KR20190141482A - Apparatus and method of analyzing stress of accident tolerant fuel and computer readable medium - Google Patents

Abstract

According to an embodiment of the present invention, a stress analysis device of accident tolerant fuel is configured of a multi-layer structure of a cylindrical cladding pipe layer provided with a fuel pellet inside and a cylindrical coating layer which is coated onto an outer circumferential surface of the cylindrical cladding pipe layer and is formed of different materials from the cylindrical cladding pipe layer. The stress analysis device of accident tolerant fuel comprises: a modeling unit modeling a stress equation of a radial (r) direction, a circumferential (θ) direction, and an axial (z) direction with regard to the cylindrical cladding pipe layer and the cylindrical coating layer; a first calculation unit obtaining an unknown value of the stress equation by applying boundary conditions between the cylindrical cladding pipe layer and the cylindrical coating layer to the modeled stress equation; and a second calculation unit obtaining stress of the radial (r) direction, the circumferential (θ) direction, and the axial (z) direction for each of the cylindrical cladding pipe layer and the cylindrical coating layer by substituting the unknown value into the stress equation.

Description

FIELD AND METHOD OF ANALYZING STRESS OF ACCIDENT TOLERANT FUEL AND COMPUTER READABLE MEDIUM

The present application relates to an apparatus, a method and a computer readable recording medium for stress analysis of an accident resistant fuel.

A nuclear power plant is a facility that generates steam by using heat generated by nuclear fission of nuclear fuel, and then rotates a turbine to generate electricity.In the process of loading nuclear fuel into a nuclear reactor and causing nuclear fission, stress and deformation are generated in the nuclear fuel. If stresses and strains are above a certain range, the fuel's integrity will be compromised, affecting reactor safety.

At present, more than 70,000 nuclear fuel rods are loaded in the core where nuclear fission occurs in the pressurized light water reactor, which accounts for more than 80% of domestic nuclear power plants.In normal operation, the pressure of the coolant is maintained at 150 atm and the coolant temperature is 350 ℃. have.

In fuel rods of general light reactors, nuclear fuel UO2 pellets are arranged inside a cylindrical zirconium alloy cladding tube, and there is a slight gap between them, and helium is pressurized with excellent thermal conductivity.

Integrity of the cladding is very important for the interception of radioactive material during the combustion of the fuel, and it is essential to evaluate the behavior of the cladding when designing the fuel.

One way to analyze the stress of these fuels is to model them as thin-walled cylinders. The thin thickness refers to the case where the ratio of the radius to the inner surface of the cylindrical cylinder to the radial thickness of the cylindrical cylinder is 10 or more.

However, in recent years, in order to improve high temperature oxidation resistance and to improve stability in case of an accident of nuclear fuel, a multi-layered accident resistant fuel having a coated outer circumferential surface of a cladding tube has been developed.

Accordingly, there is a problem in that stress and strain of an accident resistant fuel cannot be accurately obtained through a modeling method based on a conventional thin-walled cylinder.

Korean Laid-open Patent No. 2014-0050287 (“Stress and Strain Simulation Method and Apparatus for Nuclear Fuel”, Publication Date: April 29, 2014)

SUMMARY OF THE INVENTION The present invention provides an apparatus, a method and a computer-readable recording medium for stress resistant nuclear fuel which can obtain stresses in the radial, circumferential and axial directions of accidentally resistant nuclear fuel having a multilayer structure composed of different materials.

According to one embodiment of the present invention, an accident-resistant nuclear fuel composed of a multi-layered structure of a cylindrical cladding tube layer having nuclear fuel pellets therein and a cylindrical coating layer coated on an outer circumferential surface of the cylindrical cladding layer and composed of a material different from the cylindrical cladding layer An apparatus for stress analysis, comprising: a modeling unit for modeling stress equations in a radial (r) direction, a circumferential (θ) direction, and an axial (z) direction with respect to each of the cylindrical sheath and the cylindrical coating layer; A first calculation unit applying a boundary condition between the cylindrical cladding layer and the cylindrical coating layer to the modeled stress equation to obtain an unknown figure of the stress equation; And a second calculation unit which obtains the stresses in the radial (r) direction, the circumferential (θ) direction, and the axial (z) direction for each of the cylindrical coating tube layer and the cylindrical coating layer by substituting the obtained unknown equation into the stress equation. An apparatus for stress analysis of accidentally resistant fuel is provided.

According to another embodiment of the present invention, there is provided a cylindrical coating tube layer having nuclear fuel pellets therein, and a multilayer structure of a cylindrical coating layer coated on an outer circumferential surface of the cylindrical coating tube layer and composed of a material different from that of the cylindrical coating tube layer. In the stress analysis method of the accident-resistant nuclear fuel, the modeling unit, for each of the cylindrical cladding tube layer and the cylindrical coating layer, to model the stress equation in the radial (r) direction, circumferential (θ) direction and axial (z) direction step; Obtaining a unknown value of the stress equation by applying a boundary condition between the cylindrical cladding layer and the cylindrical coating layer to the modeled stress equation in a first calculation unit; And calculating a stress in a radial (r) direction, a circumferential (θ) direction, and an axial (z) direction for each of the cylindrical coating pipe layer and the cylindrical coating layer by substituting the obtained unknown value into the stress equation in the second calculation unit. Provided is a stress analysis method of an accident resistant fuel.

According to another embodiment of the present invention, a computer-readable recording medium having recorded thereon a program for executing the method is provided.

According to one embodiment of the present invention, by obtaining an unknown value of the stress equation using boundary conditions between the cylindrical cladding layer and the cylindrical coating layer, accident-resistant nuclear fuel comprising a cylindrical cladding layer composed of a heterogeneous material and a multi-layer cladding layer composed of a cylindrical coating layer The radial, circumferential and axial directions of the stress can be obtained, and preliminary performance evaluation of the multifunctional next-generation fuels to be developed in the future can provide a design guideline when developing a new fuel.

1 is a block diagram of a stress analysis device for an accident resistant fuel according to an embodiment of the present invention.
Figure 2 illustrates a single-layered cylindrical cylinder (thick-walled cynlinder) in accordance with one embodiment of the present invention.
3 is a schematic cutaway view of an accident resistant nuclear fuel having a multilayer structure according to an embodiment of the present invention.
4 is a view for explaining a first boundary condition which is a load condition in an open gap region according to an embodiment of the present invention.
It is a figure for demonstrating the 2nd boundary condition which is a load condition in the closed gap region which concerns on one Embodiment of this invention.
6 is a flowchart illustrating a stress analysis method of an accident resistant nuclear fuel according to an embodiment of the present invention.

Hereinafter, embodiments of the present invention will be described with reference to the accompanying drawings. However, embodiments of the present invention may be modified in various other forms, and the scope of the present invention is not limited to the embodiments described below. Shapes and sizes of the elements in the drawings may be exaggerated for more clear explanation, elements represented by the same reference numerals in the drawings are the same elements.

1 is a block diagram of a stress analysis device 100 of an accident resistant nuclear fuel according to an embodiment of the present invention. 2 illustrates a single-walled cylindrical cylinder according to an embodiment of the present invention, and FIG. 3 is a schematic cutaway view of an accident resistant nuclear fuel having a multilayer structure according to an embodiment of the present invention. .

The above-described accident resistant fuel (ATF) is composed of a cylindrical cladding tube layer having nuclear fuel pellets and a cylindrical coating layer coated on the outer circumferential surface of the cylindrical cladding layer and made of a different material from the cylindrical cladding layer. Can be.

First, as illustrated in FIG. 1, the stress resistant apparatus 100 for an accident resistant fuel according to an embodiment of the present invention may include a modeling unit 110, a first calculating unit 120, and a second calculating unit 130. It may include.

The modeling unit 110 may model stress equations in the radial (r) direction, the circumferential (θ) direction, and the axial (z) direction with respect to each of the cylindrical sheath tube and the cylindrical coating layer of the accident resistant nuclear fuel.

More specifically, the modeling unit 110 reflects the elastic modulus, Poisson's ratio, and thermal expansion coefficient of each of the cylindrical cladding layer and the cylindrical coating layer, and thus the radial (r) direction, the circumferential (θ) direction, and the axis (z) with respect to the cylindrical cladding tube. The stress equation in the () direction and the radial (r) direction, the circumference (θ) direction and the axial (z) direction for the cylindrical coating layer can be modeled.

To this end, the modeling unit 110 may model an accident-resistant nuclear fuel having a multilayer structure composed of a cylindrical cladding tube layer and a cylindrical coating layer based on the cylindrical cylinder 200 having a single layer structure as shown in FIG. 2.

In FIG. 2, reference numeral 201 denotes a hollow inside the cylindrical cylinder 200, a denotes a distance to the inner surface of the cylindrical cylinder 200, b denotes a distance to an outer surface of the cylindrical cylinder 200, r Denotes a radial direction, θ denotes a tangential direction, z denotes an axial direction, ε ₀ denotes an axial strain, and CX denotes a central axis of the cylindrical cylinder 200.

That is, assuming that the cylindrical cylinder of the single-layer structure as shown in FIG. 2 is either a cylindrical cladding tube layer or a cylindrical coating layer, a structure in which a cylindrical cladding tube layer having a different diameter and a cylindrical coating layer are joined may be regarded as an accident resistant nuclear fuel.

According to one embodiment of the present invention, a stress equation for each layer (cylindrical cladding layer and cylindrical coating layer) can be modeled based on a single-cylindrical cylindrical cylinder, and then a boundary condition between the cylindrical cladding layer and the cylindrical coating layer is applied. As a result, stresses in the radial (r) direction, the circumferential (θ) direction, and the axial (z) direction with respect to each of the cylindrical coating tube layer and the cylindrical coating layer can be obtained.

3 is a schematic cutaway view of an accident resistant nuclear fuel having a multilayer structure in accordance with one embodiment of the present invention. That is, based on the cylindrical cylinder shown in FIG. 2 is a schematic cutaway view (see AA 'of FIG. 2) in which the cylindrical coating pipe layer 211 and the cylindrical coating layer 212 having different diameters are bonded, the nuclear fuel pellets in the interior 201 Not shown separately.

As shown in FIG. 3, the thickness of the cylindrical cladding layer 211 may be about 490 μm, and the thickness of the cylindrical coating layer 212 coated on the outer circumferential surface of the cylindrical cladding layer 211 may be about 80 μm. It should be noted that the specific numerical values described above are merely to aid the understanding of the invention and are not limited to the specific numerical values.

In addition, according to one embodiment of the present invention, the ratio of the radius of the sum of the radial thicknesses of the cylindrical cladding layer 211 and the cylindrical coating layer 212 to the inner surface of the cylindrical cladding layer 211 may be less than 10.

In order to model stress equations for accident resistant fuels having a structure in which cylindrical sheaths having different diameters and cylindrical coating layers are joined together, it is necessary to first model stress equations for single-cylindrical cylindrical cylinders as shown in FIG. Hereinafter, a method of modeling a stress equation of a cylindrical cylinder of a single layer structure will be described.

First, the radial strain ε _r , the circumferential strain hoop strain ε _θ , and the axial strain ε _z for the single-cylindrical cylindrical cylinder 200 shown in FIG. 2. ) And stress equilibrium relations may be defined as in Equation 1 below.

[Equation 1]

In Equation 1, ε _r is the radial strain, ε _θ is the circumferential strain, ε _z is the axial strain, u is the radial displacement, r is the radial distance from the central axis CX, σ _r is the radial stress , σ _θ means circumferential stress.

Displacement u in the radial direction from Equation 1 described above may be represented by an equation having _two unknowns C ₁ and C ₂ as follows.

[Equation 2]

는 축 방향 조사 성장(irradiation growth)을 의미한다.Where C ₁ and C ₂ are unknowns, r is the radial distance from the central axis CX, v is the poission ratio, ΔT is the temperature change, ε _{c, r} is the radial creep strain, ε _{c, z} is the axial creep strain, ε _{c, θ} is the circumferential creep strain,

Denotes axial irradiation growth.

On the other hand, using the correlation between the stress and the strain, the radial stress (σ _r ), the circumferential stress (σ _θ ) and the axial stress (σ _z ) for the single-layer cylindrical cylinder 200 shown in FIG. It can be represented by the following equation (3).

[Equation 3]

Where σ _r is The radial stress, σ _θ is the circumferential stress, σ _z is the axial stress, E is the Young's modulus, ε ₀ is the axial strain, α is the coefficient of thermal expansion, and the other parameters are as defined above.

In Equation 3, three unknowns C ₁ , C ₂ , ε ₀ are generated, and these three unknowns can be calculated using the model methodology of FRACAS. The Fuel Rod And Cladding Analysis Subcode (FRACAS) model methodology is one of the well-known methodologies for analyzing stresses by applying boundary conditions within fuel performance codes.

The model methodology of FRACAS is applied to the case of a single-layer cylindrical cylinder as shown in FIG. 2, but according to one embodiment of the present invention, a multilayer structure composed of a coating layer-coating layer by making the following assumption (using the boundary conditions described below) It can be extended to cylindrical cylinders with

(1) Multi-layered coating material having two layers (coating layer-coating layer)

(2) The two layers (coating layer-coating layer) are completely bonded

(3) Consider only elastic deformation of cladding

(4) Assumption of axisymmetric loads and deformations (no consideration of circumferential asymmetry)

(5) No axial slippage occurs when the fuel pellet contacts the cladding layer.

(6) Bending stress and strain value are not considered

(7) The fuel pellets do not deform due to the contact stress between the cladding layer and the fuel pellets.

(8) The cladding layer consists of a material having isotropy

The stress equations in the radial (r) direction, the circumferential (θ) direction, and the axial (z) direction for each of the cylindrical cladding tube layers and the cylindrical coating layer of the accident resistant nuclear fuel based on the cylindrical cylinder of the single-layer structure described above are as follows. It can be expressed as Equation 4.

[Equation 4]

Where i is a natural number, 1 is a cylindrical cladding layer, 2 is a cylindrical coating layer, σ _{r, i} is a stress in the radial direction r, σ _{θ, i} is a stress in the circumferential direction θ _{z, i} is the stress in the axial direction z, and other variables are as described above. On the other hand, the unknown to be obtained in the above equation (4) is C _{1, i} , C _{2, i} , ε ₀ .

When an accident resistant fuel is installed in the reactor, a gap exists between the fuel pellet and the cylindrical cladding layer, and as the reaction proceeds, the fuel pellet and the cylindrical cladding layer are joined to eliminate the gap.

The former may be referred to as an open gap region and the latter may be referred to as a closed gap region. The unknown equation of the stress equation is determined by substituting appropriate boundary conditions in each case.

Boundary Conditions for Open Gap Regions

4 is a view for explaining a first boundary condition which is a load condition in an open gap region according to an embodiment of the present invention.

As shown in FIG. 4, in the open gap region, a gap 201 exists between the fuel pellet 202 and the cylindrical cladding layer 211, and internal pressure P _{i is} formed by helium filled in the gap 201. , it is outside the external pressure (P _o) by the cooling water pressure can be present.

Meanwhile, R1 represents the distance between the center axis CX and the inner surface of the cylindrical cladding layer 211, and R2 represents the distance between the center axis CX and the joint surface of the cylindrical cladding layer 211 and the cylindrical cladding layer 212. Assume that the distance between the center axis CX and the outer surface of the cylindrical sheath layer 212 is R3.

In the open gap region described above, the radial stress equilibrium condition (see Equation 6 below) and the circumferential strain equilibrium condition (see Equation 6 below) at the joint surface of the cylindrical cladding layer and the cylindrical coating layer ), Radial stress equilibrium conditions on the inner surface of the cylindrical cladding layer and the outer surface of the cylindrical coating layer (see equations 1 and 2 below) and axial stress equilibrium conditions of the cylindrical cladding layer and the cylindrical coating layer The fifth equation of Equation 6) may be referred to as a boundary condition (called 'first boundary condition'), which is shown in Equation 5 below.

[Equation 5]

Where σ (R ₁ ) _{r, 1} is the radial stress at the inner surface of the cylindrical cladding layer, P _i is the internal pressure between the cylindrical cladding layer and the fuel pellets, and σ (R ₃ ) _{r, 2} is the radius at the outer surface of the cylindrical coating layer Direction stress, P _o is the external pressure acting on the outer surface of the cylindrical cladding layer, ε (R ₂ ) _{θ, 1} is the strain in the circumferential direction of the cylindrical cladding layer at the junction between the cylindrical cladding layer and the cylindrical cladding layer, ε (R _{2 θ, 2} is the strain in the circumferential direction of the cylindrical coating layer at the joint surface of the cylindrical cladding layer and the cylindrical cladding layer, σ (R ₂ ) _{r, 1} is the radial direction of the cylindrical cladding layer at the joint surface of the cylindrical cladding layer and the cylindrical cladding layer Σ (R ₂ ) _{r, 2} is the radial stress of the cylindrical coating layer at the joint surface of the cylindrical cladding layer and the cylindrical cladding layer, A ₁ is the axial area of the cylindrical cladding layer, sigma _{z, 1} is the cylindrical cladding layer of the axial stress, a ₂ in the axial direction of the cylindrical coat _Ever, σ _{z, 2} is the axial stress of the cylindrical coat, R ₁ is a distance from the inner surface of the cylindrical cladding layer from the incident resistant nuclear fuel central axis, R ₃ is the distance of the outer surface to the cylindrical cladding layer from a central axis incident resistant nuclear fuel Can be.

Meanwhile, the first calculation unit 120 substitutes the above-described first boundary condition into Equation 4 to determine an unknown value of the stress equation (C _1,1 , C _1,2 , C _2,1 , C _2,1 , ε ₀ ). Can be obtained.

Finally, the second calculating unit 130 substitutes the obtained unknown values C _1,1 , C _1,2 , C _2,1 , C _2,1 , ε ₀ into the stress equation to form the cylindrical cover pipe layer 211 and the cylindrical shape. The stress in the radial (r) direction, the circumferential (θ) direction, and the axial (z) direction for each layer of the coating layer 212 can be obtained.

Boundary Conditions for Closed Gap Regions

It is a figure for demonstrating the 2nd boundary condition which is a load condition in the closed gap region which concerns on one Embodiment of this invention.

As shown in FIG. 5, in the closed gap region, the nuclear fuel pellet 202 and the cylindrical cladding layer 211 are bonded to each other so that there is no gap.

Similarly, the distance between the center axis CX and the inner surface of the cylindrical cladding layer 211 is R1, and the distance between the center axis CX and the joint surface of the cylindrical cladding layer 211 and the cylindrical cladding layer 212 is R2, Assume that the distance between the center axis CX and the outer surface of the cylindrical sheath layer 212 is R3.

In the above closed gap region, the displacement result of the outer radius of the fuel caused by swelling or thermal expansion according to the Rigid Pellet assumption is inputted under the condition of radial displacement (u ₀ ) inside the cladding 211 and 212. do.

In addition, in the close gap region, since the fuel pellet and the coating materials 211 and 212 are assumed to be completely bonded without slipping, the coating materials 211 and 212 are also subjected to the same strain rate as the fuel pellets 202 are deformed in the axial direction. ε ₀ ) to deform.

As shown in FIG. 5, since the axial strain ε ₀ is a value previously given in the closed gap region, four unknowns C ₁ , ₁ and C ₁ except for the axial strain ε _{0 in} Equation 4. _{, 2} , C _2,1 , C _2,1 ).

Specifically, in the above-described closed gap region, the radial displacement conditions (see the first equation of Equation 6 below) inside the cylindrical cladding layer 211 and the bonding surface of the cylindrical cladding layer 211 and the cylindrical coating layer 212 are radial. Stress equilibrium conditions (see the second equation of Equation 6 below) and strain equilibrium conditions in the circumferential direction (see the third equation of Equation 6 below) and radial stress equilibrium conditions on the outer surface of the cylindrical coating layer 211 The fourth equation of Equation 6) may be referred to as a boundary condition (called a 'second boundary condition'), which is shown in Equation 6 below.

[Equation 6]

Where u (R ₁ ) is the radial displacement at the inner surface of the cylindrical cladding layer, u _o is the radial displacement of the fuel pellets, and σ (R ₂ ) _{r, 1} is the joint surface of the cylindrical cladding layer and the cylindrical cladding layer The radial stress of the cylindrical cladding layer, σ (R ₂ ) _{r, 2} is the radial stress of the cylindrical coating layer at the joint surface of the cylindrical cladding layer and the cylindrical cladding layer, ε (R ₂ ) _{θ, 1} is the cylindrical cladding layer The circumferential strain of the cylindrical cladding layer at the joint surface of the cylindrical cladding layer, ε (R ₂ ) _{θ, 2} is the circumferential strain of the cylindrical coating layer at the joint surface of the cylindrical cladding layer and the cylindrical coating layer, ε (R ₃ ) _r May be the radial strain on the outer surface of the cylindrical sheath layer.

On the other hand, the first calculation unit 120 can obtain the unknown value (C _1,1 , C _1,2 , C _2,1 , C _2,1 ) of the stress equation by substituting the above-described second boundary condition in equation (4). have.

Lastly, the second calculating unit 130 substitutes the obtained unknown values C ₁ , ₁ , C _1,2 , C _2,1 , C _2,1 into the stress equation to form the cylindrical cladding layer 211 and the cylindrical coating layer 212. The stresses in the radial (r) direction, the circumferential (θ) direction, and the axial (z) direction for each layer can be obtained.

As described above, according to one embodiment of the present invention, by obtaining the unknown value of the stress equation using the boundary condition between the cylindrical cladding tube layer and the cylindrical coating layer, a multi-layered cladding tube composed of a cylindrical cladding tube layer and a cylindrical coating layer composed of different materials. There is an advantage to obtain the stress in the radial, circumferential and axial directions of the accident-resistant fuel containing.

6 is a flowchart illustrating a stress analysis method of an accident resistant nuclear fuel according to an embodiment of the present invention.

Hereinafter, a stress analysis method for an accident resistant nuclear fuel according to an embodiment of the present invention will be described with reference to FIGS. 1 to 6. However, for simplicity of the invention, descriptions duplicated with those described in FIGS. 1 to 5 will be omitted.

First, the modeling unit 110 may model stress equations in a radial (r) direction, a circumferential (θ) direction, and an axial (z) direction for each layer of the cylindrical cladding tube and the cylindrical coating layer of the accident resistant nuclear fuel ( S601).

More specifically, the modeling unit 110 reflects the elastic modulus, Poisson's ratio, and thermal expansion coefficient of each of the cylindrical cladding layer and the cylindrical coating layer, and thus the radial (r) direction, the circumferential (θ) direction, and the axis (z) with respect to the cylindrical cladding tube. The stress equation in the () direction and the radial (r) direction, the circumference (θ) direction and the axial (z) direction for the cylindrical coating layer can be modeled.

Next, the first calculation unit 110 may obtain the unknown of the stress equation by substituting the boundary condition between the cylindrical cladding tube layer and the cylindrical coating layer (S602).

As described above, the first calculating unit 110 applies the first boundary condition to the case where the gap exists between the fuel pellet and the cylindrical cladding layer and the nuclear fuel pellet and the cylindrical cladding layer are bonded by applying the second boundary condition. If there is no gap, the unknown can be obtained for each as described above.

Finally, the second calculation unit 130 substitutes the obtained unknowns into the stress equation to calculate stresses in the radial (r) direction, the circumferential (θ) direction, and the axial (z) direction for each of the cylindrical sheath and the cylindrical coating layer. It may be (S603).

As described above, according to one embodiment of the present invention, by obtaining the unknown value of the stress equation using the boundary condition between the cylindrical cladding tube layer and the cylindrical coating layer, a multi-layered cladding tube composed of a cylindrical cladding tube layer and a cylindrical coating layer composed of different materials. There is an advantage to obtain the stress in the radial, circumferential and axial directions of the accident-resistant fuel containing.

The stress analysis method of the accident resistant nuclear fuel according to the embodiment of the present invention described above may be produced as a program for execution in a computer and stored in a computer-readable recording medium. Examples of computer-readable recording media include ROM, RAM, CD-ROM, magnetic tape, floppy disk, optical data storage, and the like. The computer readable recording medium can also be distributed over network coupled computer systems so that the computer readable code is stored and executed in a distributed fashion. And functional programs, codes and code segments for implementing the method can be easily deduced by programmers in the art to which the present invention belongs.

In addition, in describing the present invention, '~ part' may be used in various ways, for example, a processor, program instructions executed by a processor, software module, microcode, computer program product, logic circuit, application-specific integrated circuit, firmware. It may be implemented by such.

The present invention is not limited by the above-described embodiment and the accompanying drawings. It is intended to limit the scope of the claims by the appended claims, and that various forms of substitution, modification and change can be made without departing from the spirit of the present invention as set forth in the claims to those skilled in the art. Will be self explanatory.

100: stress analysis device of accident resistant fuel
110: modeling unit
120: first operation unit
130: second operation unit
200: cylindrical cylinder
201: internal (hollow)
202: nuclear fuel pellets
211: cylindrical sheath layer
212: cylindrical coating layer

Claims (10)

In the stress resistant fuel stress analysis device composed of a multi-layered structure of a cylindrical cladding tube layer having nuclear fuel pellets and a cylindrical coating layer coated on an outer circumferential surface of the cylindrical cladding layer and composed of a material different from the cylindrical cladding layer,
A modeling unit for modeling stress equations in a radial (r) direction, a circumferential (θ) direction, and an axial (z) direction with respect to each of the cylindrical coating tube layer and the cylindrical coating layer;
A first calculation unit applying a boundary condition between the cylindrical cladding layer and the cylindrical coating layer to the modeled stress equation to obtain an unknown figure of the stress equation; And
A second calculation unit for obtaining the stresses in the radial (r) direction, the circumferential (θ) direction, and the axial (z) direction for each of the cylindrical coating tube layer and the cylindrical coating layer by substituting the obtained unknown equation into the stress equation;
An apparatus for stress analysis of accident resistant fuel comprising a.
The method of claim 1,
The modeling unit,
Modeling a stress equation for an accident resistant fuel in which a gap exists between the cylindrical cladding layer and the fuel pellet,
The first boundary condition of the stress equation,
Stress equilibrium conditions in the radial direction and strain equilibrium conditions in the circumferential direction, radial stress equilibrium conditions in the inner surface of the cylindrical cladding layer and the outer surface of the cylindrical coating layer and the cylindrical cladding layer at the joint surface of the cylindrical cladding layer and the cylindrical coating layer And stress balancing conditions in the axial direction of the cylindrical coating layer.
The method of claim 1,
The modeling unit,
The cylindrical sheath layer and the fuel pellets are bonded to model stress equations for accident-resistant fuel without gaps,
The second boundary condition of the stress equation,
A displacement condition inside the cylindrical cladding layer, a radial stress equilibrium condition and a circumferential strain equilibrium condition at the joint surface of the cylindrical cladding layer and the cylindrical coating layer, and a radial stress equilibrium condition at the outer surface of the cylindrical coating layer. Device for stress analysis of accident resistant fuels.
The method of claim 1,
The modeling unit,
Reflecting the elastic modulus, Poisson's ratio, and thermal expansion coefficient of each of the cylindrical cladding layer and the cylindrical coating layer, the stress equation in the radial (r) direction, the circumferential (θ) direction and the axial (z) direction for the cylindrical cladding and the cylindrical An apparatus for stress resistant nuclear resistant fuel, which models stress equations in the radial (r) direction, the circumferential (θ) direction, and the axial (z) direction with respect to the coating layer.
The method of claim 1,
The ratio of the radius of the sum of the radial thickness of the cylindrical cladding layer and the cylindrical coating layer to the inner surface of the cylindrical cladding layer is less than 10, stress analysis device for accident resistant nuclear fuel.
The method of claim 1,
The stress equation is the following equation 1:

,

,

,

By
i is a natural number, 1 is a cylindrical coating layer, 2 is a cylindrical coating layer, σ _{r, i} is the stress in the radial direction r, σ _{θ, i} is the stress in the circumferential direction θ, and σ _{z, i} is The stress in the axial direction z, E is the young's modulus, ν is the poisson ratio, r is the radial distance from the central axis, α is the coefficient of thermal expansion, ΔT is the temperature change, ε _{c, r} is the radial creep strain, ε _{c, z} is the axial creep strain,

Is an axial irradiation growth, ε ₀ is an axial strain, the stress resistant device of an accident resistant fuel.
The method of claim 2,
The first boundary condition is represented by Equation 2:

By
Where σ (R ₁ ) _{r, 1} is the radial stress at the inner surface of the cylindrical cladding layer, P _i is the internal pressure between the cylindrical cladding layer and the fuel pellet, and σ (R ₃ ) _{r, 2} is the cylindrical coating layer The radial stress at the outer surface of, P _o is the external pressure acting on the outer surface of the cylindrical cladding layer, ε (R ₂ ) _{θ, 1} is the circumference of the cylindrical cladding layer at the joint surface of the cylindrical cladding layer and the cylindrical cladding layer Direction strain, ε (R ₂ ) _{θ, 2} is the strain in the circumferential direction of the cylindrical coating layer at the junction surface of the cylindrical cladding tube layer and the cylindrical cladding layer, σ (R ₂ ) _{r, 1} is the cylindrical cladding tube layer and the The radial stress of the cylindrical cladding layer at the joining surface of the cylindrical cladding layer, σ (R ₂ ) _{r, 2} is the radial stress of the cylindrical coating layer at the joining surface of the cylindrical cladding layer and the cylindrical cladding layer, A ₁ Silver cylindrical sheath Axial area of the tube layer, σ _{z, 1} is the axial stress of the cylindrical coating tube layer, A ₂ is the axial area of the cylindrical coating layer, σ _{z, 2} is the axial stress of the cylindrical coating layer, R ₁ is the accident resistance And a distance from the fuel central axis to the inner surface of the cylindrical cladding layer, R ₃ is the distance from the accident resistant fuel central axis to the outer surface of the cylindrical cladding layer.
The method of claim 3,
The second boundary condition is represented by Equation 3:

By
Where u (R ₁ ) is the radial displacement in the inner surface of the cylindrical sheath layer, u _o is the radial displacement of the fuel pellet, σ (R ₂ ) _{r, 1} is the cylindrical sheath layer and the cylindrical sheath layer The radial stress of the cylindrical cladding layer at the joining surface of σ (R ₂ ) _{r, 2} is the radial stress of the cylindrical coating layer at the joining surface of the cylindrical cladding layer and the cylindrical cladding layer, ε (R ₂ ) _{θ, 1} is the strain in the circumferential direction of the cylindrical cladding tube layer at the joint surface of the cylindrical cladding tube layer, ε (R ₂ ) _{θ, 2} is the joining surface of the cylindrical cladding tube layer and the cylindrical cladding tube layer The strain in the circumferential direction of the cylindrical coating layer, ε (R ₃ ) _r is the radial strain on the outer surface of the cylindrical cladding tube layer, the stress resistant fuel stress analysis device.
In the stress analysis method of accident-resistant fuel comprising a multi-layered structure of a cylindrical cladding tube layer having nuclear fuel pellets and a cylindrical coating layer coated on an outer circumferential surface of the cylindrical cladding layer and composed of a material different from that of the cylindrical cladding layer. ,
In the modeling unit, for each of the cylindrical sheath tube layer and the cylindrical coating layer, modeling the stress equation in the radial (r) direction, the circumferential (θ) direction and the axial (z) direction;
Obtaining a unknown value of the stress equation by applying a boundary condition between the cylindrical cladding layer and the cylindrical coating layer to the modeled stress equation in a first calculation unit; And
Calculating a stress in a radial (r) direction, a circumferential (θ) direction, and an axial (z) direction for each of the cylindrical coating tube layer and the cylindrical coating layer by substituting the obtained unknown value into the stress equation in the second calculating part;
Comprising a stress analysis method of accident resistant fuel.
A computer-readable recording medium having recorded thereon a program for executing the method of claim 9.

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