KR101429460B1 - Simulation method for stress and strain of nuclear fuel And Simulation Apparatus - Google Patents

Abstract

The present invention relates to a method of simulating the performance of a nuclear fuel, comprising the steps of: inputting an initial value of a nuclear fuel stress strain; and calculating an effective stress by applying an ESF (Effective-stress-function) And a third step of repeating the second step using the effective stress as a new initial value when the calculated effective stress is not in an equilibrium state.

Description

Technical Field [0001] The present invention relates to a method of simulating stress and strain of nuclear fuel,

The present invention relates to a method for simulating the performance of nuclear fuel, and more particularly, to a simulation method and a simulation apparatus for simulating the stress and strain of nuclear fuel from the initial stage of nuclear fuel fission to the end of the life of the nuclear fuel.

Nuclear power plants generate steam by using the heat generated by nuclear fission of nuclear fuel and generate steam by rotating the turbine. The nuclear fuel is stressed and deformed in the process of injecting nuclear fuel into the reactor, When the stress and deformation exceed a certain range, there arises a problem that the fuel can not be used up to a predetermined lifetime.

At present, more than 70,000 nuclear fuel rods are loaded into the core where nuclear fission occurs in the pressurized type light water reactor, which occupies more than 80% of the domestic nuclear power plants. Under normal operating conditions, the pressure of the cooling water is maintained at 150 atm, .

The fuel rod of a typical light-water reactor has nuclear fuel pellets disposed inside a cylindrical zirconium alloy cladding tube, with a slight gap therebetween, and helium having a high thermal conductivity is pressed into the gap.

The role of the cladding is critical for interception of radioactive materials during the combustion of the fuel, and the evaluation of the behavior of the cladding during fuel design is essential.

In order to analyze the performance of such nuclear fuel, it is necessary to carry out various calculations on the temperature, oxidation, stress, strain and physical properties of the nuclear fuel, The finite element method has been introduced and used.

The finite element method is the most widely used numerical analysis method in structural analysis, fluid analysis, thermal analysis, magnetic field analysis, etc. After dividing the object to be analyzed into finite number of elements (elements) and defining the representative point of this region, It is a method of solving the equation by approximating the simultaneous linear equations.

One of the most frequently used nonlinear finite element computation methods is the Newton-Rapson method, which is a method of converging to the root by using a derivative. 1 is a diagram conceptually showing a method of obtaining a solution by the Newton-Rapson method.

As shown in Fig. 1, in the nonlinear relation, when the micro increment value is given in the previous step, the Newton-Raphson method repeats the method of finding the next step X value using the slope at the increment value, .

Patent Document 1: Japanese Patent Application Laid-Open No. 11-258073 (disclosed on September 24, 1999) Patent Document 2: Japanese Patent Application Laid-Open No. 10-320432 (disclosed on December 4, 1998)

In the performance analysis of nuclear fuel, a complex nonlinear phenomenon at a relatively low degree of freedom (thermo-elastic-plastic and creep) in the nuclear fission process of nuclear fuel is simultaneously applied In particular, the convergence and accuracy of the analysis module is a very important factor.

However, the Newton-Raphson method is a method of stable calculation in many degrees of freedom. Therefore, the convergence speed is very slow and it takes a lot of computation time to solve the problem. Therefore, there is a problem in the method of analyzing nuclear fuel, Which is not suitable for use in calculating the stress and strain of nuclear fuel which must be satisfied at the same time.

Therefore, in order to simulate the stress and strain of the nuclear fuel, it is required to introduce a different analysis method from the Newton-Raphson method.

In order to simultaneously improve the convergence and accuracy of a nonlinear finite element calculation method that can rapidly converge by applying a composite nonlinear phenomenon, that is, thermal elasticity and creep, at the same time, And an ESF (Effective-Stress-Function) algorithm is applied to the strain simulation, thereby providing a method of simulating nuclear fuel stress and strain, which simultaneously satisfies both convergence and accuracy.

The technical objects to be achieved by the present invention are not limited to the above-mentioned technical problems, and other technical subjects which are not mentioned can be clearly understood by those skilled in the art from the description of the present invention .

According to an aspect of the present invention, there is provided a fuel cell system including a first step of inputting an initial value of a nuclear fuel strain, A second step of calculating an effective stress by applying an ESF (Effective-stress-function) algorithm to the initial value; And a third step of repeating the second step with the effective stress as a new initial value when the calculated effective stress is not in an equilibrium state.

The initial value of the stress strain includes a physical property value of the fuel, a boundary condition, a stress condition, and a shape condition.

Preferably, the initial value of the stress strain further includes a temperature calculation condition including a temperature at the time of combustion of the fuel, and further includes a temperature calculation step of calculating a temperature condition at the time of the fuel combustion before the execution of the second step, In the second step, the effective stress is calculated including the temperature condition calculated in the temperature calculation step.

Preferably, the simulation of stress and strain of the nuclear fuel divides the combustion period of the nuclear fuel into a plurality of time intervals, and repeats the first to third steps at each divided time.

Preferably, the second step may include: a stiffness matrix forming step of forming a stiffness matrix based on the initial value; a displacement calculating step of calculating displacement from the stiffness matrix; an increment calculating step of calculating an increment of stress; And a displacement recalculation step of reconstructing the reflected stiffness matrix and recalculating the displacement, wherein the determination of whether or not the effective stress in the third step is in an equilibrium state is made based on the fact that the displacement calculated in the displacement re- It is judged by whether or not it is equal to the calculated displacement.

The present invention also provides an input module for receiving an initial value of a nuclear fuel strain, A stiffness matrix module for constructing a stiffness matrix based on the input initial values; And a displacement calculation module for calculating the stress and strain of the nuclear fuel using the stiffness matrix module, wherein the displacement calculation module calculates the stress and strain of the nuclear fuel using the ESF calculation method. Strain simulation device.

Preferably, the initial value of the stress strain includes a physical property value of the fuel, a boundary condition, a stress condition, and a shape condition.

According to the present invention, the ESF (Effective-Stress-Function) algorithm is applied to the nonlinear finite element module applied for the stress and strain analysis in nuclear fuel performance analysis, thereby improving the convergence speed of the entire nuclear fuel analysis code, And a method and an apparatus for simulating stress and strain of a nuclear fuel having improved strain accuracy.

FIG. 1 is a graph showing a method of obtaining an X value in the next step by the Newton-Raphson method.
Fig. 2 is a graph showing a method of obtaining the effective stress in the next step by the ESF calculation method.
3 is a block diagram of a nonlinear finite element simulation system of nuclear fuel according to a preferred embodiment of the present invention.
4 is a flowchart showing a stress and strain simulation method for nuclear fuel according to a preferred embodiment of the present invention.

First, an ESF (Effective-Stress-Function) algorithm used in the present invention will be briefly described.

The ESF (Effective-Stress-Function) algorithm constructs a function by combining complex behaviors as one parameter, effective stress, in order to quickly find the equilibrium stress in each stress incremental step in a complex nonlinear problem, It is a nonlinear analysis algorithm that can quickly find the equilibrium stress by finding the solution satisfying the function. Since the ESF algorithm is known, detailed description thereof will be omitted here.

On the other hand, in order to perform nonlinear calculation in a general finite element analysis, a convergence value is obtained by performing a number of iterations through small displacement and stress increment method.

Especially, in the case of nuclear fuel behavior, the complex behavior such as thermal deformation, creep deformation, and elasto-plastic deformation behaves mutually, and the general incremental method is not suitable.

For this reason, in the present invention, the ESF which converges the creep strain and the plastic strain by connecting the finite stress as a function is defined as Equation 1 below.

는 유효 응력 함수이고,

는 유효 응력 값이며, a는 소성 거동과 관련되는 변수이고,

는 크립(creep) 거동과 관련되는 변수이며, b, c, d는 상수이다. 또, 도 2는 수학 식 1의 이해를 돕기 위해 그래프로 나타낸 것이다.here,

Is an effective stress function,

Is an effective stress value, a is a variable related to the plastic behavior,

Is a variable related to the creep behavior, and b, c, and d are constants. Fig. 2 is a graph for helping to understand Equation (1).

Hereinafter, preferred embodiments of the present invention will be described with reference to the drawings.

1 is a configuration diagram of a nonlinear finite element simulation system 10 according to a preferred embodiment of the present invention.

As shown in the figure, the nuclear fuel stress and strain simulation system 10 of the present embodiment includes a CPU (11), a storage device 12 including a ROM, a RAM or a hard disk, An input device 13 and a display device 14. An analysis program 20 for simulating the stress and strain of nuclear fuel is stored in the memory device 12. The CPU 11 execute the analysis program 20, a function as the fuel stress and strain simulation system 10 is realized.

Wherein the analysis program includes an input module for receiving an initial value of the nuclear fuel strain, a stiffness matrix module for constructing a stiffness matrix based on the input initial value, and a displacement calculating unit for calculating stress and strain of the fuel using the stiffness matrix module A calculation module, and may further include a temperature calculation module.

The function of each of these modules will be apparent from the description with reference to FIG. 4 to be described later.

In order to simulate the stress and strain of the fuel, an initial value of the stress strain is required, and the initial value of the stress strain may include the physical property value of the fuel, the boundary condition, the stress condition, and the shape condition.

The physical properties of nuclear fuel, such as tensile properties and thermal conductivity, mean the physical properties of materials of nuclear fuel.

The boundary condition is a mathematical condition that satisfies the boundary condition of a region in finding a solution of a differential equation representing a physical law in a limited space, and is a necessary condition for performing a nonlinear finite element calculation. Since the finite element method is a method of dividing an object into small objects, the boundary conditions of each small object can be set as needed.

Stress refers to the resistance that occurs when an external force acts on a material, and the stress increases as the external force increases. However, there is a limit, so that when the stress reaches its original limit, Is finally destroyed. In order to simulate the stress and strain of the nuclear fuel, an initial value of such a stress, that is, a stress condition is also required.

In addition, since the shape, degree, and boundary conditions of the fuel are influenced by the shape of the fuel, a shape condition is also required. For the shape condition, the element information and the contact coordinates are input.

If necessary, the initial value also includes a temperature calculation condition for calculating the temperature around the fuel in the combustion process of the fuel.

The length, or deformation, of an arbitrary object is proportional to the magnitude of the external force and inversely proportional to the stiffness of the object. A case where the deformation of an object shows a relation proportional to an external force and a rigidity is referred to as linear and a finite element method is applied to an object exhibiting a linear static behavior,

Is a numerical problem solving the matrix equation. Here, matrix [K] is a stiffness matrix, matrix {F} is a load vector, and matrix {u} is an unknown value, that is, an approximate deformation value of an object.

The outline of the stress and strain simulation method of nuclear fuel according to the preferred embodiment of the present invention is as follows.

First, when the physical property values, boundary conditions, stress conditions, and shape conditions of the nuclear fuel are input within a predetermined time (time step), these input values are divided into elements and nodes in the form of a finite element matrix, After constructing the matrix, the ESF algorithm is called in the nonlinear computation, and the variables constituting the function are calculated using given values, and then the effective stress satisfying the function is found by bisection. The effective stresses found in this way are the values of the equilibrium state of the current stage. Based on this, the next step is taken to find the equilibrium state in the same way.

4 is a flowchart showing the execution steps of the stress and strain simulation method of nuclear fuel according to the preferred embodiment of the present invention.

First, in step S10, an initial value of the stress strain for simulating the stress and the strain of the fuel is inputted. The initial values of the stress strain to be input include the physical property value of the fuel, the boundary condition, the stress condition, and the shape condition as described above.

Next, in step S20, the result of the previously executed calculation is initialized. In the present embodiment, the initialization in step S20 is performed after inputting the initial value of the stress strain in step S10, but initialization may be performed before step S10.

After the execution of step S20, the time loop of steps S30 to S100 is started. As previously described, the simulation of the stress and strain of the fuel is to simulate the stress and strain of the fuel at each time period from the beginning of the fuel combustion to the end of the life of the fuel, at each time of day.

For example, let t0 be the time at which the fuel starts to burn, tn be the time at which the combustion ends at the end of the life of the fuel, and t0, t1, t2, ... , tn, the time loop starts at t0 and t1, t2, ... , tn. In other words, steps S30 to S100 correspond to t0, t1, t2, ... , tn, and ends when it reaches tn.

Here, the time loop does not necessarily have to be the time from the start of the combustion of the fuel to the end of the life of the fuel. The time loop may be, for example, the time from the start of combustion to the time when half of the fuel burns , And can be set as needed.

Next, in step S30, the temperature is calculated. As described above, the temperature is important in the calculation of the carbonaceous property and creep of the fuel, in particular the creep, and the change in temperature around the fuel is an important parameter for the stress and strain of the fuel. . The temperature calculation is performed based on the temperature calculation condition, and the temperature calculation in step S30 may be omitted if necessary. The temperature calculation condition may be included in the stress condition or may be included as a separate initial value item.

Next, in step S40, a stiffness matrix is formed based on the input initial value and the temperature calculation result. The constructed stiffness matrix is, for example, a matrix as shown in equation (2).

Next, in step S50, the displacement is calculated. The displacement is calculated by calculating the stiffness matrix constructed in step S50 to obtain {u} in the above equation (2).

Next, in step S60, the increment of the stress is calculated. Calculation of the stress increment to obtain the ^{[K] {u} i +} 1 = {F} i + {F} from the ^{[K] {u} i =} {F} i of the expression (2), the increment of the stress In the calculation step, {F} is calculated for each individual element of the stiffness matrix. Equation (1) is applied to find the effective stress that simultaneously satisfies both the plastic stress and the creep stress, which are nonlinear behaviors of the nuclear fuel.

Next, in step S70, the displacement is calculated by reconstructing the stiffness matrix reflecting the stress increment calculated in step S60, which is a new initial value.

In step S80, it is determined whether or not the calculation result converges. Whether or not the calculation result converges is a judgment as to whether or not the calculation result before the increment of stress is equal to the calculation result after the increment, and when the calculation results before and after the increment are the same, they are converged. Therefore, if the calculation result converges, it is determined that the stress equilibrium at the present stage has been reached, and the calculation result at the present stage is updated in S90 for the calculation of the next step.

If the result of the calculation is not converged in step S80, the process returns to step S50, and steps S50 to S80 are repeated until the convergence is reached. If the convergence variable is out of a certain range or the number of iterations is out of a certain range, .

Next, in step S100, it is judged whether or not the time loop has ended, that is, t0, t1, t2, ... , tn, and ends the simulation if all of the stress and strain simulations are finished. If it is determined that all the stresses and strain simulations have not been completed yet, the process returns to step S3 and the simulation for the next time, To < RTI ID = 0.0 > S100 < / RTI >

If it is determined in step S100 that the time loop has ended, the result of simulation may be outputted by a method such as display using a display device or output using a printer, and then the process may be terminated.

The terms and words used in the present specification and claims should not be construed as limited to ordinary or dictionary terms and should be construed in a sense and concept consistent with the technical idea of the present invention. The embodiments described in the present specification and the configurations shown in the drawings are merely the most preferred examples of the present invention and not all of the technical ideas of the present invention are exemplified so that various equivalents And deformation.

Claims (7)

A first step of inputting an initial value of the nuclear fuel stress strain;
A second step of calculating an effective stress by applying an ESF (Effective-stress-function) algorithm to the initial value;
And repeating the second step with the effective stress as a new initial value when the calculated effective stress is not in an equilibrium state,
The second step comprises:
A stiffness matrix forming step of forming a stiffness matrix based on the initial values,
A displacement calculation step of calculating a displacement from the stiffness matrix formed,
An increment calculation step of calculating an increment of the stress,
And a displacement recalculation step of reconstructing the stiffness matrix reflecting the increment to recalculate the displacement,
The simulation of the stress and strain of the fuel is performed by dividing the combustion period of the fuel into a plurality of time intervals, repeating the first to third steps with each divided time interval unit,
Wherein the determination of whether or not the effective stress in the third step is in an equilibrium state is made by determining whether the displacement calculated in the displacement recalculation step is equal to the displacement calculated in the previous step, Way. The method according to claim 1,
Wherein the initial value of the stress strain includes a physical property value of the fuel, a boundary condition, a stress condition, and a shape condition. 3. The method of claim 2,
Wherein the initial value of the stress strain further includes a temperature calculation condition including a temperature at the time of fuel combustion,
Further comprising a temperature calculation step of calculating a temperature condition at the time of fuel combustion before the execution of the second step,
Wherein the second step includes calculating the effective stress including the temperature condition calculated in the temperature calculating step. delete delete delete delete

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