A method for checking oxygen concentration interval

Abstract

The application provides an oxygen concentration interval checking method, and relates to the technical field of lead-bismuth fast reactor oxygen concentration interval checking, and the method comprises the following steps: establishing a lead-bismuth fast reactor model, obtaining an initial oxygen concentration interval of the lead-bismuth fast reactor model, and selecting a plurality of preset oxygen concentrations from the initial oxygen concentration interval; performing physical field calculation on the fuel rod under each preset oxygen concentration to obtain physical field parameters corresponding to each preset oxygen concentration; the physical field parameters comprise temperature distribution parameters, fuel rod geometric parameters, contact stress, cladding oxidation corrosion parameters and fission gas parameters; judging whether each preset oxygen concentration meets the use requirements of the fuel rod based on the physical field parameters corresponding to each preset oxygen concentration, and determining a qualified oxygen concentration interval based on each preset oxygen concentration that meets the use requirements of the fuel rod. The qualified oxygen concentration interval is obtained by checking the initial oxygen concentration interval, and the problems of heat transfer deterioration, inability to inhibit corrosion and inability to meet the long-term use requirements of the fuel rod during fuel rod burnup can be avoided.

Description

Technical Field

[0001] This invention relates to the field of oxygen concentration range verification technology for lead-bismuth fast reactors, and more specifically, to a method for verifying oxygen concentration ranges. Background Technology

[0002] Lead-bismuth fast reactors, as one of the most promising fourth-generation reactors, have attracted widespread attention. Due to the corrosive effect of liquid lead-bismuth alloys, fuel rods are prone to failure due to liquid metal embrittlement of the cladding material, liquid metal-assisted damage, and environmental-assisted cracking. The compatibility of materials has become one of the unresolved problems in the development of lead-bismuth fast reactors. In order to reduce the corrosive effect of liquid metal on the fuel rod cladding material and ensure the integrity of the fuel rods during long-term operation, many different corrosion mitigation methods have been studied.

[0003] Currently, the mainstream corrosion mitigation and protection measures in lead-bismuth fast reactor design include: (1) selecting corrosion-resistant metal material T91 alloy; (2) maintaining a protective oxide layer on the fuel rod cladding surface by controlling the oxygen concentration of the liquid metal to change the wettability of the liquid metal and prevent further corrosion. At the same time, two oxygen concentration control methods, one for the gas phase and one for the solid phase, have been proposed and have shown good results in experimental loops. However, existing methods are limited to the corrosion behavior of lead-bismuth fast reactors themselves and only obtain results by simply fitting experimental data.

[0004] In reality, while the oxygen concentration range can ensure the existence of a protective oxide layer on the cladding surface, this oxide layer also acts as a thermal resistance for heat transfer, leading to deterioration of heat transfer on the cladding surface and affecting the complete temperature field distribution of the fuel rods. In addition, the thickness of the cladding material is weakened after corrosion, and the thinning of the cladding also affects the deformation of the fuel rods. Furthermore, due to the significant axial inhomogeneity along the fuel rod axis in actual lead-bismuth fast reactors, the corrosion behavior of the cladding will exhibit axial correlation. Therefore, the transmission of the effects of oxidation and corrosion of fuel rods is a multi-physics process.

[0005] Existing oxygen concentration control technologies for lead-bismuth fast reactors typically select only extreme or intermediate values ​​within an oxygen concentration range, without considering the multiple physical properties of the fuel rods. However, these existing oxygen concentration ranges are based solely on fuel rod material corrosion theory, resulting in inaccurate and wide-ranging ranges that cannot guarantee the oxygen concentration within this range meets the fuel rod's operational requirements. For example, the upper limit of the oxygen concentration range may lead to severe heat transfer degradation, while the lower limit may result in insufficient oxide layer thickness to suppress corrosion. Furthermore, due to the highly nonlinear nature of these effects, even the intermediate value of the oxygen concentration range may not meet the requirements for long-term fuel rod use. Therefore, existing oxygen concentration control technologies suffer from inaccurate oxygen concentration range settings, containing oxygen concentration values ​​that do not meet the fuel rod's operational requirements. This leads to heat transfer degradation or corrosion during fuel burnup, ultimately failing to meet the long-term operational needs of the fuel rods. Summary of the Invention

[0006] This invention provides a method for verifying oxygen concentration ranges to solve the technical problem that existing oxygen concentration ranges do not incorporate multi-physical characteristic analysis.

[0007] This invention provides a method for verifying oxygen concentration ranges, the method comprising the following steps:

[0008] A lead-bismuth fast reactor model is established, and an initial oxygen concentration range of the lead-bismuth fast reactor model is obtained. Multiple preset oxygen concentrations are selected from the initial oxygen concentration range. The lead-bismuth fast reactor model includes fuel rods and liquid lead-bismuth alloy, and the fuel rods include pellets and cladding.

[0009] Physical field calculations are performed on the fuel rods at each of the preset oxygen concentrations to obtain the physical field parameters corresponding to each preset oxygen concentration; wherein, the physical field parameters include temperature distribution parameters, fuel rod geometric parameters, contact stress, cladding oxidation and corrosion parameters, and fission gas parameters;

[0010] Based on the physical field parameters corresponding to each preset oxygen concentration, it is determined whether each preset oxygen concentration meets the usage requirements of the fuel rod, and a qualified oxygen concentration range is determined based on each preset oxygen concentration that meets the usage requirements of the fuel rod.

[0011] Preferably, the step of obtaining the initial oxygen concentration range of the lead-bismuth fast reactor model includes:

[0012] The lower limit of the initial oxygen concentration range is obtained based on the oxygen concentration when the oxide layer is stably generated and accumulated on the cladding surface of the fuel rod.

[0013] The oxygen concentration of the fuel rod in the liquid lead-bismuth alloy without oxide precipitation is obtained, and the upper limit of the initial oxygen concentration range is obtained.

[0014] Preferably, the step of determining whether each preset oxygen concentration meets the usage requirements of the fuel rod based on the physical field parameters corresponding to each preset oxygen concentration includes:

[0015] Determine whether each of the physical field parameters corresponding to the preset oxygen concentration is within its corresponding safety limit;

[0016] If all the physical field parameters are within their corresponding safety limits, the preset oxygen concentration is determined to meet the usage requirements of the fuel rod.

[0017] If one or more of the physical field parameters are not within their corresponding safety limits, it is determined that the preset oxygen concentration does not meet the usage requirements of the fuel rod.

[0018] Preferably, the step of determining a qualified oxygen concentration range based on preset oxygen concentrations that meet the usage requirements of the fuel rod includes:

[0019] Obtain consecutive adjacent preset oxygen concentrations within the initial oxygen concentration range that meet the usage requirements of the fuel rod to obtain a qualified oxygen concentration range; wherein, each oxygen concentration within the qualified oxygen concentration range meets the usage requirements of the fuel rod.

[0020] Preferably, the step of determining a qualified oxygen concentration range based on preset oxygen concentrations that meet the usage requirements of the fuel rod includes:

[0021] Obtain consecutive adjacent preset oxygen concentrations in the initial oxygen concentration range that do not meet the usage requirements of the fuel rod to obtain unqualified oxygen concentration ranges. Remove the unqualified oxygen concentration ranges from the initial oxygen concentration range to obtain qualified oxygen concentration ranges; wherein, each oxygen concentration in the qualified oxygen concentration range meets the usage requirements of the fuel rod.

[0022] Preferably, the step of performing physical field calculations on the fuel rods at each of the preset oxygen concentrations to obtain physical field parameters includes:

[0023] Neutron physics field calculations are performed on the fuel rod at the preset oxygen concentration to obtain neutron physics field parameters; the neutron physics field parameters include radial neutron flux density, axial neutron flux density, nucleon concentration, and volumetric heat release rate.

[0024] Preferably, the step of performing physical field calculations on the fuel rods at each of the preset oxygen concentrations to obtain physical field parameters further includes:

[0025] The temperature field parameters are calculated for the fuel rod at the preset oxygen concentration based on the neutron physics field parameters. The temperature field parameters include the maximum cladding temperature and the core temperature.

[0026] Preferably, the step of performing physical field calculations on the fuel rods at each of the preset oxygen concentrations to obtain physical field parameters further includes:

[0027] The cladding oxidation corrosion of the fuel rod is calculated under the preset oxygen concentration to obtain the cladding oxidation corrosion parameters; the cladding oxidation corrosion parameters include the magnetite layer thickness, the spinel layer thickness, and the cladding corrosion thickness.

[0028] Preferably, the step of performing physical field calculations on the fuel rods at each of the preset oxygen concentrations to obtain physical field parameters further includes:

[0029] The characteristic deformation and strain displacement field of the fuel rod are calculated under the preset oxygen concentration to obtain the contact stress and the geometric parameters of the fuel rod; the geometric parameters of the fuel rod include the inner radius of the pellet, the outer radius of the pellet, the inner radius of the cladding, the outer radius of the cladding, the gap size, and the cladding thickness.

[0030] Preferably, the step of performing physical field calculations on the fuel rods at each of the preset oxygen concentrations to obtain physical field parameters further includes:

[0031] The fission gas behavior of the fuel rod is calculated at the preset oxygen concentration to obtain the fission gas parameters; the fission gas parameters include interstitial gas pressure, intracrystalline bubble concentration, intercrystalline bubble concentration, intracrystalline gas swelling, and intercrystalline gas swelling.

[0032] The beneficial effects of the oxygen concentration range verification method provided in this embodiment of the invention are as follows: Using this oxygen concentration range verification method, a lead-bismuth fast reactor model including fuel rods and liquid lead-bismuth alloy is established. The fuel rods are placed in the liquid lead-bismuth alloy environment. An initial oxygen concentration range of the lead-bismuth fast reactor model is obtained. Multiple preset oxygen concentrations are selected from the initial oxygen concentration range. Physical field calculations are performed on the fuel rods at each preset oxygen concentration to obtain the physical field parameters corresponding to each preset oxygen concentration. Based on the physical field parameters corresponding to each preset oxygen concentration, it is determined whether each preset oxygen concentration meets the usage requirements of the fuel rods. Based on each preset oxygen concentration that meets the usage requirements of the fuel rods, a qualified oxygen concentration range is determined. This invention calculates the physical fields of fuel rods at various preset oxygen concentrations to obtain the parameters of each physical field. It then analyzes the oxygen concentration using a multi-physics approach and determines whether the preset oxygen concentration meets the fuel rod's usage requirements based on the parameters of each physical field. The qualified oxygen concentration range is formed by selecting the preset oxygen concentrations that meet the usage requirements from the initial oxygen concentration range, thus completing the verification of the initial oxygen concentration range. This narrows the initial oxygen concentration range and eliminates oxygen concentrations that do not meet the fuel rod's usage requirements. The qualified oxygen concentration range obtained in this invention meets the fuel rod's usage requirements, avoiding problems such as heat transfer deterioration during fuel rod combustion, inability to suppress corrosion, and inability to meet the long-term usage requirements of the fuel rod.

[0033] Other features and advantages of the embodiments of the present invention will be set forth in the following description, or some features and advantages may be inferred from the description or determined without doubt, or may be learned by practicing the techniques described above in the embodiments of the present invention.

[0034] To make the above-mentioned objects, features and advantages of the present invention more apparent and understandable, preferred embodiments are described below in detail with reference to the accompanying drawings. Attached Figure Description

[0035] To more clearly illustrate the technical solutions in the embodiments of the present invention or the prior art, the drawings used in the description of the embodiments or the prior art will be briefly introduced below. Obviously, the drawings described below are only embodiments of the present invention. For those skilled in the art, other drawings can be obtained based on the provided drawings without creative effort.

[0036] Figure 1 This is a flowchart of an oxygen concentration range verification method provided in an embodiment of the present invention.

[0037] Figure 2 This is a front view of a fuel rod provided in an embodiment of the present invention.

[0038] Figure 3 This is a longitudinal sectional view of a fuel rod provided in an embodiment of the present invention.

[0039] Figure 4 This is a side view of a fuel rod provided in an embodiment of the present invention. Detailed Implementation

[0040] The technical solution of the present invention will now be clearly and completely described 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.

[0041] This invention provides an oxygen concentration range verification method, which can be applied to verify whether the oxygen concentration range of a lead-bismuth fast reactor meets the usage requirements. See below. Figure 1 The flowchart shown illustrates an oxygen concentration range verification method, which includes the following steps:

[0042] S102, Establish a lead-bismuth fast reactor model, obtain the initial oxygen concentration range of the lead-bismuth fast reactor model, and select multiple preset oxygen concentrations from the initial oxygen concentration range;

[0043] The aforementioned lead-bismuth fast reactor model was established by inputting geometric parameters, material parameters, and thermal-hydraulic design parameters into Python software. Structurally, this model includes fuel rods and a liquid lead-bismuth alloy. Specifically, the fuel rods are situated within the liquid lead-bismuth alloy environment, as shown in the example below. Figure 2 The image shows a front view of a fuel rod. The fuel rod has a cylindrical structure, where r represents the radial direction, θ represents the circumferential direction, and z represents the axial direction. See also... Figure 3 The diagram shows a longitudinal sectional view of a fuel rod, which includes a cladding 31, a pellet 32, and a spring 33. The cladding 31 is made of T91 material, and the pellet 32 ​​is made of MOX fuel. There is a certain gap between the outer side of the pellet 32 ​​and the inner side of the cladding 31. The lead-bismuth fast reactor model is coupled together with a cladding corrosion module established by available space modules and molecular dynamics, a fuel rod mechanical analysis solution module established by finite element method, elastoplastic mechanics, and regression mapping methods, a fuel rod temperature field solution module established by finite volume method and heat transfer, and a fuel rod fission gas release module established by molecular dynamics and diffusion theory.

[0044] S104, Perform physical field calculations on the fuel rods at various preset oxygen concentrations to obtain the physical field parameters corresponding to each preset oxygen concentration;

[0045] The above physical field calculations include neutron physical field calculations, temperature field calculations, strain-displacement field calculations, cladding oxidation and corrosion calculations, and fission gas calculations. The physical field parameters include temperature distribution parameters, fuel rod geometric parameters, contact stress, cladding oxidation and corrosion parameters, and fission gas parameters.

[0046] S106, Based on the physical field parameters corresponding to each preset oxygen concentration, determine whether each preset oxygen concentration meets the usage requirements of the fuel rod, and determine the qualified oxygen concentration range based on each preset oxygen concentration that meets the usage requirements of the fuel rod.

[0047] The temperature distribution parameters, geometric parameters, contact stress, cladding oxidation corrosion parameters, and fission gas parameters of the fuel rods calculated under each preset oxygen concentration are compared with their respective safety limits to determine whether the preset oxygen concentration meets the usage requirements of the fuel rods. The preset oxygen concentrations that meet the usage requirements form a qualified oxygen concentration range.

[0048] The oxygen concentration range verification method provided in this embodiment of the invention obtains an initial oxygen concentration range, selects multiple preset oxygen concentrations within the initial oxygen concentration range, calculates the physical fields of the fuel rod at each preset oxygen concentration, obtains the parameters of each physical field, analyzes the oxygen concentration using multiple physical fields, and determines whether the preset oxygen concentration meets the fuel rod's usage requirements based on the parameters of each physical field at each preset oxygen concentration. The preset oxygen concentrations that meet the usage requirements within the initial oxygen concentration range constitute a qualified oxygen concentration range, thus completing the verification of the initial oxygen concentration range. This narrows the initial oxygen concentration range, eliminates oxygen concentrations that do not meet the fuel rod's usage requirements, and ensures that the oxygen concentrations in the obtained qualified oxygen concentration range all meet the fuel rod's usage requirements. This avoids problems such as heat transfer deterioration during fuel rod combustion, inability to suppress corrosion, and inability to meet the long-term usage requirements of the fuel rod.

[0049] In this embodiment of the invention, step S102 includes:

[0050] The lower limit of the initial oxygen concentration range is obtained based on the oxygen concentration when the oxide layer is stably generated and accumulated on the cladding surface of the fuel rod.

[0051] Only when an oxide layer is stably formed and accumulated on the cladding surface of the fuel rods can it be proven that the oxygen concentration has reached the lower limit requirement. If it is below this lower limit, a protective oxide layer cannot be formed on the cladding surface of the fuel rods, and therefore cannot play a role in protecting the fuel rods.

[0052] Obtain the oxygen concentration of the fuel rod in the liquid lead-bismuth alloy when no oxides are precipitated, and obtain the upper limit of the initial oxygen concentration range;

[0053] When oxides precipitate in liquid lead-bismuth alloy, it indicates that the oxygen concentration in the environment where the fuel rod is located is too high. In addition to forming a protective oxide layer on the surface of the fuel rod, oxygen can also cause oxides to precipitate in the liquid lead-bismuth alloy. Therefore, the oxygen concentration at which no oxides precipitate in the liquid lead-bismuth alloy is taken as the upper limit of the oxygen concentration.

[0054] In this embodiment of the invention, step S106 includes:

[0055] Determine whether all physical field parameters corresponding to the preset oxygen concentration are within their corresponding safety limits;

[0056] If all physical field parameters are within their corresponding safety limits, the preset oxygen concentration is determined to meet the fuel rod usage requirements.

[0057] If one or more of the physical field parameters are not within their corresponding safety limits, it is determined that the preset oxygen concentration does not meet the requirements for the use of fuel rods.

[0058] Since the lead-bismuth fast reactor will eventually be used in a nuclear power plant, there are a series of safety indicators for physical field parameters in the nuclear power plant, namely the safety limits of physical field parameters. Only by ensuring that each physical field parameter of the fuel rod is within its corresponding safety limit under the preset oxygen concentration can the stable operation of the fuel rod be guaranteed, proving that the preset oxygen concentration meets the usage requirements. If one or more of the physical field parameters of the fuel are not within their corresponding safety limits under the preset oxygen concentration, it proves that the preset oxygen concentration cannot guarantee the stable operation of the fuel rod and does not meet the usage requirements.

[0059] In this embodiment of the invention, step S106 includes:

[0060] Obtain consecutive adjacent preset oxygen concentrations within the initial oxygen concentration range that meet the usage requirements of the fuel rods to obtain a qualified oxygen concentration range; wherein, each oxygen concentration within the qualified oxygen concentration range meets the usage requirements of the fuel rods.

[0061] Since the qualified oxygen concentration range is continuous within the initial oxygen concentration range, the qualified oxygen concentration range obtained above can be obtained by selecting a preset oxygen concentration that meets the fuel rod usage requirements, and then selecting preset oxygen concentrations from both ends of the preset oxygen concentration to approach the two endpoints of the initial oxygen concentration range. All preset oxygen concentrations in the initial oxygen concentration range that meet the fuel rod usage requirements are combined to form a qualified oxygen concentration range.

[0062] In this embodiment of the invention, step S106 includes:

[0063] Obtain consecutive adjacent preset oxygen concentrations in the initial oxygen concentration range that do not meet the usage requirements of the fuel rods to obtain unqualified oxygen concentration ranges. Remove the unqualified oxygen concentration ranges from the initial oxygen concentration range to obtain qualified oxygen concentration ranges. Among them, each oxygen concentration in the qualified oxygen concentration range meets the usage requirements of the fuel rods.

[0064] Since the acceptable oxygen concentration range is continuous within the initial oxygen concentration range, the unacceptable oxygen concentration range can be obtained by starting from the two endpoints of the initial oxygen concentration range and gradually selecting a preset oxygen concentration point by point towards the middle of the initial oxygen concentration range until the selected preset oxygen concentration meets the fuel rod usage requirements. At this point, the preset oxygen concentrations that do not meet the fuel rod usage requirements constitute the unacceptable oxygen concentration range. By removing the unacceptable oxygen concentration range, the remaining oxygen concentration constitutes the acceptable oxygen concentration range.

[0065] In this embodiment of the invention, step S104 includes:

[0066] S1041, perform neutron physics field calculations on the fuel rods under a preset oxygen concentration to obtain neutron physics field parameters; the neutron physics field parameters include radial neutron flux density, axial neutron flux density, nucleon concentration and volumetric heat release rate.

[0067] Step S1041 above includes: dividing the fuel rod into multiple segments along the axial direction, and calculating the radial neutron flux density segment by segment using a one-dimensional single-group diffusion equation.

[0068]

[0069] Where φ(r) is the neutron flux density at radius r, I and K are the first and second type modified Bessel functions, respectively, and the subscripts 0 and 1 indicate the function order, r fi κ is the inner radius of the core, C is the reciprocal of the neutron diffusion length, and κ is a constant.

[0070] The axial neutron flux density is obtained by multiplying the radial neutron flux density by the axial power factor.

[0071] The nucleon concentration was obtained by calculating the burnup equation.

[0072]

[0073]

[0074]

[0075]

[0076] Where, N j (r) represents the nucleon concentration where the mass number of the radial coordinate r is equal to j, and j is... 235 U、 238 U、 239 Pu、 240 Pu、 241 Pu or 242 The mass number of any of the six nuclides, Pu. Let f(r) be the average concentration of particles with mass number equal to j in the core, f(r) be the distribution function of plutonium, A be a constant coefficient, and σ be the average concentration of plutonium. a,j For the absorption interface of nucleons with mass number equal to j, σ c,j For the total interface of nucleons with mass number equal to j, dB total For fuel consumption depth increment;

[0077] The two-dimensional distribution function of the volumetric heat release rate, based on radial neutron flux density, axial neutron flux density, and nucleon concentration, is as follows:

[0078] q″(z,r)=φ(z)·α∑ j σ f,j N j φ(r),

[0079] Where q″(z,r) is the two-dimensional distribution function of the volumetric heat release rate, α is a constant coefficient, and N j For the nucleon concentration with mass number equal to j, σ f,j Let J be the fission cross section of a nuclide with mass number j, where j is... 235 U、 238 U、 239 Pu、 240 Pu、 241 Pu or 242 The mass number of any of the six nuclides Pu, φ(r) is the neutron flux density at radius r, and φ(z) is the axial neutron flux density at axial height z.

[0080] In this embodiment of the invention, step S104 further includes:

[0081] S1043, based on neutron physics field parameters, calculates the temperature field of the fuel rod under a preset oxygen concentration to obtain temperature field parameters; the temperature field parameters include the maximum cladding temperature and the core temperature of the pellet.

[0082] The above step S1043 includes:

[0083] Using the temperature of the liquid lead-bismuth alloy as the boundary, the heat transfer between the coolant and the cladding surface of the fuel rod is obtained according to the Newton cooling formula.

[0084] Using the temperature of the liquid lead-bismuth alloy as the boundary, the heat transfer coefficient between the coolant and the cladding surface is obtained according to the Dittus-Boelter formula:

[0085]

[0086] Among them, h c,c λ is the heat transfer coefficient between the coolant and the cladding surface. c D is the thermal conductivity of the coolant. eWhere is the hydraulic diameter of the flow channel, Re is the Reynolds number of the coolant, and Pr is the Prandtl number of the coolant;

[0087] Based on the heat transfer coefficient and Newton's cooling formula, the surface temperature of the cladding is:

[0088]

[0089] Among them, T co (z) represents the surface temperature of the cladding at an axial height of z, h c,c T is the heat transfer coefficient between the coolant and the cladding surface, q" (z) is the volumetric heat release rate at an axial height of z, and T coolabt (z) represents the coolant temperature at an axial height of z;

[0090] The thermal conductivity of the cladding was calculated as follows:

[0091] k c = -6.32 × 10 -6 ·T clad (z) 2 +0.011·T clad (z)+25.7,

[0092] Among them, T clad (z) represents the cladding temperature at an axial height of z;

[0093] Considering the additional thermal resistance of the magnetite and spinel layers formed by oxidation and corrosion, the temperature difference between the inner side and the surface of the cladding is calculated using Fourier's law as follows:

[0094]

[0095] Where, ΔT c (z) represents the temperature difference between the inner side and the surface of the shell at an axial height of z, r o r is the outer radius of the shell. i Let k be the inner radius of the shell. c Let q(z) be the thermal conductivity of the cladding, and q(z) be the volumetric heat release rate at axial height z. q(z) is derived from the volumetric heat release rate and the core radius. ΔT mag The additional thermal resistance ΔT is generated by the growth of the magnetite layer. sp Additional thermal resistance resulting from the growth of the spinel layer;

[0096] The inner temperature of the shell at an axial height of z is obtained by adding the surface temperature of the shell at an axial height of z to the temperature difference between the inner side and the surface of the shell at an axial height of z.

[0097] Calculate the average of the inner temperature of the shell at the axial height z and the surface temperature of the shell at the axial height z, and use the average as the shell temperature at the axial height z.

[0098] The highest temperature of the cladding is obtained from the inner temperature of the cladding at an axial height of z and the surface temperature of the cladding at an axial height of z.

[0099] The contact thermal resistance is obtained based on Fourier's law, the convective heat transfer thermal resistance is obtained based on Newton's cooling formula, the thermal radiation thermal resistance is obtained based on Stefan-Boltzmann's law, the gap thermal resistance is obtained based on the contact thermal resistance, convective heat transfer thermal resistance and thermal radiation thermal resistance, and the gap temperature difference is obtained based on the gap thermal resistance and Newton's cooling formula.

[0100] The thermal conductivity, stoichiometric shift, and porosity of the pellet were obtained based on the fuel consumption-corrected Van Uffelen-Schubert correlation:

[0101]

[0102] with A k =A0+A x ·x+A Pu [Pu]and B k =B0+B x x+B Pu [Pu],

[0103]

[0104]

[0105] Where k0 is the thermal conductivity of the unirradiated pellet, T is the pellet temperature, x is the stoichiometric coefficient deviation, O is the oxygen content, M is the metal content, [Pu] is the plutonium content in the MOX fuel, and (1-p) 2.5 For the corrected Leob porosity correction factor, A k B k A0, A x A Pu B0, B x B Pu C, D, and E are correlation coefficients obtained by fitting experimental data of unburned MOX fuel, and k is the correlation coefficient. irr B is the thermal conductivity of MOX fuel considering irradiation effects. total It is the fuel consumption depth GWd / tHM, k inf It is based on the asymptotic thermal conductivity under high fuel consumption, according to two sets of experimental data. φ(r) is the fitting coefficient, p is the porosity, and φ(r) is the neutron flux density at radius r.

[0106] A one-dimensional steady-state differential equation for the thermal conductivity of the core is established, with the core surface temperature and the volumetric heat release rate of the core as boundary conditions. After discretizing the equation, the core temperature is obtained using the TDMA method and the discretized one-dimensional steady-state differential equation for the thermal conductivity of the core:

[0107]

[0108] in, To represent the thermal conductivity at position y of the core block at temperature T after considering the irradiation effect, where S is the control volume surface area. The unit vector is the surface normal vector of the control unit. The term representing the internal heat source generated by fission. Based on the volumetric heat release rate and the control volume, it is obtained Let y be the core temperature at core position y, and V be the volume of the control volume.

[0109] The core temperature is obtained based on the core temperature at position y and the core center radius.

[0110] In this embodiment of the invention, step S104 further includes:

[0111] S1045, calculate the cladding oxidation corrosion of the fuel rods under a preset oxygen concentration to obtain the cladding oxidation corrosion parameters; the cladding oxidation corrosion parameters include the magnetite layer thickness, spinel layer thickness, and cladding corrosion thickness.

[0112] During the corrosion of liquid lead-bismuth alloy (LBE), the cladding forms a double-layered oxide layer on the surface. The outer layer is a loose magnetite layer, mainly composed of Fe3O4, into which LBE can penetrate. The inner layer is a dense spinel layer, mainly composed of Fe. 2.4 Cr 0.6 O4, the spinel layer has a certain barrier effect on LBE, which can play a role in protecting the cladding;

[0113] The oxidation and corrosion of the cladding mainly depends on the oxygen concentration in the LBE. The oxide layer formed after oxidation and corrosion protects the cladding but also becomes a thermal resistance to heat transfer. This includes the additional thermal resistance generated by the growth of the magnetite layer and the additional thermal resistance generated by the growth of the spinel layer. These factors will cause the heat transfer on the cladding surface to deteriorate, thus affecting the temperature field of the fuel rod. Changes in the cladding temperature in the temperature field of the fuel rod will affect the rate of oxidation and corrosion of the cladding.

[0114] The above step S1045 includes:

[0115] Based on the available space model, dissolution corrosion model, and oxygen diffusion kinetics theory proposed by Martinelli et al., an oxidation corrosion model of the cladding in a lead-bismuth fast reactor was established. In the available space model, the resistance of the oxide layer to oxygen diffusion is neglected, assuming that oxygen can diffuse to the oxide-cladding contact surface. Simultaneously, Fe ions in the spinel layer continuously diffuse towards the contact surface between the magnetite and spinel layers, causing the spinel and magnetite layers to grow laterally at their contact surface. Based on this model, the thicknesses of the spinel layer, magnetite layer, and cladding oxidation corrosion thickness were calculated as follows:

[0116]

[0117]

[0118] h cor =a cor ·h Magnetitte +b cor ·h Spinel ,

[0119] Among them, h Spinel h is the thickness of the spinel layer. Magnetite h is the thickness of the magnetite layer. cor The thickness of the cladding due to oxidation and corrosion. This represents the molar concentration of Fe per unit volume in the medium Magnetite. This represents the molar concentration of Fe per unit volume in the medium Spinel. This represents the molar concentration of Fe per unit volume in the medium Steel. This is the oxygen activity coefficient when dissolved oxygen is in equilibrium with the liquid lead-bismuth alloy. K is the oxygen activity coefficient at the interface between the spinel layer and the magnetite layer. I For the iron gap to form an equilibrium constant, K v D is the equilibrium constant for cation vacancy formation. I D is the interstitial diffusion coefficient. v Let a be the vacancy diffusion coefficient. cor and b cor This is the proportionality coefficient;

[0120] In calculating the oxide corrosion thickness of the cladding, the thicknesses of the magnetite and spinel layers can be proportionally adjusted. When calculating the oxide layer thickness, oxygen concentration plays a dominant role, primarily reflected in the oxygen activity coefficient parameter. and In addition, the concentration of Fe in different media is closely related to the concentration of oxygen. The diffusion of oxygen is the main reason for the formation of magnetite and spinel layers. The formation process of oxide layer is the process of oxygen occupying Fe vacancies. This process is accelerated as the oxygen concentration increases.

[0121] In this embodiment of the invention, step S1047 further includes:

[0122] S1047, perform characteristic deformation and strain displacement field calculations on the fuel rods under a preset oxygen concentration to obtain contact stress and fuel rod geometric parameters; fuel rod geometric parameters include inner radius of the pellet, outer radius of the pellet, inner radius of the cladding, outer radius of the cladding, gap size, and cladding thickness.

[0123] The above step S1047 includes:

[0124] Step (1): Calculate the characteristic deformation of the core block to obtain the characteristic deformation parameters of the core block;

[0125] The initial elastic modulus and initial Poisson's ratio of the core were obtained by fitting experimental data from Hirooka and Kato:

[0126] v MOX,0 =0.3192·(1-x)+0.3152·x,

[0127] E MOX,0 =218.74·(1-x)+249.45·x,

[0128] Among them, v MOX,0 E is the initial Poisson's ratio of the core. MOX,0 denoted as the initial elastic modulus of the core, and x as the stoichiometric coefficient offset;

[0129] The initial Poisson's ratio of the core is corrected based on the porosity and stoichiometric coefficient offsets to obtain the corrected Poisson's ratio of the core:

[0130] v MOX =(v MOX,0 -0.0027·p)·(1+x·0.7868),

[0131] Where, ν MOX To determine the Poisson's ratio of the core after taking into account porosity and stoichiometric offset, where p is porosity and x is stoichiometric offset;

[0132] The initial elastic modulus of the core is corrected based on porosity, stoichiometric coefficient shift, and core temperature to obtain the corrected elastic modulus of the core:

[0133]

[0134] Among them, E MOX To account for the elastic modulus of the core after considering porosity, stoichiometric coefficient shift, and temperature, where p is the porosity and x is the stoichiometric coefficient shift, Let y be the core temperature at core position y;

[0135] The thermal expansion of the core block is calculated using a purely empirical formula as follows:

[0136]

[0137]

[0138] Where ΔL / L0 is the thermal expansion, T M This refers to the melting point temperature of the MOX core. This refers to the melting point temperature of uranium dioxide pellets. Let b0, b1, b2, and b3 be the melting point temperature of the plutonium dioxide core, and b0, b1, b2, and b3 be constants. Let y be the core temperature at core position y;

[0139] Since the densification behavior of MOX fuel pellets is similar to that of conventional UO2 pellets, mainly caused by radionuclide migration induced by irradiation, observations of in-pile irradiation experiments show that the densification rate of MOX fuel pellets gradually decreases with increasing burnup, eventually reaching zero at burnup levels of 5 to 10 GWd / MTU. Based on a semi-empirical formula, the densification deformation of MOX fuel pellets is captured as follows:

[0140]

[0141] Where, ΔL d / L0 is the compaction deformation variable, B total For fuel consumption depth;

[0142] The percentage of gap closure caused by core repositioning and the displacement caused by repositioning are calculated using semi-empirical formulas similar to the Oguma model:

[0143]

[0144]

[0145] Where ΔG / G is the percentage of gap closure caused by chip repositioning, P is the local line power, and B is the value of B. local The local burn-out depth is denoted by , and reloc is the displacement caused by relocation.

[0146] During the burnup process of the pellets, a porosity increase occurs at the edges, known as the high-burnup edge. This high-burnup edge region can be distinguished by submicron pellets and high porosity. The thickness and porosity increase of the high-burnup edge were modeled using optical microscopy measurements, resulting in the following formula:

[0147]

[0148]

[0149] Among them, t rim For high fuel consumption edge thickness, B total For burn depth, P rim B represents the increase in porosity at the high-fuel-consumption edge. local This refers to the depth of localized burnout.

[0150] Step (2): Calculate the characteristic deformation of the shell to obtain the characteristic deformation parameters of the shell;

[0151] The elastic modulus of the shell was obtained by fitting experimental data from Krishna as follows:

[0152]

[0153] Among them, E T91 T is the Young's modulus of the T91 shell. clad (z) represents the cladding temperature at an axial height of z;

[0154] Calculate the thermal expansion coefficient of the cladding:

[0155] α T91 = (3.50 × 10 -9 ·T clad (z) 3 -5.77×10 -6 ·T clad (z) 2 +0.0059·T clad (z)+10.33)×10 -6 ;

[0156] Where, α T91 The thermal expansion coefficient of the T91 cladding is T. clad (z) represents the cladding temperature at an axial height of z;

[0157] The creep behavior of the shell is described using the three-stage creep model proposed by Krishna et al., which posits that the material undergoes three stages during the process of increasing stress: instantaneous creep, steady creep, and creep failure.

[0158] To determine the cladding creep stage, if the cladding is in the initial stage where the creep rate rises rapidly due to dislocation increase and work hardening, it is considered the instantaneous creep stage. The instantaneous creep rate of the cladding can be obtained using Norton's power law.

[0159]

[0160] in, σ is the instantaneous creep rate. clad For the equivalent stress of the shell, A T Here, n is a material constant, and n is a stress exponent, whose values ​​represent different creep mechanisms in the material.

[0161] When the shell reaches equilibrium through processes such as dislocation annihilation and rearrangement, it is considered to be in the stable creep stage. The stable creep rate of the shell can be obtained using the modified Bird-Mukherjee-Dorn equation:

[0162]

[0163] in, For the stable creep rate, D is the diffusion coefficient, where b is the Burgers vector, k is the Boltzmann constant, and σ th For threshold stress, σ clad For the equivalent stress of the shell, A T E is a material constant, n is the stress exponent, and its value represents different creep mechanisms in the material. T91 The elastic modulus of the shell;

[0164] When the shell is in a state of rapid creep rate increase due to the formation and growth of cavities, it is in the creep failure stage. The creep failure rate of the shell can be obtained by the modified Monkman-Grant equation:

[0165]

[0166] in, C represents the creep failure rate. MMG To correct the Monkman-Grant constant, t r For the fracture time, ε f To disrupt the strain;

[0167] Based on existing irradiation experimental data, an empirical formula is derived to calculate the irradiation swelling of the casing:

[0168]

[0169] Where, ΔV irr / V0 represents the irradiation swelling dose, D irr This refers to the irradiation dose;

[0170] The fracture stress of the cladding is calculated using the classic critical fracture stress formula from the theory of liquid metal embrittlement:

[0171]

[0172] Where μ is the proportionality coefficient, E T91 γ is the elastic modulus of the shell. p and γ sl These represent the contributions to plastic deformation and solid-liquid interface free energy, respectively, where c is a material-related constant, and σ is the σ-coefficient. c This represents the fracture stress of the cladding.

[0173] Step (3) Calculate the displacement field of the fuel rods to obtain the geometric parameters and contact stress of the fuel rods;

[0174] The strain tensor of the core is obtained based on the modified elastic modulus, modified Poisson's ratio, thermal expansion, densification deformation, and elastoplastic constitutive equation of the core. The strain tensor of the cladding is obtained based on the elastic modulus, thermal expansion coefficient, irradiation swelling, creep rate, and elastoplastic constitutive equation of the cladding.

[0175] The elastoplastic constitutive equation is:

[0176]

[0177] ε ij Let σ be the strain tensor. jj For stress tensor, Let ν be the plastic strain tensor, ν be Poisson's ratio, E be the elastic modulus, and σ be the elastic modulus. kk The diagonal elements of the two-dimensional stress tensor, where α is the coefficient of thermal expansion, t is time, and ∫αdt is the amount of thermal expansion;

[0178] According to the Von Mises equivalent stress formula, the equivalent stress is:

[0179]

[0180] Where, σ e For the equivalent stress, σ θ For circumferential equivalent stress, σ r For radial equivalent stress, σ z This is the axial equivalent stress;

[0181] Determine the magnitude of the equivalent stress and the yield stress of the core. If the equivalent stress is less than the yield stress of the core, use the strain tensor of the core as the output; if the equivalent stress is greater than the yield stress of the core, update the plastic strain tensor increment according to the Prandtl-Reuss flow rule.

[0182]

[0183] Where, σ e For equivalent stress, S ij Let dε be the deviatoric stress tensor. P For the equivalent plastic strain increment, To obtain the increment of the plastic strain tensor, a linear hardening model is established. The yield stress of the core is updated based on the linear hardening model. The strain requirements of the linear hardening model are set. The equivalent stress, the strain tensor of the core, the increment of the strain tensor of the core, and the yield stress of the core are iterated using the regression mapping algorithm and the Newton-Raphson algorithm until the strain state of the core under the equivalent stress meets the strain requirements of the linear hardening model.

[0184] Determine the magnitudes of the equivalent stress and the yield stress of the shell. If the equivalent stress is less than the yield stress of the shell, use the strain tensor of the shell as the output; if the equivalent stress is greater than the yield stress of the shell, update the plastic strain tensor increment according to the Prandtl-Reuss flow rule.

[0185]

[0186] Where, σ e For equivalent stress, S ij Let dε be the deviatoric stress tensor. p For the equivalent plastic strain increment, To determine the increment of the plastic strain tensor, a Ludwik hardening model is established.

[0187]

[0188] Where, ε [l The equivalent plastic strain is given by σ′0, where σ′0 is the yield stress after cladding renewal, σ0 is the current cladding yield stress, n is the hardening exponent, and K is the strengthening coefficient. The relevant parameters σ0, n, and K of the T91 material were obtained by fitting uniaxial tensile test curves at different temperatures.

[0189]

[0190]

[0191]

[0192] in, Let y be the core temperature at core position y.

[0193] The strain requirements of the Ludwik hardening model are set, and the equivalent stress, the strain tensor of the shell, the increment of the strain tensor of the shell, and the yield stress of the shell are iterated using the regression mapping algorithm and the Newton-Raphson algorithm until the strain state of the shell under the equivalent stress meets the strain requirements of the Ludwik hardening model.

[0194] The geometry of the fuel cell and cladding is discretized and modeled using axisymmetric three-node triangular elements. The cladding strain and displacement are solved using finite element analysis and the cladding strain tensor. Similarly, the fuel cell strain and displacement are solved using the same finite element analysis and the fuel cell strain tensor. The existing geometric parameters of the cladding are obtained from the original geometric parameters and displacements of the cladding. The existing geometric parameters of the fuel cell are also obtained from the original geometric parameters and displacements of the fuel cell. The geometric parameters of the cladding include the inner radius, outer radius, and thickness. The geometric parameters of the fuel cell include the inner radius and outer radius. These cladding and fuel cell geometric parameters together constitute the fuel rod's geometric parameters.

[0195] When calculating the geometric parameters of the cladding, due to the influence of oxidation and corrosion, the cladding will undergo different degrees of oxidation and corrosion under different oxygen concentrations. The oxidized and corroded portion of the cladding should be deducted from the initial thickness of the cladding. That is, the initial size of the cladding should be the cladding thickness minus the depth of oxidation and corrosion, and then the deformation of the cladding should be considered.

[0196] h cladding0 =h c0 -h cor ,

[0197] Among them, h cladding0 Considering the initial thickness of the cladding after oxidation and corrosion, h c0 h is the initial thickness of the casing. cor The thickness of the cladding due to oxidation and corrosion;

[0198] The gap size is obtained based on the values ​​of the existing geometric parameters of the shell and the core. The gap size is then corrected based on the percentage of gap closure caused by core repositioning, the displacement caused by repositioning, the roughness of the outer side of the core, and the roughness of the inner side of the shell.

[0199] Determine whether the gap has closed. If the gap has not closed, there is no contact stress. If the gap has closed, establish a preset distance based on the roughness of the outer side of the core and the roughness of the inner side of the cladding. Iterate the contact stress using the test stress and pseudo-interference methods, and establish a contact stress iteration module. Assume that the contact stress between each axial layer in the finite element sub-mesh is zero. When the PCMI effect occurs, iterate and update the contact stress according to the contact stress iteration module. Stop the iteration when the interaction distance between the fuel and the cladding is less than the preset distance, and obtain the final contact stress.

[0200] In this embodiment of the invention, step S104 further includes:

[0201] S1049, Calculate the fission gas behavior of the fuel rod under a preset oxygen concentration to obtain fission gas parameters; the fission gas parameters include interstitial gas pressure, intragranular bubble concentration, intergranular bubble concentration, intragranular gas swelling, and intergranular gas swelling.

[0202] The above step S1049 includes:

[0203] A cross-scale model based on molecular dynamics was established to divide the fission gas into two parts: the intragranular part and the grain boundary part.

[0204] The concentration of intracrystalline bubbles is obtained based on the diffusion equation of intracrystalline fission gas:

[0205]

[0206] The concentration of intergranular bubbles is obtained based on the intergranular fission gas concentration evolution equation:

[0207]

[0208] Where D is the diffusion coefficient of a single molecule, α is the solubility, β is the capture rate, y is the rate of fission gas production, F is the fission rate of the fuel rod, and t is time. The effective diffusion coefficient is given by c1, where c1 is the concentration of monatomic gas, m is the gas concentration in the intracrystalline bubble, and N is the effective diffusion coefficient. gf R is the concentration of intergranular bubbles, R is the amount of fission gas released, r is the radial coordinate, a is a constant coefficient, and N is the number of intergranular bubbles. ig The concentration of bubbles within the crystal is υ, which is a constant coefficient.

[0209] The concentration of intergranular bubbles is obtained based on the evolution equation of intergranular fission gas concentration;

[0210] Construct the ideal gas equation and obtain the interstitial gas pressure P using the ideal gas equation. gas ;

[0211] Based on the fission gas diffusion theory and the concentration of gas molecules and bubbles within the crystal, the intracrystalline gas swelling is obtained as follows:

[0212]

[0213] Where, (ΔV / V) ig For intracrystalline gas swelling, N ig R represents the concentration of bubbles within the crystal. ig The radius of the bubble within the crystal;

[0214] Based on the Pastore model, a fission gas conservation equation is established. Based on this equation, the saturated release of fission gas, and diffusion kinetics, the intergranular gas swelling is derived as follows:

[0215]

[0216] Where, (ΔV / V) gf For intergranular gas swelling, N gf R represents the concentration of intergranular bubbles. gf Let be the radius of the intergranular bubble, and a be a material constant.

[0217] In this embodiment of the invention, the lead-bismuth fast reactor model is coupled with a cladding corrosion module established by available space modules and molecular dynamics, a fuel rod mechanical analysis and solution module established by finite element method, elastoplastic mechanics and regression mapping method, a fuel rod temperature field solution module established by finite volume method and heat transfer, and a fuel rod fission gas release module established by molecular dynamics and diffusion theory. The coupling of each module is achieved through multi-layer iterative loops, and complete information on fuel rod heat transfer performance, mechanical behavior, irradiation behavior and fission gas behavior is obtained. Physical field parameters are obtained and compared with safety limits to determine whether the oxygen concentration meets the fuel rod usage requirements.

[0218] In this embodiment of the invention, see as follows: Figure 4 The image shows a side view of a fuel rod, where r o r is the outer radius of the shell. i Let be the inner radius of the casing, and t be the difference between the outer radius and the inner radius of the casing.

[0219] In this embodiment of the invention, when comparing the various physical field parameters of the fuel rod with their corresponding safety limits, the following steps are taken: determining whether the temperature field parameters of the fuel rod, i.e., the core temperature and the highest temperature of the cladding, are within their corresponding safety limits; determining whether the oxidation and corrosion parameters of the cladding, i.e., the thickness of the magnetite layer, the thickness of the spinel layer, and the corrosion thickness of the cladding, are within their corresponding safety limits; determining whether the geometric parameters of the fuel rod, i.e., the inner radius of the core, the outer radius of the core, the inner radius of the cladding, the outer radius of the cladding, the gap size, and the cladding thickness, are within their corresponding safety limits; determining whether the contact stress is within its corresponding safety limits; and determining whether the fission gas parameters of the fuel rod, i.e., the interstitial gas pressure, the concentration of intracrystalline bubbles, the concentration of intercrystalline bubbles, the intracrystalline gas swelling, and the intercrystalline gas swelling, are within their corresponding safety limits. Only when all parameters are within their safety limits can it be determined that the oxygen concentration meets the requirements for fuel rod use.

[0220] In this embodiment of the invention, unlike existing schemes that analyze oxygen concentration based on material corrosion theory, a multi-physics-based oxygen concentration range verification scheme is proposed. This scheme considers factors from multiple physical fields such as thermodynamics, mechanics, and corrosion kinetics, enabling a more comprehensive evaluation of the long-term operational performance of fuel rods in a lead-bismuth fast reactor under a preset oxygen concentration environment. Considering that the fuel rods will eventually be used in a nuclear power plant, the corrosion theory of the lead-bismuth fast reactor is coupled with fuel behavior by combining actual fuel performance conditions during operation. This provides an oxygen concentration range verification method applicable to practical situations, overcoming the shortcomings of current decoupled analysis theories of cladding corrosion behavior that are not conservative enough, thus ensuring the safe operation of the lead-bismuth fast reactor. Furthermore, when calculating the physical field of the fuel rods, axial segmental calculations are adopted to consider the axial non-uniformity of the fuel rods, providing an important reference for the structural design of the fuel rods and the verification of the oxygen concentration range.

[0221] In the description of this invention, it should be noted that the terms "upper", "lower", "front", "horizontal", etc., indicate the orientation or positional relationship based on the orientation or positional relationship shown in the accompanying drawings. They are only for the convenience of describing this invention and simplifying the description, and do not indicate or imply that the device or element referred to must have a specific orientation, or be constructed and operated in a specific orientation. Therefore, they should not be construed as limitations on this invention.

[0222] In the description of this invention, it should be noted that, unless otherwise explicitly specified and limited, the term "installation" should be interpreted broadly. For example, it can refer to a fixed connection, a detachable connection, or an integral connection; it can refer to a mechanical connection or an electrical connection; it can refer to a direct connection or an indirect connection through an intermediate medium; it can refer to the internal connection of two components. Those skilled in the art can understand the specific meaning of the above terms in this invention based on the specific circumstances.

[0223] Finally, it should be noted that the above embodiments are only used to illustrate the technical solutions of the present invention, and not to limit them; although the present invention has been described in detail with reference to the foregoing embodiments, those skilled in the art should understand that modifications can still be made to the technical solutions described in the foregoing embodiments, or equivalent substitutions can be made to some or all of the technical features; and these modifications or substitutions do not cause the essence of the corresponding technical solutions to deviate from the scope of the technical solutions of the embodiments of the present invention.

Claims

1. A method for verifying oxygen concentration ranges, characterized in that, The oxygen concentration range verification method includes the following steps: A lead-bismuth fast reactor model is established, and an initial oxygen concentration range of the lead-bismuth fast reactor model is obtained. Multiple preset oxygen concentrations are selected from the initial oxygen concentration range. The lead-bismuth fast reactor model includes fuel rods and liquid lead-bismuth alloy, and the fuel rods include pellets and cladding. Physical field calculations are performed on the fuel rods at each of the preset oxygen concentrations to obtain the physical field parameters corresponding to each preset oxygen concentration; wherein, the physical field parameters include temperature distribution parameters, fuel rod geometric parameters, contact stress, cladding oxidation and corrosion parameters, and fission gas parameters; Based on the physical field parameters corresponding to each preset oxygen concentration, it is determined whether each preset oxygen concentration meets the usage requirements of the fuel rod, and a qualified oxygen concentration range is determined based on each preset oxygen concentration that meets the usage requirements of the fuel rod. The step of performing physical field calculations on the fuel rods at each of the preset oxygen concentrations to obtain physical field parameters includes: Neutron physics field calculations are performed on the fuel rod at the preset oxygen concentration to obtain neutron physics field parameters; the neutron physics field parameters include radial neutron flux density, axial neutron flux density, nucleon concentration, and volumetric heat release rate; The fuel rod was divided into multiple segments along the axial direction, and the radial neutron flux density was calculated segment by segment using a one-dimensional single-group diffusion equation. ， in, Let be the neutron flux density at radius r, and let I and K be the modified Bessel functions of the first and second kind, respectively. Subscripts 0 and 1 indicate the order of the functions. The inner radius of the core is... The neutron diffusion length is the reciprocal of the neutron diffusion length, and C is a constant. The axial neutron flux density is obtained by multiplying the radial neutron flux density by the axial power factor. The nucleon concentration was calculated using the burnup equation. ， in, Let r be the mass number of nucleons equal to j, where j is the mass number of any of the six nuclides: 235U, 238U, 239Pu, 240Pu, 241Pu, or 242Pu. Let f(r) be the average concentration of particles with mass number equal to j in the core, f(r) be the distribution function of plutonium, and A be a constant coefficient. For the absorption interface of nucleons with mass number j, For the total interface of nucleons with mass number j, For fuel consumption depth increment; The two-dimensional distribution function of the volumetric heat release rate, based on radial neutron flux density, axial neutron flux density, and nucleon concentration, is as follows: ， in, Let be the two-dimensional distribution function of the volumetric heat release rate. The constant coefficient, For the nucleon concentration with a mass number equal to j, Let be the fission cross section of a nuclide with mass number j, where j is the mass number of any of the six nuclides: 235U, 238U, 239Pu, 240Pu, 241Pu, or 242Pu. (r) represents the neutron flux density at radius r. Let z be the axial neutron flux density at an axial height of z.

2. The oxygen concentration range verification method according to claim 1, characterized in that, The step of obtaining the initial oxygen concentration range of the lead-bismuth fast reactor model includes: The lower limit of the initial oxygen concentration range is obtained based on the oxygen concentration when the oxide layer is stably generated and accumulated on the cladding surface of the fuel rod. The oxygen concentration of the fuel rod in the liquid lead-bismuth alloy without oxide precipitation is obtained, and the upper limit of the initial oxygen concentration range is obtained.

3. The oxygen concentration range verification method according to claim 1, characterized in that, The step of determining whether each preset oxygen concentration meets the usage requirements of the fuel rod based on the physical field parameters corresponding to each preset oxygen concentration includes: Determine whether each of the physical field parameters corresponding to the preset oxygen concentration is within its corresponding safety limit; If all the physical field parameters are within their corresponding safety limits, the preset oxygen concentration is determined to meet the usage requirements of the fuel rod. If one or more of the physical field parameters are not within their corresponding safety limits, it is determined that the preset oxygen concentration does not meet the usage requirements of the fuel rod.

4. The oxygen concentration range verification method according to claim 1, characterized in that, The step of determining a qualified oxygen concentration range based on preset oxygen concentrations that meet the usage requirements of the fuel rods includes: Obtain consecutive adjacent preset oxygen concentrations within the initial oxygen concentration range that meet the usage requirements of the fuel rod to obtain a qualified oxygen concentration range; wherein, each oxygen concentration within the qualified oxygen concentration range meets the usage requirements of the fuel rod.

5. The oxygen concentration range verification method according to claim 1, characterized in that, The step of determining a qualified oxygen concentration range based on preset oxygen concentrations that meet the usage requirements of the fuel rods includes: Obtain consecutive adjacent preset oxygen concentrations in the initial oxygen concentration range that do not meet the usage requirements of the fuel rod to obtain unqualified oxygen concentration ranges. Remove the unqualified oxygen concentration ranges from the initial oxygen concentration range to obtain qualified oxygen concentration ranges; wherein, each oxygen concentration in the qualified oxygen concentration range meets the usage requirements of the fuel rod.

6. The oxygen concentration range verification method according to claim 1, characterized in that, Also includes: Based on the neutron physics field parameters, the temperature field of the fuel rod is calculated at the preset oxygen concentration to obtain the temperature field parameters. The temperature field parameters include the maximum cladding temperature and the core center temperature.

7. The oxygen concentration range verification method according to claim 6, characterized in that, Also includes: The oxidation corrosion of the fuel rod under the preset oxygen concentration is calculated to obtain the oxidation corrosion parameters of the fuel rod. The cladding oxidation corrosion parameters include the magnetite layer thickness, spinel layer thickness, and cladding corrosion thickness.

8. The oxygen concentration range verification method according to claim 7, characterized in that, Also includes: The characteristic deformation and strain displacement field of the fuel rod are calculated under the preset oxygen concentration to obtain the contact stress and the geometric parameters of the fuel rod; the geometric parameters of the fuel rod include the inner radius of the pellet, the outer radius of the pellet, the inner radius of the cladding, the outer radius of the cladding, the gap size, and the cladding thickness.

9. The oxygen concentration range verification method according to claim 8, characterized in that, Also includes: The fission gas behavior of the fuel rod is calculated at the preset oxygen concentration to obtain the fission gas parameters; the fission gas parameters include interstitial gas pressure, intracrystalline bubble concentration, intercrystalline bubble concentration, intracrystalline gas swelling, and intercrystalline gas swelling.

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