, it means that the design unit is filled with solid material. (3) The material properties of fluids and solids are all constant, and the material properties in the design domain are interpolated through the unit material density; 1. Fluid flow governing equations: Consider the mass conservation equation for incompressible flow and laminar flow: (▽u)=0.

[0023] Conservation of Momentum: ; f is a dimensionless volume force, which characterizes the fluid resistance of porous media flow. According to Darcy's law, the volume force is proportional to the velocity u; where α is the reflectivity of the porous medium. For the fluid domain, the fluid can flow freely without being restricted by the volume force, α=0; for the solid domain, the fluid is subject to infinite resistance in the solid domain and cannot flow freely, α is infinite.

[0024] In order to characterize the relationship between the density and volume force corresponding to the solid domain and the fluid domain, the RAMP interpolation function, a reasonable approximate model of material properties, can be used to interpolate α; ; After integration, we get: ; 2. Heat transfer control equation: (1) Heat transfer in the solid domain: ; (2) Heat transfer in the fluid domain: ; The integrated solid-fluid heat transfer control equation is: ; k s and k f are the thermal conductivity of solid materials and liquid materials respectively; C p is the constant-pressure specific heat capacity of the fluid; T is the local temperature in each domain; Q is the heat generated by the heat source per unit volume.

[0025] In the topology optimization process of conjugate heat transfer problems, since there are both solid and liquid phases, it cannot be regarded as a single heat conduction or heat convection problem. The distribution of fluid and solid domains can only be determined after optimization. We cannot know in advance that a certain heat transfer control equation should be used at each point, so the heat transfer control equation needs to be processed. Fluid fractions are usually introduced to solve this problem, unifying the two equations into the following single equation applicable to fluid and solid domains: (considering thermal conductivity, specific heat capacity, and density): .

[0026] 3. Heat flow boundary conditions (1) Temperature-related heat sources: Assuming that the ideal heat source temperature is TQ, its heat generation is proportional to the temperature difference between the heat source and a certain point. According to Newton's cooling formula, the heat source term Q can be expressed as: .

[0027] (2) Temperature-independent heat source: Assuming that the total heat generated by the heat source is Qin, and the heat source is evenly distributed in the design area with an area of ​​A, the heat source term Q can be expressed as: .

[0028] In the topology optimization design domain, the remaining thermal boundaries are set as adiabatic boundary conditions, namely: .

[0029] 3: Selection of interpolation function in topology optimization: The interpolation function in RAMP form is the most commonly used function in flow problems or flow-heat transfer coupling problems, such as the interpolation function of thermal conductivity shown in the formula: ; Ks represents the thermal conductivity of the solid, Kf represents the thermal conductivity of the fluid, and q is the penalty factor of the interpolation function. According to this formula, a graph showing the change of the corresponding thermal conductivity interpolation function with the design variables can be drawn. In the research example of the present invention, the thermal conductivity of the fluid is taken as 0.6 [W / (m*k)]; the solid domain is set to copper, and the thermal conductivity of the solid is taken as 153 [W / (m*k)]. The difference curve is compared near γ=1 and γ=0 to see whether the curve is steep or smooth (steep when close to 0; smooth when close to 1. Therefore, the medium-density area is quickly penalized). In the present invention, q is habitually taken as 0.01. In this case, the intermediate density will also quickly tend to 0 or 1 between multiple iterations, which suppresses the generation of intermediate density, making the conversion between physical parameters of different materials more obvious, and the design results more practical.

[0030] Four: Density filtering and projection method: Common filtering techniques used in topology optimization require information about neighboring cells, which is not easy to obtain for fine grids or complex design domains and geometries. When the design domain is divided into multiple non-overlapping regions, the complexity of the problem in parallel computing is further increased. The density filter can be implicitly defined as the solution of a Helmholtz-type partial differential equation, that is, density filtering can be achieved by solving the Helmholtz partial differential equation: ; To solve the partial differential equation, the solution is obtained, that is, the filtered design variable, r is the length parameter of the filter radius rfilter, and r is a length parameter similar to the filter radius rfilter. This filtering technology only needs to optimize the mesh information required for the finite element discretization of the model, so it is better suitable for complex model design domains.

[0031] In the process of using Helmholtz filters, there are usually many intermediate density units, and this phenomenon will be further aggravated as the value of r increases. To solve this problem caused by density filtering, all filtered density values ​​exceeding the threshold η are gamma-projected to 1, and density values ​​below the threshold η are projected to 0, ensuring the sudden change of the material density design variable from 0 to 1 and defining a clear fluid-solid boundary. The physical density γ obtained by projection is calculated by the smooth function controlled by the projection parameter β as follows: ; Where e represents a natural constant, γ i represents any material density design variable; This expression can be further simplified using the hyperbolic tangent function tanh as: ; Among them, γ is the design variable after projection, γ β is the projection point, and the projection point value is 0.5. The filtered result is shown in the figure. In order to avoid falling into the local optimal solution problem during the optimization process, a continuous change method is adopted, β represents the projection slope, and the value represents the clarity of the result. As the β value gradually increases, the fluid-solid boundary becomes clearer, and the β value is 8 or its multiples. In the present invention, the value is 16.

[0032] 5. Dual-objective topology optimization: In the optimization design of fluid, enhancing heat transfer performance and reducing flow resistance are contradictory. To solve this problem, a dual objective function weighted method is used. t , and the total potential energy of the fluid J f Two objective functions are normalized. At the same time, the weight coefficient of the objective function is introduced to form the topology optimization objective function, which is expressed as J=ω1J' t +ω2J' f .

[0033] The above is a detailed description of an embodiment of the present invention, but the content is only a preferred embodiment of the present invention and cannot be considered to limit the scope of implementation of the present invention. All equivalent changes and improvements made within the scope of the present invention should still fall within the scope of the patent coverage of the present invention.

Claims

1. A Pin-Fin structure topology optimization design method based on variable density method, characterized in that: The following steps are involved: Determine whether the inlet flow rate of the design unit is determined. When the inlet flow rate is determined, calculate the inlet Reynolds number according to the inlet flow rate and the target size, and draw the Pareto front under the inlet Reynolds number according to the fitting equation; Based on the Pareto front curve, the heat transfer objective function J under the inlet Reynolds number is calculated respectively. t and the total potential energy objective function J f The minimum value of the inlet Reynolds number is obtained. t And the objective function J f The value range of ; select the operating point that meets the set heat sink performance requirements on the Pareto front; When the inlet flow rate is uncertain, the objective function J is set t And the objective function J f The target value of J is selected to meet the set operating condition point; t and J f Substitute the target value into the fitting equation to calculate the inlet Reynolds number, calculate the inlet flow velocity based on the inlet Reynolds number, draw the corresponding Pareto front, and mark the operating point; According to the distribution of the operating condition points on the Pareto frontier, the objective function J is determined. t And the objective function J f The weights ω1 and ω2 are used to construct the model according to the inlet Reynolds number and the weights ω1 and ω2, respectively, to form the total objective function J of topology optimization, and to implement topology optimization, including interpolating the density of solid materials and establishing the control equations of fluid flow and heat transfer, to obtain the two-dimensional optimization results of topology optimization; The two-dimensional optimization result is reconstructed into a three-dimensional model, the three-dimensional model is simulated, the simulation result is compared with the two-dimensional optimization result, and the topological structure that meets the optimization design requirements is screened.

2. The Pin-Fin structure topology optimization design method based on variable density method according to claim 1, characterized in that: The heat exchange objective function formula is J t =ST average ,ST average represents the average temperature of the solid and fluid domains in the design unit; The objective function formula of the total potential energy of the fluid is: ； Where u represents the fluid velocity, α is the reflectivity of the porous medium, T is the local temperature in the domain, γ represents the material density design variable with a value range of [0,1], and μ represents the fluid viscosity.

3. The Pin-Fin structure topology optimization design method based on variable density method according to claim 2 is characterized in that: The process of interpolating the density of solid materials in the topology optimization is as follows: The RAMP interpolation function model is used to interpolate the physical properties of solid materials. The interpolation function is: ； In the formula, K s Represents the thermal conductivity of the solid, K f represents the thermal conductivity of the fluid, q is the penalty factor of the interpolation function, and multiple iterations are performed until the material density design variable approaches 0 or 1.

4. The Pin-Fin structure topology optimization design method based on variable density method according to claim 3 is characterized in that: When the design domain is divided into multiple non-overlapping regions, density filtering is performed by solving the Helmholtz partial differential equation: ； The solution obtained by solving the partial differential equation is the design variable after filtering, r is the length parameter of the filter radius rfilter; Project the design variables. All material density design variables exceeding the threshold η are projected to 1, and those below the threshold η are projected to 0. The physical density obtained by projection is The smooth function expression controlled by the projection parameter β: ； Where e represents a natural constant, γ i represents any material density design variable; The expression can be simplified by using the hyperbolic tangent function tanh as follows: ； in, is the design variable after projection, γ β is the projection point.

5. The Pin-Fin structure topology optimization design method based on variable density method according to claim 3 is characterized in that: The process of establishing the control equation of fluid flow in the topology optimization is as follows: The conservation of momentum of the fluid is expressed according to the following formula: ； Where f is the dimensionless volume force, which is proportional to the velocity u, ρ is the fluid density, and p represents the pressure. In the fluid domain, α is 0, and in the solid domain, α is infinite. The RAMP interpolation function model is used to interpolate α, and the formula is: ； α s represents the reflectivity of the solid porous medium, α f Represents the porous medium reflectivity of the fluid; The integrated fluid flow control equation is: 。 6. The Pin-Fin structure topology optimization design method based on variable density method according to claim 5 is characterized in that: The process of establishing the heat transfer control equation in the topology optimization is as follows: The equation for heat transfer from a heat source in a solid domain is: , the equation for heat transfer from a heat source in a fluid domain is , C p is the constant pressure specific heat capacity of the fluid; T is the local temperature in each domain; Q is the heat generated by the heat source per unit volume; The integrated solid-fluid heat transfer control equation is: 。 7. The Pin-Fin structure topology optimization design method based on variable density method according to claim 1 is characterized in that: The overall objective function J of topology optimization is: The heat exchange objective function J t and the total potential energy objective function J f Normalize it and get J' t and J' f , then the total objective function J = ω1J' t +ω2J' f .

Images