A method and system for topology optimization of a printed circuit board heat exchanger

Abstract

The application discloses a double-fluid topology optimization construction method and system of a printed circuit board heat exchanger, and is characterized in that the printed circuit board heat exchanger has periodicity and symmetry in the height direction and the vertical flow direction, the full-scale model of the printed circuit board heat exchanger is known, the periodic boundary condition and the symmetric boundary condition of the printed circuit board heat exchanger are established, and a typical flow channel unit of the three-dimensional printed circuit board heat exchanger is selected to construct a three-dimensional single-flow channel model; then, according to the three-dimensional single-flow channel model, a topology optimization material representation method of a variable density method and a three-dimensional flow heat transfer control equation are coupled, a three-dimensional flow heat transfer problem is reduced to a two-dimensional design domain, and a double-fluid flow heat transfer dimension reduction model is formed; finally, according to the double-fluid flow heat transfer dimension reduction model, a variable density method topology optimization objective function and a filtering projection post-processing method are coupled to obtain the distribution of solid fins and fluid flow channels in the cold-side fluid flow channel and the hot-side fluid flow channel, that is, a double-fluid topology optimization model; the method is based on the above method to realize topology optimization with the aim of strengthening heat exchange and reducing flow resistance, to obtain the distribution of fluid fins in the design domain, to construct a new topology channel structure, and to improve the performance of the printed circuit board heat exchanger; compared with a traditional structure, the application can realize the improvement of 13.1% of the total heat exchange capacity under the condition of reducing the pump work of the heat exchanger by 38%.

Description

Technical Field

[0001] This invention belongs to the field of heat exchanger technology, specifically relating to a two-fluid topology optimization construction method and system for printed circuit board heat exchangers. Background Technology

[0002] Printed circuit board (PCB) heat exchangers are a new type of high-efficiency, compact heat exchanger with many advantages such as high heat transfer efficiency, wide temperature and pressure resistance, and good corrosion resistance. They are widely used in core equipment such as nuclear reactors, marine engines, and hydrogen coolers. The flow channel structure of a PCB heat exchanger has a significant impact on its flow and heat transfer performance. Its flow channel structure directly determines key indicators such as fluid inlet and outlet pressure drop and heat transfer, which in turn directly affect the heat exchanger performance and the energy consumption of auxiliary equipment.

[0003] Optimizing the flow channel structure of printed circuit board heat exchangers is crucial. Since the introduction of printed circuit board heat exchangers in 1985, researchers have developed numerous flow channel structures to improve their performance. The S-shaped fin structure proposed by Ngo et al. [Ngo TL, Kato Y, Nikitin K, et al. New printed circuit heat exchanger with S-shaped fins for hotwater supplier[J]. Experimental Thermal and Fluid Science, 2006, 30(8): 811-819.] can reduce the pressure drop of the cold-side fluid by 37%. The rounded-corner zigzag flow channel proposed by Baik et al. [Baik S, Kim SG, Lee J, et al. Study on CO2-water printed circuit heat exchanger performance operating under various CO2 phases for S-CO2 power cycle application[J]. Applied Thermal Engineering, 2017, 113: 1536-1546.] can reduce the pressure drop by 40%-65% compared with the traditional sharp-corner flow channel at the same mass flow rate. Kim et al. [Kim DE, Kim MH, Cha JE, et al. Numerical investigation on thermal–hydraulic performance of new printed circuit heat exchanger model[J]. Nuclear Engineering and Design, 2008, 238(12):3269-3276.] developed an airfoil-type printed circuit board heat exchanger, which, when having the same heat exchange capacity as a zigzag-type heat exchanger, has a pressure drop that is only 1 / 20 of the latter.Qu et al. [Qu M, Zhang Y, Zhang X, et al. Numerical analysis of the effect of wave amplitude on thermohydraulic performance in a heat exchanger with sinusoidal wavy channels[J]. International Communications in Heat and Mass Transfer, 2024, 155: 107582.] studied the PCHE of variable amplitude sinusoidal channels using CFD and improved the heat transfer performance by 36.37%. Samarmad et al. [Oleiwi Samarmad A, Mohammad Jaffal H. Performance evaluation of a printed circuit heat exchanger with a novel two-way corrugated channel[J]. Results in Engineering, 2023, 19: 101303.] and [Samarmad AO, Jaffal HM. Examining the effect of backward / forward-facing wavy channels on the thermohydraulic performance of a printed circuit heat exchanger under the laminar flow regime[J]. International Journal of Thermofluids, 2023, 20: 100485.] proposed a bidirectional corrugated channel and a front / rear corrugated channel, which improved PCHE performance by 43% and 50%, respectively.

[0004] Structural optimization methods can be categorized into three types: size optimization, shape optimization, and topology optimization. These three types of optimization methods have increasing degrees of freedom. Existing research focuses on the size and shape optimization of flow channels in printed circuit board heat exchangers, proposing typical flow channels including direct-flow channels, corrugated channels, sinusoidal channels, louvered channels, and airfoil channels. However, these two types of optimization methods require that the connection method of the structure, i.e., the topological characteristics, remain unchanged during the optimization process. Furthermore, based on theory and designer experience, they cannot fundamentally change the topological configuration of the heat exchanger flow channel structure, thus failing to achieve a transformative design of the flow channel structure. Topology optimization, on the other hand, is not subject to this restriction and can change the topological characteristics of the structure, possessing the highest degree of design freedom. Topology optimization was first applied in the field of structural mechanics. MP, Kikuchi N. Generating optimal topologies in structural design using a homogenization method [J]. Computer Methods in Applied Mechanics and Engineering, 1988, 71(2): 197-224.], used to optimize support structures to meet given loads, and later extended to the field of heat transfer [Yoon GH. Topological design of heat dissipating structure with forced convective heat transfer [J]. J Mech Sci Technol, 2010, 24(6): 1225-1233.], such as Xia et al. [Xia Y, Chen L, Luo J, et al. Numerical investigation of microchannel heat sinks with different inlets and outlets based on topology] [Optimization[J].AppliedEnergy,2023,330:120335.] A multi-inlet microchannel heat exchanger was optimized. Compared with the traditional pin-fin structure, the topology-optimized structure can achieve a 53.28% increase in Nusselt number and a 40.89% reduction in pressure drop. However, few studies have focused on topology optimization for the two-fluid flow heat transfer process occurring in printed circuit board heat exchangers, and thus cannot fundamentally improve the performance of printed circuit board heat exchangers. Summary of the Invention

[0005] To overcome the shortcomings of existing technologies, this invention aims to provide a method and system for constructing a two-fluid topology optimization model for printed circuit board heat exchangers. First, the three-dimensional cold and hot side channels of the printed circuit board heat exchanger are extracted and formed into three-dimensional typical channel units, obtaining a three-dimensional single-channel model. Then, considering a dimensionality reduction model, the three-dimensional single-channel model is reduced to a two-fluid flow and heat transfer dimensionality reduction model. Using the obtained dimensionality reduction model, typical flow and heat transfer processes occurring in the channels are extracted, and a two-fluid topology optimization model for the flow and heat transfer processes within the channels is constructed. Based on the variable density method, with maximizing the heat transfer in the cold-hot side channels as the optimization objective, topology optimization is performed under given inlet Reynolds number and inlet / outlet pressure drop constraints to obtain the distribution of solid fins and fluid channels within the channels, thus constructing the topology channel structure. Results show that, compared to existing airfoil structures, the constructed topology-optimized structure contains a complex and counterintuitive fin structure, exhibiting novel structural characteristics. Compared to existing airfoil structures, the topology-optimized structure can achieve a 13.1% increase in total heat transfer while reducing pump power by 38%, demonstrating strong performance.

[0006] To achieve the above objectives, the technical solution adopted by the present invention is as follows:

[0007] A two-fluid topology optimization construction method for printed circuit board (PCB) heat exchangers is proposed. Based on the periodicity and symmetry of the PCB heat exchanger in the height and vertical flow directions, and the known full-scale model of the PCB heat exchanger, periodic and symmetric boundary conditions are established. Typical flow channel elements of the three-dimensional PCB heat exchanger are selected to construct a three-dimensional single-channel model. Then, based on the three-dimensional single-channel model, the topology optimization material characterization method of the variable density method and the three-dimensional flow and heat transfer control equations are coupled to reduce the three-dimensional flow and heat transfer problem to a two-dimensional design domain, forming a two-fluid flow and heat transfer dimensionality reduction model. Finally, based on the two-fluid flow and heat transfer dimensionality reduction model, the topology optimization objective function of the variable density method and the filtered projection post-processing method are coupled to obtain the distribution of solid fins and fluid channels in the cold-side and hot-side fluid channels, i.e., the two-fluid topology optimization model.

[0008] The two-fluid flow heat transfer dimensionality reduction model includes a cold fluid layer describing the cold-side fluid channel, a hot fluid layer describing the hot-side fluid channel, and a solid layer describing the solid located between the cold-side and hot-side fluid channels; it includes flow control equations solved in the cold fluid layer and the hot fluid layer, and heat transfer control equations solved in the cold fluid layer, the hot fluid layer, and the solid layer, respectively; the thermal conductivity and permeability parameters of the fluid and solid regions in the cold fluid layer are different; the thermal conductivity and permeability parameters of the fluid and solid regions in the hot fluid layer are different.

[0009] A method for constructing a two-fluid topology optimization for a printed circuit board heat exchanger, specifically including the following steps:

[0010] Step 1: Construct a 3D single-channel model of the printed circuit board heat exchanger;

[0011] Step 2: Based on the three-dimensional single-channel model obtained in Step 1, the topology optimization material characterization method coupled with the variable density method and the three-dimensional flow heat transfer control equation are used to reduce the three-dimensional flow heat transfer problem to a two-dimensional design domain, and a two-fluid flow heat transfer dimensionality reduction model is constructed.

[0012] Step 3: Based on the two-fluid flow heat transfer dimensionality reduction model obtained in Step 2, the topology optimization objective function of the coupled variable density method and the post-processing method of hyperbolic tangent projection are used to construct the two-fluid topology optimization model.

[0013] The specific method for constructing the three-dimensional single-channel model in step one is as follows:

[0014] Periodic boundary conditions along the height of the printed circuit board heat exchanger and symmetrical boundary conditions perpendicular to the cold and hot flow directions of the printed circuit board heat exchanger are applied in the height direction and vertical flow direction of the printed circuit board heat exchanger, respectively. The full-scale simulation of the printed circuit board heat exchanger is replaced by simulation of typical three-dimensional flow channel elements to form a three-dimensional single flow channel model, and its three-dimensional flow and heat transfer control equations are determined.

[0015] The periodic boundary conditions are as follows:

[0016]

[0017] Among them, u * =u * (x,y,z),T * =T * (x, y, z) represent the three-dimensional velocity field and temperature field of the printed circuit board heat exchanger, respectively; the asterisk in the upper right corner of the physical quantity represents the three-dimensional physical field; the subscripts btm and top represent the bottom surface and top surface of the printed circuit board heat exchanger, respectively.

[0018] The symmetric boundary conditions are as follows:

[0019] u * ·n=0 (3)

[0020]

[0021] Where n is the wall normal vector, k fl The fluid's thermal conductivity;

[0022] The simulation of the printed circuit board heat exchanger was replaced by a three-dimensional typical flow channel unit simulation to form a three-dimensional single flow channel model, and its three-dimensional flow and heat transfer control equations were determined as follows:

[0023]

[0024] Where, p * =p * (x,y,z) represents the three-dimensional pressure field of the printed circuit board heat exchanger; ρ fl μ fl and c pfl These represent fluid density, viscosity, and specific heat at constant pressure, respectively; k s is the thermal conductivity of a solid.

[0025] The specific method for step two is as follows:

[0026] Topology optimization of the flow channel in a printed circuit board heat exchanger: Topology optimization is performed on the middle section of the flow channel, and the inlet and outlet sections are set as fluid / solid inlet / outlet extensions; the region in the middle section of the flow channel for topology optimization is the design domain, and the design variable γ is used to characterize the material distribution properties within the design domain. When the design variable γ equals 0, it corresponds to solid in the design domain, and when it equals 1, it corresponds to fluid in the design domain.

[0027]

[0028] Among them, Ω fl and Ω s Let represent fluid and solid, respectively; subscripts 1, m, and 2 are used to represent the cold fluid layer, solid layer, and hot fluid layer, respectively; based on the actual flow and heat transfer process occurring in the printed circuit board heat exchanger, the three-dimensional flow and heat transfer control equations for the cold and hot fluids within the design domain are obtained; based on the three-dimensional flow and heat transfer control equations, the two-dimensional reduced-dimensional flow control equations for the cold and hot fluid layers in the printed circuit board heat exchanger are obtained as follows:

[0029]

[0030] Equations (10) and (12) are the mass conservation equations; equations (11) and (13) are the momentum conservation equations; u1 and p1 represent the two-dimensional velocity and pressure fields in the cold fluid layer; u2 and p2 represent the two-dimensional velocity and pressure fields in the hot fluid layer; F1 and F2 are Brinkman body forces, determined by the reverse permeability α1 and α2 of the porous medium.

[0031] F1=α1(γ)u1 (14)

[0032] F2=α2(γ)u2 (15)

[0033] Based on the three-dimensional flow heat transfer control equations, the two-dimensional reduced-dimensional heat transfer control equations for the cold fluid layer, solid layer, and hot fluid layer in the printed circuit board heat exchanger are obtained as follows:

[0034]

[0035] Among them, T1, T m T1 and T2 are the two-dimensional temperatures of the cold fluid layer, solid layer, and hot fluid layer, respectively; H1 and H2 are the temperatures of the cold fluid layer, solid layer, and hot fluid layer, respectively. m H1 and H2 represent the half-heights of the cold fluid layer, solid layer, and hot fluid layer, respectively; k1(γ) represents the interpolated thermal conductivity of the cold fluid layer, and h1(γ) represents the convective diffusion coefficient between the cold fluid layer and the solid layer; k2(γ) represents the interpolated thermal conductivity of the hot fluid layer, and h2(γ) represents the convective diffusion coefficient between the hot fluid layer and the solid layer; k s It is the thermal conductivity of the solid; heat is transferred from the hot fluid layer through the solid layer to the cold fluid layer. According to the principle of thermal resistance equivalence, the convective heat transfer coefficient h1(γ) between the cold fluid layer and the solid layer is:

[0036]

[0037] Among them, R c R m and R 1m These are the thermal resistances from the cold fluid layer to the interface, from the interface to the solid layer, and from the cold fluid layer to the solid layer, respectively; the convective heat transfer coefficients of the fluid and solid in the cold fluid layer are respectively:

[0038]

[0039] Among them, h fl1 and h s1 These are the heat transfer coefficients of the fluid and solid in the cold fluid layer, respectively; similarly, the heat transfer coefficient h2(γ) between the hot fluid layer and the solid layer is:

[0040]

[0041] This yields a two-fluid flow heat transfer dimension reduction model.

[0042] The two-fluid flow heat transfer dimensionality reduction model obtained in step two has the following boundary conditions: at the inlet of the printed circuit board heat exchanger, the fluid is in fully developed flow, and the Reynolds numbers of the cold-side fluid and the hot-side fluid are Re1 and Re2, respectively; the inlet temperature of the cold-side fluid is set to T. in1 The inlet temperature of the hot-side fluid is set to T. in2 At the outlet of the printed circuit board heat exchanger, a cold-side fluid pressure boundary condition p is applied to the two-dimensional reduced-dimensional flow control equation. 1out =0, hot-side fluid pressure boundary condition p 2out=0; Apply fully developed cold-side fluid heat transfer boundary conditions to the two-dimensional reduced-dimensional heat transfer control equations. Hot-side fluid heat transfer boundary conditions The two-fluid flow heat transfer dimension reduction model uses the upper and lower sidewalls perpendicular to the flow directions of the cold and hot fluids, and sets the boundary conditions as u1·n1=0. (Cold side fluid), u2·n2=0, (Hot-side fluid); In the two-fluid flow heat transfer dimension reduction model, except for the inlet and outlet sections, and the upper and lower sidewalls perpendicular to the flow directions of the cold and hot fluids, all other fluid-solid contact surfaces are subject to no-slip and adiabatic boundary conditions u1 = 0. (Cold side fluid), u2 = 0 (Hot-side fluid).

[0043] The specific method for constructing the two-fluid topology optimization model in step three is as follows:

[0044] Step 3.1: Using the objective function of maximizing interlayer heat transfer, combined with pressure constraints, obtain the topology optimization structure that enhances heat transfer and reduces flow resistance:

[0045]

[0046] Where Q is the heat exchange between the cold-side fluid and the hot-side fluid; Δp1 is the pressure drop at the inlet and outlet of the cold-side fluid, Δp 1max Δp2 is the pressure drop constraint at the inlet and outlet of the cold-side fluid; Δp is the pressure drop at the inlet and outlet of the hot-side fluid. 2max It is a constraint on the pressure drop at the inlet and outlet of the hot-side fluid;

[0047] Step 3.2: A two-fluid topology optimization model is constructed using post-processing methods of Helmholtz filtering and hyperbolic tangent projection.

[0048] Step 3.2.1: The Helmholtz equation is used to filter the optimization design variable γ after each iteration to avoid the checkerboard phenomenon in the filtered optimization structure and to reduce the dependence of the optimization structure on the mesh.

[0049]

[0050] Where, γ f1 and γ f2 These are the filtered new design variables; r l r2 is the filter radius;

[0051] Step 3.2.2: Use hyperbolic tangent projection to post-process the filtered optimized structure to sharpen the fluid-structure interface.

[0052]

[0053] Where, γ p1 and γ p2 β1 and β2 are the projected design variables; γ is the projection slope; β1 and β2 are the projection slopes; γ is the projection slope. c1 and γ c2 The projection point is used; repeat steps 3.1 to 3.2 until the convergence criterion is met to obtain the two-fluid topology optimization model of the printed circuit board heat exchanger.

[0054] The convergence criterion described in step three is that the design variable residual is less than 0.01 or the number of iterations exceeds 400.

[0055] A two-fluid topology optimization construction system for a printed circuit board heat exchanger includes:

[0056] 3D Single-Channel Model Construction Module: Based on step one, periodic boundary conditions and symmetrical boundary conditions are applied in the height direction and vertical flow direction of the printed circuit board heat exchanger, respectively. The full-scale simulation of the printed circuit board heat exchanger is replaced by the simulation of typical 3D flow channel units to form a 3D single-channel model.

[0057] Two-fluid flow heat transfer dimensionality reduction model construction module: Based on step two, the topology optimization material characterization method of coupled variable density method and the flow heat transfer control equation, the three-dimensional flow heat transfer problem is reduced to a two-dimensional design domain to construct a two-fluid flow heat transfer dimensionality reduction model.

[0058] Two-fluid topology optimization model construction module: Based on step three, a two-dimensional two-fluid topology optimization model for the flow heat transfer process in the channel is constructed. Based on the variable density method, the heat transfer is maximized under a given pressure constraint. The topology optimization is carried out with the goal of enhancing heat transfer and reducing flow resistance, and the fin distribution in the design domain is obtained to construct a new topology channel structure.

[0059] Compared with the prior art, the beneficial effects of the present invention are as follows:

[0060] 1. This invention constructs a two-fluid flow heat transfer dimensionality reduction model based on the periodicity and symmetry of the heat exchanger's three-dimensional geometric characteristics through steps one and two, respectively. The constructed dimensionality reduction model avoids solving complex three-dimensional problems and reduces computational resources.

[0061] 2. This invention constructs a two-fluid (cold-side fluid, hot-side fluid) topology optimization method for printed circuit board heat exchangers step by step through steps one, two, and three. Under a given pressure constraint, it maximizes heat transfer, aiming to enhance heat transfer and reduce flow resistance through topology optimization, thereby obtaining the fin distribution in the design domain and designing a novel topological channel structure. This novel topology-optimized channel structure features innovative fin designs arranged in the design domain, with fins of varying sizes and complex shapes, presenting a counterintuitive design.

[0062] 3. The topology-optimized structure designed in step three of this invention exhibits superior flow heat transfer performance. Three-dimensional flow heat transfer simulations demonstrate that, compared to airfoil structures, this invention can achieve a total heat transfer increase of up to 13.1% while reducing heat exchanger pump power by up to 38%.

[0063] In summary, this invention employs a topology optimization method based on the variable density approach to sequentially construct a three-dimensional single-channel model and a two-fluid flow heat transfer dimensionality reduction model. It develops a topology optimization method for the flow channel structure of printed circuit board heat exchangers, achieving a solution for complex three-dimensional problems using the dimensionality reduction model and completing an innovative design of the heat exchanger flow channel structure. This invention has the advantages of novel structure and high performance. Attached Figure Description

[0064] Figure 1 This is a schematic diagram of the printed circuit board heat exchanger of the present invention; wherein, Figure 1 In the diagram, (a) represents the size of the topology optimization design domain. Figure 1 (b) in the figure represents the dimensions of the airfoil structure.

[0065] Figure 2 This is a flowchart of the topology optimization process of this invention.

[0066] Figure 3 This is the topology optimization result of the printed circuit board heat exchanger of the present invention under different inlet Reynolds numbers.

[0067] Figure 4 This invention relates to the three-dimensional structure of a printed circuit board heat exchanger; wherein, Figure 4 In the diagram, (a) represents the topology optimization structure. Figure 4 (b) in the diagram is an airfoil structure.

[0068] Figure 5 This is a coordinate graph of the three-dimensional simulation pumping power and heat exchange of this invention. Detailed Implementation

[0069] The specific embodiments of the present invention will be described in detail below with reference to the accompanying drawings. It should be understood that the specific embodiments described herein are for illustration and explanation only and are not intended to limit the scope of the present disclosure.

[0070] A two-fluid topology optimization construction method for printed circuit board (PCB) heat exchangers is proposed. Based on the periodicity and symmetry of the PCB heat exchanger in the height and vertical flow directions, and the known full-scale model of the PCB heat exchanger, periodic and symmetric boundary conditions are established. Typical flow channel elements of the three-dimensional PCB heat exchanger are selected to construct a three-dimensional single-channel model. Then, based on the three-dimensional single-channel model, the topology optimization material characterization method of the variable density method and the three-dimensional flow and heat transfer control equations are coupled to reduce the three-dimensional flow and heat transfer problem to a two-dimensional design domain, forming a two-fluid flow and heat transfer dimensionality reduction model. Finally, based on the two-fluid flow and heat transfer dimensionality reduction model, the topology optimization objective function of the variable density method and the filtered projection post-processing method are coupled to obtain the distribution of solid fins and fluid channels in the cold-side and hot-side fluid channels, i.e., the two-fluid topology optimization model.

[0071] The two-fluid flow heat transfer dimensionality reduction model includes a cold fluid layer describing the cold-side fluid channel, a hot fluid layer describing the hot-side fluid channel, and a solid layer describing the solid located between the cold-side and hot-side fluid channels; it includes flow control equations solved in the cold fluid layer and the hot fluid layer, and heat transfer control equations solved in the cold fluid layer, the hot fluid layer, and the solid layer, respectively; the thermal conductivity and permeability parameters of the fluid and solid regions in the cold fluid layer are different; the thermal conductivity and permeability parameters of the fluid and solid regions in the hot fluid layer are different.

[0072] A method for constructing a two-fluid topology optimization for a printed circuit board heat exchanger, specifically including the following steps:

[0073] Step 1: Construct a 3D single-channel model of the printed circuit board heat exchanger;

[0074] Periodic boundary conditions along the height of the printed circuit board heat exchanger and symmetrical boundary conditions perpendicular to the cold and hot flow directions of the printed circuit board heat exchanger are applied in the height direction and vertical flow direction of the printed circuit board heat exchanger, respectively. The full-scale simulation of the printed circuit board heat exchanger is replaced by simulation of typical three-dimensional flow channel elements to form a three-dimensional single flow channel model, and its three-dimensional flow and heat transfer control equations are determined.

[0075] The periodic boundary conditions are as follows:

[0076]

[0077] Among them, u * =u * (x,y,z),T * =T *(x, y, z) represent the three-dimensional velocity field and temperature field of the printed circuit board heat exchanger, respectively; the asterisk in the upper right corner of the physical quantity represents the three-dimensional physical field; the subscripts btm and top represent the bottom surface and top surface of the printed circuit board heat exchanger, respectively.

[0078] The symmetric boundary conditions are as follows:

[0079] u * ·n=0 (3)

[0080]

[0081] Where n is the wall normal vector, k fl The fluid's thermal conductivity;

[0082] The simulation of the printed circuit board heat exchanger was replaced by a three-dimensional typical flow channel unit simulation to form a three-dimensional single flow channel model, and its three-dimensional flow and heat transfer control equations were determined as follows:

[0083]

[0084] Where, p * =p * (x,y,z) represents the three-dimensional pressure field of the printed circuit board heat exchanger; ρ fl μ fl and c pfl These represent fluid density, viscosity, and specific heat at constant pressure, respectively; k s is the thermal conductivity of a solid.

[0085] Step 2: Based on the three-dimensional single-channel model obtained in Step 1, the topology optimization material characterization method coupled with the variable density method and the three-dimensional flow heat transfer control equation are used to reduce the three-dimensional flow heat transfer problem to a two-dimensional design domain, and a two-fluid flow heat transfer dimensionality reduction model is constructed.

[0086] Topology optimization of the flow channel in a printed circuit board heat exchanger: Topology optimization is performed on the middle section of the flow channel, and the inlet and outlet sections are set as fluid / solid inlet / outlet extensions; the region in the middle section of the flow channel for topology optimization is the design domain, and the design variable γ is used to characterize the material distribution properties within the design domain. When the design variable γ equals 0, it corresponds to solid in the design domain, and when it equals 1, it corresponds to fluid in the design domain.

[0087]

[0088] Among them, Ω fl and Ω sLet represent fluid and solid, respectively; subscripts 1, m, and 2 are used to represent the cold fluid layer, solid layer, and hot fluid layer, respectively; based on the actual flow and heat transfer process occurring in the printed circuit board heat exchanger, the three-dimensional flow and heat transfer control equations for the cold and hot fluids within the design domain are obtained; based on the three-dimensional flow and heat transfer control equations, the two-dimensional reduced-dimensional flow control equations for the cold and hot fluid layers in the printed circuit board heat exchanger are obtained as follows:

[0089]

[0090] Equations (10) and (12) are the mass conservation equations; equations (11) and (13) are the momentum conservation equations; u1 and p1 represent the two-dimensional velocity and pressure fields in the cold fluid layer; u2 and p2 represent the two-dimensional velocity and pressure fields in the hot fluid layer; F1 and F2 are Brinkman body forces, determined by the reverse permeability α1 and α2 of the porous medium.

[0091] F1=α1(γ)u1 (14)

[0092] F2=α2(γ)u2 (15)

[0093] Based on the three-dimensional flow heat transfer control equations, the two-dimensional reduced-dimensional heat transfer control equations for the cold fluid layer, solid layer, and hot fluid layer in the printed circuit board heat exchanger are obtained as follows:

[0094]

[0095] Among them, T1, T m T1 and T2 are the two-dimensional temperatures of the cold fluid layer, solid layer, and hot fluid layer, respectively; H1 and H2 are the temperatures of the cold fluid layer, solid layer, and hot fluid layer, respectively. m H1 and H2 represent the half-heights of the cold fluid layer, solid layer, and hot fluid layer, respectively; k1(γ) represents the interpolated thermal conductivity of the cold fluid layer, and h1(γ) represents the convective diffusion coefficient between the cold fluid layer and the solid layer; k2(γ) represents the interpolated thermal conductivity of the hot fluid layer, and h2(γ) represents the convective diffusion coefficient between the hot fluid layer and the solid layer; k s It is the thermal conductivity of the solid; heat is transferred from the hot fluid layer through the solid layer to the cold fluid layer. According to the principle of thermal resistance equivalence, the convective heat transfer coefficient h1(γ) between the cold fluid layer and the solid layer is:

[0096]

[0097] Among them, R c R m and R 1m These are the thermal resistances from the cold fluid layer to the interface, from the interface to the solid layer, and from the cold fluid layer to the solid layer, respectively; the convective heat transfer coefficients of the fluid and solid in the cold fluid layer are respectively:

[0098]

[0099] Among them, h fl1 and h s1 These are the heat transfer coefficients of the fluid and solid in the cold fluid layer, respectively; similarly, the heat transfer coefficient h2(γ) between the hot fluid layer and the solid layer is:

[0100]

[0101] This yields a two-fluid flow heat transfer dimension reduction model.

[0102] The two-fluid flow heat transfer dimensionality reduction model obtained in step two has the following boundary conditions: at the inlet of the printed circuit board heat exchanger, the fluid is in fully developed flow, and the Reynolds numbers of the cold-side fluid and the hot-side fluid are Re1 and Re2, respectively; the inlet temperature of the cold-side fluid is set to T. in1 The inlet temperature of the hot-side fluid is set to T. in2 At the outlet of the printed circuit board heat exchanger, a cold-side fluid pressure boundary condition p is applied to the two-dimensional reduced-dimensional flow control equation. 1out =0, hot-side fluid pressure boundary condition p 2out =0; Apply fully developed cold-side fluid heat transfer boundary conditions to the two-dimensional reduced-dimensional heat transfer control equations. Hot-side fluid heat transfer boundary conditions The two-fluid flow heat transfer dimension reduction model uses the upper and lower sidewalls perpendicular to the flow directions of the cold and hot fluids, and sets the boundary conditions as u1·n1=0. (Cold side fluid), u2·n2=0, (Hot-side fluid); In the two-fluid flow heat transfer dimension reduction model, except for the inlet and outlet sections, and the upper and lower sidewalls perpendicular to the flow directions of the cold and hot fluids, all other fluid-solid contact surfaces are subject to no-slip and adiabatic boundary conditions u1 = 0. (Cold side fluid), u2 = 0 (Hot-side fluid).

[0103] Step 3: Based on the two-fluid flow heat transfer dimensionality reduction model obtained in Step 2, the topology optimization objective function of the coupled variable density method and the post-processing method of hyperbolic tangent projection are used to construct the two-fluid topology optimization model.

[0104] Step 3.1: Using the objective function of maximizing interlayer heat transfer, combined with pressure constraints, obtain the topology optimization structure that enhances heat transfer and reduces flow resistance:

[0105]

[0106] Where Q is the heat exchange between the cold-side fluid and the hot-side fluid; Δp1 is the pressure drop at the inlet and outlet of the cold-side fluid, Δp1max Δp2 is the pressure drop constraint at the inlet and outlet of the cold-side fluid; Δp is the pressure drop at the inlet and outlet of the hot-side fluid. 2max It is a constraint on the pressure drop at the inlet and outlet of the hot-side fluid;

[0107] Step 3.2: A two-fluid topology optimization model is constructed using post-processing methods of Helmholtz filtering and hyperbolic tangent projection.

[0108] Step 3.2.1: The Helmholtz equation is used to filter the optimization design variable γ after each iteration to avoid the checkerboard phenomenon in the filtered optimization structure and to reduce the dependence of the optimization structure on the mesh.

[0109]

[0110] Where, γ f1 and γ f2 These are the filtered new design variables; r l r2 is the filter radius;

[0111] Step 3.2.2: Use hyperbolic tangent projection to post-process the filtered optimized structure to sharpen the fluid-structure interface.

[0112]

[0113] Where, γ p1 and γ p2 β1 and β2 are the projected design variables; γ is the projection slope; β1 and β2 are the projection slopes; γ is the projection slope. c1 and γ c2 The projection point is used; repeat steps 3.1 to 3.2 until the convergence criterion is met to obtain the two-fluid topology optimization model of the printed circuit board heat exchanger.

[0114] The convergence criterion described in step three is that the design variable residual is less than 0.01 or the number of iterations exceeds 400.

[0115] A two-fluid topology optimization construction system for a printed circuit board heat exchanger includes:

[0116] 3D Single-Channel Model Construction Module: Based on step one, periodic boundary conditions and symmetrical boundary conditions are applied in the height direction and vertical flow direction of the printed circuit board heat exchanger, respectively. The full-scale simulation of the printed circuit board heat exchanger is replaced by the simulation of typical 3D flow channel units to form a 3D single-channel model.

[0117] Two-fluid flow heat transfer dimensionality reduction model construction module: Based on step two, the topology optimization material characterization method of coupled variable density method and the flow heat transfer control equation, the three-dimensional flow heat transfer problem is reduced to a two-dimensional design domain to construct a two-fluid flow heat transfer dimensionality reduction model.

[0118] Two-fluid topology optimization model construction module: Based on step three, a two-dimensional two-fluid topology optimization model for the flow heat transfer process in the channel is constructed. Based on the variable density method, the heat transfer is maximized under a given pressure constraint. The topology optimization is carried out with the goal of enhancing heat transfer and reducing flow resistance, and the fin distribution in the design domain is obtained to construct a new topology channel structure.

[0119] The topology optimization process of this invention is as follows: Figure 2 As shown. First, in step one, a three-dimensional single-channel model is obtained based on the structural characteristics of the printed circuit board heat exchanger. Then, in step two, the finite element method is used to solve the governing equations to obtain the state variables based on the current structure. Subsequently, in step three, the objective function is calculated, and the sensitivity of the objective function is obtained. Finally, in step three, the design variables are updated using the globally convergent moving asymptote method (GCMMA) based on a gradient-based optimization solver. After post-processing the design variables such as filtering and projection in step three, the above steps are repeated until the convergence criterion (design variable residuals less than 10) is met. -3 (or more than 400 iterations) to obtain, for example Figure 3 The results of topology optimization are shown below under different inlet Reynolds numbers. The Reynolds numbers for topology optimization are set to 20, 40, 60, 80, 100, 150, 200, 250, and 300. Figure 3 This is a topology optimization structure obtained for a single-channel structure under different inlet Reynolds numbers. The optimized structure arranges fins of varying sizes and complex shapes within the design domain, exhibiting a counterintuitive design. As the inlet Reynolds number increases, the complexity of the hot and cold side structures increases. On the cold side, heat within the fins is transferred to the surrounding fluid via convection. At low Reynolds numbers, convective heat transfer around each fin is relatively weak, indicating a low Biot number (defined as the ratio of the thermal resistance of heat conduction within the solid to the thermal resistance of convective heat transfer around the solid). Therefore, the fin size should not be too large for effective cooling. As the Reynolds number increases, convective heat transfer becomes stronger, leading to a higher Biot number. Larger solid fins can effectively cool the channels, increasing the total heat transfer and optimizing heat exchanger performance.

[0120] To verify the benefits of the topology optimization structure, this invention employs a three-dimensional flow and heat transfer model to perform a three-dimensional simulation of the obtained topology optimization structure. Figure 4Taking a typical heat exchanger topology optimization design as an example (Reynolds number 100), the three-dimensional simulation includes topology optimization structure, airfoil structure, and straight-channel structure. The airfoil structure adopts the size optimization structure of Kim et al. [Kim TH, Kwon JG, Yoon SH, et al. Numerical analysis of air-foil shaped fin performance inprinted circuit heat exchanger in a supercritical carbon dioxide power cycle[J]. Nuclear Engineering and Design, 2015, 288: 110-118.], and its geometric dimensions are as follows. Figure 1 As shown in (b) above, the structure was stretched in the thickness direction, and its performance was verified in a three-dimensional flow heat transfer model. The inlet Reynolds numbers were set to 20, 40, 60, 80, 100, 150, 200, 250, and 300, respectively, in the three-dimensional verification. Figure 5 The total pumping power and total heat transfer of the three structures were statistically analyzed. For the printed circuit board heat exchanger, lower total pumping power and higher total heat transfer represent lower auxiliary equipment power consumption and stronger heat transfer performance, corresponding to the area in the upper left corner of the figure. It is evident that the topology-optimized structure (rhomboid) designed in this invention outperforms the airfoil structure (circular) and the straight-channel structure (square). Quantitatively, compared to the existing airfoil structure, the single-channel topology-optimized structure can achieve a 13.1% increase in total heat transfer while reducing pump power by 38%, demonstrating the advantages of the topology-optimized structure of this invention. This invention, targeting the printed circuit board heat exchanger, develops a two-fluid topology optimization dimensionality reduction model, optimizing the two-fluid flow channel structure in the printed circuit board heat exchanger and improving the flow and heat transfer performance of the heat exchanger. Compared to existing structures, the topology-optimized structure contains a complex, counterintuitive fin structure, achieving the purpose of enhanced heat transfer and reduced flow resistance. Compared to the existing airfoil structure, the single-channel topology-optimized structure can achieve a 13.1% increase in total heat transfer while reducing pump power by 38%.

[0121] The preferred embodiments of the present invention have been described in detail above with reference to the accompanying drawings. However, the present invention is not limited to the specific details of the above embodiments. Within the scope of the technical concept of the present invention, various simple modifications can be made to the technical solution of the present invention, and these simple modifications all fall within the protection scope of the present invention.

Claims

1. A method for constructing a two-fluid topology optimization for a printed circuit board heat exchanger, characterized in that, Step 1: Based on the periodicity and symmetry of the printed circuit board (PCB) heat exchanger in the height and vertical flow directions, and given the known full-scale model of the PCB heat exchanger, establish periodic and symmetric boundary conditions to construct a three-dimensional single-channel model of the PCB heat exchanger. Select typical flow channel elements of the three-dimensional PCB heat exchanger to construct a three-dimensional single-channel model. Apply periodic boundary conditions along the height direction of the PCB heat exchanger and symmetric boundary conditions perpendicular to the cold and hot flow directions of the PCB heat exchanger, respectively. Replace the full-scale simulation of the PCB heat exchanger with the simulation of the typical three-dimensional flow channel elements to form a three-dimensional single-channel model, and determine its three-dimensional flow and heat transfer control equations. Step 2: Based on the three-dimensional single-channel model obtained in Step 1, the topology optimization material characterization method coupled with the variable density method and the three-dimensional flow heat transfer control equation are used to reduce the three-dimensional flow heat transfer problem to a two-dimensional design domain, and a two-fluid flow heat transfer dimensionality reduction model is constructed. Step 3: Based on the two-fluid flow heat transfer dimension reduction model obtained in Step 2, the topology optimization objective function of the coupled variable density method and the post-processing method of hyperbolic tangent projection are used to obtain the distribution of solid fins and fluid channels in the cold-side fluid channel and the hot-side fluid channel, i.e., the two-fluid topology optimization model. Step 3.1: Using the objective function of maximizing interlayer heat transfer, combined with pressure constraints, obtain the topology optimization structure that enhances heat transfer and reduces flow resistance: in, Q It is the heat exchange between the cold-side fluid and the hot-side fluid; p 1 is the pressure drop at the inlet and outlet of the cold-side fluid. p 1max It is a constraint on the pressure drop at the inlet and outlet of the cold-side fluid; p 2 is the pressure drop at the inlet and outlet of the hot-side fluid. p 2max It is a constraint on the pressure drop at the inlet and outlet of the hot-side fluid; Step 3.2: A two-fluid topology optimization model is constructed using post-processing methods of Helmholtz filtering and hyperbolic tangent projection. Step 3.2.1: Apply the Helmholtz equation to the optimization design variables after each iteration. γ Filtering is performed to prevent the optimized structure from exhibiting a checkerboard pattern and to reduce the optimized structure's dependence on the mesh: in, γ f1 and γ f2 These are the filtered new design variables; r l and r 2 is the filtration radius; Step 3.2.2: Use hyperbolic tangent projection to post-process the filtered optimized structure to sharpen the fluid-structure interface. in, γ p1 and γ p2 These are the projected design variables; β 1 and β 2 represents the projection slope; γ c1 and γ c2 The projection point is used; repeat steps 3.1 to 3.2 until the convergence criterion is met to obtain the two-fluid topology optimization model of the printed circuit board heat exchanger.

2. The method for constructing a two-fluid topology optimization for a printed circuit board heat exchanger according to claim 1, characterized in that, The two-fluid flow heat transfer dimensionality reduction model includes a cold fluid layer describing the cold-side fluid channel, a hot fluid layer describing the hot-side fluid channel, and a solid layer describing the solid located between the cold-side and hot-side fluid channels; it includes flow control equations solved in the cold fluid layer and the hot fluid layer, and heat transfer control equations solved in the cold fluid layer, the hot fluid layer, and the solid layer, respectively; the thermal conductivity and permeability parameters of the fluid region and the solid region within the cold fluid layer are different; The thermal conductivity and permeability parameters of the fluid and solid regions within the thermal fluid layer are different.

3. The method for constructing a two-fluid topology optimization for a printed circuit board heat exchanger according to claim 1, characterized in that, The periodic boundary conditions are as follows: （1） （2） in, u * = u * ( x,y,z ), T * = T * ( x,y,z The numbers represent the three-dimensional velocity field and temperature field of the printed circuit board heat exchanger, respectively; the asterisk in the upper right corner of the physical quantity represents the three-dimensional physical field; the subscripts btm and top represent the bottom surface and top surface of the printed circuit board heat exchanger, respectively. The symmetric boundary conditions are as follows: （3） （4） in, n Let be the wall normal vector. k fl The fluid's thermal conductivity; The simulation of the printed circuit board heat exchanger was replaced by a three-dimensional typical flow channel unit simulation to form a three-dimensional single flow channel model, and its three-dimensional flow and heat transfer control equations were determined as follows: （5） （6） （7） （8） in, p * = p * ( x,y,z ( ) represents the three-dimensional pressure field of a printed circuit board heat exchanger; ρ fl , μ fl and c pfl These are fluid density, viscosity, and specific heat at isobaric pressure, respectively. k s is the thermal conductivity of a solid.

4. The method for constructing a two-fluid topology optimization for a printed circuit board heat exchanger according to claim 1, characterized in that, The specific method for step two is as follows: Topology optimization of the flow channel in a printed circuit board heat exchanger: The middle section of the flow channel is selected for topology optimization, and the inlet and outlet sections are set as fluid / solid inlet / outlet extensions. The area in the middle section of the flow channel for topology optimization is the design domain, using design variables. γ Characterizing the material distribution properties within the design domain, design variables γ When the value is 0, it corresponds to a solid design domain; when the value is 1, it corresponds to a fluid design domain. （9） Among them, Ω fl and Ω s Let represent fluid and solid, respectively; subscripts 1, m, and 2 are used to represent the cold fluid layer, solid layer, and hot fluid layer, respectively; based on the actual flow and heat transfer process occurring in the printed circuit board heat exchanger, the three-dimensional flow and heat transfer control equations for the cold and hot fluids within the design domain are obtained; based on the three-dimensional flow and heat transfer control equations, the two-dimensional reduced-dimensional flow control equations for the cold and hot fluid layers in the printed circuit board heat exchanger are obtained as follows: （10） （11） （12） （13） Equations (10) and (12) are the mass conservation equations; Equations (11) and (13) are the momentum conservation equations. u 1 and p 1 represents the two-dimensional velocity and pressure fields in the cold fluid layer; u 2 and p 2 represents the two-dimensional velocity and pressure fields in the thermal fluid layer; F 1 and F 2 is the Brinkman volume force, determined by the reverse osmosis rate of porous media. α 1 and α 2. Decision: （14） （15） Based on the three-dimensional flow heat transfer control equations, the two-dimensional reduced-dimensional heat transfer control equations for the cold fluid layer, solid layer, and hot fluid layer in the printed circuit board heat exchanger are obtained as follows: （16） （17） （18） in, T 1. T m , T 2 represents the two-dimensional temperatures of the cold fluid layer, the solid layer, and the hot fluid layer, respectively; H 1. H m , H 2 represents the half-height of the cold fluid layer, the solid layer, and the hot fluid layer, respectively; k 1( γ The interpolated thermal conductivity of the cold fluid layer is represented by ). h 1( γ () represents the convective diffusion coefficient between the cold fluid layer and the solid layer; k 2( γ The interpolated thermal conductivity of the thermal fluid layer is represented by ). h 2( γ () represents the convective diffusion coefficient between the thermal fluid layer and the solid layer; k s It is the thermal conductivity of the solid; heat is transferred from the hot fluid layer through the solid layer to the cold fluid layer. According to the principle of thermal resistance equivalence, it is the convective heat transfer coefficient between the cold fluid layer and the solid layer. h 1( γ )for: （19） （20） in, R c , R m ,and R 1m These are the thermal resistances from the cold fluid layer to the interface, from the interface to the solid layer, and from the cold fluid layer to the solid layer, respectively; the convective heat transfer coefficients of the fluid and solid in the cold fluid layer are respectively: （21） （22） in, h fl1 and h s1 These are the heat transfer coefficients of the fluid and solid in the cold fluid layer, respectively; similarly, they are the heat transfer coefficients of the coupling between the hot fluid layer and the solid layer. h 2( γ )for: （23） （24） This yields a two-fluid flow heat transfer dimension reduction model.

5. The method for constructing a two-fluid topology optimization for a printed circuit board heat exchanger according to claim 1, characterized in that, The two-fluid flow heat transfer dimensionality reduction model obtained in step two has the following boundary conditions: at the inlet of the printed circuit board heat exchanger, the fluid is in fully developed flow, and the Reynolds numbers of the cold-side fluid and the hot-side fluid are respectively... Re 1 and Re 2; The cold side fluid inlet temperature is set to T in1 The hot-side fluid inlet temperature is set to T in2 At the outlet of the printed circuit board heat exchanger, cold-side fluid pressure boundary conditions are applied to the two-dimensional reduced-dimensional flow control equations. p 1out = 0, Hot-side fluid pressure boundary condition p 2out = 0; Apply fully developed cold-side fluid heat transfer boundary conditions to the two-dimensional reduced-dimensional heat transfer control equations. T 1 / x = 0, Heat transfer boundary condition on the hot side fluid T 2 / x = 0; The two-fluid flow heat transfer dimension reduction model uses the upper and lower sidewalls perpendicular to the flow directions of the cold and hot fluids, and sets them as symmetric boundary conditions. u 1• n 1 = 0, - n 1•( k 1( γ ) ▽T 1) = 0 (cold side fluid). u 2• n 2 = 0, - n 2•( k 2( γ ) ▽T 2) = 0 (hot-side fluid); In the two-fluid flow heat transfer dimension reduction model, except for the inlet and outlet sections, and the upper and lower sidewalls perpendicular to the flow directions of the cold and hot fluids, all other fluid-solid contact surfaces are subject to no-slip and adiabatic boundary conditions. u 1 = 0, - n 1•( k 1( γ ) ▽T 1) = 0 (cold side fluid). u 2 = 0, - n 2•( k 2( γ ) ▽T 2) = 0 (hot side fluid).

6. The method for constructing a two-fluid topology optimization for a printed circuit board heat exchanger according to claim 5, characterized in that, The convergence criterion described in step three is that the design variable residual is less than 0.01 or the number of iterations exceeds 400.

7. A system based on the two-fluid topology optimization construction method for a printed circuit board heat exchanger according to any one of claims 1 to 6, characterized in that, include: 3D Single-Channel Model Construction Module: Based on step one, periodic boundary conditions and symmetrical boundary conditions are applied in the height direction and vertical flow direction of the printed circuit board heat exchanger, respectively. The full-scale simulation of the printed circuit board heat exchanger is replaced by the simulation of typical 3D flow channel units to form a 3D single-channel model. Two-fluid flow heat transfer dimensionality reduction model construction module: Based on step two, the topology optimization material characterization method of coupled variable density method and the flow heat transfer control equation, the three-dimensional flow heat transfer problem is reduced to a two-dimensional design domain to construct a two-fluid flow heat transfer dimensionality reduction model. Two-fluid topology optimization model construction module: Based on step three, a two-dimensional two-fluid topology optimization model for the flow heat transfer process in the channel is constructed. Based on the variable density method, the heat transfer is maximized under a given pressure constraint. The topology optimization is carried out with the goal of enhancing heat transfer and reducing flow resistance, and the fin distribution in the design domain is obtained to construct a new topology channel structure.

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