CN114564896B - Forced convection micro-channel heat exchanger design method based on multi-scale topological optimization - Google Patents
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Abstract
The method comprises the steps of constructing a bottom structure of the forced convection microchannel heat exchanger, wherein the bottom structure is isotropic and comprises open pores, and changing the porosity by changing the geometric parameters of the bottom structure; calculating effective permeability and effective heat conductivity coefficients of the bottom layer structures corresponding to different porosities by adopting a lattice Boltzmann method; fitting the scattered points obtained by numerical simulation by polynomials to obtain functional relation formulas of effective permeability and effective heat conductivity coefficient along with the change of porosity respectively; and (3) constructing a flow heat exchange process in the forced convection heat exchanger under a macroscopic scale, and adopting a functional relation to replace the effective permeability and the effective heat conductivity coefficient in a macroscopic equation to obtain the optimized arrangement of the bottom layer structures with different porosities in the heat exchanger based on the macroscopic topological optimization of a density method, namely the optimally designed heat exchanger.
Description
Technical Field
The invention relates to the technical field of heat exchangers, in particular to a design method of a forced convection microchannel heat exchanger based on multi-scale topological optimization.
Background
With miniaturization, integration and high performance of electronic chips, the heat flux density of the electronic chips is higher and higher, and partial devices even exceed 100W/cm 2 . Most electronic devices require operating temperatures within the range of-20 to 80 ℃, and thermal management of chips is becoming increasingly important to technicians. Among the heat dissipation means, the forced convection microchannel heat exchanger is attracting attention due to the characteristics of high heat exchange efficiency, low noise, low flow demand and the like. The forced convection micro-channel heat exchanger consists of solid material with high heat conductivity and fluid flow channel, and the micro-channel heat exchanger and the fluid flow channelThe heat source contacts, the solid diffuses the heat into the micro-channel heat exchanger, and the heat exchange fluid flows through the flow channel to take away the heat in the micro-channel heat exchanger. Therefore, the flow channel layout in the forced convection microchannel heat exchanger is one of the important factors affecting the forced convection heat transfer performance. For forced convection microchannel heat exchangers, flow resistance and heat exchange performance are two important indicators for performance measurement. In practical situations, the flow resistance and the heat exchange performance often contradict each other, and the improvement of the heat exchange performance is often accompanied by the increase of the flow resistance. How to balance the two indexes of flow resistance and heat exchange performance and to exert the potential of the micro-channel heat exchanger to the greatest extent is the key of the problem. Conventional channel layout designs such as straight channels, wavy channels, serpentine channels, fractal channels are often based on theory, experience and intuition of designers, and therefore the optimality thereof cannot be ensured. Conventional optimization methods, including size optimization, shape optimization, require a given pre-determined shape and assembly, and their natural drawbacks in design freedom limit the performance of the microchannel heat exchanger. Topology optimization can overcome the above drawbacks well as an optimization means with the highest degree of freedom of design. Density methods are one of the common methods of topological optimization, which essentially optimizes the distribution of materials over the design domain, often resulting in porous media between solids and fluids for some areas. However, for the present time, we will typically post-treat the structure based on density topology optimization, eliminating these porous media regions. However, eliminating these porous medium regions not only increases the difficulty of optimization and increases the amount of calculation, but also deteriorates the performance of the heat exchanger, and the constraint conditions for partial optimization cannot be completely satisfied.
The above information disclosed in the background section is only for enhancement of understanding of the background of the invention and therefore may contain information that does not form the prior art that is already known to a person of ordinary skill in the art.
Disclosure of Invention
The invention aims to provide a design method of a forced convection microchannel heat exchanger based on multi-scale topological optimization, which adopts a multi-scale idea, calculates the relation of effective heat conductivity coefficient and effective permeability along with porosity change by adopting a lattice Boltzmann method aiming at some underlying structures, scale-improves the relation, adopts the relation to carry out macroscopic topological optimization, and deducts the obtained optimization result into a porous medium domain consisting of the underlying structures. The forced convection heat exchanger obtained by optimization through the method has more excellent performance, and can realize higher heat exchange efficiency under the condition of smaller pressure drop.
In order to achieve the above object, the present invention provides the following technical solutions:
the design method of the forced convection microchannel heat exchanger based on multi-scale topological optimization comprises the following steps:
constructing a substructure of a forced convection microchannel heat exchanger, the substructure having isotropy and comprising open pores, changing porosity by changing geometric parameters of the substructure;
calculating effective permeability and effective heat conduction coefficients of the bottom layer structures corresponding to different porosities by adopting a lattice Boltzmann method, wherein periodic boundary conditions are applied to the bottom layer structures in the z direction, differential pressure is given in the x direction, flow is simulated, the effective permeability is obtained according to Darcy's law, periodic boundary conditions are applied to the bottom layer structures in the y direction and the z direction by adopting the lattice Boltzmann method, temperature difference is given in the x direction, heat conduction is simulated, and the effective heat conduction coefficients are obtained according to Fourier heat conduction law;
fitting the scattered points obtained by numerical simulation by polynomials to obtain functional relation formulas of effective permeability and effective heat conductivity coefficient along with the change of porosity respectively;
the flow heat exchange process in the forced convection heat exchanger under the macro scale is constructed as follows:
wherein, the u speed field, T is temperature, Q is heat source, ρ, c p And v corresponds to the density, specific heat capacity and kinematic viscosity of the fluid, respectively, K (gamma) and lambda (gamma) are the effective permeability and gamma for the porosity of the underlying structure, respectivelyEffective thermal conductivity;
and the functional relation is adopted to replace the effective permeability and the effective heat conductivity coefficient in the macroscopic equation, and the macroscopic topology optimization based on the density method is adopted to obtain the optimized arrangement of the bottom structures with different porosities in the heat exchanger so as to optimally design the heat exchanger.
In the design method of the forced convection microchannel heat exchanger based on the multi-scale topological optimization, the porosity change range is (0, 1).
In the design method of the forced convection microchannel heat exchanger based on multi-scale topological optimization, binary models of different bottom structures under different porosities are reconstructed to calculate effective permeability and effective heat conductivity.
A heat exchanger obtained according to the method of designing a forced convection microchannel heat exchanger based on multiscale topological optimization described above.
In the technical scheme, the design method of the forced convection microchannel heat exchanger based on multi-scale topological optimization has the following beneficial effects: the design method of the forced convection microchannel heat exchanger based on the multi-scale topological optimization can adopt a plurality of reasonable micro structures to deduct the porous medium area obtained by the macroscopic topological optimization, so that the porous medium area can be manufactured, the improving effect of the porous medium on the performance of the heat exchanger is reserved, and the comprehensive performance of the heat exchanger is further improved.
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In order to more clearly illustrate the embodiments of the present application or the technical solutions in the prior art, the drawings that are needed in the embodiments will be briefly described below, and it is obvious that the drawings in the following description are only examples described in the present invention, and that other drawings can be obtained according to these drawings by a person having ordinary skill in the art.
FIG. 1 is a schematic diagram of a selected Gyroid minimum three-period curved surface bottom structure of a forced convection microchannel heat exchanger design method based on multi-scale topological optimization in the invention;
FIG. 2 is a schematic diagram of a computational model of a multi-scale topological optimization of a forced convection microchannel heat exchanger design method based on the multi-scale topological optimization of the present invention;
FIG. 3 is a schematic diagram of a result obtained by performing multi-scale topological optimization design on a Gyroid minimum three-period curved surface bottom structure based on a multi-scale topological optimization-based forced convection microchannel heat exchanger design method;
fig. 4 is a schematic diagram of a calculated conventional parallel flow channel heat exchanger.
Detailed Description
For the purpose of making the objects, technical solutions and advantages of the embodiments of the present invention more clear, the technical solutions of the embodiments of the present invention will be clearly and completely described below with reference to fig. 1 to 4 of the embodiments of the present invention, and it is apparent that the described embodiments are some embodiments of the present invention, but not all embodiments. All other embodiments, based on the embodiments of the invention, which are apparent to those of ordinary skill in the art without inventive faculty, are intended to be within the scope of the invention.
Thus, the following detailed description of the embodiments of the invention, as presented in the figures, is not intended to limit the scope of the invention, as claimed, but is merely representative of selected embodiments of the invention. All other embodiments, based on the embodiments of the invention, which are apparent to those of ordinary skill in the art without inventive faculty, are intended to be within the scope of the invention.
It should be noted that: like reference numerals and letters denote like items in the following figures, and thus, once an item is defined in one figure, further definition and explanation thereof is not necessary in the following figures.
In the description of the present invention, it should be understood that the terms "center", "longitudinal", "lateral", "length", "width", "thickness", "upper", "lower", "front", "rear", "left", "right", "vertical", "horizontal", "top", "bottom", "inner", "outer", "clockwise", "counterclockwise", etc. indicate orientations or positional relationships based on the orientations or positional relationships shown in the drawings are merely for convenience in describing the present invention and simplifying the description, and do not indicate or imply that the apparatus or elements referred to must have a specific orientation, be configured and operated in a specific orientation, and thus should not be construed as limiting the present invention.
Furthermore, the terms "first," "second," and the like are used for descriptive purposes only and are not to be construed as indicating or implying a relative importance or implying a number of technical features being indicated. Thus, a feature defining "a first", "a second" or the like may include, explicitly or implicitly, one or more such feature. In the description of the present invention, the meaning of "a plurality" is two or more, unless explicitly defined otherwise.
In the present invention, unless explicitly specified and limited otherwise, the terms "mounted," "connected," "secured," and the like are to be construed broadly, and may be, for example, fixedly connected, detachably connected, or as a unit; can be directly connected or indirectly connected through an intermediate medium, and can be communicated with the inside of two elements or the interaction relationship of the two elements. The specific meaning of the above terms in the present invention can be understood by those of ordinary skill in the art according to the specific circumstances.
In the present invention, unless explicitly specified and limited otherwise, the "upper" or "lower" of a first feature may include the first and second features being in direct contact, or may include the first and second features not being in direct contact but being in contact with each other through another feature therebetween. Also, the "above," "over" and "on" the second feature includes the first feature being directly above and obliquely above the second feature, or simply indicating that the first feature is higher in level than the second feature. The "under", "under" and "beneath" the second feature includes the first feature being directly under and obliquely under the second feature, or simply means that the first feature is less level than the second feature.
In order to make the technical scheme of the present invention better understood by those skilled in the art, the present invention will be further described in detail with reference to the accompanying drawings. As shown in fig. 1-3, the forced convection microchannel heat exchanger design method based on multi-scale topological optimization includes,
constructing a substructure of a forced convection microchannel heat exchanger, the substructure having isotropy and comprising open pores, changing porosity by changing geometric parameters of the substructure;
calculating effective permeability and effective heat conduction coefficients of the bottom layer structures corresponding to different porosities by adopting a lattice Boltzmann method, wherein periodic boundary conditions are applied to the y direction and the z direction of the bottom layer structures, a pressure difference is given in the x direction, the flow is simulated, the effective permeability is obtained according to Darcy's law, the periodic boundary conditions are applied to the y direction and the z direction of the bottom layer structures by adopting the lattice Boltzmann method, a temperature difference is given in the x direction, the heat conduction is simulated, and the effective heat conduction coefficient is obtained according to the Fourier heat conduction law;
fitting the scattered points obtained by numerical simulation by polynomials to obtain functional relation formulas of effective permeability and effective heat conductivity coefficient along with the change of porosity respectively;
the flow heat exchange process in the forced convection heat exchanger under the macro scale is constructed as follows:
wherein, the u speed field, T is temperature, Q is heat source, ρ, c p And v corresponds to the density, specific heat capacity and kinematic viscosity of the fluid, respectively, K (gamma) and lambda (gamma) being the effective permeability and the effective thermal conductivity, respectively, of the underlying structure when the porosity of the underlying structure is gamma;
and the functional relation is adopted to replace the effective permeability and the effective heat conductivity coefficient in the macroscopic equation, and the macroscopic topology optimization based on the density method is adopted to obtain the optimized arrangement of the bottom structures with different porosities in the heat exchanger, namely the optimally designed heat exchanger.
In the preferred embodiment of the design method of the forced convection microchannel heat exchanger based on multi-scale topological optimization, the porosity variation range is 0.5-0.8.
In the preferred embodiment of the design method of the forced convection microchannel heat exchanger based on multi-scale topological optimization, binary models of different substructures under different porosities are reconstructed to calculate effective permeability and effective heat conductivity.
In one embodiment, in the method, based on a selected bottom layer structure, a binary model under different porosities is established, the relation between the effective heat conductivity coefficient and the effective permeability along with the change of the porosity is calculated by adopting a lattice Boltzmann method, and the relation is subjected to scale promotion and substituted into a macroscopic topology optimization method based on a density method to obtain the forced convection heat exchanger based on the bottom layer structure. The porosity of each part of the micro-channel heat exchanger designed based on the optimization method is determined through topological optimization, and the micro-channel heat exchanger designed by the method has the characteristics of better performance, better satisfaction of design constraint conditions and the like.
In one embodiment, the multi-scale topological optimization is essentially based on the distribution of materials within the underlying structural optimization design domain. In the case of an optimized design, the design domain is discretized into a plurality of cells, each cell being assigned a design variable γ, γ varying between (0, 1), 0 and 1 corresponding to the solid and fluid respectively, that is, γ representing the porosity of the local cell volume, for the flow heat exchange process in a forced convection heat exchanger on a macroscopic scale, the corresponding control equation is as follows:
wherein, the u speed field, T is temperature, Q is heat source, ρ, c p And v corresponds to the density, specific heat capacity and kinematic viscosity of the fluid, respectively, K (gamma) and lambda (gamma) being the effective permeability and the effective when the porosity of the underlying structure is gamma, respectivelyThermal conductivity coefficient.
The basic flow of designing the forced convection heat exchanger by adopting the design method of the forced convection heat exchanger based on multi-scale topological optimization is as follows:
(1) An underlying structure is selected. The selection of the bottom layer structure should be in accordance with the practical situation of the design of the forced convection microchannel heat exchanger, for example, a self-supporting bottom layer structure should be adopted for three-dimensional macroscopic optimization, the bottom layer structure should have isotropic macroscopic physical properties, the bottom layer structure should have open pores, and the like.
(2) The manner of change in porosity is determined. Changing the geometric parameters of the underlying structure may change the porosity, for example, for an underlying structure composed of cylinders, changing the diameter of the cylinders may change the porosity of the structure.
(3) And reconstructing binary models of different bottom structures under different porosities for subsequent effective permeability and effective heat conductivity coefficient calculation.
(4) And calculating the effective permeability and the effective heat conductivity of the bottom layer structures corresponding to different porosities by adopting a lattice Boltzmann method. The lattice boltzmann method is a computational fluid dynamics method based on mesoscopic simulation dimensions. Compared with the traditional computational fluid dynamics method, the lattice Boltzmann method has the advantages of being simple in algorithm, capable of processing complex structures, high in parallelism and the like, and is very suitable for numerical simulation of a bottom structure. For the calculation of the effective permeability, a lattice boltzmann method is adopted, periodic boundary conditions are applied to the y direction and the x direction of the underlying structure, a pressure difference is given in the x direction, the flow is simulated, and the effective permeability is obtained according to the darcy law. And for calculating the effective heat conduction coefficient, applying periodic boundary conditions in the y direction and the x direction of the underlying structure by adopting a lattice Boltzmann method, giving a temperature difference in the x direction, simulating heat conduction, and obtaining the effective heat conduction coefficient according to a Fourier heat conduction law.
(5) And (3) performing polynomial fitting on the scattered points obtained by the numerical simulation in the step (4), and further obtaining functional relation formulas of effective permeability and effective heat conductivity coefficient along with the change of the porosity respectively.
(6) And (3) replacing K (gamma) and lambda (gamma) in equations (2) and (3) by adopting the functional relation, performing macroscopic topology optimization based on a density method, and determining the application of boundary conditions, the optimization target and the selection of optimization constraint according to actual application scenes. And according to the obtained optimization result, gamma at different positions corresponds to the underlying structure under different porosities.
As shown in fig. 1, a Gyroid minimum three-period curved surface is selected as a bottom structure, and multi-scale topology optimization is performed. The calculation area is shown in FIG. 2, the limiting porosity variation range in this example is 0.5-0.8, L=1cm, the inlet-outlet pressure difference is 1Pa, and 1×10 is applied in the design area 5 W/m 3 The solid heat conductivity coefficient is 100W/(m.K), the heat exchange fluid is air, the inlet temperature is 293.15K, and the volume constraint is that the solid volume in the design domain is at most 40% of the design domain. The optimization results are shown in fig. 3, and the different porosity values at different positions are the substructures corresponding to different porosities. In order to verify the effectiveness of the multi-scale topological optimization method in the example, the example also simulates a common parallel flow channel forced convection heat exchanger, as shown in fig. 4, the basic size and shape of the heat exchanger are the same as those of the multi-scale topological optimization heat exchanger, the inlet-outlet pressure difference is kept at 1Pa, the heat exchange fluid is selected as air, the inlet temperature is 293.15K, the solid heat conductivity coefficient is 100W/(m.K), and 1X 10 is applied at the same position in the middle square area 5 W/m 3 Is a uniform heat source of the (c).
The calculation results are shown in table 1,
table 1:
in the above results, the average temperature and the maximum temperature of the micro-channel heat exchanger adopting the multi-scale topological optimization are both obviously lower than those of the heat exchanger adopting the traditional parallel flow channels, and obviously the temperature of the micro-channel heat exchanger is more uniform than that of the micro-channel heat exchanger adopting the traditional parallel flow channels, which indicates that the heat exchanger adopting the multi-scale topological optimization has better heat exchange performance and better comprehensive performance under the condition of the same pressure drop. Meanwhile, as can be seen by comparing the data of the percentage of the solid volume in the design domain to the volume in the design domain, the heat exchanger adopting the multi-scale topological optimization saves more materials.
In another embodiment, the invention also discloses a heat exchanger, which is obtained according to the design method of the forced convection microchannel heat exchanger based on multi-scale topological optimization.
Finally, it should be noted that: the described embodiments are intended to be illustrative of only some, but not all embodiments, and all other embodiments that may be made by one skilled in the art without the benefit of the teachings of the present application are intended to be within the scope of the invention.
While certain exemplary embodiments of the present invention have been described above by way of illustration only, it will be apparent to those of ordinary skill in the art that modifications may be made to the described embodiments in various different ways without departing from the spirit and scope of the invention. Accordingly, the drawings and description are to be regarded as illustrative in nature and not as restrictive of the scope of the invention, which is defined by the appended claims.
Claims (3)
1. The design method of the forced convection microchannel heat exchanger based on the multi-scale topological optimization is characterized by comprising the following steps of:
constructing a substructure of a forced convection microchannel heat exchanger, the substructure having isotropy and comprising open pores, changing porosity by changing geometric parameters of the substructure;
calculating effective permeability and effective heat conduction coefficients of the bottom layer structures corresponding to different porosities by adopting a lattice Boltzmann method, wherein periodic boundary conditions are applied to the y direction and the z direction of the bottom layer structures, a pressure difference is given in the x direction, the flow is simulated, the effective permeability is obtained according to Darcy's law, the periodic boundary conditions are applied to the y direction and the z direction of the bottom layer structures by adopting the lattice Boltzmann method, a temperature difference is given in the x direction, the heat conduction is simulated, and the effective heat conduction coefficient is obtained according to the Fourier heat conduction law;
fitting the scattered points obtained by numerical simulation by polynomials to obtain functional relation formulas of effective permeability and effective heat conductivity coefficient along with the change of porosity respectively;
the flow heat exchange process in the forced convection heat exchanger under the macro scale is constructed as follows:
wherein, the u speed field, T is temperature, Q is heat source, ρ, c p And v correspond to the density, specific heat capacity and kinematic viscosity of the fluid, respectively, and κ (γ) and λ (γ) are the effective permeability and the effective thermal conductivity of the underlying structure when the porosity of the underlying structure is γ, respectively; and the functional relation is adopted to replace the effective permeability and the effective heat conductivity coefficient in the macroscopic equation, and the macroscopic topology optimization based on the density method is adopted to obtain the optimized arrangement of the bottom structures with different porosities in the heat exchanger so as to optimally design the heat exchanger.
2. The method for designing a forced convection microchannel heat exchanger based on multi-scale topological optimization of claim 1, wherein the binary model of different underlying structures at different porosities is reconstructed to calculate the effective permeability and the effective thermal conductivity.
3. A heat exchanger obtainable according to a method of designing a forced convection microchannel heat exchanger based on multiscale topological optimization according to claim 1 or 2.
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| CN111709096A (en) * | 2020-06-08 | 2020-09-25 | 西安交通大学 | Design method of special-shaped fin structure for strengthening natural convection heat transfer |
| CN113094944A (en) * | 2021-03-22 | 2021-07-09 | 华中科技大学 | Micro-channel radiator and microscopic scale topology optimization design method thereof |
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