Fuel rod static instability analysis method and device, storage medium and computer equipment

Abstract

The invention relates to the technical field of fuel assembly fluid-solid coupling analysis and the technical field of computers, and discloses a fuel rod static instability analysis method and device, a storage medium and computer equipment. The method comprises the steps that a transverse vibration displacement expansion of a fuel rod is constructed, and a disturbance potential function under the condition that the influence of fluid speed is considered is established; based on the disturbance potential function, a mechanical model of the fluid acting force borne by the fuel rod in the transverse direction is built, and the transverse vibration displacement of the fuel rod and the fluid acting force in the transverse direction are solved; based on a QR decomposition algorithm, transverse vibration displacement and fluid acting force are analyzed, the static instability state of the fuel rod is determined, the reactor fuel rod is used as an analysis object, an axial flow fuel rod fluid-solid coupling control equation is established, a characteristic value solving method is provided, the static instability characteristic of the fuel rod is clarified through the solved characteristic value, and the stability of the fuel rod is improved. The influence mechanism of the axial flow velocity of the coolant on the static stability of the fuel rod is revealed.

Description

TECHNICAL FIELD

[0001] The present application relates to the technical field of fuel assembly fluid-structure coupling analysis and the technical field of computers, and in particular to a fuel rod static instability analysis method and device, a storage medium and a computer device. BACKGROUND

[0002] The structural vibration of a reactor fuel rod occurs under the axial excitation of a coolant, and in turn, the structural vibration has an impact on the coolant flow, which is a typical fluid-structure coupling problem in the field of nuclear engineering.

[0003] In previous studies, it is generally believed that the vibration mechanism of the fuel rod is turbulent excitation, and only the micro-amplitude vibration of the fuel rod is concerned. However, with the continuous increase of the power of future reactors and the continuous deepening of the design of miniaturization and compactness, the flow velocity of the coolant around the fuel rod may be further increased. When the flow velocity of the coolant reaches a certain threshold, the fuel rod will lose its original stable configuration and occur buckling (i.e., static instability). The main reason for static instability is that the coolant and the fuel rod form a fluid-structure coupling system, and the stiffness in the system is negatively affected by the flow velocity of the coolant. SUMMARY

[0004] Therefore, the present application provides a fuel rod static instability analysis method and device, a storage medium and a computer device, which take the reactor fuel rod as the analysis object, establish the fluid-structure coupling control equation of the axial flow fuel rod, and provide an eigenvalue solving method. The static instability characteristics of the fuel rod are clear through the solved eigenvalue, which is beneficial to reveal the influence mechanism of the axial flow velocity of the coolant on the static stability of the fuel rod.

[0005] According to one aspect of the present application, a fuel rod static instability analysis method is provided, which comprises:

[0006] For the fuel rod in the reactor reaction process, a transverse vibration displacement expansion formula of the fuel rod is constructed, wherein the transverse vibration displacement expansion formula mathematically characterizes the transverse vibration displacement of the fuel rod through a series form of a modal function, the modal function satisfies the physical boundary conditions of the fuel rod, and the physical boundary conditions include that the displacement of both ends of the fuel rod is zero;

[0007] Based on the disturbance effect caused by the transverse vibration of the fuel rod, a disturbance potential function of the disturbance effect considering the influence of the fluid velocity is established, and based on the disturbance potential function, a mechanical model of the fluid action force acting on the fuel rod in the transverse direction is constructed;

[0008] The transverse vibration displacement of the fuel rod in the reactor reaction process is solved by using the transverse vibration displacement expansion formula, and the fluid action force acting on the fuel rod in the transverse direction is solved based on the mechanical model;

[0009] The fuel rod static instability state analysis module is configured to analyze the solved transverse vibration displacement and fluid force based on a QR decomposition algorithm, and determine a static instability state of the fuel rod based on an analysis result, wherein the static instability state includes a progressive stable state, a divergent instability state, and a critical instability state.

[0010] According to another aspect of the present application, a fuel rod static instability analysis device is provided, and the device includes:

[0011] A fuel rod vibration displacement modal construction module is configured to construct a transverse vibration displacement expansion formula of a fuel rod during a reactor reaction process, wherein the transverse vibration displacement expansion formula mathematically characterizes the transverse vibration displacement of the fuel rod through a series form of modal functions, and the modal functions satisfy physical boundary conditions of the fuel rod, and the physical boundary conditions include zero displacement at both ends of the fuel rod.

[0012] A fluid mechanics model construction module is configured to establish a disturbance potential function of a disturbance effect caused by the transverse vibration of the fuel rod under consideration of fluid velocity, and construct a mechanics model of fluid force acting on the fuel rod in the transverse direction based on the disturbance potential function.

[0013] A vibration displacement and fluid force solving module is configured to solve the transverse vibration displacement of the fuel rod during the reactor reaction process by using the transverse vibration displacement expansion formula, and solve the fluid force acting on the fuel rod in the transverse direction based on the mechanics model.

[0014] The fuel rod static instability state analysis module is configured to analyze the solved transverse vibration displacement and fluid force based on a QR decomposition algorithm, and determine a static instability state of the fuel rod based on an analysis result, wherein the static instability state includes a progressive stable state, a divergent instability state, and a critical instability state.

[0015] According to yet another aspect of the present application, a storage medium having a computer program stored thereon is provided, and the program is executed by a processor to implement the above-mentioned fuel rod static instability analysis method.

[0016] According to still another aspect of the present application, a computer device is provided, and includes a storage medium, a processor, and a computer program stored on the storage medium and executable on the processor, and the processor implements the above-mentioned fuel rod static instability analysis method when executing the program.

[0017] By means of the technical scheme, the application provides a fuel rod static instability analysis method and device, a storage medium and a computer device, takes a reactor fuel rod as an analysis object, establishes an axial flow fuel rod fluid-solid coupling control equation, and provides an eigenvalue solving method, so that the static instability characteristics of the fuel rod are clear through the solved eigenvalue, and the influence mechanism of the coolant axial flow velocity on the static stability of the fuel rod is revealed.

[0018] The above description is only a summary of the technical scheme of the application, in order to more clearly understand the technical means of the application, the application can be implemented according to the content of the specification, and in order to make the above and other purposes, characteristics and advantages of the application more obvious and easy to understand, the following specific embodiments of the application are described. BRIEF DESCRIPTION OF DRAWINGS

[0019] The accompanying drawings described herein are used to provide further understanding of the application, and form a part of the application. The schematic embodiments of the application and the description thereof are used to explain the application, and do not constitute an improper limitation on the application. In the drawings:

[0020] Figure 1 A flowchart of a fuel rod static instability analysis method provided by an embodiment of the application is shown;

[0021] Figure 2 A flowchart of another fuel rod static instability analysis method provided by an embodiment of the application is shown;

[0022] Figure 3 A structural diagram of a fuel rod static instability analysis device provided by an embodiment of the application is shown. DETAILED DESCRIPTION

[0023] In the following, the application will be described in detail with reference to the drawings and in combination with the embodiments. It should be noted that the embodiments in the application and the features in the embodiments can be combined with each other without conflict.

[0024] In the embodiment, a fuel rod static instability analysis method is provided, as shown in the figure, the method comprises: Figure 1

[0025] Step 101, for a fuel rod in a reactor reaction process, a transverse vibration displacement expansion formula of the fuel rod is constructed, wherein the transverse vibration displacement expansion formula mathematically characterizes the transverse vibration displacement of the fuel rod through a series form of a modal function, the modal function satisfies a physical boundary condition of the fuel rod, and the physical boundary condition includes that the displacement of both ends of the fuel rod is zero.

[0026] ​In the above embodiments of the present application, for the problem of how the coolant flow rate affects the static stability of the fuel rod, the linear vibration control equation of the fuel rod is derived through the Hamilton principle and the inviscid potential flow theory. By extracting the eigenvalues of the Jacobian matrix of the control equation at the fixed point, the static stability of the fuel rod (i.e. the buckling instability critical flow rate) is judged, so that the key factors such as reactor power and flow distribution can be comprehensively considered in the design stage, thereby improving the reliability of the reactor operation. Specifically, in the static instability analysis of the fuel rod, the following assumptions are made:

[0027] 1. The fuel rod has a slenderness ratio and a symmetrical geometric cross-section in the predetermined large slenderness ratio range;

[0028] 2. Only the lateral vibration of the fuel rod is considered;

[0029] 3. The size of the fluid domain is in the range of much larger than the radial size of the structure;

[0030] 4. The fluid (coolant) density is less than the density of the fuel rod material.

[0031] In a nuclear reactor, for example, a pressurized water reactor fuel rod, the length of the pressurized water reactor fuel rod is generally on the order of several meters, for example, the common length can reach 4 meters, and the diameter can be 10 millimeters, so the calculated slenderness ratio (length to diameter ratio) is 400, which belongs to the large slenderness ratio range. This large slenderness ratio makes the fuel rod more similar to the characteristics of a beam structure in terms of mechanical behavior, and its lateral vibration characteristics are more pronounced and more prone to buckling instability and other phenomena when subjected to external forces. In terms of symmetrical geometric cross-section, the cross-section of the pressurized water reactor fuel rod is generally circular, which has high symmetry. This symmetrical geometric cross-section makes the mechanical properties of the fuel rod uniform in all directions, so that the calculation model can be simplified by using symmetry when analyzing its vibration and stability problems, reducing the complexity of the analysis. Taking a typical fuel rod in the coolant channel of a pressurized water reactor as an example, in a pressurized water reactor, the coolant channel is designed to ensure that the coolant can fully remove the heat generated by the fuel rod, and the lateral size of the coolant channel (such as the height or width of the channel) is usually on the order of tens of centimeters, for example, the height of some pressurized water reactor channels can reach 30-50 centimeters. When the diameter of the fuel rod is 10 millimeters, it can be seen that the size of the fluid domain (measured in lateral size) is much larger than the radial size of the structure, i.e. it meets the range of much larger than the radial size of the structure. This size difference allows the fluid domain to be approximated as an infinite or semi-infinite space when analyzing the interaction between the fluid and the fuel rod, thereby simplifying the establishment and solution process of the fluid dynamics model. For example, in the establishment of the mechanical model of the fluid force, the complex influence of the fluid domain boundary on the fluid flow and pressure distribution can be ignored, and some simplified theories and methods can be used to describe the action of the fluid on the fuel rod.

[0032] Further, for the fuel rod in the reactor reaction process, the lateral vibration displacement expansion formula of the fuel rod is constructed. Since the actual vibration of the fuel rod is the vibration of a continuous system with infinite degrees of freedom, direct analysis is very complex. The lateral vibration displacement expansion formula can represent the continuous vibration displacement with a finite series, can convert the infinite degree of freedom system into a finite degree of freedom system, and thus can simplify the complexity of the problem and reduce the difficulty of analysis and calculation. At the same time, the lateral vibration displacement expansion formula corresponds to different vibration modes of the fuel rod, and each vibration mode has independent vibration frequency and damping characteristics. Through the lateral vibration displacement expansion formula, the complex vibration of the fuel rod can be decomposed into a linear combination of various vibration modes, which is convenient for analyzing the vibration characteristics of each vibration mode respectively, without considering all possible vibration conditions at the same time.

[0033] In particular, the lateral vibration displacement expansion formula mathematically characterizes the lateral vibration displacement of the fuel rod through the series form of the modal function. The modal function is a mathematical function used to describe the lateral vibration displacement of the fuel rod, which is usually expanded in series form. These modal functions need to satisfy the geometric and physical boundary conditions of the fuel rod, such as displacement and rotation angle conditions of fixed or free ends. More specifically, the physical boundary conditions can include displacement of zero at both ends of the fuel rod (fixed end) or bending moment of zero (free end), etc. The selection of the modal function determines the distribution form of the vibration displacement and is the basis of structural dynamics analysis. In addition, the modal function can accurately describe the lateral vibration displacement distribution of the fuel rod at different positions, and the series form can take a sufficient number of terms as needed to approximate the real vibration displacement of the fuel rod, improve the description accuracy, and the expanded lateral vibration displacement not only contains the spatial information of the fuel rod vibration (through the modal function), but also contains the time information (through the time function), so that the subsequent dynamic vibration behavior of the fuel rod in the reaction process can be comprehensively described, such as the change of vibration frequency and amplitude with time, etc.

[0034] Optionally, for step 101, "constructing the lateral vibration displacement expansion formula of the fuel rod", specifically comprising:

[0035] Step 1011, obtaining the length of the fuel rod and the axial coordinate of the fuel rod.

[0036] Step 1012, according to the Rayleigh-Ritz method, the length of the fuel rod and the axial coordinate of the fuel rod, expanding the lateral vibration displacement of the fuel rod into a finite series of modal functions to obtain the lateral vibration displacement expansion formula of the fuel rod, wherein the lateral vibration displacement expansion formula of the fuel rod is:

[0037]

[0038] w is the transverse vibration displacement of the fuel rod, M is the total number of series terms, m is the first series expansion parameter in the transverse direction, w m (t) is the generalized coordinate of the transverse vibration of the fuel rod with respect to time t in the longitudinal direction, L is the length of the fuel rod, z is the axial coordinate of the fuel rod, and sin is the modal function.

[0039] In the above embodiments of the present application, after the length of the fuel rod and the axial coordinate of the fuel rod are obtained, the transverse vibration displacement w of the fuel rod can be expanded into a finite series of modal functions (the modal functions satisfy the physical boundary conditions of the fuel rod) according to the Rayleigh-Ritz method.

[0040] In step 102, based on the disturbance effect caused by the transverse vibration of the fuel rod, a disturbance potential function of the disturbance effect considering the influence of fluid velocity is established, and based on the disturbance potential function, a mechanical model of the fluid force acting on the fuel rod in the transverse direction is constructed.

[0041] Then, the disturbance potential function can quantify the fluid disturbance caused by the transverse vibration of the fuel rod, so that the influence of fluid velocity on the disturbance potential function can be considered when constructing the mechanical model subsequently. The change of fluid velocity will change the momentum transfer and energy distribution of fluid, and then affect the force of fluid acting on the fuel rod, therefore, the mechanical model constructed by considering the influence of fluid velocity can capture these changes, and then the fluid force acting on the fuel rod in the transverse direction can be calculated more accurately. Since the traditional mechanical model ignores the influence of fluid velocity on the disturbance effect, it will cause errors in the calculation result, and the mechanical model of the present application can reduce the errors and improve the accuracy of the calculation result by considering the influence of fluid velocity.

[0042] Optionally, in step 102, based on the disturbance effect caused by the transverse vibration of the fuel rod, a disturbance potential function of the disturbance effect considering the influence of fluid velocity is established, and based on the disturbance potential function, a mechanical model of the fluid force acting on the fuel rod in the transverse direction is constructed, specifically including:

[0043] In step 1021, the length and radius of the fuel rod are obtained.

[0044] In step 1022, the total velocity potential of the fluid around the fuel rod is represented as the superposition of the uniform flow velocity and the disturbance potential function, and based on the representation form of the total velocity potential of the fluid after superposition, and combined with the influence of the length, radius and transverse vibration displacement of the fuel rod on the fluid flow, the spatial constraint condition required to be satisfied by the total velocity potential of the fluid is obtained.

[0045] In step 1023, a solution of the Laplace equation under the constraint of the spatial boundary condition is solved to obtain a perturbation potential function under the influence of the fluid velocity, where the perturbation potential function is a solution satisfying the Laplace equation and conforming to the spatial boundary condition, and the perturbation potential function represents the flow characteristics of the fluid under the constraint of the spatial boundary condition around the fuel rod. The expression of the total velocity potential of the superimposed fluid is:

[0046] Φ = Uz + φ,

[0047] The spatial boundary condition is:

[0048]

[0049] The perturbation potential function under the influence of the fluid velocity is:

[0050]

[0051] Φ is the total velocity potential of the superimposed fluid, U is the uniform flow velocity of the fluid around the fuel rod, z is the axial coordinate of the fuel rod, φ is the perturbation potential function, L is the length of the fuel rod, r is the radial coordinate of the fuel rod, a is the radius of the fuel rod, w is the transverse vibration displacement of the fuel rod, θ is the circumferential coordinate of the fuel rod, in the series term, M is the total number of series terms, m and n are series expansion parameters in the transverse direction, the series expansion parameters include a first series expansion parameter m and a second series expansion parameter n, the series expansion parameters are used for finite series expansion of the transverse vibration displacement of the fuel rod, w m (t) is the generalized coordinate of the transverse vibration of the fuel rod with respect to time t in the longitudinal direction, β mn is a first series coupling coefficient related to m and n, K1 is a second type of modified Bessel function, is the first order derivative of w n (t), w n (t) is the generalized coordinate of the transverse vibration of the fuel rod with respect to time t in the transverse direction, and are the partial derivatives of φ with respect to z and r respectively, are the partial derivatives of w with respect to t and z respectively, is the derivative of the function K1(mπr / L) with respect to r, cos is the cosine function, φ r→∞ is the limit value of φ when r approaches infinity.

[0052] At step 1024, a value of the perturbation potential function in the total velocity potential of the fluid is represented as a surface boundary integral form of the fuel rod according to the Cauchy-Lagrange integral formula and the space boundary condition, a distributed pressure calculation process is constructed based on a process of gradient calculation of the perturbation potential function, the surface boundary integral form of the fuel rod is substituted into the distributed pressure calculation process, and a distributed pressure on the surface of the fuel rod is obtained, and the calculated distributed pressure is integrated to obtain a mechanical model of fluid acting force on the fuel rod in the transverse direction, wherein the mechanical model is:

[0053]

[0054] F x is the fluid acting force on the fuel rod in the transverse direction, p f is the fluid density, and m (t) is a function representing a change of the interaction force between the fluid and the fuel rod with time t, is a first-order derivative of m (t), and m is a first mode parameter of the interaction between the fluid and the fuel rod, and sin is a sine function.

[0055] In the above embodiments of the present application, the total velocity potential of the fluid is first decomposed into a superposition of a uniform flow and a perturbation velocity field. The perturbation velocity field is characterized by the gradient of the perturbation potential function, and this decomposition can decompose the fluid flow into a basic flow and a local perturbation caused by vibration, and establish a physical model basis for subsequent analysis.

[0056] Then, the space boundary condition is established in combination with the geometric characteristics and vibration characteristics of the fuel rod. The non-penetration condition of the surface of the fuel rod requires that the fluid normal velocity component must be strictly matched with the transverse vibration velocity of the rod body, and this condition converts the length, radius and other static parameters of the fuel rod and the dynamic vibration displacement (i.e. transverse vibration displacement) into a space constraint on the fluid velocity field, forming a necessary condition for mathematical solution, i.e. a space constraint condition to be satisfied by the total velocity potential of the fluid.

[0057] Then, under the above space boundary condition constraint, the specific form of the perturbation potential function is obtained by solving the fluid control equation (such as Laplace equation), for which the mechanical vibration of the fuel rod is coupled with the fluid flow through the fluid dynamics equation, so that the perturbation potential function contains both the fluid basic flow information and the dynamic modulation effect caused by vibration, and finally a complete expression is obtained which reflects both the macroscopic motion characteristics of the fluid and the coupling influence of the solid vibration.

[0058] Specifically, the uniform flow velocity of the fluid around the fuel rod is U, and the total velocity potential of the fluid can be described as follows:

[0059] Φ=Uz+φ,

[0060] In the formula, φ is the perturbation potential function, which is the core physical quantity, and is used to represent the perturbation situation caused by the transverse motion of the fuel rod in the fluid, considering the following spatial boundary conditions:

[0061]

[0062] In the formula, r, θ, and z are the radial, circumferential, and axial coordinates, respectively, L is the length of the fuel rod, and a is the radius of the fuel rod, and then the perturbation potential function can be obtained as:

[0063]

[0064] In the formula, M is the total number of series terms, indicating the number of terms taken in the summation process, which determines the accuracy and range of the summation, U is the uniform flow velocity of the fluid around the fuel rod, reflecting the speed of the fluid around the fuel rod, and is one of the important factors affecting the perturbation potential function, w m (t) is the generalized coordinate of the transverse vibration of the fuel rod in the longitudinal direction with respect to time t, which is used to describe the state of the transverse motion of the fuel rod at different times. β mn is the first series coupling coefficient related to m and n, which has different calculation formulas according to whether m+n is odd or even:

[0065]

[0066] K1 is the second type of modified Bessel function, which is a special mathematical function used to describe physical problems with specific boundary conditions in the field of fluid mechanics. L is the length of the fuel rod, which is used for dimensionless processing. r is the radial coordinate of the fuel rod, indicating the distance from a point in the fluid to the axis of the fuel rod, θ is the circumferential coordinate of the fuel rod, used to describe the position of a point in the fluid in the circumferential direction around the axis of the fuel rod, z is the axial coordinate of the fuel rod, indicating the position along the axis of the fuel rod, and different combinations of m and n correspond to different physical modes.

[0067] Then, according to the Cauchy-Lagrange integral formula, the fluid force acting on the fuel rod in the transverse direction can be obtained as:

[0068]

[0069] In the formula, ρ f is the fluid density.

[0070] Furthermore, when deriving the mechanical model of the fluid forces acting on the fuel rod in the transverse direction using the Cauchy-Lagrange integral formula and spatial boundary conditions, the Cauchy-Lagrange integral formula is an important tool in fluid mechanics for handling potential flow problems. When the fluid around the fuel rod can be considered as potential flow, the perturbation potential function Φ satisfies the Laplace equation. Using mathematical methods such as Green's theorem, combined with spatial boundary conditions (such as boundary conditions on the fuel rod surface, including impenetrability conditions), the value of the perturbation potential function in the flow field can be expressed as an integral of the boundary conditions on the fuel rod surface. Specifically:

[0071] Let the surface area of ​​the fuel rod be S. Given appropriate boundary conditions on the fuel rod surface, such as zero normal velocity (impenetrable condition), using Green's third law, for any point in the flow field, the perturbation potential function Φ can be expressed as an integral form on the surface of the fuel rod, i.e.:

[0072]

[0073] Where P is a point in the flow field, Q is a point on the surface of the fuel rod, and r = |PQ|;

[0074] It is the derivative along the outer normal of the fuel rod surface.

[0075] Next, according to Bernoulli's equation in fluid mechanics, in incompressible, inviscid, steady-state or quasi-steady-state potential flow, the pressure p is related to the disturbance potential function Φ. The total pressure p total It can be represented as:

[0076]

[0077] Where p∞ is the incoming flow pressure, and ρ is the fluid density (same as ρ). f ), This refers to the incoming flow velocity (same as U). The distributed pressure pp∞ can be calculated by the gradient of the perturbation potential function, i.e.:

[0078]

[0079] Next, by substituting the boundary integral expression of the perturbation potential function on the fuel rod surface into the pressure formula, the distributed pressure p(s)-p∞ on the fuel rod surface can be calculated, where s is the arc length parameter of the fuel rod surface, and F is the fluid force F acting on the fuel rod in the transverse direction (let's say the x-direction). xThe distributed pressure on the surface of the fuel rod can be obtained by integrating the distributed pressure on the surface. To this end, through a series of mathematical derivations and simplifications, the expression of the distributed pressure is substituted into the above integral formula, and the boundary integral form of the perturbation potential function and the related boundary conditions are combined, and finally the mechanical model of the fluid force acting on the fuel rod in the transverse direction is obtained, which comprehensively considers the interaction between the fluid and the fuel rod, the characteristics of the fluid and the geometric characteristics of the fuel rod and other factors.

[0080] In step 103, the transverse vibration displacement of the fuel rod during the reaction process of the reactor is solved by using the transverse vibration displacement expansion formula, and the fluid force acting on the fuel rod in the transverse direction is solved based on the mechanical model.

[0081] Then, the transverse vibration displacement expansion formula and the mechanical model can more accurately describe the vibration characteristics of the fuel rod and the fluid force, reduce the calculation error, provide convenience for subsequent analysis of the dynamic response of the fuel rod during the operation of the reactor, and help to predict the vibration behavior and safety of the fuel rod.

[0082] In step 104, the transverse vibration displacement and the fluid force solved are analyzed based on the QR decomposition algorithm, and the static instability state of the fuel rod is determined based on the analysis result, wherein the static instability state includes a gradual stability state, a divergent instability state and a critical instability state.

[0083] Then, the transverse vibration displacement and the fluid force solved can be analyzed by using the QR decomposition algorithm. QR decomposition is to decompose a matrix into a product of an orthogonal matrix Q and an upper triangular matrix R, that is, A=QR, where A is the matrix to be decomposed.

[0084] Optionally, for step 104, "based on the QR decomposition algorithm, the transverse vibration displacement and the fluid force solved are analyzed, and the static instability state of the fuel rod is determined based on the analysis result", specifically includes:

[0085] In step 1041, a fuel rod vibration control equation is constructed, and the fuel rod vibration control equation is discretized and matrix processed in combination with the transverse vibration displacement and the fluid force to obtain a matrix form of the fuel rod transverse vibration control equation.

[0086] In step 1042, the static instability state of the fuel rod is determined based on the matrix form of the fuel rod transverse vibration control equation, wherein the fuel rod vibration control equation is:

[0087]

[0088] The matrix form of the fuel rod transverse vibration control equation is:

[0089]

[0090] p s is the fuel rod density, A is the fuel rod cross-sectional area, w is the transverse vibration displacement of the fuel rod, t is time, E is the elastic modulus, I is the cross-sectional moment of inertia, z is the axial coordinate of the fuel rod, F x is the fluid force acting on the fuel rod in the transverse direction, M, C and K are respectively the mass matrix, the damping matrix and the stiffness matrix of the fluid-structure coupling system, the fluid-structure coupling system including the coolant regarded as a fluid and the fuel rod, the components of M, C and K are respectively M(i,j), C(i,j) and K(i,j), and are respectively the second-order derivative and the first-order derivative of w, δ ij is the Kronecker symbol, 1 when i=j, otherwise 0, M is the total number of series terms, m is the first series expansion parameter in the transverse direction, a is the radius of the fuel rod, p f is the fluid density, l m is the first mode parameter of the fluid-fuel rod interaction, b mi and b mj are respectively the second series coupling coefficient and the third series coupling coefficient characterizing the fluid-fuel rod interaction force under the longitudinal mode parameter, U is the uniform flow velocity of the fluid around the fuel rod, L is the length of the fuel rod, i and j are respectively the first variable and the second variable in (i,j), b ij and b ji are respectively the fourth series coupling coefficient and the fifth series coupling coefficient characterizing the fluid-fuel rod interaction force, a0 and a1 are respectively the first Rayleigh damping coefficient and the second Rayleigh damping coefficient, l i and l j are respectively the second mode parameter and the third mode parameter of the fluid-fuel rod interaction.

[0091] Step 1043, converting the matrix form of the fuel rod transverse vibration control equation into a single degree of freedom system expression, and converting the single degree of freedom system expression into a matrix expression for solving eigenvalues through a state vector, solving the eigenvalues of the matrix expression by a QR decomposition algorithm, and obtaining the static instability state of the fuel rod based on the solved eigenvalues, wherein the matrix expression is:

[0092]

[0093] q is a state vector, is the first-order derivative of q, H is the matrix expression for solving eigenvalues, 0 is a zero matrix, I is a unit matrix, and T is a transpose.

[0094] Step 1044, when the real part of the solved eigenvalue is negative, the static instability state of the fuel rod is a progressive stable state, when the real part of the solved eigenvalue is positive, the static instability state of the fuel rod is a divergent instability state, and when the real part of the solved eigenvalue is zero, the static instability state of the fuel rod is a critical instability state.

[0095] In the above embodiments of the present application, the Rayleigh damping coefficient, i.e. the Rayleigh damping coefficient, assumes that the damping matrix of the structure is a combination of the mass matrix and the stiffness matrix, which is an orthogonal damping, and the damping matrix can be expressed as a linear combination of the mass matrix and the stiffness matrix. Specifically, the axial stress-strain relationship of the fuel rod can be expressed as:

[0096]

[0097] In the formula, u is the axial displacement of the fuel rod, and the vibration potential energy and kinetic energy of the fuel rod are:

[0098]

[0099] Combining the Hamilton principle:

[0100]

[0101] The vibration control equation of the fuel rod can be derived:

[0102]

[0103] In the formula, E is the elastic modulus of the fuel rod, ρ s is the density of the fuel rod, and I is the cross-sectional moment of inertia of the fuel rod.

[0104] Substituting the transverse vibration displacement and the fluid force into the vibration control equation of the fuel rod, the matrix form of the transverse vibration control equation of the fuel rod is:

[0105]

[0106] In the formula, M, C and K are the system mass matrix, damping matrix and stiffness matrix respectively, and their components are respectively:

[0107]

[0108] In the formula, δ ij is the Kronecker symbol, in order to obtain the eigenvalue of the fuel rod vibration system, the matrix form of the transverse vibration control equation of the fuel rod can be rewritten as the following single degree of freedom system:

[0109]

[0110] In the formula Therefore, it is transformed into the eigenvalue problem of the following matrix H:

[0111]

[0112] The eigenvalue of the matrix H can be obtained by the QR decomposition algorithm, and the stability of the fuel rod vibration system can be judged by the sign of the real part of the eigenvalue: if the real part of the eigenvalue is negative, it means that the fuel rod vibration is in a gradually stable state; if the real part of the eigenvalue is positive, it means that the fuel rod vibration is in a divergent unstable state; if the real part of the eigenvalue is zero, it means that the fuel rod vibration system is in a critical unstable state. Through the above process, the stability of the fuel rod vibration system under different axial flow velocities U can be obtained, and thus the variation law of the critical unstable state flow velocity with the axial flow velocity can be obtained.

[0113] In a specific embodiment, as shown in Figure 2 , given a fuel rod with a slenderness ratio and a symmetric geometric cross section conforming to a preset large slenderness ratio range, only considering transverse vibration, the fluid domain size conforms to the range of being much larger than the structural radial size, the fluid density is less than the density of the fuel rod, the flow field control equation is established, and the fluid-structure coupling boundary coordination condition is determined, the transverse fluid force of the fuel rod is solved, the fuel rod vibration equation is constructed by combining the fuel rod constitutive relation and the Hamilton principle, the generalized eigenvalue of the finite-dimensional vibration equation is solved by using the Rayleigh-Ritz method, and finally the stability is judged by the real part and the imaginary part of the solved eigenvalue.

[0114] By applying the technical solution of the embodiment, the reactor fuel rod is taken as the analysis object, the fluid-structure coupling control equation of the axial flow fuel rod is established, and the eigenvalue solving method is provided. The static instability characteristics of the fuel rod are clear by solving the eigenvalue, which is conducive to revealing the influence mechanism of the axial flow velocity of the coolant on the static stability of the fuel rod.

[0115] Further, as Figure 1 a specific implementation of the method, the embodiment of the present application provides a fuel rod static instability analysis device, as shown in Figure 3 , the device comprises:

[0116] A fuel rod vibration displacement modal construction module 201 is configured to construct a transverse vibration displacement expansion formula of a fuel rod in a reactor during a reactor reaction process, wherein the transverse vibration displacement expansion formula mathematically characterizes the transverse vibration displacement of the fuel rod through a series form of a modal function.

[0117] A fluid mechanics model construction module 202 is configured to establish a disturbance potential function of a disturbance effect of the fuel rod under consideration of the influence of fluid velocity based on the disturbance effect caused by the transverse vibration of the fuel rod, and construct a mechanics model of fluid action force on the fuel rod in the transverse direction based on the disturbance potential function.

[0118] a vibration displacement and fluid force solving module 203, configured to solve the transverse vibration displacement of the fuel rod in the reactor reaction process by using the transverse vibration displacement expansion formula, and solve the fluid acting force acting on the transverse direction of the fuel rod based on the mechanical model;

[0119] a fuel rod static instability state analysis module 204, configured to analyze the solved transverse vibration displacement and fluid acting force based on a QR decomposition algorithm, and determine the static instability state of the fuel rod based on the analysis result, wherein the static instability state includes a progressive stable state, a divergent instability state and a critical instability state.

[0120] It should be noted that other corresponding descriptions of the various functional units involved in the fuel rod static instability analysis device provided in the embodiments of the present application can refer to the corresponding descriptions in the method, and will not be described here.

[0121] Based on the above method as Figure 1 indicated, correspondingly, the embodiments of the present application also provide a storage medium having a computer program stored thereon, which is executed by a processor to implement the fuel rod static instability analysis method as Figure 1 indicated above.

[0122] Based on such understanding, the technical solutions of the present application can be embodied in the form of a software product, which can be stored in a non-volatile storage medium (which can be a CD-ROM, a U disk, a mobile hard disk, etc.), and includes a plurality of instructions for causing a computer device (which can be a personal computer, a server, or a network device, etc.) to execute the methods described in various implementation scenarios of the present application.

[0123] Based on the above method as Figure 1 indicated, and Figure 3 the virtual device embodiment as Figure 1 indicated, in order to achieve the above purpose, the embodiments of the present application also provide a computer device, which can be a personal computer, a server, a network device, etc., and the computer device includes a storage medium and a processor; the storage medium is used to store a computer program; the processor is used to execute the computer program to implement the fuel rod static instability analysis method as indicated above.

[0124] Optionally, the computer device can further include a user interface, a network interface, a camera, a radio frequency (RF) circuit, a sensor, an audio circuit, a WI-FI module, and the like. The user interface can include a display screen, an input unit such as a keyboard, and the like. Optionally, the user interface can further include a USB interface, a card reader interface, and the like. The network interface can optionally include a standard wired interface, a wireless interface (such as a Bluetooth interface, a WI-FI interface), and the like.

[0125] Those skilled in the art can understand that the computer device structure provided by the embodiment does not constitute a limitation on the computer device, and can include more or fewer components, or combine certain components, or different component arrangements.

[0126] The storage medium can further include an operating system, a network communication module. The operating system is a program for managing and saving computer device hardware and software resources, supporting the running of information processing programs and other software and / or programs. The network communication module is used to realize the communication between the components in the storage medium and the communication with other hardware and software in the entity device.

[0127] Through the description of the above embodiments, those skilled in the art can clearly understand that the present application can be realized by means of software and necessary general hardware platform, or by hardware to build the lateral vibration displacement expansion formula of the fuel rod, based on the disturbance effect caused by the lateral vibration of the fuel rod, to establish the disturbance potential function under the consideration of fluid velocity, and to build the mechanical model of the fluid force acting on the fuel rod in the lateral direction, to solve the lateral vibration displacement of the fuel rod and the fluid force in the lateral direction; based on the QR decomposition algorithm, the lateral vibration displacement and the fluid force are analyzed to determine the static instability state of the fuel rod, to take the reactor fuel rod as the analysis object, to establish the axial flow fuel rod fluid-solid coupling control equation, and to provide the eigenvalue solving method. The eigenvalue solving method clearly shows the static instability characteristics of the fuel rod, which is beneficial to reveal the influence mechanism of the coolant axial flow velocity on the static stability of the fuel rod.

[0128] Those skilled in the art can understand that the modules or flows in the drawings are not necessarily necessary for implementing the present application. Those skilled in the art can understand that the modules in the device in the implementation scenario can be distributed in the device in the implementation scenario according to the description of the implementation scenario, or can be changed and located in one or more devices different from the implementation scenario. The modules of the above implementation scenario can be combined into one module, or can be further split into multiple sub-modules.

[0129] The above application number is only for description, and does not represent the advantages and disadvantages of the implementation scene. The above disclosure is only some specific implementation scenes of the application, but the application is not limited thereto, and any changes made by those skilled in the art shall fall within the protection scope of the application.

Claims

1. A method for analyzing the static instability of fuel rods, characterized in that, The method includes: For the fuel rods in the reactor reaction process, a lateral vibration displacement expansion formula for the fuel rods is constructed. The lateral vibration displacement expansion formula is used to mathematically represent the lateral vibration displacement of the fuel rods through the series form of modal functions. The modal functions satisfy the physical boundary conditions of the fuel rods, including the fact that the displacements at both ends of the fuel rods are zero. Based on the disturbance effect caused by the lateral vibration of the fuel rod, a disturbance potential function of the disturbance effect is established considering the influence of fluid velocity, and based on the disturbance potential function, a mechanical model of the fluid force on the fuel rod in the lateral direction is constructed. Using the aforementioned lateral vibration displacement expansion formula, the lateral vibration displacement of the fuel rods during the reactor reaction process is solved, and based on the aforementioned mechanical model, the fluid force acting on the fuel rods in the lateral direction is solved. Based on the QR decomposition algorithm, the obtained lateral vibration displacement and fluid force are analyzed, and based on the analysis results, the static instability state of the fuel rod is determined. The static instability state includes asymptotic stability state, divergent instability state and critical instability state.

2. The method according to claim 1, characterized in that, The disturbance effect caused by the lateral vibration of the fuel rod is used to establish the disturbance potential function of the disturbance effect considering the influence of fluid velocity, including: Obtain the length and radius of the fuel rod; The total velocity potential of the fluid around the fuel rod is expressed as the superposition of the uniform velocity and the disturbance potential function. Based on the expression of the total velocity potential of the fluid after superposition, and combined with the influence of the length, radius and lateral vibration displacement of the fuel rod on the fluid flow, the spatial constraints that the total velocity potential of the fluid needs to satisfy are obtained. Using spatial constraints as spatial boundary conditions, the solution of the Laplace equation under spatial boundary conditions is obtained, yielding the perturbation potential function considering the influence of fluid velocity. This perturbation potential function is the solution that satisfies the Laplace equation and conforms to the spatial boundary conditions. The perturbation potential function characterizes the flow characteristics of the fluid around the fuel rod under spatial boundary conditions. The total velocity potential of the superimposed fluid is expressed as follows: Φ=Uz+φ, The spatial boundary conditions are as follows: The disturbance potential function considering the influence of fluid velocity is: Φ represents the total velocity potential of the superimposed fluid, U represents the uniform velocity of the fluid surrounding the fuel rod, z represents the axial coordinate of the fuel rod, φ represents the disturbance potential function, L represents the length of the fuel rod, r represents the radial coordinate of the fuel rod, a represents the radius of the fuel rod, w represents the lateral vibration displacement of the fuel rod, and θ represents the circumferential coordinate of the fuel rod. In the series terms, M represents the total number of series terms, and m and n are both series expansion parameters in the lateral direction. The series expansion parameters include the first series expansion parameter m and the second series expansion parameter n. The series expansion parameters are used to perform a finite series expansion of the lateral vibration displacement of the fuel rod. m (t) is a generalized coordinate representing the transverse vibration of the fuel rod as a function of time t, expanded in the longitudinal direction. β mn K1 represents the first-series coupling coefficients related to m and n, and K1 is the modified Bessel function of the second kind. For w n The first derivative of (t), w n (t) is a generalized coordinate representing the lateral vibration of a fuel rod as a function of time t, expanded in the lateral direction. and Take the partial derivatives of φ with respect to z and r, respectively. Take the partial derivatives of w with respect to t and z, respectively. Let φ be the derivative of the function K1(mπr / L) with respect to r, cos be the cosine function, and φ| r→∞ Let φ be the limit value as r approaches infinity.

3. The method according to claim 2, characterized in that, The mechanical model of the fluid forces acting on the fuel rod in the lateral direction, based on the perturbation potential function, includes: Based on the Cauchy-Lagrange integral formula and spatial boundary conditions, the value of the disturbance potential function within the total velocity potential of the fluid is expressed as the boundary integral form of the fuel rod surface. Based on the gradient calculation process of the disturbance potential function, a distributed pressure calculation process is constructed. The boundary integral form of the fuel rod surface is then substituted into the distributed pressure calculation process to obtain the distributed pressure on the fuel rod surface. Integrating the calculated distributed pressure yields the mechanical model of the fluid force acting on the fuel rod in the transverse direction. The mechanical model is as follows: F x ρ is the fluid force acting on the fuel rod in the lateral direction. f For fluid density, ξ m (t) is a function characterizing the change of the interaction force between the fluid and the fuel rod with time t. For ξ m The first derivative of (t), λ m Let be the first mode parameter of the fluid-fuel rod interaction, and sin be the sine function.

4. The method according to claim 1, characterized in that, The expansion formula for the lateral vibration displacement of the fuel rod includes: Obtain the length and axial coordinate of the fuel rod; Based on the Rayleigh-Ritz method, the length of the fuel rod, and the axial coordinates of the fuel rod, the lateral vibration displacement of the fuel rod is expanded into a finite series of modal functions, resulting in the expansion of the lateral vibration displacement of the fuel rod, wherein the expansion of the lateral vibration displacement of the fuel rod is: w represents the lateral vibration displacement of the fuel rod. In the series term, M is the total number of series terms, and m is the first-series expansion parameter in the lateral direction. m (t) is a generalized coordinate representing the change of the transverse vibration of the fuel rod with time t in a series expansion in the longitudinal direction, where L is the length of the fuel rod, z is the axial coordinate of the fuel rod, and sin is the sine function used for the modal function.

5. The method according to claim 1, characterized in that, The QR decomposition algorithm is used to analyze the obtained lateral vibration displacement and fluid force, and based on the analysis results, the static instability state of the fuel rod is determined, including: The vibration control equations of the fuel rods are constructed. The vibration control equations of the fuel rods are discretized and matrixed by combining the lateral vibration displacement and fluid force to obtain the matrix form of the lateral vibration control equations of the fuel rods. Based on the matrix form of the lateral vibration control equation of the fuel rod, the static instability state of the fuel rod is determined, wherein the vibration control equation of the fuel rod is: The matrix form of the control equation for the lateral vibration of the fuel rod is as follows: ρ s Let A be the fuel rod density, W be the fuel rod cross-sectional area, t be the lateral vibration displacement of the fuel rod, E be the elastic modulus, I be the moment of inertia of the cross section, z be the axial coordinate of the fuel rod, and F be the fuel rod density. x Let M, C, and K represent the fluid forces acting on the fuel rod in the lateral direction. M, C, and K are the mass matrix, damping matrix, and stiffness matrix of the fluid-structure interaction system, respectively. The fluid-structure interaction system includes the coolant (considered as a fluid) and the fuel rod. The components of M, C, and K are M(i,j), C(i,j), and K(i,j), respectively. and The second and first derivatives of w are respectively, δ ij The symbol is Krone, which is 1 when i = j and 0 otherwise. M is the total number of series terms, m is the first series expansion parameter in the horizontal direction, a is the radius of the fuel rod, and ρ is the total number of series terms. f For fluid density, λ m β is the first mode parameter for the interaction between the fluid and the fuel rod. mi and β mj Let be the second-order and third-order coupling coefficients characterizing the interaction force between the fluid and the fuel rod, respectively; U be the uniform flow velocity of the fluid around the fuel rod; L be the length of the fuel rod; i and j be the first and second variables in (i,j), respectively; and β be the first variable. ij and β ji These are the fourth and fifth order coupling coefficients characterizing the interaction force between the fluid and the fuel rod, respectively; a0 and a1 are the first and second Rayleigh damping coefficients, respectively; λ i and λ j These are the second and third mode parameters for the interaction between the fluid and the fuel rod, respectively.

6. The method according to claim 5, characterized in that, The determination of the static instability state of the fuel rod based on the matrix form of the lateral vibration control equation includes: The matrix form of the lateral vibration control equations of the fuel rod is converted into a single-degree-of-freedom system expression. Then, the single-degree-of-freedom system expression is transformed into a matrix expression for eigenvalue calculation using state vectors. The eigenvalues ​​of the matrix expression are solved using the QR decomposition algorithm. Based on the solved eigenvalues, the static instability state of the fuel rod is obtained. The matrix expression is as follows: q is the state vector. Let q be the first derivative, H be the matrix expression for finding eigenvalues, 0 be the zero matrix, I be the identity matrix, and T be the transpose.

7. The method according to claim 6, characterized in that, The solved eigenvalues ​​have real parts. The process of obtaining the static instability state of the fuel rod based on the solved eigenvalues ​​includes: When the real part of the solved eigenvalue is negative, the static instability state of the fuel rod is asymptotically stable. When the real part of the solved eigenvalue is positive, the static instability state of the fuel rod is a divergent instability state. When the real part of the solved eigenvalue is zero, the static instability state of the fuel rod is the critical instability state.

8. A static instability analysis device for fuel rods, characterized in that, The device includes: The fuel rod vibration displacement mode construction module is used to construct the lateral vibration displacement expansion of the fuel rod for the reactor reaction process. The lateral vibration displacement expansion is mathematically characterized by the series form of the mode function. The mode function satisfies the physical boundary conditions of the fuel rod, including that the displacement at both ends of the fuel rod is zero. The fluid dynamics model building module is used to establish the perturbation potential function of the perturbation effect caused by the lateral vibration of the fuel rod, taking into account the influence of fluid velocity, and to build a mechanical model of the fluid force on the fuel rod in the lateral direction based on the perturbation potential function. The vibration displacement and fluid force solution module is used to solve the lateral vibration displacement of the fuel rods during the reactor reaction process using the lateral vibration displacement expansion formula, and to solve the fluid force acting on the lateral direction of the fuel rods based on the mechanical model. The fuel rod static instability state analysis module is used to analyze the obtained lateral vibration displacement and fluid force based on the QR decomposition algorithm, and determine the static instability state of the fuel rod based on the analysis results. The static instability state includes asymptotic stability state, divergent instability state and critical instability state.

9. A storage medium having a computer program stored thereon, characterized in that, When the computer program is executed by a processor, it implements the method for static instability analysis of fuel rods according to any one of claims 1 to 7.

10. A computer device, comprising a storage medium, a processor, and a computer program stored on the storage medium and executable on the processor, characterized in that, When the processor executes the computer program, it implements the method for static instability analysis of fuel rods according to any one of claims 1 to 7.

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