Free Modeling and Optimization Design Method for Horizontal Wave Channels

Abstract

This invention discloses a free modeling and optimization design method for horizontally wavy channels. It employs cubic spline functions to represent amplitude, wavelet functions to represent wavelength, and truncation functions to represent waveform. Furthermore, it utilizes rational Bernstein-Bézier functions to achieve free modification of the channel's cross-sectional shape and dimensions. Based on this, a horizontally wavy channel is constructed as the basic structure of the cold plate. Using the average temperature and root-mean-square temperature of the upper and lower surfaces of the cold plate as objective functions, the NSGA-II optimization algorithm is employed to optimize the horizontally wavy channel. Simultaneously, design variables are normalized, and finally, the TOPSIS ranking method is used to select the optimal compromise solution. This invention's free modeling and optimization design method for horizontally wavy channels aims to eliminate the limitations imposed by fixed geometric structures and dimensions on heat transfer performance, thereby improving the heat dissipation performance of the horizontally wavy channel cold plate structure.

Description

Technical Field

[0001] This invention belongs to the technical field of high-power electronic liquid cooling heat sink methods, specifically involving a method for free modeling and optimization design of horizontal wave channels. Background Technology

[0002] With the continuous development of the electronics industry, high-gain, high-density, and miniaturized electronic devices have become the main trend. Electronic thermal management, as an essential aspect, has received widespread attention. In recent years, to meet heat dissipation requirements, it is necessary to research efficient and rapid cooling systems to improve heat transfer efficiency. Currently, air cooling is widely used as the main cooling method. However, due to the low thermal conductivity and heat capacity of air, this type of heat sink is not suitable for small-sized, high-power electronic devices, thus requiring alternative solutions. Liquid-cooled heat sinks offer superior performance compared to air, and different strategies based on fluid flow and heat transfer characteristics will be applied to various cold plate structure designs. Various flow channel forms and cross-sectional shapes exist in the overall design of cold plates. Flow channel forms include serpentine, parallel, tree-like, converging, or diverging channels, and cross-sectional shapes include circular, rectangular, and triangular. Existing research shows that channels employing lateral perturbation configurations can be considered as vortex generators, such as constructing cavities, adding wings (ribs or fins), using twisted bands, and designing corrugated microchannels. These methods can induce the generation of transverse and longitudinal vortices, redeveloping fluid flow and thus improving the heat transfer coefficient. Especially for corrugated channels, related research has been increasing in recent years. Corrugated channels exhibit superior heat transfer performance, mainly due to the presence of a recirculation zone and secondary flow, which remixes the fluid flow and redevelops the thermal boundary layer, thereby improving heat transfer capacity. Furthermore, by increasing the corrugation, corrugated channels can significantly increase the heat transfer area in a compact space. Their geometric characteristics include amplitude, wavelength, waveform, and cross-sectional shape and size. Different arrangements of these geometric characteristics lead to variations in the shape, size, and intensity of the recirculation zone. Therefore, when reanalyzing corrugated channels, different operating conditions and applications need to be considered to determine the impact of the corrugated channel's geometric distribution and size on cold plate design. However, existing technologies have the following problems: 1) Current horizontal corrugated channel designs only focus on two-dimensional configurations, then obtain three-dimensional corrugated configurations through simple stretching. 2) The geometric characteristics of corrugated channels are fixed in form and size, which is not conducive to further exploring their heat transfer laws and improving heat dissipation performance. 3) Since most designs involve limited local structural features, this weakens the potential of geometry to enhance heat transfer performance, and the resulting designs are relatively conventional with limited heat exchange efficiency. 4) The design process relies on the designer's experience and inspiration; whether the final result is optimal remains to be further discussed. 5) The design of corrugated channels involves adjusting and optimizing multiple parameters, requiring extensive simulations and experimental studies, resulting in high design complexity. 6) Traditional corrugated channel designs with fixed shapes and dimensions are suitable for certain specific fluid flow conditions, but have poor applicability to other fluid flow conditions. Summary of the Invention

[0003] The purpose of this invention is to provide a free modeling and optimization design method for horizontal wave channels, which aims to eliminate the limitations of fixed geometric structure and size on heat transfer performance, and to improve the heat dissipation performance by arranging the structural distribution of the horizontal wave channel cold plate.

[0004] The technical solution adopted in this invention is: a free modeling and optimization design method for horizontal wave-shaped channels. This method uses cubic spline functions to represent amplitude, wavelet functions to represent wavelength, and truncation functions to represent waveform. The rational Bernstein-Bézier function is used to achieve free modification of the channel's cross-sectional shape and size. Based on this, a horizontal wave-shaped channel is constructed as the basic structure of the cold plate. The average temperature and root mean square temperature of the upper and lower surfaces of the cold plate are used as objective functions. The NSGA-II optimization algorithm is employed to optimize the horizontal wave-shaped channel, while the design variables are normalized. Finally, the TOPSIS ranking method is used to select the optimal compromise solution.

[0005] The present invention is further characterized by including the following steps:

[0006] Step 1: Based on the configuration of the on-site electronic equipment, determine the external dimensions, hydraulic diameter, heating surface dimensions, and inlet / outlet positions of the horizontal corrugated channel cold plate.

[0007] Step 2: Determine the geometric dimensions of the flow channel inlet and outlet based on the determined cold plate dimensions; determine the heat transfer properties based on the heated surface dimensions; determine the flow properties based on the hydraulic diameter and the inlet and outlet positions of the flow channel; and determine the material properties of the heat dissipation system based on the engineering requirements.

[0008] Step 3: Based on the determined dimensions of the cold plate, construct an initial straight channel with arbitrary cross-sectional shape based on the rational Bernstein-Bézier function by parameterizing the rotation and translation matrices.

[0009] Step 4: Based on the initial straight channel, construct the geometric features of the amplitude, wavelength, and waveform of the horizontal wave channel using the arbitrary shape parametric modeling method of the wave channel;

[0010] Step 5: Based on the horizontal wave-shaped channel, establish a finite element model of the cold plate using the conjugate heat transfer control equation;

[0011] Step 6: Based on the finite element model of the cold plate, perform a mesh independence test to verify the reliability of the numerical model;

[0012] Step 7: Normalize the four design variables corresponding to the geometric features: amplitude, wavelength, waveform, and cross-sectional shape and size.

[0013] Step 8: Based on engineering requirements, construct the design variables of the optimization framework, including the control coefficients of the cubic spline function representing amplitude, the wavelet function representing wavelength, the truncation function representing waveform, and the control coefficients of the Bernstein function representing channel cross-section and channel torsion; construct the objective function of the optimization framework, including minimizing the average temperature and root mean square temperature of the top and bottom of the cold plate.

[0014] Step 9: Optimize the objective function of the optimization framework obtained in Step 8 using the NSGA-II optimization algorithm to obtain the optimized temperature distribution of the cold plate and power devices;

[0015] Step 10: Based on the numerical solution of the temperature distribution of the optimized cold plate and power devices, select the best compromise solution using the TOPSIS sorting method.

[0016] In step 2, the external dimensions of the cold plate include length L, width W, and height H; hydraulic diameter D; and the heating surface dimension W. h ×L h The heat transfer properties include the inlet fluid temperature T. in The thermal boundary of the external wall and the distance from the heat source Q; the flow property parameters include the inlet flow velocity U. in and export pressure P out The heat dissipation system is made of solid aluminum 6061-T6 and liquid transport medium water, and its properties include: solid thermal conductivity k s Fluid thermal conductivity k f Specific heat capacity of fluid at constant pressure C p And fluid density ρ.

[0017] In step 3, an initial straight-channel architecture is constructed by parameterizing rotation and translation matrices. Its fitting is performed in the XOY plane, with Z being its height direction.

[0018] In step 4, the basic architecture of the horizontal wave channel model is initially determined by studying the four design variables: amplitude, wavelength, waveform, and cross-sectional shape and size.

[0019] In step 5, the governing equations for conjugate heat transfer are established, and the boundary conditions are defined.

[0020] In step 6, the mesh independence is checked, and an unstructured tetrahedral mesh is used to mesh the finite element model.

[0021] In step 7, the design variables of the horizontal wave channel are normalized to obtain the model architecture of the horizontal wave channel.

[0022] In step 8, an optimization framework is established regarding design variables, objective functions, and constraints.

[0023] In step 9, the Non-Dominated Sorting Genetic Algorithm II (NSGA-II) is used, with the corresponding population size P and iteration number G set, and the relevant convergence criteria are set.

[0024] In step 10, the optimal compromise solution is selected by using the similarity ranking preference technique (TOPSIS) to select the best compromise solution, and the optimized model is further discussed.

[0025] The beneficial effects of this invention are:

[0026] 1) This invention can effectively perform free modeling of horizontal corrugated structure models, while taking into account four design variables: amplitude, wavelength, waveform, and cross-sectional shape and size. It overcomes the limitations of fixed geometric dimensions and shapes and realizes the design of free-form surfaces.

[0027] 2) This invention considers using cubic spline functions to represent amplitude, primarily because cubic spline functions can pass through these points and have continuous first derivatives, which is beneficial for solving the problem of sensitivity to specified points (such as amplitude boundaries). Simultaneously, a modified wavelet function is considered to represent the waveform, ensuring the continuity of the wave channel. Since the Bernstein function only requires a small number of control points to manipulate the global trend of the generated Bézier curve, eliminating the need for redundant design variables, it has advantages in constructing efficient and concise optimization systems. Therefore, the Bernstein function is considered for constructing the cross-sectional shape and size.

[0028] 3) This invention defines each design variable using a corresponding variable function, which further improves the flexibility of the entire modeling process, overcomes the limitations of traditional modeling on size and shape, and is more universal.

[0029] 4) This invention proposes a horizontal corrugated channel design scheme based on a parametric modeling system, and utilizes optimization techniques to significantly improve its heat dissipation performance, thereby ensuring its reliability. This scheme is not only applicable to cold plate heat sinks, but can also be extended to finned heat sinks and heat exchangers, providing guidance for the design of high-power electronic liquid-cooled heat sinks. Attached Figure Description

[0030] Figure 1 This is a flowchart illustrating the free modeling and optimization design method for horizontal wave channels of the present invention.

[0031] Figure 2 It is the initial straight-channel 3D model;

[0032] Figure 3 It is a horizontal wavy channel 3D model used for comparison and based on experience;

[0033] Figure 4This is a Pareto front plot with the minimum average surface temperature and root mean square temperature as objective functions;

[0034] Figure 5 It refers to the temperature distribution on the upper and lower surfaces of straight channels, uniformly wavy channels, and variable wavy channels;

[0035] Figure 6 It refers to the temperature distribution of the intermediate layer along the height direction of straight channels, uniform wavy channels, and variable wavy channels;

[0036] Figure 7 It shows the streamline distribution diagrams for straight channels, uniformly wavy channels, and variable wavy channels. Detailed Implementation

[0037] The present invention will now be described in detail with reference to the accompanying drawings and specific embodiments.

[0038] This invention provides a free modeling and optimization design method for horizontal corrugated channels, aiming to eliminate the limitations imposed by fixed geometric structures and dimensions on heat transfer performance. Through optimization techniques, the structural distribution of the cold plates in the horizontal corrugated channels is arranged, with the minimum average temperature and minimum root-mean-square temperature of the upper and lower planes used as the optimization objective functions, further improving its heat dissipation performance. This invention further explores the potential of horizontal corrugated structures in improving the heat dissipation performance of radiators, laying a theoretical foundation for related engineering practices.

[0039] Example 1

[0040] This invention provides a free modeling and optimization design method for horizontal corrugated channels. Based on parametric modeling, it allows for the free construction of corrugated channels in terms of amplitude, wavelength, waveform, and cross-section, thereby liberating fixed forms and dimensions. Specifically, this invention uses cubic spline functions to represent amplitude, wavelet functions to represent wavelength, and a newly defined truncation function to represent waveform. The Bernstein function is used to achieve free modification of the channel's cross-sectional shape and size. Based on this, this invention constructs a horizontal corrugated channel, which can serve as the basic structure of a cold plate. For the optimization problem of the horizontal corrugated channel, the average temperature and root mean square temperature of the upper and lower surfaces of the cold plate are used as objective functions. A non-dominated sorting genetic algorithm (NSGA-II) is employed for optimization, while the design variables are normalized to improve the stability of the optimization. Finally, for the optimized model, the optimal compromise solution is selected using the similarity ranking preference technique with ideal solutions (TOPSIS). This work can be applied not only to cold plates but also to components with corrugated structures such as finned radiators and heat exchangers.

[0041] Example 2

[0042] like Figure 1 As shown, the specific steps of the free modeling and optimization design method for horizontal wave channels provided by this invention are as follows:

[0043] Step 1: Determine the surface heat flux density of the power device, the basic dimensions of the cold plate, and the inlet and outlet locations of the flow channels.

[0044] Based on the configuration of the electronic equipment on site, determine the surface heat flux density Q of the power devices; the external dimensions of the cold plate: length L, width W, height H; and the location of the inlet / outlet, such as... Figure 2 As shown.

[0045] Step 2: Determine the physical boundary parameters and corresponding physical property parameters of the cold plate.

[0046] Based on the determined heat flux density and cold plate dimensions, the inlet and outlet geometric parameters, including the inlet diameter D, are determined. in and D out The heat transfer properties include the inlet fluid temperature T. in The thermal boundary of the external wall and the distance from the heat source Q; the flow property parameters include the inlet flow velocity U. in and export pressure P out The heat dissipation system is made of solid aluminum 6061-T6 and liquid transport medium water, and its properties include: solid thermal conductivity k s Fluid thermal conductivity k f Specific heat capacity of fluid at constant pressure C p And fluid density ρ.

[0047] Step 3, determine the initial straight path

[0048] An initial straight channel is constructed using rotation and translation matrices, and its fitting is performed in the XOY plane, where Z represents the height direction. The rotation and translation matrices are as follows:

[0049]

[0050] In this context, X(t,θ), Y(t,θ), and Z(t,θ) in item 1 represent the spatial positions of the corresponding geometric features in the global coordinate system; items 2 and 3 represent the spatial positions x(t,θ), y(t,θ), and z(t,θ) of the geometric features established in the local coordinate system (item 4), with item 2 representing rotation about the Z-axis (which determines that the cross-section must be perpendicular to the channel centerline) and item 3 representing rotation about the Y-axis (which determines the channel twist); item 4 is related to the shape and size of the cross-section, and the meaning of the control parameters differs in different cross-section types; item 5 represents the translation from local to global. Arbitrary cross-section types are constructed using rational Bernstein-Bézier functions, i.e.

[0051]

[0052] Among them, B i (t,θ) is established based on three points; basis function b j,2 (θ) and weighting coefficients The combination of these factors determines the shape of the cross-section. To produce cross-sectional shapes that differ along the length of the channel, This can be expressed using the Bernstein-Bézier function as follows:

[0053]

[0054] in, These are Bernstein-Bézier basis functions; The coefficients are binomial coefficients; n is the intermediate parameter control coefficient for the i-th arc; w The maximum power of the function is given. This process can achieve free construction of the cross-sectional shape using only intermediate parameter design variables, avoiding a large number of design variables in traditional design, which is beneficial for establishing a compact optimization system later.

[0055] Step 4: Construct a horizontal corrugated channel based on the initial straight channel.

[0056] Based on the initial straight channel, x(t,θ) and z(t,θ) are re-transformed to obtain

[0057]

[0058]

[0059] (1) wf(t) is a trigonometric function of parameter t, which can generate a wave-like channel. Its expression is:

[0060] wf(t)=amp(t)g(t)=amp(t)cos(freq(t)πt)

[0061] Where amp(t) is the amplitude of the wave channel; freq(t) is the wavelength of the wave channel.

[0062] (2) amp(t) can be established using a cubic spline function. Although a cubic spline function is not a necessary component for modeling wave channels, it is advantageous for solving problems sensitive to specific points (such as amplitude boundaries) because the function can pass through these points and has continuous first derivatives. The simplified cubic spline function expressing the amplitude is:

[0063] amp(t) = f(amp1,…,amp) j ,…,amp na ,t),(0≤t≤1)

[0064] Among them, amp j n is the control coefficient for amplitude; a This is the maximum value.

[0065] (3) In the expression of wf(t), since g(t) is relatively complex and may require high precision in geometric modeling, it is necessary to introduce the Haar wavelet function to reconstruct g(t). The expressions for the wavelet function and g(t) are as follows:

[0066]

[0067]

[0068] (4) Since the two endpoints of H(t) are in the interval t∈[0,1 / n] h The values ​​on the [] are all 1. When this value accumulates to 2, it is detrimental to the continuity of the wavelet channel. Therefore, the original Haar wavelet function needs to be modified, i.e.

[0069]

[0070] Here, RH(t) is the modified Haar wavelet function; the general quadratic function pi(t) can be obtained by the given boundary.

[0071] (5) Considering the different waveforms, a new waveform function is introduced, the expression of which is:

[0072]

[0073] Among them, S j (t)=cos(freq j πt); λ(t) is the truncation function, and different waveforms can be obtained by adjusting λ(t).

[0074] (6) To ensure rapid modeling, this invention sets the minimum value of λ(t) to 0.2. λ(t) is still defined using a cubic spline function, and for simplification, it can be expressed as:

[0075] λ(t)=f(λ1,…,λ j ,…,λ nλ ,t),(0≤t≤1)

[0076] Where, λ j n is the control coefficient of the waveform; λ This represents the maximum number of waveforms.

[0077] Step 5: Determine the governing equations and provide the corresponding boundary conditions based on the shape optimization criteria.

[0078] To simplify the analysis process, the conjugate heat transfer control equations are determined as follows:

[0079] Continuity equation:

[0080]

[0081] Momentum equation:

[0082]

[0083] Energy equations in solid domains:

[0084]

[0085] Energy equations in the fluid domain:

[0086]

[0087] Where u1, u2, u3 are the fluid velocities in the X, Y, and Z directions, respectively; T is the temperature field; P is the pressure field; ρ, μ, C p These are the fluid's density, dynamic viscosity, and specific heat capacity, respectively; k s k f These are the thermal conductivity coefficients of the solid and the fluid, respectively.

[0088] Step 6: Normalize the design variables.

[0089] Based on the determined geometric features, the four design variables corresponding to amplitude, wavelength, waveform, and cross-sectional shape and size are normalized to finally establish a horizontal wave channel model with arbitrarily changeable waveform and channel cross-section.

[0090] Step 7, Establish shape optimization criteria

[0091] The optimization framework is established as follows:

[0092] Find:ω

[0093]

[0094] Subject to: 0≤ω≤1

[0095] Where ω is a normalized vector group consisting of all corresponding design variables, including the control coefficient of the cubic spline function representing the amplitude, the wavelet function representing the wavelength, the newly defined truncation function representing the waveform, and the Bernstein function representing the channel cross section and channel torsion; T is the average temperature of the upper surface, RMST is the root mean square temperature of the lower surface, Ω is the integration domain, T is the temperature field of the domain, dΩ represents the differentiation with respect to a specified surface, and ∫ is the integral sign.

[0096] Step 8: Obtain the optimal horizontal corrugation structure distribution and output the results.

[0097] Based on the finite element model of the cold plate, the non-dominated sorting genetic algorithm (NSGA-II) is used to optimize the objective function and obtain the improved temperature distribution of the specified surface of the cold plate (the surface where the power devices are placed).

[0098] The non-dominated sorting genetic algorithm (NSGA-II) is used to optimize the objective function. The population size P and the number of iterations G are set, and the relevant convergence criteria are set as follows.

[0099]

[0100] Where p is the population size and gen is the current iteration number; this means that the iteration will terminate when the target value does not change in the last six iterations.

[0101] Step 9: The optimized model is further discussed using the "Top-Order Solution Approximation Method (TOPSIS)".

[0102] The optimal compromise solution is selected using the Top-Ranking-Solution (TOPSIS) method, and the process is as follows:

[0103] (1) Create a matrix (T) with m = 30 and n = 20. ij ) m×n As the objective function, where T ij To optimize the solution, the average temperature and root mean square temperature of the upper and lower surfaces of the cold plate are calculated.

[0104] (2) Normalize the initial matrix.

[0105]

[0106] (3) By introducing a weighting factor w j Weighting the normalized matrix, i.e.

[0107] a ij =w j ×t ij

[0108] (4) Define positive and negative ideal solutions as

[0109] A + =(min[a 11 ,…,a m1 ],min[a 12 ,…,a m2 ],…,min[a 1n ,…,a nm ])

[0110] A - =(max[a 11 ,…,a m1 ],max[a 12 ,…,a m2 ],…,max[a 1n ,…,a nm ])

[0111] (5) Calculate the distance between the alternative solutions and the positive / negative ideal solutions.

[0112]

[0113]

[0114] (6) Define relative fit c i for

[0115]

[0116] (7) Choose the best compromise

[0117] A best =A∈max(c i )

[0118] Example 3 (Simulation Case):

[0119] 1. Simulation parameters

[0120] refer to Figure 2 The three-dimensional dimensions of the cold plate are 20mm*80mm*10mm, the hydraulic diameter is 6mm, the heating surface size is 10mm*60mm, and the heat flux density at the inlet is q. in It is 16.67 W / cm 2 Inlet temperature T in The K value is 293.15 K, the outlet pressure p is 0, and the inlet velocity u1 = u3 = 0. The Reynolds number is 1000. The solid material is aluminum 6061-T6, and the liquid working fluid is water.

[0121] 2. Simulation Content and Results

[0122] Figure 5 This diagram shows the temperature distribution on the upper and lower surfaces of straight-channel cold plates (SC), uniformly corrugated cold plates (UHWC), and variable-corrugated cold plates (VHWC–22). For example... Figure 3 The UHWC shown is based on an empirical comparative case, while VHWC–22 is based on obtaining a Pareto front plot (e.g., Figure 4 This was obtained using the TOPSIS method. Clearly, the temperature distribution on the upper and lower surfaces of each design is almost symmetrical, indicating that the cold plate can be freely placed without considering the layout. According to... Figure 5 The temperature distribution on the target surface shows that the convective heat transfer capacity gradually decreases along the channel length, thus the temperature also gradually increases along the channel length, resulting in high temperatures being concentrated mainly in the latter half. Combined with... Figure 6The temperature distribution of the middle layer along the height of SC shows a large temperature gradient between the solid and fluid domains, indicating that heat is not effectively carried out of the cold plate system by the fluid. The temperature distribution of UHWC is better than that of SC, and the high-temperature region in the latter half becomes smaller. The highest temperature of UHWC (T0) max The temperature dropped by 5K, and the highest temperature (T) was reduced. max ) and minimum temperature (T min The difference (ΔT) was reduced by 4K. Although the average Nusselt number of UHWC (42.15) is smaller than that of the straight channel (43.31), its periodic enhancement of convection capability makes it superior to SC in overall thermodynamic performance and exhibits good temperature uniformity. The temperature distribution along the thickness direction of the intermediate layer also indicates that the cold fluid region of the fluid domain of UHWC is smaller than that of SC, and more heat flows into the fluid. In addition, the temperature distribution of the target surface of VHWC–22 was significantly improved after optimization, with most areas showing a cooler profile, proving that the variable horizontal corrugated channel is more conducive to improving heat dissipation performance. Maximum temperature (T) max The temperature difference (ΔT) decreased by a maximum of 30K, and the maximum reduction was 41K. VHWC–22 changed the original circular cross-section to a smaller, rhomboid cross-section with a straight-channel-like arrangement, resulting in a reduced convective heat transfer area. The average Nusselt number of VHWC–22 increased by 28.55 (65.92%) compared to SC and by 29.71 (70.49%) compared to UHWC. Based on the temperature distribution of the intermediate layer in the thickness direction of VHWC–22 (e.g.... Figure 6 As shown in the figure, the temperature difference between the solid domain and the fluid domain was found to be smaller, which further illustrates the superiority of the variable horizontal wave channel. Figure 7 The streamline distribution diagrams shown for straight channels, uniformly wavy channels, and variablely wavy channels indicate that, compared to SC, UHWC and VHWC–22 generated a large amount of rotating low-velocity fluid in their channels. Furthermore, UHWC and SC have the same maximum velocity (V0). max The maximum velocity value is 0.33 m / s, although the former has a larger cross-sectional area than the latter. VHWC–22 has the largest maximum velocity value of 0.62 m / s, mainly due to its smaller cross-section. Combined with the wave characteristics, this makes more high-speed fluid visible at the solid-liquid interface, which means that the resulting wavy channels are conducive to the breaking of the flow boundary layer. Figure 4 The Pareto front distributions of the objective function's mean temperature and root mean square temperature are presented. The correlation values ​​of the last 30 individuals have been normalized for a more intuitive display. The optimal structure is obtained by setting the weight ratio of mean temperature to root mean square temperature to 0.5:0.5.

[0123] Table 1 Comparison of radiator surface temperature before and after optimization.

[0124]

[0125]

[0126] By comparing and analyzing the surface temperature distribution of these three channels, it can be seen that the optimized variable corrugated channel has significantly better heat dissipation performance than the straight channel and the uniform corrugated channel, and the heat dissipation performance has been greatly improved.

Claims

1. A method for free modeling and optimization design of horizontal wave-shaped channels, characterized in that, The amplitude is represented by a cubic spline function, the wavelength by a wavelet function, and the waveform by a truncation function, and the waveform is represented by a rational Bernstein function. The Bézier function allows for free modification of the channel cross-sectional shape and size. Based on this, a horizontally wavy channel is constructed as the basic structure of the cold plate. Using the average temperature and root mean square temperature of the upper and lower surfaces of the cold plate as objective functions, the NSGA-II optimization algorithm is employed to optimize the horizontally wavy channel. Simultaneously, design variables are normalized, and finally, the TOPSIS ranking method is used to select the optimal compromise solution. The process includes the following steps: Step 1: Based on the configuration of the on-site electronic equipment, determine the external dimensions, hydraulic diameter, heating surface dimensions, and inlet / outlet positions of the horizontal corrugated channel cold plate. Step 2: Determine the geometric dimensions of the flow channel inlet and outlet based on the determined cold plate dimensions; determine the heat transfer properties based on the heated surface dimensions; determine the flow properties based on the hydraulic diameter and the inlet and outlet positions of the flow channel; and determine the material properties of the heat dissipation system based on the engineering requirements. Step 3: Based on the determined external dimensions of the cold plate, construct a rational Bernstein-based system by parameterizing the rotation and translation matrices. Bézier function for initial straight channels of arbitrary cross-sectional shapes; Step 4: Based on the initial straight channel, construct the geometric features of the amplitude, wavelength, and waveform of the horizontal wave channel using the arbitrary shape parametric modeling method of the wave channel; Step 5: Based on the horizontal wave-shaped channel, establish a finite element model of the cold plate using the conjugate heat transfer control equation; Step 6: Based on the finite element model of the cold plate, perform a mesh independence test to verify the reliability of the numerical model; Step 7: Normalize the four design variables corresponding to the geometric features: amplitude, wavelength, waveform, and cross-sectional shape and size. Step 8: Based on engineering requirements, construct the design variables of the optimization framework, including the control coefficients of the cubic spline function representing amplitude, the wavelet function representing wavelength, the truncation function representing waveform, and the control coefficients of the Bernstein function representing channel cross-section and channel torsion; construct the objective function of the optimization framework, including minimizing the average temperature and root mean square temperature of the top and bottom of the cold plate. Step 9: Optimize the objective function of the optimization framework obtained in Step 8 using the NSGA-II optimization algorithm to obtain the optimized temperature distribution of the cold plate and power devices; Step 10: Based on the numerical solution of the temperature distribution of the optimized cold plate and power devices, select the best compromise solution using the TOPSIS sorting method.

2. The method for free modeling and optimization design of horizontal wave-shaped channels as described in claim 1, characterized in that, In step 2, the external dimensions of the cold plate include length L, width W, and height H; hydraulic diameter D; and the heating surface dimension W. h L h Heat transfer properties include inlet fluid temperature. T in The thermal insulation boundary of the external wall and its distance from the heat source Q Flow property parameters include inlet velocity. U in and export pressure P out ; The heat dissipation system materials include solid aluminum 6061-T6 and liquid transport medium water. The material properties of the heat dissipation system include: solid thermal conductivity. k s Fluid thermal conductivity k f Fluid specific heat capacity at constant pressure C p and fluid density ρ .

3. The method for free modeling and optimization design of horizontal wave-shaped channels as described in claim 1, characterized in that, Step 3 specifically involves: constructing an initial straight channel based on the rotation and translation matrices of the three-dimensional Cartesian coordinate system, and fitting it to... XOY Performed in a plane. Z For the height direction, the rotation and translation matrices are: Among them, item 1 , , This corresponds to the spatial position of the geometric feature in the global coordinate system; terms 2 and 3 represent the spatial position of the geometric feature in the local coordinate system, i.e., the position established in term 4. , , Item 2 is rotation about the Z-axis, and item 3 is rotation about the Z-axis. Y Axis rotation; Item 4 is related to the cross-sectional shape and size, and the meaning of the control parameters differs in different cross-sectional types; Item 5 is the local to global translation; where, arbitrary cross-sectional types are determined by rational Bernstein... Bézier function construction, i.e.: in, It is built on three foundations; basis functions with weighting coefficients The combination of these factors determines the shape of the cross-section. Using Bernstein The Bézier function is represented as: in, For Bernstein Bézier basis functions; The coefficients are binomial coefficients; For the intermediate parameter control coefficient of the i-th arc; Let be the maximum power of the function.

4. The method for free modeling and optimization design of horizontal wave-shaped channels as described in claim 1, characterized in that, Step 4 specifically involves: constructing a horizontally wavy channel based on the initial straight channel. in, and Based on the initial straight channel Obtained by re-conversion; It's about parameters. t The trigonometric functions are expressed as: in, The wavelength of the wavy channel; The amplitude of the wave channel is established using a cubic spline function. The simplified cubic spline function expressing the amplitude is: in, This is the control coefficient for amplitude; It is the maximum value; In the expression, the Haar wavelet function is introduced to reconstruct the expression. wavelet function and The expressions are as follows: when The two endpoints are in the interval When the accumulated value reaches 2, the original Haar wavelet function is modified, that is: in, The modified Haar wavelet function; quadratic function Obtained through the given boundaries; Regarding the geometric characteristics of the waveform, a new waveform function is introduced, with the expression: in, ; This is a truncation function, adjusted by... Different waveforms are obtained; The minimum value is set to 0.2, and a cubic spline function is used. The simplified form is as follows: in, These are the control coefficients for the waveform; This represents the maximum number of waveforms.

5. The method for free modeling and optimization design of horizontal wave-shaped channels as described in claim 1, characterized in that, In step 5, the conjugate heat transfer control equation is first determined as follows: Continuity equation: Momentum equation: Energy equations in solid domains: Energy equations in the fluid domain: in, They are respectively X , Y , Z Fluid velocity in the direction; T For temperature field; P For pressure field; , , These are the fluid's density, dynamic viscosity, and specific heat capacity, respectively. , These are the thermal conductivity coefficients of the solid and the fluid, respectively. Based on this, a finite element model of a cold plate with horizontal wavy channels is established.

6. The method for free modeling and optimization design of horizontal wave-shaped channels as described in claim 1, characterized in that, In step 6, when performing the mesh independence test, an unstructured mesh is used to refine the mesh of the fluid domain. The number of meshes obtained is compared, and the optimal mesh is finally selected.

7. The method for free modeling and optimization design of horizontal wave-shaped channels as described in claim 1, characterized in that, The optimization framework established in step 8 is as follows: in, The normalized vector group consists of all corresponding design variables, including the control coefficients of the cubic spline function representing the amplitude, the wavelet function representing the wavelength, the newly defined truncation function representing the waveform, and the Bernstein function representing the channel cross section and channel torsion. The average temperature of the upper surface. The root mean square temperature of the lower surface is... For the integration domain, T For the temperature field of this region, Indicates the differentiation with respect to a specified surface. This is the integral symbol.

8. The method for free modeling and optimization design of horizontal wave-shaped channels as described in claim 1, characterized in that, In step 9, the NSGA-II optimization algorithm is used to optimize the objective function. The corresponding population size P and iteration number G are set, and the relevant convergence criteria are set as follows: Where p is the population size; gen is the current iteration number; the iteration will terminate when the target value does not change in the last six iterations; then, according to the convergence criterion, optimization is performed to obtain a better horizontal wave channel and the temperature distribution of the power device.

9. The method for free modeling and optimization design of horizontal wave-shaped channels as described in claim 1, characterized in that, Step 10 specifically includes the following steps: Step 10.1: Create a matrix with m=30 and n=20. As the objective function, where The optimized average and root mean square temperatures of the top and bottom of the cold plate; Step 10.2: Normalize the initial matrix; Step 10.3: Introduce weighting factors Weight the normalized matrix, that is: Step 10.4: Define the positive and negative ideal solutions as follows: Step 10.5: Calculate the distance between the alternative solution and the positive / negative ideal solution: Step 10.6: Define relative fit for: Step 10.7: Select the best compromise solution: 。

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