A method and apparatus for predicting fuel rod cladding behavior under axial power shift

Abstract

This invention provides a method and apparatus for predicting fuel rod cladding behavior under axial power offset. The method includes: performing neutron physics calculations on the fuel rod to determine the axial power distribution at the current time step; determining the axial power offset at the current time step based on the axial power distribution at the current time step and the initial axial power distribution of the fuel rod; performing heat transfer calculations on the fuel rod cladding based on the axial power distribution to obtain the temperature field distribution of the fuel rod cladding under the influence of the axial power offset; wherein the temperature field distribution includes the temperature on the outer side of the cladding and the temperature on the inner side of the cladding; and performing elastoplastic deformation calculations on the cladding based on the temperature field distribution under the influence of the axial power offset to obtain the deformation of the cladding under the influence of the axial power offset. This invention improves the evaluation of fuel rod cladding performance, enhances the completeness of cladding behavior prediction, and improves the safety attributes of the fuel rod cladding.

Description

Technical Field

[0001] This invention relates to the field of nuclear reactor technology, and in particular to a method and apparatus for predicting fuel rod cladding behavior under axial power offset. Background Technology

[0002] The integrity of the reactor fuel rod cladding is crucial to nuclear safety. Fuel rod cladding is a sealed, corrosion-resistant outer layer used to enclose nuclear fuel, prevent the leakage of radioactive materials, and ensure stable reactor operation. The fuel rod cladding is the first line of defense against radioactive materials. If the cladding is damaged, radioactive materials may leak into the surrounding environment, posing potential hazards to humans and ecosystems. Maintaining the integrity of the cladding is key to ensuring radiation protection. If the cladding is damaged, nuclear fuel may come into unintended contact with the coolant, leading to reactor runaway, overheating, increased steam pressure, and even a nuclear accident.

[0003] Axial power shift during fuel rod operation is a common phenomenon in nuclear reactors. Over time, the nuclear fuel in the fuel rods undergoes fission reactions, and some of the nuclear fuel is burned off. Due to uneven burning of the nuclear fuel, there may be differences in nuclear fuel content between the upper and lower parts of the fuel rod, leading to axial power shift. Furthermore, with increasing service life, fuel rods may be affected by radiation damage and thermal stress, resulting in changes in their structure and material properties. These changes may affect the thermal conductivity and reactivity of the fuel, causing axial power shift. Axial power shift can have a series of negative impacts on the stable operation of a nuclear reactor, therefore, it requires careful monitoring and control during design and operation. Taking appropriate adjustment measures, such as controlling rod movement and adjusting coolant flow rates, can help maintain the stability of the fuel rod power distribution, ensuring the safe and efficient operation of the nuclear reactor.

[0004] Power axial offset refers to the uneven power distribution across different axial locations within a reactor, and this unevenness can have a series of significant impacts on reactor operation. Considering power axial offset in fuel performance programs is of great value because it directly relates to the safety, performance, and efficiency of a nuclear reactor. Furthermore, considering power axial offset is crucial for optimizing fuel lifetime and improving reactor efficiency. By understanding the power distribution in different areas, nuclear fuel usage can be better managed, fuel cycles can be extended to maximize their length, fuel replacement frequency reduced, and reactor economics improved.

[0005] However, existing cladding behavior prediction techniques are usually implemented through fuel performance programs, focusing on aspects such as fuel pellets, cladding gaps, mechanical deformation, temperature field distribution, and fission gas pressure. These techniques introduce numerous assumptions and simplify many models for neutron physics calculations, making it impossible to accurately reproduce the axial power distribution in neutron physics. Consequently, the cladding behavior prediction is incomplete, reducing the safety properties of the cladding. Summary of the Invention

[0006] In view of this, the purpose of the present invention is to provide a method and apparatus for predicting fuel rod cladding behavior under axial power offset, which improves the evaluation of fuel rod cladding performance, enhances the completeness of cladding behavior prediction, and improves the safety properties of fuel rod cladding. It is of great value for protecting the integrity of fuel rods, preventing the leakage of radioactive materials, and ensuring reactor safety.

[0007] To achieve the above objectives, the technical solutions adopted in the embodiments of the present invention are as follows:

[0008] In a first aspect, embodiments of the present invention provide a method for predicting fuel rod cladding behavior under axial power offset, comprising:

[0009] Neutron physics calculations are performed on the fuel rods to determine the axial power distribution at the current time step, and the axial power offset at the current time step is determined based on the axial power distribution at the current time step and the initial axial power distribution of the fuel rods.

[0010] Based on the axial power distribution, heat transfer calculations are performed on the fuel rod cladding to obtain the temperature field distribution of the fuel rod cladding under the influence of the axial power offset; wherein, the temperature field distribution includes the temperature on the outer side of the cladding and the temperature on the inner side of the cladding;

[0011] Based on the temperature field distribution under the influence of the axial power offset, the elastoplastic deformation of the shell is calculated to obtain the deformation of the shell under the influence of the axial power offset.

[0012] Furthermore, this embodiment of the invention provides a first possible implementation of the first aspect, wherein the step of performing neutron physics calculations on the fuel rods to determine the axial power distribution at the current time step includes:

[0013] Calculate the axial neutron flux density of the fuel rod, and calculate the nuclide concentration at each axial position based on the axial neutron flux density and the nuclide transformation and decay process of the fuel rod material in the irradiation environment;

[0014] The power at each axial position at the current time step is calculated based on the axial neutron flux density and the nuclide concentration at each axial position, thus obtaining the axial power distribution.

[0015] Furthermore, this embodiment of the invention provides a second possible implementation of the first aspect, wherein the step of calculating the nuclide concentration at each axial position based on the axial neutron flux density and the nuclide transformation and decay process of the fuel rod material in the irradiation environment includes:

[0016] Based on the axial neutron flux density and the nuclide transformation and decay process of the fuel rod material in the irradiation environment, a nuclide burnup process equation is constructed, and the nuclide concentration at each axial position is obtained by solving the nuclide burnup process equation based on numerical integration.

[0017] Furthermore, this embodiment of the invention provides a third possible implementation of the first aspect, wherein the step of performing heat transfer calculations on the fuel rod cladding based on the axial power distribution to obtain the temperature field distribution of the fuel rod cladding under the influence of the axial power offset includes:

[0018] Obtain the thickness of the oxide layer and the dirt layer at the current time step;

[0019] The temperature drop of the cladding oxide layer is determined based on the oxide layer thickness and the axial power distribution, and the temperature drop of the fouling layer is determined based on the fouling layer thickness and the axial power distribution.

[0020] The outer temperature of the cladding under the influence of the axial power offset is determined based on the temperature drop of the oxide layer and the temperature drop of the dirt layer. The inner temperature of the cladding under the influence of the axial power offset is determined based on the outer temperature of the cladding and the axial heat flux density distribution.

[0021] Furthermore, this embodiment of the invention provides a fourth possible implementation of the first aspect, wherein the step of performing elastoplastic deformation calculation on the shell based on the temperature field distribution under the influence of the axial power offset to obtain the deformation of the shell under the influence of the axial power offset includes:

[0022] The characteristic deformation of the shell is determined based on the temperature on the outer side and the temperature on the inner side of the shell; wherein, the characteristic deformation includes the creep and thermal strain of the shell;

[0023] Based on the creep and thermal strain of the shell, an elastoplastic constitutive equation for the shell is constructed. The stress and strain of the shell under the influence of the axial power offset are calculated by solving the elastoplastic constitutive equation using the finite element method.

[0024] Furthermore, the embodiments of the present invention provide a fifth possible implementation of the first aspect, which further includes:

[0025] Elastoplastic mechanical analysis was performed on the core and the shell until the interaction distance between the core and the shell was less than a preset error distance, and the contact stress on the inner side of the shell was obtained.

[0026] The interstitial gas pressure inside the shell is determined based on the diffusion process of the fission gas and the amount of fission gas released.

[0027] The contact stress and the interstitial gas pressure are used as the boundary conditions of the elastoplastic constitutive equation.

[0028] Furthermore, this embodiment of the invention provides a sixth possible implementation of the first aspect, wherein the calculation formula for the axial power distribution is:

[0029]

[0030] Where P(z) is the power at the axial direction z, α is the conversion constant, and σ f,j For the fission cross section of nuclide j, N j (z) represents the nuclide concentration of nuclide j at the axial position z, and φ(r,z) represents the neutron flux density at the axial position r and the radial position z.

[0031] Furthermore, this embodiment of the invention provides a seventh possible implementation of the first aspect, wherein the formula for calculating the temperature on the outer side of the casing is:

[0032] T co =T coolant +ΔT ox +ΔT cRUD

[0033] Among them, T co T represents the temperature of the outer side of the casing. coolant ΔT represents the coolant temperature. ox The temperature drop of the oxide layer, ΔT CRUD This refers to the temperature drop of the dirt layer.

[0034] Furthermore, this embodiment of the invention provides an eighth possible implementation of the first aspect, wherein the formula for calculating the temperature inside the casing is:

[0035]

[0036] Among them, T ci T represents the temperature inside the casing. co The temperature of the outer side of the casing is given by P(z), the axial power at the z-axis is given by H, and t is given by t. c k is the shell thickness. c The thermal conductivity is that of the cladding.

[0037] Secondly, embodiments of the present invention also provide a fuel rod cladding behavior prediction device under axial power offset, comprising:

[0038] The first calculation module is used to perform neutron physics calculations on the fuel rod to determine the axial power distribution at the current time step, and to determine the axial power offset at the current time step based on the axial power distribution at the current time step and the initial axial power distribution of the fuel rod.

[0039] The second calculation module is used to perform heat transfer calculations on the fuel rod cladding based on the axial power distribution to obtain the temperature field distribution of the fuel rod cladding under the influence of the axial power offset; wherein, the temperature field distribution includes the temperature on the outer side of the cladding and the temperature on the inner side of the cladding.

[0040] The third calculation module is used to perform elastoplastic deformation calculation on the shell based on the temperature field distribution under the influence of the axial power offset, so as to obtain the axial distribution of the shell deformation under the influence of the axial power offset.

[0041] This invention provides a method and apparatus for predicting fuel rod cladding behavior under axial power offset. The method includes: performing neutron physics calculations on the fuel rod to determine the axial power distribution at the current time step; determining the axial power offset at the current time step based on the axial power distribution at the current time step and the initial axial power distribution of the fuel rod; performing heat transfer calculations on the fuel rod cladding based on the axial power distribution to obtain the temperature field distribution of the fuel rod cladding under the influence of the axial power offset; wherein the temperature field distribution includes the temperature on the outer side of the cladding and the temperature on the inner side of the cladding; and performing elastoplastic deformation calculations on the cladding based on the temperature field distribution under the influence of the axial power offset to obtain the deformation of the cladding under the influence of the axial power offset. This invention calculates the axial power distribution of fuel rods through neutron physics analysis during fuel rod use, enabling prediction of axial power offset at different time steps. It determines the axial heat flux density distribution based on the axial power distribution, performs heat transfer calculations on the fuel rods based on the axial heat flux density distribution, and determines the axial distribution of cladding deformation under the influence of axial power offset based on the temperature field distribution. This allows for prediction of the cladding temperature field distribution and cladding deformation under different axial power offset levels, thus improving the evaluation of fuel rod cladding performance, enhancing the completeness of cladding behavior prediction, and improving the safety attributes of the fuel rod cladding. This is of significant value for protecting the integrity of fuel rods, preventing radioactive material leakage, and ensuring reactor safety.

[0042] 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.

[0043] 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

[0044] To more clearly illustrate the specific embodiments of the present invention or the technical solutions in the prior art, the drawings used in the description of the specific embodiments or the prior art will be briefly introduced below. Obviously, the drawings described below are some embodiments of the present invention. For those skilled in the art, other drawings can be obtained from these drawings without creative effort.

[0045] Figure 1 A flowchart of a fuel rod cladding behavior prediction method under axial power offset provided by an embodiment of the present invention is shown;

[0046] Figure 2 This invention provides a diagram showing the relationship between different axial power offsets and the cladding thickness and gap gas pressure.

[0047] Figure 3 This invention provides a diagram showing the influence of different axial power offsets on oxide layer thickness and gap size.

[0048] Figure 4 A schematic diagram of a fuel rod cladding behavior prediction device under axial power offset provided in an embodiment of the present invention is shown. Detailed Implementation

[0049] To make the objectives, technical solutions, and advantages of the embodiments of the present invention clearer, the technical solutions of the present invention will be described below in conjunction with the accompanying drawings. Obviously, the described embodiments are some embodiments of the present invention, but not all embodiments.

[0050] Currently, cladding behavior prediction is typically achieved through fuel performance programs. The calculation of fuel performance focuses on aspects such as fuel pellets, cladding and gaps, mechanical deformation, temperature field distribution, and fission gas pressure. Since neutron physics is not a key component of fuel performance, numerous assumptions are introduced into neutron physics calculations. Current nuclear fuel performance programs significantly simplify the neutron physics portion, potentially presenting limitations and challenges in capturing axial power shifts. Because axial power shift calculations require neutron physics calculations, and current mainstream neutron physics programs have high computational complexity, time constraints lead fuel performance programs to opt for simpler neutron physics calculations. While typical fuel performance programs improve running speed by significantly simplifying the burnup chain, they also lose crucial axial power shift information, failing to accurately reconstruct the burnup and power distribution in neutron physics, and unable to capture the shift in axial power caused by changes in burnup.

[0051] To address the aforementioned issues, this invention provides a method and apparatus for predicting fuel rod cladding behavior under axial power offset. The following provides a detailed description of the embodiments of this invention.

[0052] This embodiment provides a method for predicting fuel rod cladding behavior under axial power offset. This method can be applied to electronic devices such as computers. See [link to documentation]. Figure 1 The flowchart shown illustrates a method for predicting fuel rod cladding behavior under axial power offset. This method mainly includes the following steps:

[0053] Step S102: Perform neutron physics calculations on the fuel rods to determine the axial power distribution at the current time step, and determine the axial power offset at the current time step based on the axial power distribution at the current time step and the initial axial power distribution of the fuel rods.

[0054] Neutron physics calculations are performed on the fuel rods to determine the neutron flux distribution. Based on this distribution, the variation of nuclide content at different axial positions at the current time step is calculated. Then, based on this variation, the axial power distribution at each axial position at the current time step is calculated. To obtain the axial power offset, the initial axial power distribution set at the start of fuel rod use is used as a reference. The relative offset between the current time step axial power and the initial axial power is calculated for each node and denoted as the axial power offset (also called the relative axial power offset).

[0055] Step S104: Perform heat transfer calculation on the fuel rod cladding based on the axial power distribution to obtain the temperature field distribution of the fuel rod cladding under the influence of the axial power offset; wherein, the temperature field distribution includes the temperature on the outside of the cladding and the temperature on the inside of the cladding.

[0056] Based on the heat transfer principles of fuel rod cladding, the temperature field distribution of the fuel rod cladding under the influence of axial power offset is obtained by solving Newton's cooling formula and Fourier's law of thermal conductivity. The temperature field can also be calculated in segments along the axial direction. Due to the influence of axial power offset, the axial distribution of heat flux density will also change, thus affecting the temperature distribution of the cladding. The temperature distribution model of the cladding can be calculated based on Fourier's law and Newton's law of cooling.

[0057] Step S106: Based on the temperature field distribution under the influence of axial power offset, perform elastoplastic deformation calculation on the shell to obtain the deformation of the shell under the influence of axial power offset.

[0058] Since the mechanical deformation of the shell is greatly affected by temperature, the axial power shift will cause changes in the axial distribution of the shell deformation. The shell deformation is solved based on the temperature field distribution under the influence of the axial power shift, yielding the shell deformation amount under the influence of the axial power shift. The aforementioned shell deformation can include characteristic deformation, stress, and strain. The mechanical calculation of shell deformation consists of two parts: characteristic deformation calculation and constitutive equation solution. Characteristic deformations of the shell, such as creep and thermal strain, which are difficult to characterize through constitutive equations, can be calculated using empirical relationships. The characteristic deformation is substituted into the elastoplastic constitutive equation as an additional plastic deformation for calculation. The elastoplastic constitutive equation is solved using the finite element method, back mapping, and Newton-Raphson iteration method to obtain the stress and strain of the shell.

[0059] The fuel rod cladding behavior prediction method provided in this embodiment predicts the axial power offset at different time steps by performing neutron physics analysis to calculate the axial power distribution of the fuel rod during its use. It determines the axial heat flux density distribution based on the axial power distribution, performs heat transfer calculations on the fuel rod based on the axial heat flux density distribution, and determines the axial distribution of cladding deformation under the influence of the axial power offset based on the temperature field distribution. This allows for the prediction of the cladding temperature field distribution and cladding deformation under different axial power offset levels, thus improving the evaluation of fuel rod cladding performance, enhancing the completeness of cladding behavior prediction, and improving the safety attributes of the fuel rod cladding. This method is of great value for protecting the integrity of the fuel rod, preventing the leakage of radioactive materials, and ensuring reactor safety.

[0060] In one embodiment, this embodiment provides an implementation method for determining the axial power distribution of the fuel rod at the current time step by performing neutron physics calculations. The specific steps are as follows:

[0061] Step (1): Calculate the axial neutron flux density of the fuel rod, and calculate the nuclide concentration at each axial position based on the axial neutron flux density and the nuclide transformation and decay process of the fuel rod material in the irradiation environment;

[0062] Since the fuel rod pellets are cylindrical or toroidal, their circumferential neutron flux distribution can be approximated as uniform. The axial neutron flux distribution is controlled by the axial power factor, using the cos(z) distribution by default. The radial neutron flux distribution is obtained by solving the one-dimensional diffusion theory of a single group. The formula for calculating the axial neutron flux density is:

[0063] φ(r, z)=CJ0(B r r)cos(B z z) (1)

[0064] Where φ(r, z) is the neutron flux density along the axial direction r and radial direction z, C is the normalized power conversion constant, and B r B is the radial geometric curvature. z Let J0 be the axial geometric curvature, and J0 be a first-order 0th-order Bessel function.

[0065] In one specific implementation, a nuclide burnup process equation is constructed based on the axial neutron flux density and the nuclide transformation and decay process of the fuel rod material in the irradiation environment. The nuclide concentration at each axial position is obtained by solving the nuclide burnup process equation by numerical integration.

[0066] Nuclide concentration (also known as nuclide density) is calculated for a specific axial node. A burnup equation for the nuclide is constructed, and the path of nuclear reaction conversion between different nuclides is modeled. The constructed burnup equation is solved by numerical integration to obtain the nuclide concentration at different axial positions.

[0067] When materials in a system are irradiated for an extended period, the nuclides within them will undergo transformations due to nuclear reactions and spontaneous radioactive decay. The time-dependent process of nuclide transformation under irradiation is called depletion or burnout. To accurately analyze nuclear systems, it is typically necessary to predict changes in the material composition. These changes lead to corresponding changes in the solutions to the transport equations. The burnout equation describing nuclide transformation and decay in an irradiated environment can be expressed as:

[0068]

[0069] Where, N j (t) represents the concentration of nuclide j at time t, N k (t) represents the concentration of nuclide k at time t, σ j (E, t) represents the transition cross section of nuclide j with energy E at time t, σ k (E, t) represents the transition cross section of nuclide k with energy E at time t, fj→k λ represents the fraction of the transformation reaction in nuclide j that produces nuclide k. j→k It is the decay constant of the decay mode in nuclide j that produces nuclide k.

[0070] In the above formula (2), nuclide N j The rate of change equals the production rate minus the loss rate. Since the burnup equation for nuclide j depends on the nuclide densities of many other nuclides, a set of first-order differential equations can be obtained. To formulate a suitable initial value problem, it is also necessary to determine the nuclide density at time 0:

[0071] N j (0)=N j，0 (3)

[0072] It can be represented more compactly as a matrix:

[0073]

[0074] Where N is the nuclide concentration vector, A(N,t) is the burnup matrix containing decay and transformation coefficients, and N0 is the initial density vector. The burnup matrix depends on N because the solution to the transport equation depends on the nuclide concentration.

[0075] The fuel consumption equation in formula (2) above is solved using numerical integration. The overall time interval is divided into smaller time steps. Within each time step, it is assumed that the fuel consumption matrix is ​​constant, and let t∈[t i , t i +h] is the i-th time step. Within the i-th time step, the solution of the above formula (2) can be written in the analytical form of matrix exponents as:

[0076] A i =A(N) i , t i (5)

[0077]

[0078] Where h is the time step (also called the time increment), and N i =N(t) i It can be calculated using a prediction-correction method, which uses multiple stages to provide higher accuracy than prediction methods. The simplest method is the CE / CM algorithm:

[0079]

[0080]

[0081] The N value at the midpoint is estimated using A, which is evaluated at the beginning of the time step. A is evaluated using the density at the midpoint and used for the integral over the entire time step.

[0082] The matrix exponents in formulas (6) to (8) above need to be calculated. These can be calculated using the incomplete part (IPF) form of the Chebyshev rational approximation method (CRAM), which offers a good balance between numerical stability and efficiency. The matrix exponents are approximately:

[0083]

[0084] In formula (9), k is the approximate order of the matrix exponent, with a maximum order of 48, α0, and θ l The coefficients are calculated using approximation, h is the time step, l is the imaginary unit with a value of 1 to k / 2, and Re is the function's real part operation.

[0085] The aforementioned nuclides may be any one or more of U235, U238, Pu239, Pu240, and Pu241, and the aforementioned transformation reaction may be any one of fission, (n, γ), (n, 2n), (n, 3n), (n, 4n), (n, p), and (n, α).

[0086] When solving the burnup equation using the rational approximation method described above, it is only necessary to construct the burnup matrix at different times and solve a set of sparse linear systems. However, constructing the burnup matrix itself involves not only solving transport equations to estimate the transformation reaction rate (in the case of transport coupling) or obtaining microscopic cross sections (in the case of transport independence), but also a series of choices regarding the included data. The burnup matrix is ​​constructed based on data from a depletion chain file, which includes a database of ENDF transient neutrons, decay products, and fission products. For each nuclide, the file includes:

[0087] 1. Possible transformation reactions, their Q values, and their products;

[0088] 2. If a nuclide is not stable, its possible decay modes, their branching ratios, and their products;

[0089] 3. If a nuclide is fissile, the yield of fission products at any number of incident neutron energies.

[0090] The aforementioned fission cross section is related to the fission product yield (FPY), which is generally also related to energy. The ENDF fission product yield sublime typically includes yields at 2 or 3 energies, calculates the average energy at which the fission event occurred, and uses linear interpolation to calculate the effective FPY using the FPY provided at adjacent energies.

[0091] Step (2): Calculate the power at each axial position at the current time step based on the axial neutron flux density and the nuclide concentration at each axial position, and obtain the axial power distribution.

[0092] The axial neutron flux density and nuclide concentration at each axial position are used to calculate the power at each axial position at the current time step. The formula for calculating the axial power distribution is as follows:

[0093] P(z)=α∑ j σ f，j N j (z)φ(r,z) (10)

[0094] Where P(z) is the power at the axial direction z, α is the conversion constant, and σ f，j For the fission cross section of nuclide j, N j (z) represents the nuclide concentration of nuclide j at the axial position z, and φ(r, z) represents the neutron flux density at the axial position r and the radial position z.

[0095] Existing fuel rod neutron physics calculations also require solving the burnup equation. However, existing fuel rod neutron physics calculations typically simplify the burnup chain significantly, retaining only some key nuclides and related reactions. The axial power distribution does not change during the calculation process, and the changes in axial power distribution cannot be captured when calculating nuclide concentrations.

[0096] The axial power distribution calculation method provided in this embodiment is based on the nuclide concentration at each axial position. When calculating the burnout chain, it considers most of the key reactions of fissile and easily fissile nuclides and performs a fine numerical solution through a prediction and correction method. This method can obtain the axial power change under different burnout conditions and accurately reflect the change in axial power distribution.

[0097] In one embodiment, this embodiment provides an implementation method for calculating the heat transfer of the fuel rod cladding based on the axial power distribution to obtain the temperature field distribution of the fuel rod cladding under the influence of the axial power offset. The specific steps are as follows:

[0098] Step 1): Obtain the thickness of the oxide layer and the dirt layer at the current time step;

[0099] Axial power deviation affects the oxidation and corrosion of the cladding, leading to oxide layer redistribution and deterioration of surface heat transfer that deviates from expectations. To accurately estimate the oxidation and corrosion rate and obtain the correct oxide layer thickness, a two-stage semi-empirical model, EPRI / KWU / CE, is used to calculate the corrosion of the cladding. The oxide growth rate equation differs before and after reaching the transition oxide thickness. The thickness of the transition oxide is calculated using the following formula:

[0100]

[0101] Among them, S trans T represents the thickness of the oxide coating, Q3 represents the activation energy of the corrosion reaction, and T represents the thickness of the oxide coating. om Let be the interface temperature between the oxide layer and the cladding, R be the ideal gas constant, and D3 and E3 be material constants. Before reaching the transition thickness, the oxidation corrosion rate follows a cubic root relationship, gradually slowing down as oxidation corrosion progresses. After reaching the transition thickness, the oxidation corrosion kinetics become linear, and the oxidation corrosion rate increases significantly.

[0102] The deposition process of the fouling layer (i.e., the CRUD layer) can be modeled using a three-node model, in which the nuclear reactor is divided into three regions: the core, the coolant, and the steam generator (S / G). The CRUD is formed by the deposition of corrosion products in the core, primarily composed of nickel and iron oxides or nickel-cobalt-iron oxides, with the stoichiometric coefficient of nickel or the sum of nickel and cobalt ranging from 0.45 to 0.75. The solubility of corrosion products at different temperatures is calculated using the chemical dissociation reaction of the corrosion products and the saturation concentration of iron ions. The mass transfer coefficient is calculated using a heat transfer analogy method, and the deposition thickness of the corrosion products in the core, i.e., the thickness of the CRUD layer, is determined through the concentration balance of the corrosion products.

[0103]

[0104] Among them, S CRUD h represents the thickness of the dirt layer. mt，s h is the mass transfer coefficient. cr c is the crystallinity coefficient. CP s represents the concentration of corrosion products. CP t represents the solubility of the corrosion products, and t represents the current time.

[0105] Step 2): Determine the temperature drop of the cladding oxide layer based on the oxide layer thickness and axial power distribution, and determine the temperature drop of the fouling layer based on the fouling layer thickness and axial power distribution;

[0106] Calculate the temperature drop of the oxide layer and the CRUD layer using Fourier's law:

[0107]

[0108]

[0109] Where, ΔT ox ΔT represents the temperature drop of the cladding oxide layer (i.e., the temperature gradient introduced by the cladding oxide layer). CRUD S is the temperature drop of the fouling layer (i.e., the temperature gradient introduced by the CRUD layer oxide layer), S is the thickness of the encapsulation oxide layer, and k is the temperature gradient of the fouling layer. ox Where is the thermal conductivity of the oxide layer, H is the conversion factor, and k is the thermal conductivity of the oxide layer. CRUDis the thermal conductivity of the CRUD layer.

[0110] Step 3): Determine the outer temperature of the cladding under the influence of axial power offset based on the temperature drop of the oxide layer and the temperature drop of the fouling layer, and determine the inner temperature of the cladding under the influence of axial power offset based on the outer temperature of the cladding and the axial heat flux density distribution.

[0111] There are two modes of heat transfer between the fuel cladding surface and the coolant: forced convection and nucleation boiling. After the coolant flows into the fuel assembly, its temperature rises as heat is continuously transferred from the fuel to the coolant. When the coolant temperature exceeds the saturation temperature, the heat transfer mode changes from forced convection to nucleation boiling. Heat transfer models are established to calculate the cladding surface temperature for both modes. The minimum value calculated by the two heat transfer model formulas is used to determine whether the heat transfer model is forced convection or nucleation boiling. Based on the assumption that coolant boiling occurs inside the CRUD layer, the Jens-Lottes correlation is used for calculations when nucleation boiling occurs, while the temperature inside the cladding is calculated using Fourier's law of thermal conductivity.

[0112] The formula for calculating the temperature on the outer side of the casing is:

[0113] T co =T coolant +ΔT ox +ΔT CRUD (15)

[0114] Among them, T co T represents the temperature on the outside of the casing. coolant ΔT represents the coolant temperature. ox For the temperature drop of the oxide layer, ΔT CRUD This is due to the temperature drop of the dirt layer.

[0115] The formula for calculating the temperature inside the casing is:

[0116]

[0117] Among them, T ci T represents the temperature inside the casing. co Let P(z) be the temperature outside the casing, P(z) be the axial power at point z, H be the conversion factor, and t be the axial power at point z. c k is the shell thickness. c The thermal conductivity is that of the cladding.

[0118] In one embodiment, this embodiment provides an implementation method for calculating the elastic-plastic deformation of the shell based on the temperature field distribution under the influence of axial power offset, thereby obtaining the deformation of the shell under the influence of axial power offset. The specific steps are as follows:

[0119] Step 1: Determine the characteristic deformation of the shell based on the temperature on the outside and inside of the shell; wherein, the characteristic deformation includes the creep and thermal strain of the shell;

[0120] The characteristic deformations of the cladding include creep and thermal expansion. For the creep behavior of the cladding material, based on Norton's creep law, a modified creep limit model is used to calculate the creep of the cladding:

[0121]

[0122] in, Let A be the creep rate, A, a, and n be material constants, E be the elastic modulus, Q be the activation energy, R be the ideal gas constant, and T be the radial mean temperature of the cladding (T = (T...). co +T ci ) / 2), σ eff For equivalent stress, Von-Mices equivalent calculation is used.

[0123] The thermal expansion of the cladding is calculated using empirical formulas:

[0124] ε th = -2.506 × 10 -5 +4.441×10 -6 T (18)

[0125] Where, ε th denoted as thermal strain, and f as the radial average temperature of the cladding.

[0126] Step 2: Based on the creep and thermal strain of the shell, construct the elastoplastic constitutive equation of the shell, and use the finite element method to solve the elastoplastic constitutive equation to calculate the stress and strain of the shell under the influence of axial power offset.

[0127] The elastoplastic constitutive equation is:

[0128]

[0129] Where, ε ij Let ν be the strain tensor, υ be Poisson's ratio, E be the elastic modulus, and δ be the elastic modulus. ij For the Kronark operator, σ ij Stress tensor.

[0130] The elastoplastic constitutive equations were solved using the finite element method to calculate the stress, strain, and displacement of the fuel rod cladding and fuel pellets. Creep, thermal strain, contact stress, and interstitial gas pressure on the cladding were substituted into the elastoplastic constitutive equations. An improved Newton-Raphson iterative method was employed to solve the plasticity problem. The Prandtl-Royce flow law was used to characterize the relationship between a portion of the stress tensor and the plastic strain increment tensor. The hardening equation and yield function of the cladding were taken from the relevant equations used in MATPRO. The contact stress and interstitial gas pressure used were calculated through the following steps. To ensure the stability, efficiency, and accuracy of the CIFF, triangular axisymmetric elements were used in the finite element calculations. In the iterative scheme of the model, the fuel cladding was divided into multiple axial segments. The deformation of the cladding was calculated in the finite element solution of the mechanical calculations, and the axial distribution of the cladding deformation under axial power offset was obtained by summarizing the results.

[0131] In one embodiment, since contact stress and gap gas pressure have a certain influence on the mechanical behavior of the cladding, and axial power offset will cause redistribution of contact stress and gap gas, affecting their axial distribution, the method provided in this embodiment further includes:

[0132] Elastoplastic mechanical analysis was performed on the core and the cladding until the interaction distance between the core and the cladding was less than the preset error distance, and the contact stress on the inner side of the cladding was obtained.

[0133] The interstitial gas pressure inside the shell is determined based on the diffusion process of fission gas and the amount of fission gas released.

[0134] Contact stress and interstitial gas pressure are used as boundary conditions for the elastoplastic constitutive equation.

[0135] To handle pellet-cladding mechanical interaction (PCMI), a gap interaction pressure iteration module can be used. The pellet deformation is obtained through external input, and the interaction pressure of each axial layer in the finite element submesh is initially assumed to be zero. When the PCMI effect occurs, the gap interaction pressure iteration module is used. In this module, the interaction pressure is updated using the following formula, and the updated interaction pressure is used as the boundary of the finite element analysis. The new deformation field under the updated interaction pressure is calculated, and the above process is repeated until the interaction distance between the fuel and cladding is lower than a set error, which is usually selected as the roughness of the pellet and cladding.

[0136] After the gap closes, the contact stress is updated using the following formula:

[0137]

[0138] in, and These are the contact stresses at the previous and current time steps, respectively; δ is the current gap size; δ0 is the gap manufacturing size; and ΔP and α are acceleration convergence coefficients.

[0139] The behavior of fissile gases includes their generation, accumulation, and release. Modeling this behavior is based on a cross-scale 0D physics model, dividing the fissile gas into intraparticle and interparticle components. Molecular dynamics rate theory and related equations are used to model its behavior. For intramolecular fissile gases, the nucleation rate, resolution, and capture rate are derived using molecular dynamics theory. The classical Booth model is used to calculate the diffusion of intraparticle fissile gases, while the interparticle fissile gas behavior model is based on Pastore's theory. The amount of fissile gas released is obtained by integrating the fissile gas diffusion equation, and the interstitial gas pressure inside the cladding is calculated using the ideal gas equation.

[0140] An ideal gas equation is constructed for the released fission gas to calculate the interstitial gas pressure:

[0141] P gas V = nRT ci (twenty one)

[0142] Where Pgas is the interstitial gas pressure, V is the pore volume, n is the amount of fission gas released, and R is the ideal gas constant. The contact stress and interstitial gas pressure under the influence of axial power offset are calculated to provide boundary conditions for the calculation of the elastoplastic constitutive equation in step 2 above.

[0143] For example, see such as Figure 2 The graph showing the influence of different axial power offsets on cladding thickness and gap gas pressure is shown in the figure, and see also... Figure 3 The diagram shows the influence of different axial power offsets on oxide layer thickness and gap size. Figure 2 The figure shows the changes in physical quantities of cladding thickness and interstitial gas pressure under different axial power offsets. Figure 3 The figure shows the changes in physical quantities of oxide layer thickness and gap size under different axial power offsets, from Figure 2 and 3 It can be seen that when the axial power offset changes, the cladding thickness, gap gas pressure, oxide layer thickness, and gap size will all change accordingly.

[0144] The fuel rod cladding behavior prediction method under axial power offset provided in this embodiment solves for the neutron flux density of the fuel rod using a complete multi-nucleus burnup chain. It obtains the radial neutron flux distribution using one-dimensional diffusion theory, and then calculates the nuclide density change over time by solving the nuclide burnup equations. Using the Chebyshev rational approximation method (CRAM), it approximates the matrix exponent during the burnup process by balancing numerical stability and efficiency, thus better simulating nuclide changes. The neutron flux density is calculated... By combining nuclide concentration with fission product yield calculations, the burnup and axial power distribution of the fuel cladding at different axial positions are derived, thus depicting the burnup of the fuel cladding at different axial positions. Using the principles of heat transfer, Newton's cooling formula and Fourier's law of thermal conductivity are employed to calculate the temperature field distribution of the fuel rod under the influence of axial power shift. Based on the temperature field analysis, the elastoplastic mechanical analysis of the cladding is performed. Using finite element technology and the Newton-Raphson iterative method, the thermo-elastoplastic constitutive equation is solved, thereby calculating the cladding deformation under the influence of axial power shift.

[0145] Corresponding to the fuel rod cladding behavior prediction method under axial power offset provided in the above embodiments, this invention provides a fuel rod cladding behavior prediction device under axial power offset, see [link to relevant documentation]. Figure 4 The diagram shows a structural schematic of a fuel rod cladding behavior prediction device under axial power offset. The device includes the following modules:

[0146] The first calculation module 41 is used to perform neutron physics calculations on the fuel rod to determine the axial power distribution at the current time step, and to determine the axial power offset at the current time step based on the axial power distribution at the current time step and the initial axial power distribution of the fuel rod.

[0147] The second calculation module 42 is used to perform heat transfer calculations on the fuel rod cladding based on the axial power distribution to obtain the temperature field distribution of the fuel rod cladding under the influence of the axial power offset; wherein, the temperature field distribution includes the temperature on the outside of the cladding and the temperature on the inside of the cladding.

[0148] The third calculation module 43 is used to perform elastic-plastic deformation calculation on the shell based on the temperature field distribution under the influence of axial power offset, and to obtain the axial distribution of the shell deformation under the influence of axial power offset.

[0149] The fuel rod cladding behavior prediction device under axial power offset provided in this embodiment predicts the axial power offset at different time steps by performing neutron physics analysis to calculate the axial power distribution of the fuel rod during its use. It determines the axial heat flux density distribution based on the axial power distribution, performs heat transfer calculations on the fuel rod based on the axial heat flux density distribution, and determines the axial distribution of cladding deformation under the influence of the axial power offset based on the temperature field distribution. This allows for the prediction of the cladding temperature field distribution and cladding deformation under different axial power offset levels, thus improving the evaluation of fuel rod cladding performance, enhancing the completeness of cladding behavior prediction, and improving the safety attributes of the fuel rod cladding. This is of great value for protecting the integrity of the fuel rod, preventing the leakage of radioactive materials, and ensuring reactor safety.

[0150] The device provided in this embodiment has the same implementation principle and technical effect as the aforementioned embodiments. For the sake of brevity, any parts not mentioned in the device embodiment can be referred to the corresponding content in the aforementioned method embodiment.

[0151] This invention provides an electronic device, which includes a processor and a memory. The memory stores a computer program that can run on the processor. When the processor executes the computer program, it implements the steps of the method provided in the above embodiments.

[0152] This invention provides a computer-readable medium storing computer-executable instructions. When these computer-executable instructions are invoked and executed by a processor, they cause the processor to implement the methods described in the above embodiments.

[0153] Those skilled in the art will understand that, for the sake of convenience and brevity, the specific working process of the system described above can be referred to the corresponding process in the foregoing embodiments, and will not be repeated here.

[0154] Furthermore, in the description of the embodiments of the present invention, unless otherwise explicitly specified and limited, the terms "installation," "connection," and "linking" should be interpreted broadly. For example, they can refer to a fixed connection, a detachable connection, or an integral connection; they can refer to a mechanical connection or an electrical connection; they can refer to a direct connection or an indirect connection through an intermediate medium; and they can refer to the internal connection of two components. Those skilled in the art can understand the specific meaning of the above terms in the present invention based on the specific circumstances.

[0155] If the aforementioned functions are implemented as software functional units and sold or used as independent products, they can be stored in a computer-readable storage medium. Based on this understanding, the technical solution of this invention, essentially, or the part that contributes to the prior art, or a portion of the technical solution, can be embodied in the form of a software product. This computer software product is stored in a storage medium and includes several instructions to cause a computer device (which may be a personal computer, server, or network device, etc.) to execute all or part of the steps of the methods described in the various embodiments of this invention. The aforementioned storage medium includes various media capable of storing program code, such as USB flash drives, portable hard drives, read-only memory (ROM), random access memory (RAM), magnetic disks, or optical disks.

[0156] In the description of this invention, it should be noted that the terms "center," "upper," "lower," "left," "right," "vertical," "horizontal," "inner," and "outer," etc., indicate the orientation or positional relationship based on the orientation or positional relationship shown in the accompanying drawings. They are used only for the convenience of describing the invention and for 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 the invention. Furthermore, the terms "first," "second," and "third" are used for descriptive purposes only and should not be construed as indicating or implying relative importance.

[0157] Finally, it should be noted that the above-described embodiments are merely specific implementations of the present invention, used to illustrate the technical solutions of the present invention, and not to limit it. The scope of protection of the present invention is not limited thereto. Although the present invention has been described in detail with reference to the foregoing embodiments, those skilled in the art should understand that any person skilled in the art can still modify or easily conceive of changes to the technical solutions described in the foregoing embodiments within the technical scope disclosed in the present invention, or make equivalent substitutions for some of the technical features; and these modifications, changes, or substitutions do not cause the essence of the corresponding technical solutions to deviate from the spirit and scope of the technical solutions of the embodiments of the present invention, and should all be covered within the scope of protection of the present invention. Therefore, the scope of protection of the present invention should be determined by the scope of the claims.

Claims

1. A method for predicting fuel rod cladding behavior under axial power offset, characterized in that, include: Neutron physics calculations are performed on the fuel rods to determine the axial power distribution at the current time step, and the axial power offset at the current time step is determined based on the axial power distribution at the current time step and the initial axial power distribution of the fuel rods. Based on the axial power distribution, heat transfer calculations are performed on the fuel rod cladding to obtain the temperature field distribution of the fuel rod cladding under the influence of the axial power offset; wherein, the temperature field distribution includes the temperature on the outer side of the cladding and the temperature on the inner side of the cladding; Based on the temperature field distribution under the influence of the axial power offset, the elastoplastic deformation of the shell is calculated to obtain the deformation of the shell under the influence of the axial power offset. The step of performing neutron physics calculations on the fuel rod to determine the axial power distribution at the current time step includes: calculating the axial neutron flux density of the fuel rod; calculating the nuclide concentration at each axial position based on the axial neutron flux density and the nuclide transformation and decay process of the fuel rod material in the irradiation environment; calculating the power at each axial position at the current time step based on the axial neutron flux density and the nuclide concentration at each axial position, thereby obtaining the axial power distribution. The step of calculating the nuclide concentration at each axial position based on the axial neutron flux density and the nuclide transformation and decay process of the fuel rod material in the irradiation environment includes: constructing a nuclide burnup process equation based on the axial neutron flux density and the nuclide transformation and decay process of the fuel rod material in the irradiation environment, and obtaining the nuclide concentration at each axial position by solving the nuclide burnup process equation based on numerical integration.

2. The fuel rod cladding behavior prediction method according to claim 1, characterized in that, The step of performing heat transfer calculations on the fuel rod cladding based on the axial power distribution to obtain the temperature field distribution of the fuel rod cladding under the influence of the axial power offset includes: Obtain the thickness of the oxide layer and the dirt layer at the current time step; The temperature drop of the cladding oxide layer is determined based on the oxide layer thickness and the axial power distribution, and the temperature drop of the fouling layer is determined based on the fouling layer thickness and the axial power distribution. The outer temperature of the cladding under the influence of the axial power offset is determined based on the temperature drop of the oxide layer and the temperature drop of the dirt layer. The inner temperature of the cladding under the influence of the axial power offset is determined based on the outer temperature of the cladding and the axial heat flux density distribution.

3. The fuel rod cladding behavior prediction method according to claim 1, characterized in that, The step of calculating the elastoplastic deformation of the shell based on the temperature field distribution under the influence of the axial power offset, and obtaining the deformation of the shell under the influence of the axial power offset, includes: The characteristic deformation of the shell is determined based on the temperature on the outer side and the temperature on the inner side of the shell; wherein, the characteristic deformation includes the creep and thermal strain of the shell; Based on the creep and thermal strain of the shell, an elastoplastic constitutive equation for the shell is constructed. The stress and strain of the shell under the influence of the axial power offset are calculated by solving the elastoplastic constitutive equation using the finite element method.

4. The fuel rod cladding behavior prediction method according to claim 3, characterized in that, Also includes: Elastoplastic mechanical analysis was performed on the core and the shell until the interaction distance between the core and the shell was less than a preset error distance, and the contact stress on the inner side of the shell was obtained. The interstitial gas pressure inside the shell is determined based on the diffusion process of the fission gas and the amount of fission gas released. The contact stress and the interstitial gas pressure are used as the boundary conditions of the elastoplastic constitutive equation.

5. The fuel rod cladding behavior prediction method according to claim 1, characterized in that, The formula for calculating the axial power distribution is: in, axial Power at that location, The transformation constant, nuclide The fission cross section, Axial position nuclides at the location The concentration of nuclides, axial radial Neutron flux density at the location.

6. The fuel rod cladding behavior prediction method according to claim 2, characterized in that, The formula for calculating the temperature on the outer side of the casing is: in, The temperature of the outer side of the casing. This refers to the coolant temperature. For the temperature drop of the oxide layer, This refers to the temperature drop of the dirt layer.

7. The fuel rod cladding behavior prediction method according to claim 2, characterized in that, The formula for calculating the temperature inside the casing is: in, The temperature inside the casing. The temperature of the outer side of the casing. axial Axial power at the location, As the conversion factor, For the thickness of the casing, The thermal conductivity is denoted by the cladding.

8. A device for predicting fuel rod cladding behavior under axial power offset, characterized in that, include: The first calculation module is used to perform neutron physics calculations on the fuel rod to determine the axial power distribution at the current time step, and to determine the axial power offset at the current time step based on the axial power distribution at the current time step and the initial axial power distribution of the fuel rod. The second calculation module is used to perform heat transfer calculations on the fuel rod cladding based on the axial power distribution to obtain the temperature field distribution of the fuel rod cladding under the influence of the axial power offset; wherein, the temperature field distribution includes the temperature on the outer side of the cladding and the temperature on the inner side of the cladding. The third calculation module is used to perform elastic-plastic deformation calculation on the shell based on the temperature field distribution under the influence of the axial power offset, and obtain the axial distribution of the shell deformation under the influence of the axial power offset. The first calculation module is further configured to calculate the axial neutron flux density of the fuel rod, calculate the nuclide concentration at each axial position based on the axial neutron flux density and the nuclide transformation and decay process of the fuel rod material in the irradiation environment, and calculate the power at each axial position at the current time step based on the axial neutron flux density and the nuclide concentration at each axial position to obtain the axial power distribution. The first calculation module is also used to construct a nuclide burnup process equation based on the axial neutron flux density and the nuclide transformation and decay process of the fuel rod material in the irradiation environment, and to obtain the nuclide concentration at each axial position by solving the nuclide burnup process equation based on numerical integration.

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