Modeling method, vibration mode acquisition method, vibration characteristic research method and system of fuel rod

Abstract

The invention relates to the technical field of nuclear reactor engineering, and discloses a fuel rod modeling method, a vibration mode obtaining method and a vibration characteristic research method and system.The vibration characteristic research method comprises the following specific steps that a fuel rod constrained by a plurality of grillages is regarded as a multi-span continuous beam structure, and a fuel rod model is constructed; dividing the fuel rod model into a plurality of sections of massless elastic beams and concentrated mass beams, and performing stress balance analysis on each section of massless elastic beam and concentrated mass beam to obtain a field transfer matrix and a point transfer matrix; based on balance analysis, a unit transfer matrix and a total transfer matrix are obtained in combination with a displacement continuity condition; solving the overall transfer matrix to obtain a modal shape of the fuel rod model; and based on the vibration mode of the fuel rod model, applying a forced load to any node in the fuel rod model, and further observing the vibration characteristics of the fuel rod model. The method solves the problem of low solving efficiency in the prior art, and has the characteristic of simplicity in operation.

Description

Technical Field

[0001] The present invention relates to the field of nuclear reactor engineering technology, and more specifically, to a fuel rod modeling method, a vibration mode acquisition method, a vibration characteristic research method and a system. Background Art

[0002] The fuel rods in large pressurized water reactors are prone to produce micro-vibrations under the action of fluid scouring, and the study of their vibration characteristics is of great significance. At present, the finite element method is a common means to study the flow-induced vibration characteristics of fuel rods. However, this method requires multiple complex steps such as geometric modeling, unit assignment, mesh discretization, modal analysis, and flow-induced vibration analysis during the solution process. Since the fuel rods are constrained by multiple grids, it is usually necessary to treat the grids as equivalent to tension and compression spring units. Using the finite element method to solve the flow-induced vibration characteristics of fuel rods is not only cumbersome to operate, but also has low solution efficiency.

[0003] The prior art provides a digital reactor simulation analysis method for flow-induced vibration of a core structure of a large pressurized water reactor, the method comprising the following steps: S1: taking the flow fields in the reactor pressure vessel lower head, the core and the fuel assembly as objects, respectively, to perform data-driven in-core flow field flow characteristics and fluid force analysis simulation; S2: according to the results of the analysis and simulation output of step S1, a structural dynamics model of finite element discrete equations for element-level fuel rods, assembly-level fuel assemblies and full-core fuel assemblies under fluid excitation is established, and a control equation solution strategy for multi-nonlinear factors and multi-space-time scale coupling of the core structure is analyzed; S3: solving the mechanical behavior of the core structure according to the control equation, and performing sensitivity analysis and uncertainty quantification on the data of the solved input-output samples, and completing the analysis of the multi-space-time scale flow-induced vibration behavior law of the core structure.

[0004] However, the existing technology has the problem of low solution efficiency. Therefore, how to invent a research method for vibration characteristics with high solution efficiency is a technical problem that urgently needs to be solved in this technical field. Summary of the invention

[0005] In order to solve the problem of low solution efficiency in the prior art, the present invention provides a fuel rod modeling method, a vibration mode acquisition method, a vibration characteristic research method and a system, which have the characteristics of simple operation.

[0006] In order to achieve the above-mentioned purpose of the present invention, the technical scheme adopted is as follows: A modeling method for fuel rods of a pressurized water reactor includes the following specific steps: treating a fuel rod constrained by multiple grids as a multi-span continuous beam structure, constructing a beam model representing the fuel rod body and a spring model of a plurality of grids; the plurality of spring models are arranged on both sides of the beam model according to their actual positions.

[0007] Preferably, the beam model adopts the Euler-Bernoulli beam model, and the spring model adopts the tension-compression spring model.

[0008] A method for obtaining vibration modes of fuel rod flow-induced vibration based on a transfer matrix method comprises the following specific steps: Constructing a fuel rod model using the fuel rod modeling method; The fuel rod model is divided into several sections of massless elastic beams and concentrated mass beams, and the force balance analysis is performed on each section of massless elastic beams and concentrated mass beams to obtain the field transfer matrix and point transfer matrix. Based on equilibrium analysis and combined with displacement continuity conditions, the unit transfer matrix and the overall transfer matrix are obtained; The overall transfer matrix is ​​solved to obtain the mode shapes of the fuel rod model.

[0009] Preferably, a force balance analysis is performed on each section of the massless elastic beam, and the specific method is as follows: Considering the shear force, bending moment, rotation angle, displacement, length, bending stiffness, and field transfer matrix of each massless elastic beam, the first i Force balance function of segment beam :

[0010] in: for i -1 Shear force at the right end of beam section, for i The shear force at the left end of the beam segment, for i -1 Bending moment at the right end of beam section, for i Bending moment at the left end of the beam segment, No. i -1 The corner at the right end of the beam, for i The corner at the left end of the beam. for i -1 The displacement of the right end of the beam, For the i The displacement of the left end of the beam segment, for i The length of the beam segment, EI is the bending stiffness of the beam, This is the field transfer matrix.

[0011] Furthermore, the force balance analysis is performed on each concentrated mass beam. The specific method is as follows: Considering the shear force, bending moment, rotation angle, displacement, field transfer matrix, and spring stiffness of each concentrated mass beam, the i Force balance function of segment beam :

[0012] in: for i The shear force at the right end of the concentrated mass segment, for i The bending moment at the right end of the concentrated mass segment, No. i The rotation angle at the right end of the concentrated mass segment, for i The displacement of the right end of the concentrated mass segment, is the point transfer matrix, k is the spring stiffness.

[0013] Furthermore, based on the equilibrium analysis and combined with the displacement continuity condition, the unit transfer matrix is ​​obtained, which is:

[0014] in: Pass a matrix to a cell.

[0015] Furthermore, the overall transfer matrix is ​​obtained, which is:

[0016] in: C is the overall transfer matrix, Z 0 is the state vector of the beam head, is the state vector at the end of the beam.

[0017] Furthermore, the overall transfer matrix is ​​solved. The specific steps are as follows: according to the boundary conditions at both ends of the fuel rod, several trial frequencies are set, and the relationship curve between the state vector of the overall transfer matrix and the frequency is plotted. Any solution with a residual force or torque of 0 is taken as the natural frequency, and the state vector corresponding to the frequency is taken as the vibration mode.

[0018] A method for studying the vibration characteristics of fuel rod flow-induced vibration includes the following specific steps: Obtaining the vibration mode of the fuel rod model by the vibration mode acquisition method; Based on the vibration mode of the fuel rod model, forced loads are applied to any nodes in the fuel rod model, and the vibration characteristics of the fuel rod model are further observed.

[0019] A vibration characteristic research system of fuel rod flow-induced vibration, used to implement the vibration characteristic research method, including a modeling module, a force balance analysis module, a calculation module, and a simulation analysis module; The modeling module is used to regard the fuel rods constrained by multiple grids as a multi-span continuous beam structure to construct a fuel rod model; The force balance analysis module is used to divide the fuel rod model into several sections of massless elastic beams and concentrated mass beams, and perform force balance analysis on each section of massless elastic beams and concentrated mass beams to obtain a field transfer matrix and a point transfer matrix; The calculation module is used to obtain the unit transfer matrix and the overall transfer matrix based on equilibrium analysis and combined with the displacement continuity condition; the overall transfer matrix is ​​solved to obtain the modal vibration shape of the fuel rod model; The simulation analysis module is used to apply a forced load to any node in the fuel rod model based on the vibration mode of the fuel rod model, and further observe the vibration characteristics of the fuel rod model.

[0020] The beneficial effects of the present invention are as follows: In view of the above problems, the present invention proposes a method for studying the vibration characteristics of fuel rod flow-induced vibration based on the transfer matrix method. This method does not require grid division or unit selection, but directly incorporates the spring support force into the point transfer matrix and solves the overall transfer matrix through boundary conditions. The entire solution process has efficient computing performance and supports parametric analysis functions. BRIEF DESCRIPTION OF THE DRAWINGS

[0021] Figure 1 The present invention is a flow chart of a method for modeling fuel rods of a pressurized water reactor.

[0022] Figure 2 This is a schematic diagram of the M310 fuel rod model in Example 1.

[0023] Figure 3 It is a schematic diagram of the multi-span continuous beam structure in Example 1.

[0024] Figure 4 The present invention is a flow chart of a method for obtaining vibration modes of flow-induced vibration of fuel rods based on a transfer matrix method.

[0025] Figure 5 In Example 2 L Schematic diagram of a massless elastic beam and a concentrated mass.

[0026] Figure 6 It is the first i Schematic diagram of force analysis of a massless elastic beam.

[0027] Figure 7 It is the first i Schematic diagram of segment concentrated mass force analysis.

[0028] Figure 8 The present invention is a flow chart of a method for studying the vibration characteristics of flow-induced vibration of fuel rods. DETAILED DESCRIPTION

[0029] The present invention is described in detail below with reference to the accompanying drawings and specific embodiments.

[0030] Example 1 like Figure 1 As shown, a modeling method for fuel rods of a pressurized water reactor includes the following specific steps: treating the fuel rods constrained by multiple grids as a multi-span continuous beam structure, constructing a beam model representing the fuel rod body and a spring model of a plurality of grids; the plurality of spring models are arranged on both sides of the beam model according to their actual positions.

[0031] In this embodiment, Figure 2 As shown, the fuel rod includes a lower end plug, a cladding, an air chamber, and an upper end plug; a fuel core is arranged in the cladding, and a spring is arranged in the air chamber; the fuel rod is provided with a plurality of grid constraints.

[0032] like Figure 3 As shown, in a specific embodiment, assuming that the fuel rod remains flat and perpendicular to the neutral axis, the beam model adopts the Euler-Bernoulli beam model, and the spring model adopts the tension-compression spring model. Among them, 8 tension-compression spring models are provided at the left end of the beam model, and 16 tension-compression spring models are provided at the right end of the beam model.

[0033] Example 2 like Figure 4 As shown, a method for obtaining vibration modes of fuel rod flow-induced vibration based on a transfer matrix method includes the following specific steps: Constructing a fuel rod model using the fuel rod modeling method; like Figure 5 As shown, the fuel rods are divided into L The massless elastic beam and the concentrated mass beam are constructed, and the force balance analysis is performed on each massless elastic beam and the concentrated mass beam to obtain the field transfer matrix and the point transfer matrix. Based on equilibrium analysis and combined with displacement continuity conditions, the unit transfer matrix and the overall transfer matrix are obtained; The overall transfer matrix is ​​solved to obtain the mode shapes of the fuel rod model.

[0034] In a specific embodiment, Figure 6 As shown in the figure, the force balance analysis is performed on each section of massless elastic beam. The specific method is as follows: Considering the shear force, bending moment, rotation angle, displacement, length, bending stiffness, and field transfer matrix of each massless elastic beam, the first i Force balance function of segment beam :

[0035] in: for i-1 Shear force at the right end of beam section, for i The shear force at the left end of the beam segment, for i -1 Bending moment at the right end of beam section, for i Bending moment at the left end of the beam segment, No. i -1 The corner at the right end of the beam, for i The corner at the left end of the beam. for i -1 The displacement of the right end of the beam, For the i The displacement of the left end of the beam segment, for i The length of the beam segment, EI is the bending stiffness of the beam, This is the field transfer matrix.

[0036] In a specific embodiment, Figure 7 As shown in the figure, the force balance analysis is performed on each concentrated mass beam. The specific method is as follows: Considering the shear force, bending moment, rotation angle, displacement, field transfer matrix, and spring stiffness of each concentrated mass beam, the i Force balance function of segment beam :

[0037] in: for i The shear force at the right end of the concentrated mass segment, for i The bending moment at the right end of the concentrated mass segment, No. i The rotation angle at the right end of the concentrated mass segment, for i The displacement of the right end of the concentrated mass, is the point transfer matrix, k is the spring stiffness.

[0038] Furthermore, based on the equilibrium analysis and combined with the displacement continuity condition, the unit transfer matrix is ​​obtained, which is:

[0039] in: Pass a matrix to a cell.

[0040] Furthermore, the overall transfer matrix is ​​obtained, which is:

[0041] in: Cis the overall transfer matrix, Z 0 is the state vector of the beam head, is the state vector at the end of the beam.

[0042] In a specific embodiment, the overall transfer matrix is ​​solved, and the specific steps are as follows: according to the boundary conditions at both ends of the fuel rod, several trial frequencies are set, and a curve of the relationship between the state vector of the overall transfer matrix and the frequency is drawn, and any solution with a residual force or torque of 0 is taken as the natural frequency, and the state vector corresponding to the frequency is taken as the vibration mode.

[0043] The present invention proposes a method for studying the flow-induced vibration characteristics of fuel rods based on the transfer matrix method, aiming to achieve a rapid solution to the flow-induced vibration characteristics of fuel rods, while at the same time providing key technical support for the design and operation of pressurized water reactors in order to avoid grid division and unit selection.

[0044] Example 3 like Figure 8 As shown, a method for studying the vibration characteristics of fuel rod flow-induced vibration includes the following specific steps: Obtaining the vibration mode of the fuel rod model by the vibration mode acquisition method; Based on the vibration mode of the fuel rod model, forced loads are applied to any nodes in the fuel rod model, and the vibration characteristics of the fuel rod model are further observed.

[0045] Example 4 A vibration characteristic research system of fuel rod flow-induced vibration, used to implement the vibration characteristic research method, including a modeling module, a force balance analysis module, a calculation module, and a simulation analysis module; The modeling module is used to regard the fuel rods constrained by multiple grids as a multi-span continuous beam structure to construct a fuel rod model; The force balance analysis module is used to divide the fuel rod model into several sections of massless elastic beams and concentrated mass beams, and perform force balance analysis on each section of massless elastic beams and concentrated mass beams to obtain a field transfer matrix and a point transfer matrix; The calculation module is used to obtain the unit transfer matrix and the overall transfer matrix based on equilibrium analysis and combined with the displacement continuity condition; the overall transfer matrix is ​​solved to obtain the modal vibration shape of the fuel rod model; The simulation analysis module is used to apply a forced load to any node in the fuel rod model based on the vibration mode of the fuel rod model, and further observe the vibration characteristics of the fuel rod model.

[0046] Obviously, the above embodiments of the present invention are only examples for clearly explaining the present invention, and are not intended to limit the implementation methods of the present invention. Any modifications, equivalent substitutions and improvements made within the spirit and principles of the present invention shall be included in the protection scope of the claims of the present invention.

Claims

1. A modeling method for a fuel rod of a pressurized water reactor, characterized in that: The method comprises the following specific steps: treating the fuel rods constrained by multiple grids as a multi-span continuous beam structure, constructing a beam model representing the fuel rod body and a spring model of a plurality of grids; and arranging the plurality of spring models on both sides of the beam model according to their actual positions.

2. The fuel rod modeling method according to claim 1, characterized in that: The beam model adopts the Euler-Bernoulli beam model, and the spring model adopts the tension-compression spring model.

3. A method for obtaining vibration modes of fuel rod flow-induced vibration based on transfer matrix method, characterized in that: The specific steps include: Constructing a fuel rod model using the fuel rod modeling method as claimed in claim 1; The fuel rod model is divided into several sections of massless elastic beams and concentrated mass beams, and the force balance analysis is performed on each section of massless elastic beams and concentrated mass beams to obtain the field transfer matrix and point transfer matrix. Based on equilibrium analysis and combined with displacement continuity conditions, the unit transfer matrix and the overall transfer matrix are obtained; The overall transfer matrix is ​​solved to obtain the mode shapes of the fuel rod model.

4. The method for obtaining vibration modes of fuel rod flow-induced vibration based on transfer matrix method according to claim 3, characterized in that: The force balance analysis is performed on each section of massless elastic beam. The specific method is as follows: Considering the shear force, bending moment, rotation angle, displacement, length, bending stiffness, and field transfer matrix of each massless elastic beam, the first i Force balance function of segment beam : in: for i -1 Shear force at the right end of beam section, for i The shear force at the left end of the beam segment, for i -1 Bending moment at the right end of beam section, for i Bending moment at the left end of the beam segment, No. i -1 The corner at the right end of the beam, for i The corner at the left end of the beam. for i -1 The displacement of the right end of the beam, For the i The displacement of the left end of the beam segment, for i The length of the beam segment, EI is the bending stiffness of the beam, This is the field transfer matrix.

5. The method for obtaining vibration modes of fuel rod flow-induced vibration based on transfer matrix method according to claim 4, characterized in that: The force balance analysis is performed on each concentrated mass beam. The specific method is as follows: Considering the shear force, bending moment, rotation angle, displacement, field transfer matrix, and spring stiffness of each concentrated mass beam, the i Force balance function of segment beam : in: for i The shear force at the right end of the concentrated mass segment, for i The bending moment at the right end of the concentrated mass segment, No. i The rotation angle at the right end of the concentrated mass segment, for i The displacement of the right end of the concentrated mass segment, is the point transfer matrix, k is the spring stiffness.

6. The method for obtaining vibration modes of fuel rod flow-induced vibration based on transfer matrix method according to claim 5, characterized in that: Based on the equilibrium analysis and combined with the displacement continuity condition, the unit transfer matrix is ​​obtained, which is: in: Pass a matrix to a cell.

7. The method for obtaining vibration modes of fuel rod flow-induced vibration based on transfer matrix method according to claim 5, characterized in that: The overall transfer matrix is ​​obtained, which is: in: C is the overall transfer matrix, Z 0 is the state vector of the beam head, is the state vector at the end of the beam.

8. The method for obtaining vibration modes of fuel rod flow-induced vibration based on transfer matrix method according to claim 5, characterized in that: The overall transfer matrix is ​​solved. The specific steps are as follows: according to the boundary conditions at both ends of the fuel rod, several trial frequencies are set, and the relationship curve between the state vector of the overall transfer matrix and the frequency is plotted. Any solution with a residual force or torque of 0 is taken as the natural frequency, and the state vector corresponding to the frequency is taken as the vibration mode.

9. A method for studying the vibration characteristics of fuel rod flow-induced vibration, characterized in that : Includes the following specific steps: Obtaining the vibration mode of the fuel rod model by the vibration mode acquisition method as described in any one of claims 3 to 8; Based on the vibration mode of the fuel rod model, forced loads are applied to any nodes in the fuel rod model, and the vibration characteristics of the fuel rod model are further observed.

10. A vibration characteristic research system for fuel rod flow-induced vibration, characterized in that : Used to implement the vibration characteristics research method as claimed in claim 9, comprising a modeling module, a force balance analysis module, a calculation module, and a simulation analysis module; The modeling module is used to regard the fuel rods constrained by multiple grids as a multi-span continuous beam structure to construct a fuel rod model; The force balance analysis module is used to divide the fuel rod model into several sections of massless elastic beams and concentrated mass beams, and perform force balance analysis on each section of massless elastic beams and concentrated mass beams to obtain a field transfer matrix and a point transfer matrix; The calculation module is used to obtain the unit transfer matrix and the overall transfer matrix based on equilibrium analysis and combined with the displacement continuity condition; Solve the overall transfer matrix to obtain the mode shapes of the fuel rod model; The simulation analysis module is used to apply a forced load to any node in the fuel rod model based on the vibration mode of the fuel rod model, and further observe the vibration characteristics of the fuel rod model.

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