Integrated launch antenna heat dissipation channel topology optimization design method

Abstract

The application discloses a topology optimization design method for integrated emission antenna heat dissipation flow channels, and specifically relates to the following steps: establishing a simplified two-dimensional plane heat source model; initializing and applying boundary conditions at the inlet; distributing compact support radial basis functions with an expansion coefficient on the obtained finite element grid nodes divided in a design domain, then linearly superimposing the radial basis functions to obtain a parameterized level set function; obtaining the distribution of solid and fluid in the design domain according to the level set function value; solving the heat exchange performance of the heat dissipation flow channel configuration represented by the parameterized level set function; establishing a mathematical model of the topology optimization problem, calculating the sensitivity of the objective function and the constraint condition with respect to the design variable expansion coefficient; and obtaining a complete heat dissipation flow channel design. The method can meet the demand of maximizing the heat exchange capacity at a high heat flow density heat source while simplifying the calculation, and improve the heat dissipation performance.

Description

Technical Field

[0001] This invention belongs to the field of heat dissipation channel layout design, specifically relating to an integrated transmitting antenna heat dissipation channel topology optimization design method. Background Technology

[0002] With the advent of the 5G era, the integration and power density of electronic devices are increasing dramatically, and transmitting antennas are no exception. Their high power, high density, and integration lead to increasingly demanding requirements for thermal control technology. To ensure the reliability and stability of the T-components within integrated transmitting antennas, efficient heat dissipation system design has become an urgent need. Liquid coolers, due to their high cooling performance and uniformity, are often used as an efficient heat dissipation method in transmitting antenna heat dissipation system design. However, traditional heat dissipation channel design based on experience is insufficient to further improve heat dissipation efficiency. The heat dissipation channel layout design of integrated transmitting antennas has become a pressing issue, and combining it with topology optimization technology is a feasible method to find the optimal heat dissipation channel layout.

[0003] Topology optimization design is a design method that seeks the optimal material distribution corresponding to the objective function within the design domain while satisfying constraints. Originating in the field of structural mechanics, it has been widely applied to heat dissipation channel design due to its high degree of design freedom. To date, topology optimization has evolved to include homogenization methods, variable density methods, level set methods, and the BESO method. Among these, the level set method can obtain topological configurations with smooth and clear boundaries; however, traditional level set methods require solving HJ partial differential equations, which are computationally difficult and complex. Summary of the Invention

[0004] The purpose of this invention is to provide an integrated method for optimizing the topology of the heat dissipation channel of a transmitting antenna. It adopts a parametric level set method, which simplifies the calculation and designs a heat dissipation channel topology with smooth and clear boundaries. It can also meet the requirement of maximizing heat transfer at high heat flux density heat sources and improve heat dissipation performance.

[0005] The technical solution adopted in this invention is an integrated transmitting antenna heat dissipation channel topology optimization design method, which specifically includes the following steps:

[0006] Step 1: Establish a simplified two-dimensional planar heat source model;

[0007] Step 2: Using the simplified two-dimensional planar heat source model as the design object, perform finite element mesh generation on it, initialize it with the spread factor as the design variable, and apply boundary conditions at the inlet;

[0008] Step 3: Distribute the tightly supported radial basis functions with expansion coefficients onto the finite element mesh nodes obtained in Step 2 within the design domain. Then, linearly superimpose these radial basis functions to obtain the parameterized level set function. Finally, obtain the distribution of solids and fluids in the design domain based on the level set function value.

[0009] Step 4: Solve for the heat transfer performance of the heat dissipation channel configuration represented by the parameterized level set function;

[0010] Step 5: Establish a mathematical model for the topology optimization problem, and calculate the sensitivity of the objective function and constraints to the expansion coefficients of the design variables;

[0011] Step 6: Obtain a heat dissipation channel that meets the design requirements and has clear boundaries. Then, perform three-dimensional stretching based on the heat dissipation channel boundaries to obtain the complete heat dissipation channel design.

[0012] The invention is further characterized in that,

[0013] Step 1 specifically involves: simplifying the integrated transmitting antenna structure, simplifying the dimensions of the integrated transmitting antenna, the dimensions of the flow channel inlet and outlet, and the dimensions of the heat-generating device, taking the array size of the integrated transmitting antenna as the design domain, distributing the flow channel inlet and outlet on both sides, taking the heat-generating device as the heat source, and establishing a simplified two-dimensional planar heat source model.

[0014] In step 2, the boundary conditions applied at the inlet of the simplified two-dimensional planar heat source model are as follows:

[0015]

[0016] In the formula, Γ in p is the entrance boundary. in For inlet pressure, u * The velocity is dimensionless.

[0017] Step 3 specifically involves:

[0018] Step 3.1: Distribute the compactly supported radial basis functions (CSRBF) with the spread coefficient onto the finite element mesh nodes obtained in Step 2 within the design domain to obtain the parameterized level function Φ(x,t), which is the product of the compactly supported radial basis function vector and the spread vector:

[0019]

[0020] In the formula, Let be the vector form of the tightly supported radial basis functions distributed on each finite element mesh node. Let α(t) be the compactly supported radial basis function at the i-th finite element mesh node; α(t) is the vector form of the spread coefficient corresponding to each finite element mesh node.i (t) is the expansion coefficient corresponding to the i-th finite element mesh node; i is the label of the finite element mesh node, which takes values ​​from 1 to N, and N is the number of finite element mesh nodes; the resulting parameterized level set function Φ(x,t) is an N×N matrix;

[0021] A single CSRBF can be represented as:

[0022]

[0023] In the formula, r is the support radius defined in Euclidean space, and its expression is:

[0024]

[0025] In the formula, d I This represents any sampling point (x, y) and interpolation control point (x, y) within the support radius. i ,y i The distance between ) is where i is the label of the finite element mesh node; d mI This reflects the range of influence of the basis functions at the control points;

[0026] Step 3.2: Represent the compactly supported radial basis functions distributed on each finite element mesh node as a vector, denoted as:

[0027]

[0028] In the formula, These are the radial basis functions distributed on the i-th finite element mesh node, where i takes values ​​from 1 to N, and N is the number of finite element mesh nodes.

[0029] The vector formed by the spread coefficients corresponding to each finite element mesh node is denoted as:

[0030] α(t)=[α1(t),α2(t),...,α N (t)]

[0031] In the formula, α1(t), α2(t), ..., α N (t) represents the expansion coefficients corresponding to the i-th finite element mesh node, where i ranges from 1 to N, and N is the number of finite element mesh nodes; t is the number of iteration steps;

[0032] The parameterized level set function Φ(x,t) yields the distribution of solids and fluids in the design domain through the following expression, which represents the heat dissipation channel configuration expressed by the parameterized level set function:

[0033]

[0034] In the formula, Φ(x,t) is the parameterized level set function; x=(x,y) is the spatial coordinate of any point in the design domain, x and y are the x and y coordinates in a Cartesian coordinate system, and t is the time step. Ω s and Ω l They represent the solid domain and the fluid domain, respectively, and Γ is the boundary between the fluid domain and the solid domain. The three satisfy the relation Ω. s ∩Ω l =Γ.

[0035] Step 4 specifically involves: using a Heaviside projection method to map the parameterized level set function onto the finite element mesh element to obtain the pseudo density of the mesh element; interpolating the dimensionless flow resistance coefficient based on the obtained pseudo density of the mesh element; and using the dimensionless conjugate heat transfer control equations of incompressible steady laminar flow to solve the finite element problem.

[0036] In step 4, the Heaviside projection method used is represented as follows:

[0037]

[0038] In the formula, Φ = Φ(x,t) is the parameterized level set function value, and h is a parameter representing the bandwidth between the completely solid domain Φ < -h and the completely fluid domain Φ > h. Using the parameterized level set function value corresponding to each finite element mesh element, the parameterized level set function is mapped onto the finite element mesh element through the above Heaviside projection equation, resulting in the pseudo-density of the mesh element:

[0039] ρ e =H(Φ).

[0040] In step 4, the dimensionless conjugate heat transfer governing equations consist of the dimensionless forms of the continuity equation, the momentum conservation equation, and the energy conservation equation:

[0041] The continuity equation is:

[0042]

[0043] The momentum conservation equation is:

[0044]

[0045] In the continuity equation and the dynamic conservation equation, the dimensionless velocity u * Dimensionless pressure p * Reynolds number Re and dimensionless gradient operator The definition is as follows:

[0046]

[0047] F * Since it is a dimensionless volume force, according to Darcy's law, it can be expressed as:

[0048] F * =-α * u *

[0049] In the formula, α * For dimensionless permeability, after Darcy interpolation, it is expressed as:

[0050]

[0051] In the formula, q is the penalty factor, with a value of 0.01, and Da is the Darcy number, with a value of 10. -4 .

[0052] The energy conservation equation is:

[0053]

[0054] In the formula, Q * The dimensionless heat generation rate, which is related to temperature T, is expressed as:

[0055] Q * =(1-ρ e )β(1-T * )

[0056] In the formula, ρ e β is the pseudo density of the grid cells, and β is the heat production coefficient;

[0057] Dimensionless temperature T * The definitions of Prandtl number and Prandtl number are as follows:

[0058]

[0059] In the formula, T B and T w Average temperature and wall temperature, C p and k f Specific heat capacity and thermal conductivity of the fluid, respectively;

[0060] Introducing the pseudo-density of the grid cells, the final energy conservation equation is:

[0061]

[0062] Step 5 specifically involves:

[0063] Step 5.1: First, determine the objective function that maximizes the heat exchange at the heat source, expressed as:

[0064]

[0065] In the formula, Dheat The region at the heat source is represented by H(Φ), which represents the pseudo-density of the mesh elements obtained by mapping the parameterized level set function onto the finite element mesh elements. β represents the heat generation rate, which is taken as 100 in this example. T * Dimensionless temperature;

[0066] The objective function for minimizing power dissipation is expressed as:

[0067]

[0068] In the formula, D represents the design domain. For the dimensionless gradient operator, u * For dimensionless velocity, α * Permeability is a dimensionless quantity.

[0069] Step 5.2: The weighted objective function of the two objective functions—heat exchange at the heat source and fluid dissipation power—is expressed as follows:

[0070] J = w1J th -w2J f w1 + w2 = 1

[0071] In the formula, w1 is the weighting coefficient for heat exchange and w2 is the weighting coefficient for power dissipation. In this example, both are taken as 0.5.

[0072] Step 5.3: The mathematical model for the topology optimization problem is as follows:

[0073] max J = w1J th -w2J f

[0074]

[0075]

[0076]

[0077]

[0078]

[0079] Step 5.4: Perform sensitivity analysis. Using the adjoint method, obtain the expression for the sensitivity of the objective function to the pseudo-density field of the projected grid cells:

[0080]

[0081] In the formula, ρ e For the pseudo-density field of the grid cells, λ T As the adjoint variable, it is solved through the adjoint equation, which is constructed as follows:

[0082]

[0083] In the formula, R represents the governing equation, and s represents the state variables, namely u, p, and T;

[0084] According to the chain rule, the expression for the sensitivity of the objective function with respect to the spread coefficient is:

[0085]

[0086] In the formula, ρ e H(Φ) represents the pseudo-density field of the grid cells, H(Φ) is the Heaviside projection equation, Φ is the parameterized level set function, and α is the spread coefficient.

[0087] Step 6 specifically involves:

[0088] Based on the sensitivity solution in step 5, the MMA optimization method is used to gradually update the value of the expansion coefficient, thereby changing the shape of the parameterized level set function. The iteration is then judged to determine whether it has converged. If it has not converged, the process returns to step 3. If it has converged, a heat dissipation channel with clear boundaries that meets the design requirements is obtained based on the final parameterized level set function. Then, the complete heat dissipation channel design is obtained by three-dimensional stretching based on the boundary of the heat dissipation channel.

[0089] The beneficial effects of this invention are:

[0090] 1. Unlike traditional straight or S-shaped heat dissipation channels, the method of this invention can design heat dissipation channels that meet design requirements without relying on the designer's design experience. At the same time, the designed channels are more in line with the actual problems, improving efficiency and design quality.

[0091] 2. Traditional variable-density topology designs produce flow channels with rough and unclear boundaries, requiring iterative projections to obtain clearer heat dissipation channel boundaries. This invention uses parameterized level set functions to represent heat dissipation channels within the design domain, resulting in smooth and clear boundaries for the topologically derived channels. This method meets the requirement of maximizing heat transfer at high heat flux density heat sources, thus improving heat dissipation performance.

[0092] 3. The HJ partial differential equations in the traditional level set method are very difficult to solve and slow because the level set function is implicitly expressed. Using the parameterized level set in the method of this invention, the level set function can be explicitly expressed, and the HJ partial differential equations to be solved can be transformed into ordinary differential equations, reducing the difficulty of solving and improving the solution speed.

[0093] 4. In the topology optimization of heat dissipation channels, the method of this invention employs the mature gradient method—the Moving Asymptote Method (MMA)—to solve the optimization problem, and the optimization convergence process is stable. The parameterized level set method explicitly expresses the level set function, transforming it into solving ordinary differential equations, which greatly reduces the difficulty of the solution, but it has not yet been applied to the layout design of integrated transmit antenna heat dissipation channels. Attached Figure Description

[0094] Figure 1 This is a flowchart illustrating the integrated transmitting antenna heat dissipation channel topology optimization design method of the present invention;

[0095] Figure 2 This is a schematic diagram of the design domain and boundary conditions for the topology optimization problem of the integrated transmitting antenna heat dissipation channel of this invention;

[0096] Figure 3 This is a schematic diagram of the final parameterized level set function obtained by the topology optimization method of this invention;

[0097] Figure 4 The method of this invention is a topology optimization method that yields an integrated transmit antenna heat dissipation channel configuration with clear boundaries;

[0098] Figure 5 The temperature cloud map is a simulation result of the temperature distribution at the heat source of a liquid-cooled radiator designed using the method of this invention. Detailed Implementation

[0099] The present invention will now be described in detail with reference to the accompanying drawings and specific embodiments.

[0100] Example 1

[0101] This invention provides a method for optimizing the topology of the heat dissipation channel of an integrated transmitting antenna, referring to... Figure 1 This includes the following steps:

[0102] Step 1: Simplify the integrated transmitting antenna structure, simplify the size of the integrated transmitting antenna, the size of the flow channel inlet and outlet, and the size of the heat-generating device. Take the array size of the integrated transmitting antenna as the design domain, distribute the flow channel inlet and outlet on both sides, take the heat-generating device as the heat source, and establish a simplified two-dimensional planar heat source model.

[0103] Reference Figure 2 The simplified integrated transmitting antenna has a two-dimensional planar heat source model with a design domain size of 8L×8L, a flow channel inlet and outlet width of 0.8L, and a heat source size of 1.6L×1.6L, where L is the characteristic length, which is taken as 10mm in this example.

[0104] Step 2: Using the simplified two-dimensional planar heat source model as the design object, perform finite element mesh generation on it, and initialize it with the expansion coefficient as the design variable. To ensure a constant input power, apply boundary conditions at the inlet of the simplified two-dimensional planar heat source model after initialization.

[0105] In step 2, the boundary conditions applied at the inlet of the simplified two-dimensional planar heat source model are as follows:

[0106]

[0107] In the formula, Γ in p is the entrance boundary. in For inlet pressure, u * The velocity is dimensionless.

[0108] Step 3: Distribute the compactly supported radial basis functions (CSRBF) with expansion coefficients on the finite element mesh nodes obtained in Step 2 within the design domain. Then, linearly superimpose these radial basis functions to obtain the parameterized level set function. Based on the parameterized level set function value, the distribution of solids and fluids in the design domain is obtained, which is the heat dissipation channel configuration represented by the parameterized level set function.

[0109] Step 3.1: Distribute the compactly supported radial basis functions (CSRBF) with the spread coefficient onto the finite element mesh nodes obtained in Step 2 within the design domain to obtain the parameterized level function Φ(x,t), which is the product of the compactly supported radial basis function vector and the spread vector:

[0110]

[0111] In the formula, Let be the vector form of the tightly supported radial basis functions distributed on each finite element mesh node. Let α(t) be the compactly supported radial basis function at the i-th finite element mesh node; α(t) is the vector form of the spread coefficient corresponding to each finite element mesh node. i (t) represents the expansion coefficient corresponding to the i-th finite element mesh node; i is the label of the finite element mesh node, ranging from 1 to N, where N is the number of finite element mesh nodes; the resulting parameterized level set function Φ(x,t) is an N×N matrix. Compactly supported radial basis functions (CSRBFs) are characterized by high accuracy and good smoothness, and are often used as an effective tool for representing multivariate functions using univariate functions.

[0112] A single CSRBF can be represented as:

[0113]

[0114] In the formula, r is the support radius defined in Euclidean space, and its expression is:

[0115]

[0116] In the formula, d I This represents any sampling point (x, y) and interpolation control point (x, y) within the support radius. i ,y i The distance between ) is where i is the label of the finite element mesh node; d mI This reflects the range of influence of the basis function at the control point, and its value is generally selected between 2 and 4.

[0117] Step 3.2: Represent the compactly supported radial basis functions distributed on each finite element mesh node as a vector, denoted as:

[0118]

[0119] In the formula, These are the radial basis functions distributed on the i-th finite element mesh node, where i takes values ​​from 1 to N, and N is the number of finite element mesh nodes.

[0120] The vector formed by the spread coefficients corresponding to each finite element mesh node is denoted as:

[0121] α(t)=[α1(t),α2(t),...,α N (t)]

[0122] In the formula, α1(t), α2(t), ..., α N (t) represents the expansion coefficients corresponding to the i-th finite element mesh node, where i ranges from 1 to N, and N is the number of finite element mesh nodes; t is the iteration step, and the value of the expansion coefficient changes with each iteration step.

[0123] In this embodiment, the parameterized level set function Φ(x,t) yields the distribution of solids and fluids in the design domain through the following expression, which represents the heat dissipation channel configuration expressed by the parameterized level set function:

[0124]

[0125] In the formula, Φ(x,t) is the parameterized level set function; x=(x,y) is the spatial coordinate of any point in the design domain, x and y are the x and y coordinates in a Cartesian coordinate system, and t is the time step. Ω s and Ω l They represent the solid domain and the fluid domain, respectively, and Γ is the boundary between the fluid domain and the solid domain. The three satisfy the relation Ω. s ∩Ω l =Γ.

[0126] Step 4: In order to solve the heat transfer performance of the heat dissipation channel configuration represented by the parameterized level set function, a Heaviside projection method is adopted to map the parameterized level set function onto the finite element mesh element to obtain the pseudo density of the mesh element. The dimensionless flow resistance coefficient is interpolated based on the obtained pseudo density of the mesh element, and the dimensionless conjugate heat transfer control equations of incompressible steady laminar flow are used to solve the finite element problem.

[0127] The Heaviside projection method used here is represented as:

[0128]

[0129] In the formula, Φ = Φ(x,t) is the parameterized level set function value, and h is a parameter representing the bandwidth between the completely solid domain (Φ < -h) and the completely fluid domain ((Φ > h)). Using the parameterized level set function value corresponding to each finite element mesh element, the parameterized level set function is mapped onto the finite element mesh element through the above Heaviside projection equation, resulting in the pseudo-density of the mesh element:

[0130] ρ e =H(Φ);

[0131] For incompressible steady laminar flow, the dimensionless conjugate heat transfer governing equations consist of dimensionless forms of the continuity equation, the momentum conservation equation, and the energy conservation equation:

[0132] The continuity equation is:

[0133]

[0134] The momentum conservation equation is:

[0135]

[0136] In the continuity equation and the dynamic conservation equation, the dimensionless velocity u * Dimensionless pressure p * Reynolds number Re and dimensionless gradient operator The definition is as follows:

[0137]

[0138] F * Since it is a dimensionless volume force, according to Darcy's law, it can be expressed as:

[0139] F * =-α * u *

[0140] In the formula, α* For dimensionless permeability, after Darcy interpolation, it is expressed as:

[0141]

[0142] In the formula, q is the penalty factor, with a value of 0.01, and Da is the Darcy number, with a value of 10. -4 .

[0143] The energy conservation equation is:

[0144]

[0145] In the formula, Q * The dimensionless heat generation rate, which is related to temperature T, is expressed as:

[0146] Q * =(1-ρ e )β(1-T * )

[0147] In the formula, ρ e β is the pseudo density of the grid cells, and β is the heat production coefficient, which is 100 in this example.

[0148] Dimensionless temperature T * The definitions of Prandtl number and Prandtl number are as follows:

[0149]

[0150] In the formula, T B and T w Average temperature and wall temperature, C p and k f The specific heat capacity and thermal conductivity of the fluid are respectively used. In this example, the cooling medium is water, and the Prandtl number at room temperature and pressure is 6.78.

[0151] Introducing the pseudo-density of the grid cells, we obtain the final energy conservation equation:

[0152]

[0153] Step 5: Based on the dimensionless conjugate heat transfer control equations of the incompressible steady laminar flow in Step 4, with the weighted function that maximizes heat transfer and minimizes power dissipation at the heat source as the objective and fluid volume fraction as the constraint, establish a mathematical model for the topology optimization problem. The sensitivity analysis adopts the adjoint method and the chain rule to calculate the sensitivity of the objective function and the constraint conditions with respect to the expansion coefficient of the design variables.

[0154] Step 5.1: First, determine the objective function that maximizes the heat exchange at the heat source, expressed as:

[0155]

[0156] In the formula, D heat The region at the heat source is represented by H(Φ), which represents the pseudo-density of the mesh elements obtained by mapping the parameterized level set function onto the finite element mesh elements. β represents the heat generation rate, which is taken as 100 in this example. T * The value is a dimensionless temperature.

[0157] The objective function for minimizing power dissipation is expressed as:

[0158]

[0159] In the formula, D represents the design domain. For the dimensionless gradient operator, u * For dimensionless velocity, α * Permeability is a dimensionless quantity.

[0160] Step 5.2: The weighted objective function of the two objective functions—heat exchange at the heat source and fluid dissipation power—is expressed as follows:

[0161] J = w1J th -w2J f w1 + w2 = 1

[0162] In the formula, w1 is the weighting coefficient for heat exchange and w2 is the weighting coefficient for power dissipation. In this example, both are taken as 0.5.

[0163] Step 5.3: The mathematical model for the topology optimization problem is as follows:

[0164] max J = w1J th -w2J f

[0165]

[0166]

[0167]

[0168]

[0169]

[0170] Step 5.4: Perform sensitivity analysis. Using the adjoint method, obtain the expression for the sensitivity of the objective function to the pseudo-density field of the projected grid cells:

[0171]

[0172] In the formula, ρ e For the pseudo-density field of the grid cells, λ TAs the adjoint variable, it is solved through the adjoint equation, which is constructed as follows:

[0173]

[0174] In the formula, R represents the governing equation, and s represents the state variables, namely u, p, and T;

[0175] According to the chain rule, the expression for the sensitivity of the objective function with respect to the spread coefficient is:

[0176]

[0177] In the formula, ρ e H(Φ) represents the pseudo-density field of the grid cells, H(Φ) is the Heaviside projection equation, Φ is the parameterized level set function, and α is the spread coefficient.

[0178] Step 6: Based on the sensitivity solution from Step 5, use the MMA optimization method to gradually update the value of the expansion coefficient, thereby changing the shape of the parameterized level set function. Determine whether the iteration has converged. If it has not converged, return to Step 3. If it has converged, obtain a heat dissipation channel that meets the design requirements and has clear boundaries based on the final parameterized level set function. Then, by three-dimensionally stretching the heat dissipation channel boundary, the complete heat dissipation channel design can be obtained.

[0179] In this embodiment, the parameterized level set function obtained by the final topology optimization is as follows: Figure 3 As shown, the corresponding heat dissipation channel configuration is as follows: Figure 4 As shown, it can be seen that the boundary of the integrated transmitting antenna heat dissipation channel configuration obtained by topology optimization is very clear and smooth.

[0180] The beneficial effects of the present invention can be further illustrated by the following simulation examples:

[0181] 1. Simulation model parameters

[0182] The liquid-cooled radiator measures 86mm*86mm*16mm and consists of three layers. The top and bottom cover plates are 3mm thick, the flow channel layer is 10mm thick, and the inlet cross-section of the heat dissipation channel is 10mm*10mm. The power output at the four heat sources is 26W, the inlet velocity is 0.01m / s, and the Reynolds number is 100. The liquid-cooled radiator is made of 6061 aluminum alloy, and water is used as the cooling fluid.

[0183] In contrast, a traditional S-shaped flow channel liquid-cooled radiator model is set up, and the same boundary conditions are applied.

[0184] 2. Comparison of Simulation Results

[0185] The simulation results of the temperature distribution at the heat source of the liquid-cooled radiator designed using the method of this invention are as follows: Figure 5 As shown.

[0186] Table 1. Comparison of heat dissipation performance between the heat dissipation channel designed using this method and the traditional S-shaped channel design.

[0187] Design Methodology highest temperature at the heat source Average temperature of heat source Root mean square value of heat source temperature This method 51.9℃ 49.15℃ 5.1971℃ Traditional S-shaped 58.2℃ 55.225℃ 5.8573℃

[0188] As shown in Table 1, the heat dissipation channel obtained by the method of this invention significantly outperforms the traditional S-shaped channel design in terms of heat dissipation performance. The highest temperature at the heat source decreases by 6.3℃, the average temperature at the heat source decreases by 6.075℃, and the root mean square value of the heat source temperature decreases by 0.6602℃. This invention simplifies calculations while designing a heat dissipation channel topology with smooth and clear boundaries, and it meets the requirement of maximizing heat transfer at high heat flux density heat sources, thus improving heat dissipation performance.

[0189] Example 2

[0190] An integrated transmitting antenna heat dissipation channel topology optimization design method, characterized by the following steps:

[0191] Step 1: Establish a simplified two-dimensional planar heat source model;

[0192] Step 2: Using the simplified two-dimensional planar heat source model as the design object, perform finite element mesh generation on it, initialize it with the spread factor as the design variable, and apply boundary conditions at the inlet;

[0193] Step 3: Distribute the tightly supported radial basis functions with expansion coefficients onto the finite element mesh nodes obtained in Step 2 within the design domain. Then, linearly superimpose these radial basis functions to obtain the parameterized level set function. Finally, obtain the distribution of solids and fluids in the design domain based on the level set function value.

[0194] Step 4: Solve for the heat transfer performance of the heat dissipation channel configuration represented by the parameterized level set function;

[0195] Step 5: Establish a mathematical model for the topology optimization problem, and calculate the sensitivity of the objective function and constraints to the expansion coefficients of the design variables;

[0196] Step 6: Obtain a heat dissipation channel that meets the design requirements and has clear boundaries. Then, perform three-dimensional stretching based on the heat dissipation channel boundaries to obtain the complete heat dissipation channel design.

[0197] Example 3

[0198] The integrated transmitting antenna heat dissipation channel topology optimization design method specifically includes the following steps:

[0199] Step 1: Establish a simplified two-dimensional planar heat source model;

[0200] Step 2: Using the simplified two-dimensional planar heat source model as the design object, perform finite element mesh generation on it, initialize it with the spread factor as the design variable, and apply boundary conditions at the inlet;

[0201] Step 3: Distribute the tightly supported radial basis functions with expansion coefficients onto the finite element mesh nodes obtained in Step 2 within the design domain. Then, linearly superimpose these radial basis functions to obtain the parameterized level set function. Finally, obtain the distribution of solids and fluids in the design domain based on the level set function value.

[0202] Step 4: Solve for the heat transfer performance of the heat dissipation channel configuration represented by the parameterized level set function;

[0203] Step 5: Establish a mathematical model for the topology optimization problem, and calculate the sensitivity of the objective function and constraints to the expansion coefficients of the design variables;

[0204] Step 6: Obtain a heat dissipation channel that meets the design requirements and has clear boundaries. Then, perform three-dimensional stretching based on the heat dissipation channel boundaries to obtain the complete heat dissipation channel design.

[0205] Step 1 specifically involves: simplifying the integrated transmitting antenna structure, simplifying the dimensions of the integrated transmitting antenna, the dimensions of the flow channel inlet and outlet, and the dimensions of the heat-generating device, taking the array size of the integrated transmitting antenna as the design domain, distributing the flow channel inlet and outlet on both sides, taking the heat-generating device as the heat source, and establishing a simplified two-dimensional planar heat source model.

Claims

1. An integrated transmitting antenna heat dissipation channel topology optimization design method, characterized in that, Specifically, the following steps are included: Step 1: Establish a simplified two-dimensional planar heat source model; Step 2: Using the simplified two-dimensional planar heat source model as the design object, perform finite element mesh generation on it, initialize it with the spread factor as the design variable, and apply boundary conditions at the inlet; Step 3: Distribute the tightly supported radial basis functions with expansion coefficients onto the finite element mesh nodes obtained in Step 2 within the design domain. Then, linearly superimpose these radial basis functions to obtain the parameterized level set function. Finally, obtain the distribution of solids and fluids in the design domain based on the level set function value. Step 4: Solve for the heat transfer performance of the heat dissipation channel configuration represented by the parameterized level set function; Step 4 specifically involves: using a Heaviside projection method to map the parameterized level set function onto the finite element mesh element to obtain the pseudo density of the mesh element; interpolating the dimensionless flow resistance coefficient based on the obtained pseudo density of the mesh element; and using the dimensionless conjugate heat transfer control equations of incompressible steady laminar flow to solve the finite element problem. In step 4, the dimensionless conjugate heat transfer governing equations consist of the dimensionless forms of the continuity equation, the momentum conservation equation, and the energy conservation equation. composition: The continuity equation is: The momentum conservation equation is: In the continuity equation and the dynamic conservation equation, dimensionless velocity Dimensionless pressure Reynolds number and dimensionless gradient operator The definition is as follows: Since it is a dimensionless volume force, according to Darcy's law, it can be expressed as: In the formula, For dimensionless permeability, after Darcy interpolation, it is expressed as: In the formula, Da is the penalty factor, and Da is the Darcy number. The energy conservation equation is: In the formula, The dimensionless heat generation rate, which is related to temperature T, is expressed as: In the formula, For the pseudo density of the grid cells, The heat production coefficient; Dimensionless temperature The definitions of Prandtl number and Prandtl number are as follows: In the formula, and Average temperature and wall temperature, respectively and Specific heat capacity and thermal conductivity of the fluid, respectively; Introducing the pseudo-density of the grid cells, the final energy conservation equation is: ； Step 5: Establish a mathematical model for the heat dissipation channel topology optimization problem, and calculate the sensitivity of the objective function and constraints to the expansion coefficients of the design variables; Step 5 specifically involves: Step 5.1: First, determine the objective function that maximizes the heat exchange at the heat source, expressed as: In the formula, D heat Indicates the area at the heat source. H (Φ) represents the pseudo density of the mesh element obtained by mapping the parameterized level set function onto the finite element mesh element; The objective function for minimizing power dissipation is expressed as: In the formula, D For design domain; Step 5.2: The weighted objective function of the two objective functions—heat exchange at the heat source and fluid dissipation power—is expressed as follows: In the formula, The weighting factor for heat exchange is... The weighting factor is the power dissipation factor. Step 5.3: The mathematical model for the topology optimization problem is as follows: Step 5.4: Perform sensitivity analysis. Using the adjoint method, obtain the expression for the sensitivity of the objective function to the pseudo-density field of the projected grid cells: In the formula, For the pseudo density field of the grid cells, As the adjoint variable, it is solved through the adjoint equation, which is constructed as follows: In the formula, R Represents the governing equations. s These are state variables, namely u, p, and T; According to the chain rule, the expression for the sensitivity of the objective function with respect to the spread coefficient is: In the formula, For the Heaviside projection equation, For parameterized level set functions, This is the expansion factor; Step 6: Obtain a heat dissipation channel that meets the design requirements and has clear boundaries. Then, perform three-dimensional stretching based on the heat dissipation channel boundaries to obtain the complete heat dissipation channel design.

2. The integrated transmitting antenna heat dissipation channel topology optimization design method according to claim 1, characterized in that, Step 1 specifically involves: simplifying the integrated transmitting antenna structure, simplifying the dimensions of the integrated transmitting antenna, the dimensions of the flow channel inlet and outlet, and the dimensions of the heat-generating device, taking the array size of the integrated transmitting antenna as the design domain, distributing the flow channel inlet and outlet on both sides, taking the heat-generating device as the heat source, and establishing a simplified two-dimensional planar heat source model.

3. The integrated transmitting antenna heat dissipation channel topology optimization design method according to claim 1, characterized in that, In step 2, the boundary conditions applied at the inlet of the simplified two-dimensional planar heat source model are as follows: In the formula, Γ in p is the entrance boundary. in For inlet pressure, u * The velocity is dimensionless.

4. The integrated transmitting antenna heat dissipation channel topology optimization design method according to claim 1, characterized in that, Step 3 specifically involves: Step 3.1: Distribute the tightly supported radial basis functions with expansion coefficients onto the finite element mesh nodes obtained in Step 2 within the design domain to obtain the parameterized level functions. That is, the product of the compactly supported radial basis function vector and the extension vector: In the formula, Let be the vector form of the tightly supported radial basis functions distributed on each finite element mesh node. Let be the compactly supported radial basis function on the i-th finite element mesh node; The vector form of the expansion coefficient at each finite element mesh node. Let be the expansion coefficient corresponding to the i-th finite element mesh node; i is the label of the finite element mesh node, taking values ​​from 1 to 1. N , N The number of nodes in the finite element mesh; The obtained parameterized level set function For one N × N Matrix; A single CSRBF is represented as: In the formula, r is the support radius defined in Euclidean space, and its expression is: In the formula, Represents any sampling point within the support radius. With interpolation control points The distance between them, where i is the label of the finite element mesh node; This reflects the range of influence of the basis functions at the control points; Step 3.2: Represent the compactly supported radial basis functions distributed on each finite element mesh node as a vector, denoted as: In the formula, These are the radial basis functions distributed on the i-th finite element mesh node, where i ranges from 1 to... N Take values ​​in sequence, N The number of nodes in the finite element mesh; The vector formed by the spread coefficients corresponding to each finite element mesh node is denoted as: In the formula, These are the spread coefficients corresponding to the i-th finite element mesh node, where i ranges from 1 to... N Take values ​​in sequence, N The number of nodes in the finite element mesh; t is the number of iterations; Parameterized level set function The distribution of solids and fluids in the design domain can be obtained through the following expression, which is the heat dissipation channel configuration represented by the parameterized level set function: In the formula, For parameterized level set functions; is the spatial coordinate of any point within the design domain, where x and y are the horizontal and vertical coordinates in a Cartesian coordinate system, and t is the time step; and These represent the solid domain and the fluid domain, respectively. It is the boundary between the fluid domain and the solid domain, and the three satisfy the following relationship. .

5. The integrated transmitting antenna heat dissipation channel topology optimization design method according to claim 1, characterized in that, In step 4, the Heaviside projection method used is represented as follows: In the formula, Here, h represents the parameterized level set function value, and h is the value representing the complete solid domain. With the fully fluid domain The parameters of the bandwidth are used to map the parameterized level set function value corresponding to each finite element mesh element into the finite element mesh element through the Heaviside projection equation mentioned above, resulting in the pseudo density of the mesh element: r e =H(Φ).

6. The integrated transmitting antenna heat dissipation channel topology optimization design method according to claim 1, characterized in that, Step 6 specifically involves: Based on the sensitivity solution in step 5, the MMA optimization method is used to gradually update the value of the expansion coefficient, thereby changing the shape of the parameterized level set function. The iteration is then judged to determine whether it has converged. If it has not converged, the process returns to step 3. If it has converged, a heat dissipation channel with clear boundaries that meets the design requirements is obtained based on the final parameterized level set function. Then, the complete heat dissipation channel design is obtained by three-dimensional stretching based on the boundary of the heat dissipation channel.

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