Two-dimensional and three-dimensional coupling finite element analysis method

Abstract

The two-dimensional and three-dimensional coupling finite element analysis method comprises the following steps that a cross section of a simulation structure is determined, and the cross section is an interface of a two-dimensional structure and a three-dimensional structure; establishing a simulation model, and assigning a two-dimensional structure and a three-dimensional structure; calculating an initial temperature field of the simulation model, and calculating an average temperature at a two-dimensional and three-dimensional coupling interface; and assigning the average temperature to the two-dimensional structure and the three-dimensional structure at the interface, and carrying out temperature field iteration until a steady-state temperature field is obtained. According to the method, the temperature calculation of the three-dimensional grid model and the temperature calculation of the two-dimensional grid model can be accurately coupled together, and meanwhile, the continuity of the temperature and the heat flow at the interface is ensured.

Description

Technical Field

[0001] This invention relates to the field of thermal analysis of aero-engines, and more specifically to the field of finite element heat transfer analysis technology. Background Technology

[0002] Thermal analysis is a crucial step in aero-engine design, primarily involving calculating the temperature field distribution of various components to provide input for strength design. Full three-dimensional heat transfer design analysis is rarely used due to its massive mesh size, high computational resource consumption, and long processing time. Generally, two-dimensional models are used for simplification; however, traditional two-dimensional models are not very accurate and prone to errors. Therefore, a coupled two-dimensional and three-dimensional approach is now employed for calculations.

[0003] For example, in the simulation of the tenon joint of a turbine disk, the tenon and mortise are generally three-dimensional structures, while the turbine disk is two-dimensional. How to accurately couple the three-dimensional mesh with the temperature calculation of the two-dimensional mesh model, while ensuring the continuity of temperature and heat flow, is an urgent problem to be solved. Summary of the Invention

[0004] One object of the present invention is to provide a two-dimensional and three-dimensional coupled finite element analysis method.

[0005] The two-dimensional and three-dimensional coupled finite element analysis method to achieve the above objectives includes the following steps:

[0006] Determine the cross-section of the simulated structure, where the cross-section is the interface between the two-dimensional and three-dimensional structures;

[0007] Establish a simulation model and assign values ​​to its two-dimensional and three-dimensional structures;

[0008] Calculate the initial temperature field of the simulation model and the average temperature at the two-dimensional and three-dimensional coupling interface;

[0009] The average temperature is assigned to the two-dimensional and three-dimensional structures at the interface, and the temperature field is iterated until a steady-state temperature field is obtained.

[0010] In one or more embodiments, the step of calculating the average temperature at the interface is as follows:

[0011] The interface between the three-dimensional structure and the two-dimensional structure is divided into multiple first boundary lines, each of which is parallel to the second boundary line of the two-dimensional structure.

[0012] The average value of the node temperatures on the upper and lower sides of the first and second boundary lines is calculated.

[0013] The average temperature values ​​of each node on each first boundary line and each node on each second boundary line are obtained sequentially.

[0014] In one or more embodiments, the first-layer unit radial dimensions of the two-dimensional structure and the three-dimensional structure are made consistent.

[0015] In one or more embodiments, the material properties and initial temperature of each node in the two-dimensional and three-dimensional structures are assigned.

[0016] In one or more embodiments, the simulated structure is a turbine rotor structure, the cross-section is the contact surface between the tenon and the turbine disk, the tenon is a three-dimensional structure, and the disk is a two-dimensional structure.

[0017] In one or more embodiments, the thermal conductivity of each node in the two-dimensional structure and the three-dimensional structure is assigned the same value.

[0018] In one or more embodiments, the two-dimensional structure is a two-dimensional axisymmetric model.

[0019] In one or more embodiments, the two-dimensional structure and the three-dimensional structure are disconnected at the interface.

[0020] In one or more embodiments, when calculating the initial temperature field of the simulation model, no heat transfer boundary is loaded at the mesh at the interface of the two-dimensional and three-dimensional structures.

[0021] The aforementioned two-dimensional and three-dimensional coupled finite element analysis method is based on the principle of conservation of heat flux density at the interface. It uses the average temperature at the interface to accurately couple the temperature calculation of the three-dimensional mesh with that of the two-dimensional mesh model, ensuring the continuity of temperature and heat flux. At the same time, it requires less computational resources and has a shorter calculation time, which can improve the accuracy of strength and life assessment in subsequent strength analysis calculations. Attached Figure Description

[0022] The above and other features, properties and advantages of the present invention will become more apparent from the following description taken in conjunction with the accompanying drawings and embodiments, wherein:

[0023] Figure 1 Schematic diagram of turbine rotor structure;

[0024] Figure 2 This is a schematic diagram of a two-dimensional and three-dimensional coupled mesh of a turbine rotor structure;

[0025] Figure 3A This is a schematic diagram of the first and second boundary lines;

[0026] Figure 3B This is a schematic diagram of the interface between two-dimensional and three-dimensional meshes;

[0027] Figure 4 This is a flowchart of the two-dimensional and three-dimensional coupled finite element analysis method;

[0028] Figure 5This is a schematic diagram of the temperature field iteration process. Detailed Implementation

[0029] The present invention will be further described below with reference to specific embodiments and accompanying drawings. More details are set forth in the following description in order to provide a full understanding of the present invention. However, the present invention can obviously be implemented in many other ways different from those described herein. Those skilled in the art can make similar extensions and derivations based on actual application situations without departing from the spirit of the present invention. Therefore, the scope of protection of the present invention should not be limited by the content of this specific embodiment.

[0030] It should be noted that these and other accompanying drawings are merely examples and are not drawn to scale, and should not be construed as limiting the scope of protection of the present invention.

[0031] Thermal analysis of aero-engines encompasses multiple aspects, including temperature distribution, heat load, and thermal stress of various engine components. However, full three-dimensional heat transfer design analysis is generally not used in practical engineering applications due to its massive mesh size, high computational resource consumption, and long processing time.

[0032] Traditional heat transfer design analysis typically uses a two-dimensional axisymmetric model to simplify a three-dimensional structure. The two-dimensional axisymmetric model assumes that the physical phenomenon or structure is symmetrical along a certain axis, changing only in the other two directions, and is suitable for systems or structures that are symmetrical along that axis. Using a two-dimensional axisymmetric model is an effective simplification method that can quickly obtain preliminary design results. However, two-dimensional models are less refined than three-dimensional models, and are therefore prone to errors, resulting in insufficient accuracy in the calculation results.

[0033] Figure 1 The diagram illustrates the turbine rotor disk connection structure of an aero-engine, including turbine blades 1, turbine disk 3, front sealing disk 4, drum shaft 5, internal tenon groove 6, and disk tenon joint 2. The high-pressure turbine disk is a critical component of the engine; its temperature distribution affects the engine's lifespan and safety. Temperature field calculations will be used to assess static strength, lifespan, and deformation.

[0034] The turbine shaft 5 connects the turbine disk to other engine components, such as the compressor or gearbox. The front sealing disc 4 is located in front of the turbine and is connected to the turbine disk 3. The internal tenon 6 is located on the turbine disk and is used to mate with the tenons of the turbine blades, forming a tenon-and-disc joint 2. Common tenon-and-disc joint methods include dovetail, T-joint, and bevel tenon structures. The turbine blades are tightly connected by tenons mating with the tenons on the turbine disk. This connection structure needs to ensure that the blades can operate stably under high temperature and high speed rotation conditions, while also ensuring that the blades can withstand centrifugal force.

[0035] Turbine blades are key components in turbine stages that withstand the impact of high-temperature combustion gases and convert their kinetic energy into mechanical work. The joints of high-pressure turbine blades experience significant stress and are highly sensitive to temperature levels and gradients.

[0036] High-pressure turbine rotor assemblies exhibit distinct three-dimensional structural features, with the mortise and tenon joints exhibiting particularly complex three-dimensional structures. For the three-dimensional discrete region, despite the equivalence treatment of structure and flow heat transfer by two-dimensional methods, it is still impossible to accurately capture the actual temperature distribution at points such as the mortise joints. Traditional two-dimensional models struggle to realistically describe the flow and heat conduction at the mortise and tenon joints. Furthermore, the temperature distribution in the mortise joint region significantly impacts the stress and lifespan of the disk; as a key area of ​​strength concern, accurate acquisition of the temperature field distribution at this location is crucial.

[0037] Furthermore, due to the complexity and irregularity of the structure, the use of equivalent methods often introduces certain errors, affecting the accuracy of strength and life assessment at that location and reducing the reliability of the tenon joint design.

[0038] Based on this, taking into account both economic and accuracy factors, a two-dimensional and three-dimensional coupling method was adopted to simulate the rotor disk connection.

[0039] Because the turbine disk has a relatively uniform structure, a two-dimensional axisymmetric model can effectively simulate the temperature field distribution at that location. Considering both computational cost and efficiency, the three-dimensional tenon and mortise structure is retained, along with a section of the turbine disk's fan-shaped segment. Heat transfer analysis is performed by coupling this three-dimensional fan-shaped segment with the two-dimensional rotor disk. Figure 2 As shown, the two-dimensional rotor disk structure B and the three-dimensional tenon and mortise structure A are adjacent to each other at the connection area between the turbine disk sector and the rotor disk.

[0040] The proposed two-dimensional and three-dimensional coupled finite element analysis method is based on the principle of conservation of heat flux density at the interface. It is used to accurately couple the temperature calculation of the three-dimensional mesh with that of the two-dimensional mesh model, while also ensuring the continuity of temperature and heat flux.

[0041] Those skilled in the art will understand that this method is not only applicable to turbine disk tenon joints, but also to other engine application scenarios and connection structures that require the preservation of three-dimensional structural features.

[0042] Reference Figure 4 and Figure 5 The method includes the following steps: determining the cross-section of the simulation structure, which is the interface between the two-dimensional and three-dimensional structures; establishing a simulation model and assigning values ​​to the two-dimensional and three-dimensional structures; calculating the initial temperature field of the simulation model and calculating the average temperature at the two-dimensional and three-dimensional coupling interface; assigning the average temperature to the two-dimensional and three-dimensional structures at the interface and iterating the temperature field until a steady-state temperature field is obtained.

[0043] Specifically, in the first step, the geometric model is preprocessed by truncating it at a suitable cross-sectional location. Geometric structures with the same radial height are then selected on both sides of the interface at the truncated location to prepare for the next step of finite element mesh generation. The principle for selecting the cross-sectional surface is to preserve as many of the necessary 3D structural features as possible while facilitating the generation of a regular mesh after truncation. The 3D model is truncated, retaining the parts with the necessary 3D structural features, while replacing the 3D structure with a 2D axisymmetric model for the remaining parts.

[0044] For a turbine rotor structure, the cross-section is the contact surface between the tenon and the turbine disk. The cross-section serves as the interface between the two-dimensional disk structure and the three-dimensional tenon structure. The two-dimensional structure is a two-dimensional axisymmetric model.

[0045] In the second step, the finite element model is preprocessed, and meshes and boundaries are generated for both two-dimensional and three-dimensional structures. Values ​​are assigned to each node, including loading material properties, initial temperature, and loading heat transfer boundaries.

[0046] Preferably, a separate single-layer mesh is generated at the interface to ensure that its size remains consistent at the interface, making the first-layer unit radial dimension of the two-dimensional and three-dimensional structures consistent, thereby ensuring the accuracy of the calculation. For example... Figure 3A As shown, the radial direction refers to Figure 3A The vertical direction within the model; ensuring that the solid thermal conductivity λ assigned to each node in both the two-dimensional and three-dimensional structures is consistent. The model is disconnected at the interface.

[0047] In the third step, the initial temperature field is calculated, which involves performing initial calculations using the initial assignment conditions to obtain the two-dimensional and three-dimensional temperature fields after the initial evolution. The initial temperature field calculation does not apply any heat transfer boundaries; the original heat transfer boundaries are applied at other locations to solve for the initial temperature field.

[0048] Heat flux density, also known as heat transfer density, refers to the thermal energy passing through a unit area per unit time. Heat flux density is conserved at interfaces. Based on the principle of heat flux density conservation, and according to the formula for calculating solid thermal conductivity, if the thermal conductivity of two-dimensional and three-dimensional geometric structures and the dimensions of the solid micro-elements remain consistent, then if the temperature gradient at the interface remains consistent, the heat flux density passing through the upper and lower micro-elements can be guaranteed to remain consistent.

[0049] To ensure a consistent heat flux density at the interface, the following formula must be satisfied: q1 = q2, where q is the heat flux density. According to Fourier's law of heat conduction, we have... Where λ is the thermal conductivity of the material, in W / m·K; ΔL1 is the unit radial dimension of the first layer of adjacent 3D grids at the interface, in m; ΔL2 is the unit radial dimension of the first layer of adjacent 2D grids at the interface, in m; ΔT1 is the radial temperature difference of the first layer of adjacent 3D grids at the interface, in K; ΔT2 is the radial temperature difference of the first layer of adjacent 2D grids at the interface, in K.

[0050] When ΔL1 = ΔL2, then ΔT1 = ΔT2, therefore 0.5 × (T up +T down ) = T w ,like Figure 3A As shown. T w Interface node temperature, in K, T up Temperature of adjacent mesh nodes at the interface between the 3D mesh and the interface, in K and T. down This represents the temperature of adjacent grid nodes at the interface between the two-dimensional grid and the interface, in Kelvin.

[0051] Based on the above formula, in the fourth step, the node temperature is extracted, and the average temperature at the two-dimensional coupling interface is calculated.

[0052] Reference Figures 3A-3B As shown, the specific method for calculating the average temperature at the interface includes the following steps: The interface N between the three-dimensional structure and the two-dimensional structure is divided into multiple first boundary lines N1, and each first boundary line N1 is parallel to the second boundary line M of the two-dimensional structure.

[0053] The average value of the node temperatures on both the upper and lower sides of the first boundary line N1 and the second boundary line M is calculated. The first boundary line N1 and the second boundary line M are as follows: Figure 3A As shown, the node temperatures on both the upper and lower sides of the interface are extracted, and the average temperature of the nodes on both sides is calculated. That is, the temperature data T of the cell adjacent to the first boundary line N1 is used. up Temperature data T of the cell adjacent to the second boundary line M down The average value obtained from the two points is used to calculate the average temperature T at the node where the first boundary line N1 and the second boundary line M are located. w For example, the node data of each node in the plane where the first boundary line N1 of the 3D mesh is located is [X N ,Y N ,T up The data for each node in the two-dimensional grid is [X]. M ,Y M ,T down Given the same X and Y positions, it can be determined by T. up T down Obtain the average value T at the boundary line w The nodal temperature T at the interface, i.e., the first boundary line N1 and the second boundary line M, is obtained. w Then, it is used as a type of boundary condition for the next round of iteration.

[0054] The average temperature values ​​of each node on each first boundary line and each node on each second boundary line are obtained sequentially. For example, the average temperature of each node on the first boundary line N1 is obtained first, and then the average temperature of each node on the first boundary line N1' is obtained, until the node temperature values ​​of all the first boundary lines of the three-dimensional structure interface N are obtained.

[0055] By extracting the temperatures of adjacent mesh nodes from the 3D and 2D models at the interface, taking the average value, and assigning it to the nodes at the interface as a boundary condition, it can be ensured that the temperature gradients of adjacent nodes in the 2D and 3D models at the interface remain consistent.

[0056] Obtain the average temperature T of the nodes where the first boundary line N1 and the second boundary line M are located. w Then, the temperature field is iterated, and the temperature change value ΔT between the two iterations is judged. When the temperature change value ΔT is less than the specified residual, the calculation is considered to have converged; otherwise, the iteration continues until the steady-state temperature field is obtained.

[0057] The above method, based on the principle of heat flux density conservation, realizes coupled temperature field calculation of three-dimensional and two-dimensional models in finite element analysis, and has the following advantages:

[0058] (1) It helps to ensure the structural features of the complex three-dimensional model itself, and compared with the two-dimensional axisymmetric model, it can improve the calculation accuracy of thermal analysis simulation results;

[0059] (2) Compared with the full 3D model or the sector segment model, the coupled model has a smaller number of meshes, occupies less computing resources, and has a shorter computation time;

[0060] (3) It retains the structural features of the complex three-dimensional model, which can ensure the accuracy of strength and life assessment in subsequent strength analysis calculations.

[0061] It should be noted that the use of terms such as "first" and "second" to define the components in the above content is merely for the purpose of distinguishing the corresponding components. Unless otherwise stated, the above terms have no special meaning and therefore should not be construed as limiting the scope of protection of this application.

[0062] Furthermore, this application uses specific terms to describe embodiments of the application. For example, "an embodiment," "one embodiment," and / or "some embodiments" refer to a particular feature, structure, or characteristic related to at least one embodiment of the application. Therefore, it should be emphasized and noted that "an embodiment," "one embodiment," or "an alternative embodiment" mentioned twice or more in different locations in this specification do not necessarily refer to the same embodiment. In addition, certain features, structures, or characteristics in one or more embodiments of the application can be appropriately combined.

[0063] While the present invention has been disclosed above with reference to preferred embodiments, it is not intended to limit the invention. Any variations and modifications can be made by those skilled in the art without departing from the spirit and scope of the invention. Therefore, any modifications, equivalent changes, and alterations made to the above embodiments based on the technical essence of the present invention, without departing from the scope of the invention, fall within the protection scope defined by the claims of the present invention.

Claims

1. A two-dimensional and three-dimensional coupled finite element analysis method, characterized in that, Includes the following steps: Determine the cross-section of the simulated structure, where the cross-section is the interface between the two-dimensional and three-dimensional structures; Establish a simulation model and assign values ​​to its two-dimensional and three-dimensional structures; Calculate the initial temperature field of the simulation model and the average temperature at the two-dimensional and three-dimensional coupling interface; The average temperature is assigned to the two-dimensional and three-dimensional structures at the interface, and the temperature field is iterated until a steady-state temperature field is obtained.

2. The two-dimensional and three-dimensional coupled finite element analysis method as described in claim 1, characterized in that, The steps for calculating the average temperature at the interface are as follows: The interface between the three-dimensional structure and the two-dimensional structure is divided into multiple first boundary lines, each of which is parallel to the second boundary line of the two-dimensional structure. The average value of the node temperatures on the upper and lower sides of the first and second boundary lines is calculated. The average temperature values ​​of each node on each first boundary line and each node on each second boundary line are obtained sequentially.

3. The two-dimensional and three-dimensional coupled finite element analysis method as described in claim 1, characterized in that, Make the first-layer unit radial dimension consistent in both two-dimensional and three-dimensional structures.

4. The two-dimensional and three-dimensional coupled finite element analysis method as described in claim 1, characterized in that, Assign material properties and initial temperature to each node of the two-dimensional and three-dimensional structures.

5. The two-dimensional and three-dimensional coupled finite element analysis method as described in claim 1, characterized in that, The simulated structure is a turbine rotor structure, the cross-section is the contact surface between the tenon and the turbine disk, the tenon is a three-dimensional structure, and the disk is a two-dimensional structure.

6. The two-dimensional and three-dimensional coupled finite element analysis method as described in claim 1, characterized in that, The thermal conductivity of each node in the two-dimensional and three-dimensional structures is made to be consistent.

7. The two-dimensional and three-dimensional coupled finite element analysis method as described in claim 1, characterized in that, The two-dimensional structure is a two-dimensional axisymmetric model.

8. The two-dimensional and three-dimensional coupled finite element analysis method as described in claim 1, characterized in that, The two-dimensional structure and the three-dimensional structure are separated at the interface.

9. The two-dimensional and three-dimensional coupled finite element analysis method as described in claim 1, characterized in that, When calculating the initial temperature field of the simulation model, no heat transfer boundary is loaded at the mesh at the interface of the two-dimensional and three-dimensional structures.

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