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

Abstract

The invention discloses a modeling calculation method, system and equipment for fuel rod cladding rupture failure and a medium. The method comprises the following steps: determining initial conditions, and inputting the geometric dimension of the fuel rod and the material attributes and boundary conditions of the corresponding fuel and cladding; calculating the temperature distribution of the fuel and the cladding at each moment based on the physical properties of the fuel, the cladding and the gap between the fuel and the cladding; calculating the thickness and the mass of an oxide layer, and calculating the volume fraction of Zr-4 converted from an alpha phase to a beta phase through a crystal phase change model; the high-temperature creep strain rate of the cladding is calculated through a high-temperature creep model, the circumferential creep strain of the cladding and the circumferential stress of the cladding are calculated, the volume of gas in the cladding is updated, and the gas pressure is calculated; and based on the high-temperature creep strain rate of the cladding, calculating the circumferential creep strain or the circumferential stress of the cladding, and evaluating whether the cladding is cracked or not through a cladding cracking failure criterion and obtaining the cracking time. The method can accurately determine the cracking time of the cladding.

Description

Technical Field

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

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

[0003] At present, there are two main development directions for accident-resistant fuel cladding, one is the zirconium alloy surface coating technology, and the other is the development of new cladding materials to replace zirconium alloy. However, these two technologies have not yet been applied in large-scale engineering. At present, most of the light water reactor fuel cladding is mainly zirconium alloy. Under accident conditions, especially in the loss of coolant accident (LOCA), when the temperature exceeds 1000K-1100K, the crystal phase structure of the zirconium alloy changes. 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 accelerate the oxidation of the cladding, causing the cladding to become thinner. When the deformation of the cladding reaches a certain degree, the cladding will rupture and fail, destroying the first barrier of radiation restriction 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. It has more advantages in computational fluid dynamics, but it cannot obtain accurate solutions for multi-physics field coupling problems involving heat transfer and solid mechanics.

[0005] From the perspective of improving reactor safety and economy, it is essential to develop computational tools that can reliably assess the thermodynamic behavior and integrity of nuclear fuel rods in reactors during accidents. Summary of the invention

[0006] In order to overcome at least one of the defects and shortcomings of the existing technology, the first purpose of the present invention is to provide a reliable and accurate modeling and calculation method for the rupture failure of the fuel rod cladding in a LOCA accident, which adopts the Norton high-temperature creep model, the Leistikow high-temperature oxidation model, the Massih crystal phase change model and the full coupling calculation of heat conduction, based on the input fuel rod design parameters and boundary conditions, calculates the temperature and stress distribution at each moment, and the total strain composition of the cladding, and evaluates the rupture failure time of the cladding through three failure criteria of overstrain, overstress and plastic strain rate, so as to obtain an accurate and reliable cladding rupture time.

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

[0008] A third object of the present invention is to provide a storage medium.

[0009] A fourth object of the present invention is to provide a computing device.

[0010] In order to achieve the first objective of the present invention, the present invention provides a modeling and calculation method for fuel rod cladding rupture failure in a LOCA accident, which specifically includes the following steps:

[0011] Determine the initial conditions, input the fuel rod geometry and the corresponding fuel, cladding material properties and boundary conditions;

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

[0013] Based on the changes in the thermodynamic material properties of Zr-4 at high temperatures, the thickness and mass of the oxide layer are calculated using the high-temperature oxidation model, and the volume fraction of Zr-4 transformed from α phase to β phase is calculated using the crystal phase change model.

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

[0015] High temperature creep strain rate based on cladding Calculate the hoop creep strain ε of the cladding creep Or the hoop stress of the cladding σ θ , the cladding rupture failure criterion is used to evaluate whether the cladding has ruptured and obtain the rupture time.

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

[0017]

[0018] Where ρ is the density of the material (kg / m3), C p is the heat capacity of the fuel material (J / kg / Kelvin), T is the temperature of the material (Kelvin), t is the time (seconds), k is the thermal conductivity of the material (J / m / Kelvin), r is the distance from the center line of the material (m), and q is the heat generation rate of the material per unit volume (J / m3).

[0019] When used to calculate the heat transfer process and temperature distribution in the fuel, the material is the fuel; when used to calculate the heat transfer process and temperature distribution in 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 outer surface temperature of the cladding, the average linear heat power of the fuel, and the gas temperature of the boost chamber are input as boundary conditions. The coolant pressure is applied to the outer surface of the cladding through the solid mechanics module in COMSOL, and the outer surface temperature and formula (1) are realized through the solid heat transfer module in COMSOL. The average linear heat power of the fuel and the gas temperature of the boost chamber are used as the conditions for calculating the heat release of the fuel and the internal gas pressure, respectively.

[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 the volume fraction of Zr-4 converted to β phase needs to be calculated through the crystal phase change model. The specific calculation equation is:

[0022]

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

[0024]

[0025] In the formula, k 0 represents the kinetic prefactor, 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 spanRepresents a 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 / CE oxidation model, the Leistikow relation and the Prater-Courtright model, wherein:

[0027] For temperatures below 673 K, the EPRI / KWU / CE oxidation model is used, which is

[0028]

[0029] In the formula, S represents the thickness of the oxide layer, C 1 , C 2 It represents the oxidation rate constant before and after the transition, that is, before and after the critical oxide layer thickness is reached, Q 1 , Q 2 represents the oxidation activation energy before and after the transition, t represents the time, and T represents the temperature of the cladding;

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

[0031]

[0032] In the formula, ξ s represents the thickness of the oxide layer, ξ g represents the mass of the oxide layer, R represents the ideal gas state constant, A s The oxidation rate constant, A, represents the thickness of the oxide layer g The oxidation rate constant, Q, represents the mass of the oxide layer. s The high temperature oxidation activation energy, Q, represents the thickness of the oxide layer g The high temperature oxidation activation energy that indicates the quality of the oxide layer;

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

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

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

[0036]

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

[0038] when When the value of y is calculated according to formula (2), the value of ln(A) between pure α phase and 50% α + 50% β phase, 50% α + 50% β phase and pure β phase is creep ), Q creep 、n c Perform linear interpolation; When the pure α phase and pure β phase are ln(A creep ), Q creep 、n c The above high temperature creep model is calculated by the creep interface in COMSOL solid mechanics.

[0039] As a preferred technical solution, after calculating the cladding strain at each moment, due to the change in the gap volume between the cladding and the fuel, it is necessary to update the strain calculated at each moment, using the ideal gas state equation, 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, and T ave represents the average temperature of the outer surface of the fuel and the inner surface of the cladding. The gas volume is calculated by the generalized stretching operator and the integral operator in COMSOL, and the gas pressure is calculated by the global differential equation.

[0042] As a preferred technical solution, there are three cladding rupture failure criteria, including:

[0043] ① Overstress failure criterion: When the local hoop stress is greater than the ultimate rupture stress, the cladding ruptures, that is:

[0044] σ θ >σ b

[0045]

[0046] Among them, σb represents the ultimate rupture stress (MPa), a and b are constants determined experimentally, depending on the crystalline phase of the material. Similar to the high temperature creep model, for Zr-4 in a mixed phase state, the rupture stress is calculated by using a and b linear interpolation method between pure α, 50% α + 50% β and pure β. The specific calculation parameters are as follows:

[0047]

[0048] η represents the oxygen mass fraction in the cladding, η 0 is the oxygen mass fraction in the initial state. The oxygen mass fraction at each moment is further calculated by the high temperature oxidation model.

[0049]

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

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

[0052]

[0053] Pick as the limiting plastic strain rate.

[0054] ③ Super strain failure test: When the local hoop creep strain exceeds a limit value, the cladding fails due to rupture, that is:

[0055] ε creep >∈ b

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

[0057] The present invention can adopt two-dimensional axisymmetry to model the fuel rod, adopt one-dimensional non-steady-state heat conduction equation to calculate the temperature distribution of the fuel and the cladding, adopt the Norton high-temperature creep model, the Leistikow high-temperature oxidation model, and the Massih crystal phase change model to process the thermodynamic behavior of the fuel rod under accident conditions, and adopt three rupture failure criteria of overstrain, overstress and plastic strain rate to evaluate the rupture failure time of the cladding.

[0058] The method can be based on a multi-physics field finite element analysis platform to analyze and calculate the thermodynamic properties of the cladding of a pressurized water reactor fuel rod under a loss of coolant accident, taking into account the thermodynamic behaviors of the zirconium alloy cladding material at high temperatures, such as thermal creep, crystal phase change, and high-temperature oxidation, and determine the cladding rupture time through a rupture criterion.

[0059] In order to achieve the above second objective, the present invention provides a modeling and calculation system for fuel rod cladding rupture failure in a LOCA accident, comprising the following modules:

[0060] The determination module is used to determine the initial conditions, input the fuel rod geometry and the corresponding fuel and cladding material properties and boundary conditions;

[0061] Heat transfer module, used to calculate the temperature change and distribution of fuel, cladding and the gap between them;

[0062] The crystal phase judgment module is used to calculate the thickness and mass of the oxide layer through the high-temperature oxidation model, and to calculate the volume fraction of Zr-4 converted from α to β phase;

[0063] Thermodynamic coupling calculation module, used to calculate the high-temperature creep and high-temperature oxidation behavior of the cladding in the event of a loss of coolant accident;

[0064] Gas pressure update module, used to recalculate the gas pressure based on the changes in the internal gas space at each moment;

[0065] The cladding rupture failure judgment module is used to evaluate whether the cladding has been ruptured according to the cladding rupture failure criterion to obtain the cladding failure rupture time.

[0066] In order to achieve the third objective, the present invention provides a storage medium storing a program, which, when executed by a processor, implements the modeling and calculation method for the rupture failure of a fuel rod cladding in a LOCA accident.

[0067] In order to achieve the fourth purpose mentioned above, the present invention provides a computing device, including a processor and a memory for storing a program executable by the processor, and when the processor executes the program stored in the memory, the modeling and calculation method for the rupture failure of the fuel rod cladding in the LOCA accident mentioned above is implemented.

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

[0069] (1) The present invention takes into account the high-temperature creep, crystal phase change and high-temperature oxidation behavior of the Zr-4 cladding under a coolant loss accident. Through the high-temperature oxidation and crystal phase change model, the thickness and mass of the oxide layer can be accurately calculated, and the volume fraction of Zr-4 transformed from the α phase to the β phase can be determined. Then, the high-temperature creep rate of Zr-4 in the corresponding crystal phase state is calculated by thermo-solid coupling, and the corresponding creep strain is calculated. The rupture failure time is evaluated according to the rupture failure criterion, thereby more reliably evaluating the thermodynamic performance of the cladding under a coolant accident.

[0070] (2) The present invention 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 invention provides three available rupture failure criteria, which can be used to evaluate the rupture failure time of Zr-4 cladding from different angles according to needs, and has a certain degree of universality.

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

[0073] Figure 1 It is a flow chart of a modeling and calculation method for fuel rod cladding rupture failure in a LOCA accident in an embodiment of the present invention;

[0074] Figure 2 A schematic diagram of the deformation state of the cladding at the moment of rupture failure calculated in an embodiment of the present invention (the legend indicates the engineering hoop creep strain) (magnified 15 times in the radial direction for easy visualization);

[0075] Figure 3 A comparison chart of the internal gas pressure change calculated for the IFA650.2 case in the embodiment of the present invention and the calculation results and experimental results of other existing fuel performance codes;

[0076] Figure 4 A comparison diagram of the external contour diagram of the rupture moment calculated in the embodiment of the present invention and the calculation results and experimental results of other existing fuel performance codes;

[0077] Figure 5 This is a graph showing the change of oxide layer thickness over time calculated by the high temperature oxidation model in an embodiment of the present invention. DETAILED DESCRIPTION

[0078] In order to make the purpose, technical solution and advantages of the present invention more clearly understood, the present invention is further described in detail below in conjunction with the accompanying drawings and embodiments. It should be understood that the specific embodiments described herein are only used to explain the present invention and are not intended to limit the present invention.

[0079] The present invention provides a modeling and calculation method for the rupture failure of the fuel rod cladding in a LOCA accident. In the case of a loss of coolant accident, the cladding is exposed to a high-temperature steam environment. For the Zr-4 cladding (zirconium alloy cladding), there is not enough coolant to take away the heat for the cladding, resulting in the cladding temperature rapidly increasing to above 1000K. With the increase in temperature and the increase in 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 a crystal phase change, resulting in the cladding hoop strain, stress or strain rate exceeding a certain threshold, resulting in rupture. These phenomena are 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, see Figure 1 The present invention provides a modeling and calculation method for cladding bulging and rupture of a fuel rod in a coolant loss accident, comprising the following steps:

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

[0082] Enter the geometry of the fuel rods;

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

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

[0085] In some embodiments of the present invention, some design parameters are given in Table 1. IFA650.2 is a calculation example used for verification of the present invention, which is used to compare with other fuel performance codes and is modeled in COMSOL. For the verification example IFA650.2, the fuel material is UO 2 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 mm Fuel diameter 8.29 mm Fuel level 8 mm Cladding outer diameter 9.5 mm Shell thickness 0.57 mm Total free gas volume 17.4 cubic centimeters Gas volume of the air chamber 15.8 cubic centimeters

[0088] Step S2: Calculate the temperature distribution of the fuel and the cladding at each moment based on the average linear thermal 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 properties of the gap between the fuel and the cladding are the thermodynamic properties of the gap material.

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

[0091]

[0092] Where ρ is the density of the material (kg / m3); C p is the heat capacity of the material (joules / kilograms / Kelvin); T is the temperature of the material (Kelvin); t is the time (seconds); k is the thermal conductivity of the material (joules / meter / Kelvin); r is the distance from the center line of the material at each position inside the material (meters); q is the heat generation rate of the material per unit volume (joules / cubic meter), q lin is the average line thermal power of the fuel, r pellet Indicates the radius of the material.

[0093] Formula (1) can be used to calculate the heat transfer process and temperature distribution in the fuel. As for the heat transfer process and temperature distribution in the cladding and the gap between the fuel pellet and the cladding, since there is no heat source, the source term q in the formula is discarded, that is, q = 0 at this time.

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

[0095] Formula (1) is calculated 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, transforming from a hexagonal crystal (α phase) to a cubic crystal (β phase), the crystal phase state of Zr-4 will significantly affect the high temperature rate, and the volume fraction of Zr-4 transformed from the α phase to the β phase needs to be calculated through a crystal phase change model.

[0097] The crystal phase change model is:

[0098]

[0099] Where y represents the volume fraction of Zr-4 converted to β phase, k s Indicates the rate parameter, the unit is 1 / second; y s represents the equilibrium value of y.

[0100] Among them, k s and s Calculated by formula (3) and (5) respectively:

[0101]

[0102]

[0103] Among them, k 0 represents the kinetic prefactor (1 / second); Q p represents the effective activation energy, k b represents the Boltzmann constant, k m is a constant, In some embodiments of the present invention, for Zr-4 material, (Kelvin), when Zr-4 transforms from α phase to β phase, k m = 0, when Zr-4 transforms from β phase to α phase, k m =0.2, in case of loss of coolant accident, take k m =0.

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

[0105]

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

[0107] For Zr-4, T cent =1159-0.096w, T span =44+0.026w, w represents hydrogen concentration, the unit is one part per million mass concentration. When y<0.01, Zr-4 is treated as pure α phase, and when y>0.99, Zr-4 is treated as pure β phase. The crystal phase change model is calculated using COMSOL partial differential equations.

[0108] In addition, high temperature will significantly accelerate the oxidation rate of Zr-4. Therefore, different high-temperature oxidation models are used to calculate the thickness and quality of the oxide layer according to different temperature ranges.

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

[0110] For temperatures below 673 K, the EPRI / KWU / CE oxidation model is used, as shown in formula (6):

[0111]

[0112] Where S represents the thickness of the oxide layer, micrometer, C 1 , C 2 It represents the oxidation rate constant before and after the transition, that is, before and after the critical oxide layer thickness is reached, Q 1 , Q 2 represents the oxidation activation energy before and after the transition, t represents the time in seconds, and T represents the temperature of the cladding in Kelvin.

[0113] In some embodiments of the present invention, for Zr-4, C 1 =6.3×10 9 (micrometers 3 / day), C 2 =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 mass of the oxide layer are calculated using the Leistikow relationship:

[0115]

[0116]

[0117] In the formula, ξ s represents the thickness of the oxide layer, ξ g represents the mass of the oxide layer, R represents the ideal gas state constant, A s The oxidation rate constant, A, represents the thickness of the oxide layer. g The oxidation rate constant, Q, represents the mass of the oxide layer s The high temperature oxidation activation energy, Q, represents the thickness of the oxide layer g It indicates the high temperature oxidation activation energy of the oxide layer mass.

[0118] For the range above 1900K, the Prater-Courtright model is used for calculation. The calculation relationship of the Leistikow relation and the Prater-Courtright model is the same, except that the specific values ​​of the parameters are different. In some embodiments of the present invention, the values ​​of the parameters are summarized based on the experimental data of the corresponding temperature range, and the parameter values ​​are obtained by using the method disclosed in the document "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 the temperature range of 1800K-1900K, the two relationships are linearly interpolated to obtain the thickness and mass of the oxide layer.

[0120] The specific calculation parameters of 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: According to the volume fraction y of Zr-4 converted from α phase to β phase calculated in step S3, the high temperature creep rate of the cladding is calculated 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 represents the creep strength coefficient, σ eff represents effective stress, i.e. Mises stress, n c represents the stress index, Q creep represents the activation energy of creep deformation, T represents the temperature of the cladding, and R represents the ideal gas state constant.

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

[0128] Table 3

[0129]

[0130] when When the value of y is calculated according to formula (2), the ln(A) between pure α phase and 50% α + 50% β phase, 50% α + 50% β phase and pure β phase is creep ), Q creep 、n c Perform linear interpolation; When the pure α phase and pure β phase are ln(A creep ), Q creep 、n c The above high temperature creep model is calculated by the creep interface in COMSOL solid mechanics.

[0131] In addition to high temperature creep, the cladding will also have material strains such as elastic strain and thermal expansion. These strains will also affect the gas volume inside the cladding, causing changes in 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, ε creep Represents the hoop creep strain of the cladding.

[0136] Based on the calculated total hoop strain ε of the cladding, since the gap volume between the cladding and the fuel changes, the internal gas volume needs to be updated based on the strain calculated at each moment, and the gas pressure needs to be calculated.

[0137] Among them, the ideal gas state equation is used, and the specific calculation formula of gas pressure is:

[0138]

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

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

[0141]

[0142] Where 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, ε creep Represents the hoop creep strain of the cladding.

[0143] The high temperature creep rate and The calculation of thermal expansion and elastic strain is achieved by inputting material parameters such as thermal expansion coefficient and Young's modulus according to formula (9). 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, as well as the local stress in all directions.

[0144] ε creep and A can be input via the Creep interface in Solid Mechanics creep 、n c , Q creep Calculated.

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

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

[0147] ① Overstress failure criterion: When the local hoop stress is greater than the ultimate rupture stress, the cladding will rupture, that is:

[0148] σ θ >σ b (15)

[0149]

[0150] Among them, σ θ represents the hoop stress of the cladding, σ brepresents the ultimate rupture stress, the unit is MPa, a, b are parameters, the specific values ​​can be determined by experiment, depending on the crystal phase of the material, the calculation formula of the rupture stress is also based on the empirical model summarized by the experiment, a, b are the values ​​fitted by the corresponding literature according to the data (in some embodiments of the present invention, the method in the document "Burst Criterion of Zircaloy Fuel Claddings In a Loss-of-CoolantAccident" is used to determine the values ​​of a, b). Similar to the high temperature creep model, for Zr-4 in a mixed phase state, the ultimate rupture stress is calculated by using a and b using the linear interpolation method between pure α, 50% α + 50% β and pure β. The specific calculation parameters are shown in Table 4.

[0151] Table 4

[0152]

[0153] η( / ) represents the oxygen mass fraction in the cladding, η 0 is the oxygen mass fraction in the initial state. In some embodiments of the present invention, η 0 Take 0.0012. The oxygen mass fraction at each moment is further calculated by the high temperature oxidation model.

[0154]

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

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

[0157]

[0158] Pick As the limiting plastic strain rate, It represents the plastic strain rate, which theoretically includes the plastic strain rate and the creep strain rate of the cladding. However, the yield stress of Zr-4 is relatively large. In the event of a coolant loss accident, the effective stress will not exceed the yield stress until the cladding ruptures and fails. Therefore, the high-temperature creep rate of the cladding is the main factor, that is,

[0159] ③ Super strain failure test: When the local hoop creep strain exceeds a limit value, the cladding will rupture and fail.

[0160] Right now:

[0161] ε creep >∈ b (19)

[0162] ε creep Represents the local hoop creep strain, using ∈ b =40% engineering hoop strain is taken as the ultimate strain, and the corresponding true hoop strain is 33.6%.

[0163] The overstress rupture failure criterion is an empirical formula obtained through single-rod rupture experiments on fresh fuel rods. It may not be applicable to the simulation of high-burnup fuel rods, which will lead to premature prediction of cladding rupture. For high-burnup fuel rods, the overstrain rupture failure criterion is widely used. The overstrain and other two rupture failure criteria can be combined. As long as one of the rupture failure criteria is met, the cladding is considered to be ruptured.

[0164] Using the method provided in this embodiment, first obtain the heat conduction and temperature distribution of the current time step, and combine the crystal phase change model and the high-temperature oxidation model to obtain the volume fraction y of Zr-4 converted to the β phase and the thickness and mass of the oxide layer. Then, based on the volume fraction y and the temperature distribution, the high-temperature creep rate is obtained through the high-temperature creep model. At the same time, the total strain, circumferential strain, circumferential stress and plastic strain rate of the cladding at each position are calculated. The internal gas pressure is updated according to the magnitude of the total strain. Finally, a judgment is made based on the provided rupture failure criterion. If the failure criterion is met, the calculation is terminated and the relevant data is output. Otherwise, the calculation of the next time step is performed. The calculation stops until the failure criterion is met or the last time step is reached. The solution results obtained using the method described in this embodiment can be used as a reference for detailed research on the rupture failure of the cladding under the condition of loss of coolant accident.

[0165] The present invention uses a multi-physics field fully coupled simulation calculation method based on the COMSOL platform. In terms of thermodynamics and solid mechanics coupling, the physical field interface can be used to perform mechanical analysis on the deformation behavior of the cladding under the coolant loss accident, and the generalized stretching operator and the integral operator can be used to update the gas volume and calculate the gas pressure at each time step based on the strain, so as to more accurately calculate the strain and evaluate the rupture time. Compared with the code, it is more convenient and has higher calculation accuracy. In addition, the present invention provides three rupture failure criteria, allowing users to freely choose according to their needs, and taking into account the high-temperature oxidation of the cladding, which is more comprehensive.

[0166] For the convenience of comparison, the super strain rupture failure criterion was selected to simulate the IFA650.2 experiment, just like other fuel performance analysis codes. The calculated rupture time was about 98.3s. Figure 2 is the deformation state of the cladding at the moment of failure. The maximum strain is in the middle position, which may be related to the axial distribution of the thermal power of the fuel line and the thermal boundary conditions. Figure 3 The calculated internal gas pressure variation diagram 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 invention is closer to the experimental data than the results of other fuel performance codes. Figure 4 This is a comparison diagram of the external contour diagram of the rupture moment calculated by the present invention with the calculation results and experimental results of other existing fuel performance codes. Through the comparison, it can be seen that the present invention can better simulate the outer shell contour. Figure 5 The graph showing the thickness and mass of the oxide layer calculated by the oxidation model of the present invention as a function of temperature shows that the oxidation rate gradually increases with increasing temperature.

[0167] Example 2

[0168] This embodiment provides a modeling and calculation system for fuel rod cladding rupture failure in a LOCA accident, including 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 fuel rod geometry and the corresponding fuel and cladding material properties and boundary conditions;

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

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

[0172] Thermodynamic coupling calculation module, used to calculate the high-temperature creep and high-temperature oxidation behavior of the cladding in the event of a loss of coolant accident;

[0173] Gas pressure update module, 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 has been ruptured according to the cladding rupture failure criterion to obtain the cladding failure rupture time.

[0175] Example 3

[0176] This embodiment also provides a storage medium, which may be a storage medium such as ROM, RAM, disk, or CD. The storage medium stores one or more programs. When the programs are executed by the processor, a modeling and calculation method for the rupture failure of the fuel rod cladding in a LOCA accident provided in the above-mentioned embodiment 1 is implemented.

[0177] Example 4

[0178] This embodiment provides a computing device, which may be a desktop computer, a laptop computer, a smart phone, a PDA handheld terminal, a tablet computer or other terminal device with a display function. The computing device includes a processor and a memory, and the memory stores one or more programs. When the processor executes the program stored in the memory, a modeling and calculation method for fuel rod cladding rupture failure in a LOCA accident in the above-mentioned embodiment 1 is implemented.

[0179] The embodiments of the present invention provide a modeling method, system, medium and equipment for the rupture failure of the fuel rod cladding in a LOCA accident. In the case of a loss of coolant accident, the cladding is exposed to a high-temperature steam environment. For Zr-4 material, as the temperature increases and the internal and external pressure difference increases, the crystal phase changes, and the oxidation rate and creep rate increase significantly. These phenomena are considered in the model for full coupling calculation, and a cladding rupture failure criterion is provided to evaluate the cladding rupture failure time, thereby making the thermal performance analysis of the fuel rod under the loss of coolant accident more accurate.

[0180] On the basis of the disclosed contents of the aforementioned embodiments of the present invention, through the present invention, it is also possible to modify the cladding geometric dimensions, thermodynamic properties, high-temperature creep model, high-temperature oxidation model, and crystal phase change model on the basis of the existing fuel rod model by using COMSOL (the modifications include: the material properties of different ATF cladding materials, the high-temperature creep rate and high-temperature oxidation rate in the LOCA accident will also be different, and the existing calculation model can be selected by researching the literature and inputting it into the corresponding module. Taking FeCrAl cladding as an example, unlike Zr-4, this material will not undergo crystal phase change and can be ignored. The creep rate and oxidation rate under high temperature conditions are significantly lower than those of Zr-4. It is necessary to modify the creep strength coefficient and oxidation rate constant, stress exponent, creep deformation activation energy, and oxidation activation energy, or select other models for calculation as needed, and the plastic strain of the material needs to be considered) to study the bulging rupture behavior of other ATF cladding materials and perform related calculations.

[0181] The above embodiments are preferred implementation modes of the present invention, but the implementation modes of the present invention are not limited to the above embodiments. Any other changes, modifications, substitutions, combinations, and simplifications that do not deviate from the spirit and principles of the present invention should be equivalent replacement methods and are included in the protection scope of the present invention.

Claims

1. A modeling and calculation method for the failure of fuel rod cladding rupture in a LOCA accident, characterized in that: The material of the cladding is Zr-4, and the following steps are included: Determine the initial conditions, input the fuel rod geometry and the corresponding fuel, cladding material properties and boundary conditions; Calculate the temperature distribution of the fuel and the cladding at each time based on the physical properties of the fuel, the cladding, and the gap between the fuel and the cladding; Based on the changes in the thermodynamic material properties of Zr-4 at high temperatures, the thickness and mass of the oxide layer are calculated using the high-temperature oxidation model, and the volume fraction of Zr-4 transformed from α phase to β phase is calculated using the crystal phase change model. Calculation of high temperature creep strain rate of cladding by high temperature creep model Calculate the hoop creep strain ε of the cladding creep and the hoop stress of the cladding σ θ , and update the gas volume inside the cladding and calculate the gas pressure; High temperature creep strain rate based on cladding Calculate the hoop creep strain ε of the cladding creep Or the hoop stress of the cladding σ θ , the cladding rupture failure criterion is used to evaluate whether the cladding rupture occurs and obtain the rupture time.

2. The modeling and calculation method for the rupture failure of the fuel rod cladding in a LOCA accident according to claim 1 is characterized in that: The calculation formula for the temperature distribution of the fuel and cladding at each moment is: Where ρ is the density of the material, C p is the heat capacity of the material, T is the temperature of the material, t is the time, k is the thermal conductivity of the material, r is the distance from the center line of the material to each position inside the material, q is the heat generation rate of the material per unit volume, q lin is the average line thermal power of the fuel, r pellet Indicates the radius of the material; When used to calculate the temperature distribution in the fuel, the material is the fuel; when used to calculate the temperature distribution of the cladding and the gap between the fuel and the cladding, q=0, and the material is the cladding.

3. The modeling and calculation method for fuel rod cladding rupture failure in a LOCA accident according to claim 1 is characterized in that: The crystal phase change model is: Where y represents the volume fraction of Zr-4 converted to β phase, t is the time, k is s represents the rate parameter, y s represents the equilibrium value of y; Among them, the rate parameter k s The equilibrium value y s The calculation formula is: Where k0 represents the kinetic prefactor, 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 a material parameter related to the temperature span of the mixed phase region.

4. The modeling and calculation method for fuel rod cladding rupture failure in a LOCA accident according to claim 1 is characterized in that: The high temperature oxidation model is any one of the EPRI / KWU / CE oxidation model, the Leistikow relation and the Prater-Courtright model, wherein: For temperatures below 673 K, the EPRI / KWU / CE oxidation model is used, which is In the formula, S represents the thickness of the oxide layer, C1 and C2 represent the oxidation rate constants before and after the transition, i.e. before and after the critical oxide layer thickness is reached, Q1 and Q2 represent the oxidation activation energy before and after the transition, t represents the time, and T represents the temperature of the cladding; For the temperature range of 673K ​​to 1800K, the Leistikow relation is expressed as: In the formula, ξ s represents the thickness of the oxide layer, ξ g represents the mass of the oxide layer, R represents the ideal gas state constant, A s The oxidation rate constant, A, represents the thickness of the oxide layer g The oxidation rate constant, Q, represents the mass of the oxide layer. s The high temperature oxidation activation energy, Q, represents the thickness of the oxide layer g The high temperature oxidation activation energy that indicates the quality of the oxide layer; For the range above 1900K, the Prater-Courtright model is used for calculation. The expression of the Prater-Courtright model is consistent with that of the Leistikow relation, except that the values ​​of the parameters are different.

5. The modeling and calculation method for fuel rod cladding rupture failure in a LOCA accident according to claim 1 is characterized in that: According to the calculated β phase mass fraction, the high temperature creep rate is calculated, and the high temperature creep model is: In the formula, A creep represents the creep strength coefficient, σ eff represents effective stress, i.e. Mises stress, n c represents the stress index, Q creep represents the activation energy of creep deformation, T represents the temperature, and R represents the ideal gas state constant; Among them, the mass fraction of β phase y determines the crystal phase state of Zr-4, A creep , Q creep 、n c The size is related to the crystal phase state of Zr-4.

6. The modeling and calculation method for fuel rod cladding rupture failure in a LOCA accident according to claim 1 is characterized in that: For the calculation of internal gas pressure, it is necessary to update based on the strain calculated at each moment, using the ideal gas state equation. The specific calculation formula is: Where P is the gas pressure, n is the number of moles of gas, R is the ideal gas constant, V is the volume of the cavity formed by the fuel and the cladding, and T is ave Represents the average temperature of the outer surface of the fuel and the inner surface of the cladding.

7. A modeling and calculation method for fuel rod cladding rupture failure in a LOCA accident according to any one of claims 1 to 6, characterized in that: There are three types of cladding rupture failure criteria, including: Overstress failure criterion: When the local outdoor hoop stress is greater than the ultimate rupture stress, the cladding ruptures, that is: s θ >s b Among them, σ b represents the ultimate rupture stress, a and b are constants depending on the crystalline phase of the material, η represents the oxygen mass fraction in the cladding, η0 is the oxygen mass fraction in the initial state, σ b represents the ultimate rupture stress; Overstrain failure criterion: When the local hoop creep strain exceeds a limit value, the cladding fails due to rupture, namely: e creep >∈ b Among them, ∈ b is the ultimate strain; Plastic strain rate criterion: When the plastic strain rate exceeds a preset limit value, the cladding will rupture, that is: in, represents the plastic strain rate, is the limiting plastic strain rate.

8. A modeling and calculation system for fuel rod cladding rupture failure in LOCA accident, characterized in that: For implementing the method described in any one of claims 1 to 7, the system comprises the following modules: The determination module is used to determine the initial conditions, input the fuel rod geometry and the corresponding fuel and cladding material properties and boundary conditions; Heat transfer module, used to calculate the temperature change and distribution of fuel, cladding and the gap between them; The crystal phase judgment module is used to calculate the thickness and mass of the oxide layer through the high-temperature oxidation model, and to calculate the volume fraction of Zr-4 converted from α to β phase; Thermodynamic coupling calculation module, used to calculate the high-temperature creep and high-temperature oxidation behavior of the cladding in the event of a loss of coolant accident; Gas pressure update module, used to recalculate the gas pressure based on the changes in the internal gas space at each moment; The cladding rupture failure judgment module is used to evaluate whether the cladding has been ruptured according to the cladding rupture failure criterion to obtain the cladding failure rupture time.

9. A storage medium storing a program, characterized in that: When the program is executed by a processor, a modeling and calculation method for fuel rod cladding rupture failure in a LOCA accident as described in any one of claims 1 to 7 is implemented.

10. A computing device comprising a processor and a memory for storing a program executable by the processor, characterized in that: When the processor executes the program stored in the memory, the modeling and calculation method for the rupture and failure of the fuel rod cladding in a LOCA accident described in any one of claims 1 to 7 is implemented.

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