A numerical calculation method for structural strength of micro heat exchange tube bundle

Abstract

A numerical calculation method for structural strength of micro heat exchange tube bundle, which belongs to the technical field of finite element analysis of micro heat exchange tube bundle structure in heat exchange equipment. The method comprises the following steps: firstly, the specific geometric structure of the micro heat exchange tube bundle is determined, and the structure is simplified. A repetitive pre-cooling sheet heat exchange tube bundle is selected as a model object, a corresponding structure model is established, and a structured grid is divided; then, the flow and heat exchange of the cold and hot fluids through the tube bundle inside and outside the micro heat exchange tube bundle are numerically simulated, and the pressure and temperature data on the boundary of the micro tube bundle are obtained, which will be used as the basis input for subsequent strength calculation; then, the strength calculation is carried out. The complex micro heat exchange tube bundle is simplified into a repetitive pre-cooling sheet heat exchange tube bundle, which reduces the calculation difficulty, thereby effectively reducing the calculation time and improving the calculation efficiency.

Description

TECHNICAL FIELD

[0001] The present application relates to a structure strength numerical calculation method suitable for micro heat exchange tube bundle, which belongs to the technical field of micro heat exchange tube bundle structure finite element analysis in heat exchange equipment. BACKGROUND

[0002] With the rapid development of aerospace technology, the importance of hypersonic propulsion technology under high Mach number in the field of modern aircraft is increasing day by day, which has become one of the key technologies of current research. In practical application, when the flight speed of aerospace vehicle gradually increases, the stagnation temperature of engine incoming flow will rise significantly, which will lead to the deterioration of air compressibility, resulting in the sharp reduction of the performance of power system, and seriously affecting the overall performance of the aircraft. At the same time, the thermal protection problem faced by the aircraft under high speed flight state becomes more and more difficult, and the high temperature environment poses a great threat to the stability and reliability of the aircraft structure and components. The reasonable arrangement of pre-cooling heat exchanger at the position of engine inlet can effectively cool the incoming air, which can significantly improve the compression performance of air and further improve the working efficiency of power system, and can effectively alleviate the pressure of thermal protection, providing reliable guarantee for the stable operation of aerospace vehicle under high Mach number flight condition, laying a solid foundation for the further development and application of hypersonic propulsion technology, and having important practical application value and broad development prospect.

[0003] However, the existing strength calculation method for micro heat exchange tube bundle of pre-cooling heat exchanger is usually complex, and due to the large number of heat exchange tube bundles in the pre-cooling heat exchanger, the calculation process is time-consuming. SUMMARY

[0004] In order to solve the problems existing in the prior art, the purpose of the present application is to calculate the structure strength of micro heat exchange tube bundle on the basis of fluid flow and heat exchange in micro heat exchange tube bundle, simplify the complex micro heat exchange tube bundle by reasonable simplification, simplify it into repetitive pre-cooling sheet heat exchange tube bundle, reduce the calculation difficulty, and then use APDL command stream programming software to calculate the strength, so as to solve the problems of complex strength calculation and slow calculation speed of micro heat exchange tube bundle.

[0005] The present application relates to a structure strength numerical calculation method suitable for micro heat exchange tube bundle, which belongs to the technical field of micro heat exchange tube bundle structure finite element analysis in heat exchange equipment.

[0006] Step 1: determine the geometric structure of micro heat exchange tube bundle, specifically including defining the number of tubes, the number of rows, the inner diameter, the outer diameter, the tube spacing, the number of support plates, and the number and position of inlet and outlet fixed constraints of micro heat exchange tube bundle, and simplifying the structure model, selecting a repetitive pre-cooling sheet heat exchange tube bundle as a calculation model;

[0007] Step 2: Use modeling software to establish a repetitive pre-cooling fin heat exchange tube bundle calculation model for the simplified process in Step 1. Add a boundary layer to the interface between the heat exchange tube bundle and the fluid, and perform structured mesh division on the model. Complete the mesh division under the premise of ensuring mesh quality.

[0008] Step 3: Determine the temperature, pressure, flow rate, and flow of the helium gas inside the simplified repetitive pre-cooling fin heat exchange tube bundle and the air outside the heat exchange tube bundle. Then simulate and analyze the flow of helium gas inside the micro heat exchange tube bundle and air outside the tube bundle, as well as the heat exchange between the cold and hot fluids passing through the tube bundle.

[0009] Step 4: Based on the flow and heat exchange analysis and calculation in Step 3, extract the temperature and pressure data of the micro heat exchange tube bundle and the tube bundle interface, and then provide it to the finite element analysis platform strength calculation end for interpolation calculation.

[0010] Step 5: Import the simplified repetitive pre-cooling fin heat exchange tube bundle mesh model into the command stream programming software. Then set the calculation type and specify the heat exchange tube bundle element type as shell element. Next, define the material properties of the heat exchange tube bundle, including but not limited to elastic modulus, Poisson's ratio, and thermal expansion coefficient, to ensure that the parameters reflect the actual characteristics of the material. The command stream programming software is ANSYS Mechanical APDL.

[0011] Step 6: Add boundary conditions to the inner and outer walls of the micro heat exchange tube bundle. Set the interface type between the inner and outer fluids and the inner and outer walls of the tube bundle to "coupled wall". Extract the temperature and pressure data of the inner and outer fluids and the heat exchange tube bundle interface in Step 4, and interpolate them onto the grid nodes to add boundary conditions to the inner and outer walls of the tube bundle. Then load the temperature and pressure loads into the model to ensure that the load distribution accurately reflects the actual working conditions to support subsequent strength analysis and calculation.

[0012] Step 6-1: Use the KNN (K-Nearest Neighbors) method to interpolate the temperature and pressure loads. Extract the flow field information from the CFD simulation, including the coordinates of the grid nodes and the corresponding temperature and pressure data, as the reference data set. Calculate the distance between the heat exchange structure surface grid nodes and all flow field boundary grid nodes, and select the nearest k known node data.

[0013] Assuming the interpolation target point is , the nearby points are , and the geometric distance is:

[0014] Therefore, the nearest k points are

[0015]

[0016] wherein d k is the distance range of the adjacent points.

[0017] Step 6-2: Weighted average is performed on the node data on the k known flow field boundaries, and the weighted average is taken as the estimated value of the heat exchange structure surface grid node. The estimated value is calculated for all heat exchange structure surface grid nodes to obtain the temperature and pressure data corresponding to the heat exchange structure surface grid node, i.e. the structure surface temperature and pressure load.

[0018] The average value of the k adjacent point data is taken as the estimated value of the target interpolation point, and thus the temperature and pressure data of the heat exchange structure surface grid node can be calculated.

[0019]

[0020] wherein F0 is the estimated value of the heat exchange structure grid node, F i is the known data of the flow field boundary grid node, λ i is the weight of the adjacent point relative to the target interpolation node, and the weight of the k points is calculated as follows.

[0021]

[0022] Step 6-3: The temperature and pressure data of the heat exchange structure grid node are loaded onto the heat exchange structure to complete the loading of the temperature and pressure load. At the same time, since the temperature distribution is different at different places on the heat exchange structure, and the material properties are different at different temperatures, the material properties are different at different places on the entire heat exchange structure. Then the material properties at different temperatures are retrieved from the material library to define the material properties of the heat exchange structure finite element.

[0023] Step 7: The constraints of the pre-cooling fin heat exchange tube bundle inlet and outlet and the constraints of the support plates distributed with the tube bundle are added. The constraints of the pre-cooling fin heat exchange tube bundle inlet and outlet are set as fixed constraints, and the 13 support plates distributed with the tube bundle are set as beam elements. The constraints of the support plates on the heat exchange tube bundle are realized by connecting the beam elements and the shell elements. The RBE3 method is used to connect and constrain the support plates and the heat exchange tube bundle, and the heat exchange tube bundle is constrained by the node element degrees of freedom at both ends.

[0024] The RBE3 element is an interpolation element without stiffness matrix, only involving force distribution. It has one master node with six degrees of freedom and multiple slave nodes with only translational degrees of freedom involved, and rotational degrees of freedom are not involved. The node force distribution is similar to the internal force distribution of the cross section of the beam element.

[0025]

[0026] wherein F M is the force of the master node, and F SiFNode force of the main node distributed to the slave node, shear force distribution of beam section; W K Weight coefficient of the interpolation point, W i Weight coefficient.

[0027]

[0028] Where, F SiM Node force of the main node distributed to the slave node by least square method, similar to the bending normal stress distribution of beam section; r M Vector radius of the main node to the weighted geometric center; r i Vector radius of the slave node to the geometric center; W i Weight coefficient.

[0029] Step 8: Solve, perform strength calculation on the model under the conditions of temperature, pressure load and constraint, ensure that the load and constraint conditions accurately reflect the actual structure characteristics, so as to realize the mechanical analysis of the heat exchange tube bundle under the working state.

[0030] According to the structure motion equation, the displacement and stress and strain are obtained by coupling solution calculation.

[0031]

[0032] The left side of the equation is the structure term, including the inertia force term , the elastic force term ; the right side is the action force term.

[0033] Where, [M] is the mass matrix; [C] is the damping matrix; is the stiffness matrix; is the acceleration vector, is the velocity vector, x is the displacement vector, is the resultant force on the heat exchange tube.

[0034] The external force of the tube bundle under the action of transverse flow includes the action of fluid additional mass, additional damping and additional stiffness. Generally speaking, they can be regarded as functions of the acceleration component, velocity component and displacement component of the tube bundle, and therefore can be expressed in the following form:

[0035]

[0036] In the formula, is the additional mass; is the additional damping; is the additional stiffness; is the fluid force on the tube bundle. The total damping value is positive, indicating that the system has vibration energy loss, and the total stiffness value Positive indicates that the system has the ability to maintain stability.

[0037] The present application has the following beneficial effects:

[0038] 1) By reasonably simplifying the structure of the micro heat exchange tube bundle of the pre-cooler, the complex micro heat exchange tube bundle is simplified into a repetitive pre-cooling sheet heat exchange tube bundle, the calculation difficulty is reduced, thereby effectively reducing the calculation time and improving the calculation efficiency.

[0039] 2) Combined with the command stream programming technology, the surface temperature and pressure data of the heat exchange tube bundle can be effectively extracted and quickly calculated. The KNN method is used for temperature and pressure load interpolation to accurately obtain the temperature and pressure data of the grid nodes, and the boundary conditions and loads are reasonably added to ensure the accuracy of the calculation results.

[0040] The method simplifies the structure of the micro heat exchange tube bundle of the pre-cooling heat exchanger, and combines the command stream programming technology to realize the effective extraction and quick calculation of the surface temperature and pressure data of the heat exchange tube bundle. This method not only improves the calculation efficiency, but also ensures the accuracy of the results, providing strong support for the design and optimization of the pre-cooling heat exchanger. BRIEF DESCRIPTION OF DRAWINGS

[0041] Figure 1 The present application is a complete flowchart.

[0042] Figure 2 The present application is a schematic diagram of the overall structure calculation model of the heat exchanger.

[0043] Figure 3 The present application is a schematic diagram of the structure of 4 rows of 98 micro heat exchange tube bundles.

[0044] Figure 4 The present application is a strain distribution curve diagram of 4 rows of heat exchange micro tube bundles.

[0045] Figure 5 The present application is a strain distribution waterfall diagram of 4 rows of heat exchange micro tube bundles.

[0046] Figure 6 The present application is a comparison curve diagram of the maximum strain value of the micro heat exchange tube bundle under the design condition and the actual strain value of the micro heat exchange tube bundle.

[0047] In the figure: 1, first part of the heat exchanger model cavity, 2, second part of the heat exchanger model cavity, 3, heat exchange core, 4, micro heat exchange tube bundle, 5, helium gas outlet manifold, 6, helium gas inlet manifold, 7, heat exchange tube row, 8, support plate. DETAILED DESCRIPTION

[0048] The present application will be further described in detail below in conjunction with the flowchart in Figure 1

[0049] ​The application discloses a numerical calculation method for structural strength of a micro heat exchange tube bundle.

[0050] Step 1: determining the geometric structure of the micro heat exchange tube bundle, specifically including defining the number of tubes, the number of rows, the inner diameter, the outer diameter, the tube spacing, the number of support plates and the number and position of the inlet and outlet fixed constraints of the micro heat exchange tube bundle, and simplifying the structural model, and selecting a repetitive pre-cooling sheet heat exchange tube bundle as a calculation model;

[0051] Step 2: using modeling software UG to establish the repetitive pre-cooling sheet heat exchange tube bundle calculation model simplified in step 1, adding a boundary layer to the interface between the heat exchange tube bundle and the fluid, and performing structured grid division on the model, and completing the grid division under the premise of ensuring the grid quality;

[0052] Step 3: determining the flow conditions such as the temperature, pressure, flow velocity and flow rate of the helium gas in the simplified repetitive pre-cooling sheet heat exchange tube bundle and the air outside the tube bundle, and then simulating and analyzing the flow of the helium gas in the repetitive pre-cooling sheet heat exchange tube bundle and the air outside the tube bundle and the heat exchange of the cold and hot fluids through the tube bundle;

[0053] Step 4: on the basis of the flow and heat exchange analysis and calculation in step 3, extracting the temperature and pressure data of the cold and hot fluids and the interface between the tube bundle, and then providing the data to the strength calculation end of a finite element analysis platform for interpolation calculation;

[0054] Step 5: importing the grid model of the simplified repetitive pre-cooling sheet heat exchange tube bundle in the command stream programming software ANSYS Mechanical APDL, then setting the calculation type, and specifying the element type of the heat exchange tube bundle as a shell element; then, defining the material properties of the heat exchange tube bundle by using parameterized language command stream programming, including but not limited to the elastic modulus, the Poisson's ratio and the thermal expansion coefficient, to ensure that the parameters reflect the actual characteristics of the material;

[0055] Step 6: adding boundary conditions to the inner and outer walls of the micro heat exchange tube bundle, setting the interface type between the inner and outer fluids and the inner and outer walls of the tube bundle as a "coupled wall", and adding the boundary conditions to the inner and outer walls of the tube bundle by using the method of interpolating the temperature and pressure data of the interface between the inner and outer fluids and the heat exchange tube bundle on the grid nodes through parameterized language command stream programming; then, loading the temperature and pressure loads to the model, to ensure that the load distribution accurately reflects the actual working condition, so as to support the subsequent strength analysis and calculation;

[0056] Step 6-1: Interpolate the temperature and pressure load using the KNN (K-Nearest Neighbors) method, extract the flow field information from the CFD simulation, including the coordinates of the grid nodes and the corresponding temperature and pressure data as the reference data set. Calculate the distance between the surface grid nodes of the heat exchange structure and all the flow field boundary grid nodes, and select the nearest k known node data.

[0057] Assuming the interpolation target point is , the nearby point is , and the geometric distance is:

[0058] Therefore, the k nearest points are

[0059]

[0060] where d k is the distance range of the nearby points.

[0061] Step 6-2: Weighted average the k known node data on the flow field boundary, and use it as the estimated value of the heat exchange structure surface grid node. Calculate the estimated value for all heat exchange structure surface grid nodes to obtain the temperature and pressure data corresponding to the heat exchange structure surface grid nodes, i.e. the structure surface temperature and pressure load.

[0062] The average value of the k nearest point data is used as the estimated value of the target interpolation point, from which the following can be calculated:

[0063]

[0064] where F0 is the estimated value of the heat exchange structure grid node, F i is the known data of the flow field boundary grid node,

[0065] λ i is the weight of the nearby point relative to the target interpolation node, and the weight of the k points is calculated as follows:

[0066]

[0067] Step 6-3: Load the temperature and pressure data of the grid nodes on the heat exchange structure onto the heat exchange structure to complete the loading of the temperature and pressure load. At the same time, due to the different temperature distributions on the heat exchange structure, the material properties at different temperatures have certain differences, so the material properties are different at different places on the entire heat exchange structure; then retrieve the material properties at different temperatures from the material library to define the material properties of the heat exchange structure finite elements.

[0068] Step 7: The constraints of the inlet and outlet of the micro heat exchange tube bundle and the constraints of the support plates distributed with the tube bundle are added by using command stream programming. The constraints of the inlet and outlet of the pre-cooling sheet heat exchange tube bundle are set as fixed constraints, and the 13 support plate constraints distributed with the tube bundle are set as beam elements. The constraints of the heat exchange tube bundle by the support plates are realized by connecting the beam elements and the shell elements. The connection constraints of the support plates and the heat exchange tube bundle are realized by using the RBE3 method. The two ends of the heat exchange tube bundle are constrained by the node element degrees of freedom.

[0069] The RBE3 element is an interpolation element without a stiffness matrix, only involving force distribution. One master node and six degrees of freedom can be involved, and multiple slave nodes and only translational degrees of freedom are involved. The node force distribution is similar to the internal force distribution of the cross section of the beam element.

[0070]

[0071] wherein, F SiF is the node force of the master node to the slave node, which is the shear force distribution of the beam cross section; W i is the weight coefficient.

[0072]

[0073] wherein, F SiM is the node force of the master node to the slave node by the least square method, which is similar to the bending normal stress distribution of the beam cross section; r M is the vector radius from the master node to the weighted geometric center; r i is the vector radius from the slave node to the geometric center; W i is the weight coefficient.

[0074] Step 8: Solve in the command stream programming environment. The strength calculation of the model under the conditions of temperature, pressure load and constraint is carried out to ensure that the load and constraint conditions accurately reflect the actual structure characteristics, so as to realize the mechanical analysis of the heat exchange tube bundle under the working state.

[0075] According to the structure motion equation, the displacement and stress and strain are obtained.

[0076]

[0077] The left side of the equation is the structure term, including the inertia force term and the elastic force term ; the right side is the acting force term.

[0078] wherein, [M] is the mass matrix; [C] is the damping matrix; is the stiffness matrix; is the acceleration vector, is the velocity vector, and x is the displacement vector. is the resultant force on the heat exchange tube.

[0079] The external force on the tube bundle under the action of cross flow includes the action of fluid added mass, added damping and added stiffness. Generally speaking, they can be regarded as the function of acceleration component, velocity component and displacement component of the tube bundle, and thus can be expressed in the following form:

[0080]

[0081] In the formula, is the added mass; is the added damping; is the added stiffness; is the fluid force on the tube bundle. The total damping value is positive, indicating that the system has a loss of vibration energy. The total stiffness value is positive, indicating that the system has the ability to maintain stability.

[0082] Embodiment

[0083] The technical solutions in the embodiment of the application will be described below. The examples described below are only design working condition cases in the calculation process.

[0084] The application provides a structure strength numerical calculation method for micro heat exchange tube bundles based on a parameterized language command flow programming environment, combining a flow Figure 1 Further explanation of the application, the heat exchanger model cavity includes two parts of the heat exchanger model cavity first part 1 and the heat exchanger model cavity second part 2, the heat exchanger core 3 and the micro heat exchange tube bundle 4 are arranged in the heat exchanger model cavity second part 2, and the two ends of the heat exchange tube bundle 4 are respectively provided with the helium gas outlet header 5 and the helium gas inlet header 6. Thirteen supporting plates 8 are arranged between the heat exchange tube rows 7, and the included angle between the adjacent two supporting plates 8 is 30°. The heat exchange tube rows 7 are 4 rows, and there are 98 tubes in total;

[0085] The method specifically includes the following specific steps: step 1: determining the geometric structure of the micro heat exchange tube bundle, specifically including defining the single row of 24 heat exchange fine tubes of the micro heat exchange tube bundle, 4 rows of 98 tubes, the outer diameter of the heat exchange tube is 1 mm, the inner diameter is 0.8 mm, the tube spacing is 1.25 mm, there are 13 supporting plates, and the number and position of the inlet and outlet 2 fixed constraints are defined, and the structure model is simplified, and a repetitive pre-cooling sheet heat exchange tube bundle is selected as a calculation model;

[0086] Step 2: a repetitive pre-cooling sheet heat exchange tube bundle calculation model simplified in step 1 is established in a three-dimensional modeling software UG, a boundary layer is added to the interface between the heat exchange tube bundle and the fluid, and the model is structured mesh division, and the mesh division is completed under the premise of ensuring the mesh quality, and the number of meshes is more than 20 million.

[0087] Step 3: Determine the temperature, pressure, flow velocity, and flow rate of the helium gas inside the repeated pre-cooling fin heat exchange tube bundle and the air outside the tube bundle by adding boundary conditions of 3 m / s and 750 K at a gauge pressure of 0.128 MPa to the air inlet of the pre-cooling heat exchange structure model, and adding boundary conditions of 166.7 m / s and 190 K at a gauge pressure of 4 MPa to the helium gas inlet. Then, simulate and analyze the flow of helium gas inside the repeated pre-cooling fin heat exchange tube bundle and air outside the tube bundle, as well as the heat exchange between the cold and hot fluids passing through the tube bundle.

[0088] Step 4: Based on the flow and heat exchange analysis and calculation in Step 3, extract the temperature and pressure data of the repeated pre-cooling fin heat exchange tube bundle and the tube bundle interface. The temperature load range varies with the tube bundle position, ranging from 223.384 K to 934.905 K, and the pressure load range is from 3.2718 MPa to 3.89227 MPa. Then, provide the temperature and pressure data to the finite element analysis platform for interpolation calculation.

[0089] Step 5: Import the simplified grid model of the repeated pre-cooling fin heat exchange tube bundle into the command stream programming software ANSYS Mechanical APDL. Then, set the calculation type and specify the shell element type for the heat exchange tube bundle. Next, define the material properties of the heat exchange tube bundle using parameterized language command stream programming, with an elastic modulus of 20400, a Poisson's ratio of 0.32, and a thermal expansion coefficient of 0.000018, to ensure that the parameters reflect the actual characteristics of the material.

[0090] Step 6: Add boundary conditions to the inner and outer walls of the repeated pre-cooling fin heat exchange tube bundle. Set the interface type between the inner and outer fluids and the inner and outer walls of the tube bundle to "coupled wall". Extract the temperature and pressure data of the interface between the inner and outer fluids and the heat exchange tube bundle from Step 4, and interpolate the data onto the grid nodes to add boundary conditions to the inner and outer walls of the tube bundle. Then, load the temperature and pressure loads onto the model to ensure that the load distribution accurately reflects the actual working conditions, supporting subsequent strength analysis and calculation.

[0091] Step 6-1: Use the KNN (K-Nearest Neighbors) method to interpolate the temperature and pressure loads. Extract the flow field information from the CFD simulation, including the coordinates of the grid nodes and the corresponding temperature and pressure data, as the reference data set. Calculate the distance between the heat exchange structure surface grid nodes and all the flow field boundary grid nodes, and select the nearest k known node data.

[0092] Assuming the interpolation target point is , the nearest point is , and the geometric distance is:

[0093] Therefore, the k points close to the target interpolation point are,

[0094]

[0095] wherein d k is the distance range of the close points.

[0096] Step 6-2: Weighted average is performed on the node data on the k known flow field boundaries, and the weighted average is taken as the estimated value of the heat exchange structure surface grid node. The estimated value is calculated for all heat exchange structure surface grid nodes, and the temperature and pressure data corresponding to the heat exchange structure surface grid node are obtained, i.e. the structure surface temperature and pressure load.

[0097] The average value of the k close point data is taken as the estimated value of the target interpolation point, and thus,

[0098]

[0099] wherein F0 is the estimated value of the heat exchange structure grid node, F i is the known data of the flow field boundary grid node,

[0100] λ i is the weight of the close point relative to the target interpolation node, and the weight of the k points is calculated as follows,

[0101]

[0102] Step 6-3: The temperature and pressure data of the grid nodes on the heat exchange structure are loaded onto the heat exchange structure to complete the loading of the temperature and pressure load. At the same time, since the temperature distribution is different at different places on the heat exchange structure, and the material properties are different at different temperatures, the material properties are different at different places on the entire heat exchange structure. Then, the material properties at different temperatures are retrieved from the material library, and the material properties of the heat exchange structure finite element are defined.

[0103] Step 7: The constraints of the pre-cooling sheet heat exchange tube bundle inlet and outlet and the constraints of the support plates distributed with the tube bundle are added. The constraints of the micro heat exchange tube bundle inlet and outlet are set as fixed constraints, and the constraints of the 13 support plates distributed with the tube bundle are set as beam elements. The constraints of the support plates on the heat exchange tube bundle are realized through the connection of the beam elements and the shell elements. The RBE3 method is used to connect and constrain the support plates and the heat exchange tube bundle. The two ends of the heat exchange tube bundle are constrained through the node element degrees of freedom;

[0104] RBE3 unit is an interpolation value unit, without stiffness matrix, only involving force distribution, one master node and six degrees of freedom, multiple slave nodes and only translational freedom are involved, rotational freedom is not involved, the distribution of node force is similar to the internal force distribution of beam cross section, and the node force is shown as follows,

[0105]

[0106] Wherein, F SiF is the force distribution of the master node to the slave node, the shear force distribution of the beam section; W i is the weight coefficient.

[0107]

[0108] Wherein, F SiM is the force distribution of the master node to the slave node by least square method, similar to the bending normal stress distribution of the beam section; r M is the vector radius from the master node to the weighted geometric center; r i is the vector radius from the slave node to the geometric center; W i is the weight coefficient.

[0109] Step 8: solving, strength calculation of the model under the conditions of temperature, pressure load and constraint, ensuring that the load and constraint conditions accurately reflect the actual structure characteristics, so as to realize the mechanical analysis of the heat exchange tube bundle under the working state.

[0110] According to the structure motion equation, the displacement and stress and strain are obtained by coupling solution calculation.

[0111]

[0112] The left side of the equation is the structure term, including the inertia force term , the elastic force term ; the right side is the action force term.

[0113] Wherein, [M] is the mass matrix; [C] is the damping matrix; is the stiffness matrix; is the acceleration vector, is the velocity vector, x is the displacement vector, is the resultant force on the heat exchange tube.

[0114] The external force of the tube bundle under the action of transverse flow includes the action of fluid additional mass, additional damping and additional stiffness. Generally speaking, they can be regarded as the functions of acceleration component, velocity component and displacement component of the tube bundle, and therefore can be expressed in the following form:

[0115]

[0116] wherein, is the additional mass; is the additional damping; is the additional stiffness; is the fluid force on the tube bundle. The total damping value is positive indicating that the system has a loss of vibrational energy. The total stiffness value is positive indicating that the system has the ability to maintain stability.

[0117] The maximum stress and maximum deformation displacement under the design condition can be obtained by the above calculation, as shown in Table 1.

[0118] Table 1

[0119]

[0120] Meanwhile, by calculation, the numerical simulation result and the test result value under the normal temperature condition are compared, it is found that the vibration deformation displacement obtained by the numerical simulation deviates from the test value within 8%, which indicates that the numerical calculation method for the structural strength of the micro heat exchange tube bundle is feasible, and the reliability of the result of the present application is verified.

Claims

1. A numerical calculation method for the structural strength of micro heat exchanger tube bundles, characterized in that, Includes the following steps: Step 1: Determine the geometry of the micro heat exchanger bundle and simplify the structural model into a repetitive precooling plate heat exchanger bundle calculation model; Step 2: Use modeling software to establish a calculation model of the repetitive precooling plate heat exchanger tube bundle in Step 1, and perform structured mesh generation on the model. Add a boundary layer to the interface between the heat exchanger tube bundle and the fluid. Complete the mesh generation while ensuring the mesh quality. Step 3: Determine the flow conditions of temperature, pressure, velocity, and flow rate of the cold fluid helium gas inside the repeatable precooling heat exchange tube bundle and the hot fluid air outside the tube bundle, and then simulate and analyze the flow of helium gas inside the micro heat exchange tube bundle and the heat exchange through the tube bundle via the cold and hot fluids. Step 4: Based on the flow heat transfer analysis calculation in Step 3, extract the temperature and pressure data of the hot and cold fluids and the interface between the tube bundle and the micro heat transfer tube bundle, respectively; Step 5: Import the simplified repetitive precooling plate heat exchanger bundle mesh model into the command-line programming software, set the calculation type, and specify the element type of the heat exchanger bundle as shell element; and define the material properties of the heat exchanger bundle; Step 6: Add boundary conditions to the inner and outer walls of the micro heat exchanger bundle by interpolating the temperature and pressure data of the hot and cold fluids and the interface of the bundle to the mesh nodes, and set the interface type of the fluids inside and outside the bundle and the inner and outer walls of the bundle to "coupled wall"; then load temperature and pressure loads onto the model; Step 6-1: Use the KNN method to interpolate the temperature and pressure loads and extract the flow field information from the CFD simulation; calculate the distance between the grid nodes on the heat transfer structure surface and all flow field boundary grid nodes, and select the k closest known node data. Assume the interpolation target point is The nearest point is Then its geometric distance is: ; Therefore, the k nearest points are: ； Where, d k The range of distances to nearby points; Step 6-2: Take a weighted average of the node data on the k known flow field boundaries and use it as the estimated value of the grid node on the heat transfer structure surface. Calculate the estimated value of all grid nodes on the heat transfer structure surface to obtain the temperature and pressure data corresponding to the grid node on the heat transfer structure surface, i.e., the temperature and pressure load on the structure surface. Using the average of the k nearest neighboring data points as the estimate of the target interpolation point, the following calculation is performed: ； Where F0 is the estimated value of the heat exchange structure mesh node, F i The known data for the flow field boundary grid nodes, λ i These are the weights of the nearest points relative to the target interpolation node. The weights of the k points are calculated as follows: ； Step 6-3: Load the temperature and pressure data of the mesh nodes on the heat exchange structure onto the heat exchange structure to complete the loading of temperature and pressure loads; define the various physical properties of the heat exchange structure by retrieving material properties at different temperatures from the material library; Step 7: Add constraints to the inlet and outlet of the micro heat exchange tube bundle and the support plate distributed with the tube bundle. Set the constraints of the inlet and outlet of the precooling plate heat exchange tube bundle as fixed constraints. Set the constraints of the support plate distributed with the tube bundle as beam elements. The support plate constrains the heat exchange tube bundle by connecting the beam elements with the shell elements. Use the RBE3 method to constrain the connection between the support plate and the heat exchange tube bundle. At the same time, the two ends of the heat exchange tube bundle are constrained by the degree of freedom of the node elements. Step 8: Perform strength calculations on the model under temperature, pressure load, and constraint conditions to achieve mechanical analysis of the heat exchange tube bundle under working conditions; The displacement and stress-strain are obtained by performing coupled solution calculations based on the following structural motion equations. ； Where [M] is the mass matrix; [C] is the damping matrix; Here is the stiffness matrix; It is the acceleration vector. x is the velocity vector, and x is the displacement vector. It is the resultant force acting on the heat exchange tube; The external forces acting on the tube bundle under transverse flow include the effects of fluid-added mass, added damping, and added stiffness, and can be considered as functions of the tube bundle's acceleration, velocity, and displacement components: ； In the formula, For added mass; For additional damping; To add stiffness; The tube bundle is subjected to fluid forces; total damping value A positive value indicates that the system has energy loss due to vibration; the total stiffness value is... A positive value indicates that the system has the ability to maintain stability.

2. The numerical calculation method for the structural strength of micro heat exchanger tube bundles according to claim 1, characterized in that, In step 1, the geometric structure of the micro heat exchange tube bundle includes the number of tubes, the number of rows, the inner diameter, the outer diameter, the tube spacing, the number of support plates, and the number and position of inlet and outlet fixed constraints.

3. The numerical calculation method for the structural strength of micro heat exchanger tube bundles according to claim 1, characterized in that: In step 5, the material properties include elastic modulus, Poisson's ratio, and coefficient of thermal expansion.

4. The numerical calculation method for the structural strength of micro heat exchanger tube bundles according to claim 1, characterized in that, In step 6-1, the flow field information in the CFD simulation includes the coordinates of the grid nodes and the corresponding temperature and pressure data.

5. The numerical calculation method for the structural strength of micro heat exchanger tube bundles according to claim 1, characterized in that, Step 7 specifically involves: The RBE3 element is an interpolation element with no stiffness matrix. The nodal forces are represented as follows: ； Among them, F M Principal node force, F SiF The distribution of force from the master node to the slave nodes, and the shear force distribution across the beam cross section; W K W represents the weight coefficients of the interpolation points. i For weighting coefficients; ； Among them, F SiM The nodal forces distributed from the master node to the slave nodes using the least squares method; r M The radius vector from the master node to the weighted geometric center; r i Let be the radius vector from the node to the geometric center.

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