CN117973248A - Modeling analysis method for surface deletion and eccentricity of pressurized water reactor fuel core block - Google Patents
Modeling analysis method for surface deletion and eccentricity of pressurized water reactor fuel core block Download PDFInfo
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- 238000004458 analytical method Methods 0.000 title claims abstract description 31
- 238000012217 deletion Methods 0.000 title claims abstract description 22
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- 239000000446 fuel Substances 0.000 claims abstract description 176
- 239000008188 pellet Substances 0.000 claims abstract description 115
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- OOAWCECZEHPMBX-UHFFFAOYSA-N oxygen(2-);uranium(4+) Chemical group [O-2].[O-2].[U+4] OOAWCECZEHPMBX-UHFFFAOYSA-N 0.000 description 2
- 238000012805 post-processing Methods 0.000 description 2
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- FCTBKIHDJGHPPO-UHFFFAOYSA-N uranium dioxide Inorganic materials O=[U]=O FCTBKIHDJGHPPO-UHFFFAOYSA-N 0.000 description 2
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Abstract
The invention discloses a modeling analysis method for surface deletion and eccentricity of a pressurized water reactor fuel pellet, which comprises the following steps: drawing a three-dimensional geometric model of the fuel rod according to the geometric shape and parameters of the fuel rod of the pressurized water reactor, and modifying the three-dimensional geometric model of the fuel rod to obtain the geometric model of the fuel core corresponding to the surface deficiency or the eccentricity when researching the surface deficiency and the eccentricity of the fuel core; setting corresponding variables and physical processes in a geometric domain according to physical processes related to the nuclear fuel rod, and performing coordinate system conversion on the related variables to establish a pressurized water reactor fuel three-dimensional model; based on the fuel working condition, the physical properties of the fuel pellets and the cladding and related physical processes, a pressurized water reactor fuel three-dimensional model is adopted to calculate the temperature distribution of the fuel pellets and the cladding and the stress and strain conditions of the cladding, and the result is output. By the method, the temperature distribution near the missing surface of the fuel pellet, the stress and the distribution condition of the cladding, and the temperature distribution of the fuel rod when the fuel pellet is eccentric can be obtained.
Description
Technical Field
The invention relates to the field of nuclear reactor fuel rod thermal performance analysis, in particular to a system, medium and equipment for a modeling analysis method for surface deletion and eccentricity of a pressurized water reactor fuel pellet.
Background
Under normal conditions, pressurized water reactor nuclear fuel rods have an axisymmetric geometry. In some cases, however, the geometry of the nuclear fuel rod will no longer be perfectly symmetrical, such as a missing fuel pellet surface (MPS), a fuel pellet centerline offset from the centerline of the rod. In the International Atomic Energy Agency (IAEA) study report, the loss of fuel pellet surface (MPS) was identified as a significant cause of cladding failure. In the vicinity of the missing areas of the surface of the fuel pellets, the gap between the cladding and the fuel is significantly larger than in the non-missing areas, resulting in local temperature anomalies of the fuel and the cladding and local stress concentrations of the cladding adjacent to the defective areas, which may lead to cladding failure during rapid increases in reactor power. Fuel pellet offset is also an important phenomenon, and when the centerline of the fuel pellet and the centerline of the fuel rod deviate, there is a significant difference in distribution and concentricity of the temperature and stress fields of the fuel and cladding, which is related to the design and safe operation of the nuclear fuel. Therefore, modeling analysis of these problems, and their understanding is deepened, which is necessary to improve the safety of the reactor.
The traditional fuel performance codes mostly use a 1.5-dimensional or 2-dimensional axisymmetric geometric model, such as a mainstream nuclear fuel program FRAPCON, BISON, FALCON and the like, but the 1.5-dimensional and 2-dimensional axisymmetric model cannot be suitable for researching asymmetric problems such as surface loss and eccentricity of a fuel pellet.
Disclosure of Invention
In order to solve the problem that the conventional 1.5-dimensional and 2-dimensional axisymmetric nuclear fuel performance analysis codes cannot calculate and analyze nuclear fuel under an asymmetric geometric state, the first aim of the invention is to provide a modeling analysis method for the surface deletion and eccentricity of a pressurized water reactor fuel pellet, to establish a fuel rod three-dimensional model, to completely couple the calculation of heat transfer science and solid mechanics, and to consider a plurality of physical processes such as thermal expansion, creep, fission gas generation and release, and the like, so as to calculate the transient temperature distribution of the pellet and the cladding and the stress strain of the cladding under the conditions of normal, fuel pellet surface deletion, fuel pellet eccentricity, and the like.
A second object of the present invention is to provide a pressurized water reactor fuel pellet surface loss and eccentricity calculation system.
A third object of the present invention is to provide a storage medium.
It is a fourth object of the present invention to provide a computing device.
In order to achieve the above purpose, the three-dimensional modeling analysis method for the surface deletion and the eccentricity of the fuel pellet of the pressurized water reactor provided by the invention is characterized in that a three-dimensional geometric model is drawn, a plurality of physical processes such as solid mechanics and fission gas release, densification, thermal expansion strain, creep strain and the like are coupled by using a heat conduction and heat convection calculation mode, and the temperature distribution, the stress and the strain of the transient fuel pellet and the cladding are calculated, and the conditions of the fuel pellet surface deletion and the eccentricity are corresponding to the fuel geometry through changing, and the method specifically comprises the following steps:
(1) Drawing a three-dimensional geometric model of the fuel rod according to the geometric shape and parameters of the fuel rod of the pressurized water reactor, and dividing grids; the geometry of normal fuel has a complete geometry, whereas the surface deletions and eccentricities of the fuel pellets need to be modified on the basis of the complete geometry to correspond to the respective situation.
(2) Inputting physical properties of materials, setting corresponding physical processes and differential equations in a geometric domain according to related physical processes of the nuclear fuel rod, and performing coordinate system conversion on related variables to establish a three-dimensional model of pressurized water reactor fuel.
(3) Calculating the temperature distribution of the fuel pellets and the cladding and the stress and strain conditions of the cladding by adopting a pressurized water reactor fuel three-dimensional model based on the fuel working condition, the physical properties of the fuel pellets and the cladding and related physical processes;
(4) And outputting a calculation result.
As a preferred technical scheme, the thermo-mechanical behavior of the missing and eccentric surfaces of the fuel pellets is compared and analyzed by utilizing the COMSOL post-processing capability.
As an optimal technical scheme, the fuel rod adopts a three-dimensional geometric model, grid division flexibly uses a built-in mapping and sweeping grid drawing method of COMSOL to draw a hexahedral calculation grid suitable for the three-dimensional model of the fuel rod, and has higher calculation precision, smaller calculation scale and better convergence compared with the tetrahedral grid.
As the preferable technical scheme, the heat transfer calculation of the fuel pellets and the cladding in the fuel is carried out by the following specific calculation formula:
where ρ is the density of the material, C p is the heat capacity of the fuel pellet or cladding, T is the temperature of the fuel pellet or cladding, τ is time, k is the thermal conductivity of the fuel pellet or cladding, r is the distance from the centerline of the fuel pellet, and q is the rate of heat generation of the fuel pellet per unit volume. Equation (1) is used to calculate the heat transfer process and temperature distribution within the fuel pellets, whereas the source term q in equation (1) is omitted for the heat transfer process and temperature distribution of the cladding and the gap between the fuel pellets and the cladding, since there is no heat source.
As a preferred solution, the heat transfer between the fuel pellets and the fissile gas, the fissile gas and the cladding is calculated by modeling using the following radial heat fluxes:
Q＝(hg+hs+hr)(Tf-Tc)
Where Q is the heat flux of the outer and inner fuel surfaces, h g is the gas thermal conductance, h s is the solid-solid contact thermal conductance, h r is the radiant heat transfer thermal conductance, the sum of which represents the total thermal conductance across the gap, and T f and T c are the temperature of the outer and inner fuel and cladding surfaces, respectively.
As a preferred solution, the convective heat transfer between the jacket and the coolant is calculated, i.e
Q '=h×Δt (2), wherein Q' is the heat exchange amount per unit volume; h is the convection heat exchange coefficient of the heat exchange surface, and DeltaT is the temperature difference of the two materials of the heat exchange surface. The formula (1) and the formula (2) are calculated by adopting a heat transfer module in COMSOL.
As a preferred technical scheme, the deformation behavior of the fuel and the cladding is calculated by an equation of a COMSOL solid mechanics module:
Where σ is the cauchy stress tensor and F v is the physical force per unit volume, determined by the applied force, thermal expansion, material creep, fuel densification and fission gas expansion.
As a preferable technical scheme, in order to calculate the release of fission gas to grain boundaries, a Booth-type diffusion model is realized by using a numerical solution method, and the model is described by the following equation:
where C is the concentration of fissile gas atoms in the fuel grain, D is the diffusion coefficient of the fissile gas in the fuel grain, and Q fg is the volumetric rate of fissile gas atom generation. A two-dimensional rectangular assembly is used, where one direction represents the radial coordinates of the grains within the fuel pellet and the other direction represents the radial coordinates within the spherical grains. By replacing η=r/g r, the equation () is converted into a dimensionless form, resulting in:
release rate R gb of fission gas to grain boundary is
As a preferred solution, the fissile gas, after being released to the surface of the fuel grains, is trapped in the bubbles between the fuel grains. Once the gas accumulated on the grain boundaries reaches the saturated gas concentration G bsat, the fissile gas is released into the air gap and the air chamber, and the grain boundary saturated gas concentration G bsat is calculated as follows:
f(θfg)＝1-1.5cos(θfg)+0.5cos3(θfg) (8)
Where r f is the grain boundary bubble radius, f (θ fg) is a function explaining the bubble shape, θ fg is the half dihedral angle between the bubble surfaces, f B is the grain boundary fraction at saturation, k B is the boltzmann constant, T is the temperature, γ se is the surface tension of the bubble, and g r is the grain radius. P ext is the externally applied static pressure.
As a preferred solution, in calculating the directional component of the creep of the material, the directional stress in the cylindrical coordinate system needs to be used, and the three-dimensional geometric model of COMSOL is built in the rectangular coordinate system, so the stress matrix needs to be converted from the rectangular coordinate system to the cylindrical coordinate system by the following mathematical relationship:
σc＝βσdβT (9)
where σ d is the representation of the stress matrix in the Cartesian coordinate system, σ c is the representation of the stress matrix in the cylindrical coordinate system, and β is the matrix of the direction cosine of the representation of the cylindrical coordinate system in the Cartesian coordinate system.
In order to achieve the purpose, the modeling analysis system for the surface deletion and the eccentricity of the pressurized water reactor fuel core block provided by the invention is characterized in that a 3-dimensional local model of a fuel rod is built on a COMSOL (compact solid oxide fuel cell) multi-physical platform, a hexahedral grid is drawn, and three basic modules, namely a heat conduction module, a solid mechanics module and a fission gas release module, are arranged.
The 3-dimensional model may be used to represent fuel pellet surface loss and fuel pellet offset relative to a 1.5 or 2-dimensional model, while the hexahedral mesh has higher computational accuracy, smaller computational scale, and better convergence.
The heat conduction module is used for calculating the temperature change and distribution conditions of the fuel pellets, the cladding and the gap between the fuel pellets and the cladding;
the solid mechanical module calculates the mechanical interaction and stress strain of the annular fuel pellet and the cladding through coupling thermal strain, creep, air pressure, densification and the like;
the fission gas release module is used for calculating the release amount of the fission gas so as to calculate the gas pressure and the property of the gas.
In order to achieve the third object, the present invention provides a storage medium storing a program which, when executed by a processor, implements a modeling analysis method of surface loss and decentration of a pressurized water reactor fuel pellet as described above.
In order to achieve the fourth object, the present invention provides a computing device, which includes a processor and a memory for storing a program executable by the processor, wherein the processor implements the modeling analysis method for the surface loss and eccentricity of the pressurized water reactor fuel pellet when executing the program stored by the memory.
Compared with the prior art, the invention has at least the following beneficial effects:
(1) The invention adopts the modes of heat transfer and solid mechanics full coupling calculation, and couples fission gas release thermal strain, creep, air pressure, densification and the like, establishes a pressurized water reactor fuel three-dimensional model, can accurately calculate thermodynamic behaviors of pressurized water reactor fuel and cladding, and further can calculate the surface deletion and eccentricity of a fuel pellet by changing a geometric model, thereby being convenient for analyzing the influence of the two asymmetric states on the fuel cladding.
(2) The invention can lead the calculated temperature distribution of the fuel pellet and the cladding to be more accurate in the stress and strain results of the cladding;
(3) The method is suitable for three-dimensional modeling and calculation of various different fuels and cladding of the pressurized water reactor, and has certain flexibility and universality.
(4) The invention adopts the three-dimensional model of the fuel rod, and the post-treatment result has better visual effect.
Drawings
FIG. 1 is a schematic flow chart of a modeling analysis method for surface deletion and eccentricity of a pressurized water reactor fuel pellet in an embodiment of the invention;
FIG. 2 is a schematic diagram showing a comparison of the three-dimensional model of the nuclear fuel with the results of calculation of the centerline temperatures of other nuclear fuel analysis programs or codes;
FIG. 3 is a partial result display diagram of the fuel pellet surface loss and eccentricity calculated in accordance with the present invention, wherein (a) and (b) are diagrams of the cladding stress distribution (N/m 2) of the fuel pellet surface loss, (c) is a schematic diagram of the temperature distribution of the fuel pellet surface loss, and (d) is a schematic diagram of the temperature distribution of the fuel pellet eccentricity.
Detailed Description
The present invention will be described in further detail with reference to the drawings and examples, in order to make the objects, technical solutions and advantages of the present invention more apparent. It should be understood that the specific embodiments described herein are for purposes of illustration only and are not intended to limit the scope of the invention.
Example 1
Pressurized water reactor solid fuel rods normally have axisymmetric geometry, but due to manufacturing imperfections and improper placement, non-axisymmetric geometry that can cause missing fuel pellet surfaces and decentration (pellet centerline offset from fuel rod centerline) will have a significant impact on the thermo-mechanical behavior of the fuel rods. The conventional 1.5-dimensional or two-dimensional axisymmetric nuclear fuel performance analysis model or program cannot analyze the problems. According to the modeling analysis method for the surface loss and the eccentricity of the pressurized water reactor fuel pellet, a three-dimensional model is built, calculation of complete coupling heat transfer theory and solid mechanics is performed, and a plurality of physical processes such as thermal expansion, creep deformation, fission gas generation and release are considered, so that the transient temperature distribution of the pellet and the cladding and the stress strain of the cladding under the conditions of normal conditions, the surface loss of the fuel pellet, the eccentricity of the fuel pellet and the like can be calculated.
Specifically, the modeling analysis method for the surface deletion and eccentricity of the pressurized water reactor fuel pellet provided by the invention comprises the following steps:
S1: drawing a three-dimensional model of the fuel rod on a COMSOL multiple physical platform, drawing the three-dimensional geometric model of the fuel rod according to the geometric shape and parameters of the pressurized water reactor fuel rod, and dividing grids; the geometry of normal fuel has a complete geometry, whereas the surface deletions and eccentricities of the fuel pellets need to be modified on the basis of the complete geometry to correspond to the respective situation.
In the step, a hexahedral mesh is drawn by using a map built in COMSOL and a swept mesh drawing method. Grid division flexibly uses a built-in mapping and sweeping grid drawing method of COMSOL to draw a hexahedral calculation grid suitable for the fuel rod three-dimensional model. The hexahedral mesh has higher computational accuracy, smaller computational scale, and better convergence than the tetrahedral mesh.
In this step, the complete three-dimensional model is calculated to verify its accuracy by modifying the geometry to correspond to the surface defects or eccentricities of the pellets, and then it is calculated and compared for analysis of the performance differences. In the geometric drawing module of COMSOL, the geometry of the fuel pellets corresponding to surface defects or decentration may be drawn using a drawing tool.
S2: physical properties of the input fuel and the cladding, in this embodiment, the fuel pellet is uranium dioxide material and the cladding is zirconium alloy. Of course, in other embodiments, other materials may be used for the cladding and the physical properties corresponding to the material are entered. According to the physical process related to the nuclear fuel rod, setting corresponding variables and physical processes in a geometric domain, and carrying out coordinate system conversion on the related variables to establish a pressurized water reactor fuel three-dimensional model. In the creep calculation, the directional components of the stress matrix in the cylindrical coordinate system are needed to be used, and the model is built in the Cartesian coordinate system, so that the model needs to be subjected to coordinate system conversion, and the formulas 9 and 10 are shown;
the heat conduction calculation formula of the fuel pellets and the cladding in the fuel at each moment is as follows:
Where ρ is the density of the material, C p is the heat capacity of the fuel pellet or cladding, T is the temperature of the unmodified fuel pellet or cladding, T is time, k is the thermal conductivity of the fuel pellet or cladding, r is the distance of each location inside the fuel pellet from the centerline of the fuel pellet, q is the rate of heat generation of the fuel pellet per unit volume, d is the differential sign, and is a generic mathematical representation.
Equation (1) is used to calculate the heat transfer process and the temperature distribution within the fuel pellets, whereas for the heat transfer process and the temperature distribution of the cladding and the gap between the fuel pellets and the cladding, the source term q in equation (1) is truncated, i.e., at this point q=0, because there is no heat source.
The heat transfer between the fuel pellets and the fissile gas, the fissile gas and the cladding was modeled using the following radial heat fluxes:
Q＝(hg+hs+hr)(Tf-Tc) (2)
Where Q is the heat flux of the outer and inner fuel surfaces, h g is the gas conductance, h s is the solid-solid contact conductance, h r is the radiant heat transfer conductance, the sum of which represents the total heat conduction across the gap, and T f and T c are the temperature of the outer and inner fuel and cladding surfaces, respectively.
Calculating the convective heat transfer between the jacket and the coolant, i.e
Q′＝h*ΔT (3)
Wherein Q' is the heat exchange amount per unit volume; delta T is the temperature difference of the two materials of the heat exchange surface, and h is the convective heat exchange coefficient of the heat exchange surface.
The formula (1) and the formula (2) are calculated by adopting a heat transfer module in COMSOL.
The deformation behavior of the fuel and the cladding is calculated through the built-in equation of COMSOL solid mechanics:
Where σ is the cauchy stress tensor and F v is the physical force per unit volume, determined by the applied force, thermal expansion, material creep, fuel densification and fission gas expansion.
To calculate the release of fissile gas into the grain boundaries, a numerical solution method was applied to implement a Booth-type diffusion model described in terms of the following equation:
Where C is the concentration of fissile gas atoms in the fuel grain, t is time, D is the diffusion coefficient of the fissile gas in the fuel grain, and Q fg is the volumetric rate at which the fissile gas atoms are generated. A two-dimensional rectangular assembly is used, where one direction represents the radial coordinates of the grains within the fuel pellet and the other direction represents the radial coordinates within the spherical grains. By replacing η=r/g r, the equation (4) is converted into a dimensionless form, yielding:
release rate R gb of fission gas to grain boundary is
After release to the surface of the fuel particles, the fissile gas is trapped in the bubbles between the fuel grains. Once the gas accumulated on the grain boundaries reaches the saturated gas concentration G bsat, the fissile gas is released into the air gap and the air chamber, and the grain boundary saturated gas concentration G bsat is calculated as follows:
f(θfg)＝1-1.5cos(θfg)+0.5cos3(θfg) (8)
Where θ fg is the half dihedral angle between the bubble surfaces, r f is the grain boundary bubble radius, f (θ fg) is a function explaining the bubble shape, f B is the grain boundary fraction at saturation, k B is the boltzmann constant, T is the temperature, γ se is the surface tension of the bubble, g r is the grain radius, P ext is the externally applied static pressure, η is the intermediate variable of the transformation, and y is the coordinates.
In calculating the directional component of the creep of the material, the directional stress in the cylindrical coordinate system needs to be used, and the three-dimensional geometric model of COMSOL is built in the rectangular coordinate system, so the stress matrix needs to be converted from the rectangular coordinate system to the cylindrical coordinate system by the following mathematical relationship:
σc＝βσdβT (9)
Where σ d is the representation of the stress matrix in the cartesian coordinate system, σ c is the representation of the stress matrix in the cylindrical coordinate system, β is the matrix of the direction cosine of the representation of the cylindrical coordinate system in the cartesian coordinate system, and the superscript T represents the transpose of the matrix.
S3: calculating the temperature distribution of the fuel pellets and the cladding and the stress and strain conditions of the cladding through a pressurized water reactor fuel three-dimensional model based on the fuel working conditions, the physical properties of the fuel pellets and the cladding and related physical processes;
the method is used for calculating, firstly, the heat conduction, heat convection and temperature distribution of the current time step are calculated, the stress and strain of the cladding are calculated through temperature coupling solid mechanics, and the thermodynamic behavior of the fuel and the cladding is calculated in a three-dimensional simulation mode through the coupling of the release amount of fission gas and the pressure and the gas property of the gas.
As shown in fig. 2, the drawings are respectively: FRAPTRAN codes, BISON codes and ABAQUS calculated temperature of different positions of the fuel rod and a temperature change curve with burnup, which is calculated by the three-dimensional model established by the invention. According to the comparison of the graphs, the three-dimensional nuclear fuel method has certain accuracy on the performance calculation of the nuclear fuel. Fig. 2 is a graph showing the temperature change with burnup obtained when a normal fuel pellet is used, fig. 3 is a graph showing the temperature distribution or stress distribution when the surface of the fuel chip is missing or eccentric calculated by the method of the present invention, and (a) and (b) are typical stress distributions at different times when the surface of the fuel pellet is missing, and peak stresses are respectively present on the inner surface and the outer surface of the cladding near the defect. The stress distribution of the clad at the eccentric appears to be uneven, and does not show a remarkable stress concentration phenomenon, the main phenomenon is temperature distribution shift, so the stress distribution of the clad at the eccentric is not given.
S4: and outputting a calculation result, and comparing and analyzing the thermo-mechanical behaviors of the surface deletion and the eccentricity of the fuel pellet by utilizing the COMSOL post-processing capability.
The impact of these two conditions on the pressurized water reactor fuel rod can be evaluated by comparing the temperature and stress profiles or profiles calculated for normal, surface loss, and off-center fuel. The thermo-mechanical behaviour of the fuel rods is significantly different compared to normal. As shown in fig. 3, as in the related document, when the surface of the fuel pellet is missing, the cladding in the vicinity of the defect appears to have a remarkable stress concentration phenomenon; and when the fuel pellets are eccentric, the temperature distribution of the fuel is significantly shifted.
Example 2
The embodiment provides a calculation system for surface deletion and eccentricity of a pressurized water reactor fuel pellet, which comprises a heat transfer module, a solid mechanics module and a fission gas release module.
In this embodiment, the heat generation of the fuel pellets and the heat conduction in the fuel pellets, air gaps, and cladding are all calculated by the COMSOL heat transfer module, and the other modules are coupled by temperature.
In this embodiment, the stress strain of the fuel clad is calculated by the solid mechanical module of COMSOL, which couples the physical processes of thermal expansion strain, creep strain, gas pressure, coolant pressure, etc. by applying a strain boundary load.
In this embodiment, the fission gas releasing module calculates that the fission gas is released to the grain boundary, and implements the Booth-type diffusion model by applying a numerical solution method, and the fission gas stays in the bubbles between the fuel grains after being released to the surface of the fuel grains. Once the gas accumulated at the grain boundaries reaches the saturated gas concentration G bsat, the fissile gas is released into the air gap and the plenum, and the amount of fissile gas released into the plenum is calculated. The module is coupled with heat and solid mechanics through fission product expansion, physical properties and gas pressure.
Example 3
The present embodiment also provides a storage medium, which may be a storage medium such as a ROM, a RAM, a magnetic disk, or an optical disk, and stores one or more programs that, when executed by a processor, implement the modeling analysis method for surface loss and decentration of a pressurized water reactor fuel pellet in embodiment 1.
Example 4
The embodiment provides a computing device, which may be a desktop computer, a notebook computer, a smart phone, a PDA handheld terminal, a tablet computer or other terminal devices with display function, and the computing device includes a processor and a memory, where the memory stores one or more programs, and when the processor executes the programs stored in the memory, the modeling analysis method for the surface loss and the eccentricity of the pressurized water reactor fuel core block in embodiment 1 is implemented.
According to the modeling analysis method for the surface deletion and the eccentricity of the pressurized water reactor fuel pellet, uranium dioxide fuel is used as fuel, a cladding material is zirconium alloy, processes such as heat transfer, solid mechanics, fission gas generation and release are considered, a pressurized water reactor fuel three-dimensional model is built based on a COMSOL (compact solid state reactor) multiple physical platforms, and the modeling analysis method can be used for performance simulation calculation of pressurized water reactor nuclear fuel. On the basis, the geometric state of the model is modified, so that the thermodynamic behavior of the fuel pellet in the absence and eccentricity of the surface of the fuel pellet can be calculated and analyzed. The obtained results show that when the surface of the fuel pellet is missing, local high points appear on the fuel temperature near the defect, local low points appear on the cladding temperature, and the cladding near the defect shows obvious stress concentration phenomenon; when the fuel pellets are eccentric, the temperature distribution of the fuel is obviously uneven, and compared with the normal fuel, the highest temperature of the eccentric fuel can move from the central line to the direction opposite to the eccentric direction.
According to the embodiment of the invention, on the existing solid fuel model, the material physical properties of the solid fuel pellet fuel and the material physical properties of the cladding can be quickly adjusted by using COMSOL, so that the effect of quickly modeling and calculating various fuel and cladding materials can be achieved. Based on COMSOL multiple physical platforms, a three-dimensional model of the fuel rod is established, a plurality of physical processes such as solid heat transfer, air gap heat transfer, thermal expansion, creep, fission gas generation, release, densification and the like are coupled, and the computing capability of the fuel rod to the service performance of the pressurized water reactor can be verified by comparing the results with the results of computing codes of other fuel performances. On the basis, the two abnormal geometries of the surface deletion and the eccentricity of the fuel pellet are calculated and analyzed by changing the geometric state.
The above examples are preferred embodiments of the present invention, but the embodiments of the present invention are not limited to the above examples, and any other changes, modifications, substitutions, combinations, and simplifications that do not depart from the spirit and principle of the present invention should be made in the equivalent manner, and the embodiments are included in the protection scope of the present invention.
Claims (10)
1. A modeling analysis method for the surface deletion and eccentricity of a pressurized water reactor fuel pellet is characterized by comprising the following steps:
drawing a three-dimensional geometric model of the fuel rod according to the geometric shape and parameters of the fuel rod of the pressurized water reactor, dividing grids, and modifying the three-dimensional geometric model of the fuel rod to obtain the geometric model of the fuel core corresponding to the surface deficiency or the eccentricity when researching the surface deficiency and the eccentricity of the fuel core;
Setting corresponding variables and physical processes in a geometric domain according to physical processes related to the nuclear fuel rod, and performing coordinate system conversion on the related variables to establish a pressurized water reactor fuel three-dimensional model;
Based on the fuel working condition, the physical properties of the fuel pellets and the cladding and related physical processes, calculating the temperature distribution of the fuel pellets and the cladding and the stress and strain conditions of the cladding by adopting a pressurized water reactor fuel three-dimensional model, and outputting a calculation result.
2. The modeling analysis method for surface loss and decentration of a pressurized water reactor fuel pellet according to claim 1, wherein after outputting the calculation result, the thermo-mechanical behavior of the surface loss and decentration of the fuel pellet is comparatively analyzed.
3. The modeling analysis method for surface deletion and eccentricity of fuel pellets of a pressurized water reactor according to claim 1, wherein the heat conduction calculation of the fuel pellets and cladding in the fuel rod is as follows:
Wherein ρ is the density of the material, C p is the heat capacity of the fuel pellet or cladding, T is the temperature of the unmodified fuel pellet or cladding, T is the time, k is the thermal conductivity of the fuel pellet or cladding, r is the distance of each position inside the fuel pellet from the centerline of the fuel pellet, q is the heat generation rate of the fuel pellet per unit volume, and d is the differential sign;
Wherein, the formula (1) is used for calculating the heat transfer process and the temperature distribution in the fuel pellet, and the heat transfer process and the temperature distribution of the cladding and the gap between the fuel pellet and the cladding are omitted because of no heat source, so the source term q in the formula (1);
The heat transfer between the fuel pellets and the fissile gas, the fissile gas and the cladding was calculated by modeling using the following radial heat fluxes:
Q＝(hg+hs+hr)(Tf-Tc) (2)
Wherein Q is the heat flux of the outer surface of the fuel and the inner surface of the fuel, h g is the gas conductance, h s is the solid-solid contact conductance, h r is the radiant heat transfer conductance, and T f and T c are the temperature of the outer surface of the fuel and the inner surface of the cladding, respectively;
The convective heat transfer between the jacket and the coolant is calculated, i.e
Q′＝h*ΔT (3)
Wherein Q' is the heat exchange amount per unit volume; h is the convection heat exchange coefficient of the heat exchange surface, and DeltaT is the temperature difference of the heat exchange surface.
4. The modeling analysis method for surface deletion and eccentricity of pressurized water reactor fuel pellets according to claim 1, wherein the calculation formula of deformation behavior of fuel and cladding is as follows:
where σ is the cauchy-stress tensor and F v is the physical force per unit volume, determined by the applied load, thermal expansion, material creep, fuel densification and gas pressure.
5. The modeling analysis method of surface deletion and decentration of pressurized water reactor fuel pellets according to claim 1, wherein for calculating fission gas release to grain boundaries, a numerical solution method is applied to realize a Booth-type diffusion model, which is described by the following equation:
Where C is the concentration of fissile gas atoms in the fuel particles, t is the time, D is the diffusion coefficient of the fissile gas in the fuel particles, and Q fg is the volumetric rate at which the fissile gas atoms are generated.
6. The modeling analysis method of the surface defect and decentration of a pressurized water reactor fuel pellet according to claim 5, wherein after the fission gas is released to the surface of the fuel crystal grains, the fission gas is retained in the bubbles between the fuel crystal grains, and once the gas accumulated on the grain boundary reaches the saturated gas concentration G bsat, the fission gas is released to the air gap and the air chamber, and the grain boundary saturated gas concentration G bsat is calculated as follows:
f(θfg)＝1-1.5cos(θfg)+0.5cos3(θfg)
Where r f is the grain boundary bubble radius, f (θ fg) is a function explaining the bubble shape, θ fg is the dihedral angle between the bubble surfaces, f B is the grain boundary fraction at saturation, k B is the boltzmann constant, T is the temperature, γ se is the surface tension of the bubble, g r is the grain radius, and P ext is the externally applied static pressure.
7. The modeling analysis method for surface loss and eccentricity of a pressurized water reactor fuel pellet according to claim 1, wherein the following mathematical relationship is used to transform a stress matrix from a rectangular coordinate system to a cylindrical coordinate system when calculating the directional component of material creep:
σc＝βσdβT
Wherein σ d is the representation of the stress matrix in the Cartesian coordinate system, σ c is the representation of the stress matrix in the cylindrical coordinate system, β is the matrix of the direction cosine of the representation of the cylindrical coordinate system in the Cartesian coordinate system, and the superscript T is the transpose.
8. A computing system for surface loss and eccentricity of pressurized water reactor fuel pellets, for implementing the method of any of claims 1-7, the system comprising the following modules:
The heat conduction module is used for calculating the temperature change and distribution conditions of the fuel pellet, the cladding and the gap between the fuel pellet and the cladding;
The solid mechanical module is used for calculating the mechanical interaction, stress and strain of the fuel pellet and the cladding through coupling thermal expansion strain, irradiation swelling and creep strain processes;
And the fission gas release module is used for calculating the release amount of the fission gas so as to calculate the pressure of the gas and the influence on the physical property of the gas.
9. A storage medium storing a program which, when executed by a processor, implements a modeling analysis method of surface loss and decentration of a pressurized water reactor fuel pellet as defined in any one of claims 1 to 7.
10. A computing device comprising a processor and a memory for storing a program executable by the processor, wherein the processor, when executing the program stored in the memory, implements a method of modeling analysis of surface defects and eccentricities of pressurized water reactor fuel pellets as set forth in any of claims 1-7.
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