Double-fluid topological optimization construction method and system for printed circuit board heat exchanger

Abstract

The invention discloses a double-fluid topological optimization construction method and system for a printed circuit board heat exchanger, and the method comprises the steps: building a periodic boundary condition and a symmetric boundary condition of the printed circuit board heat exchanger based on the periodicity and symmetry of the height direction and the vertical flowing direction of the printed circuit board heat exchanger and the known full-scale model of the printed circuit board heat exchanger; selecting a typical flow channel unit of the three-dimensional printed circuit board type heat exchanger, and constructing a three-dimensional single flow channel model; then, according to the three-dimensional single-flow-channel model, a topological optimization material characterization method of a coupling variable density method and a three-dimensional flow heat transfer control equation, dimensionality reduction is conducted on the three-dimensional flow heat transfer problem to a two-dimensional design domain, and a two-fluid flow heat transfer dimensionality reduction model is formed; and finally, according to the two-fluid flow heat transfer dimension reduction model, coupling a variable density method topological optimization objective function and a filtering projection post-processing method, obtaining distribution of solid fins and fluid flow channels in the cold side fluid flow channel and the hot side fluid flow channel, namely a two-fluid topological optimization model. According to the method, topological optimization is carried out with heat exchange enhancement and flow resistance reduction as targets on the basis of the method, distribution of fluid fins in a design domain is obtained, a novel topological channel structure is constructed, and the performance of the printed circuit board type heat exchanger is improved; compared with a traditional structure, the total heat exchange amount can be increased by 13.1% under the condition that the pump work of the heat exchanger is reduced by 38%.

Description

Technical Field

[0001] The present invention belongs to the technical field of heat exchangers, and in particular relates to a dual-fluid topology optimization construction method and system for a printed circuit board type heat exchanger. Background Art

[0002] Printed circuit board heat exchanger is a new type of efficient and compact heat exchanger with many advantages such as high heat transfer efficiency, wide temperature and pressure resistance, and good corrosion resistance. It is widely used in core equipment such as nuclear reactors, ship engines, and hydrogen coolers. The flow channel structure of the printed circuit board heat exchanger has a close impact on its flow and heat transfer performance. Its flow channel structure directly determines key indicators such as the inlet and outlet pressure drop of the fluid and the heat transfer capacity, which is directly related to the performance of the heat exchanger and the energy consumption of auxiliary equipment.

[0003] It is very important to optimize the design of the flow channel structure of the printed circuit board heat exchanger. Since the printed circuit board heat exchanger was proposed in 1985, researchers have developed many flow channel structures to improve its 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 zigzag flow channel proposed by Baik et al. [Baik S, Kim SG, Lee J, et al. Study on CO2-waterprinted 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-angle 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 a wing-shaped channel printed circuit board heat exchanger, which has the same heat transfer capacity as the zigzag channel, but the pressure drop 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 flow channels through CFD and improved the heat transfer performance by 36.37%. The two-way corrugated flow channel and front / rear corrugated flow channel proposed by 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.] improved the PCHE performance by 43% and 50%, respectively.

[0004] Structural optimization methods can be divided into three categories: size optimization, shape optimization, and topology optimization [Du J. Structural Optimization and its Application in Vibration and Acoustic Design [M]. Tsinghua University Press, 2015.] These three types of optimization methods have increasing degrees of freedom in optimization. Existing studies have optimized the size and shape of the flow channel structure of printed circuit board heat exchangers, and proposed typical flow channels including straight channels, corrugated channels, sinusoidal channels, louver channels, and airfoil channels. However, these two types of optimization methods require that the connection method of the structure, that is, the topological characteristics, remain unchanged during the optimization process. At the same time, based on theory and designer experience, it is impossible to fundamentally change the flow channel structure of the heat exchanger from the topological configuration, thereby achieving a revolutionary design of the flow channel structure. Topological optimization is not subject to this restriction and can change the topological characteristics of the structure, with the highest degree of design freedom. Topological optimization was first used 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 the support structure to meet the given load, and later extended to the field of flow 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].Applied Energy, 2023, 330:120335.] optimized a multi-inlet microchannel heat exchanger. Compared with the traditional pin-fin structure, the topological optimization structure can achieve a 53.28% increase in Nusselt number and a 40.89% reduction in pressure drop. However, there are few literatures that conduct topological optimization on the dual-fluid flow heat transfer process in printed circuit board heat exchangers, which cannot fundamentally improve the performance of printed circuit board heat exchangers. Summary of the invention

[0005] In order to overcome the defects of the above-mentioned prior art, the purpose of the present invention is to provide a dual-fluid topology optimization construction method and system for a printed circuit board heat exchanger. First, the three-dimensional cold side and hot side flow channels of the printed circuit board heat exchanger are extracted and formed into a three-dimensional typical flow channel unit to obtain a three-dimensional single flow channel model; then, considering the dimensionality reduction model, the three-dimensional single flow channel model is reduced to form a dual-fluid flow heat transfer dimensionality reduction model. Using the obtained dimensionality reduction model, the typical flow heat transfer process occurring in the flow channel is extracted, and a dual-fluid topology optimization model for the flow heat transfer process in the flow channel is constructed; based on the variable density method, the heat transfer of the cold-hot side flow channel is maximized as the optimization goal, and the topology optimization is performed under the given inlet Reynolds number and inlet and outlet pressure drop constraints to obtain the distribution of solid fins and fluid flow channels in the flow channel, and construct a topological flow channel structure. The results show that compared with the existing structural airfoil structure, the constructed topology optimization structure has a complex and counterintuitive fin structure, which has new structural characteristics; compared with the existing airfoil structure, the topology optimization structure can achieve a 13.1% increase in total heat transfer under the condition of a 38% reduction in pump work, and has the characteristics of strong performance.

[0006] In order to achieve the above object, the technical solution adopted by the present invention is as follows:

[0007] A dual-fluid topology optimization construction method for a printed circuit board heat exchanger is disclosed. Based on the periodicity and symmetry of the height direction and the vertical flow direction of the printed circuit board heat exchanger, and the known full-scale model of the printed circuit board heat exchanger, periodic boundary conditions and symmetric boundary conditions of the printed circuit board heat exchanger are established, and typical flow channel units of the three-dimensional printed circuit board heat exchanger are selected to construct a three-dimensional single-channel model; then, based on the three-dimensional single-channel model, a topology optimization material characterization method of a coupled variable density method and a three-dimensional flow heat transfer control equation are used to reduce the three-dimensional flow heat transfer problem to a two-dimensional design domain to form a dual-fluid flow heat transfer reduced dimension model; finally, based on the dual-fluid flow heat transfer reduced dimension model, a coupled variable density method topology optimization objective function and a filtered projection post-processing method are used 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, namely, a dual-fluid topology optimization model.

[0008] The dual-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 fluid channel and the hot-side fluid channel; 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 conductivities of the fluid region and the solid region in the cold fluid layer are different, and the permeability parameters of the fluid region and the solid region in the cold fluid layer are different; the thermal conductivities of the fluid region and the solid region in the hot fluid layer are different, and the permeability parameters of the fluid region and the solid region in the hot fluid layer are different.

[0009] A dual-fluid topology optimization construction method for a printed circuit board type heat exchanger specifically comprises the following steps:

[0010] Step 1, constructing a three-dimensional single-channel model of a printed circuit board type heat exchanger;

[0011] Step 2: Based on the three-dimensional single-channel model obtained in step 1, the topological optimization material characterization method of the coupled 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 reduced dimension model is constructed;

[0012] Step three, based on the two-fluid flow heat transfer dimensionality reduction model obtained in step two, the topology optimization objective function of the coupled variable density method and the post-processing method of hyperbolic tangent projection, a two-fluid topology optimization model is constructed.

[0013] The specific method of constructing the three-dimensional single flow channel model in step 1 is:

[0014] Periodic boundary conditions along the height direction of the printed circuit board heat exchanger and symmetric boundary conditions perpendicular to the flow directions of the cold side fluid and the hot side fluid of the printed circuit board heat exchanger are adopted 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 three-dimensional typical flow channel unit simulation to form a three-dimensional single flow channel model, and its three-dimensional flow heat transfer control equation is determined.

[0015] The periodic boundary conditions are:

[0016]

[0017] Among them, u * =u * (x,y,z),T * =T * (x, y, z) are the three-dimensional velocity field and temperature field of the printed circuit board heat exchanger, respectively; the asterisk on the upper right 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:

[0019] u * n=0 (3)

[0020]

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

[0022] The three-dimensional typical flow channel unit simulation replaces the full-scale simulation of the printed circuit board type heat exchanger to form a three-dimensional single flow channel model, and its three-dimensional flow heat transfer control equation is determined as follows:

[0023]

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

[0025] The specific method of step 2 is:

[0026] Topology optimization of the flow channel of the printed circuit board heat exchanger: the middle part of the flow channel is taken for topology optimization, and the inlet and outlet parts are set as fluid / solid inlet and outlet extension sections; the area where the topology optimization is performed in the middle part of the flow channel is the design domain, and the design variable γ is used to characterize the material distribution properties in the design domain. When the design variable γ is equal to 0, it corresponds to the solid in the design domain, and when it is equal to 1, it corresponds to the fluid in the design domain:

[0027]

[0028] Among them, Ω fl and Ω s 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; according to the actual flow and heat transfer process in the printed circuit board heat exchanger, the three-dimensional flow and heat transfer control equations of the cold fluid and hot fluid in the design domain are obtained respectively; according to the three-dimensional flow and heat transfer control equations, the two-dimensional reduced dimension flow control equations of the cold fluid layer and the hot fluid layer in the printed circuit board heat exchanger are obtained as follows:

[0029]

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

[0031]

[0032] F2=α2(γ)u2 (15)

[0033] According to the three-dimensional flow heat transfer control equation, 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, T2 are the two-dimensional temperatures of the cold fluid layer, solid layer, and hot fluid layer respectively; H1, H m , H2 are 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 convection 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 convection diffusion coefficient between the hot fluid layer and the solid layer; k s 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 thermal resistance equivalent principle, 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 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; the convective heat transfer coefficients of the fluid and solid in the cold fluid layer are:

[0038]

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

[0040]

[0041] That is, the dimension reduction model of two-fluid flow heat transfer is obtained.

[0042] The two-fluid flow heat transfer dimensionality reduction model obtained in step 2 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 hot side fluid inlet temperature is set to T in2 ; At the outlet of the printed circuit board heat exchanger, the cold side fluid pressure boundary condition p is applied to the two-dimensional reduced dimension flow control equation 1out = 0, hot side fluid pressure boundary condition p 2out = 0; fully developed cold side fluid heat transfer boundary conditions are applied to the two-dimensional reduced dimension heat transfer governing equation Hot side fluid heat transfer boundary conditions The upper and lower side walls of the two-fluid flow heat transfer reduction model are perpendicular to the flow direction of the cold side fluid and the hot side fluid, and are set as symmetric boundary conditions (cold side fluid), (hot side fluid); In the two-fluid flow heat transfer reduction model, except for the inlet section, outlet section, upper side wall and lower side wall of the two-fluid flow heat transfer reduction model perpendicular to the flow direction of the cold side fluid and the hot side fluid, the rest of the fluid and solid contact surfaces are subject to no-slip and adiabatic boundary conditions u1=0, (cold side fluid), (hot side fluid).

[0043] The specific method of constructing the dual-fluid topology optimization model in step 3 is:

[0044] Step 3.1, using the objective function of maximizing interlayer heat transfer and combining it with pressure constraints, obtain the topological 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 inlet and outlet pressure drop of the cold side fluid, Δp 1max is the pressure drop constraint of the cold side fluid inlet and outlet; Δp2 is the pressure drop of the hot side fluid inlet and outlet, Δp 2max is the pressure drop constraint of the hot side fluid inlet and outlet;

[0047] Step 3.2, using the post-processing method of Helmholtz filtering and hyperbolic tangent projection to construct a two-fluid topology optimization model;

[0048] Step 3.2.1, use the Helmholtz equation to filter the optimization design variable γ after each iteration to avoid the checkerboard phenomenon of the optimized structure after filtering and alleviate the dependence of the optimized structure on the grid:

[0049]

[0050] Among them, γ f1 and γ f2 is the new design variable after filtering; r l and r2 is the filter radius;

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

[0052]

[0053] Among them, γ p1 and γ p2 is the design variable after projection; β1 and β2 are the projection slopes; γ c1 and γ c2 is the projection point; repeat steps 3.1 to 3.2 until the convergence criterion is met, and the dual-fluid topology optimization model of the printed circuit board heat exchanger is obtained.

[0054] The convergence criterion in step 3 is that the design variable residual is less than 0.01 or the iteration number exceeds 400 steps.

[0055] A dual-fluid topology optimization construction system for a printed circuit board type heat exchanger, comprising:

[0056] Three-dimensional single-channel model building module: According to step 1, periodic boundary conditions and symmetric boundary conditions are applied in the height direction and vertical flow direction of the printed circuit board type heat exchanger respectively, and the full-scale simulation of the printed circuit board type heat exchanger is replaced by the three-dimensional typical flow channel unit simulation to form a three-dimensional single-channel model;

[0057] Two-fluid flow heat transfer dimensionality reduction model construction module: According to step 2, the topological optimization material characterization method of the coupled variable density method and the 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;

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

[0059] Compared with the prior art, the present invention has the following beneficial effects:

[0060] 1. The present invention constructs a two-fluid flow heat transfer dimensionality reduction model based on the periodicity and symmetry of the three-dimensional geometric characteristics of the heat exchanger through steps 1 and 2. The constructed dimensionality reduction model avoids solving three-dimensional complex problems and reduces computing resources;

[0061] 2. The present invention constructs a topological optimization method for a printed circuit board heat exchanger with two fluids (cold side fluid and hot side fluid) step by step through steps 1, 2 and 3. The method maximizes the heat transfer under a given pressure constraint, performs topological optimization with the goal of enhancing heat transfer and reducing flow resistance, obtains the fin distribution in the design domain, and designs a new topological channel structure. The new topological optimized channel structure arranges an innovative fin design in the design domain, with fins of different sizes and complex shapes, presenting a counter-intuitive design;

[0062] 3. The topological optimization structure designed in step 3 of the present invention has better flow and heat transfer performance. Three-dimensional flow and heat transfer simulation proves that, compared with the airfoil structure, the present invention can achieve a 13.1% increase in total heat transfer capacity while reducing the heat exchanger pump work by 38%.

[0063] In summary, the present invention adopts a topology optimization method based on the variable density method, sequentially constructs a three-dimensional single flow channel model and a two-fluid flow heat transfer dimensionality reduction model, develops a topology optimization method for the flow channel structure of a printed circuit board heat exchanger, realizes the alternative solution of the dimensionality reduction model to three-dimensional complex problems, and completes the innovative design of the flow channel structure of the heat exchanger. The present invention has the advantages of new structure and strong performance. BRIEF DESCRIPTION OF THE DRAWINGS

[0064] Figure 1 Schematic diagram of the printed circuit board heat exchanger of the present invention; wherein, Figure 1 (a) is the size of the topology optimization design domain, Figure 1 (b) is the airfoil structural dimension.

[0065] Figure 2 It is the topology optimization flow chart of the present invention.

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

[0067] Figure 4 The three-dimensional structure of the printed circuit board type heat exchanger of the present invention; wherein, Figure 4 (a) is the topology optimized structure, Figure 4 (b) is the airfoil structure.

[0068] Figure 5 It is a coordinate diagram of the three-dimensional simulation of pumping power and heat exchange capacity of the present invention. DETAILED DESCRIPTION

[0069] The specific embodiments disclosed in the present invention are described in detail below in conjunction with the accompanying drawings. It should be understood that the specific embodiments described herein are only used to illustrate and explain the present disclosure, and are not used to limit the present disclosure.

[0070] A dual-fluid topology optimization construction method for a printed circuit board heat exchanger is disclosed. Based on the periodicity and symmetry of the height direction and the vertical flow direction of the printed circuit board heat exchanger, and the known full-scale model of the printed circuit board heat exchanger, periodic boundary conditions and symmetric boundary conditions of the printed circuit board heat exchanger are established, and typical flow channel units of the three-dimensional printed circuit board heat exchanger are selected to construct a three-dimensional single-channel model; then, based on the three-dimensional single-channel model, a topology optimization material characterization method of a coupled variable density method and a three-dimensional flow heat transfer control equation are used to reduce the three-dimensional flow heat transfer problem to a two-dimensional design domain to form a dual-fluid flow heat transfer reduced dimension model; finally, based on the dual-fluid flow heat transfer reduced dimension model, a coupled variable density method topology optimization objective function and a filtered projection post-processing method are used 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, namely, a dual-fluid topology optimization model.

[0071] The dual-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 fluid channel and the hot-side fluid channel; 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 conductivities of the fluid region and the solid region in the cold fluid layer are different, and the permeability parameters of the fluid region and the solid region in the cold fluid layer are different; the thermal conductivities of the fluid region and the solid region in the hot fluid layer are different, and the permeability parameters of the fluid region and the solid region in the hot fluid layer are different.

[0072] A dual-fluid topology optimization construction method for a printed circuit board type heat exchanger specifically comprises the following steps:

[0073] Step 1, constructing a three-dimensional single-channel model of a printed circuit board type heat exchanger;

[0074] Periodic boundary conditions along the height direction of the printed circuit board heat exchanger and symmetric boundary conditions perpendicular to the flow directions of the cold side fluid and the hot side fluid of the printed circuit board heat exchanger are adopted 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 three-dimensional typical flow channel unit simulation to form a three-dimensional single flow channel model, and its three-dimensional flow heat transfer control equation is determined.

[0075] The periodic boundary conditions are:

[0076]

[0077] Among them, u * =u * (x,y,z),T * =T *(x, y, z) are the three-dimensional velocity field and temperature field of the printed circuit board heat exchanger, respectively; the asterisk on the upper right 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:

[0079] u * n=0 (3)

[0080]

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

[0082] The three-dimensional typical flow channel unit simulation replaces the full-scale simulation of the printed circuit board type heat exchanger to form a three-dimensional single flow channel model, and its three-dimensional flow heat transfer control equation is determined as follows:

[0083]

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

[0085] Step 2: Based on the three-dimensional single-channel model obtained in step 1, the topological optimization material characterization method of the coupled 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 reduced dimension model is constructed;

[0086] Topology optimization of the flow channel of the printed circuit board heat exchanger: the middle part of the flow channel is taken for topology optimization, and the inlet and outlet parts are set as fluid / solid inlet and outlet extension sections; the area where the topology optimization is performed in the middle part of the flow channel is the design domain, and the design variable γ is used to characterize the material distribution properties in the design domain. When the design variable γ is equal to 0, it corresponds to the solid in the design domain, and when it is equal to 1, it corresponds to the fluid in the design domain:

[0087]

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

[0089]

[0090] Among them, equations (10) and (12) are mass conservation equations; equations (11) and (13) are momentum conservation equations; u1 and p1 represent the two-dimensional velocity field and pressure field in the cold fluid layer; u2 and p2 represent the two-dimensional velocity field and pressure field in the hot fluid layer; F1 and F2 are Brinkman volume forces, which are 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] According to the three-dimensional flow heat transfer control equation, 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, T2 are the two-dimensional temperatures of the cold fluid layer, solid layer, and hot fluid layer respectively; H1, H m , H2 are 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 convection 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 convection diffusion coefficient between the hot fluid layer and the solid layer; k s 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 thermal resistance equivalent principle, 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 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; the convective heat transfer coefficients of the fluid and solid in the cold fluid layer are:

[0098]

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

[0100]

[0101] That is, the dimension reduction model of two-fluid flow heat transfer is obtained.

[0102] The two-fluid flow heat transfer dimensionality reduction model obtained in step 2 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 hot side fluid inlet temperature is set to T in2 ; At the outlet of the printed circuit board heat exchanger, the cold side fluid pressure boundary condition p is applied to the two-dimensional reduced dimension flow control equation 1out = 0, hot side fluid pressure boundary condition p 2out = 0; fully developed cold side fluid heat transfer boundary conditions are applied to the two-dimensional reduced dimension heat transfer governing equation Hot side fluid heat transfer boundary conditions The upper and lower side walls of the two-fluid flow heat transfer reduction model are perpendicular to the flow direction of the cold side fluid and the hot side fluid, and are set to symmetric boundary conditions u1·n1=0, (cold side fluid), u2·n2=0, (hot side fluid); In the two-fluid flow heat transfer reduction model, except for the inlet section, outlet section, upper side wall and lower side wall of the two-fluid flow heat transfer reduction model perpendicular to the flow direction of the cold side fluid and the hot side fluid, the rest of the fluid and solid contact surfaces are subject to no-slip and adiabatic boundary conditions u1=0, (cold side fluid), (hot side fluid).

[0103] Step three, based on the two-fluid flow heat transfer dimensionality reduction model obtained in step two, the topology optimization objective function of the coupled variable density method and the post-processing method of hyperbolic tangent projection, a two-fluid topology optimization model is constructed.

[0104] Step 3.1, using the objective function of maximizing interlayer heat transfer and combining it with pressure constraints, obtain the topological 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 inlet and outlet pressure drop of the cold side fluid, Δp 1maxis the pressure drop constraint of the cold side fluid inlet and outlet; Δp2 is the pressure drop of the hot side fluid inlet and outlet, Δp 2max is the pressure drop constraint of the hot side fluid inlet and outlet;

[0107] Step 3.2, using the post-processing method of Helmholtz filtering and hyperbolic tangent projection to construct a two-fluid topology optimization model;

[0108] Step 3.2.1, use the Helmholtz equation to filter the optimization design variable γ after each iteration to avoid the checkerboard phenomenon of the optimized structure after filtering and alleviate the dependence of the optimized structure on the grid:

[0109]

[0110] Among them, γ f1 and γ f2 is the new design variable after filtering; r l and r2 is the filter radius;

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

[0112]

[0113] Among them, γ p1 and γ p2 is the design variable after projection; β1 and β2 are the projection slopes; γ c1 and γ c2 is the projection point; repeat steps 3.1 to 3.2 until the convergence criterion is met, and the dual-fluid topology optimization model of the printed circuit board heat exchanger is obtained.

[0114] The convergence criterion in step 3 is that the design variable residual is less than 0.01 or the iteration number exceeds 400 steps.

[0115] A dual-fluid topology optimization construction system for a printed circuit board type heat exchanger, comprising:

[0116] Three-dimensional single-channel model building module: According to step 1, periodic boundary conditions and symmetric boundary conditions are applied in the height direction and vertical flow direction of the printed circuit board type heat exchanger respectively, and the full-scale simulation of the printed circuit board type heat exchanger is replaced by the three-dimensional typical flow channel unit simulation to form a three-dimensional single-channel model;

[0117] Two-fluid flow heat transfer dimensionality reduction model construction module: According to step 2, the topological optimization material characterization method of the coupled variable density method and the 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;

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

[0119] The topology optimization process of the present invention is as follows Figure 2 As shown. First, in step 1, a three-dimensional single-channel model is obtained according to the structural characteristics of the printed circuit board heat exchanger. Then, in step 2, the finite element method is used to solve the control equation according to the current structure to obtain the state variables. Then, in step 3, the objective function is calculated, and the sensitivity of the objective function is obtained in step 3. Finally, in step 3, the moving asymptote method GCMMA based on the global convergence of the gradient-based optimization solver is used to update the design variables. After filtering and projecting the design variables in step 3, the above steps are repeated until the convergence criterion is met (the residual of the design variable is less than 10 -3 or iterates more than 400 steps), we get Figure 3 The topology optimization results under different inlet Reynolds numbers are shown. The topology optimization Reynolds numbers are set to 20, 40, 60, 80, 100, 150, 200, 250, and 300. Figure 3 It is the topological optimization structure obtained under different inlet Reynolds numbers for a single-channel structure. The optimized structure arranges fins in the design domain. The fins are of different sizes and complex shapes, presenting a counterintuitive design. As the inlet Reynolds number increases, the complexity of the cold and hot side structures increases. On the cold side, the heat in the fins will be transferred to the fluid around the fins through convective heat transfer. At low Reynolds numbers, the convective heat transfer around each fin is relatively weak, indicating that the Biot number is small (which is defined as the ratio of the thermal resistance of heat conduction inside the solid to the thermal resistance of convective heat transfer around the solid). Therefore, in order to effectively cool the fins, the size of the fins should not be too large. As the Reynolds number increases, the convective heat transfer becomes stronger, resulting in a higher Biot number. Larger solid fins can effectively cool the channel, increase the total heat transfer, and optimize the performance of the heat exchanger.

[0120] In order to verify the usefulness of the topology optimization structure, the present invention uses a three-dimensional flow heat transfer model to perform a three-dimensional simulation of the obtained topology optimization structure. Figure 4Taking the typical heat exchanger topology optimization design shown in Figure 1 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 (b) The above structure was stretched in the thickness direction and its performance was verified in a three-dimensional flow and heat transfer model. The inlet Reynolds numbers were set to 20, 40, 60, 80, 100, 150, 200, 250, and 300 in the three-dimensional verification. Figure 5 The total pumping power and total heat transfer of the three structures were counted. For printed circuit board heat exchangers, 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 can be seen that the topology optimization structure (diamond) designed by the present invention performs better than the airfoil structure (circle) and the straight channel structure (square). Quantitatively, compared with the existing airfoil structure, the single-channel topology optimization structure can achieve a 13.1% increase in total heat transfer under the condition of a 38% reduction in pump work, which proves the advantage of the topology optimization structure of the present invention. The present invention develops a dual-fluid topology optimization dimensionality reduction model for printed circuit board heat exchangers, optimizes the design of the dual-fluid flow channel structure in the printed circuit board heat exchanger, and improves the flow heat transfer performance of the heat exchanger. Compared with the existing structure, the topology optimization structure has a complex and counterintuitive fin structure, which achieves the purpose of enhancing heat transfer and reducing flow resistance. Compared with the existing airfoil structure, the single-channel topology optimization structure can achieve a 13.1% increase in total heat transfer under the condition of a 38% reduction in pump work.

[0121] The preferred embodiments of the present invention are described in detail above in conjunction with the accompanying drawings. However, the present invention is not limited to the specific details in the above embodiments. Within the technical concept of the present invention, a variety of simple modifications can be made to the technical solution of the present invention, and these simple modifications all belong to the protection scope of the present invention.

Claims

1. A dual-fluid topology optimization construction method for a printed circuit board type heat exchanger, characterized in that: Based on the periodicity and symmetry of the height direction and the vertical flow direction of the printed circuit board heat exchanger, and the known full-scale model of the printed circuit board heat exchanger, the periodic boundary conditions and symmetric boundary conditions of the printed circuit board heat exchanger are established, and the 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, based on the three-dimensional single flow channel model, the topological optimization material characterization method of the coupled 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 to form a two-fluid flow heat transfer reduced dimension model; finally, based on the two-fluid flow heat transfer reduced dimension model, the variable density method topology optimization objective function and the filtered 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, namely, the two-fluid topology optimization model.

2. The dual-fluid topology optimization construction method of a printed circuit board type heat exchanger according to claim 1, characterized in that: The dual-fluid flow heat transfer dimensionality reduction model comprises 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 fluid channel and the hot-side fluid channel; comprises 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 coefficients of the fluid region and the solid region in the cold fluid layer are different, and the permeability parameters of the fluid region and the solid region in the cold fluid layer are different; The thermal conductivity of the fluid region and the solid region in the thermal fluid layer are different, and the permeability parameters of the fluid region and the solid region in the thermal fluid layer are different.

3. The dual-fluid topology optimization construction method of a printed circuit board type heat exchanger according to claim 1, characterized in that: The specific steps include: Step 1, constructing a three-dimensional single-channel model of a printed circuit board type heat exchanger; Step 2: Based on the three-dimensional single-channel model obtained in step 1, the topological optimization material characterization method of the coupled 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 reduced dimension model is constructed; Step three, based on the two-fluid flow heat transfer dimensionality reduction model obtained in step two, the topology optimization objective function of the coupled variable density method and the post-processing method of hyperbolic tangent projection, a two-fluid topology optimization model is constructed.

4. The dual-fluid topology optimization construction method of a printed circuit board type heat exchanger according to claim 3, characterized in that: The specific method of constructing the three-dimensional single flow channel model in step 1 is: Periodic boundary conditions along the height direction of the printed circuit board heat exchanger and symmetric boundary conditions perpendicular to the flow directions of the cold side fluid and the hot side fluid of the printed circuit board heat exchanger are adopted 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 three-dimensional typical flow channel unit simulation to form a three-dimensional single flow channel model, and its three-dimensional flow heat transfer control equation is determined.

5. The dual-fluid topology optimization construction method of a printed circuit board type heat exchanger according to claim 4, characterized in that: The periodic boundary conditions are: Among them, u * =u * (x,y,z),T * =T * (x, y, z) are the three-dimensional velocity field and temperature field of the printed circuit board heat exchanger, respectively; the asterisk on the upper right 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: u * ·n=0 (3) -n·(k fl ▽T * )=0 (4) Where n is the wall normal vector, k fl is the thermal conductivity of the fluid; The three-dimensional typical flow channel unit simulation replaces the full-scale simulation of the printed circuit board type heat exchanger to form a three-dimensional single flow channel model, and its three-dimensional flow heat transfer control equation is determined as follows: ▽·u * ＝0 (5) r fl (u * ·▽)u * =▽·[-p * +m fl (▽u * +(▽u * ) T )] (6) ρ fl c pfl (u * ·▽)T * =k fl ▽ 2 T * (7) k s ▽ 2 T * =0 (8) Among them, p * =p * (x, y, z) is the three-dimensional pressure field of the printed circuit board heat exchanger; ρ fl , μ fl and c pfl are the fluid density, viscosity and specific heat at constant pressure respectively; k s is the thermal conductivity of the solid.

6. The dual-fluid topology optimization construction method of a printed circuit board type heat exchanger according to claim 3, characterized in that: The specific method of step 2 is: Topology optimization of the flow channel of the printed circuit board heat exchanger: the middle part of the flow channel is taken for topology optimization, and the inlet and outlet parts are set as fluid / solid inlet and outlet extension sections; the area where the topology optimization is performed in the middle part of the flow channel is the design domain, and the design variable γ is used to characterize the material distribution properties in the design domain. When the design variable γ is equal to 0, it corresponds to the solid in the design domain, and when it is equal to 1, it corresponds to the fluid in the design domain: Among them, Ω fl and Ω s 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; according to the actual flow and heat transfer process in the printed circuit board heat exchanger, the three-dimensional flow and heat transfer control equations of the cold fluid and hot fluid in the design domain are obtained respectively; according to the three-dimensional flow and heat transfer control equations, the two-dimensional reduced dimension flow control equations of the cold fluid layer and the hot fluid layer in the printed circuit board heat exchanger are obtained as follows: ▽·u1＝0 (10) ▽·u2＝0 (12) Among them, equations (10) and (12) are mass conservation equations; equations (11) and (13) are momentum conservation equations; u1 and p1 represent the two-dimensional velocity field and pressure field in the cold fluid layer; u2 and p2 represent the two-dimensional velocity field and pressure field in the hot fluid layer; F1 and F2 are Brinkman volume forces, which are determined by the reverse permeability α1 and α2 of the porous medium: F1=α1(γ)u1 (14) F2=α2(γ)u2 (15) According to the three-dimensional flow heat transfer control equation, 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: Among them, T1, T m T1, T2 are the two-dimensional temperatures of the cold fluid layer, solid layer, and hot fluid layer respectively; H1, H m , H2 are 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 convection 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 convection diffusion coefficient between the hot fluid layer and the solid layer; k s 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 thermal resistance equivalent principle, the convective heat transfer coefficient h1(γ) between the cold fluid layer and the solid layer is: Among them, R c , R m , and R 1m 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; the convective heat transfer coefficients of the fluid and solid in the cold fluid layer are: Among them, h fl1 and h s1 are the heat transfer coefficients of the fluid and solid in the cold fluid layer, respectively; similarly, the heat transfer coefficient h2(γ) coupled between the hot fluid layer and the solid layer is: That is, the dimension reduction model of two-fluid flow heat transfer is obtained.

7. The dual-fluid topology optimization construction method of a printed circuit board type heat exchanger according to claim 6, characterized in that: The two-fluid flow heat transfer dimensionality reduction model obtained in step 2 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 hot side fluid inlet temperature is set to T in2 ; At the outlet of the printed circuit board heat exchanger, the cold side fluid pressure boundary condition p is applied to the two-dimensional reduced dimension flow control equation 1out = 0, hot side fluid pressure boundary condition p 2out = 0; fully developed cold side fluid heat transfer boundary conditions are applied to the two-dimensional reduced dimension heat transfer governing equation Hot side fluid heat transfer boundary conditions The upper and lower side walls of the two-fluid flow heat transfer reduction model perpendicular to the flow direction of the cold side fluid and the hot side fluid are set as symmetric boundary conditions u1·n1=0, -n1·(k1(γ)▽T1)=0 (cold side fluid), u2·n2=0, -n2·(k2(γ)▽T2)=0 (hot side fluid); in the two-fluid flow heat transfer reduction model, except for the inlet section, outlet section, and the upper and lower side walls of the two-fluid flow heat transfer reduction model perpendicular to the flow direction of the cold side fluid and the hot side fluid, the rest of the fluid and solid contact surfaces are subject to no-slip and adiabatic boundary conditions u1=0, -n1·(k1(γ)▽T1)=0 (cold side fluid), u2=0, -n2·(k2(γ)▽T2)=0 (hot side fluid).

8. The dual-fluid topology optimization construction method of a printed circuit board type heat exchanger according to claim 3, characterized in that: The specific method of constructing the dual-fluid topology optimization model in step 3 is: Step 3.1, using the objective function of maximizing interlayer heat transfer and combining it with pressure constraints, obtain the topological optimization structure that enhances heat transfer and reduces flow resistance: Where Q is the heat exchange between the cold side fluid and the hot side fluid; Δp1 is the inlet and outlet pressure drop of the cold side fluid, Δp 1max is the pressure drop constraint of the cold side fluid inlet and outlet; Δp2 is the pressure drop of the hot side fluid inlet and outlet, Δp 2max is the pressure drop constraint of the hot side fluid inlet and outlet; Step 3.2, using the post-processing method of Helmholtz filtering and hyperbolic tangent projection to construct a two-fluid topology optimization model; Step 3.2.1, use the Helmholtz equation to filter the optimization design variable γ after each iteration to avoid the checkerboard phenomenon of the optimized structure after filtering and alleviate the dependence of the optimized structure on the grid: -r1 2 ▽ 2 c f1 +g f1 =γ1 (26) -r2 2 ▽ 2 γ f2 +γ f2 =γ2 (27) where γ f1 and γ f2 is the new design variable after filtering; r l and r2 is the filter radius; Step 3.2.2, post-process the filtered optimized structure using hyperbolic tangent projection to sharpen the fluid-solid interface: Among them, γ p1 and γ p2 is the design variable after projection; β1 and β2 are the projection slopes; γ c1 and γ c2 is the projection point; repeat steps 3.1 to 3.2 until the convergence criterion is met, and the dual-fluid topology optimization model of the printed circuit board heat exchanger is obtained.

9. The dual-fluid topology optimization construction method of a printed circuit board type heat exchanger according to claim 8, characterized in that: The convergence criterion in step 3 is that the design variable residual is less than 0.01 or the iteration number exceeds 400 steps.

10. A system based on the dual-fluid topology optimization construction method of a printed circuit board type heat exchanger according to any one of claims 1 to 9, characterized in that: include: Three-dimensional single-channel model building module: According to step 1, periodic boundary conditions and symmetric boundary conditions are applied in the height direction and vertical flow direction of the printed circuit board type heat exchanger respectively, and the full-scale simulation of the printed circuit board type heat exchanger is replaced by the three-dimensional typical flow channel unit simulation to form a three-dimensional single-channel model; Two-fluid flow heat transfer dimensionality reduction model construction module: According to step 2, the topological optimization material characterization method of the coupled variable density method and the 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; Two-fluid topology optimization model construction module: According to step three, a two-dimensional two-fluid topology optimization model for the flow and heat transfer process in the flow channel is constructed. Based on the variable density method, the heat transfer is maximized under a given pressure constraint. Topology optimization is performed with the goal of enhancing heat transfer and reducing flow resistance. The fin distribution in the design domain is obtained, and a new topological channel structure is constructed.

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