CN116796385A - Composite radiator design method based on multi-material topological optimization - Google Patents
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Abstract
The invention discloses a composite radiator design method based on multi-material topological optimization, which comprises the following steps: establishing the geometric dimension of the two-dimensional design domain of the radiator and the position of the inlet and outlet of the runner; determining boundary conditions of the heat sink and physical properties of the materials used; introducing a material pseudo density gamma as a design variable, and constructing an ordered interpolation model of physical properties of different materials; taking the maximum heat transfer quantity and the minimum flow dissipation under the volume fraction constraint as optimization targets, and establishing a multi-material topological optimization model; updating design variables through an optimization algorithm based on a finite element analysis method to obtain an optimized topological shape of the two-dimensional radiator; and establishing a geometric model of the three-dimensional composite radiator according to the optimization result, and analyzing and verifying the performance of the geometric model. The method can obtain a high-efficiency heat dissipation path according to specific cooling requirements, optimize the distribution positions of different heat conducting materials in the heat radiator, and provide a heat management scheme with cost effectiveness while greatly improving cooling performance.
Description
Technical Field
The invention belongs to the technical field of electronic equipment, and particularly relates to a composite radiator design method based on multi-material topological optimization.
Background
In recent years, the ever smaller transistor size in electronic devices and the ever higher integration density of chips within the devices have driven a rapid development in device performance, but the resultant heat flux has also increased significantly. Furthermore, the heat flux generated within the device from the core local heating spot may rise to 8 times the average heat flux, as in the literature: "Ansari D, kim K Y.hotspot thermal management using amicrochannel-pinfin hybrid heat sink [ J ]. International Journal of Thermal Sciences,2018, 134:27-39". Heat is not timely conducted away causing the equipment to overheat and malfunction, resulting in serious damage. Ensuring that an electronic device is able to effectively dissipate heat is a prerequisite to maintain its performance and reliability. Therefore, proper thermal management is becoming more and more important, and the development of new and efficient heat dissipation systems is becoming urgent.
The liquid cooling radiator takes away heat generated by the electronic element through forced convection heat exchange generated by the liquid flowing through the internal channel, so that the electronic equipment is ensured to operate at a safe temperature. Heat sinks are popular because of their high heat transfer efficiency, small installation space required, and high reliability. The heat sink may be made from a variety of materials including aluminum alloys, copper, and other materials. Copper has excellent thermal conductivity making it an ideal heat sink material, however, is relatively heavy and expensive. Aluminum heat sinks have lower thermal conductivity but can provide a more lightweight solution. In addition, conventional single material cooling techniques cannot maintain the temperature uniformity conditions of the device surface due to the large difference in heat generated at the core of the electronic device from other background areas. If the heat sink structure is designed according to the core area, an increase in pumping power may be caused for the background area. Thus, a composite cold plate made of copper and aluminum provides a cost-effective, high performance and lightweight heat pipe understanding solution that meets a wide range of application requirements.
Conventional heat sink design processes often rely on empirical methods, which can lead to sub-optimal thermal performance of the designed structure and uncertain design cycles, as in the literature: "Dbouk T.A review about the engineering design of optimal heat transfer systems using topology optimization [ J ]. Applied Thermal Engineering,2017, 112:841-854". The structure of the flow channel is critical to the heat transfer performance of the radiator, and a most effective novel cooling channel design structure can be found for the radiator based on the conventional conjugate heat transfer topology optimization method. However, multi-material topology optimization methods tend to focus on static structure optimization problems, with relatively little research on the material distribution problems of the heat sink. Therefore, the composite radiator is designed by adopting multi-material topological optimization, the flowing heat dissipation path and the position distribution of the two materials in the radiator are optimized, and a more efficient cooling solution is provided for electronic equipment.
Disclosure of Invention
The invention aims to provide a composite radiator design method based on multi-material topological optimization, which can obtain a high-efficiency radiating path according to specific cooling requirements, optimize the distribution positions of different heat conducting materials in a radiator and provide a cost-effective heat management scheme while greatly improving cooling performance.
The technical scheme adopted by the invention is as follows:
the design method of the composite radiator based on the multi-material topological optimization specifically comprises the following steps: establishing the geometric dimension of the two-dimensional design domain of the radiator and the position of the inlet and outlet of the runner; determining boundary conditions of the heat sink and physical properties of the materials used; introducing a material pseudo density gamma as a design variable, and constructing an ordered interpolation model of physical properties of different materials; taking the maximum heat transfer quantity and the minimum flow dissipation under the volume fraction constraint as optimization targets, and establishing a multi-material topological optimization model; based on a finite element analysis method, solving a conjugate heat transfer multi-physical field, and updating design variables through an optimization algorithm to obtain an optimized topological shape of the two-dimensional radiator; and establishing a geometric model of the three-dimensional composite radiator according to the optimization result, and analyzing and verifying the performance of the geometric model.
The invention is also characterized in that:
the design method of the composite radiator based on the multi-material topological optimization is implemented according to the following steps:
step 1, determining the geometric dimension of a topological optimization two-dimensional design domain and the distribution of fluid inlets and outlets according to the configuration condition of electronic equipment;
step 2, determining the flow heat property parameters of the fluid and different solid materials, and boundary conditions of the inlet, the outlet and the wall surface of the flow channel;
step 3, constructing an ordered interpolation function of physical properties of multiple materials represented by a single design variable, and establishing a damping coefficient expression in a flow control equation for distinguishing fluid and solid states;
step 4, based on actual engineering requirements, taking the linear combination of the maximum heat transfer quantity and the flow power dissipation of the radiator as an optimization target, and establishing a mathematical model of multi-material topological optimization;
step 5, based on a finite element analysis method, solving a conjugate heat transfer multi-physical field, and updating design variables through an optimization algorithm to obtain an optimized topological structure of the two-dimensional radiator;
and 6, constructing a geometric model of the three-dimensional composite radiator based on the topological boundary of the two-dimensional optimization result obtained in the step 5, and further determining the configuration of the whole flow channel and the distribution condition of multiple materials in the whole radiator.
The method also comprises the following two steps:
step 7, determining the flow heat boundary condition of the three-dimensional composite radiator obtained in the step 6, dispersing the structure according to solving requirements, and carrying out finite element method solving analysis;
and 8, determining the effect of optimizing the structure by analyzing the temperature performance index of the surface of the heat source and the flow performance index of the channel.
In the step 1, the determined geometric dimensions of the two-dimensional design domain are length L and width W; the distribution of the positions of the entrances and exits is as follows: the characteristic length is D on the central line of the design domain, on the diagonal line of the design domain or on the four corners of the design domain in a staggered mode.
The multi-solid material determined in step 2 comprises copper and aluminum 6061, and the densities are ρ respectively 1 And ρ 2 The constant pressure heat capacity is c respectively 1 And c 2 The heat conductivity coefficient is k respectively 1 And k 2 The method comprises the steps of carrying out a first treatment on the surface of the The fluid cooling working medium is water, and the density is ρ 3 Constant pressure heat capacity of c 3 A thermal conductivity of k 3 The method comprises the steps of carrying out a first treatment on the surface of the The determined boundary conditions include an inlet flow velocity U in Inlet temperature T in Outlet pressure P out An adiabatic boundary condition of the outer wall surface, and a heat generating source Q according to the distribution of the solid material.
The ordered interpolation function in step 3 is specifically:
the physical properties of the multi-material are characterized by pseudo-density gamma as a single design variable, when gamma=0 represents copper material, when gamma=0.5 represents aluminum 6061, and when gamma=1 represents cooling medium water; according to the ordering of the material properties: ρ 1 >ρ 2 >ρ 3 、k 1 >k 2 >k 3 And c 1 <c 2 <c 3 And based on a method of ordered punishment solid isotropic materials, an ordered interpolation function of materials related to gamma is constructed, and the expression is:
in the formula (1), E represents physical property parameters of the material, including density, constant pressure heat capacity and heat conductivity coefficient; subscript i equals 1, 2, and 3 for copper, aluminum 6061, and water, respectively; p represents a penalty parameter for the interpolation function.
The damping coefficient expression in the step 3 is specifically:
the damping coefficient alpha (gamma) is a quantity related to gamma, fluid and solid states are distinguished by the value of the damping coefficient, and is characterized as solid material when the damping coefficient reaches the maximum, and is characterized as fluid material when the value of the damping coefficient is close to zero, and the interpolation expression is as follows:
in the formula (2), the amino acid sequence of the compound,
in the formula (2) and the formula (3), alpha max For maximum reverse osmosis rate, da is darcy number, e is natural constant, s is control parameter for regulating convexity of interpolation curve, and b represents intermediate conversion point for controlling interpolation curve from maximum value to minimum value.
The step 4 is specifically as follows:
and 4.1, taking a linear combination of the maximum heat transfer quantity and the minimum flow power dissipation as an optimization target J, and respectively carrying out normalization treatment on the optimization target J, wherein the expression is as follows:
in the formula (4), the amino acid sequence of the compound,
in the formula (4) and the formula (5), J Q For heat transfer quantity J f For flow dissipated power, subscript 0 denotes the initial value of the optimization objective, T Q Is the ideal temperature of the heat source, h is the heating coefficient, T is the temperature in the design domain, Ω is the design domain, μ is the hydrodynamic viscosity, u is the scalar of the fluid flow velocity;
and 4.2, introducing an optimization target into a topological optimization mathematical model, and establishing corresponding constraints, wherein the constraints comprise a flow control equation, a heat transfer control equation, an average volume constraint determined by limiting material cost and a constraint range of a design variable, and the expression is as follows:
in the formula (6), the amino acid sequence of the compound,is a gradient operator, u is a velocity vector, P is pressure, V total Representing the total volume of the design field, +.>Representing the average volume constraint.
The step 5 is specifically as follows:
obtaining the value of the objective function in the step 4 through the solution of the finite element, calculating the sensitivity of the objective function to the design variable in the step 4 by applying an accompanying method, further searching the optimization direction of the design variable which has obvious influence on the hydrothermal performance, updating the design variable by adopting a moving asymptote algorithm, and repeating the process until the iteration stop condition is met;
the stopping conditions of the moving asymptote algorithm are as follows: giving the maximum iteration step number as 500, and designating the tolerance of the objective function as a convergence condition: i J k+1 -J k |≤10 -6 Wherein k represents the iteration step number, and when the optimization reaches the maximum iteration step number or meets the convergence condition, the calculation is terminated, and a two-dimensional optimization result is obtained.
The step 6 is specifically as follows:
extracting the topological boundary of the two-dimensional optimization structure obtained in the step 5, importing the topological boundary into modeling software to establish a three-dimensional composite radiator model, keeping the normal section of the three-dimensional model consistent with the two-dimensional optimization result, and determining that the internal dimensions of the model are length L, width W and height H and the external dimensions are length L 1 Width W 1 And height H 1 The characteristic length of the access opening is D.
The beneficial effects of the invention are as follows:
(1) Compared with a radiator made of uniform materials, the radiator made of copper and aluminum is used, the problem of nonuniform core hot spot temperature in electronic equipment can be effectively solved by utilizing the characteristics of the materials, and the radiator has the advantages of simultaneously taking into consideration the performance of high heat conductivity and low cost;
(2) Compared with the traditional design method, the method of the invention applies the topological optimization to the structural design of the composite radiator, greatly eliminates the interference of human factors, can automatically search the flowing heat dissipation path based on the optimization target in the actual engineering, and increases the design freedom of the flow channel structure. In addition, the method improves the capability and efficiency of heat convection of the radiator by changing the flow mode of the cooling working medium;
(3) The method is based on an ordered SIMP interpolation method, two solid materials and one fluid material are represented by a single design variable, the number of variables in the design and the influence of unstable factors are reduced, and the conjugate heat transfer process of multi-material topological optimization is realized. The distribution and the shape of two solid materials in the radiator are optimized through given targets and heat sources, so that the heat conduction performance of different materials can be better exerted, the temperature uniformity and the heat conduction efficiency of the whole radiator are further improved, and the radiator has a certain guiding significance for developing a novel high-efficiency radiator.
Drawings
FIG. 1 is a flow chart of the method of the present invention;
FIG. 2 is a schematic representation of a two-dimensional model of a multi-material topology optimization obtained in example 1 of the present invention;
FIG. 3 is a schematic view of a three-dimensional composite radiator model and dimensions of the inlet and outlet on the center line obtained in example 1 of the present invention;
FIG. 4 shows the temperature distribution of the upper surface of the three-dimensional composite radiator obtained in example 1 of the present invention;
FIG. 5 shows the temperature distribution of the upper surface of a three-dimensional uniformly distributed radiator in the conventional design;
FIG. 6 is a cross-sectional flow velocity vector diagram of a three-dimensional composite heat sink obtained in example 1 of the present invention;
FIG. 7 is a graph showing the average temperature of the method of example 1 of the present invention versus the conventional design method at different heat source heat flux densities;
FIG. 8 is a schematic diagram of a three-dimensional composite radiator model and dimensions of the inlet and outlet on a diagonal obtained in example 2 of the present invention;
fig. 9 is a schematic diagram of a three-dimensional composite radiator model and dimensions in which inlets and outlets are staggered at four corners, which is obtained in example 3 of the present invention.
In the figure, copper, aluminum and 6061,3 are used for cooling working medium water.
Detailed Description
The invention will be described in detail below with reference to the drawings and the detailed description.
As shown in fig. 1, the design method of the composite radiator based on multi-material topological optimization is implemented specifically according to the following steps:
step 1, determining the geometric dimensions of the topological optimization two-dimensional design as length L and width W according to the configuration condition of the electronic equipment, and determining the position distribution of an entrance, wherein the position distribution of the entrance determined by the method can be as follows: the characteristic lengths are D on the central line of the design domain, on the diagonal line of the design domain or on the four corners of the design domain in a staggered manner;
step 2, determining flow thermal property parameters of fluid and different solid materials and boundary conditions of a runner inlet, a runner outlet and a wall surface in order to analyze physical phenomena in an actual system;
wherein the defined multi-solid material comprises copper and aluminum 6061, the densities are ρ respectively 1 And ρ 2 The constant pressure heat capacity is c respectively 1 And c 2 The heat conductivity coefficient is k respectively 1 And k 2 The method comprises the steps of carrying out a first treatment on the surface of the The determined fluid cooling working medium is water, and the density is ρ 3 Constant pressure heat capacity of c 3 A thermal conductivity of k 3 The method comprises the steps of carrying out a first treatment on the surface of the The determined boundary conditions include an inlet flow velocity U in Inlet temperature T in Outlet pressure P out An adiabatic boundary condition of the outer wall surface and a heat generating source Q according to the solid material distribution;
step 3, in order to enable the design variables to represent different materials, constructing an ordered interpolation function of physical properties of multiple materials represented by a single design variable, and establishing a damping coefficient expression in a flow control equation for distinguishing fluid and solid states;
the ordered interpolation function is specifically:
characterizing the physical properties of the multi-material by pseudo-density γ as a single design variable, when γ=0 represents copper material; when γ=0.5 represents aluminum 6061; when γ=1 represents cooling medium water. According to the ordering of the material properties: ρ 1 >ρ 2 >ρ 3 、k 1 >k 2 >k 3 And c 1 <c 2 <c 3 And constructing a gamma-related material interpolation function based on an ordered punishment solid isotropic material method (Solid Isotropic Material with Penalization, SIMP), wherein the expression is as follows:
in the formula (1), E represents physical property parameters of the material, including density, constant pressure heat capacity and heat conductivity coefficient; subscript i equals 1, 2, and 3 for copper, aluminum 6061, and water, respectively; p represents a penalty parameter for the interpolation function.
The damping coefficient expression is specifically:
the damping coefficient alpha (gamma) is a quantity related to gamma, fluid and solid states are distinguished by the value of the damping coefficient, and is characterized as solid material when the damping coefficient reaches the maximum, and is characterized as fluid material when the value of the damping coefficient is close to zero, and the interpolation expression is as follows:
in the formula (2), the amino acid sequence of the compound,
in the formula (2) and the formula (3), alpha max For maximum reverse osmosis rate, da is Darcy number, e is natural constant, s is control parameter for regulating convexity of interpolation curve, b is intermediate conversion point for controlling interpolation curve from maximum value to minimum value；
And 4, based on actual engineering requirements, taking the linear combination of the maximum heat transfer quantity and the flow power dissipation of the radiator as an optimization target, and establishing a mathematical model of multi-material topological optimization, wherein the specific steps are as follows:
step 4.1, taking a linear combination of the maximum heat transfer quantity and the minimum flow power dissipation as an optimization target J, and respectively carrying out normalization treatment on the two target orders of magnitude of difference, wherein the expression is as follows:
in the formula (4), the amino acid sequence of the compound,
in the formula (4) and the formula (5), J Q For heat transfer quantity J f For flow dissipated power, subscript 0 denotes the initial value of the optimization objective, T Q Is the ideal temperature of the heat source, h is the heating coefficient, T is the temperature in the design domain, Ω is the design domain, μ is the hydrodynamic viscosity, u is the scalar of the fluid flow velocity;
and 4.2, introducing an optimization target into a topological optimization mathematical model, and establishing corresponding constraints, wherein the constraints comprise a flow control equation, a heat transfer control equation, an average volume constraint determined by limiting material cost and a constraint range of a design variable, and the expression is as follows:
in the formula (6), the amino acid sequence of the compound,is a gradient operator, u is a velocity vector, P is pressure, V total Representing the total volume of the design field, +.>Representing an average volume constraint;
and 5, solving the conjugated heat transfer multi-physical field based on a finite element analysis method, and updating design variables through an optimization algorithm to obtain an optimized topological structure of the two-dimensional radiator. The method comprises the following specific steps:
obtaining the value of the objective function in the step 4 through the solution of the finite element, calculating the sensitivity of the objective function to the design variable in the step 4 by applying an accompanying method, further searching the optimization direction of the design variable which has obvious influence on the hydrothermal performance, updating the design variable by adopting a moving asymptote algorithm (MMA), and repeating the process until the iteration stop condition is met;
the stopping conditions of the moving asymptote algorithm are as follows: giving the maximum iteration step number as 500, and designating the tolerance of the objective function as a convergence condition: i J k+1 -J k |≤10 -6 Where k represents the number of iteration steps. And when the optimization reaches the maximum iteration step number or meets the convergence condition, the calculation is terminated, and a two-dimensional optimization result is obtained.
Step 6, extracting the topological boundary of the two-dimensional optimization structure obtained in the step 5, importing the topological boundary into modeling software CreoParametric, carrying out smooth processing on the topological boundary, establishing a three-dimensional composite radiator model, and further determining the configuration of the whole flow channel and the distribution condition of two materials of copper and aluminum 6061 in the whole radiator, wherein the topological structure of the normal section of the three-dimensional model is consistent with the two-dimensional optimization result, the determined internal dimensions of the model are length L, width W and height H, and the external dimensions are length L 1 Width W 1 And height H 1 The characteristic length of the access opening is D.
And 7, determining the flow heat boundary condition of the three-dimensional composite radiator obtained in the step 6, dispersing the structure according to solving requirements, and carrying out finite element method solving analysis, wherein the method comprises the following specific steps of:
step 7.1, determining a flow heat boundary condition of the three-dimensional composite radiator, which comprises the following steps: position of heat generating source and heat flux density Q, inlet flow rate U in Inlet temperature T in Outlet pressure P out And an insulating boundary of the outer wall;
step 7.2, determining the size and discrete form of the grid by utilizing grid independence test according to the geometric dimension and the physical field requirement of the radiator, wherein the grid dividing unit adopts unstructured tetrahedral elements to adapt to geometrically irregular calculation domains, and generating thin boundary layer grids on the wet peripheral surface so as to accurately capture fluid close to the wall surface;
and 7.3, carrying out finite element solving analysis by using commercial software CoololMultiphysics.
And 8, determining the effect of optimizing the structure by analyzing the temperature performance index of the surface of the heat source and the flow performance index of the channel.
Wherein, the surface temperature performance index expression is as follows:
in the formulas (7) and (8),represents average temperature, RMST represents root mean square of temperature;
the flow coefficient of friction of the flow channel is expressed as follows:
in the formula (9), ΔP represents the pressure drop at the inlet and outlet of the flow channel, l represents the length of the flow channel, U avg Indicating the average velocity of the fluid.
Example 1
1. Simulation model parameter setting:
in this embodiment, a two-dimensional model of the radiator optimized by the method of the present invention is shown in fig. 2, a structure of a three-dimensional composite radiator obtained based on a two-dimensional topology structure is shown in fig. 3, and its internal dimensions are 100mm×100mm×7mm, and its external dimensions are104mm multiplied by 11mm, the thickness of the shell is 2mm, the inlet and the outlet of the flow channel are distributed on the central line of the radiator, the characteristic length of the inlet and the outlet of the flow channel is 10mm, and the heat flow density of the heat source is set to 20000W/m 2 The inlet flow rate was 0.03m/s, the inlet temperature was 293.15K, the ambient temperature was 293.15K, the outlet pressure was 0Pa, the other external walls were adiabatic boundary conditions, and the densities of copper, aluminum 6061 and water were 8960kg/m, respectively 3 、2700kg/m 3 And 998kg/m 3 The thermal conductivity was 400W/(mK), 155W/(mK) and 0.6W/(mK), respectively.
In fig. 3, reference numeral 1 represents a copper material, reference numeral 2 represents an aluminum material, and reference numeral 3 represents water, and it can be seen that the distribution of the three materials exhibits an irregular shape. From the whole, the fluid is divided into three main flow channels after entering from the inlet, each branch flow is divided into finer branches, and the last branch flow is converged and flows out at the outlet position; the copper material 1 is distributed around the flow channel in a large area, and the heat transfer rate is increased through the high heat conductivity of the copper material so as to thin a thermal boundary layer formed by the fluid-solid interface; the aluminum material 2 is distributed at the position with less heat dissipation requirement and is surrounded by the copper material 1 or distributed at four corners of the radiator, so that the economic benefit of the material is increased.
2. Simulation content and result comparison
The grid analysis and multi-physical field finite element solution process is performed in Comsol Multiphysics. The performance comparison results of the composite radiator with the inlet and outlet on the central line and the conventional radiator with the multi-material topological optimization design are shown in table 1. As can be seen from the results in Table 1, the temperature and flow performance index are both improved greatly, the average temperature of the heat source is reduced by 7.41K, the root mean square of the temperature is reduced by 1.99K, and the flow friction coefficient is reduced by 0.74. The optimized cooling performance of the radiator is improved, the required pumping power is further reduced, and a certain positive effect on energy conservation is achieved.
Table 1 Performance comparison of Multi-Material topology optimization designed composite radiator with Access at center line and traditional radiator
| Scheme for the production of a semiconductor device | Average temperature (K) | Root mean square of temperature (K) | Coefficient of friction |
| Topology optimization structure | 321.06 | 3.98 | 0.74 |
| Traditional design structure | 328.47 | 5.97 | 1.48 |
As shown in fig. 4, the temperature distribution of the upper surface of the three-dimensional composite radiator optimized by the method of the invention is shown in fig. 5, the temperature distribution of the upper surface of the three-dimensional uniformly distributed radiator designed by the conventional method is shown in fig. 5. It can be seen that the temperatures of the heat sources of the two designs gradually increase along the flow direction of the cooling medium, and the high-temperature hot spot areas are mainly concentrated at the outlet side positions. This is because as the fluid advances toward the outlet, it absorbs a significant amount of the heat generated by the heat source, resulting in a temperature rise. Compared with the temperature distribution of the traditional design, the range of the high-temperature area of the optimized heat source is smaller, and the temperature distribution gradient is more uniform. The maximum temperature is reduced by 10.3K, and the heating condition of the heat source is effectively controlled.
As shown in fig. 6, in order to obtain the flow channel velocity vector diagram of the cross section of the three-dimensional composite radiator optimized by the method of the invention, it can be seen that the optimized flow velocity is uniformly distributed at each tributary position, and the unnecessary flow separation phenomenon in the flow channel is reduced. Meanwhile, a fluid stagnation area is almost not formed at the corner of the optimized flow channel, and the fluids are more easily mixed, so that the energy loss of the radiator system is smaller, and the radiating efficiency is higher.
To further illustrate the effect of the present invention, the heat flux density of the heat source is from 5000W/m 2 ～60000W/m 2 Further describing the temperatures below, FIG. 7 is a graph of the average temperature of the present invention versus the average temperature of a conventional design at different heat source heat flux densities. As can be seen from fig. 7, the average temperature increases linearly with the heat flux density, the optimized temperature curve is distributed entirely below the conventionally designed temperature curve, and the slope of the curve is greater. The improved effect of the optimized radiator is improved more when the radiator is applied to high heat flux density.
Example 2
1. Simulation model parameter setting:
the structure of the three-dimensional composite radiator optimized by the method of the present invention is shown in FIG. 8, the internal dimension is 100mm×100mm×7mm, the external dimension is 104mm×104mm×11mm, the thickness of the shell is 2mm, the inlet and outlet of the flow channel are distributed on the diagonal line of the radiator, the characteristic length of the inlet and outlet of the flow channel is 10mm, and the heat flow density of the heat source is set to 20000W/m 2 The inlet flow rate was 0.03m/s, the inlet temperature was 293.15K, the ambient temperature was 293.15K, the outlet pressure was 0Pa, the other external walls were adiabatic boundary conditions, and the densities of copper, aluminum 6061 and water were 8960kg/m, respectively 3 、2700kg/m 3 And 998kg/m 3 The thermal conductivity was 400W/(mK), 155W/(mK) and 0.6W/(mK), respectively. It can be seen that the fluid, after entering from the inlet, is first divided into two main flow channels, then divided into fine branches, finally converged to the outlet and discharged, and both the copper material 1 and the aluminum material 2 are in an irregularly distributed shape.
2. Simulation content and result comparison
The grid analysis and multi-physical field finite element solution process is performed in Comsol Multiphysics. The performance comparison results of the composite radiator with the inlet and outlet on diagonal multi-material topology optimization design and the conventional radiator are shown in table 2. As can be seen from the results in Table 2, the average temperature of the heat source was reduced by 6.55K, the root mean square of the temperature was reduced by 1.59K, and the flow friction coefficient was reduced by 0.6.
Table 2 comparison of Performance of Multi-Material topology optimization designed composite radiator with Access to the diagonal and traditional radiator
| Scheme for the production of a semiconductor device | Average temperature (K) | Root mean square of temperature (K) | Coefficient of friction |
| Topology optimization structure | 322.19 | 4.13 | 0.59 |
| Traditional design structure | 328.74 | 5.72 | 1.19 |
Example 3
1. Simulation model parameter setting:
the structure of the three-dimensional composite radiator optimized by the method of the embodiment is shown in FIG. 9, the internal dimension is 100mm multiplied by 7mm, the external dimension is 104mm multiplied by 11mm, the thickness of the shell is 2mm, the inlets and the outlets of the flow channels are distributed on four corners of the radiator in a staggered manner, the characteristic length of the inlets and the outlets of the flow channels is 10mm, and the heat flow density of the heat source is set to 20000W/m 2 Inlet flow rateAt 0.03m/s, an inlet temperature of 293.15K, an ambient temperature of 293.15K, an outlet pressure of 0Pa, an adiabatic boundary condition for the other external walls, and densities of copper, aluminum 6061 and water of 8960kg/m, respectively 3 、2700kg/m 3 And 998kg/m 3 The thermal conductivity was 400W/(mK), 155W/(mK) and 0.6W/(mK), respectively. It can be seen that the fluid, after entering from the inlet, first creates a main flow channel, then divides into fine branches, finally converges to the outlet and flows out, and both the copper material 1 and the aluminum material 2 take on an irregularly distributed shape.
2. Simulation content and result comparison
The grid analysis and multi-physical field finite element solution process is performed in Comsol Multiphysics. The performance comparison results of the composite radiator and the conventional radiator with the multi-material topology optimization design, wherein the inlets and outlets are distributed at the four corners of the radiator in a staggered manner, are shown in table 3. As can be seen from the results in Table 3, the average temperature of the heat source was reduced by 8.14K, the root mean square of the temperature was reduced by 2.67K, and the flow friction coefficient was reduced by 0.1.
Table 3 Performance comparison of a composite radiator with multiple material topology optimization design and a traditional radiator with inlets and outlets distributed at four corners of the radiator in a staggered manner
| Scheme for the production of a semiconductor device | Average temperature (K) | Root mean square of temperature (K) | Coefficient of friction |
| Topology optimization structure | 313.03 | 1.96 | 0.33 |
| Traditional design structure | 321.17 | 4.63 | 0.43 |
Claims (10)
1. The composite radiator design method based on multi-material topological optimization is characterized by comprising the following steps of: establishing the geometric dimension of the two-dimensional design domain of the radiator and the position of the inlet and outlet of the runner; determining boundary conditions of the heat sink and physical properties of the materials used; introducing a material pseudo density gamma as a design variable, and constructing an ordered interpolation model of physical properties of different materials; taking the maximum heat transfer quantity and the minimum flow dissipation under the volume fraction constraint as optimization targets, and establishing a multi-material topological optimization model; based on a finite element analysis method, solving a conjugate heat transfer multi-physical field, and updating design variables through an optimization algorithm to obtain an optimized topological shape of the two-dimensional radiator; and establishing a geometric model of the three-dimensional composite radiator according to the optimization result, and analyzing and verifying the performance of the geometric model.
2. The composite heat sink design method based on multi-material topology optimization of claim 1, wherein the method is implemented specifically according to the following steps:
step 1, determining the geometric dimension of a topological optimization two-dimensional design domain and the distribution of fluid inlets and outlets according to the configuration condition of electronic equipment;
step 2, determining the flow heat property parameters of the fluid and different solid materials, and boundary conditions of the inlet, the outlet and the wall surface of the flow channel;
step 3, constructing an ordered interpolation function of physical properties of multiple materials represented by a single design variable, and establishing a damping coefficient expression in a flow control equation for distinguishing fluid and solid states;
step 4, based on actual engineering requirements, taking the linear combination of the maximum heat transfer quantity and the flow power dissipation of the radiator as an optimization target, and establishing a mathematical model of multi-material topological optimization;
step 5, based on a finite element analysis method, solving a conjugate heat transfer multi-physical field, and updating design variables through an optimization algorithm to obtain an optimized topological structure of the two-dimensional radiator;
and 6, constructing a geometric model of the three-dimensional composite radiator based on the topological boundary of the two-dimensional optimization result obtained in the step 5, and further determining the configuration of the whole flow channel and the distribution condition of multiple materials in the whole radiator.
3. The composite heat sink design method based on multi-material topology optimization of claim 2, further comprising the steps of:
step 7, determining the flow heat boundary condition of the three-dimensional composite radiator obtained in the step 6, dispersing the structure according to solving requirements, and carrying out finite element method solving analysis;
and 8, determining the effect of optimizing the structure by analyzing the temperature performance index of the surface of the heat source and the flow performance index of the channel.
4. The method for designing a composite radiator based on multi-material topological optimization according to claim 2, wherein in step 1, the determined geometric dimensions of the two-dimensional design domain are length L and width W; the distribution of the positions of the entrances and exits is as follows: the characteristic length is D on the central line of the design domain, on the diagonal line of the design domain or on the four corners of the design domain in a staggered mode.
5. The method for designing a composite heat sink based on multi-material topology optimization of claim 2, wherein the multi-solid materials determined in step 2 comprise copper and aluminum 6061 with densities ρ, respectively 1 And ρ 2 The constant pressure heat capacity is c respectively 1 And c 2 The heat conductivity coefficient is k respectively 1 And k 2 The method comprises the steps of carrying out a first treatment on the surface of the The fluid cooling working medium is water, and the density is ρ 3 Constant pressure heat capacity of c 3 A thermal conductivity of k 3 The method comprises the steps of carrying out a first treatment on the surface of the The determined boundary conditions include an inlet flow velocity U in Inlet temperature T in Outlet pressure P out An adiabatic boundary condition of the outer wall surface, and a heat generating source Q according to the distribution of the solid material.
6. The composite heat sink design method based on multi-material topology optimization of claim 2, wherein the ordered interpolation function in step 3 is specifically:
the physical properties of the multi-material are characterized by pseudo-density gamma as a single design variable, when gamma=0 represents copper material, when gamma=0.5 represents aluminum 6061, and when gamma=1 represents cooling medium water; according to the ordering of the material properties: ρ 1 >ρ 2 >ρ 3 、k 1 >k 2 >k 3 And c 1 <c 2 <c 3 And based on a method of ordered punishment solid isotropic materials, an ordered interpolation function of materials related to gamma is constructed, and the expression is:
in the formula (1), E represents physical property parameters of the material, including density, constant pressure heat capacity and heat conductivity coefficient; subscript i equals 1, 2, and 3 for copper, aluminum 6061, and water, respectively; p represents a penalty parameter for the interpolation function.
7. The method for designing a composite radiator based on multi-material topological optimization according to claim 6, wherein the damping coefficient expression in step 3 is specifically:
the damping coefficient alpha (gamma) is a quantity related to gamma, fluid and solid states are distinguished by the value of the damping coefficient, and is characterized as solid material when the damping coefficient reaches the maximum, and is characterized as fluid material when the value of the damping coefficient is close to zero, and the interpolation expression is as follows:
in the formula (2)，
In the formula (2) and the formula (3), alpha max For maximum reverse osmosis rate, da is darcy number, e is natural constant, s is control parameter for regulating convexity of interpolation curve, and b represents intermediate conversion point for controlling interpolation curve from maximum value to minimum value.
8. The method for designing a composite radiator based on multi-material topological optimization according to claim 2, wherein the step 4 is specifically:
and 4.1, taking a linear combination of the maximum heat transfer quantity and the minimum flow power dissipation as an optimization target J, and respectively carrying out normalization treatment on the optimization target J, wherein the expression is as follows:
in the formula (4), the amino acid sequence of the compound,
in the formula (4) and the formula (5), J Q For heat transfer quantity J f For flow dissipated power, subscript 0 denotes the initial value of the optimization objective, T Q Is the ideal temperature of the heat source, h is the heating coefficient, T is the temperature in the design domain, Ω is the design domain, μ is the hydrodynamic viscosity, u is the scalar of the fluid flow velocity;
and 4.2, introducing an optimization target into a topological optimization mathematical model, and establishing corresponding constraints, wherein the constraints comprise a flow control equation, a heat transfer control equation, an average volume constraint determined by limiting material cost and a constraint range of a design variable, and the expression is as follows:
in the formula (6), the amino acid sequence of the compound,is a gradient operator, u is a velocity vector, P is pressure, V total Representing the total volume of the design field, +.>Representing the average volume constraint.
9. The method for designing a composite radiator based on multi-material topological optimization according to claim 2, wherein the step 5 is specifically:
obtaining the value of the objective function in the step 4 through the solution of the finite element, calculating the sensitivity of the objective function to the design variable in the step 4 by applying an accompanying method, further searching the optimization direction of the design variable which has obvious influence on the hydrothermal performance, updating the design variable by adopting a moving asymptote algorithm, and repeating the process until the iteration stop condition is met;
the stopping conditions of the moving asymptote algorithm are as follows: giving the maximum iteration step number as 500, and designating the tolerance of the objective function as a convergence condition: i J k+1 -J k |≤10 -6 Wherein k represents the iteration step number, and when the optimization reaches the maximum iteration step number or meets the convergence condition, the calculation is terminated, and a two-dimensional optimization result is obtained.
10. The method for designing a composite radiator based on multi-material topological optimization according to claim 2, wherein step 6 is specifically:
extracting the topological boundary of the two-dimensional optimization structure obtained in the step 5, importing the topological boundary into modeling software to establish a three-dimensional composite radiator model, keeping the normal section of the three-dimensional model consistent with the two-dimensional optimization result, and determining that the internal dimensions of the model are length L, width W and height H and the external dimensions are length L 1 Width W 1 And height H 1 The characteristic length of the access opening is D.
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