CN116738707A - Equivalent mechanical property prediction method and system for partial periodic heat exchanger channel - Google Patents
Equivalent mechanical property prediction method and system for partial periodic heat exchanger channel Download PDFInfo
- Publication number
- CN116738707A CN116738707A CN202310680460.2A CN202310680460A CN116738707A CN 116738707 A CN116738707 A CN 116738707A CN 202310680460 A CN202310680460 A CN 202310680460A CN 116738707 A CN116738707 A CN 116738707A
- Authority
- CN
- China
- Prior art keywords
- equivalent
- heat exchanger
- periodic
- exchanger channel
- coefficient
- Prior art date
- Legal status (The legal status is an assumption and is not a legal conclusion. Google has not performed a legal analysis and makes no representation as to the accuracy of the status listed.)
- Granted
Links
- 230000000737 periodic effect Effects 0.000 title claims abstract description 158
- 238000000034 method Methods 0.000 title claims abstract description 62
- 239000011159 matrix material Substances 0.000 claims abstract description 66
- 238000006073 displacement reaction Methods 0.000 claims abstract description 62
- 238000004364 calculation method Methods 0.000 claims abstract description 59
- 238000010008 shearing Methods 0.000 claims abstract description 51
- 238000004088 simulation Methods 0.000 claims abstract description 31
- 239000000463 material Substances 0.000 claims abstract description 24
- 210000004027 cell Anatomy 0.000 claims description 67
- 239000013598 vector Substances 0.000 claims description 28
- 238000013461 design Methods 0.000 claims description 15
- 238000000265 homogenisation Methods 0.000 claims description 15
- 239000007769 metal material Substances 0.000 claims description 6
- 239000002131 composite material Substances 0.000 claims description 3
- 238000004590 computer program Methods 0.000 claims description 3
- 238000012545 processing Methods 0.000 claims description 2
- 230000000875 corresponding effect Effects 0.000 claims 7
- 230000002596 correlated effect Effects 0.000 claims 1
- 238000005516 engineering process Methods 0.000 description 5
- 238000004458 analytical method Methods 0.000 description 4
- 238000013178 mathematical model Methods 0.000 description 3
- 230000000750 progressive effect Effects 0.000 description 3
- 238000003491 array Methods 0.000 description 2
- 238000010801 machine learning Methods 0.000 description 2
- 230000008092 positive effect Effects 0.000 description 2
- 230000008569 process Effects 0.000 description 2
- 238000004422 calculation algorithm Methods 0.000 description 1
- 238000012937 correction Methods 0.000 description 1
- 230000007547 defect Effects 0.000 description 1
- 238000011161 development Methods 0.000 description 1
- 238000010586 diagram Methods 0.000 description 1
- 230000000694 effects Effects 0.000 description 1
- 230000006870 function Effects 0.000 description 1
- 238000010438 heat treatment Methods 0.000 description 1
- 238000012986 modification Methods 0.000 description 1
- 230000004048 modification Effects 0.000 description 1
- 230000003287 optical effect Effects 0.000 description 1
- 238000005457 optimization Methods 0.000 description 1
- 238000005057 refrigeration Methods 0.000 description 1
- 239000004065 semiconductor Substances 0.000 description 1
- 238000012549 training Methods 0.000 description 1
Classifications
-
- G—PHYSICS
- G06—COMPUTING; CALCULATING OR COUNTING
- G06F—ELECTRIC DIGITAL DATA PROCESSING
- G06F30/00—Computer-aided design [CAD]
- G06F30/20—Design optimisation, verification or simulation
-
- G—PHYSICS
- G06—COMPUTING; CALCULATING OR COUNTING
- G06F—ELECTRIC DIGITAL DATA PROCESSING
- G06F17/00—Digital computing or data processing equipment or methods, specially adapted for specific functions
- G06F17/10—Complex mathematical operations
- G06F17/11—Complex mathematical operations for solving equations, e.g. nonlinear equations, general mathematical optimization problems
-
- G—PHYSICS
- G06—COMPUTING; CALCULATING OR COUNTING
- G06F—ELECTRIC DIGITAL DATA PROCESSING
- G06F2111/00—Details relating to CAD techniques
- G06F2111/04—Constraint-based CAD
-
- G—PHYSICS
- G06—COMPUTING; CALCULATING OR COUNTING
- G06F—ELECTRIC DIGITAL DATA PROCESSING
- G06F2119/00—Details relating to the type or aim of the analysis or the optimisation
- G06F2119/08—Thermal analysis or thermal optimisation
-
- G—PHYSICS
- G06—COMPUTING; CALCULATING OR COUNTING
- G06F—ELECTRIC DIGITAL DATA PROCESSING
- G06F2119/00—Details relating to the type or aim of the analysis or the optimisation
- G06F2119/14—Force analysis or force optimisation, e.g. static or dynamic forces
-
- Y—GENERAL TAGGING OF NEW TECHNOLOGICAL DEVELOPMENTS; GENERAL TAGGING OF CROSS-SECTIONAL TECHNOLOGIES SPANNING OVER SEVERAL SECTIONS OF THE IPC; TECHNICAL SUBJECTS COVERED BY FORMER USPC CROSS-REFERENCE ART COLLECTIONS [XRACs] AND DIGESTS
- Y02—TECHNOLOGIES OR APPLICATIONS FOR MITIGATION OR ADAPTATION AGAINST CLIMATE CHANGE
- Y02T—CLIMATE CHANGE MITIGATION TECHNOLOGIES RELATED TO TRANSPORTATION
- Y02T90/00—Enabling technologies or technologies with a potential or indirect contribution to GHG emissions mitigation
Landscapes
- Engineering & Computer Science (AREA)
- Physics & Mathematics (AREA)
- General Physics & Mathematics (AREA)
- Theoretical Computer Science (AREA)
- Mathematical Physics (AREA)
- Mathematical Optimization (AREA)
- Data Mining & Analysis (AREA)
- General Engineering & Computer Science (AREA)
- Computational Mathematics (AREA)
- Mathematical Analysis (AREA)
- Pure & Applied Mathematics (AREA)
- Computer Hardware Design (AREA)
- Operations Research (AREA)
- Evolutionary Computation (AREA)
- Algebra (AREA)
- Geometry (AREA)
- Databases & Information Systems (AREA)
- Software Systems (AREA)
- Investigating Strength Of Materials By Application Of Mechanical Stress (AREA)
- Management, Administration, Business Operations System, And Electronic Commerce (AREA)
Abstract
The invention belongs to the technical field of prediction of equivalent mechanical properties of plate-fin heat exchangers, and discloses a method and a system for predicting equivalent mechanical properties of a periodic heat exchanger channel, wherein a simplified solving equation of upper and lower limits of equivalent stiffness coefficients of partial periodic distributed heat exchanger channels relative to deformation energy forms is constructed; establishing a heat exchanger channel unit finite element model, and setting geometric parameters and material properties of the heat exchanger channel unit finite element model; setting a unit characteristic strain field, completing stretching and shearing simulation under a nine-group node displacement constraint equation, and solving an upper limit of an equivalent stiffness coefficient; setting a unit characteristic stress field, calculating an equivalent flexibility coefficient matrix of a heat exchanger channel, and inverting, wherein an inverse matrix of the equivalent flexibility coefficient matrix is an equivalent stiffness coefficient lower limit. The invention ensures the calculation precision by defining the deformation energy equation of equivalent rigidity and equivalent flexibility coefficient under the loading of the characteristic strain field and the characteristic stress field, and provides method guidance for the equivalent mechanical property prediction of the plate-fin heat exchanger.
Description
Technical Field
The invention belongs to the technical field of prediction of equivalent mechanical properties of plate-fin heat exchangers, and particularly relates to a prediction method of equivalent mechanical properties of a part of periodic heat exchanger channels.
Background
At present, along with the rapid development of social industrialization, the world demand for energy is increasing. While most energy utilization is related to heat management, heat exchangers are becoming a core device of thermodynamic systems and are receiving increasing attention. The plate-fin heat exchanger used in high-temperature and high-pressure environment needs to pay attention to the integrity and reliability, and the mechanical properties of the plate-fin heat exchanger need to be evaluated and analyzed.
However, currently, a numerical simulation method is adopted for predicting the strength performance of the heat exchanger channel, so that the calculation time is long, and the model establishment and grid division processes are complex. Meanwhile, for the heat exchanger channel with the ultra-large pipe length-pipe diameter ratio, grid division work is difficult to carry out by utilizing numerical simulation software, so that great burden is brought to computer operation, and the use of the method is greatly limited. Therefore, the method of progressive homogenization is generally considered to evaluate the equivalent mechanical properties of the channels of the periodic heat exchanger with the same cold and hot sides, so as to achieve the purpose of rapidly and accurately analyzing the strength properties of the channels of the heat exchanger.
However, in practical engineering application, the cold and hot sides of some heat exchanger working conditions have different flow rates, operating pressures and temperatures, which results in different cold and hot channel structures of the plate-fin heat exchanger used. Therefore, it is desirable to provide a mechanical property prediction method for a partially periodically distributed plate-fin heat exchanger.
Through the above analysis, the problems and defects existing in the prior art are as follows: the prior progressive homogenization method can not analyze the equivalent mechanical properties of partial periodic heat exchanger channels with different cold and hot sides, and needs to provide an implementation method for predicting the equivalent mechanical properties of the plate-fin heat exchangers with partial periodic distribution.
Disclosure of Invention
Aiming at the problems existing in the prior art, the invention provides an equivalent mechanical property prediction method for a part of periodic heat exchanger channels, in particular to an equivalent mechanical property prediction method, an equivalent mechanical property prediction system, an equivalent mechanical property prediction medium, an equivalent mechanical property prediction device and a terminal for a part of periodic plate-fin heat exchanger channels based on a homogenization theory.
The invention is realized in such a way that an equivalent mechanical property prediction method for a partial periodic heat exchanger channel comprises the following steps: the system constructs a simplified solving equation of the upper and lower limits of equivalent rigidity coefficients of partial periodic distribution heat exchanger channels relative to deformation energy forms; establishing a heat exchanger channel unit finite element model, and setting geometric parameters and material properties of the heat exchanger channel unit finite element model; setting a unit characteristic strain field, completing stretching and shearing simulation under a nine-group node displacement constraint equation, and solving an upper limit of an equivalent stiffness coefficient; setting a unit characteristic stress field, calculating an equivalent flexibility coefficient matrix of a heat exchanger channel, and inverting, wherein an inverse matrix of the equivalent flexibility coefficient matrix is an equivalent stiffness coefficient lower limit;
The method for calculating the equivalent mechanical properties of the channels of the constructed partial periodic heat exchanger can be applied to the structural design of plate-fin heat exchangers with different cold and hot side channel structures or arrangement modes; according to the actual working condition and the design parameters of the heat exchanger, the method is used for calculation; constructing a single cell finite element calculation model of the plate-fin heat exchanger with partial periodic characteristics according to the calculation model, inputting corresponding geometric parameters, material parameters and working conditions, and performing simulation by using the established software system to perform prediction calculation on equivalent mechanical properties of the partial periodic heat exchanger channel; and finally, obtaining the upper limit value and the lower limit value of the equivalent stiffness coefficient of the partial periodic plate-fin heat exchanger channel.
Further, the equivalent mechanical property prediction method for the partial periodic heat exchanger channel comprises the following steps:
firstly, based on a homogenization theory, setting characteristic displacement respectively, and establishing a simplified solving equation of the upper and lower limits of equivalent stiffness coefficients of partial periodically distributed heat exchanger channels with respect to deformation energy forms;
step two, establishing a heat exchanger channel unit finite element model, and setting geometric parameters and material properties of the heat exchanger channel unit finite element model;
Step three, applying node periodic displacement constraint conditions to the periodic surface of the channel unit cell finite element model of the heat exchanger, applying node rigid displacement constraint conditions to the aperiodic surface, setting a unit characteristic strain field, completing stretching and shearing simulation under nine groups of node displacement constraint equations, and solving the upper limit of an equivalent stiffness coefficient;
and step four, applying a node periodic displacement constraint condition to the periodic surface of the heat exchanger channel unit cell finite element model, setting a free boundary condition to the aperiodic surface, setting a unit characteristic stress field, and completing calculation of an equivalent flexibility coefficient matrix of the heat exchanger channel through stretching and shearing simulation under a nine-group node displacement constraint equation, wherein an inverse matrix of the equivalent flexibility coefficient matrix is an equivalent rigidity coefficient lower limit. And finally, calculating equivalent mechanical properties of the heat exchanger channels with different cold and hot channel structures by taking average values of the upper and lower limits of the equivalent stiffness coefficients of the heat exchanger channels.
Further, in step one, by setting the characteristic displacement respectivelyAndthe unit characteristic strain field or the unit characteristic stress field and the strain field due to the unit cell heterogeneity are converted into the characteristic strain field directly applied on the boundary, directly given by setting the boundary node displacement constraint. The upper and lower marks indicate macroscopic k-l direction deformation After that, the deformation in m direction is fine, k, l, m=1, 2,3. Thereby deriving the equivalent stiffness coefficient of the channels of the partially periodically distributed heat exchanger>And equivalent compliance coefficient->The equation is solved based on simplification of the deformation energy ii form. The method provides a simplified mathematical model for calculating equivalent mechanical properties of the partial periodic structure, and avoids the problems of complex deduction, programming, calculation and the like.
For the energy form equation of the upper limit of the equivalent stiffness coefficient:
diagonal stiffness coefficient:
off-diagonal stiffness coefficient:
wherein ,for equivalent stiffness coefficient, superscript H represents equivalent; i, j, k, l are all direction vectors, and the values of the direction vectors are 1,2 and 3; y is the unit cell volume; II is deformation energy;Is a unit characteristic strain field.
For the energy form equation of the lower limit of the equivalent stiffness coefficient:
diagonal compliance coefficient:
off-diagonal compliance coefficient:
lower limit of equivalent stiffness coefficient:
wherein ,the superscript H represents the equivalent for the equivalent compliance coefficient;The characteristic strain field corresponds to the unit characteristic stress field; i, j, k, l are all direction vectors, and the values of the direction vectors are 1,2 and 3; y is the unit cell volume; the II is deformation energy.
Further, geometric parameters of the heat exchanger channel unit cell finite element model in the second step comprise unit cell length, unit cell width, unit cell height, channel wall thickness and channel spacing, and material properties comprise elastic modulus, poisson ratio and temperature; materials include metallic materials, non-metallic materials, and composite materials.
In the third step, three types of node sets of vertical surfaces, edges and vertexes are set for the partial periodic heat exchanger channel unit finite element model, and different node displacement constraint equations are respectively defined for each corresponding node set of the periodic surface and the non-periodic surface of the partial periodic heat exchanger channel unit finite element model; and setting a unit characteristic strain field, respectively completing stretching and shearing simulation under nine groups of node displacement constraint equations, finally leading out deformation energy II results, and completing calculation of the equivalent stiffness coefficient upper limit of the partial periodic distribution heat exchanger channel. The method provides a simplified mathematical model for calculating equivalent mechanical properties of the partial periodic structure, and avoids the problems of complex deduction, programming, calculation and the like.
The boundary constraint equation for calculating the upper limit of the equivalent stiffness coefficient is as follows:
stretching in the x direction:
stretching in the y direction:
stretching in the z direction:
stretching in x and y directions:
stretching in x and z directions:
stretching in y and z directions:
shearing in xy direction:
shearing in xz direction:
shearing in yz direction:
wherein ,the deformation field is a unit characteristic strain field under rigid deformation, and represents deformation of a part of periodic structure in the macroscopic k-l direction under rigid deformation and in the microscopic m direction. U+ is the surface of the unit cell that is positive perpendicular to the x-axis, U-is the surface of the unit cell that is negative perpendicular to the x-axis, and the surfaces V+, V-, W+ and W-are similarly defined. a, b, c each represent a unit cell In the directions along the x, y and z coordinate axes.
According to nine groups of stretching and shearing simulation, a deformation energy II result is derived, and a partial periodic distribution heat exchanger channel equivalent stiffness coefficient upper limit matrix is obtained through solvingEquivalent elastic modulus, poisson ratio and shear modulus;
wherein ,is an equivalent stiffness coefficient upper limit matrix;The inverse matrix is the equivalent stiffness coefficient upper limit matrix, namely the equivalent flexibility coefficient matrix; i, j, k, l are all direction vectors, and the values of the direction vectors are 1,2 and 3; e is the equivalent elastic modulus; v is the equivalent Poisson's ratio; g is the equivalent shear modulus; x, y, z are coordinate axis directions.
In the fourth step, three types of node sets including a vertical face, an edge and a vertex are set for the partial periodic heat exchanger channel unit finite element model, and a node displacement constraint equation is defined for the corresponding node set of the periodic surface of the partial periodic heat exchanger channel unit finite element model; setting a free boundary condition on the aperiodic surface, setting a unit characteristic stress field, completing the stretching and shearing simulation under a nine-group node displacement constraint equation, and finally directly leading out a deformation energy II result to complete the calculation of an equivalent flexibility coefficient matrix; inverting the equivalent flexibility coefficient matrix, wherein the inverse matrix of the equivalent flexibility coefficient matrix is the lower limit result of the equivalent rigidity coefficient. The method provides a simplified mathematical model for calculating equivalent mechanical properties of the partial periodic structure, and avoids the problems of complex deduction, programming, calculation and the like.
The boundary constraint equation for calculating the equivalent stiffness coefficient lower limit is as follows:
stretching in the x direction:
stretching in the y direction:
stretching in the z direction:
and (3) shearing in the yz direction:
shearing in the xz direction:
shearing in the xy direction:
stretching in x and y directions:
stretching in x and z directions:
y and z stretching:
wherein ,the characteristic strain field corresponding to the unit characteristic stress field under the flexible deformation represents the deformation of a part of periodic structure in the macroscopic k-l direction under the flexible deformation and in the microscopic m direction. U+ is a unit cell surface perpendicular to the positive direction of the x-axis, U-is a verticalThe surface of the unit cell, which is negative in the x-axis, is defined similarly to the surfaces V+, V-, W+ and W-. a, b, c represent the lengths of the unit cells along the x, y, and z coordinate axes, respectively.
According to nine groups of stretching and shearing simulation, a deformation energy II result is derived, and a partial periodic heat exchanger channel unit cell equivalent flexibility coefficient matrix is obtained through numerical solutionSolving the corresponding equivalent elastic modulus, poisson ratio and shear modulus; equivalent flexibility coefficient matrix corresponds to equivalent rigidity coefficient lower limit matrix of partial periodic heat exchanger channel +.>
wherein ,is an equivalent rigidity coefficient lower limit matrix;An inverse matrix of the equivalent stiffness coefficient lower limit matrix; i, j, k, l are all direction vectors, and the values of the direction vectors are 1,2 and 3; e is the equivalent elastic modulus; v is the equivalent Poisson's ratio; g is the equivalent shear modulus; x, y, z are coordinate axis directions.
Respectively solving the upper and lower limits of equivalent stiffness coefficients of the channels on the cold and hot sides of the partial periodic heat exchanger, and completing the calculation of equivalent mechanical properties of the channels of the partial periodic heat exchanger with different cold and hot channel structures in an average value mode;
wherein, the subscript U represents the equivalent mechanical modulus corresponding to the upper limit of the equivalent stiffness coefficient; subscript S represents the equivalent mechanical modulus corresponding to the lower limit of the equivalent stiffness coefficient; avg represents the average value.
Another object of the present invention is to provide an equivalent mechanical property prediction system for a partial periodic heat exchanger channel, which uses the partial periodic heat exchanger channel, and the equivalent mechanical property prediction system for the partial periodic heat exchanger channel includes:
the characteristic displacement setting module is used for setting characteristic displacement based on a homogenization theory, and establishing a simplified solving equation of the upper and lower limits of equivalent stiffness coefficients of the partial periodic distribution heat exchanger channels relative to the deformation energy form;
the partial periodic heat exchanger channel model building module is used for building a partial periodic heat exchanger channel unit finite element model and setting geometric parameters and material properties of the partial periodic heat exchanger channel unit finite element model;
the method comprises the steps of applying node periodic displacement constraint conditions to periodic surfaces of a partial periodic heat exchanger channel unit cell finite element model, applying node rigid displacement constraint conditions to non-periodic surfaces, setting unit characteristic strain fields, completing stretching and shearing simulation under nine groups of node displacement constraint equations, deriving deformation energy II results, and solving partial periodic heat exchanger channel equivalent stiffness coefficient upper limits;
The system comprises a partial periodic heat exchanger channel equivalent stiffness coefficient lower limit calculation module, a node periodic displacement constraint condition, a free boundary condition, a unit characteristic stress field, a stretching and shearing simulation under nine groups of node displacement constraint equations, a partial periodic heat exchanger channel equivalent stiffness coefficient matrix and a matrix inversion determination module, wherein the node periodic displacement constraint condition is applied to the periodic surface of a partial periodic heat exchanger channel unit finite element model, the free boundary condition is set for an aperiodic surface, the unit characteristic stress field is set, and the partial periodic heat exchanger channel equivalent stiffness coefficient lower limit is determined by the matrix inversion.
The invention also aims to provide an application of the equivalent mechanical property prediction method to the structural design of the plate-fin heat exchanger, wherein the equivalent mechanical property prediction method is used for calculation according to actual working conditions and design parameters of the heat exchanger; constructing a single cell finite element calculation model of the plate-fin heat exchanger with partial periodic characteristics according to the calculation model, inputting corresponding geometric parameters, material parameters and working conditions, and performing simulation by using the established software system to perform prediction calculation on equivalent mechanical properties of the partial periodic heat exchanger channel; and finally obtaining the upper limit value and the lower limit value of the equivalent rigidity coefficient of the partial periodic plate-fin heat exchanger channel.
Another object of the present invention is to provide a computer device comprising a memory and a processor, the memory storing a computer program which, when executed by the processor, causes the processor to perform the steps of the method for predicting equivalent mechanical properties of a partial periodic heat exchanger channel.
Another object of the present invention is to provide a computer readable storage medium storing a computer program which, when executed by a processor, causes the processor to perform the steps of the method for predicting equivalent mechanical properties of a partial periodic heat exchanger channel.
The invention further aims to provide an information data processing terminal which is used for realizing the equivalent mechanical property prediction system for the partial periodic heat exchanger channel.
In combination with the technical scheme and the technical problems to be solved, the technical scheme to be protected has the following advantages and positive effects:
first, the present invention simplifies the actual deformation state of the partial periodically distributed heat exchanger channels into a rigid deformation and flexible deformation interval. And setting three types of node sets of vertical surfaces, edges and vertexes for the partial periodic heat exchanger channel unit finite element calculation model, and respectively defining different node displacement constraint equations for each corresponding node set of the periodic surface and the aperiodic surface of the calculation model. The non-periodic surface of the heat exchanger channel unit cell is respectively provided with loading conditions of rigid unit characteristic strain and flexible unit characteristic stress, other surfaces are set as periodic boundary conditions, and the calculation of the equivalent mechanical properties of partial periodic heat exchanger channels with different cold and hot channel structures can be completed. The established method for calculating the equivalent mechanical properties of the partial periodic heat exchanger channels can be applied to the strength design of the plate-fin heat exchanger.
The invention respectively provides a unit characteristic strain field when solving the upper limit and the lower limit of the equivalent stiffness coefficient of the partial periodic heat exchanger channelCharacteristic strain field corresponding to unit characteristic stress field +.>By defining deformation energy form equations of equivalent stiffness and equivalent flexibility coefficient under the characteristic strain field and characteristic stress field loading respectively, the problems of complex programming, repeated calculation and the like realized by a conventional calculation method are avoided on the premise of ensuring the calculation accuracy. The upper and lower limit results of the equivalent stiffness coefficient can be obtained by calculating the deformation energy results directly output by the finite element.
Secondly, the method for predicting the equivalent mechanical properties of the partial periodic heat exchanger channels constructed by the invention can be generally applied to the structural design of the partial periodic heat exchanger channels with different cold and hot sides, can improve the accuracy of predicting the equivalent mechanical properties of the partial periodic heat exchanger channels, reduces the calculated amount and can be widely popularized.
The plate-fin heat exchanger used in high-temperature and high-pressure environment needs to pay attention to the integrity and reliability, and the mechanical properties of the plate-fin heat exchanger need to be evaluated and analyzed. However, the current technology is only applicable to mechanical property analysis of periodic heat exchanger channels with the same cold and hot sides. However, the cold and hot sides of the heat exchanger operating conditions typically have different flow rates, operating pressures and temperatures, resulting in different cold and hot channel configurations for the plate fin heat exchanger used. Therefore, the invention provides an equivalent mechanical property prediction method for partial periodic heat exchanger channels.
Thirdly, the equivalent mechanical property prediction method provided by the embodiment of the invention is specifically applied and has positive effects:
1) Consider the aperiodic factor: in practice, the hot and cold side channels of a plate-fin heat exchanger generally have different configurations, which results in a non-periodic nature of the direction of stacking of the hot and cold channels. The conventional progressive homogenization method is only suitable for calculating the equivalent mechanical property of the periodic structure. Therefore, the aperiodic factors need to be considered in the prediction method and the corresponding correction needs to be performed. According to the invention, the actual deformation state of the partial periodic distribution heat exchanger channels is simplified into the rigid deformation and flexible deformation interval, and the calculation of equivalent mechanical properties of the partial periodic heat exchanger channels with different cold and hot channel structures can be completed.
2) Optimizing a finite element calculation model: the finite element calculation model is a core part of a prediction method, and needs to be optimized to improve calculation accuracy and efficiency. The invention provides a part periodic unit characteristic strain fieldCharacteristic strain field corresponding to unit characteristic stress field +.>By defining deformation energy form equations of equivalent stiffness and equivalent flexibility coefficient under the characteristic strain field and characteristic stress field loading respectively, the problems of complex programming and repeated calculation of conventional numerical calculation are avoided on the premise of ensuring calculation accuracy. The upper and lower limit results of the equivalent stiffness coefficient can be obtained by calculating the deformation energy results directly output by the finite element.
3) Consider a variety of heat exchanger configurations: the implementation object of the invention is a plate-fin heat exchanger, but in practical application, the prediction method can be suitable for other heat exchanger structures of different types, and the requirements of different application scenes are met.
4) Consider a variety of materials and operating conditions: different materials and working conditions can have different effects on the equivalent mechanical properties of the heat exchanger. The prediction method can consider various materials and working conditions to meet the requirements of different application scenes, and provides accurate prediction results for heat exchanger channels under different materials and working conditions.
5) Introducing a machine learning technology: the equivalent mechanical property data set of the corresponding partial periodic heat exchanger channel of the actual working condition and the design parameter can be input into the model for training by introducing a machine learning algorithm, so that an accurate and rapid prediction result is obtained.
6) Big data technology is applied: the equivalent mechanical property data of partial periodic heat exchanger channels under different working conditions can be analyzed by utilizing a big data technology, so that an equivalent mechanical property prediction model under different working conditions is obtained, and a more accurate and reliable prediction result is provided for engineering design.
Drawings
In order to more clearly illustrate the technical solutions of the embodiments of the present invention, the drawings that are needed in the embodiments of the present invention will be briefly described below, and it is obvious that the drawings described below are only some embodiments of the present invention, and other drawings may be obtained according to these drawings without inventive effort for a person skilled in the art.
FIG. 1 is a flow chart of a method for predicting equivalent mechanical properties of a partial periodic heat exchanger channel provided by an embodiment of the invention;
fig. 2 is a schematic diagram of a method for predicting equivalent mechanical properties of a partial periodic heat exchanger channel according to an embodiment of the present invention.
Detailed Description
The present invention will be described in further detail with reference to the following examples in order to make the objects, technical solutions and advantages of the present invention more apparent. It should be understood that the specific embodiments described herein are for purposes of illustration only and are not intended to limit the scope of the invention.
Aiming at the problems existing in the prior art, the invention provides an equivalent mechanical property prediction method for a part of periodic heat exchanger channels, and the invention is described in detail below with reference to the accompanying drawings.
As shown in fig. 1, the method for predicting equivalent mechanical properties of a part of periodic heat exchanger channels provided by the embodiment of the invention comprises the following steps:
s101, based on a homogenization theory, establishing a simplified solving equation of the upper and lower limits of equivalent stiffness coefficients of partial periodically distributed heat exchanger channels with respect to deformation energy forms;
s102, establishing a heat exchanger channel unit finite element model, and setting geometric parameters and material properties of the heat exchanger channel unit finite element model;
s103, setting a unit characteristic strain field, completing stretching and shearing simulation under a nine-group node displacement constraint equation, and solving an equivalent stiffness coefficient upper limit;
s104, setting a unit characteristic stress field, and completing calculation of an equivalent flexibility coefficient matrix of the heat exchanger channel, wherein an inverse matrix of the equivalent flexibility coefficient matrix is an equivalent rigidity coefficient lower limit.
As a preferred embodiment, as shown in fig. 2, the method for predicting the upper and lower limits of equivalent mechanical properties of a partial periodic heat exchanger channel based on a homogenization theory provided by the embodiment of the invention includes the following steps:
(1) Based on homogenization theory, respectively setting characteristic displacement andEstablishing a simplified solving equation of the upper and lower limits of equivalent rigidity coefficients of partial periodic distribution heat exchanger channels with respect to deformation energy forms, wherein the method specifically comprises the following steps:
According to the homogenization theory, the macroscopic scale and the microscopic scale of the heat exchanger channel are related by utilizing small parameters, and the characteristic displacement is set andConsidering the unit characteristic stress field or the unit characteristic stress field and the strain field caused by the unit heterogeneity as the characteristic stress field directly applied on the boundary, the unit characteristic stress field or the unit characteristic stress field and the strain field caused by the unit heterogeneity can be directly given by setting the displacement constraint of the boundary node, so that the equivalent stiffness coefficient and the equivalent flexibility coefficient of the partial periodic distribution heat exchanger channel can be deduced based on the variationSimplifying and solving an equation in the form of a shape energy II;
for the energy form equation of the upper limit of the equivalent stiffness coefficient:
diagonal stiffness coefficient:
off-diagonal stiffness coefficient:
wherein ,for equivalent stiffness coefficient, superscript H represents equivalent; i, j, k, l are all direction vectors, and the values of the direction vectors are 1,2 and 3; y is the unit cell volume; II is deformation energy;The strain field is characterized by units, and the boundary constraint equation is as follows: />
Stretching in the x direction:
stretching in the y direction:
stretching in the z direction:
stretching in x and y directions:
stretching in x and z directions:
stretching in y and z directions:
shearing in xy direction:
shearing in xz direction:
shearing in yz direction:
wherein ,the deformation field is a unit characteristic strain field under rigid deformation, and represents deformation of a part of periodic structure in the macroscopic k-l direction under rigid deformation and in the microscopic m direction. U+ is the surface of the unit cell that is positive perpendicular to the x-axis, U-is the surface of the unit cell that is negative perpendicular to the x-axis, and the surfaces V+, V-, W+ and W-are similarly defined. a, b, c represent the lengths of the unit cells along the x, y, and z coordinate axes, respectively.
For the energy form equation of the lower limit of the equivalent stiffness coefficient:
diagonal compliance coefficient:
off-diagonal compliance coefficient:
lower limit of equivalent stiffness coefficient:
wherein ,the superscript H represents the equivalent for the equivalent compliance coefficient; i, j, k, l are all direction vectors, and the values of the direction vectors are 1,2 and 3; y is the unit cell volume; the II is deformation energy.The boundary constraint equation of the characteristic strain field corresponding to the unit characteristic stress field is as follows:
stretching in the x direction:
stretching in the y direction:
stretching in the z direction:
and (3) shearing in the yz direction:
shearing in the xz direction:
shearing in the xy direction:
stretching in x and y directions:
stretching in x and z directions:
y and z stretching:
wherein ,the characteristic strain field corresponding to the unit characteristic stress field under the flexible deformation represents the deformation of a part of periodic structure in the macroscopic k-l direction under the flexible deformation and in the microscopic m direction. U+ is the surface of the unit cell that is positive perpendicular to the x-axis, U-is the surface of the unit cell that is negative perpendicular to the x-axis, and the surfaces V+, V-, W+ and W-are similarly defined. a, b, c represent the lengths of the unit cells along the x, y, and z coordinate axes, respectively.
(2) Dividing a heat exchanger channel into various representative volume units according to regions, establishing a heat exchanger channel unit finite element model, and setting geometric parameters and material properties of the heat exchanger channel unit finite element model; wherein the geometric parameters comprise unit cell length, unit cell width, unit cell height, channel wall thickness and channel spacing, and the material properties comprise elastic modulus, poisson ratio and temperature; materials include metallic materials, non-metallic materials, and composite materials.
(3) Setting three types of node sets of a vertical face, a side and a vertex for the heat exchanger channel unit finite element model, and applying a node periodic displacement constraint condition to the periodic surface of the heat exchanger channel unit finite element model; and applying node rigidity displacement constraint conditions to the aperiodic surface, setting a unit characteristic strain field, completing stretching and shearing simulation under nine groups of node displacement constraint equations, finally directly deriving deformation energy II results, and solving the upper limit of equivalent rigidity coefficients of partial periodically distributed heat exchanger channels.
(4) Setting three types of node sets of a vertical face, a side and a vertex for the heat exchanger channel unit finite element model, and applying a node periodic displacement constraint condition to the periodic surface of the heat exchanger channel unit finite element model; setting a free boundary condition for the aperiodic surface, setting a unit characteristic stress field, and finally directly deriving a deformation energy II result through stretching and shearing simulation under a nine-group node displacement constraint equation to finish the calculation of the equivalent flexibility coefficient matrix of the heat exchanger channel; and inverting the flexibility matrix to obtain the equivalent rigidity coefficient lower limit of the partial periodic distribution heat exchanger channel.
The equivalent mechanical property prediction system for the partial periodic heat exchanger channel provided by the embodiment of the invention comprises the following components:
The characteristic displacement setting module is used for setting characteristic displacement based on a homogenization theory, and establishing a simplified solving equation of the upper and lower limits of equivalent stiffness coefficients of the partial periodic distribution heat exchanger channels relative to the deformation energy form;
the heat exchanger channel model building module is used for building a heat exchanger channel unit finite element model and setting geometric parameters and material properties of the heat exchanger channel unit finite element model;
the rigidity coefficient upper limit calculation module is used for applying node periodic displacement constraint conditions to the periodic surface of the heat exchanger channel unit cell finite element model, applying node rigid displacement constraint conditions to the non-periodic surface, setting a unit characteristic strain field, completing stretching and shearing simulation under nine groups of node displacement constraint equations, deriving deformation energy II results, and solving the equivalent rigidity coefficient upper limit of the partial periodic distribution heat exchanger channel;
the equivalent stiffness coefficient lower limit calculation module is used for applying node periodic displacement constraint conditions to the periodic surface of the heat exchanger channel unit cell finite element model, setting free boundary conditions to the aperiodic surface, setting unit characteristic stress fields, calculating an equivalent stiffness coefficient matrix of the heat exchanger channel through stretching and shearing simulation under nine groups of node displacement constraint equations, and determining the equivalent stiffness coefficient lower limit by inverting the matrix.
As a preferred embodiment, the method for calculating the equivalent mechanical properties of the partial periodic heat exchanger channels constructed by the equivalent mechanical property prediction system for the partial periodic heat exchanger channels provided by the embodiment of the invention can be applied to structural designs of plate-fin heat exchangers with different cold-hot side channel structures or arrangement modes. In a specific application, a user can calculate according to actual working conditions and design parameters of the heat exchanger by using the method provided by the embodiment of the invention. Specifically, a user needs to construct a single-cell finite element calculation model of the plate-fin heat exchanger with partial periodic characteristics according to the calculation model provided by the invention, input corresponding geometric parameters, material parameters and working conditions, and simulate by using a software system established by the prediction method to perform prediction calculation of equivalent mechanical properties of a partial periodic heat exchanger channel. Finally, the user can obtain the upper and lower limit values of the equivalent stiffness coefficient of the partial periodic plate-fin heat exchanger channel. The method for predicting the equivalent mechanical properties of the partial periodic heat exchanger channels improves the accuracy of predicting the equivalent mechanical properties of the partial periodic heat exchanger channels and reduces the calculated amount. The method can be applied to various occasions needing to use the plate-fin heat exchanger, such as the fields of petrochemical industry, electric power, refrigeration, heating and the like. According to the method provided by the embodiment of the invention, equivalent mechanical performance parameters of the plate-fin heat exchanger with different cold and hot sides can be obtained by calculation, and the structural design and optimization of the plate-fin heat exchanger can be performed according to the parameters.
The equivalent mechanical property prediction method for the partial periodic heat exchanger channel provided by the embodiment of the invention is based on a homogenization theory, and utilizes small parameters to correlate the heat exchanger on a macroscopic scale with channel unit cells on a microscopic scale. Considering that the heat exchanger channel has uneven characteristics on a microscopic scale due to the existence of holes, substituting mechanical variables which are gradually expanded by small parameters into a unit cell control equation, and assuming that the actual deformation state of the part of periodically distributed heat exchanger channel is between rigid deformation and flexible deformation; by defining the unit characteristic strain and the unit characteristic stress, the characteristic displacement is respectively set andThe upper and lower equivalent stiffness coefficient limits of the partial periodic distribution heat exchanger channels are established, and the simplified solving equation of the deformation energy form is as follows:
for the energy form equation of the upper limit of the equivalent stiffness coefficient:
diagonal stiffness coefficient:
off-diagonal stiffness coefficient:
wherein ,for equivalent stiffness coefficient, superscript H represents equivalent; i, j, k, l are all direction vectors, and the values of the direction vectors are 1,2 and 3; y is the unit cell volume; II is deformation energy;Is a unit characteristic strain field.
For the energy form equation of the lower limit of the equivalent stiffness coefficient:
diagonal compliance coefficient:
Off-diagonal compliance coefficient:
lower limit of equivalent stiffness coefficient:
wherein ,the superscript H represents the equivalent for the equivalent compliance coefficient; i, j, k, l are all direction vectors, and the values of the direction vectors are 1,2 and 3; y is the unit cell volume; the II is deformation energy.The characteristic strain field corresponds to the unit characteristic stress field.
Analyzing a part of periodic distribution heat exchanger channel model, setting three types of node sets of a vertical face, an edge and a vertex on a channel unit cell calculation model, and respectively defining different node displacement constraint equations for each corresponding node set of a periodic surface and a non-periodic surface of the calculation model; and then setting a unit characteristic stress field and a unit characteristic stress field, respectively completing the stretching and shearing simulation under nine groups of node displacement constraint equations, and finally deriving a deformation energy II result, thus completing the calculation of the upper and lower limits of the equivalent stiffness coefficient of the heat exchanger channel.
(1) The boundary constraint equation for the upper limit calculation of the equivalent stiffness coefficient is as follows:
stretching in the x direction:
stretching in the y direction:
stretching in the z direction:
stretching in x and y directions:
stretching in x and z directions:
stretching in y and z directions:
shearing in xy direction:
shearing in xz direction:
shearing in yz direction:
wherein ,the deformation field is a unit characteristic strain field under rigid deformation, and represents deformation of a part of periodic structure in the macroscopic k-l direction under rigid deformation and in the microscopic m direction. U+ is the surface of the unit cell that is positive perpendicular to the x-axis, U-is the surface of the unit cell that is negative perpendicular to the x-axis, and the surfaces V+, V-, W+ and W-are similarly defined. a, b, c represent the lengths of the unit cells along the x, y, and z coordinate axes, respectively.
According to the nine groups of stretching and shearing simulation, the deformation energy II result is derived, and the partial periodic distribution heat exchanger channel equivalent stiffness coefficient upper limit matrix is obtained by solvingAnd further solving the corresponding equivalent elastic modulus, poisson ratio and shear modulus.
wherein ,is an equivalent stiffness coefficient upper limit matrix;An inverse matrix of the equivalent stiffness coefficient upper limit matrix; i, j, k, l are all direction vectors, and the values of the direction vectors are 1,2 and 3; e is the equivalent elastic modulus; v is the equivalent Poisson's ratio; g is the equivalent shear modulus; x, y, z are coordinate axis directions.
(2) The boundary constraint equation for the equivalent stiffness coefficient lower limit calculation is as follows:
stretching in the x direction:
stretching in the y direction:
stretching in the z direction:
and (3) shearing in the yz direction:
shearing in the xz direction:
shearing in the xy direction:
stretching in x and y directions:
stretching in x and z directions:
y and z stretching:
wherein ,the characteristic strain field corresponding to the unit characteristic stress field under the flexible deformation represents the part of the periodic structure under the flexible deformationDeformation in macroscopic k-l direction followed by deformation in microscopic m direction. U+ is the surface of the unit cell that is positive perpendicular to the x-axis, U-is the surface of the unit cell that is negative perpendicular to the x-axis, and the surfaces V+, V-, W+ and W-are similarly defined. a, b, c represent the lengths of the unit cells along the x, y, and z coordinate axes, respectively.
According to the nine groups of stretching and shearing simulation, a deformation energy II result is derived, and a heat exchanger channel unit cell equivalent flexibility coefficient matrix is obtained by numerical solutionAnd solving the corresponding equivalent elastic modulus, poisson ratio and shear modulus. The equivalent flexibility coefficient matrix corresponds to the equivalent rigidity coefficient lower limit matrix of the heat exchanger channel>
wherein ,is an equivalent rigidity coefficient lower limit matrix;An inverse matrix of the equivalent stiffness coefficient lower limit matrix; i, j, k, l are all direction vectors, and the values of the direction vectors are 1,2 and 3; e is the equivalent elastic modulus; v is the equivalent Poisson's ratio; g is the equivalent shear modulus; x, y, z are coordinate axis directions.
And finally, respectively solving the upper and lower limits of equivalent stiffness coefficients of the rectangular and circular channels on the cold side and the hot side of the heat exchanger, and finishing the calculation of equivalent mechanical properties of the heat exchanger channels with different cold-hot channel structures in an average value mode.
Wherein, the subscript U represents the equivalent mechanical modulus corresponding to the upper limit of the equivalent stiffness coefficient; subscript S represents the equivalent mechanical modulus corresponding to the lower limit of the equivalent stiffness coefficient; avg represents the average value.
In order to prove the inventive and technical value of the technical solution of the present invention, this section is an application example on specific products or related technologies of the claim technical solution.
The method for predicting the equivalent mechanical properties of the partial periodic heat exchanger channels established by the embodiment of the invention can be used for structural design of the plate-fin heat exchanger channels.
As a preferred embodiment, a part of the periodic heat exchanger channel unit finite element model is built. And fitting the relation functions of average equivalent Young's modulus, shear modulus, poisson's ratio and temperature of the partial periodic circular and rectangular heat exchange channels respectively.
And carrying out thermal-mechanical deformation analysis on the partial periodic heat exchanger core equivalent model under the assumed temperature field, and finding that the calculation errors of the mechanical deformation and the thermal deformation of the partial periodic heat exchanger channel equivalent mechanical model are respectively smaller than 4% and 1% per mill, but the calculation time of the equivalent model can be reduced by more than 70 times compared with the actual model. The method can rapidly and accurately realize the analysis and calculation of the intensity of the partial periodic micro-channel heat exchanger, effectively avoid the complex modeling process of an actual model and greatly improve the calculation efficiency.
It should be noted that the embodiments of the present invention can be realized in hardware, software, or a combination of software and hardware. The hardware portion may be implemented using dedicated logic; the software portions may be stored in a memory and executed by a suitable instruction execution system, such as a microprocessor or special purpose design hardware. Those of ordinary skill in the art will appreciate that the apparatus and methods described above may be implemented using computer executable instructions and/or embodied in processor control code, such as provided on a carrier medium such as a magnetic disk, CD or DVD-ROM, a programmable memory such as read only memory (firmware), or a data carrier such as an optical or electronic signal carrier. The device of the present invention and its modules may be implemented by hardware circuitry, such as very large scale integrated circuits or gate arrays, semiconductors such as logic chips, transistors, etc., or programmable hardware devices such as field programmable gate arrays, programmable logic devices, etc., as well as software executed by various types of processors, or by a combination of the above hardware circuitry and software, such as firmware.
The foregoing is merely illustrative of specific embodiments of the present invention, and the scope of the invention is not limited thereto, but any modifications, equivalents, improvements and alternatives falling within the spirit and principles of the present invention will be apparent to those skilled in the art within the scope of the present invention.
Claims (10)
1. The equivalent mechanical property prediction method for the partial periodic heat exchanger channel is characterized by comprising the following steps of: the system constructs a simplified solving equation of the upper and lower limits of equivalent rigidity coefficients of partial periodic distribution heat exchanger channels relative to deformation energy forms; establishing a heat exchanger channel unit finite element model, and setting geometric parameters and material properties of the heat exchanger channel unit finite element model; setting a unit characteristic strain field, completing stretching and shearing simulation under a nine-group node displacement constraint equation, and solving an upper limit of an equivalent stiffness coefficient; and setting a unit characteristic stress field, calculating an equivalent flexibility coefficient matrix of the heat exchanger channel, and inverting, wherein an inverse matrix of the equivalent flexibility coefficient matrix is an equivalent stiffness coefficient lower limit.
2. The method for predicting equivalent mechanical properties of a partial periodic heat exchanger channel according to claim 1, comprising the steps of:
Firstly, based on a homogenization theory, setting characteristic displacement respectively, and establishing a simplified solving equation of the upper and lower limits of equivalent stiffness coefficients of partial periodically distributed heat exchanger channels with respect to deformation energy forms;
step two, establishing a heat exchanger channel unit finite element model, and setting geometric parameters and material properties of the heat exchanger channel unit finite element model;
step three, applying node periodic displacement constraint conditions to the periodic surface of the channel unit cell finite element model of the heat exchanger, applying node rigid displacement constraint conditions to the aperiodic surface, setting a unit characteristic strain field, completing stretching and shearing simulation under nine groups of node displacement constraint equations, and solving the upper limit of an equivalent stiffness coefficient;
and step four, applying a node periodic displacement constraint condition to the periodic surface of the heat exchanger channel unit cell finite element model, setting a free boundary condition to the aperiodic surface, setting a unit characteristic stress field, and completing calculation of an equivalent flexibility coefficient matrix of the heat exchanger channel through stretching and shearing simulation under a nine-group node displacement constraint equation, wherein an inverse matrix of the equivalent flexibility coefficient matrix is an equivalent rigidity coefficient lower limit.
3. The method for predicting equivalent mechanical properties of a partial periodic heat exchanger channel according to claim 2, wherein in step one, according to a homogenization theory, a macroscopic scale and a microscopic scale of the heat exchanger channel are correlated by using small parameters; by separately setting characteristic displacements
and
Converting a unit characteristic stress field or a unit characteristic stress field and a strain field caused by unit heterogeneity into a characteristic stress field directly applied to a boundary, and directly setting by setting boundary node displacement constraint, thereby deriving an equivalent stiffness coefficient and an equivalent flexibility coefficient of a part of periodically distributed heat exchanger channel based on a simplified solving equation of deformation energy II form;
for the energy form equation of the upper limit of the equivalent stiffness coefficient:
diagonal stiffness coefficient:
off-diagonal stiffness coefficient:
wherein ,for equivalent stiffness coefficient, superscript H represents equivalent; i, j, k, l are all direction vectors, and the values of the direction vectors are 1,2 and 3; y is the unit cell volume; II is deformation energy;A unit characteristic strain field;
for the energy form equation of the lower limit of the equivalent stiffness coefficient:
diagonal compliance coefficient:
off-diagonal compliance coefficient:
lower limit of equivalent stiffness coefficient:
wherein ,the superscript H represents the equivalent for the equivalent compliance coefficient; i, j, k, l are all direction vectors, and the values of the direction vectors are 1,2 and 3; y is the unit cell volume; II is deformation energy;The characteristic strain field corresponds to the unit characteristic stress field.
4. The method for predicting equivalent mechanical properties of a partial periodic heat exchanger channel according to claim 2, wherein the geometric parameters of the heat exchanger channel unit cell finite element model in the second step include unit cell length, unit cell width, unit cell height, channel wall thickness and channel spacing, and the material properties include elastic modulus, poisson ratio and temperature; materials include metallic materials, non-metallic materials, and composite materials.
5. The method for predicting equivalent mechanical properties of a partial periodic heat exchanger channel according to claim 2, wherein in the third step, three types of node sets of elevation, edge and vertex are set for a unit cell finite element model of the heat exchanger channel, and different node displacement constraint equations are defined for each corresponding node set of the periodic surface and the non-periodic surface of the unit cell finite element model of the heat exchanger channel; setting a unit characteristic strain field, respectively completing stretching and shearing simulation under nine groups of node displacement constraint equations, finally leading out deformation energy II results, and completing calculation of the upper limit of the equivalent stiffness coefficient of the partial periodic distribution heat exchanger channel;
the boundary constraint equation for calculating the upper limit of the equivalent stiffness coefficient is as follows:
stretching in the x direction:
stretching in the y direction:
stretching in the z direction:
stretching in x and y directions:
stretching in x and z directions:
stretching in y and z directions:
shearing in xy direction:
shearing in xz direction:
shearing in yz direction:
wherein ,the deformation field is a unit characteristic strain field under rigid deformation, and represents deformation of a part of periodic structure in the macroscopic k-l direction under rigid deformation and in the microscopic m direction; u+ is a single cell surface perpendicular to the positive x-axis, U-is a single cell surface perpendicular to the negative x-axis, and the surfaces V+, V-, W+ and W-are similarly defined; a, b, c represent the lengths of the unit cells along the x, y and z coordinate axes, respectively;
According to nine groups of stretching and shearing simulation, a deformation energy II result is derived, and a partial periodic distribution heat exchanger channel equivalent stiffness coefficient upper limit matrix is obtained through solvingEquivalent elastic modulus, poisson ratio and shear modulus;
wherein ,is equivalent to the rigidityA coefficient upper limit matrix;An inverse matrix of the equivalent stiffness coefficient upper limit matrix; i, j, k, l are all direction vectors, and the values of the direction vectors are 1,2 and 3; e is the equivalent elastic modulus; v is the equivalent Poisson's ratio; g is the equivalent shear modulus; x, y, z are coordinate axis directions.
6. The method for predicting equivalent mechanical properties of a partial periodic heat exchanger channel according to claim 2, wherein in step four, three types of node sets of elevation, edge and vertex are set for a unit cell finite element model of the heat exchanger channel, and a node displacement constraint equation is defined for a corresponding node set of a periodic surface of the unit cell finite element model of the heat exchanger channel; setting a free boundary condition on the aperiodic surface, setting a unit characteristic stress field, completing the stretching and shearing simulation under a nine-group node displacement constraint equation, and finally directly leading out a deformation energy II result to complete the calculation of an equivalent flexibility coefficient matrix; inverting the equivalent flexibility coefficient matrix, wherein the inverse matrix of the equivalent flexibility coefficient matrix is the lower limit result of the equivalent stiffness coefficient;
The boundary constraint equation for calculating the equivalent stiffness coefficient lower limit is as follows:
stretching in the x direction:
stretching in the y direction:
stretching in the z direction:
and (3) shearing in the yz direction:
shearing in the xz direction:
shearing in the xy direction:
stretching in x and y directions:
stretching in x and z directions:
y and z stretching:
wherein ,the characteristic strain field corresponding to the unit characteristic stress field under the flexible deformation represents the deformation of a part of periodic structure in the macroscopic k-l direction under the flexible deformation and in the microscopic m direction; u+ is a single cell surface perpendicular to the positive x-axis, U-is a single cell surface perpendicular to the negative x-axis, and the surfaces V+, V-, W+ and W-are similarly defined; a, b, c represent the lengths of the unit cells along the x, y and z coordinate axes, respectively;
according to nine groups of stretching and shearing simulation, a deformation energy II result is derived, and a heat exchanger channel unit cell equivalent flexibility coefficient matrix is obtained through numerical solutionSolving the corresponding equivalent elastic modulus, poisson ratio and shear modulus; equivalent flexibility coefficient matrix corresponds to equivalent rigidity coefficient lower limit matrix of heat exchanger channel>
wherein ,is an equivalent rigidity coefficient lower limit matrix;An inverse matrix of the equivalent stiffness coefficient lower limit matrix; i, j, k, l are all direction vectors, and the values of the direction vectors are 1,2 and 3; e is the equivalent elastic modulus; v is the equivalent Poisson's ratio; g is the equivalent shear modulus; x, y and z are coordinate axis directions;
Respectively solving the upper and lower limits of equivalent stiffness coefficients of rectangular and circular channels on the cold side and the hot side of the heat exchanger, and completing calculation of equivalent mechanical properties of the heat exchanger channels with different cold and hot channel structures in an average value mode;
wherein, the subscript U represents the equivalent mechanical modulus corresponding to the upper limit of the equivalent stiffness coefficient; subscript S represents the equivalent mechanical modulus corresponding to the lower limit of the equivalent stiffness coefficient; avg represents the average value.
7. An application of the equivalent mechanical property prediction method according to any one of claims 1 to 6 in the structural design of a plate-fin heat exchanger, wherein the equivalent mechanical property prediction method is used for calculation according to actual working conditions and design parameters of the heat exchanger; constructing a single cell finite element calculation model of the plate-fin heat exchanger with partial periodic characteristics according to the calculation model, inputting corresponding geometric parameters, material parameters and working conditions, and performing simulation by using the established software system to perform prediction calculation on equivalent mechanical properties of the partial periodic heat exchanger channel; and finally obtaining the upper limit value and the lower limit value of the equivalent rigidity coefficient of the partial periodic plate-fin heat exchanger channel.
8. An equivalent mechanical property prediction system for a partial periodic heat exchanger channel, applying the equivalent mechanical property prediction method for a partial periodic heat exchanger channel according to any one of claims 1 to 6, comprising:
The characteristic displacement setting module is used for setting characteristic displacement based on a homogenization theory, and establishing a simplified solving equation of the upper and lower limits of equivalent stiffness coefficients of the partial periodic distribution heat exchanger channels relative to the deformation energy form;
the heat exchanger channel model building module is used for building a heat exchanger channel unit finite element model and setting geometric parameters and material properties of the heat exchanger channel unit finite element model;
the rigidity coefficient upper limit calculation module is used for applying node periodic displacement constraint conditions to the periodic surface of the heat exchanger channel unit cell finite element model, applying node rigid displacement constraint conditions to the non-periodic surface, setting a unit characteristic strain field, completing stretching and shearing simulation under nine groups of node displacement constraint equations, deriving deformation energy II results, and solving the equivalent rigidity coefficient upper limit of the partial periodic distribution heat exchanger channel;
the equivalent stiffness coefficient lower limit calculation module is used for applying node periodic displacement constraint conditions to the periodic surface of the heat exchanger channel unit cell finite element model, setting free boundary conditions to the aperiodic surface, setting unit characteristic stress fields, calculating an equivalent stiffness coefficient matrix of the heat exchanger channel through stretching and shearing simulation under nine groups of node displacement constraint equations, and determining the equivalent stiffness coefficient lower limit by inverting the matrix.
9. A computer readable storage medium storing a computer program which, when executed by a processor, causes the processor to perform the steps of the equivalent mechanical property prediction method for a partial periodic heat exchanger channel as claimed in any one of claims 1 to 6.
10. An information data processing terminal for implementing the equivalent mechanical property prediction system for a partial periodic heat exchanger channel according to claim 7.
Priority Applications (1)
| Application Number | Priority Date | Filing Date | Title |
|---|---|---|---|
| CN202310680460.2A CN116738707B (en) | 2023-06-08 | 2023-06-08 | Equivalent mechanical property prediction method and system for partial periodic heat exchanger channel |
Applications Claiming Priority (1)
| Application Number | Priority Date | Filing Date | Title |
|---|---|---|---|
| CN202310680460.2A CN116738707B (en) | 2023-06-08 | 2023-06-08 | Equivalent mechanical property prediction method and system for partial periodic heat exchanger channel |
Publications (2)
| Publication Number | Publication Date |
|---|---|
| CN116738707A true CN116738707A (en) | 2023-09-12 |
| CN116738707B CN116738707B (en) | 2024-05-17 |
Family
ID=87903801
Family Applications (1)
| Application Number | Title | Priority Date | Filing Date |
|---|---|---|---|
| CN202310680460.2A Active CN116738707B (en) | 2023-06-08 | 2023-06-08 | Equivalent mechanical property prediction method and system for partial periodic heat exchanger channel |
Country Status (1)
| Country | Link |
|---|---|
| CN (1) | CN116738707B (en) |
Cited By (1)
| Publication number | Priority date | Publication date | Assignee | Title |
|---|---|---|---|---|
| CN117540494A (en) * | 2024-01-10 | 2024-02-09 | 天目山实验室 | Aviation cabin structure reduced order analysis method, system and equipment |
Citations (4)
| Publication number | Priority date | Publication date | Assignee | Title |
|---|---|---|---|---|
| US20060139347A1 (en) * | 2004-12-27 | 2006-06-29 | Choi Min G | Method and system of real-time graphical simulation of large rotational deformation and manipulation using modal warping |
| CN112560167A (en) * | 2020-11-10 | 2021-03-26 | 北京航空航天大学 | Wing structure mechanics high-fidelity reduced-order simulation method, electronic equipment and storage medium |
| CN115718962A (en) * | 2022-11-25 | 2023-02-28 | 大连理工大学 | Efficient buckling optimization method for reinforced shell based on beam shell coupling model |
| CN115859715A (en) * | 2022-11-23 | 2023-03-28 | 西部超导材料科技股份有限公司 | Method for calculating equivalent performance of periodic porous structure material |
-
2023
- 2023-06-08 CN CN202310680460.2A patent/CN116738707B/en active Active
Patent Citations (4)
| Publication number | Priority date | Publication date | Assignee | Title |
|---|---|---|---|---|
| US20060139347A1 (en) * | 2004-12-27 | 2006-06-29 | Choi Min G | Method and system of real-time graphical simulation of large rotational deformation and manipulation using modal warping |
| CN112560167A (en) * | 2020-11-10 | 2021-03-26 | 北京航空航天大学 | Wing structure mechanics high-fidelity reduced-order simulation method, electronic equipment and storage medium |
| CN115859715A (en) * | 2022-11-23 | 2023-03-28 | 西部超导材料科技股份有限公司 | Method for calculating equivalent performance of periodic porous structure material |
| CN115718962A (en) * | 2022-11-25 | 2023-02-28 | 大连理工大学 | Efficient buckling optimization method for reinforced shell based on beam shell coupling model |
Non-Patent Citations (2)
| Title |
|---|
| 冯琨程;刘波;张恩阳;: "板翅式换热器夹层结构等效模型研究及数值分析", 玻璃钢/复合材料, no. 01, 28 January 2016 (2016-01-28) * |
| 张洪武;吴敬凯;付振东;: "周期性点阵桁架材料力学性能分析的一种新的多尺度计算方法", 固体力学学报, no. 02, 15 April 2011 (2011-04-15) * |
Cited By (2)
| Publication number | Priority date | Publication date | Assignee | Title |
|---|---|---|---|---|
| CN117540494A (en) * | 2024-01-10 | 2024-02-09 | 天目山实验室 | Aviation cabin structure reduced order analysis method, system and equipment |
| CN117540494B (en) * | 2024-01-10 | 2024-04-05 | 天目山实验室 | Aviation cabin structure reduced order analysis method, system and equipment |
Also Published As
| Publication number | Publication date |
|---|---|
| CN116738707B (en) | 2024-05-17 |
Similar Documents
| Publication | Publication Date | Title |
|---|---|---|
| EP3944125B1 (en) | Method and system for manufacturing a heat exchanger for supercritical pressure fluid | |
| Geyer et al. | Automated metamodel generation for Design Space Exploration and decision-making–A novel method supporting performance-oriented building design and retrofitting | |
| CN116738707B (en) | Equivalent mechanical property prediction method and system for partial periodic heat exchanger channel | |
| Li et al. | A new approach to solve uncertain multidisciplinary design optimization based on conditional value at risk | |
| Yi et al. | Dynamic integration between building energy simulation (BES) and computational fluid dynamics (CFD) simulation for building exterior surface | |
| US20240320398A1 (en) | Multiscale analysis method, system, media and device for thermal-mechanical coupling performance of heat exchanger | |
| CN112906272B (en) | Reactor steady-state physical thermal full-coupling fine numerical simulation method and system | |
| CN116595884B (en) | Method for realizing ultra-real-time calculation of miniature nuclear reactor system | |
| Chronis et al. | Generative fluid dynamics: integration of fast fluid dynamics and genetic algorithms for wind loading optimization of a free form surface | |
| Sadeghi Tabar et al. | Efficient spot welding sequence simulation in compliant variation simulation | |
| CN110717275A (en) | Three-dimensional neutron flux numerical simulation method for pressurized water reactor core | |
| Tlija et al. | A novel model for the tolerancing of nonrigid part assemblies in computer aided design | |
| Sun et al. | An intelligent plate fin-and-tube heat exchanger design system through integration of CFD, NSGA-II, ANN and TOPSIS | |
| Park et al. | A new framework for efficient sequential sampling-based RBDO using space mapping | |
| CN117272745A (en) | Thermal coupling simulation method combining thermal model and high-temperature creep analysis | |
| CN109214100B (en) | Sheet material rapid forming prediction method | |
| CN117057002A (en) | Underground factory building ventilation modeling method and system | |
| CN105808820A (en) | High-precision numerical value method for solving interval heat convection diffusion problem | |
| CN116090260A (en) | System simulation method for full coupling of reactor | |
| CN116757027B (en) | Construction method and system of general database of equivalent mechanical properties of heat exchanger channel | |
| CN115169265A (en) | Method, system, device and medium for analyzing blending coefficient based on numerical analysis | |
| Chen et al. | Variation Analysis Method Based on Product Feature Information Network | |
| Hong et al. | Fixturing Scheme Design in the Shipbuilding Industry: A Fixture Amount and Layout Optimization for Curved Compliant Parts | |
| CN111861011A (en) | Supercritical pressure fluid convection heat exchange performance prediction method and system | |
| Liu et al. | Compliant assembly variation modeling for thin-walled structures considering clamping constraints and geometric deviations based on isogeometric analysis |
Legal Events
| Date | Code | Title | Description |
|---|---|---|---|
| PB01 | Publication | ||
| PB01 | Publication | ||
| SE01 | Entry into force of request for substantive examination | ||
| SE01 | Entry into force of request for substantive examination | ||
| GR01 | Patent grant | ||
| GR01 | Patent grant |