Liquid sodium-cooled reactor oxide fuel cladding failure analysis method and system

Abstract

The application discloses a cladding rupture analysis method and system for oxide fuel of a liquid sodium-cooled reactor, first, a node division is performed on a simulated reactor core part, then a neutron dynamics model is established according to different severe accident conditions, and model structure parameters, operation parameters and the like are determined, an improved Ross-Stoute model is used to calculate air gap heat conduction, a Trap-release model is used to calculate a fission gas release rate, an improved ideal gas state equation is used to calculate gas cavity and molten cavity pressure, a GRASS-SST model is used to calculate fuel swelling, transient safety analysis parameters are calculated in real time, and a plurality of failure criteria are adopted to determine whether the fuel cladding fails according to thermodynamic analysis results. Compared with the prior art, the method considers a plurality of factors influencing reactivity, makes the modeling of the sodium-cooled fast reactor core more fine, improves the stability and calculation efficiency of the numerical algorithm, and can more accurately and efficiently simulate and analyze the reactor core nuclear reaction under a severe accident.

Description

Technical Field

[0001] This invention belongs to the technical field of safety analysis of severe accidents in sodium-cooled block reactors, specifically relating to a method and system for analyzing the cladding damage of oxide fuel in liquid sodium-cooled reactors. Background Technology

[0002] Currently, accident analysis software for liquid metal cooling suffers from severe deficiencies in simulating the crucial physical phenomenon of fuel cladding failure. It has only developed empirical models and has not considered physical models closely related to liquid metal coolant cladding failure, such as grain growth, fission gas release, fuel and cladding swelling, fission gas chamber pressure, molten void pressure growth, and eutectic melting. Furthermore, it does not include more detailed failure criteria such as biaxial stress fracture, fracture pressure, transient fracture temperature, metallic fuel failure criteria, and Larson-Miller parameters.

[0003] Given the importance of fuel cladding failure, and the fact that current liquid metal-cooled reactor accident simulation software cannot fully and clearly describe this physical phenomenon, it is both necessary and urgent to conduct in-depth mechanistic research and develop a liquid metal coolant fuel cladding failure module. Summary of the Invention

[0004] The technical problem to be solved by the present invention is to provide a method and system for analyzing the cladding damage of oxide fuel in liquid sodium-cooled reactors, which addresses the shortcomings of the prior art and solves the technical problem of failure of sodium-cooled fast reactor fuel cladding under the coupled effects of many factors such as heat transfer, irradiation, mechanical stress and chemical corrosion.

[0005] The present invention adopts the following technical solution:

[0006] A method for analyzing cladding damage of oxide fuel in a liquid sodium-cooled reactor includes the following steps:

[0007] S1. Establish a mechanical model of oxide fuel rods in a liquid sodium-cooled reactor;

[0008] S2. Input the operating parameters into the fuel rod mechanical model established in step S1, recalculate the temperature, pressure, and fission gas release rate of each node in combination with the heat transfer and phase change models, and update the physical property parameters of the node in combination with the equation of state.

[0009] S3. Perform transient initialization on the physical property parameters updated in step S2, and complete the power and reactivity calculations;

[0010] S4. Based on the power and reactivity calculations in step S3, establish a gap heat transfer model according to the improved Ross-Stoute model, divide the heat transfer between fuel and cladding into radiation heat transfer, gas conduction and solid-solid conduction, and calculate and correct the heat transfer coefficient of the fuel cladding gap.

[0011] S5. Establish a phenomenological model of fission gas release rate based on the Trap-release model to obtain the fission gas release amount;

[0012] S6. Calculate the pressure inside the melting cavity using the improved ideal gas equation;

[0013] S7. Based on the fission gas release amount calculated in step S5, calculate the internal pressure of the bubble, determine the axial strain of the mesh, and calculate the change in fuel rod volume fraction caused by the expansion of solid fission products in relation to the volume fraction change and fuel consumption, and calculate the new change in fuel rod volume fraction.

[0014] S8. Combining the heat transfer coefficient obtained in step S4, the pressure inside the molten cavity obtained in step S6, and the new change in fuel rod volume fraction obtained in step S7, the calculation for each time step is completed sequentially according to the air gap temperature convergence principle, and the failure criteria are used to determine whether the fuel rod has failed.

[0015] Specifically, in step S1, radial and axial nodes are divided according to the structural parameters of the oxide fuel in the liquid sodium cold reactor. Each channel represents a fuel rod, the fuel rod cladding and related coolant, and a small portion of the component pipe wall. Within the channel, the flow is set as one-dimensional axial, and the temperature fields of the fuel, cladding, coolant and structure are set as two-dimensional radial and axial. The channel length represents the length of the entire component, from the coolant inlet to the coolant outlet. One region represents the fuel rod section, including the fuel pellet, the upper and lower conversion zones and the gas chamber, while other regions represent the upper and lower reflector layers of the fuel rod.

[0016] Specifically, in step S4, the heat transfer coefficient h of the fuel cladding air gap... gap for:

[0017] h gap =h g +h r +h s

[0018] Among them, h g h is the heat transfer coefficient of gas conduction within the fuel cladding gap. r h is the radiative heat transfer coefficient. s The heat transfer coefficient for solid-to-solid thermal conduction.

[0019] Specifically, in step S5, the mass G of the fission gas produced... m for:

[0020]

[0021] The fission gas release dn is:

[0022] dn = dn1 + dn2

[0023] Where dn1 is the amount of gas released in terms of time increment dt, dn2 is the amount of trapped gas released back onto the fuel surface, and P i Let f be the power of the axial segment j, Δt be the time step, and f be the power of the axial segment j. g MW represents the fraction of gas atoms produced in each fission. fg E is the molar mass of the fission gas. f This refers to the energy generated in each fission.

[0024] Furthermore, the amount of gas released, dn1, expressed in terms of time increment dt, and the amount of gas released from the trapped gas onto the fuel surface, dn2, are respectively:

[0025] dn1=k′Gdt

[0026] dn2=k'kcdt

[0027] Where k′ is the proportion of free gas that escapes to the surface without being captured, k represents the probability of the trapped gas being released per unit time, G is the fission gas productivity, and c is the amount of gas retained in the fuel grains.

[0028] Specifically, in step S6, the total amount of gas M in the central melting cavity cav and total volume V cav They are respectively:

[0029]

[0030]

[0031] Among them, M c,i The original gas volume in the central cavity, This represents the total amount of grain boundary gas released into the melt cavity within a time step. This represents the total amount of gas released from within the grains into the melt cavity during the time step. This represents the total amount of pre-formed pore gas released into the molten cavity within a given time step. V represents the total amount of gas released from the fuel crack into the molten cavity within a time step. c,i The original gas volume in the central cavity, The total volume of grain boundary gas released into the melt cavity within the time step is given. This represents the total volume of gas released from within the grains into the melt cavity during the time step. The total volume of pre-formed pore gas released into the molten cavity within the time step. This represents the total volume of gas released from the fuel crack into the molten cavity within a time step.

[0032] Specifically, in step S7, the reasons for the axial and radial expansion of the fuel rod include non-equilibrium fission gas bubbles, expansion of solid fission products, and cladding swelling caused by irradiation. The volume expansion caused by solid fission products and the volume change of bubbles calculated using non-equilibrium bubble film properties are calculated respectively. Finally, the axial and radial components of the expansion are determined, and the inner radius at the new moment is calculated as follows:

[0033]

[0034] Where, r i Let t be the inner radius of the casing, t be the running time, and Δt be the time step. This represents the change in volume fraction.

[0035] Specifically, in step S8, the failure criteria include biaxial stress failure, Larson-Miller lifetime fraction, failure pressure, and transient failure temperature.

[0036] Furthermore, the biaxial stress failure criterion:

[0037] logθ=-15.22+9.5342log[log(σ * / σ)]

[0038] θ=t r exp(-Q / RT)

[0039] Where θ is the mandrel parameter; t r The rupture time is expressed in hours (h); T is the temperature; Q = 83508 cal / mole; R is the universal gas constant; σ is the circumferential stress; σ * =135ksi;r o r is the outer radius of the shell; i Where is the inner radius of the casing; P is the gas pressure inside the rod;

[0040] Larson-Miller lifetime fractional failure criterion:

[0041]

[0042] Among them, t r The fracture time is given by C, which is a constant depending on the material and takes the value of 20. LMP is the experimentally determined Larson-Miller parameter, and T is the cladding temperature.

[0043] The rupture time is expressed as a lifetime fraction:

[0044]

[0045] Where L is the lifetime fraction, i is the time step, and Δt is the time step. i The time step length;

[0046] Breakage pressure criteria:

[0047]

[0048] Where P is the rupture pressure, ksi; σ is the circumferential stress; a0 = 1.799988 × 10 1 a1 = 2.866442 × 10 -2 a2 = -3.986012 × 10 -4 a3 = 2.408207 × 10 -6 a4 = -8.090292 × 10 -9 a5 = 1.607218 × 10 -11 a6 = -1.962158 × 10 -14 a7 = 1.487159 × 10 -17 a8 = -6.821934 × 10 -21 a9 = 1.735220 × 10 -24 ;a 10 =1.879417×10 -28 ;

[0049] Failure criterion based on damage temperature:

[0050] T f =2358.4-36.41σ+0.5649σ 2 -3.455×10 -3 σ 3

[0051] for T≤5.56K / s

[0052] T f =2484.8-37.80σ+0.5827σ 2 -3.585×10 -3 σ 3

[0053] forT≥111K / s

[0054] Among them, T f σ is the failure temperature, and σ is the circumferential stress.

[0055] Secondly, embodiments of the present invention provide a cladding damage analysis system for oxide fuel in a liquid sodium-cooled reactor, comprising:

[0056] Build modules to establish a mechanical model of oxide fuel rods in a liquid sodium-cooled reactor;

[0057] The parameter module inputs operating parameters into the fuel rod mechanical model established by the construction module, recalculates the temperature, pressure, and fission gas release rate of each node in combination with the heat transfer and phase change models, and updates the physical property parameters of the node in combination with the equation of state.

[0058] The calculation module performs transient initialization of the physical property parameters updated by the parameter module, and completes the power and reactivity calculations.

[0059] The coefficient module, based on the power and reactivity calculations of the calculation module, establishes a gap heat conduction model according to the improved Ross-Stoute model, divides the heat transfer between fuel and cladding into radiation heat transfer, gas conduction and solid-solid heat conduction, and calculates and corrects the heat transfer coefficient of the fuel cladding air gap.

[0060] The processing module establishes a phenomenological model of fission gas release rate based on the Trap-release model to obtain the fission gas release amount;

[0061] The superposition module uses an improved ideal gas equation to calculate the pressure inside the melting cavity;

[0062] The volume module calculates the internal pressure of the bubbles based on the fission gas release calculated by the processing module, determines the axial strain of the mesh, calculates the change in fuel rod volume fraction caused by the expansion of solid fission products by relating the volume fraction change to fuel consumption, and calculates the new change in fuel rod volume fraction.

[0063] The analysis module combines the heat transfer coefficient obtained from the coefficient module, the pressure inside the molten cavity obtained from the processing module, and the new fuel rod volume fraction change obtained from the volume module. Based on the air gap temperature convergence principle, it completes the calculation for each time step in sequence and determines whether the fuel rod has failed through the failure criteria.

[0064] Compared with the prior art, the present invention has at least the following beneficial effects:

[0065] A method for analyzing cladding failure of oxide fuel in liquid sodium-cooled reactors is proposed. This method involves detailed mesh generation of fuel elements, coupling multiple physical processes such as fission gas release, grain growth, fuel swelling, and air gap heat conduction. This helps to better simulate the cladding failure process under severe accident conditions, analyze the failure probability, and assess the impact of failure on reactor safety and reliability. This assessment aids in developing emergency measures and safety strategies to respond to severe accidents, thereby reducing risks and improving reactor safety.

[0066] Furthermore, in the sodium-cooled fast reactor, each channel represents a fuel element, and the structure of the fuel element is divided into axial and radial meshes. Setting the coolant flow as one-dimensional and the temperature and pressure fields as two-dimensional distributions further facilitates problem simplification and analysis.

[0067] Furthermore, by using commonly used air gap models and empirical formulas, combined with specific geometric models and physical property parameters, the heat transfer coefficient of the fuel cladding air gap is precisely derived theoretically. Based on the fact that air gap heat transfer involves radiation conduction, heat conduction, and heat transfer, the air gap thermal conductivity is calculated in three parts to provide a more accurate assessment of thermal conductivity.

[0068] Furthermore, the mass of fission gas generated at a certain power level is calculated from the mass of fission gas produced in each fission, and the release rate and escape rate are combined to process the amount of fission gas released.

[0069] Furthermore, based on the model developed by Weisman et al., fission gases were released in two ways: (1) directly onto the fuel surface; and (2) trapped in the fuel matrix and subsequently released onto the surface. The release amount was calculated by the proportion k' of free gas that escaped to the surface without being captured and the proportion k of gas trapped in the matrix per unit time, respectively.

[0070] Furthermore, after the fuel melting begins, five parts are assumed to enter the melting cavity: (1) central hole; (2) connecting pores; (3) closed pores; (4) pre-made pores; and (5) fuel cracks. The mass and volume of gas migrating into the melting cavity from each part are calculated.

[0071] Furthermore, the causes of axial and radial expansion of the fuel rods are categorized into three factors: non-equilibrium fission gas bubbles, expansion of solid fission products, and cladding swelling caused by irradiation. The pressure and volume of the fission gas bubbles are calculated using the ideal gas law, and the change in fuel volume fraction caused by the expansion of solid fission products is calculated using the volume change fraction and burnup.

[0072] Furthermore, the biaxial stress failure criterion is applicable to the failure analysis of metallic and oxide materials under high temperature and high pressure conditions. It evaluates the failure behaviors of materials such as fatigue, plastic deformation, and crack propagation under multiaxial stress conditions, and can more accurately predict material failure. The Larson-Miller lifetime fraction is applicable to materials in high-temperature environments and is used to estimate the material lifetime at high temperatures. It considers the influence of temperature and time on the material lifetime and expresses it as a dimension-independent value. This simplified representation makes the assessment of material lifetime more convenient. The failure pressure criterion is applicable to various materials and stress states and is used to calculate the failure pressure under a given stress condition. The transient failure temperature criterion is applicable to materials under high temperature and unsteady-state conditions and is used to evaluate the influence of thermal stability and thermal stress on failure. It is understood that the beneficial effects of the second aspect mentioned above can be found in the relevant descriptions in the first aspect mentioned above, and will not be repeated here.

[0073] In summary, this invention considers multiple factors affecting reactivity, resulting in more refined modeling of the sodium-cooled fast reactor core, improved stability and computational efficiency of the numerical algorithm, and the ability to more accurately and efficiently simulate and analyze core nuclear reactions under severe accidents.

[0074] The technical solution of the present invention will be further described in detail below with reference to the accompanying drawings and embodiments. Attached Figure Description

[0075] Figure 1 This is a flowchart illustrating the analysis process of this invention;

[0076] Figure 2 It is an axial mesh structure for the channel;

[0077] Figure 3 It is a radial mesh structure for the channel. Detailed Implementation

[0078] The technical solutions of the embodiments of the present invention will be clearly and completely described below with reference to the accompanying drawings. Obviously, the described embodiments are only some, not all, of the embodiments of the present invention. Based on the embodiments of the present invention, all other embodiments obtained by those skilled in the art without creative effort are within the scope of protection of the present invention.

[0079] In the description of this invention, it should be understood that the terms "comprising" and "including" indicate the presence of the described features, integrals, steps, operations, elements and / or components, but do not exclude the presence or addition of one or more other features, integrals, steps, operations, elements, components and / or collections thereof.

[0080] It should also be understood that the terminology used in this specification is for the purpose of describing particular embodiments only and is not intended to limit the invention. As used in this specification and the appended claims, the singular forms “a,” “an,” and “the” are intended to include the plural forms unless the context clearly indicates otherwise.

[0081] It should also be further understood that the term "and / or" as used in this specification and the appended claims refers to any combination and all possible combinations of one or more of the associated listed items, and includes such combinations. For example, A and / or B can represent three cases: A alone, A and B simultaneously, and B alone. Additionally, the character " / " in this invention generally indicates that the preceding and following objects have an "or" relationship.

[0082] It should be understood that although terms such as first, second, third, etc., may be used in the embodiments of the present invention to describe the preset range, these preset ranges should not be limited to these terms. These terms are only used to distinguish the preset ranges from one another. For example, without departing from the scope of the embodiments of the present invention, the first preset range may also be referred to as the second preset range, and similarly, the second preset range may also be referred to as the first preset range.

[0083] Depending on the context, the word "if" as used here can be interpreted as "when," "when," "in response to determination," or "in response to detection." Similarly, depending on the context, the phrase "if determination" or "if detection (of the stated condition or event)" can be interpreted as "when determination," "in response to determination," "when detection (of the stated condition or event)," or "in response to detection (of the stated condition or event)."

[0084] The accompanying drawings illustrate various structural schematic diagrams according to embodiments disclosed in this invention. These drawings are not to scale, and some details have been enlarged for clarity, and some details may have been omitted. The shapes of the various regions and layers shown in the drawings, as well as their relative sizes and positional relationships, are merely exemplary and may deviate from reality due to manufacturing tolerances or technical limitations. Furthermore, those skilled in the art can design regions / layers with different shapes, sizes, and relative positions as needed.

[0085] This invention provides a method for analyzing the cladding failure of oxide fuel in liquid sodium-cooled reactors. It explores the fuel failure mechanism for liquid metal-cooled reactor types, thereby developing a preliminarily validated fuel cladding failure model. The developed model includes a series of fuel cladding failure models covering grain growth, fission gas release, fuel swelling, irradiation-induced cladding swelling, fission gas chamber pressure, molten void pressure growth, fuel cladding gap thermal conductivity, fuel axial growth reactivity model, fuel rod failure criteria, and material properties. Numerical calculations are performed on the core behavior of sodium-cooled block reactors under severe accident conditions.

[0086] Please see Figure 1 This invention discloses a method for analyzing cladding damage of oxide fuel in a liquid sodium-cooled reactor, comprising the following steps:

[0087] S1. Based on the structural parameters of the oxide fuel rods in the sodium-cooled fast reactor, radial and axial nodes are divided, and a mechanical model of the fuel rods is established.

[0088] Each channel represents a fuel rod, its cladding, the associated coolant, and a small portion of the component pipe wall. Within the channel, flow is assumed to be one-dimensional axially, while the temperature fields of the fuel, cladding, coolant, and structure are assumed to be two-dimensional radially and axially. Different channels can be used to account for variations in the radial and azimuth design geometry of the reactor core, power output, coolant flow rate, and burnup.

[0089] The channel length represents the total length of the component, from the coolant inlet to the coolant outlet; for several axial regions, please refer to [link / reference needed]. Figure 2 One region represents the fuel rod section, including the fuel pellets, the transition zone, and the gas chamber. The other regions represent the upper and lower reflector layers of the fuel rod. Generally, the radial dimensions and thermal properties of the reflector layers are constant, and the gas chamber can be located above or below the fuel pellet section.

[0090] Figure 2 The diagram shows an axial grid structure used for the channel, with coolant nodes interspersed with fuel, cladding, reflector, and structural nodes throughout the channel.

[0091] Figure 3 This displays a radial mesh structure used for temperature calculations in the fuel, cladding, coolant, and structural regions within an axial mesh node. Nodes in the fuel region are built on an equal radial difference basis or an equal mass basis, with the first and last nodes being half the size.

[0092] S2. Input the initial coolant and fuel temperature and pressure, initial reactor power, air gap thermal conductivity and other operating parameters. Based on the mechanical model established in step S1, combined with the heat transfer and phase change model, recalculate the temperature, pressure, fission gas release rate and other parameters of each node, and update the physical property parameters of the node in combination with the equation of state.

[0093] S3. After the steady-state calculation is completed, the running parameters updated in step S2 are transmitted to the transient calculation module.

[0094] S4. Based on S3, a gap heat transfer model is established according to the improved Ross-Stoute model. The heat transfer between fuel and cladding is divided into three parts: radiation heat transfer, gas conduction, and solid-solid conduction. The heat transfer coefficient of the fuel cladding air gap is calculated and corrected.

[0095] Radiative heat transfer coefficient h r The specific calculations are as follows:

[0096]

[0097] Where, q r For heat transfer from a hot surface to a cold surface, A f T is the heat transfer area of ​​the outer surface of the fuel. f T represents the outer surface temperature of the fuel.c This is the temperature of the inner surface of the casing.

[0098] The heat transfer coefficient h of gas conduction within the fuel cladding gap g The specific calculations are as follows:

[0099]

[0100] Where, k g Let be the thermal conductivity of the interstitial gas, (Δr) g This represents the total effective size of the fuel cladding clearance.

[0101] The heat transfer coefficient h of solid-solid thermal conductivity s The specific calculations are as follows:

[0102]

[0103] Where H is the hardness of the softer component between the fuel and the cladding, A,m is a coefficient determined experimentally, and R is the root mean square of the roughness of the fuel and the cladding.

[0104] The heat transfer coefficient h of the fuel cladding air gap gap The result is obtained by summing the three parts mentioned above:

[0105] h gap =h g +h r +h s

[0106] S5. Based on the Trap-release model, a phenomenological model of fission gas release rate is established. This model shows that the gas is released in two ways: directly onto the fuel surface and trapped in the fuel matrix and subsequently released onto the surface, providing a more mechanistic treatment of fission gas release.

[0107] The fission process occurring in the fuel during irradiation produces solid and gaseous fission products. In the model, these gaseous products either precipitate as gaseous bubbles at grain boundaries, are contained within microbubbles in the fuel matrix, or are released into the available free volume of the fuel rod chambers and the fuel center cavity. Intraparticle gas does not participate in fuel expansion but becomes important during fuel melting. Release into the free volume alters the gas mixture and reduces the thermal conductivity of the gas in the interstitial spaces; therefore, fission gas release, fuel expansion, and fuel rod temperature distribution are closely related. The mass of fission gas generated, G... m for:

[0108]

[0109] Among them, f g The fraction of gas atoms produced in each fission, Δt is the time step, and MW fgP is the molar mass of the fission gas. j E represents the power of node j in the axial segment. f This refers to the energy generated in each fission.

[0110] Fission gas generation mass G of radial grid i for:

[0111] G i =G m f i

[0112] coefficient f i Related to the radial power factor:

[0113]

[0114] Among them, f g The fraction of gas atoms produced in each fission, Δt is the time step, and MW fg P is the molar mass of the fission gas. j E represents the power of node j in the axial segment. f S represents the energy produced in each fission. i M is the radial power shape factor of radial grid i. i Let N be the fuel mass of radial grid i, and N be the number of radial grids.

[0115] Because fission gases generated at fuel grain boundaries and within fuel grains have different effects on fuel expansion and molten chamber pressurization, they need to be distinguished. The fuel cladding damage module uses the input parameter f. gb To control the amount of gas located at the grain boundaries and the amount of gas located within the fuel grains;

[0116] Among them, the amount of fission gas generated at the grain boundaries of radial grid i:

[0117] G gb,i =G i f gb

[0118] fission gas generation within the grains of radial grid i:

[0119] G fm,i =G i (1-f gb )

[0120] If the fission gas is set to be isotropic, the isotropic model is used to calculate the amount of fission gas retained; otherwise, the retention-release model is used to calculate the amount of fission gas retained, thereby calculating the amount of fission gas released at the end of the time step.

[0121] If the fission gas is assumed to be isotropic, the isotropic model is used to calculate the amount of fission gas retained. In the isotropic fission gas release model, release is considered as a function of a single release rate f, which is a function of temperature, representing the probability that gas atoms retained per unit time will be released. At all locations, the fundamental rate equation controlling the amount of gas retained in the fuel can be given by:

[0122]

[0123] Since the migration rate of gas atoms is a thermally activated process, the release rate can be assumed to be expressed by the following formula:

[0124] f = A α exp(-Q α / RT)

[0125] Where S is the amount of fission gas retained in the fuel, f is the partial release rate of the residual gas, G is the fission gas productivity, and Q... α This refers to the activation energy released.

[0126] If the model assumes that the fission gas is anisotropic, the retention rate of the fission gas is calculated using a trap-release model. A phenomenological model of the fission gas release rate is established based on the trap-release model, which assumes that the gas is released in two ways: directly onto the fuel surface and trapped in the fuel matrix and subsequently released to the surface, providing a more mechanistic treatment of the fission gas release.

[0127] Of which, the amount of gas generated is directly released:

[0128] dn1=k′Gdt

[0129] Where dn1 is the amount of gas released in terms of time increment dt, and k′ is the proportion of free gas that escapes to the surface without being captured.

[0130] The amount of gas retained in the fuel grains is calculated by subtracting the total amount of gas released from the total amount of gas produced.

[0131] c = Gt - n

[0132] Let k represent the probability of the trapped gas being released per unit time, and dn represent the amount of trapped gas released. f It is given by the following formula:

[0133] dn f =kcdt

[0134] Of this portion of gas, a fraction k′ was not rediscounted:

[0135] dn2=k'kcdt

[0136] Where dn2 is the amount of trapped gas that is released back onto the fuel surface, the total amount of released gas dn is given by the following formula:

[0137] dn = dn1 + dn2

[0138] S6. As volatile fission products are released from the fuel, they enter the free volume associated with the fuel rod and mix uniformly with the existing gas. Considering that the free volume is the volume of the fission gas chamber, the central fuel voids independent of the central molten fuel cavity, the fuel cladding gaps, and the crack volume within the fuel, a uniform ideal gas mixture in pressure equilibrium is formed. Using the improved ideal gas equation, the pressure within the molten cavity is calculated. The total amount and volume of gas in the molten cavity are the sum of the amounts from the initial central cavity, grain boundaries, grain interiors, manufacturing pores, and fuel cracks.

[0139] Prior to the pressure calculations, the total number of moles of fissile gas and helium was known, although their distribution was unknown. The pressure P in the fissile gas chamber... g The specific calculations are as follows:

[0140]

[0141] Where, n T The total amount of gaseous substance is represented by the subscripts p, v, g, and k, which refer to the gas chamber, central cavity, fuel cladding gap, and fracture, respectively. MZ represents the total number of axial segments, IETA represents the innermost node of the fracture zone, and NT represents the total number of radial nodes.

[0142] The radial range of the melting chamber is determined by the relationship between the radial element temperature and the solidus temperature. When the solidus temperature is reached, the element begins to melt; when the liquidus temperature is reached, the element is completely melted. The melting fraction f of the radial grid i is... m,i for:

[0143]

[0144] Among them, T 2,i T is the fuel temperature at the end of the time step. s T is the solidus temperature. l This is the liquidus temperature;

[0145] This leads to the incremental melt fraction ratio R. IMF for:

[0146]

[0147] When melting begins in the axial segment, five components are considered: gas and volume moving from the initial central cavity, grain boundaries, grain interiors, manufacturing pores, and fuel cracks into the melting cavity. Before melting, it is assumed that the central cavity and the remaining free volume within the fuel rod are in equilibrium. During fuel melting, it is assumed that the gas and its volume from grain boundaries, manufacturing pores, and fuel cracks are immediately released into the melting cavity. The changes in the amount and volume of matter within the radial grid are as follows:

[0148] ΔM k,i,j (Δt)=M(t) k,i,j R IMF,i,j

[0149] Where k = gb, c, af, ck, respectively represent the four regions of grain boundary, grain interior, pre-made pores and fuel fractures;

[0150] The total change within a time step is obtained by summing:

[0151]

[0152] j cavb and j cavt These refer to the lower and upper boundaries of the molten cavity, respectively. z The outer boundary of the molten cavity in the radial direction;

[0153] Summing across all relevant grids yields the total volume change of the fuel due to thermal effects:

[0154]

[0155] Molten cavitation pressure P cav The specific calculations are as follows:

[0156]

[0157] Among them, M cav T represents the total amount of gas in the molten cavity. cav V is the temperature of the melting cavity. cav This represents the volume of the molten cavity.

[0158] Total gas volume M in the molten cavity cav , melt cavity volume V cav The specific calculation is as follows:

[0159]

[0160]

[0161] The total amount and volume of gas in the central molten cavity are obtained by superimposing the quantities discussed in the previous sections:

[0162]

[0163]

[0164] S7. The expansion of the fuel rod along the axial and radial directions is due to three reasons: non-equilibrium fission gas bubbles, expansion of solid fission products, and cladding swelling caused by irradiation. Based on the fission gas release calculated in step S5, the shape of the fission gas bubbles is spherical. The internal pressure of the bubbles is calculated. The creep characteristics of the fuel determine the rate of volume change, and the axial strain of the mesh is determined. The volume fraction change is related to the fuel burnup, and the change in fuel rod volume fraction caused by the expansion of solid fission products is calculated. The expansion is isotropic and directed outward. One-third of the volume change occurs axially, and the rest occurs radially. The new change in fuel rod volume fraction is thus calculated.

[0165] If the bubble is spherical, then the radius r of the fission gas bubble is... B The pressure caused by surface tension and the internal pressure P of the fission gas bubble fg Specifically:

[0166]

[0167] The pressure caused by surface tension is determined based on the relationship between surface tension and bubble radius:

[0168]

[0169] The pressure inside a fission gas bubble can be determined by the ideal gas equation:

[0170] P fg =M fg RT / V fg

[0171] Among them, A pg Q is the pre-exponential constant. pg Here, is the exponential calibration constant, T is the temperature, γ is the surface tension, and M is the surface tension. fg V represents the amount of fission gas within the bubble. fg Let be the volume of the fission gas bubble.

[0172] The relationship when the pressures inside and outside the bubble are in equilibrium is as follows:

[0173] P fg =P γ +P σ

[0174] Among them, P σ The hydrostatic pressure is determined by the stress state of the fuel grid. Substituting the above equation into the equation determines the volume V of the bubble at equilibrium. e for:

[0175]

[0176] By relating the volume fraction change to fuel burnup, the change in fuel rod volume fraction caused by the expansion of solid fission products is calculated:

[0177]

[0178] Where, ε sfp is the expansion rate parameter of solid fission products, and B is the fuel consumption;

[0179] The expansion is isotropic and directed outwards. Assuming that one-third of the volume change occurs axially and the remainder occurs radially, the new change in fuel rod volume fraction is calculated.

[0180]

[0181] Where Σ is the negative fraction of density change;

[0182] The negative density variation form Σ given in the nuclear systems materials handbook is:

[0183]

[0184] Where Φ is the fast neutron flux and α is the calibration constant, which is 0.75;

[0185] The τ gestation parameters are:

[0186] τ = 4.742 - 0.2326β + 2.717β 2

[0187] The parameter for R(T) as a function of temperature is:

[0188] R(T)=0.01[exp(0.0419+1.498β+0.122β 2 -0.332β 3 -0.441β 4 )]

[0189] β=(T-500) / 1000

[0190] The volume expansion caused by the solid transformation products and the change in bubble volume calculated using non-equilibrium bubble film properties were calculated separately. Finally, the axial and radial components of the expansion were determined, and the inner radius at the new moment was calculated.

[0191]

[0192] S8. Combining the thermodynamic variables obtained in steps S4 to S7, and based on the air gap temperature convergence principle, perform calculations for each time step in sequence, and determine whether the fuel rod has failed using the failure criteria.

[0193] Failure criteria for determining whether a fuel rod has failed:

[0194] 1. Biaxial stress failure

[0195] Based on failure index parameters such as the surface temperature T and circumferential stress σ of the fuel element, the estimated fracture time t at the current moment is predicted. r When the ratio of the problem time to the rupture time is greater than or equal to 1.0, the fuel cladding meets the biaxial stress failure criterion.

[0196] The model is from the Nuclear Systems Material Handbook, abbreviated as NSMH below, and is based on a cladding of 20% cold-worked 316SS that has not been irradiated.

[0197] logθ=-15.22+9.5342log[log(σ * / σ)]

[0198] θ=t r exp(-Q / RT)

[0199] Where θ is the mandrel parameter; t r The rupture time is expressed in hours (h); T is the temperature; Q = 83508 cal / mole; R is the universal gas constant; σ is the circumferential stress; σ * =135ksi;r o r is the outer radius of the shell; i denoted as the inner radius of the cladding; P is the gas pressure inside the rod (or the interface pressure).

[0200] 2. Larson-Miller lifetime fraction

[0201] Based on failure index parameters such as surface temperature T and circumferential stress σ of fuel elements, creep failure time is estimated and damage fraction D is calculated. When the damage fraction is greater than or equal to 1.0, the fuel cladding meets the Larson-Miller life fraction failure criterion.

[0202] The Larson-Miller lifetime fraction criterion calculates the damage fraction D by estimating the creep failure time. The damage fraction D is expressed as the ratio of time to failure time. The following formula is derived from the LMP lifetime fraction calculation formula in the TEECH software:

[0203]

[0204] Among them, t r The fracture time is given by C, which is a constant depending on the material and takes the value of 20. LMP is the experimentally determined Larson-Miller parameter, and T is the cladding temperature.

[0205] The fracture time is expressed as a lifetime fraction:

[0206]

[0207] Where L is the lifetime fraction, i is the time step, and Δt is the time step. i The time step length.

[0208] 3. Damage pressure

[0209] The failure pressure P at the current moment is predicted based on the circumferential stress σ of the fuel element. When the ratio of the internal pressure of the fuel element to the failure pressure is greater than or equal to 1.0, the fuel cladding meets the failure pressure criterion.

[0210] The model is from NSMH and is used for unirradiated FTR cladding:

[0211]

[0212] Where P is the rupture pressure, ksi; σ is the circumferential stress; a0 = 1.799988 × 10 1 a1 = 2.866442 × 10 -2 a2 = -3.986012 × 10 -4 a3 = 2.408207 × 10 -6 a4 = -8.090292 × 10 -9 a5 = 1.607218 × 10 -11 a6 = -1.962158 × 10 -14 a7 = 1.487159 × 10 -17 a8 = -6.821934 × 10 -21 a9 = 1.735220 × 10 -24 ;a 10 =1.879417×10 -28 .

[0213] 4. Transient failure temperature

[0214] Based on the empirical relationship between the surface temperature T of the fuel element and the temperature rise rate, linear interpolation is performed between 5.56 K / s and 111.1 K / s. Then, the fuel cladding failure temperature T is predicted by combining the circumferential stress σ. f When the ratio of fuel element temperature to failure temperature is greater than or equal to 1.0, the fuel cladding meets the failure temperature criterion.

[0215] The model is from NSMH and is used for unirradiated cladding. It involves two temperature rise rates, 5.56 and 111.1 K / s, with linear interpolation performed if the rate falls between them.

[0216] T f =2358.4-36.41σ+0.5649σ 2 -3.455×10 -3 σ 3

[0217] for T≤5.56K / s

[0218] T f =2484.8-37.80σ+0.5827σ 2 -3.585×10 -3 σ 3

[0219] forT≥111K / s

[0220] Among them, T f σ is the failure temperature, and σ is the circumferential stress.

[0221] In another embodiment of the present invention, a cladding damage analysis system for oxidized fuel in a liquid sodium-cooled reactor is provided. This system can be used to implement the above-mentioned cladding damage analysis method for oxidized fuel in a liquid sodium-cooled reactor. Specifically, the cladding damage analysis system for oxidized fuel in a liquid sodium-cooled reactor includes modules, modules, modules, modules, and modules.

[0222] Among them, the construction module establishes a mechanical model of oxide fuel rods in a liquid sodium cold reactor;

[0223] The parameter module inputs operating parameters into the fuel rod mechanical model established by the construction module, recalculates the temperature, pressure, and fission gas release rate of each node in combination with the heat transfer and phase change models, and updates the physical property parameters of the node in combination with the equation of state.

[0224] The calculation module performs transient initialization of the physical property parameters updated by the parameter module, and completes the power and reactivity calculations.

[0225] The coefficient module, based on the power and reactivity calculations of the calculation module, establishes a gap heat conduction model according to the improved Ross-Stoute model, divides the heat transfer between fuel and cladding into radiation heat transfer, gas conduction and solid-solid heat conduction, and calculates and corrects the heat transfer coefficient of the fuel cladding air gap.

[0226] The processing module establishes a phenomenological model of fission gas release rate based on the Trap-release model to obtain the fission gas release amount;

[0227] The superposition module uses an improved ideal gas equation to calculate the pressure inside the melting cavity;

[0228] The volume module calculates the internal pressure of the bubbles based on the fission gas release calculated by the processing module, determines the axial strain of the mesh, calculates the change in fuel rod volume fraction caused by the expansion of solid fission products by relating the volume fraction change to fuel consumption, and calculates the new change in fuel rod volume fraction.

[0229] The analysis module combines the heat transfer coefficient obtained from the coefficient module, the pressure inside the molten cavity obtained from the processing module, and the new fuel rod volume fraction change obtained from the volume module. Based on the air gap temperature convergence principle, it completes the calculation for each time step in sequence and determines whether the fuel rod has failed through the failure criteria.

[0230] In another embodiment of the present invention, a terminal device is provided, comprising a processor and a memory. The memory stores a computer program, which includes program instructions. The processor executes the program instructions stored in the computer storage medium. The processor may be a Central Processing Unit (CPU), or other general-purpose processors, digital signal processors (DSPs), application-specific integrated circuits (ASICs), field-programmable gate arrays (FPGAs), or other programmable logic devices, discrete gate or transistor logic devices, discrete hardware components, etc. It is the computing and control core of the terminal, suitable for implementing one or more instructions, specifically suitable for loading and executing one or more instructions to achieve a corresponding method flow or corresponding function. The processor described in this embodiment of the present invention can be used in the operation of a method for analyzing the cladding damage of oxide fuel in a liquid sodium cold reactor, including:

[0231] A mechanical model of oxide fuel rods in a liquid sodium-cooled reactor was established. Operating parameters were input into the fuel rod mechanical model, and the temperature, pressure, and fission gas release rate of each node were recalculated using heat transfer and phase change models. The physical properties of the nodes were updated using the equation of state. Transient initialization of the updated physical properties was performed, and power and reactivity calculations were completed. Based on the power and reactivity calculations, a gap heat conduction model was established according to the improved Ross-Stoute model. Heat transfer between the fuel and cladding was divided into radiative heat transfer, gas conduction, and solid-solid conduction. The heat transfer coefficient of the fuel cladding gap was calculated and corrected. Based on the Trap- The release model establishes a phenomenological model of fission gas release rate to obtain the fission gas release amount; the pressure inside the molten cavity is calculated using the improved ideal gas equation; based on the fission gas release amount, the internal pressure of the bubble is calculated, the axial strain of the mesh is determined, and the volume fraction change is calculated in relation to the fuel combustion, resulting in the change in fuel rod volume fraction due to the expansion of solid fission products, thus calculating the new change in fuel rod volume fraction; combining the heat transfer coefficient, the pressure inside the molten cavity, and the new change in fuel rod volume fraction, the calculation for each time step is completed sequentially according to the air gap temperature convergence principle, and the failure criteria are used to determine whether the fuel rod has failed.

[0232] In another embodiment of the present invention, a storage medium is also provided, specifically a computer-readable storage medium (memory). This computer-readable storage medium is a memory device in a terminal device used to store programs and data. It is understood that the computer-readable storage medium here can include both the built-in storage medium in the terminal device and extended storage media supported by the terminal device. The computer-readable storage medium provides storage space that stores the terminal's operating system. Furthermore, this storage space also stores one or more instructions suitable for loading and execution by a processor. These instructions can be one or more computer programs (including program code). It should be noted that the computer-readable storage medium here can be high-speed RAM or non-volatile memory, such as at least one disk storage device.

[0233] One or more instructions stored in a computer-readable storage medium can be loaded and executed by a processor to implement the corresponding steps of the cladding damage analysis method for oxide fuel in a liquid sodium-cooled reactor in the above embodiments; one or more instructions in the computer-readable storage medium are loaded and executed by the processor to perform the following steps:

[0234] A mechanical model of oxide fuel rods in a liquid sodium-cooled reactor was established. Operating parameters were input into the fuel rod mechanical model, and the temperature, pressure, and fission gas release rate of each node were recalculated using heat transfer and phase change models. The physical properties of the nodes were updated using the equation of state. Transient initialization of the updated physical properties was performed, and power and reactivity calculations were completed. Based on the power and reactivity calculations, a gap heat conduction model was established according to the improved Ross-Stoute model. Heat transfer between the fuel and cladding was divided into radiative heat transfer, gas conduction, and solid-solid conduction. The heat transfer coefficient of the fuel cladding gap was calculated and corrected. Based on the Trap- The release model establishes a phenomenological model of fission gas release rate to obtain the fission gas release amount; the pressure inside the molten cavity is calculated using the improved ideal gas equation; based on the fission gas release amount, the internal pressure of the bubble is calculated, the axial strain of the mesh is determined, and the volume fraction change is calculated in relation to the fuel combustion, resulting in the change in fuel rod volume fraction due to the expansion of solid fission products, thus calculating the new change in fuel rod volume fraction; combining the heat transfer coefficient, the pressure inside the molten cavity, and the new change in fuel rod volume fraction, the calculation for each time step is completed sequentially according to the air gap temperature convergence principle, and the failure criteria are used to determine whether the fuel rod has failed.

[0235] In summary, this invention provides a method and system for analyzing the cladding damage of oxide fuel in a liquid sodium-cooled reactor. It develops functions for air gap heat conduction, fission gas release, pressure in gas cavities and molten cavities, and fuel swelling, thereby achieving the capability for safe analysis of fuel cladding damage.

[0236] Those skilled in the art will clearly understand that, for the sake of convenience and brevity, the above-described division of functional units and modules is merely an example. In practical applications, the above functions can be assigned to different functional units and modules as needed, that is, the internal structure of the device can be divided into different functional units or modules to complete all or part of the functions described above. The functional units and modules in the embodiments can be integrated into one processing unit, or each unit can exist physically separately, or two or more units can be integrated into one unit. The integrated unit can be implemented in hardware or as a software functional unit. Furthermore, the specific names of the functional units and modules are only for easy differentiation and are not intended to limit the scope of protection of this application. The specific working process of the units and modules in the above system can be referred to the corresponding process in the foregoing method embodiments, and will not be repeated here.

[0237] In the above embodiments, the descriptions of each embodiment have different focuses. For parts that are not described in detail or recorded in a certain embodiment, please refer to the relevant descriptions of other embodiments.

[0238] Those skilled in the art will recognize that the units and algorithm steps of the various examples described in conjunction with the embodiments disclosed in this invention can be implemented in electronic hardware, or a combination of computer software and electronic hardware. Whether these functions are implemented in hardware or software depends on the specific application and design constraints of the technical solution. Those skilled in the art can use different methods to implement the described functions for each specific application, but such implementations should not be considered beyond the scope of this invention.

[0239] In the embodiments provided by this invention, it should be understood that the disclosed devices / terminals and methods can be implemented in other ways. For example, the device / terminal embodiments described above are merely illustrative. For instance, the division of modules or units is only a logical functional division, and in actual implementation, there may be other division methods. For example, multiple units or components may be combined or integrated into another system, or some features may be ignored or not executed. Furthermore, the coupling or direct coupling or communication connection shown or discussed may be through some interfaces; the indirect coupling or communication connection between devices or units may be electrical, mechanical, or other forms.

[0240] The units described as separate components may or may not be physically separate. The components shown as units may or may not be physical units; that is, they may be located in one place or distributed across multiple network units. Some or all of the units can be selected to achieve the purpose of this embodiment according to actual needs.

[0241] Furthermore, the functional units in the various embodiments of the present invention can be integrated into one processing unit, or each unit can exist physically separately, or two or more units can be integrated into one unit. The integrated unit can be implemented in hardware or as a software functional unit.

[0242] If the integrated module / unit is implemented as a software functional unit and sold or used as an independent product, it can be stored in a computer-readable storage medium. Based on this understanding, all or part of the processes in the methods of the above embodiments can also be implemented by a computer program instructing related hardware. The computer program can be stored in a computer-readable storage medium, and when executed by a processor, it can implement the steps of the various method embodiments described above. The computer program includes computer program code, which can be in the form of source code, object code, executable files, or certain intermediate forms. The computer-readable medium can include: any entity or device capable of carrying the computer program code, recording media, USB flash drives, portable hard drives, magnetic disks, optical disks, computer memory, read-only memory (ROM), random access memory (RAM), electrical carrier signals, telecommunication signals, and software distribution media, etc. It should be noted that the content included in the computer-readable medium can be appropriately added or removed according to the requirements of legislation and patent practice in the jurisdiction. For example, in some jurisdictions, according to legislation and patent practice, computer-readable media do not include electrical carrier signals and telecommunication signals.

[0243] This application is described with reference to flowchart illustrations and / or block diagrams of methods, apparatus (systems), and computer program products according to embodiments of this application. It will be understood that each block of the flowchart illustrations and / or block diagrams, and combinations of blocks in the flowchart illustrations and / or block diagrams, can be implemented by computer program instructions. These computer program instructions can be provided to a processor of a general-purpose computer, special-purpose computer, embedded processor, or other programmable data processing apparatus to produce a machine, such that the instructions, which execute via the processor of the computer or other programmable data processing apparatus, generate instructions for implementing the flowchart... Figure 1 One or more processes and / or boxes Figure 1 A device that provides the functions specified in one or more boxes.

[0244] These computer program instructions may also be stored in a computer-readable storage medium that can direct a computer or other programmable data processing device to function in a particular manner, such that the instructions stored in the computer-readable storage medium produce an article of manufacture including instruction means, which are implemented in a process Figure 1 One or more processes and / or boxes Figure 1 The function specified in one or more boxes.

[0245] These computer program instructions may also be loaded onto a computer or other programmable data processing equipment to cause a series of operational steps to be performed on the computer or other programmable equipment to produce a computer-implemented process, thereby providing instructions that execute on the computer or other programmable equipment for implementing the process. Figure 1 One or more processes and / or boxes Figure 1 The steps of the function specified in one or more boxes.

[0246] The above content is only for illustrating the technical concept of the present invention and should not be construed as limiting the scope of protection of the present invention. Any modifications made to the technical solution based on the technical concept proposed in this invention shall fall within the scope of protection of the claims of this invention.

Claims

1. A method for analyzing cladding damage of oxide fuel in liquid sodium-cooled reactors, characterized in that, Includes the following steps: S1. Establish a mechanical model of oxide fuel rods in a liquid sodium-cooled reactor. Based on the structural parameters of oxide fuel in a liquid sodium-cooled reactor, divide the system into radial and axial nodes. Each channel represents a fuel rod, the cladding of the fuel rod, the related coolant, and a small portion of the component pipe walls. Within the channel, the flow is set as one-dimensional in the axial direction, and the temperature fields of the fuel, cladding, coolant, and structure are set as two-dimensional in the radial and axial directions. The channel length represents the length of the entire assembly, from the coolant inlet to the coolant outlet. One area represents the fuel rod section, including the fuel pellets, the upper and lower conversion zones, and the gas chamber. Other areas represent the upper and lower reflector layers of the fuel rod. S2. Input the operating parameters into the fuel rod mechanical model established in step S1, recalculate the temperature, pressure, and fission gas release rate of each node in combination with the heat transfer and phase change models, and update the physical property parameters of the node in combination with the equation of state. S3. Perform transient initialization on the physical property parameters updated in step S2, and complete the power and reactivity calculations; S4. Based on the power and reactivity calculations in step S3, establish a gap heat transfer model according to the improved Ross-Stoute model, divide the heat transfer between fuel and cladding into radiation heat transfer, gas conduction and solid-solid conduction, and calculate and correct the heat transfer coefficient of the fuel cladding gap. S5. Establish a phenomenological model of fission gas release rate based on the Trap-release model to obtain the fission gas release amount; S6. Calculate the pressure inside the melting cavity using the improved ideal gas equation; S7. Based on the fission gas release calculated in step S5, calculate the internal pressure of the bubble, determine the axial strain of the mesh, and calculate the change in fuel rod volume fraction caused by the expansion of solid fission products in relation to the volume fraction change and fuel consumption. Calculate the new change in fuel rod volume fraction. The reasons for the axial and radial expansion of the fuel rod include non-equilibrium fission gas bubbles, solid fission product expansion, and cladding swelling caused by irradiation. Calculate the volume expansion caused by solid fission products and the bubble volume change calculated using non-equilibrium bubble film properties, respectively. Finally, determine the axial and radial components of the expansion, and calculate the inner radius at the new moment as follows: in, The inner radius of the shell, For runtime, For time step, This represents the change in volume fraction; S8. Combining the heat transfer coefficient obtained in step S4, the pressure inside the molten cavity obtained in step S6, and the new change in fuel rod volume fraction obtained in step S7, the calculation for each time step is completed sequentially according to the air gap temperature convergence principle, and the failure criteria are used to determine whether the fuel rod has failed.

2. The method for analyzing cladding damage of oxide fuel in liquid sodium-cooled reactors according to claim 1, characterized in that, In step S4, the heat transfer coefficient of the fuel cladding air gap h gap for: in, h g The heat transfer coefficient is the gas conduction coefficient within the fuel cladding gap. h r The radiative heat transfer coefficient is... h s The heat transfer coefficient for solid-to-solid thermal conduction.

3. The method for analyzing cladding damage of oxide fuel in liquid sodium-cooled reactors according to claim 1, characterized in that, In step S5, the mass of fission gas generated G m for: fission gas release dn for: in, dn 1 represents time increments dt The amount of gas released is indicated. dn 2 represents the amount of trapped gas that is released back onto the fuel surface. The power of the axial segment j during operation. For time step, This represents the fraction of gas atoms produced in each fission. Let be the molar mass of the fission gas. This refers to the energy generated in each fission.

4. The method for analyzing cladding damage of oxide fuel in liquid sodium-cooled reactors according to claim 3, characterized in that, In time increment dt The amount of gas released is indicated dn 1. The amount of trapped gas that is released back onto the fuel surface dn 2 are respectively: in, k´ The proportion of free gas that escapes to the surface and is not captured. This represents the probability of the trapped gas being released per unit of time. G For fission gas productivity, c This refers to the amount of gas retained in the fuel grains.

5. The method for analyzing cladding damage of oxide fuel in liquid sodium-cooled reactors according to claim 1, characterized in that, In step S6, the total amount of gas in the central melting cavity and total volume They are respectively: in, The original gas volume in the central cavity. This represents the total amount of grain boundary gas released into the melt cavity within a time step. This represents the total amount of gas released from within the grains into the melt cavity during the time step. This represents the total amount of pre-formed pore gas released into the molten cavity within a given time step. This represents the total amount of gas released from the fuel crack into the molten cavity within a time step. The original gas volume in the central cavity, The total volume of grain boundary gas released into the melt cavity within the time step is given. This represents the total volume of gas released from within the grains into the melt cavity during the time step. The total volume of pre-formed pore gas released into the molten cavity within the time step. This represents the total volume of gas released from the fuel crack into the molten cavity within a time step.

6. The method for analyzing cladding damage of oxide fuel in liquid sodium-cooled reactors according to claim 1, characterized in that, In step S8, the failure criteria include biaxial stress failure, Larson-Miller lifetime fraction, failure pressure, and transient failure temperature.

7. The method for analyzing cladding damage of oxide fuel in a liquid sodium-cooled reactor according to claim 6, characterized in that, Biaxial stress failure criterion: in, θ For mandrel parameters; t r The rupture time is expressed in hours (h). T For temperature; Q =83508 cal / mole; R This is the universal gas constant; σ It is circumferential stress; σ =135 ksi; Larson-Miller lifetime fractional failure criterion: in, t r For the time of rupture, C The constant value is 20, which depends on the material. LMP The Larson-Miller parameters were determined experimentally. T This refers to the cladding temperature; The rupture time is expressed as a lifetime fraction: in, L Lifespan fraction i For the number of steps, t i The time step length; Breakage pressure criteria: in, P The rupture pressure is ksi; σ It is circumferential stress; a 0 = 1.799988 × 10 1 ; a 1 = 2.866442 × 10 -2 ; a 2 = -3.986012 × 10 -4 ; a 3 = 2.408207 × 10 -6 ; a 4 = -8.090292 × 10 -9 ; a 5 = 1.607218 × 10 -11 ; a 6 = -1.962158 × 10 -14 ; a 7 = 1.487159 × 10 -17 ; a 8 = -6.821934 × 10 -21 ; a 9 = 1.735220 × 10 -24 ; a 10 =1.879417×10 -28 ; Failure criterion based on damage temperature: in, T f The failure temperature. σ This is circumferential stress.

8. A system for analyzing cladding damage of oxide fuel in a liquid sodium-cooled reactor, characterized in that, include: The module is constructed to establish a mechanical model of oxide fuel rods in a liquid sodium cold reactor. Based on the structural parameters of oxide fuel in a liquid sodium cold reactor, radial and axial nodes are divided. Each channel represents a fuel rod, the cladding of the fuel rod, the associated coolant, and a small portion of the component pipe walls. Within the channel, the flow is set as one-dimensional in the axial direction, and the temperature fields of the fuel, cladding, coolant, and structure are set as two-dimensional in the radial and axial directions. The channel length represents the length of the entire assembly, from the coolant inlet to the coolant outlet. One area represents the fuel rod section, including the fuel pellets, the upper and lower conversion zones, and the gas chamber. Other areas represent the upper and lower reflector layers of the fuel rod. The parameter module inputs operating parameters into the fuel rod mechanical model established by the construction module, recalculates the temperature, pressure, and fission gas release rate of each node in combination with the heat transfer and phase change models, and updates the physical property parameters of the node in combination with the equation of state. The calculation module performs transient initialization of the physical property parameters updated by the parameter module, and completes the power and reactivity calculations. The coefficient module, based on the power and reactivity calculations of the calculation module, establishes a gap heat conduction model according to the improved Ross-Stoute model, divides the heat transfer between fuel and cladding into radiation heat transfer, gas conduction and solid-solid heat conduction, and calculates and corrects the heat transfer coefficient of the fuel cladding air gap. The processing module establishes a phenomenological model of fission gas release rate based on the Trap-release model to obtain the fission gas release amount; The superposition module uses an improved ideal gas equation to calculate the pressure inside the melting cavity; The volume module, based on the fission gas release calculated by the processing module, calculates the internal pressure of the bubbles and determines the axial strain of the mesh; it calculates the change in fuel rod volume fraction caused by the expansion of solid fission products in relation to the volume fraction change and fuel burnup; it calculates the new change in fuel rod volume fraction, considering that the axial and radial expansion of the fuel rod is caused by non-equilibrium fission gas bubbles, solid fission product expansion, and cladding swelling caused by irradiation; it calculates the volume expansion caused by solid fission products and the bubble volume change calculated using non-equilibrium bubble film properties, respectively, and finally determines the axial and radial components of the expansion, calculating the inner radius at the new moment as follows: in, The inner radius of the shell, For runtime, For time step, This represents the change in volume fraction; The analysis module combines the heat transfer coefficient obtained from the coefficient module, the pressure inside the molten cavity obtained from the processing module, and the new fuel rod volume fraction change obtained from the volume module. Based on the air gap temperature convergence principle, it completes the calculation for each time step in sequence and determines whether the fuel rod has failed through the failure criteria.

Images