A multi-scale fast calculation method for heat exchange performance of printed circuit board heat exchanger

Abstract

The application discloses a kind of for printed circuit board heat exchanger heat transfer performance multi-scale fast calculation method, comprising: extracting printed circuit board heat exchanger unit structure, carries out fluid domain periodic heat transfer simulation and obtains surface heat transfer coefficient distribution;Carry out unit structure in analogy heat conduction problem calculation, obtain parameter distribution;Calculate heat exchanger macroscopic equivalent heat conduction coefficient and convective heat transfer parameter;Macroscopic equivalent heat conduction equation and cold / hot fluid one-dimensional flow heat transfer equation are constructed, and finite volume method is solved, obtains printed circuit board heat exchanger solid region temperature distribution and cold / hot fluid temperature distribution along the way.The application can be aimed at the printed circuit board heat exchanger heat transfer performance of periodic repeating unit structure and carry out fast calculation, avoid the problem that one-dimensional calculation solid heat conduction process is not clear and three-dimensional numerical simulation calculation amount is big, has application value in the design and optimization of guiding printed circuit board heat exchanger structure.

Description

Technical Field

[0001] This invention belongs to the field of heat exchanger design and verification technology, and specifically relates to a multi-scale rapid calculation method for the heat exchange performance of printed circuit board heat exchangers. Background Technology

[0002] Heat exchangers are core components for heat transfer and exchange, and are widely used in various fields of production and daily life, including HVAC, chemical engineering, energy and power, electrical components, and aerospace. Compact heat exchangers, represented by printed circuit board (PCB) heat exchangers, have attracted widespread attention in new power cycles such as supercritical carbon dioxide due to their advantages such as large heat transfer area, high heat transfer efficiency, small size, and resistance to high temperature and pressure. They also show significant application prospects for heat exchange within confined spaces such as automobiles and ships. Developing efficient and accurate performance design and verification methods for PCB heat exchangers is of great significance for improving the design level of energy equipment.

[0003] For the design and verification of heat exchangers, existing methods typically employ one-dimensional calculations based on heat transfer correlations to quickly assess the inlet and outlet temperatures and heat transfer of cold / hot fluids flowing through the heat exchanger, as exemplified by CN121953727A. This calculation process requires knowledge of the convective heat transfer coefficients of the cold / hot side fluids and the thermal resistance of the intermediate solid region. However, obtaining these convective heat transfer coefficients and thermal resistances in practical applications is difficult. Conducting experimental studies under different heat exchanger channel structures and multiple operating conditions to obtain these parameters requires significant manufacturing and experimental costs. Using numerical simulation methods to obtain these parameters also requires assumptions about the correlation forms between Nusselt number, Reynolds number, Prandtl number, and geometric parameters, and equivalent treatment of complex channel forms such as rectangular, semi-circular, and zigzag shapes, as well as the structures of their turbulence-causing elements, which limits the accuracy of one-dimensional calculations. On the other hand, if a three-dimensional high-precision numerical simulation is used to calculate the flow and heat transfer process inside the printed circuit board, at least a long section of heat exchange unit with the same length as the heat exchanger needs to be cut. The required computational grid often reaches millions of units, and the efficiency of fluid-structure interaction calculation is low. It requires a lot of computing resources and is difficult to calculate the entire printed circuit board heat exchanger, which often contains hundreds of fluid channels. Summary of the Invention

[0004] To overcome the shortcomings of the prior art, the present invention aims to provide a multi-scale rapid calculation method for the heat exchange performance of printed circuit board heat exchangers. This method obtains macroscopic equivalent heat conduction and convection heat transfer parameters through three-dimensional numerical simulation of the heat exchanger unit structure, and combines the coupled calculation of the equivalent heat conduction equation and the one-dimensional fluid flow equation to quickly obtain the average temperature distribution law of the printed circuit board heat exchanger and the cold / hot fluid, thereby realizing the performance evaluation of the heat exchanger.

[0005] To achieve the above objectives, the technical solution adopted by the present invention is as follows: A multi-scale rapid calculation method for the heat transfer performance of a printed circuit board heat exchanger includes the following steps: Step 1: Extract the unit structure of the printed circuit board heat exchanger. For its fluid region, periodic flow boundary conditions are adopted for the inlet and outlet, and isothermal or isothermal flow boundary conditions are adopted for the flow / solid interface. Perform flow heat transfer calculation of the unit structure and obtain the convective heat transfer coefficient distribution on the surface of the flow / solid interface. Step 2: For the solid region of the extracted unit structure, perform analogous heat conduction calculations to obtain the parameter field in the unit structure. N j , M 0 and M r , representing the effects of solid temperature gradient, solid average temperature and fluid average temperature on the temperature field within the unit structure, respectively; Step 3, based on the unit structure parameter field N j , M 0 and M r Calculate the macroscopic equivalent thermal conductivity of the heat exchanger K ij Heat transfer parameters corresponding to the average temperature of the solid H 0,i and the heat transfer parameters corresponding to the average fluid temperature H r,i ; Step 4: Using the controlled volume method, the macroscopic equivalent heat conduction equation and the one-dimensional flow heat transfer equation of the cold / hot fluid are solved in a coupled manner to obtain the temperature distribution of the solid region of the printed circuit board heat exchanger and the temperature distribution of the cold / hot fluid along the flow path.

[0006] In one embodiment, step 1, the convective heat transfer coefficient at the fluid / solid interface surface h The calculation method is as follows: in T f The average temperature of the fluid inlet and outlet sections of the unit structure is given. q and T w These represent the local heat flux density and interface temperature at the fluid / solid interface, respectively.

[0007] In one embodiment, step 2, parameter field N j , M 0 and M r The following thermal conductivity problems were obtained by solving them separately within the solid region of the unit structure: in, λ ij and λ ik All are thermal conductivity tensors of heat exchanger materials; y i 、y j and y k All coordinates are internal coordinates of the unit structure; h r For the first r Heat transfer coefficient at the boundary of each fluid channel; V c The volume of the solid region in the unit structure; n i For the unit outward normal vector component; This represents the surface of all fluid channels in the unit structure. Represents the unit structure r Each fluid channel surface dA For surface area infinitesimal elements; subscript i , j and k All represent spatial directions. A subscript repeated twice in the formula indicates summation over that subscript in three spatial directions; subscript r Indicates the fluid number.

[0008] In one embodiment, in step 3, the macroscopic equivalent thermal conductivity of the heat exchanger K ij Heat transfer parameters corresponding to the average temperature of the solid H 0,i Heat transfer parameters corresponding to the average temperature of the fluid H r,i The calculation method is as follows: in Represents a solid region of a unit structure. d y represents the volume element of the solid region.

[0009] In one embodiment, in step 4, the macroscopic equivalent heat conduction equation and the one-dimensional flow heat transfer equation of the cold / hot fluid for the printed circuit board heat exchanger are respectively: in, T 0 represents the temperature of the solid to be solved. The first one to be solved r The temperature of the fluid; For the first r The product of the specific heat capacity and mass flow rate of a fluid; x i and x j For the three-dimensional spatial coordinates of the heat exchanger, the subscript repeated twice indicates the summation of that subscript in the three spatial directions; x f Represents the one-dimensional spatial direction coordinates of the cold / hot fluid channel; the summation symbol... n Indicates the number of fluid channels in the unit structure; T 1 represents the temperature correction value at the flow / solid interface in the fluid channel, and its calculation method is as follows: In the above equations T 0 and The spatial distribution of the finite volume can be discretized and solved using the finite volume method.

[0010] Compared with the prior art, the beneficial effects of the present invention are: For the design and verification calculations of printed circuit board (PCB) heat exchangers, existing one-dimensional calculations suffer from unknown thermal resistance in the solid region between the cold / hot fluids, lacking effective theoretical guidance and requiring assumptions and simplifications. Meanwhile, three-dimensional high-precision numerical simulations involve large mesh sizes, and their fluid-structure interaction consumes significant computational resources. This invention provides a multi-scale rapid calculation method for the heat transfer performance of PCB heat exchangers. It can quickly obtain macroscopic equivalent thermal conductivity and convective heat transfer parameters through three-dimensional numerical simulation of unit structures, avoiding complex three-dimensional calculations of the complete structure. Furthermore, by combining the equivalent thermal conductivity equation and the one-dimensional fluid flow equation, the average temperature distribution of the PCB heat exchanger and the cold / hot fluids can be quickly obtained, thus enabling rapid evaluation of heat exchanger performance. This method has significant application prospects in the verification and optimization design of PCB heat exchangers. Attached Figure Description

[0011] Figure 1 This is a schematic diagram of the complete heat exchange channel of a rectangular channel printed circuit board heat exchanger.

[0012] Figure 2 This is a schematic diagram of the unit structure of a rectangular channel printed circuit board heat exchanger.

[0013] Figure 3 A flowchart of a multi-scale rapid calculation method for the heat transfer performance of printed circuit board heat exchangers.

[0014] Figure 4 The distribution of convective heat transfer coefficient on the channel surface.

[0015] Figure 5 Parametric fields for solving element structures N k Distribution diagram.

[0016] Figure 6 Parametric fields for solving element structures M 0 distribution diagram.

[0017] Figure 7 Parametric fields for solving element structures M r Distribution diagram.

[0018] Figure 8 The average three-field synergistic angle of several enhanced heat transfer structures is used to measure the change in inlet velocity. Detailed Implementation

[0019] The embodiments of the present invention will now be described in detail with reference to the accompanying drawings and examples.

[0020] In an embodiment of the present invention, with Figure 1 and Figure 2 Taking a periodic channel of a rectangular channel printed circuit board heat exchanger as an example, the heat exchange medium is supercritical carbon dioxide. The channel is 300 mm long, the total width of the solid region is 2 mm, and the height is 3 mm. Two rectangular channels are symmetrically distributed, with a width of 1.6 mm and a height of 1 mm, and the distance between the two channels is 0.5 mm. The supercritical carbon dioxide mass flow rate on both the cold and hot sides is 0.006504 kg / s, the inlet temperature on the cold side is 573 K, and the inlet temperature on the hot side is 823 K. The physical properties are constants. The side of the solid region has periodic boundary conditions, and the thermal conductivity of the solid metal is 19 W / (m·K). Figure 3 As shown, this example demonstrates a multi-scale rapid calculation method for the heat transfer performance of printed circuit board heat exchangers. The main steps are as follows: Step 1, extract the structure of the heat exchanger unit on the printed circuit board, such as Figure 2 As shown, periodic flow boundary conditions are used at the inlet and outlet for the fluid region, and isothermal boundary conditions are used at the flow / solid interface. Flow heat transfer calculations are performed on the unit structure, and the convective heat transfer coefficient is calculated at the flow / solid interface surface. h : in T f This represents the average temperature of the fluid inlet and outlet sections of the unit. q and T w These represent the local heat flux density and interface temperature at the fluid / solid interface, respectively. The convective heat transfer coefficient distribution at the fluid / solid interface surface is obtained as follows: Figure 4 As shown.

[0021] Step 2: For the extracted solid region of the unit structure, perform analogous heat conduction calculations and parameter field analysis. N j , M 0 and M r The following thermal conductivity problems were obtained by solving them separately within the solid region of the unit structure: Among them, parameter field N j , M 0 and M r , representing the effects of solid temperature gradient, solid average temperature and fluid average temperature on the temperature field within the unit structure, respectively; λ ij and λ ik All are thermal conductivity tensors of heat exchanger materials; y i 、y j and y k All coordinates are internal coordinates of the unit structure; h r For the first r Heat transfer coefficient at the boundary of each fluid channel; V c The volume of the solid region in the unit structure; n i For the unit outward normal vector component; This represents the surface of all fluid channels in the unit structure. Represents the unit structure r Each fluid channel surface dA For surface area infinitesimal elements; subscript i , j and k All represent spatial directions. A subscript repeated twice in the formula indicates summation over that subscript in three spatial directions; subscript r Indicates the fluid number. The obtained parameter field. N j , M 0 and M r Distribution as Figure 5 , Figure 6 and Figure 7 As shown.

[0022] Step 3, based on the unit structure parameter field N j ,M 0 and M r Calculate the macroscopic equivalent thermal conductivity of the heat exchanger K ij Heat transfer parameters corresponding to the average temperature of the solid H 0,i Heat transfer parameters corresponding to the average temperature of the fluid H r,i .in K ij , H 0,i and H r,i The calculation method is as follows: in Represents a solid region of a unit structure. d y represents the volume element of the solid region. The calculation yields... K ij of xx , yy , zz The three components are 14.51 W / (m·K), 9.56 W / (m·K), and 16 W / (m·K), with the off-diagonal component being zero; H 0,i The three components are -6.62 W / (m²). 2 ·K), -29.20 W / (m 2 ·K), -2.277 W / (m 2 ·K); Cold fluid channel H 1,i The three components are 9.33 W / (m²). 2 ·K), -40.41 W / (m 2 ·K), 1.22 W / (m 2 ·K); Hot fluid channel H 2,i The three components are -15.90 W / (m²). 2 ·K), 11.22 W / (m 2 ·K), -3.48 W / (m 2 ·K).

[0023] Step 4: Using the controlled volume method, the macroscopic equivalent heat conduction equation and the one-dimensional flow heat transfer equation of the cold / hot fluid are solved in a coupled manner. The solved macroscopic equivalent heat conduction equation and the one-dimensional flow heat transfer equation of the cold / hot fluid are as follows: in, T 0 represents the temperature of the solid to be solved. The first one to be solved r The temperature of the fluid; For the first r The product of the specific heat capacity and mass flow rate of a fluid; x i and x j For the three-dimensional spatial coordinates of the heat exchanger, the subscript repeated twice indicates the summation of that subscript in the three spatial directions; x f Represents the one-dimensional spatial direction coordinates of the cold / hot fluid channel; the summation symbol... n Indicates the number of fluid channels in the unit structure; T 1 represents the temperature correction value at the flow / solid interface in the fluid channel, and its calculation method is as follows: The temperature distribution in the solid region of the printed circuit board heat exchanger and the temperature distribution along the flow path of the cold / hot fluid are obtained from the solution. Figure 8 As shown in the figure, the temperature distribution along the circuit obtained from the three-dimensional numerical simulation is compared. It can be seen that, apart from the temperature deviation between the inlet and outlet parts caused by the inlet effect, the temperature distribution along the circuit obtained by the multi-scale rapid calculation method of the heat transfer performance of the printed circuit board heat exchanger is in good agreement with the results of the three-dimensional numerical equation, proving the effectiveness of the method in calculating the temperature distribution and performance prediction of the printed circuit board heat exchanger.

Claims

1. A multi-scale rapid calculation method for the heat transfer performance of a printed circuit board heat exchanger, characterized in that, Includes the following steps: Step 1: Extract the unit structure of the printed circuit board heat exchanger. For its fluid region, periodic flow boundary conditions are adopted for the inlet and outlet, and isothermal or isothermal flow boundary conditions are adopted for the flow / solid interface. Perform flow heat transfer calculation of the unit structure and obtain the convective heat transfer coefficient distribution on the surface of the flow / solid interface. Step 2: For the solid region of the extracted unit structure, perform analogous heat conduction calculations to obtain the parameter field in the unit structure. N j , M 0 and M r , representing the effects of solid temperature gradient, solid average temperature and fluid average temperature on the temperature field within the unit structure, respectively; Step 3, based on the unit structure parameter field N j , M 0 and M r Calculate the macroscopic equivalent thermal conductivity of the heat exchanger K ij Heat transfer parameters corresponding to the average temperature of the solid H 0,i and the heat transfer parameters corresponding to the average fluid temperature H r,i ; Step 4: Using the controlled volume method, the macroscopic equivalent heat conduction equation and the one-dimensional flow heat transfer equation of the cold / hot fluid are solved in a coupled manner to obtain the temperature distribution of the solid region of the printed circuit board heat exchanger and the temperature distribution of the cold / hot fluid along the flow path.

2. The multi-scale rapid calculation method for the heat transfer performance of a printed circuit board heat exchanger according to claim 1, characterized in that, In step 1, the convective heat transfer coefficient at the fluid / solid interface surface... h The calculation method is as follows: in T f The average temperature of the fluid inlet and outlet sections of the unit structure is given. q and T w These represent the local heat flux density and interface temperature at the fluid / solid interface, respectively.

3. The multi-scale rapid calculation method for the heat transfer performance of a printed circuit board heat exchanger according to claim 1, characterized in that, Step 2, parameter field N j , M 0 and M r The following thermal conductivity problems were obtained by solving them separately within the solid region of the unit structure: in, λ ij and λ ik All are thermal conductivity tensors of heat exchanger materials; y i 、y j and y k All coordinates are internal coordinates of the unit structure; h r For the first r Heat transfer coefficient at the boundary of each fluid channel; V c The volume of the solid region in the unit structure; n i For the unit outward normal vector component; This represents the surface of all fluid channels in the unit structure. Represents the unit structure r Each fluid channel surface dA It is a surface area micro-element.

4. The multi-scale rapid calculation method for the heat transfer performance of a printed circuit board heat exchanger according to claim 1, characterized in that, In step 3, the macroscopic equivalent thermal conductivity of the heat exchanger... K ij Heat transfer parameters corresponding to the average temperature of the solid H 0,i Heat transfer parameters corresponding to the average temperature of the fluid H r,i The calculation method is as follows: in Represents a solid region of a unit structure. d y represents the volume element of the solid region.

5. The multi-scale rapid calculation method for the heat transfer performance of a printed circuit board heat exchanger according to claim 1, characterized in that, In step 4, the macroscopic equivalent heat conduction equation and the one-dimensional flow heat transfer equation of the cold / hot fluid for the printed circuit board heat exchanger are respectively: in, T 0 represents the temperature of the solid to be solved. The first one to be solved r The temperature of the fluid; For the first r The product of the specific heat capacity and mass flow rate of a fluid; x i and x j The coordinates of the heat exchanger are in three-dimensional space. x f Represents the one-dimensional spatial direction coordinates of the cold / hot fluid channel; the summation symbol... n Indicates the number of fluid channels in the unit structure; T 1 represents the temperature correction value at the flow / solid interface in the fluid channel, and its calculation method is as follows: In the above equations T 0 and The spatial distribution is discretized and solved using the finite volume method.

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