Modeling and calculation method, system, device and medium for fuel rod cladding rupture failure

Abstract

The application discloses a fuel rod cladding rupture failure modeling calculation method, system, equipment and medium. The material of the cladding is Zr-4, and the method comprises the following steps: determining initial conditions, inputting fuel rod geometric dimensions and corresponding fuel, cladding material properties and boundary conditions; calculating the temperature distribution of fuel and cladding at each time based on the physical properties of fuel, cladding and the gap between fuel and cladding; calculating the thickness and mass of the oxidation layer, calculating the volume fraction of Zr-4 converted from alpha phase to beta phase through a crystal phase change model; calculating the high-temperature creep strain rate of the cladding through a high-temperature creep model, calculating the hoop creep strain of the cladding and the hoop stress of the cladding, and updating the gas volume in the cladding and calculating the gas pressure; based on the high-temperature creep strain rate of the cladding, calculating the hoop creep strain of the cladding or the hoop stress of the cladding, evaluating whether the cladding ruptures through a cladding rupture failure criterion and obtaining the rupture time. The application can accurately determine the time of cladding rupture.

Description

TECHNICAL FIELD

[0001] The present application relates to the field of nuclear reactor fuel rod thermal performance analysis, and particularly relates to a modeling calculation method, system, equipment and medium for fuel rod cladding rupture failure in a LOCA accident. BACKGROUND

[0002] Zirconium alloy has been used as a cladding material for uranium dioxide fuel since 1950 due to its good oxidation resistance, excellent neutron irradiation resistance, good ductility and low neutron absorption cross section. After the Fukushima nuclear accident, it was found that zirconium alloy cladding oxidizes quickly at high temperatures, producing hydrogen and posing a safety risk of hydrogen explosion. Therefore, accident tolerant fuel (ATF) materials have attracted widespread attention.

[0003] Currently, there are two main development directions for accident tolerant fuel cladding: one is surface coating technology for zirconium alloy, and the other is development of new cladding materials to replace zirconium alloy. However, these two technologies have not been widely used in engineering applications. Currently, most light water reactor fuel cladding is made of zirconium alloy. Under accident conditions, especially in a loss of coolant accident (LOCA), when the temperature exceeds 1000K-1100K, the crystal structure of zirconium alloy changes, and the increase in high temperature and internal and external pressure difference will cause the zirconium alloy cladding to accelerate outward creep. In addition, the high-temperature steam environment will also accelerate the oxidation of the cladding, causing the cladding to thin. When the cladding deformation reaches a certain degree, the cladding will rupture and fail, destroying the first barrier of radiation confinement and causing safety risks.

[0004] The method provided in "Extension of the OFFBEAT fuel performance code to finite strains and validation against LOCA experiments" is developed based on the OpenFOAM platform and uses the finite volume method, which has more advantages in computational fluid dynamics. However, it cannot obtain accurate solutions for problems involving multiple physical field coupling such as heat transfer and solid mechanics.

[0005] From the perspective of improving reactor safety and economy, it is essential to develop a calculation tool that can reliably evaluate the thermodynamic behavior and integrity of nuclear fuel rods in accidents in the reactor. SUMMARY

[0006] To at least overcome one of the defects and deficiencies existing in the prior art, the first object of the present application is to provide a reliable and accurate modeling and calculation method for fuel rod cladding rupture failure in a LOCA accident, which adopts a Norton high-temperature creep model, a Leistikow high-temperature oxidation model, a Massih crystal phase change model and a full-coupling calculation mode of heat conduction, calculates temperature and stress distribution at each time and total strain composition of the cladding based on input fuel rod design parameters and boundary conditions, and evaluates the rupture failure time of the cladding through three failure criteria of superstrain, superstress and plastic strain rate to obtain an accurate and reliable rupture time of the cladding.

[0007] The second object of the present application is to provide a modeling and calculation system for fuel rod cladding rupture failure in a LOCA accident.

[0008] The third object of the present application is to provide a storage medium.

[0009] The fourth object of the present application is to provide a computing device.

[0010] To achieve the first object of the present application, the present application provides a modeling and calculation method for fuel rod cladding rupture failure in a LOCA accident, which specifically comprises the following steps:

[0011] Determine initial conditions, input fuel rod geometric dimensions and corresponding material properties of fuel and cladding and boundary conditions;

[0012] Calculate temperature distribution of fuel and cladding at each time based on physical properties of fuel, cladding and the gap between fuel and cladding;

[0013] Based on the change of thermodynamic material properties of Zr-4 at high temperature, calculate the thickness and mass of the oxidation layer through a high-temperature oxidation model and calculate the volume fraction of Zr-4 converted from alpha phase to beta phase through a crystal phase change model;

[0014] Calculate high-temperature creep strain rate of the cladding through a high-temperature creep model Calculate hoop creep strain ε of the cladding creep and hoop stress σ of the cladding θ , and update the volume of gas inside the cladding and calculate the gas pressure;

[0015] Based on the high-temperature creep strain rate of the cladding Calculate hoop creep strain ε of the cladding creep or hoop stress σ of the cladding θ , evaluate whether the cladding ruptures through a cladding rupture failure criterion and obtain the rupture time.

[0016] As a preferred technical solution, the heat transfer calculation of fuel, cladding and the gap between fuel and cladding is specifically calculated by the following formula:

[0017]

[0018] where p is the density of the material (kg / m3), C p is the heat capacity of the fuel material (J / kg / K), T is the temperature of the material (K), t is time (s), k is the thermal conductivity of the material (J / m / K), r is the distance of the material from the centerline of the material (m), and q is the heat generation rate per unit volume of the material (J / m3).

[0019] where, when used to calculate the heat transfer process and temperature distribution within the fuel, the material is the fuel, when used to calculate the heat transfer process and temperature distribution of the cladding and the gap between the fuel and the cladding, q = 0, and the material is the cladding.

[0020] As a preferred technical solution, the coolant pressure, the cladding outer surface temperature, the fuel average linear heat power, and the plenum gas temperature are input as boundary conditions. The coolant pressure is applied on the cladding outer surface through the solid mechanics module in COMSOL, the outer surface temperature and formula (1) are realized through the solid heat transfer module in COMSOL. The fuel average linear heat power and the plenum gas temperature are respectively the conditions for calculating the fuel heat release and the internal gas pressure.

[0021] As a preferred technical solution, since Zr-4 undergoes a crystal phase change at high temperature, from hexagonal crystal (α phase) to cubic crystal (β phase), the crystal phase state of Zr-4 will significantly affect the high temperature rate, and it is necessary to calculate the volume fraction of Zr-4 converted into β phase through a crystal phase change model. The specific calculation equation is:

[0022]

[0023] where y represents the volume fraction of Zr-4 converted into β phase, t is time, k s represents the rate parameter, y s represents the equilibrium value of y; wherein k s and y s are calculated by (3) (5) respectively:

[0024]

[0025] where k0 represents the kinetic pre-factor, Q p represents the effective activation energy, k b represents the Boltzmann constant, k m is a constant, represents the heating rate, T cent represents the material parameter related to the temperature center of the mixed phase region, T span represents the material parameter related to the temperature span of the mixed phase region.

[0026] As a preferred technical solution, the high-temperature oxidation model is any one of the EPRI / KWU / C-E oxidation model, the Leistikow relationship, and the Prater-Courtright model, wherein:

[0027] For a temperature below 673 K, the EPRI / KWU / C-E oxidation model is used, which is

[0028]

[0029] In the formula, S represents the thickness of the oxidation layer, C1 and C2 represent oxidation rate constants before and after the transition, i.e., before and after reaching the critical oxidation layer thickness, Q1 and Q2 represent oxidation activation energies before and after the transition, t represents time, and T represents the temperature of the cladding;

[0030] For a temperature range of 673 K to 1800 K, the Leistikow relationship is expressed as:

[0031]

[0032] In the formula, ξ s represents the thickness of the oxidation layer, ξ g represents the mass of the oxidation layer, R represents the ideal gas constant, A s represents the oxidation rate constant of the oxidation layer thickness, A g represents the oxidation rate constant of the oxidation layer mass, Q s represents the high-temperature oxidation activation energy of the oxidation layer thickness, Q g represents the high-temperature oxidation activation energy of the oxidation layer mass;

[0033] For a range above 1900 K, the Prater-Courtright model is used for calculation, and the expression of the Prater-Courtright model is consistent with that of the Leistikow relationship, except that the values of the parameters are different.

[0034] The high-temperature oxidation model and the crystal phase change model described above are calculated through the domain partial differential equation module in COMSOL.

[0035] As a preferred technical solution, according to the calculated mass fraction of the β phase, the high-temperature creep rate is calculated, and the high-temperature creep model is:

[0036]

[0037] In the formula, In the formula, A creep represents the creep intensity coefficient, σ eff represents the effective stress, i.e., the Mises stress, and nc represents stress exponent, Q creep represents creep deformation activation energy, T represents temperature, and R represents ideal gas state constant; wherein, A creep , Q creep , n c The size of is related to the crystal phase state of Zr-4, and takes different values in alpha phase and beta phase, as shown in the following table:

[0038] When , the size of y is calculated according to formula (2) between pure alpha phase and 50% alpha + 50% beta phase, 50% alpha + 50% beta phase and pure beta phase, and linear interpolation is performed on ln(A creep ), Q creep , n c ; When creep , linear interpolation is performed on ln(A creep ), Q c , n ave between pure alpha phase and pure beta phase. The above high temperature creep model is calculated through the creep interface in COMSOL solid mechanics.

[0039] As a preferred technical solution, after calculating the cladding strain at each moment, the gap volume between the cladding and the fuel changes, and it is necessary to update based on the strain calculated at each moment. The ideal gas state equation is used, and the specific calculation formula is:

[0040]

[0041] In the formula, n represents the number of moles of gas, R represents the ideal gas state constant, V represents the volume of the cavity formed by the fuel and the cladding, T θ represents the average temperature of the outer surface of the fuel and the inner surface of the cladding. The calculation of the gas volume is realized through the generalized stretching operator and the integral operator in COMSOL, and the gas pressure is calculated through the global differential differential equation.

[0042] As a preferred technical solution, the cladding rupture failure criterion has three kinds, including:

[0043] ① Super stress failure criterion: when the local hoop stress is greater than the limit rupture stress, the cladding ruptures, that is:

[0044] σ b

[0045]

[0046] Wherein, σ brepresents the limit fracture stress (MPa), a, b are constants determined by experiment, and depend on the crystalline phase of the material. Similar to the high temperature creep model, for Zr-4 in mixed phase state, linear interpolation method is used for a, b between pure alpha, 50% alpha + 50% beta and pure beta. The specific calculation parameters are as follows:

[0047]

[0048] η represents the oxygen mass fraction in the cladding, and η0 is the oxygen mass fraction in the initial state. The oxygen mass fraction at each time is further calculated by the high temperature oxidation model.

[0049]

[0050] In the formula, r o represents the outer surface radius of the cladding (m), r i represents the inner surface radius of the cladding (m), ρ Zr represents the density of Zr-4 (kg / m3), ξ g represents the oxide layer mass (kg / m3), ξ s represents the oxide layer thickness (m).

[0051] ② Plastic strain rate criterion: when the plastic strain rate (including creep, plastic strain, etc.) exceeds a limit value, the cladding is fractured. That is:

[0052]

[0053] Take as the limit plastic strain rate.

[0054] ③ Superstrain failure criterion: when the local hoop creep strain exceeds a limit value, the cladding is fractured and fails, that is:

[0055] ε creep >∈ b

[0056] ε creep represents the local hoop creep strain.

[0057] The application can model and process the fuel rod by adopting two-dimensional axisymmetric, calculate the temperature distribution of the fuel and the cladding by adopting one-dimensional unsteady heat conduction equation, process the thermodynamic behavior of the fuel rod under accident conditions by adopting Norton high temperature creep model, Leistikow high temperature oxidation model and Massih crystalline phase change model, and evaluate the cladding fracture failure time by adopting three fracture failure criteria of superstrain, superstress and plastic strain rate.

[0058] The method can be based on a multi-physical field finite element analysis platform, and thermal mechanical properties of a zirconium alloy cladding of a fuel rod of a pressurized water reactor under a loss of coolant accident are analyzed and calculated, thermal mechanical behaviors of the zirconium alloy cladding, such as thermal creep, phase change and high-temperature oxidation, are considered, and a rupture criterion is used to determine a time of rupture of the cladding.

[0059] To achieve the second purpose, the application provides a modeling and calculation system for cladding rupture failure of a fuel rod in a LOCA accident, comprising the following modules:

[0060] A determination module is configured to determine initial conditions, input fuel rod geometric dimensions and corresponding material properties of fuel and cladding, and boundary conditions;

[0061] A heat conduction module is configured to calculate temperature changes and distributions of fuel, cladding and a gap between the fuel and the cladding;

[0062] A phase judgment module is configured to calculate thickness and mass of an oxidation layer through a high-temperature oxidation model, and to calculate a volume fraction of Zr-4 converted from alpha phase to beta phase;

[0063] A thermal mechanical coupling calculation module is configured to calculate high-temperature creep and high-temperature oxidation behaviors of the cladding in the LOCA accident;

[0064] A gas pressure updating module is configured to recalculate gas pressure based on changes of an internal gas space at each time point;

[0065] A cladding rupture failure judgment module is configured to evaluate whether the cladding ruptures through a cladding rupture failure criterion, to obtain a cladding failure rupture time.

[0066] To achieve the third purpose, the application provides a storage medium storing a program, and the program is executed by a processor to implement the modeling and calculation method for cladding rupture failure of a fuel rod in a LOCA accident.

[0067] To achieve the fourth purpose, the application provides a computing device comprising a processor and a memory for storing a program executable by the processor, and the processor executes the program stored in the memory to implement the modeling and calculation method for cladding rupture failure of a fuel rod in a LOCA accident.

[0068] Compared with the prior art, the application has at least the following beneficial effects:

[0069] (1) The present application considers the high-temperature creep, crystal phase change and high-temperature oxidation behavior of Zr-4 cladding under the loss-of-coolant accident, and through the high-temperature oxidation and crystal phase change model, the thickness and mass of the oxidation layer can be accurately calculated, the volume fraction of Zr-4 converted from the alpha phase to the beta phase can be judged, and then the high-temperature creep rate of Zr-4 in the corresponding crystal phase state can be calculated in a thermal-solid coupling manner, the corresponding creep strain can be calculated, and the rupture failure time can be evaluated according to the rupture failure criterion, so that the thermodynamic performance of the cladding under the coolant accident can be more reliably evaluated.

[0070] (2) The present application adopts a gas pressure updating method, which can automatically calculate the gas volume between the fuel and the cladding at each moment based on the deformation state of the cladding, and calculate the gas pressure according to the ideal gas state equation.

[0071] (3) The present application provides three available rupture failure criteria, which can evaluate the rupture failure time of the Zr-4 cladding from different angles as needed, and has a certain universality.

[0072] (4) The present application adopts a relatively comprehensive oxidation model, which can calculate the mass and thickness of the oxidation layer in most temperature ranges. BRIEF DESCRIPTION OF DRAWINGS

[0073] Figure 1 It is a flowchart of the modeling and calculation method of the rupture failure of the fuel rod cladding in a LOCA accident in the embodiment of the present application;

[0074] Figure 2 It is a schematic diagram of the deformation state of the cladding at the rupture failure time calculated in the embodiment of the present application (the legend represents the engineering hoop creep strain) (for the convenience of visualization, the radial direction is enlarged by 15 times);

[0075] Figure 3 It is a comparison diagram of the internal gas pressure change of the IFA650.2 case calculated in the embodiment of the present application and the calculation results and experimental results of other existing fuel performance codes;

[0076] Figure 4 It is a comparison diagram of the external contour diagram at the rupture time calculated in the embodiment of the present application and the calculation results and experimental results of other existing fuel performance codes;

[0077] Figure 5 It is a diagram of the change of the oxidation layer thickness with time calculated by the high-temperature oxidation model in the embodiment of the present application. DETAILED DESCRIPTION

[0078] In order to make the objects, technical solutions and advantages of the present application clearer, the present application will be further described in detail below with reference to the drawings and embodiments. It should be understood that the specific embodiments described herein are only used to explain the present application and not used to limit the present application.

[0079] The present application provides a modeling and calculation method for fuel rod cladding rupture failure in a LOCA accident. In a loss of coolant accident, the cladding is exposed to a high-temperature steam environment. For a Zr-4 cladding (zirconium alloy cladding), the cladding temperature will rapidly increase to more than 1000K because there is not enough coolant to take away the heat of the cladding. With the increase of temperature and the increase of the internal and external pressure difference, the high temperature not only accelerates the thermal creep rate and oxidation rate of Zr-4, but also causes crystal phase change, resulting in that the cladding hoop strain, stress or strain rate exceeds a certain threshold value, and rupture occurs. These phenomena are all considered in the model for full coupling calculation, and three different cladding rupture failure criteria are provided to evaluate the cladding rupture failure time.

[0080] Specifically, referring to Figure 1 The present application provides a modeling and calculation method for fuel rod cladding rupture failure in a LOCA accident. In a loss of coolant accident, the cladding is exposed to a high-temperature steam environment. For a Zr-4 cladding (zirconium alloy cladding), the cladding temperature will rapidly increase to more than 1000K because there is not enough coolant to take away the heat of the cladding. With the increase of temperature and the increase of the internal and external pressure difference, the high temperature not only accelerates the thermal creep rate and oxidation rate of Zr-4, but also causes crystal phase change, resulting in that the cladding hoop strain, stress or strain rate exceeds a certain threshold value, and rupture occurs. These phenomena are all considered in the model for full coupling calculation, and three different cladding rupture failure criteria are provided to evaluate the cladding rupture failure time.

[0081] Step S1: determining initial conditions, inputting corresponding design parameters, material properties and boundary conditions of the fuel rod.

[0082] Input the geometric size of the fuel rod;

[0083] Input the material properties of the fuel and the cladding, such as thermal conductivity, constant-pressure heat capacity, density, Poisson's ratio, Young's modulus, etc.

[0084] The boundary conditions include the average linear heat power of the fuel, the coolant pressure, and the cladding outer surface temperature measured based on experiments.

[0085] In some embodiments of the present application, some design parameters are given in Table 1. IFA650.2 is a calculation example used for verification of the present application, used for comparison with other fuel performance codes, and modeled in COMSOL. For the verification example IFA650.2, the fuel material is UO2, the cladding material is Zr-4, and the internal gas is He.

[0086] Table 1

[0087] Design Parameters (Geometric Dimensions) Value Effective Fuel Length 500 millimetres Fuel Diameter 8.29 millimetres Fuel Height 8 millimetres Cladding Outside Diameter 9.5 millimetres Cladding Thickness 0.57 millimetres Total Free Gas Volume 17.4 cubic centimetres Plenum Gas Volume 15.8 cubic centimetres

[0088] Step S2: calculating the temperature distribution of the fuel and the cladding at each time based on the average linear heat power of the fuel and the physical properties of the fuel, the cladding and the gap between the fuel and the cladding.

[0089] The physical property of the gap between the fuel and the cladding is the thermal property of the gas gap material.

[0090] The formula for calculating the temperature distribution of the fuel and the cladding at each moment is as follows:

[0091]

[0092] In the formula, p is the density of the material (kg / m3); C p is the heat capacity of the material (J / kg / K); T is the temperature of the material (K); t is the time (s); k is the thermal conductivity of the material (J / m / K); r is the distance from the center line of the material to each position inside the material (m); q is the heat generation rate of the unit volume of the material (J / m3), q lin is the average linear heat power of the fuel, r pellet represents the radius of the material.

[0093] Formula (1) can be used to calculate the heat transfer process and temperature distribution in the fuel, and 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, the source term q in the formula is omitted, that is, q = 0 at this time.

[0094] The material in formula (1) is fuel or cladding, when used to calculate the heat transfer process and temperature distribution in the fuel, the material is fuel, and when used to calculate the heat transfer process and temperature distribution of the cladding and the gap between the fuel pellets and the cladding, that is, q = 0, the material is cladding.

[0095] Formula (1) is calculated by using the solid heat transfer module in COMSOL.

[0096] Step S3: Based on the temperature distribution calculated in step S2, since Zr-4 undergoes a crystal phase change at high temperature, from hexagonal crystal (α phase) to cubic crystal (β phase), the crystal phase state of Zr-4 will significantly affect the high temperature rate, and a crystal phase change model is needed to calculate the volume fraction of Zr-4 converted from α phase to β phase.

[0097] The crystal phase change model is:

[0098]

[0099] In the formula, y represents the volume fraction of Zr-4 converted to β phase, k s represents the rate parameter, with a unit of 1 / s; y s represents the equilibrium value of y.

[0100] wherein k s and y s are calculated by formula (3) (5) respectively:

[0101]

[0102]

[0103] where k0represents the kinetic pre-exponential factor (1 / sec); Q p represents the effective activation energy, k b represents the Boltzmann constant, k m is a constant, represents the heating rate, which is taken as the average heating rate. In some embodiments of the present application, for Zr-4 material, (Kelvin), k m = 0 when Zr-4 is transforming from the beta phase to the alpha phase, k m = 0.2, which is taken as k m = 0 in the loss-of-coolant accident.

[0104] The equilibrium value of y s is calculated as follows:

[0105]

[0106] where T cent represents the material parameter related to the temperature center of the mixed phase region, T span represents the material parameter related to the temperature span of the mixed phase region, in Kelvin.

[0107] For Zr-4, T cent = 1159 - 0.096w, T span = 44 + 0.026w, where w represents the hydrogen concentration in parts-per-million mass. Zr-4 is treated as pure alpha phase when y < 0.01 and as pure beta phase when y > 0.99. The phase change model is calculated using COMSOL partial differential equations.

[0108] In addition, high temperature also significantly accelerates the oxidation rate of Zr-4, therefore, different high temperature oxidation models are used to calculate the thickness and mass of the oxidation layer according to different temperature intervals.

[0109] The high temperature oxidation models include the EPRI / KWU / C-E oxidation model, the Leistikow correlation and the Prater-Courtright model.

[0110] where for temperatures below 673 K, the EPRI / KWU / C-E oxidation model is used, as shown in equation (6):

[0111]

[0112] In the formula, S represents the thickness of the oxide layer in micrometers, C1 and C2 represent the oxidation rate constants before and after the transition, i.e., before and after reaching the critical oxide layer thickness, Q1 and Q2 represent the oxidation activation energies before and after the transition, t represents time in seconds, and T represents the coating temperature in Kelvin.

[0113] In some embodiments of the present invention, for Zr-4, C1 = 6.3 × 10⁻⁴. 9 (micrometer) 3 / day), C2=8.04×10 7 +2.59×10 8 (7.46×10 -15 φ) 0.25 (micrometers / day) (Kelvin), (Kelvin).

[0114] For the temperature range of 673K ​​to 1800K, the thickness and quality of the oxide layer are calculated using the Leistikow relation:

[0115]

[0116]

[0117] In the formula, ξ s ξ represents the thickness of the oxide layer. g The mass of the oxide layer is represented by R, the ideal gas state constant is represented by A. s A represents the oxidation rate constant representing the thickness of the oxide layer. g The oxidation rate constant, Q, represents the quality of the oxide layer. s Q represents the high-temperature oxidation activation energy, which indicates the thickness of the oxide layer. g High-temperature oxidation activation energy represents the quality of the oxide layer.

[0118] For temperatures above 1900 K, the Prater-Courtright model is used for calculations. The calculation relationships between the Leistikow relation and the Prater-Courtright model are the same, only the specific values ​​of each parameter differ. In some embodiments of this invention, the values ​​of each parameter are summarized based on experimental data for the corresponding temperature range. The method for determining the parameter values ​​follows the method disclosed in the literature "Recommendations and supporting information on the choice of zirconium oxidation models in severe accident codes." In a specific example, the parameter values ​​are shown in Table 2.

[0119] For a temperature range of 1800K-1900K, linear interpolation of the two relationships is used to obtain the thickness and quality of the oxide layer.

[0120] The specific calculation parameters for each oxidation model are shown in Table 2.

[0121] Table 2

[0122]

[0123] The above high-temperature oxidation model is calculated using domain differential equations in COMSOL.

[0124] Step S4: Based on the volume fraction y of Zr-4 transforming from the α phase to the β phase calculated in Step S3, calculate the high-temperature creep rate of the cladding using Norton's law, i.e., the high-temperature creep model:

[0125]

[0126] In the formula, A represents the high-temperature creep strain rate of the cladding. creep σ represents the creep strength coefficient. eff This represents the effective stress, also known as the Mises stress, n. c Q represents the stress index. creep The value represents the activation energy for creep deformation, T represents the temperature of the cladding, and R represents the ideal gas state constant.

[0127] Among them, the β phase mass fraction y determines the crystal phase state of Zr-4, A creep Q creep n c The value of is related to the crystal phase state of Zr-4, and takes different values ​​in the α phase and β phase. In some embodiments of the present invention, the values ​​are shown in Table 3.

[0128] Table 3

[0129]

[0130] when When, the magnitude of y is calculated according to formula (2), and ln(A) is compared between pure α phase and 50% α + 50% β phase, 50% α + 50% β phase and pure β phase. creep ), Q creep n c Perform linear interpolation; At that time, between the pure α phase and the pure β phase, the ratio of ln(A) creep ), Q creep n c Linear interpolation was performed. The above high-temperature creep model was calculated using the creep interface in COMSOL Solid Mechanics.

[0131] In addition to the high temperature creep, the cladding will also have elastic strain, thermal expansion and other material strain, which will also affect the volume of the gas inside the cladding, causing the change of the internal gas pressure. The specific calculation is as follows:

[0132]

[0133] ε th = α th (T-293.15) (11)

[0134] ε = ε ela + ε th + ε creep (12)

[0135] In the formula, ε ela represents the elastic strain of the cladding, ε th represents the thermal expansion strain of the cladding, ε represents the total hoop strain of the cladding, σ represents the local stress of the cladding, α the represents the thermal expansion coefficient of the cladding, E represents the Young's modulus of the cladding, and ε creep represents the hoop creep strain of the cladding.

[0136] Based on the calculated total hoop strain ε of the cladding, due to the change of the gap volume between the cladding and the fuel, it is necessary to update the internal gas volume based on the strain calculated at each moment, and to calculate the gas pressure.

[0137] Wherein, the ideal gas state equation is adopted, and the specific calculation formula of the gas pressure is:

[0138]

[0139] In the formula, P is the gas pressure, n represents the number of moles of gas (moles), R represents the ideal gas constant, V represents the volume of the cavity formed by the fuel and the cladding, T ave represents the average temperature of the outer surface of the fuel and the inner surface of the cladding. The calculation of the gas volume is realized by the generalized stretching operator and the integral operator in COMSOL, and the calculation of the gas pressure is realized by the global differential equation.

[0140] After calculating the gas pressure, the hoop stress of the cladding is calculated:

[0141]

[0142] In the formula, P is the gas pressure, P coolant is the coolant pressure, which is one of the input boundary conditions, r i is the inner diameter of the cladding, r o is the outer diameter of the cladding, s cladding is the thickness of the cladding, and ε creep represents the hoop creep strain of the cladding.

[0143] The high-temperature creep rate of the cladding and By formula (9), for the calculation of thermal expansion and elastic strain, by inputting material parameters such as thermal expansion coefficient and Young's modulus, the linear elastic material interface and thermal expansion interface of the solid mechanics module of COMSOL can be used to calculate the corresponding size and strain rate, and the local stress in each direction.

[0144] ε creep and A creep , n c , Q creep can be input by the creep interface of solid mechanics.

[0145] Step S5: Based on the hoop creep strain ε creep , the creep strain rate or the hoop stress σ θ of the cladding calculated in step S4, whether the cladding ruptures and the cladding rupture time are evaluated by three different cladding rupture failure criteria.

[0146] The three different cladding rupture failure criteria are as follows:

[0147] ① Super-stress failure criterion: when the local hoop stress is greater than the ultimate rupture stress, the cladding ruptures, that is:

[0148] σ θ > σ b (15)

[0149]

[0150] Where σ θ represents the hoop stress of the cladding, σ b represents the ultimate rupture stress, unit is megapascal, a, b are parameters, the specific values of which can be determined by experiments, and depend on the crystal phase of the material. The calculation formula of the rupture stress is also an empirical model based on experiments, and a, b are values fitted according to data in the corresponding literature (in some embodiments of the present application, the method in the literature “Burst Criterion of Zircaloy Fuel Claddings In a Loss-of-Coolant Accident” is used to determine the values of a and b). Similar to the high-temperature creep model, for Zr-4 in mixed phase state, linear interpolation method is used for a and b between pure α, 50% α+50% β and pure β. The specific calculation parameters are as follows in Table 4.

[0151] Table 4

[0152]

[0153] η( / ) represents the oxygen mass fraction in the cladding, η0 is the oxygen mass fraction in the initial state, in some embodiments of the present application, η0 takes 0.0012. The oxygen mass fraction at each time is further calculated by a high-temperature oxidation model.

[0154]

[0155] In the formula, r o represents the cladding outer surface radius (m), r i represents the cladding inner surface radius (m), ρ Zr represents the density of Zr-4 (kg / m3), ξ g represents the mass of the oxide layer (kg / m3), represents the metal surface radius (m), ξ s represents the oxide layer thickness (m), R PB = 1.56, R PB represents the Pilling-Bedworth ratio of Zr-4, which refers to the volume ratio of the oxide film and the metal consumed to generate the oxide film, and is a material property, which takes 1.56 for Zr-4.

[0156] ② Plastic strain rate criterion: the cladding ruptures when the plastic strain rate (including creep, plastic strain, etc.) exceeds a preset limit value. That is:

[0157]

[0158] Take as the limit plastic strain rate, represents the plastic strain rate, which theoretically includes the plastic strain rate and the creep strain rate of the cladding, but the yield stress of Zr-4 is large, and in the coolant loss accident, the effective stress will not exceed the yield stress until the cladding ruptures and fails, so the high-temperature creep rate of the cladding is mainly considered, that is,

[0159] ③ Superstrain failure criterion: the cladding ruptures and fails when the local hoop creep strain exceeds a limit value,

[0160] That is:

[0161] ε creep >∈ b (19)

[0162] ε creep represents the local hoop creep strain, and the engineering hoop strain of ∈ b = 40% is selected as the limit strain, and the corresponding true hoop strain is 33.6%.

[0163] The over-stress rupture failure criterion is an empirical formula obtained by single-rod rupture experiments on fresh fuel rods, and can not be applicable to the simulation of high burnup fuel rods, which can cause the rupture of the cladding to be predicted too early. For high burnup fuel rods, the over-strain rupture failure criterion is widely used, which can combine the over-strain and the other two rupture failure criteria, and the cladding is considered to rupture as long as one of the rupture failure criteria is satisfied.

[0164] By using the method provided in the embodiment, the heat conduction and temperature distribution of the current time step are obtained first, and the volume fraction y of the Zr-4 transformed into the beta phase, the thickness and mass of the oxidation layer are obtained by combining the crystal phase change model and the high-temperature oxidation model, then the high-temperature creep rate is obtained by the high-temperature creep model based on the volume fraction y and the temperature distribution, and the total strain, the hoop strain, the hoop stress and the plastic strain rate of the cladding at each position are calculated, the internal gas pressure is updated according to the size of the total strain, and finally the rupture failure criterion is judged according to the provided rupture failure criterion, if the failure criterion is satisfied, the calculation is ended, and the relevant data are output, otherwise the calculation of the next time step is performed. Until the failure criterion is satisfied or the last time step is reached, the calculation is stopped. The solving result of the method provided in the embodiment can be used as a reference for detailed research on the bulging rupture failure of the cladding under the coolant loss accident condition.

[0165] The application uses a multi-physical field full-coupling simulation calculation method based on the COMSOL platform, in the aspect of thermodynamics and solid mechanics coupling, the mechanical analysis of the deformation behavior of the cladding under the coolant loss accident can be performed by using the physical field interface, and the gas volume is updated at each time step based on the strain by using the generalized stretching operator and the integral operator, the gas pressure is calculated, the strain is more accurately calculated and the rupture time is more accurately evaluated. Compared with the code, it is more convenient and has higher calculation accuracy. In addition, the application provides three rupture failure criteria, which allows users to freely select according to needs, and considers the high-temperature oxidation of the cladding, which is more comprehensive.

[0166] For convenience of comparison, the over-strain rupture failure criterion is selected for simulation of the IFA650.2 experiment, and the calculated rupture time is about 98.3s, Figure 2 For the deformation state of the cladding at the failure moment, the strain is the largest at the middle position, which can be related to the axial distribution of the fuel rod thermal power and the thermal boundary condition. Figure 3The internal gas pressure variation diagram calculated by the present application is compared with the calculation results of other fuel performance codes (Extension of the OFFBEAT fuel performance code to finite strains and validation against LOCA experiments). It can be seen that the internal gas pressure calculated by the present application is closer to the experimental data than the results of other fuel performance codes. Figure 4 The external profile diagram at the rupture time calculated by the present application is compared with the calculation results of other existing fuel performance codes and experimental results. Through comparison, it can be seen that the present application can better simulate the external cladding profile. Figure 5 The thickness and mass of the oxidation layer calculated by the oxidation model of the present application vary with temperature. It is obvious that the oxidation rate gradually increases with the increase of temperature.

[0167] Embodiment 2

[0168] The present embodiment provides a modeling and calculation system for fuel rod cladding rupture failure in a LOCA accident, which comprises a determination module, a heat conduction module, a crystal phase judgment module, a thermodynamic coupling calculation module, and a cladding rupture failure judgment module.

[0169] The determination module is used to determine the initial conditions, input the geometric size of the fuel rod and the material properties of the corresponding fuel and cladding, and input the boundary conditions;

[0170] The heat conduction module is used to calculate the heat generation of the fuel and the heat conduction in the fuel, gas gap, and cladding;

[0171] The crystal phase judgment module is used to calculate the thickness and mass of the oxidation layer through a high-temperature oxidation model, and is used to calculate the volume fraction of Zr-4 converted from α to β phase;

[0172] The thermodynamic coupling calculation module is used to calculate the high-temperature creep and high-temperature oxidation behavior of the cladding in the loss of coolant accident;

[0173] The gas pressure updating module is used to update the gas volume inside the cladding and calculate the gas pressure;

[0174] The cladding rupture failure judgment module is used to evaluate whether the cladding ruptures through the cladding rupture failure criterion, so as to obtain the cladding failure rupture time.

[0175] Embodiment 3

[0176] The embodiment also provides a storage medium, which can be a ROM, a RAM, a magnetic disk, an optical disk or the like storage medium, and the storage medium stores one or more programs, and the programs are executed by a processor to implement the modeling calculation method for fuel rod cladding rupture failure in a LOCA accident provided in the above embodiment 1.

[0177] Embodiment 4

[0178] The embodiment provides a computing device, which can be a desktop computer, a notebook computer, a smart phone, a PDA handheld terminal, a tablet computer or other terminal device with a display function, and the computing device comprises a processor and a memory, and the memory stores one or more programs, and the processor executes the programs stored in the memory to implement the modeling calculation method for fuel rod cladding rupture failure in a LOCA accident provided in the above embodiment 1.

[0179] The modeling method, system, medium and device for fuel rod cladding rupture failure in a LOCA accident provided by the embodiment of the application, in the coolant loss accident, the cladding is exposed to a high-temperature steam environment, for Zr-4 material, with the increase of temperature and the increase of internal and external pressure difference, the crystal phase changes, the oxidation rate and the creep rate significantly increase, these phenomena are considered in the model for full-coupling calculation, and the cladding rupture failure criterion is provided to evaluate the cladding rupture failure time, so that the thermal performance analysis of the fuel rod in the coolant loss accident is more accurate.

[0180] On the basis of the foregoing disclosure of the embodiment of the application, by using COMSOL, the cladding geometric size, thermodynamic properties, high-temperature creep model, high-temperature oxidation model and crystal phase change model are modified (the modification contents include: the material properties of different ATF cladding materials, the high-temperature creep rate and the high-temperature oxidation rate in the LOCA accident are also different, the existing calculation models can be selected by researching the literature and input into the corresponding modules, for example, the FeCrAl cladding, which is different from Zr-4, the material does not change the crystal phase, and can not be considered, the creep rate and the oxidation rate under the high-temperature condition are significantly lower than those of Zr-4, and the parameters such as the creep strength coefficient and the oxidation rate constant, the stress index, the creep deformation activation energy and the oxidation activation energy need to be modified, or other models are selected for calculation according to the needs, and the plastic strain of the material needs to be considered), which is used for studying the bulging rupture behavior of other ATF cladding materials and performing relevant calculation.

[0181] The above embodiment is a preferred embodiment of the application, but the embodiment of the application is not limited to the above embodiment, and any change, modification, replacement, combination, simplification made without departing from the spirit and principle of the application should be an equivalent replacement mode, which is included in the protection scope of the application.

Claims

1. A method of modeling and calculating fuel rod cladding rupture failure in a LOCA accident, characterized by, The cladding is made of Zr-4, and comprises the following steps: determining initial conditions, inputting fuel rod geometric dimensions and corresponding fuel, cladding material properties and boundary conditions; calculating fuel and cladding temperature distributions at each time based on physical properties of fuel, cladding and the gap between fuel and cladding; calculating the thickness and mass of the oxidation layer through a high-temperature oxidation model and calculating the volume fraction of Zr-4 converted from alpha phase to beta phase through a crystal phase change model based on changes in high-temperature thermodynamic material properties of Zr-4; calculating a hoop creep strain rate of the cladding by a high temperature creep model calculating a hoop creep strain of the cladding and a hoop stress of the cladding and updating the gas volume inside the cladding and calculating the gas pressure; High temperature creep strain rate based on cladding , calculating hoop creep strain of the cladding or hoop stress of the cladding , evaluating whether the cladding ruptures and obtaining a rupture time by a cladding rupture failure criterion.

2. The method of claim 1, wherein, the formula for calculating the fuel and cladding temperature distribution at each time is: wherein is the density of the material, is the heat capacity of the material, T is the temperature of the material, t is time, is the thermal conductivity of the material, is the distance of each location inside the material from the center line of the material, is the heat production rate per volume of material, is the average linear heat power of the fuel, denotes the radius of the material; wherein, when used for calculating the temperature distribution in the fuel, the material is the fuel, when used for calculating the temperature distribution in the cladding and the gap between the fuel and the cladding, = 0, and the material is the cladding.

3. The method of claim 1, wherein, the crystal phase change model is: where y represents the volume fraction of Zr-4 converted to the β phase, t is time, represents the rate parameter, represents the equilibrium value of y; where the rate parameter and the equilibrium value of y is given by wherein represents the kinetic pre-exponential factor, represents the effective activation energy, represents the Boltzmann constant, is a constant, represents the heating rate, represents a material parameter related to the temperature center of the mixed phase region, represents a material parameter related to the temperature span of the mixed phase region.

4. The method of claim 1, wherein, the high-temperature oxidation model is any one of the EPRI / KWU / C-E oxidation model, the Leistikow relationship and the Prater-Courtright model, wherein: for a temperature below 673 K, the EPRI / KWU / C-E oxidation model is used, and the EPRI / KWU / C-E oxidation model is: where S represents the thickness of the oxide layer, 、 denotes the oxidation rate constant before and after the transition, i.e. before and after the critical oxide layer thickness is reached, 、 denotes the oxidation activation energy before and after the transition, denotes time, denotes the temperature of the material, which is the cladding; for a temperature range of 673 K to 1800 K, the Leistikow relationship is expressed as: wherein represents the thickness of the oxide layer, represents the mass of the oxide layer, R represents the ideal gas constant, represents the oxidation rate constant of the oxide layer thickness, represents the oxidation rate constant of the oxide layer mass, represents the high-temperature oxidation activation energy of the oxide layer thickness, represents the high-temperature oxidation activation energy of the oxide layer mass; for a range above 1900 K, the Prater-Courtright model is used for calculation, and the expression of the Prater-Courtright model is consistent with that of the Leistikow relationship, except that the values of the parameters are different.

5. The method of claim 1, wherein, according to the calculated beta phase mass fraction, the high-temperature creep rate is calculated, and the high-temperature creep model is: wherein represents the creep strength coefficient, eff represents the effective stress, i.e. the Mises stress, represents the stress exponent, represents the creep deformation activation energy, R represents the ideal gas constant; Wherein, the phase mass fraction y determines the crystal phase state of Zr-4, , , The size is related to the crystal phase state of Zr-4.

6. The method of claim 1, wherein, for internal gas pressure calculation, it is necessary to update based on the strain calculated at each time, and the ideal gas state equation is used, and the specific calculation formula is: In the formula, P is the gas pressure, n indicates the number of moles of the gas, R indicates the ideal gas constant, V indicates the volume of the cavity formed by the fuel and the cladding, Tf indicates the average temperature of the outer surface of the fuel and the inner surface of the cladding.

7. The method for modeling and calculating the rupture failure of fuel rod cladding in a LOCA accident according to any one of claims 1-6, characterized in that, the cladding rupture failure criterion has three kinds, including: over-stress failure criterion: when the local outer ring stress is greater than the limit rupture stress, the cladding ruptures, that is: wherein represents the limit fracture stress, , b are constants, depending on the crystalline phase of the material, represents the mass fraction of oxygen in the cladding, is the mass fraction of oxygen in the initial state; over-strain failure criterion: when the local ring creep strain exceeds a limit value, the cladding ruptures and fails, that is: wherein ε is the ultimate strain; plastic strain rate criterion: when the plastic strain rate exceeds a preset limit value, the cladding ruptures, that is: wherein, represents the plastic strain rate, is the ultimate plastic strain rate.

8. A system for modeling and calculating fuel rod cladding rupture failure in a LOCA accident, characterized by, the system for implementing the method of any one of claims 1-7 comprises the following modules: a determination module for determining initial conditions, inputting fuel rod geometric dimensions and corresponding fuel, cladding material properties and boundary conditions; a heat conduction module for calculating temperature changes and distributions of fuel, cladding and the gap therebetween; a crystal phase judgment module for calculating the thickness and mass of the oxidation layer through a high-temperature oxidation model and for calculating the volume fraction of Zr-4 converted from alpha phase to beta phase; a thermodynamic coupling calculation module for calculating high-temperature creep and high-temperature oxidation behavior of the cladding in a loss of coolant accident; a gas pressure updating module for recalculating the gas pressure based on changes in the internal gas space at each time; a cladding rupture failure judgment module for evaluating whether the cladding ruptures through the cladding rupture failure criterion to obtain a cladding failure rupture time.

9. A storage medium storing a program, characterized by comprising: the program is executed by a processor to implement the modeling and calculation method of the cladding rupture failure of the fuel rod in the LOCA accident according to any one of claims 1-7.

10. A computing device comprising a processor and a memory for storing processor-executable programs, characterized in that, The processor implements the modeling calculation method of the fuel rod cladding rupture failure in the LOCA accident according to the program stored in the memory.

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