Pressurized water reactor fuel rod performance analysis method and system

Abstract

The invention discloses a pressurized water reactor fuel rod performance analysis method and system, and relates to the technical field of fuel performance analysis, and the method comprises the following steps: constructing a solid heat conduction equation of a pellet and a cladding based on a plurality of physical property parameters; solving the solid heat conduction equation under the temperature boundary condition to obtain the temperature distribution of the pellet and the cladding; constructing all strain models of the pellet and the cladding according to the temperature distribution of the pellet and the cladding; inputting a plurality of strain models and a plurality of physical property parameters into a mechanical control equation for describing stress and strain under a pressure boundary condition to obtain stress and strain distribution of the pellet and the cladding; and inputting the temperature distribution of the cladding into the cladding corrosion layer thickness model to obtain the cladding radiation layer thickness. According to the method, the influence of various fuel in-pile behaviors is considered, and the calculation accuracy of the mechanical property of the fuel is improved.

Description

Technical Field

[0001] The present invention relates to the technical field of fuel performance analysis, and in particular to a pressurized water reactor fuel rod performance analysis method and system. Background Art

[0002] Uranium dioxide (UO2), a traditional oxide ceramic fuel pellet, is widely used in pressurized water reactors. However, the extreme environment of high temperature, high pressure, and high radiation within the nuclear reactor core poses a significant challenge to the safety of nuclear fuel, making it a major factor limiting the development of nuclear reactors.

[0003] To improve the economics of nuclear power while ensuring the inherent safety of fuel rods and to find the optimal balance between safety and economics, in-depth research into fuel rod performance (including thermal and mechanical properties) is essential. However, in-pile irradiation experiments on fuel rods are often time-consuming, costly, and require demanding experimental conditions. Therefore, existing fuel performance analysis methods typically combine existing domestic and international experimental data with mechanistic models, using computer simulation to predict fuel rod performance and accurately predict the evolution of fuel rod in-pile irradiation performance.

[0004] When analyzing the performance of fuel rods, existing performance analysis methods generally do not fully consider the various in-pile behaviors of the fuel. They only consider some important behaviors such as the thermal expansion of the pellets and cladding, and the swelling behavior of the pellets. This may lead to inaccurate analysis of the mechanical properties of the fuel under some special operating conditions. Summary of the Invention

[0005] Based on the above-mentioned defects in the prior art, the present invention provides a pressurized water reactor fuel rod performance analysis method and system to solve the existing problems.

[0006] The present invention adopts the following technical solutions:

[0007] In a first aspect, the present invention provides a method for analyzing the performance of a pressurized water reactor fuel rod, comprising the following steps:

[0008] According to the pellet type and cladding type of the nuclear fuel rod, multiple physical property parameters of the pellet and cladding are obtained, and the solid heat conduction equation of the pellet and cladding is constructed based on the multiple physical property parameters;

[0009] The gap heat transfer model between the pellet and cladding and the heat transfer model between the cladding and the coolant are used as temperature boundary conditions to solve the solid heat conduction equation and obtain the temperature distribution of the pellet and cladding.

[0010] Multiple strain models of the pellets and cladding are constructed based on their temperature distributions. Using the coolant pressure and the cavity pressure between the pellets and cladding as pressure boundary conditions, multiple strain models and physical property parameters are input into the mechanical governing equations for describing stress and strain to obtain stress and strain distributions of the pellets and cladding. The strain models include a densification model, a relocation model, a swelling model, a creep model, an irradiation growth model, and a thermal expansion model.

[0011] The temperature distribution of the cladding is input into the cladding corrosion layer thickness model to obtain the cladding radiation layer thickness.

[0012] Preferably, the nuclear fuel rod includes a uranium dioxide pellet and a Zr-4 alloy cladding, and the physical property parameters include thermal conductivity, specific heat capacity, density, Young's modulus and Poisson's ratio.

[0013] Preferably, the solid heat conduction equation is specifically as follows:

[0014]

[0015] Where ρ is the density of the pellet or cladding, C p is the specific heat capacity of the pellet or cladding, k is the thermal conductivity of the pellet or cladding, T represents the temperature, q represents the power of the pellet, is the gradient.

[0016] Preferably, the gap heat transfer model is specifically as follows:

[0017] q gap =h eff (T p -T c );

[0018] Where q gap is the heat flux through the gas gap, h eff is the equivalent heat convection heat transfer coefficient, T p and T c represent the fuel pellet surface temperature and the cladding inner surface temperature respectively;

[0019] The heat exchange model is specifically shown as follows:

[0020] q s =h co (T cl -T co );

[0021] Where q s is the heat flux density on the cladding surface, h co is the convective heat transfer coefficient at the coolant-shell interface, T cl and T coare the coolant temperatures at the outer wall of the cladding and its corresponding nodes, respectively.

[0022] Preferably, the mechanical control equation is specifically as follows:

[0023]

[0024] σ[C]·[ε];

[0025] Where σ is the Cauchy stress tensor, F v is the body force, [C] is the constitutive matrix, and ε is the strain.

[0026] Preferably, the cladding corrosion layer thickness model is specifically as follows:

[0027]

[0028] Where S i+1 is the thickness of the corrosion layer at time i+1, S i is the thickness of the corrosion layer at time i, t is time, A is a constant, Q1 and Q2 are the activation energies before and after the corrosion transition, R is the gas constant, T1 is the metal oxide interface temperature, Δw is the corrosion weight gain, T0 is the interface temperature between the corrosion layer and the coolant, λ is the thermal conductivity of the corrosion layer, γ is the conversion constant between the corrosion layer thickness and weight gain, q s is the heat flux density on the cladding surface, k o is the radiation impact weight.

[0029] In a second aspect, the present invention further provides a pressurized water reactor fuel rod performance analysis system, comprising:

[0030] A construction module is used to obtain multiple physical properties of the pellets and cladding according to the pellet type and cladding type of the nuclear fuel rod, and to construct solid heat conduction equations of the pellets and cladding based on the multiple physical properties;

[0031] The temperature solving module is used to solve the solid heat conduction equation using the gap heat transfer model between the pellet and cladding and the heat exchange model between the cladding and the coolant as temperature boundary conditions to obtain the temperature distribution of the pellet and cladding;

[0032] A stress solver module is used to construct multiple strain models of the pellet and cladding based on their temperature distributions. The module uses coolant pressure and the cavity pressure between the pellet and cladding as pressure boundary conditions, inputs multiple strain models and physical property parameters into the mechanical governing equations describing stress and strain, and obtains the stress and strain distributions of the pellet and cladding. The strain models include a densification model, a relocation model, a swelling model, a creep model, an irradiation growth model, and a thermal expansion model.

[0033] The corrosion solution module is used to input the temperature distribution of the cladding into the cladding corrosion layer thickness model to obtain the cladding radiation layer thickness.

[0034] Compared with the prior art, the at least one technical solution adopted by the present invention can achieve the following beneficial effects:

[0035] The present invention first constructs solid heat conduction equations for the pellets and cladding based on multiple physical properties of the fuel rods. Using a heat transfer model for the gap between the pellets and cladding, and a heat exchange model between the cladding and the coolant, as temperature boundary conditions, the solid heat conduction equations are solved under these temperature boundary conditions to obtain the temperature distributions of the pellets and cladding. Based on these temperature distributions, multiple strain models for the pellets and cladding are constructed. This method considers the effects of various fuel in-pile behaviors, including densification, reorientation, radiation swelling, and thermal expansion of UO2 pellets and radiation growth, thermal expansion, and creep of Zr-4 cladding. These multiple strain models are then input into the governing mechanical equations describing stress and strain to obtain the stress and strain distributions of the pellets and cladding, improving the accuracy of performance analysis. BRIEF DESCRIPTION OF THE DRAWINGS

[0036] In order to more clearly illustrate the embodiments of the present invention or the technical solutions in the prior art, the following briefly introduces the drawings required for use in the embodiments or the description of the prior art. Obviously, the drawings described below are only some embodiments of the present invention. For ordinary technicians in this field, other drawings can be obtained based on these drawings without paying any creative work.

[0037] Figure 1 This is a flow chart of a method for analyzing the performance of a pressurized water reactor fuel rod according to the present invention;

[0038] Figure 2 This is a temperature comparison diagram of different fuel rods according to an embodiment of the present invention;

[0039] Figure 3 Graph showing permanent hoop strain values of different fuel rods according to an embodiment of the present invention. DETAILED DESCRIPTION

[0040] The following will clearly and completely describe the technical solutions in the embodiments of the present invention in conjunction with the accompanying drawings. Obviously, the described embodiments are only part of the embodiments of the present invention, not all of the embodiments. Based on the embodiments of the present invention, all other embodiments obtained by ordinary technicians in this field without making creative efforts are within the scope of protection of the present invention.

[0041] This invention discloses a program capable of analyzing the in-pile performance of fuel rods composed of UO2 fuel pellets and Zr-4 alloy cladding. Based on the reactor environment (power, neutron flux rate, and coolant parameters), the program analyzes the fuel rod's in-pile performance, including the temperature distribution of the pellets and cladding, the stress and strain distribution within the materials, and cladding corrosion. These properties are of great concern in nuclear reactors and often determine the safety of the reactor.

[0042] The program development relies on the MOOSE finite element platform, which has been tested many times internationally. It has many advantages, including: open source and modular architecture, cross-scale and multi-dimensional computing capabilities, high-performance parallel computing capabilities, and the convenience of multi-physics field coupling. These enable it to develop fuel performance analysis programs.

[0043] First, through investigation, the physical property model of uranium dioxide pellets and zirconium alloy cladding materials was obtained, and the thermal conductivity, specific heat capacity, density and input power were substituted into the heat transfer equation. The gap heat transfer model was applied to the core-cladding gap, and the third-type boundary condition was adopted between the cladding and the coolant to calculate the temperature distribution inside the fuel rod; the obtained temperature distribution was substituted into various fuel pile behavior models to calculate the strain caused by different behaviors; according to the physical parameters and the above-mentioned strain model, they were substituted into the mechanical equation to complete the solution and obtain the distribution of stress, strain and displacement in the fuel rod; according to the temperature distribution, power and gas parameters, they were substituted into the fission gas release model to calculate the fission gas released into the cavity, and then the cavity pressure was calculated; according to the temperature distribution of the cladding and coolant, and the heat flux density of the fuel rod, the thickness of the cladding corrosion layer was calculated; finally, the thermal and mechanical performance calculations of the program were verified based on experimental data.

[0044] The present invention proposes a method for analyzing the performance of pressurized water reactor fuel rods, referring to Figure 1 , including the following steps:

[0045] S1: Obtain multiple physical property parameters of the nuclear fuel rod pellets and cladding according to the specific pellet type and cladding type.

[0046] In the present invention, the fuel rod uses uranium dioxide as the pellet and Zr-4 alloy as the cladding, and the physical properties of the uranium dioxide pellet and the Zr-4 alloy cladding are determined, including thermal conductivity, specific heat capacity, density, Young's modulus and Poisson's ratio.

[0047] The thermal conductivity of the uranium dioxide pellets is as follows:

[0048]

[0049]

[0050] Where k 95 is the thermal conductivity of unirradiated uranium dioxide at 95% of theoretical density, T n It is the result of dividing the material temperature by 1000. is the temperature of UO2, k is the thermal conductivity of uranium dioxide with a theoretical density of 100%, f d is the correction term for dissolved fission products, f p is the correction term for precipitated fission products, f por is the porosity term, f x is the deviation from stoichiometric correction term, which is set to 1 for uranium dioxide fuel, f r is the radiation damage correction term, is the ultimate thermal conductivity of uranium dioxide.

[0051] The thermal conductivity of UO2 is obtained by multiplying the 95% thermal conductivity of unirradiated uranium dioxide in formula (1) by the correction factor in formula (2) as shown in formula (3) to obtain the final thermal conductivity of UO2.

[0052] The specific heat capacity of UO2 is as follows:

[0053]

[0054] Where, is the constant-pressure specific heat capacity of uranium dioxide, C1, C2, C3, θ, E a is a constant in the model, and its specific value is shown in Table 1.

[0055] Table 1 Specific heat capacity material constants of uranium dioxide

[0056]

[0057]

[0058] The specific UO2 density is as follows:

[0059]

[0060] Where, is the density of uranium dioxide, c, b, c, and d are the material parameters in the model. For specific values, refer to Table 2.

[0061] Table 2 Density material parameter values of uranium dioxide

[0062]

[0063] The Young's modulus and Poisson's ratio of UO2 are as follows:

[0064]

[0065] Where, and are Young's modulus and Poisson's ratio of uranium dioxide pellets respectively; D is the percentage of theoretical density of uranium dioxide pellets.

[0066] The thermal conductivity of Zr-4 is as follows:

[0067]

[0068] Where k Zr-4 represents the thermal conductivity of Zr-4, T Zr-4 Indicates the temperature of Zr-4 alloy.

[0069] The specific heat capacity of Zr-4 is as follows:

[0070] C Zr-4 =255.66+0.1024T Zr-4 (9);

[0071] Where C Zr4 is the constant-pressure specific heat capacity of Zr-4.

[0072] The density of Zr-4 is as follows:

[0073] ρ Zr-4 =6595.2-0.1477T Zr-4 (10);

[0074] Where, ρ Zr-4 is the density of Zr-4;

[0075] The Young's modulus and Poisson's ratio of Zr-4 are as follows:

[0076] E c =108.8×10 9 -5.475×10 7 T Zr-4 (11);

[0077] v c =0.30 (12);

[0078] Where, E c is the Young's modulus of Zr-4 alloy; v c is the Poisson's ratio of Zr-4 alloy.

[0079] The above are the physical property models of UO2 and Zr-4 materials used in the program, which will participate in heat transfer and mechanical calculations.

[0080] S2: Based on the power input by the program and the physical parameters in step S1, the solid heat conduction equation (13) inside the pellet and cladding is constructed; the gap heat transfer model (15) between the pellet and cladding is established; the heat transfer model between the outer surface of the cladding and the coolant is established (16); the temperature distribution of the coolant along the axial height of the fuel rod is calculated based on the parameters at the coolant inlet and the internal heat flux density; the temperature of the outer surface of the cladding is determined by applying the third type boundary condition, and then the temperature distribution inside the pellet and cladding is solved by equation (13). Among them, equations (15) and (16) are two temperature boundary conditions, and equation (13) is solved.

[0081] According to the research law of heat conduction, the temperature change inside the fuel pellet and cladding can be given by the heat conduction differential equation, which is in the form of:

[0082]

[0083] Where ρ represents the density of the pellet or cladding, C p represents the specific heat capacity of the pellet or cladding, k represents the thermal conductivity of the pellet or cladding, T represents the temperature, and q represents the power of the pellet.

[0084] In program modeling, it is usually chosen to simplify the calculation of gap heat transfer, and the thermal resistance method is used instead of the refined calculation. The equivalent thermal convection heat transfer coefficient is usually used to represent the thermal resistance. Taking into account the different heat transfer mechanisms in the gas gap, the equivalent thermal convection heat transfer coefficient is composed of the gas thermal conductivity heat transfer coefficient, the radiation heat transfer coefficient, and the contact heat conduction heat transfer coefficient, as shown in the following formula:

[0085] h eff =h gas +h rad +h con (14);

[0086] Where h eff 、h gas 、h rad and h con They represent the equivalent heat convection heat transfer coefficient, gas heat conduction heat transfer coefficient, radiation heat conduction heat transfer coefficient and contact heat conduction heat transfer coefficient respectively.

[0087] The radial heat transfer between the pellet and the cladding is calculated by the equivalent heat convection coefficient in equation (15), that is:

[0088] q gap =h eff (T p -T c ) (15);

[0089] Where q gap is the heat flux through the gas gap, T p and Tc represent the fuel pellet surface temperature and the cladding inner surface temperature respectively.

[0090] The reactor coolant enters the reactor driven by the main pump, flows through the core, and then flows out of the outlet pipe of the reactor vessel, enters the steam generator, and then returns to the main pump. The coolant in the primary circuit carries away the heat generated by the fuel. This heat is generated by the core block, transferred through the core-package gap and the inside of the cladding, and finally enters the coolant. In the performance analysis and calculation of the fuel, the heat exchange between the cladding and the coolant also plays a role in determining the temperature boundary conditions of the fuel rods. The temperature difference between the cladding surface and the coolant is calculated based on Equation (16):

[0091] q s =h co (T cl -T co ) (16);

[0092] Where q s is the heat flux density on the cladding surface; h co is the convective heat transfer coefficient at the coolant-shell interface; T cl and T co are the coolant temperatures at the outer wall of the cladding and its corresponding nodes, respectively.

[0093] According to the coolant flow rate, flow pattern and heat flux density of the outer wall of the cladding, the heat transfer from the outer wall of the cladding to the coolant can be divided into different heat transfer states. For forced convection heat transfer, the form of the convection heat transfer coefficient is given by the Dittus-Boelter model:

[0094]

[0095] The gap heat transfer model is used to transfer heat between the core block and the cladding, and the convection heat transfer is used to transfer heat between the cladding and the coolant. The temperature distribution inside the material is solved by the solid heat conduction equation.

[0096] During the calculation process, it is assumed that the coolant channel is a single closed channel, so the temperature distribution of the coolant satisfies the following form:

[0097]

[0098] Where, T co (z) represents the coolant temperature at the fuel rod height z / K; T in is the coolant inlet temperature / K; q″(z) represents the heat flux density of the fuel rod at height z / W·m -2 ; C co is the specific heat capacity of the coolant / J·kg -1 ·K -1 ; G represents the coolant mass flow rate / kg·s-1 ·m -2 ; A f Indicates the coolant flow area / m 2 ; D0 is the outer diameter of the cladding / m.

[0099] S3: A fuel rod burnup model is constructed based on the power input in step S2 and the simulation start time. The strain models for the pellets and cladding are determined based on the temperature distribution calculated in step S2, along with the burnup, neutron fluence rate, linear power, and other material parameters. These models include: pellet densification, reorientation, irradiation swelling, and thermal expansion; and cladding irradiation growth, thermal expansion, and creep. Except for creep, which is a plastic strain, all other strain models are intrinsic strain models, and they all play a role in the mechanical solution.

[0100] Fuel consumption model

[0101] Burnup is directly related to the fuel type and reactor power history. Due to the spatial effect of power distribution, burnup is also a function of space. The calculation formulas for different burnup description methods are given below:

[0102] Total energy generated per unit mass of heavy metals:

[0103]

[0104] The proportion of heavy elements that undergo fission in the initial load of heavy elements:

[0105]

[0106] Number of fission reactions per cubic meter of fuel:

[0107]

[0108] Where: q v (r,z) represents the volume power of the fuel / W·m -3 ; ρ(r,z) represents density / kg·m -3 ;f ρ is the density correction factor; f U is the mass conversion coefficient between UO2 / MOX and U / U+Pu; is the fission rate / fissions·m -3 ·s -1 ; α is the average energy produced by each fission (3.28451×10 -11 J.fission -1 ); M is the molar mass / g·mol -1 ; N a is Avogadro's constant.

[0109] Constructing a strain model of fuel pile behavior

[0110] Densified model

[0111] The densification behavior of the core block is due to the pores in the UO2 produced by the irradiation becoming smaller, and the core block volume becoming smaller. This is a process of microstructural evolution caused by the effects of irradiation, temperature and stress. The strain model is as follows:

[0112]

[0113] Where, ε d represents the volume strain caused by densification; Δρ D represents the change in theoretical density of pellets due to densification, which is set to 0.01; Bu represents the average fuel consumption of pellets / MWd·t -1 (U); Bu D Indicates the fuel consumption when densification is completed, take 5000; C D As a parameter determined by temperature, its form is as shown in formula (23).

[0114] Repositioning Model

[0115] The effect of cracks in UO2 pellets on gap width is primarily due to reorientation behavior. Thermal gradients within fuel pellets in light water reactors result in corresponding stress gradients exceeding the fuel's fracture stress, leading to radial cracks. The free surface of the cracks results in an overall increase in pellet diameter. The strain model is as follows:

[0116]

[0117] u rel =(42b / (1+b)+0.274P lin +3)G0 / 100 (25);

[0118] b=exp(-4+Bu 0.25 ) (26);

[0119] Where, ε r represents the linear strain in the radial direction caused by relocation; u rel represents the radial displacement caused by relocation; r u is the radius of the core; P lin is the linear power of the core block; G0 is the initial core-pack gap; Bu is the burnup / MWd·t -1 (U).

[0120] Swelling model

[0121] Irradiation swelling of UO2 fuel is a volume expansion phenomenon caused by the accumulation of fission products and microstructural evolution during nuclear reactor operation. Gaseous products such as xenon (Xe) and krypton (Kr) produced by the fission reaction gather at grain boundaries and defects to form bubbles. The combined atomic volume of solid fission products (such as molybdenum and cesium) is larger than that of the original uranium atoms, resulting in lattice distortion and volume expansion. The corresponding strain model is as follows:

[0122] Δε ss =2.5×10 -29 ΔBu (27);

[0123] Δε gs =8.8×10 -56 ΔBu(2800-T) 11.73 ×exp(-0.0162(2800-T)-8.0×10 -27 Bu)(28);

[0124] Where Δε ss represents the volume strain of solid swelling; ΔBu represents the fuel consumption increment / fissions·m -3 ; Δε gs represents the volume strain of gas expansion; Bu represents fuel consumption / fissions·m -3 .

[0125] Creep model

[0126] Creep is the phenomenon of slow and irreversible plastic deformation of a material under constant stress over time. It is a time-dependent behavior of the material's mechanical properties. Its essence is the dynamic evolution of the material's microstructure (such as lattice, dislocations, grain boundaries, etc.) under the combined effects of stress and temperature. The creep model of Zr-4 material is as follows:

[0127]

[0128] Where, represents the thermal creep strain rate of the cladding; A0 is the material parameter, which is 3.14×10 24 ; σ m is the equivalent stress of the cladding; G is the shear modulus of the cladding material; n is the material parameter, which is taken as 5; Q is the activation energy; R is the ideal gas constant, which is taken as 8.314; represents the cladding irradiation creep strain rate; C0, C1, and C2 are material parameters, which are 2.846×10 -24 , 0.85, 1.0, φ is the neutron flux rate / n·m -2 ·s -1 .

[0129] Irradiation growth model

[0130] Irradiation growth is the phenomenon of anisotropic dimensional change in nuclear materials under neutron irradiation. Its core characteristic is that the material volume remains basically stable, but significant elongation occurs in a specific direction (such as the axial direction). Its strain model is as follows:

[0131] ε i =Aexp(240.8 / T)(φt) 0.5 (1-3f z )(1+2CW) (31);

[0132] Δε l =-(1-(1+Δε i ) -0.5 ) (32);

[0133] Where, ε i represents the strain in the axial direction of the cladding caused by irradiation growth; φt represents the fast neutron flux; f z represents the structural correction factor; CW represents cold working; A is a constant, which is 1.407×10 -16 ; Δε l represents the strain in the radial and circumferential directions of irradiation growth.

[0134] Thermal expansion model

[0135] Thermal expansion is a physical phenomenon in which a material changes in volume or size due to temperature changes. Its essence is the adjustment of lattice spacing caused by the intensification of atomic / molecular thermal vibrations. Because the thermal expansion coefficient of UO2 pellets is greater than that of the Zr-4 cladding, when power changes rapidly, the radial thermal expansion of the pellets is greater than that of the cladding. At this time, the distance between the core and cladding will become smaller, and even the core and cladding will contact, generating contact pressure. The thermal expansion model of uranium dioxide is as follows:

[0136]

[0137] Where, α p represents the thermal expansion linear strain of the core block; a, b, c, d represent material constants, respectively. For specific values, refer to Table 3.

[0138] Table 3 Material constant values in formula (33)

[0139]

[0140]

[0141] For the thermal expansion model of the cladding, the components of the thermal expansion strain in the three directions are as follows:

[0142] ε′ 11 =6.48×10 -6 T Zr-4-1.95×10 -3 (34);

[0143] ε′ 22 =5.63×10 -6 T Zr-4 -1.69×10 -3 (35);

[0144] ε′ 33 =1.04×10 -5 T Zr-4 -3.11×10 -3 (36);

[0145] Where ε′ 11 Represents the thermal expansion strain in the circumferential direction; ε′ 22 represents the radial thermal expansion strain; ε′ 33 Represents the axial thermal expansion strain; the model should satisfy the temperature T Zr-4 <1083K, and assuming <cos 2 θ>=0.71013, <sin 2 φ>=0.30822, where θ is the angle between the radial direction of the cladding and the c-axis of the single crystal, and φ is the angle between the circumferential direction of the cladding and the projection of the c-axis of the grain on the circumferential-axial plane of the cladding.

[0146] S4: Based on the mechanical physical parameters of the core block and cladding in step S2, namely Young's modulus and Poisson's ratio, the constitutive matrix of the material is constructed to describe the relationship between the stress and strain of the material; the pressure boundary conditions of the core block and cladding are given according to the pressure of the coolant (external pressure) and the internal pressure of the core package cavity; the boundary conditions, the constitutive matrix of the material and the strain model in step S3 are substituted into the mechanical control equations (37 and 38) to solve the stress σ and strain ε distribution inside the material.

[0147] To describe the governing equations of mechanics for an object, we first assume that the material experiences infinitesimal strains and displacements, satisfying the following equations in static equilibrium:

[0148]

[0149] σ=[C]·[ε] (38);

[0150] Where, σ, F v represents the Cauchy stress tensor and body force, [C] represents the constitutive matrix at each point in the material, and is the strain tensor.

[0151] When developing the material model, small strain conditions are assumed, allowing the total strain to be expressed as the sum of the individual components. The total strain in the fuel pellet and cladding material can be written as the accumulation of strains resulting from the various physical behaviors of the materials within the reactor. Due to the small strain conditions, this accumulation can be written in the pellet as follows:

[0152] ε totp =ε ep +ε pp +ε thp +ε d +ε r +ε gs +ε ss (39);

[0153] Where, ε totp represents the total strain of the core block, ε ep represents the elastic strain of the core block, ε pp represents the plastic strain of the core block, ε thp represents the thermal expansion strain of the core block, ε d represents the densification strain of the core block, ε r represents the relocation strain of the core block, ε gs represents the gas swelling strain of the core, ε ss Represents the solid swelling strain of the core.

[0154] For the cladding, the total strain can be written as follows:

[0155] ε totc =ε ec +ε pc +ε thc +ε i +ε tcc +ε icc (40);

[0156] Where, ε ec represents the elastic strain of the cladding, ε pc represents the plastic strain of the cladding, ε thc represents the thermal expansion strain of the cladding, ε ig represents the irradiation growth strain of the cladding, ε tcc and ε icc represent the thermal creep strain and irradiation creep strain of the cladding, respectively.

[0157] S5: Based on the temperature distribution inside the pellet obtained in step S2, the stress distribution inside the pellet in step S4, and the power density, uranium dioxide grain size, bubble size and other parameters input by the program, a fission gas diffusion equation is established and the gas concentration inside the grains and on the grain boundaries, as well as the fission gas release rate, are obtained based on the analytical solution; based on the fission gas release, the internal pressure of the cavity is iteratively calculated and transmitted back to the pressure boundary setting in step S4.

[0158] In the actual modeling and calculation process of fission gas release, only a few key parameters need to be considered: the number of gas atoms within the grain, the number of gas atoms on the grain boundary, and the number of saturated gas atoms on the grain boundary. The model assumes that fission gas will be released once the number of gas atoms on the grain boundary reaches the saturated gas number on the grain boundary. The number of saturated gas atoms on the grain boundary is:

[0159]

[0160] Where γ is the surface tension of the bubble; r is the radius of the bubble; k B is the Boltzmann constant; f(θ) is the correction function for the non-spherical shape of the bubble; P EXT is the hydrostatic pressure; V c is saturation is the coverage of grain boundaries.

[0161] The fission gas release model is based on reasonable assumptions and deductions based on solving the diffusion equation, and ultimately obtains the gas concentrations within the crystal and on the grain boundaries:

[0162]

[0163] Where G0 represents the density of gas atoms in the grain; G B represents the density of gas atoms on the grain boundary; G n represents the number density of gas atoms in different groups inside the grain; D represents the gas diffusion coefficient; t is time; a is the grain radius; q is a function simplified by mathematical solution; A n , B n is the material parameter, and its value is as follows:

[0164]

[0165] The diffusion coefficient is a function of temperature as follows:

[0166]

[0167] When G B (τ2)≥G s hour,

[0168] F R =fG s (45);

[0169]

[0170] Where 0<f≤1, the amount of fission gas produced is:

[0171]

[0172] Where β is the fission gas production rate; W R is the fission rate; E is the enrichment.

[0173]

[0174] Where P is the internal pressure of the fuel rod / Pa; n is the amount of gas substance / mol; T gas is the temperature of the air cavity / K, taking the average temperature of the inner wall of the cladding and the outer wall of the pellet; V is the volume of the cavity / m 3 The internal pressure is calculated using the ideal gas state equation above, and the amount of fission gas released can be related to n in the equation.

[0175] S6: Calculate the cladding corrosion layer thickness distributed along the height (Equations 51 and 52) based on the cladding temperature distribution, coolant temperature distribution (Equation 18) and heat flux density obtained in step S2.

[0176] Zr-4 alloy corrodes in water, forming an oxide layer on the metal surface. This phenomenon affects both the heat transfer and mechanical properties of the cladding, so a modeling method is used to calculate the evolution of the oxide layer within the stack. The calculation of the oxide layer thickness is divided into two stages: before and after the transition. The corrosion rate before and after the transition varies significantly, with a transition occurring when the oxide layer thickness reaches 2μm. The corrosion rate equations before and after the transition are as follows:

[0177]

[0178] Where S is the thickness of the corrosion layer; T1 is the metal oxide interface temperature; C1 and C2 correspond to the rate constants before and after the transition; Q1 and Q2 are the activation energies before and after the corrosion transition; t is time; and R is the gas constant, which is 1.98. The final analytical solution is given directly, where the corrosion layer thickness model before the transition is:

[0179]

[0180] After the turning point:

[0181]

[0182] k0=11863+3.5×10 4 (1.91×10 -15 φ) 0.24 (53);

[0183] s i+1 =Δw i+1 γ×10 4 (54);

[0184] Where, t represents time; A is a constant, which is 6.3×10 9 ; Q1 and Q2 are activation energies, which are 32289 and 27354 respectively; R is a constant, which is 1.98; T1 represents the interface temperature between the cladding and the corrosion layer; Δw represents the corrosion weight gain; T0 represents the interface temperature between the corrosion layer and the coolant; λ represents the thermal conductivity of the corrosion layer; γ is the conversion constant between the corrosion layer thickness and the weight gain, which is 0.6789; k0 is the irradiation influence weight; φ is the neutron fluence rate.

[0185] S7: Experimentally verify the core temperature of the pellet obtained in step S2 and the average strain of the cladding obtained in step S4. Model and calculate the fuel behavior in the real reactor based on the fuel rod parameters provided in the experiment. Verify the program's thermal and mechanical analysis and calculation capabilities through comparison.

[0186] The pellet center temperature test was conducted on 10 different fuel rods: IFA-432r1, IFA-432r3, IFA-513r1, IFA-513r6, IFA-515.10rA1, IFA-515.10rB1, IFA-558r6, IFA-562r18, IFA-597r8, and IFA-677.1r2. The validation set included the average center temperature of the IFA-562r18 rod and the top and bottom temperatures (thermocouple measurements) of the remaining fuel rod pellets. The final temperature verification comparison chart is shown below. Figure 2 The error of temperature calculation is generally within 20%. From an overall perspective, the temperature prediction results of the program are acceptable. The sources of error may include inaccurate calculation of the gap distance between the pellet and the cladding and inherent experimental measurement errors.

[0187] In order to verify the program's prediction of cladding deformation, 17 different fuel rods were selected as test objects, and their life cycles all included the final power ramp. The final verification and comparison results are as follows Figure 3 , where the horizontal axis is the name of the verified fuel rod, and the vertical axis is the permanent strain value of the fuel cladding at the end of its life. The calculation results of the program are all within a reasonable range.

[0188] Based on the same concept, the present invention also provides a pressurized water reactor fuel rod performance analysis system, which includes a construction module, a temperature solving module, a stress solving module and a corrosion solving module.

[0189] The construction module is used to obtain multiple physical properties of the pellets and cladding according to the pellet type and cladding type of the nuclear fuel rod, and to construct the solid heat conduction equations of the pellets and cladding based on the multiple physical properties.

[0190] The temperature solution module is used to solve the solid heat conduction equation using the gap heat transfer model between the core block and the cladding and the heat exchange model between the cladding and the coolant as temperature boundary conditions to obtain the temperature distribution of the core block and the cladding.

[0191] The stress solving module is used to construct multiple strain models of the core block and cladding based on their temperature distribution. The coolant pressure and the cavity pressure between the core block and cladding are used as pressure boundary conditions. Multiple strain models and multiple physical property parameters are input into the mechanical control equations used to describe stress and strain to obtain the stress and strain distribution of the core block and cladding. Among them, the strain models include densification model, relocation model, swelling model, creep model, irradiation growth model and thermal expansion model.

[0192] The corrosion solution module is used to input the temperature distribution of the cladding into the cladding corrosion layer thickness model to obtain the cladding radiation layer thickness.

[0193] The present invention is a method for theoretically calculating the thermal and mechanical properties of conventional pressurized water reactor fuel rods. The invention can predict the evolution of the irradiation performance of the fuel rods within the stack, which is of great significance for optimizing fuel design, improving the inherent safety of fuel rods, and reducing the cost of nuclear power.

[0194] Compared with the existing technology, the present invention takes into account the influence of various fuel pile behaviors, including: densification, repositioning, radiation swelling and thermal expansion of UO2 pellets, and radiation growth, thermal expansion and creep of Zr-4 cladding. The invented program solves the variables of thermal and force fields respectively through strong coupling, including: temperature, stress, strain, displacement. The development of the program relies on MOOSE, and therefore inherits many advantages of MOOSE. The biggest advantage is integration: the program itself has most of the functions of fuel performance analysis, and users can add new models to existing models according to their needs. The program has integration and flexibility that general fuel performance analysis programs do not have, and has demonstrated outstanding capabilities in calculation accuracy and rapid convergence.

[0195] Although the preferred embodiments of the present invention have been described, those skilled in the art may make additional changes and modifications to these embodiments once they have learned the basic creative concept. Therefore, the appended claims are intended to be interpreted as including the preferred embodiments and all changes and modifications that fall within the scope of the present invention.

[0196] Obviously, those skilled in the art may make various modifications and variations to the present invention without departing from the spirit and scope of the present invention. Thus, if such modifications and variations fall within the scope of the claims and their equivalents, the present invention is intended to include such modifications and variations.

Claims

1. A method for analyzing the performance of a pressurized water reactor fuel rod, characterized in that: The following steps are involved: According to the pellet type and cladding type of the nuclear fuel rod, multiple physical property parameters of the pellet and cladding are obtained, and the solid heat conduction equation of the pellet and cladding is constructed based on the multiple physical property parameters; The gap heat transfer model between the pellet and cladding and the heat transfer model between the cladding and the coolant are used as temperature boundary conditions to solve the solid heat conduction equation and obtain the temperature distribution of the pellet and cladding. Multiple strain models of the pellets and cladding are constructed based on their temperature distributions. Using the coolant pressure and the cavity pressure between the pellets and cladding as pressure boundary conditions, multiple strain models and physical property parameters are input into the mechanical governing equations for describing stress and strain to obtain stress and strain distributions of the pellets and cladding. The strain models include a densification model, a relocation model, a swelling model, a creep model, an irradiation growth model, and a thermal expansion model. The temperature distribution of the cladding is input into the cladding corrosion layer thickness model to obtain the cladding radiation layer thickness.

2. A method for analyzing the performance of a pressurized water reactor fuel rod according to claim 1, characterized in that: The nuclear fuel rod includes a uranium dioxide pellet and a Zr-4 alloy cladding, and the physical property parameters include thermal conductivity, specific heat capacity, density, Young's modulus and Poisson's ratio.

3. A method for analyzing the performance of a pressurized water reactor fuel rod according to claim 1, characterized in that: The solid heat conduction equation is specifically as follows: Where ρ is the density of the pellet or cladding, C p is the specific heat capacity of the pellet or cladding, k is the thermal conductivity of the pellet or cladding, T represents the temperature, q represents the power of the pellet, is the gradient.

4. A method for analyzing the performance of a pressurized water reactor fuel rod according to claim 1, characterized in that: The gap heat transfer model is specifically as follows: q gap =h eff (T p -T c ); Where q gap is the heat flux through the gas gap, h eff is the equivalent heat convection heat transfer coefficient, T p and T c represent the fuel pellet surface temperature and the cladding inner surface temperature respectively; The heat exchange model is specifically shown as follows: q s =h co (T cl -T co ); Where q s is the heat flux density on the cladding surface, h co is the convective heat transfer coefficient at the coolant-shell interface, T cl and T co are the coolant temperatures at the outer wall of the cladding and its corresponding nodes, respectively.

5. A method for analyzing the performance of a pressurized water reactor fuel rod according to claim 1, characterized in that: The mechanical control equation is specifically as follows: σ=[C]·[ε]; Where σ is the Cauchy stress tensor, F v is the body force, [C] is the constitutive matrix, and ε is the strain.

6. A method for analyzing the performance of a pressurized water reactor fuel rod according to claim 1, characterized in that: The cladding corrosion layer thickness model is specifically as follows: Where S i+1 is the thickness of the corrosion layer at time i+1, S i is the thickness of the corrosion layer at time i, t is time, A is a constant, Q1 and Q2 are the activation energies before and after the corrosion transition, R is the gas constant, T1 is the metal oxide interface temperature, Δw is the corrosion weight gain, T0 is the interface temperature between the corrosion layer and the coolant, λ is the thermal conductivity of the corrosion layer, γ is the conversion constant between the corrosion layer thickness and weight gain, q s is the heat flux density on the cladding surface, k o is the radiation impact weight.

7. A pressurized water reactor fuel rod performance analysis system, characterized in that: include: A construction module is used to obtain multiple physical properties of the pellets and cladding according to the pellet type and cladding type of the nuclear fuel rod, and to construct solid heat conduction equations of the pellets and cladding based on the multiple physical properties; The temperature solving module is used to solve the solid heat conduction equation using the gap heat transfer model between the pellet and cladding and the heat exchange model between the cladding and the coolant as temperature boundary conditions to obtain the temperature distribution of the pellet and cladding; A stress solver module is used to construct multiple strain models of the pellet and cladding based on their temperature distributions. The module uses coolant pressure and the cavity pressure between the pellet and cladding as pressure boundary conditions, inputs multiple strain models and physical property parameters into the mechanical governing equations describing stress and strain, and obtains the stress and strain distributions of the pellet and cladding. The strain models include a densification model, a relocation model, a swelling model, a creep model, an irradiation growth model, and a thermal expansion model. The corrosion solution module is used to input the temperature distribution of the cladding into the cladding corrosion layer thickness model to obtain the cladding radiation layer thickness.

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