Methods for predicting the growth of oxidation corrosion products and localized corrosion

Abstract

This invention provides a method for predicting the growth of oxidation corrosion products and localized corrosion. It employs a dynamic balance between the deposition rate of corrosion products on the fuel rod cladding and the erosion rate of the CRUD by the coolant to calculate the target thickness of the CRUD deposition layer, thus predicting the numerical value of CRUD growth. By calculating the heat transfer parameters of the CRUD, the contact temperature between the CRUD and the fuel rod cladding is obtained, and the oxide layer thickness is calculated based on the contact temperature. This enables numerical prediction of localized corrosion caused by CRUD, i.e., CILC, revealing the impact of oxidation corrosion products on core safety. Furthermore, this method has significant value for predicting fuel rod integrity, preventing radioactive material leakage, and ensuring reactor safety.

Description

Technical Field

[0001] This invention relates to the field of prediction technology for oxidation and corrosion products of the primary loop system of nuclear power plants and reactor core safety, and in particular to methods for predicting the growth of core oxidation and corrosion products and localized corrosion of fuel cladding. Background Technology

[0002] The CRUD (Chalk River Unidentified Deposit) formed on the fuel rod cladding of a pressurized water reactor (PWR) core has a porous structure, which adds additional thermal resistance to the fuel rod heat exchanger, leading to reduced core heat exchange efficiency, excessively high local temperatures, and localized cladding corrosion. This poses a threat to fuel rod integrity and reactor safety. However, due to the diversity of CRUD morphology and the complexity of two-phase flow, the impact and mechanism of CRUD on reactor safety characteristics are not fully understood. Existing studies simulating corrosion product deposition mainly focus on the transport and metric distribution of corrosion products, with limited research on the growth of oxidative corrosion products, porous media heat transfer, and heat transfer-induced localized corrosion. Therefore, a numerical prediction technique suitable for CRUD growth and CILC (CRUD-induced localized corrosion) is urgently needed to reveal the impact of oxidative corrosion products on core safety. Summary of the Invention

[0003] In view of this, the purpose of the present invention is to provide a method for predicting the growth of oxidation corrosion products and localized corrosion, so as to alleviate the above-mentioned problems.

[0004] In a first aspect, embodiments of the present invention provide a method for predicting the growth of oxidation corrosion products and localized corrosion. The method includes: acquiring a first parameter and calculating the growth rate per unit area of ​​corrosion products based on the first parameter and a growth model; wherein the first parameter includes the temperature and flow velocity of the near-wall fluid, and multiple growth condition calculation parameters; calculating the target thickness of the corrosion product deposition layer CRUD based on the growth rate per unit area of ​​the corrosion products; wherein the target thickness of the deposition layer is used to characterize the thickness of the deposition layer obtained by the simultaneous deposition and erosion of corrosion products at any given time; acquiring a second parameter and calculating the heat transfer parameters of the CRUD based on the second parameter and a calculation model; wherein the heat transfer parameters include thermal conductivity, bubble detachment diameter, bubble detachment frequency, and nucleation site density; calculating the contact temperature based on the heat transfer parameters; wherein the contact temperature is used to characterize the temperature between the CRUD and the fuel rod cladding, and an oxide layer also exists between the CRUD and the fuel rod cladding; acquiring a third parameter and calculating the oxide layer thickness based on the third parameter and the contact temperature; and generating localized corrosion results of the oxide layer based on the oxide layer thickness.

[0005] Preferably, the corrosion products include dissolution corrosion products and particulate corrosion products, the growth model includes a dissolution growth model, a particle growth model, and an erosion model, and the growth condition parameters include: dissolution growth condition parameters, particle growth condition parameters, and erosion condition parameters; the step of calculating the unit area growth rate of the corrosion products based on the first parameter and the growth model includes: calculating the unit area deposition rate of the dissolution corrosion products based on the dissolution growth condition parameters and the dissolution growth model; calculating the unit area deposition rate of the particulate corrosion products based on the particle growth condition parameters and the particle growth model; calculating the unit area erosion rate of the corrosion products based on the erosion condition parameters and the erosion model; and calculating the unit area growth rate of the corrosion products based on the unit area deposition rate of the dissolution corrosion products, the unit area deposition rate of the particulate corrosion products, and the unit area erosion rate of the corrosion products.

[0006] Preferably, the calculation model includes: the KI model, the Cole model, and the YK model; the second parameters include: liquid phase density, gas phase density, contact angle, gravitational acceleration, surface tension, cavity density, cavity orifice radius, maximum cavity radius of the bubble, minimum cavity radius of the bubble, and cavity cone angle; the step of calculating the heat transfer parameters of CRUD based on the second parameters and the calculation model includes: calculating the bubble detachment diameter based on the liquid phase density, gas phase density, contact angle, gravitational acceleration, surface tension, and the KI model; calculating the bubble detachment frequency based on the bubble detachment diameter, liquid phase density, gas phase density, gravitational acceleration, and the Cole model; and calculating the nucleation site density based on the cavity density, contact angle, cavity cone angle, cavity orifice radius, maximum cavity radius of the bubble, minimum cavity radius of the bubble, and the YK model.

[0007] Preferably, the step of calculating the bubble detachment diameter based on the liquid phase density, gas phase density, contact angle, gravitational acceleration, surface tension, and the KI model includes: the expression for the KI model is as follows:

[0008]

[0009] Among them, D w Indicates the diameter of the bubble detachment, ρ f ρ represents the density of the liquid phase. v σ represents the gas phase density, θ represents the surface tension, and σ represents the surface density. w denoted by , where represents the contact angle, and g represents the gravitational acceleration.

[0010] Preferably, the step of calculating the bubble escape frequency based on the bubble escape diameter, liquid phase density, gas phase density, gravitational acceleration, and the Cole model includes: The expression for the Cole model is as follows:

[0011]

[0012] Where f represents the bubble detachment frequency, g represents the gravitational acceleration, and ρ f ρ represents the density of the liquid phase. v D represents the gas phase density. w This indicates the diameter at which the bubble detaches.

[0013] Preferably, the step of calculating the nucleation site density based on the cavity density, cavity opening radius, contact angle, cavity cone angle, maximum cavity radius of the bubble, minimum cavity radius of the bubble, and the YK model includes: The expression for the YK model is as follows:

[0014]

[0015] Where, N ω N represents the density of nucleation sites. s Represents the cavity density, θ w Represents the contact angle, r max r represents the maximum cavity radius of the bubble. min β represents the minimum cavity radius of the bubble, r represents the cavity cone angle, and r represents the cavity opening radius.

[0016] Preferably, the third parameter includes multiple constant coefficients; the step of calculating the oxide layer thickness based on the third parameter and the contact temperature further includes: calculating the transition thickness based on the third parameter and the contact temperature; if the oxide layer thickness is less than the transition thickness, calculating the oxide layer thickness according to the third parameter and the contact temperature using a first thickness calculation model; or, if the oxide layer thickness is greater than the transition thickness, calculating the oxide layer thickness according to the third parameter and the contact temperature using a second thickness calculation model.

[0017] Preferably, the step of calculating the transition thickness based on the third parameter and the contact temperature includes: calculating the transition thickness based on the third parameter and the contact temperature according to the following formula:

[0018]

[0019] Among them, S trans Indicates the transition thickness; D3, Q3, E3, and R all represent constant coefficients; T om Indicates the contact temperature.

[0020] Preferably, the step of calculating the oxide layer thickness according to the third parameter and the contact temperature using the first thickness calculation model includes: the expression for the first thickness calculation model is as follows:

[0021]

[0022] Among them, S ox The oxide layer thickness is represented by k1, Q1, and R, which are all constant coefficients. om Indicates the contact temperature.

[0023] Preferably, the third parameter further includes the irradiation enhancement factor and the reactor fast neutron flux; the step of calculating the oxide layer thickness according to the third parameter and the contact temperature using the second thickness calculation model includes: the expression for the second thickness calculation model is as follows:

[0024]

[0025] k2=C0f OX

[0026]

[0027] Among them, S ox The values ​​represent the oxide layer thickness, k2, C0, M, Po, Q1, and R are all constant coefficients, and T represents the oxide layer thickness. om Indicates the contact temperature, f OX Φ represents the irradiation enhancement factor, and Φ represents the reactor fast neutron flux.

[0028] The embodiments of the present invention bring the following beneficial effects:

[0029] This invention provides a method for predicting the growth of oxidation corrosion products and localized corrosion. It employs a dynamic balance between the deposition rate of corrosion products on the fuel rod cladding and the erosion rate of the CRUD by the coolant to calculate the target thickness of the CRUD deposition layer, thus predicting the numerical value of CRUD growth. By calculating the heat transfer parameters of the CRUD, the contact temperature between the CRUD and the fuel rod cladding is obtained, and the oxide layer thickness is calculated based on the contact temperature. This enables numerical prediction of localized corrosion caused by CRUD, i.e., CILC, revealing the impact of oxidation corrosion products on core safety. Furthermore, this method is of significant value for predicting fuel rod integrity, preventing radioactive material leakage, and ensuring reactor safety.

[0030] Other features and advantages of the invention will be set forth in the following description, and will be apparent in part from the description, or may be learned by practicing the invention. The objects and other advantages of the invention are realized and obtained through the structures particularly pointed out in the description and the drawings.

[0031] 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

[0032] 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.

[0033] Figure 1 A flowchart illustrating a method for predicting the growth of oxidation corrosion products and localized corrosion, provided in an embodiment of the present invention;

[0034] Figure 2 A schematic diagram of CRUD growth provided in an embodiment of the present invention;

[0035] Figure 3 A logic diagram illustrating the principle of predicting the growth of oxidation corrosion products and localized corrosion, provided in an embodiment of the present invention;

[0036] Figure 4 A schematic diagram illustrating four internal configurations of a CRUD provided in an embodiment of the present invention;

[0037] Figure 5 A simulation calculation flowchart is provided for an embodiment of the present invention. Detailed Implementation

[0038] 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 clearly and completely described below with reference to the accompanying drawings. Obviously, the described embodiments are only some embodiments of the present invention, not all embodiments. 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.

[0039] To facilitate understanding of this embodiment, the embodiments of the present invention will be described in detail below.

[0040] This invention provides a method for predicting the growth of oxidation corrosion products and localized corrosion, such as... Figure 1 As shown, the method includes the following steps:

[0041] Step S102: Obtain the first parameter, and calculate the growth rate of corrosion products per unit area based on the first parameter and the growth model;

[0042] In practical applications, CRUD growth mainly consists of two processes: deposition and erosion; for example... Figure 2As shown, corrosion products from the primary loop of a pressurized water reactor (PWR) enter the core along with the coolant flow. Driven by supercooled boiling, they precipitate, crystallize, and deposit from the coolant. The deposition of dissolved corrosion products is mainly driven by solubility changes with temperature, while the deposition of particulate corrosion products is mainly driven by Brownian motion. Simultaneously, the coolant and the reactor wall move relative to each other at a high rate, and the flow shear force of the coolant erodes the CRUD (Crucible Interrupted Water Surface). In the early stages of reactor operation, the deposition rate is greater than the erosion rate, and the CRUD thickness, i.e., the deposition layer of corrosion products, gradually increases. After a period of operation, the deposition rate and erosion rate tend to converge, at which point the thickness hardly changes.

[0043] Therefore, corrosion products in the primary coolant are classified into dissolution corrosion products and particulate corrosion products. Growth models include dissolution growth models, particulate growth models, and erosion models. The first parameter includes the near-wall fluid temperature T. f The parameters include the flow velocity v and several growth conditions; these growth conditions include: dissolution growth conditions, particle growth conditions, and erosion conditions. It should be noted that the temperature T of the near-wall fluid mentioned above... f The flow velocity v can be directly simulated and calculated using CFD (Computational Fluid Dynamics) in electronic devices. This involves modeling the geometry of the simulated object, spatially discretizing it to generate a mesh, setting initial and boundary conditions such as temperature, flow velocity, pressure, and heat source for the simulated operating conditions, and then discretizing the governing equations using the finite volume method to obtain a set of algebraic equations. These equations are then iteratively solved to obtain the fluid flow and temperature field distribution at different times. Other parameters for the growth conditions can be calculated or queried based on the corresponding conditions; the specific acquisition method can be set according to the actual situation.

[0044] Specifically, the process of calculating the growth rate per unit area of ​​corrosion products based on the first parameter and the growth model is as follows:

[0045] (A1) The deposition rate of dissolution corrosion products per unit area was calculated based on the dissolution growth condition parameters and the dissolution growth model.

[0046] Specifically, the deposition process of dissolved corrosion products is mainly divided into two steps: crystallization and mass transfer. As the core temperature rises, the solubility of soluble substances gradually decreases, leading to supersaturation of soluble substances in the coolant. The dissolved corrosion products that enter the supersaturated region are deposited on the outer surface of the fuel rods through crystallization and mass transfer.

[0047] ① When the dissolved corrosion products in the coolant become supersaturated, the dissolved substances crystallize out. The crystallization coefficient here depends on variables such as temperature, impurities, surface tension, ion dehydration, and the activation barrier energy for diffusion hopping. The crystallization coefficient can be expressed using the Arrhenius equation as follows:

[0048]

[0049] Among them, h cr k represents the crystallinity coefficient. r0 Q represents the constant for calculating the crystallinity coefficient. cr R represents the activation potential energy, and R represents a constant coefficient, such as the universal gas constant. f This indicates the temperature of the fluid near the wall.

[0050] ② Calculate the mass transfer coefficient between the fuel rod surface and the coolant under turbulent conditions; by analogy with the DB formula for heat transfer, a mass transfer formula applicable to pressurized water reactor conditions can be established. In the mass transfer formula, the Prandtl number is replaced by the Schmidt number (i.e., the ratio of momentum diffusivity to mass diffusivity), and the Nusselt number is replaced by the Schwoder number;

[0051] The expression for the Schmidt number is as follows:

[0052]

[0053] Among them, Sc s The figure represents the Schmitt number of the dissolved substance, μ represents the dynamic viscosity, and ρ represents the kinetic viscosity. f D represents the density of the liquid phase. ab This represents the diffusion coefficient of the dissolved substance.

[0054] The Reynolds number is expressed as follows:

[0055]

[0056] Where Re represents the Reynolds number of the dissolved substance, v represents the flow velocity of the fluid near the wall, μ represents the dynamic viscosity, and ρ represents the velocity of the fluid near the wall. f D represents the density of the liquid phase. e Indicates the hydraulic diameter.

[0057] The expression for the Sherwood number is as follows:

[0058] Sh s =0.0165×Re 0.86 ×Sc s 0.33 (4)

[0059] Among them, Sh s Re represents the Sherwood number of the dissolved substance, Re represents the Reynolds number of the dissolved substance, and Sc represents the Reynolds number of the dissolved substance. s This indicates the Schmitt number of the dissolved substance.

[0060] The mass transfer coefficient of the dissolved corrosion products is calculated according to the following formula:

[0061]

[0062] Among them, h mt_s Sh represents the mass transfer coefficient of the dissolved substance. s D represents the Sherwood number of the dissolved substance. ab D represents the diffusion coefficient of the dissolved substance. e Indicates the hydraulic diameter.

[0063] Therefore, the mass transfer coefficient h of the dissolved corrosion products can be calculated according to the above formulas (2)-(5). mt_s .

[0064] ③ Once a steady state is reached, the deposition rate, mass transfer rate, and crystallization rate are equal. At this point, the deposition rate per unit area of ​​the dissolved corrosion products can be calculated.

[0065]

[0066] Where, m s h represents the deposition rate of dissolved corrosion products per unit area. cr h represents the crystallinity coefficient. mt_s c represents the mass transfer coefficient of the dissolved substance. Fe c Ni and c Cr These represent the dissolved concentrations of Fe, Ni, and Cr elements in the mainstream, respectively. Fe s Ni and s Cr These represent the saturation concentrations of the dissolved substances for Fe, Ni, and Cr, respectively.

[0067] Therefore, the above formula (6) can also be called the dissolution growth model. The dissolution growth working condition parameters obtained include at least: crystallization coefficient calculation constant, activation potential energy, universal gas constant, dynamic viscosity, liquid phase density, dissolved diffusion coefficient, hydraulic diameter, dissolved diffusion coefficient, multiple dissolved saturation concentrations and dissolved concentrations, etc.

[0068] (A2) The deposition rate of particle corrosion products per unit area was calculated based on particle growth parameters and particle growth model.

[0069] Specifically, unlike the deposition of soluble substances, particulate corrosion products in the coolant can be deposited on the surface via convective mass transfer, independent of the coolant's saturation state. Assuming that the deposition of particulate corrosion products primarily depends on a Brownian motion-controlled mass transfer process, the mass transfer formula is used, similar to that for dissolved corrosion products, and an appropriate diffusion coefficient is applied for calculation. For small particles, the adhesion probability to the surface is approximately 1, and the near-wall particle concentration is approximately 0. Therefore, the mass transfer coefficient for particulate corrosion products is calculated as follows:

[0070]

[0071] Among them, h mt_p k represents the mass transfer coefficient of particulate matter. p T represents the Boltzmann constant. f The temperature of the fluid near the wall is represented by μ, and the dynamic viscosity is represented by r. p ρ represents the particle radius. f D represents the density of the liquid phase. e The value represents the hydraulic diameter, and v represents the velocity of the fluid near the wall.

[0072] Once the system reaches a steady state, the deposition rate of particulate corrosion products per unit area can be calculated using the following formula:

[0073] m p =h mt_p ×(p Fe +p Ni +p Cr (8)

[0074] Where, m p h represents the deposition rate per unit area of ​​particulate corrosion products. mt_p p represents the mass transfer coefficient of particulate matter. Fe p Ni and p Cr These represent the particulate matter concentrations of Fe, Ni, and Cr elements, respectively. That is, the above formula (8) can also be called the expression of the particle growth model. The particle growth conditions obtained include at least the following parameters: Boltzmann constant, dynamic viscosity, particle radius, etc. Some of the same conditions can be obtained from any growth conditions parameter, or they can be obtained from different growth conditions parameters. The specific settings can be made according to the actual situation.

[0075] (A3) The corrosion rate per unit area of ​​corrosion products is calculated based on the corrosion working condition parameters and the corrosion model.

[0076] Specifically, the CRUD (Crane Deposition Effect) on the fuel rod cladding surface separates from the surface due to shear forces caused by coolant flow, and the erosion of the CRUD is proportional to the shear force of the coolant. Under turbulent flow, shear stress is proportional to flow velocity, and the erosion rate is proportional to shear stress. The erosion rate per unit area of ​​the CRUD is calculated as follows:

[0077]

[0078] Where τ represents shear force, μ represents dynamic viscosity, and ρ f Let D represent the liquid density, v represent the flow velocity of the fluid near the wall, and D represent the liquid density. e Indicates hydraulic diameter, in meters (m) r k represents the erosion rate per unit area of ​​corrosion products. er W represents the erosion constant. aE represents the work done by sediments adhering to a surface. tot x represents the total adhesion energy. f This indicates the thickness of the sedimentary layer, i.e., the current thickness of the sedimentary layer.

[0079] Therefore, the above formula (9) is the expression of the erosion model. The erosion condition parameters obtained include at least: erosion constant, work done by the deposits on the surface, total adhesion energy and current deposition layer thickness of CRUD, so as to calculate the erosion rate per unit area of ​​corrosion products based on the erosion condition parameters and formula (9).

[0080] (A4) The growth rate of corrosion products per unit area is calculated based on the deposition rate of dissolved corrosion products per unit area, the deposition rate of particulate corrosion products per unit area, and the erosion rate of corrosion products per unit area.

[0081] Specifically, the growth rate of corrosion products per unit area is calculated according to the following formula:

[0082] m*=m s +m p -m r (10)

[0083] Where m* represents the growth rate of corrosion products per unit area, m s The m represents the deposition rate of dissolved corrosion products per unit area. p The m represents the deposition rate of particulate corrosion products per unit area. r This indicates the rate of erosion per unit area of ​​corrosion products.

[0084] In summary, the growth rate per unit area of ​​corrosion products, i.e. the net growth of corrosion products per unit area, can be calculated using formulas (6), (8), (9) and (10).

[0085] Step S104: Calculate the target thickness of the corrosion product deposition layer CRUD based on the growth rate per unit area of ​​the corrosion products; wherein, the target thickness of the deposition layer is used to characterize the thickness of the deposition layer obtained by the combined action of deposition and erosion of the corrosion products at any time.

[0086] After calculating the corrosion product growth rate per unit area, integrating the corrosion product growth rate m* over time yields the thickness grown within a certain time period, i.e., the current thickness x. f and the calculated thickness x f Substitute the values ​​into formula (9) for iterative calculation. The expected thickness is reached after a certain period of time. The thickness at this time is called the target thickness of the CRUD deposition layer, thus realizing the numerical prediction of CRUD growth.

[0087] Step S106: Obtain the second parameter, and calculate the heat transfer parameters of CRUD based on the second parameter and the calculation model;

[0088] Because the CRUD (Chemical Refrigerant Container) is primarily a porous medium, its interior is filled with varying proportions of water and steam depending on the operating conditions. Under conditions of supercooled boiling, nucleation sites continuously generate bubbles, leading to pore formation. Therefore, the overall structure of the CRUD is a porous medium with distributed pores. The presence of the CRUD alters the local thermal resistance and surface properties of the cladding. On one hand, the CRUD increases the thermal resistance of the fuel rod cladding, resulting in decreased heat transfer performance; on the other hand, the CRUD's porous structure, with its complex, irregular micro-surface, provides more nucleation sites for bubble formation, thereby enhancing heat transfer.

[0089] like Figure 3 As shown, CRUD heat transfer is mainly divided into two parts: internal heat exchange within the CRUD and heat exchange between the CRUD's outer surface and the coolant. Specifically, internal heat exchange within the CRUD is primarily conducted heat, which is categorized into four states or models based on the volume ratio of vapor, liquid, and solid within the CRUD. Figure 4 As shown, the four models are defined as follows:

[0090] (a) Flooding model: No boiling occurs in the CRUD; the CRUD is filled with water.

[0091] (b) Mixture model: In CRUD, supercooled boiling occurs, and steam and water mix in the pores;

[0092] (c) Dryout model: The CRUD is completely dried out and filled with steam;

[0093] (d) Particle model: The interior of the CRUD is filled or partially filled with other solid particles.

[0094] In this embodiment of the invention, the thermal conductivity of the porous medium portion of the CRUD is calculated based on the assumption of being filled with water. The thermal conductivity of the pore portion is calculated based on the cavitation fraction determined by the boiling condition, and the gas-water volume ratio within the pores is obtained for calculation. The overall thermal conductivity of the CRUD is calculated as follows:

[0095]

[0096] Where, k eff k represents the thermal conductivity of a porous medium filled with water. crud φ represents thermal conductivity, φ represents porosity, and k represents thermal conductivity. skeleton k represents the thermal conductivity of the sedimentary skeleton. liquid f represents the thermal conductivity of water. chimThe region is defined by the influence of porosity, α represents the cavitation fraction, and k vapor This represents the thermal conductivity of steam. It should be noted that the thermal conductivity k of the aforementioned sedimentary layer framework... skeleton The porosity φ can be obtained by performing thermal conductivity and AFM tests on CRUD. The void fraction α can be obtained by geometrically modeling the simulated object using CFD, spatially discretizing and meshing, inputting boundary conditions such as temperature, flow rate, pressure, and heat source, discretizing the control equations of the multiphase flow model using the finite volume method to obtain a set of algebraic equations, and iteratively solving them. The remaining parameters can be obtained directly or by querying.

[0097] Furthermore, regarding the heat exchange between the CRUD's outer surface and the coolant, as the heat flux density gradually increases, the coolant undergoes subcooling and boiling, entering a two-phase flow state. The wall heat flux distribution model proposed by the Rensselaer Polytechnic Institute (RPI) is then used to calculate the heat exchange between the CRUD and the coolant. The RPI model divides the total heat flux at the wall into three parts: convective heat flux, quenching heat flux, and evaporative heat flux.

[0098]

[0099] in, Represents the wall heat flux density. Represents convective heat flux density. Indicates the heat flux density during quenching. This represents the evaporative heat flux density.

[0100] Wherein, convective heat flux density is the energy transferred by convective heat transfer between the fluid and the wall, and its expression is as follows:

[0101]

[0102] in, h represents the convective heat flux density. C T represents the single-phase heat transfer coefficient. w T represents the wall temperature. l Indicates the liquid phase temperature, A b This indicates the area covered by steam.

[0103] Quenching heat flux density is the transient energy transfer near the water wall after the bubble detaches from the wall, and its expression is as follows:

[0104]

[0105] in, k represents the heat flux density during quenching. l λ represents the constant coefficient, λ1 represents the statistical parameter, and T represents the bubble growth period. w T represents the wall temperature. l Indicates the liquid phase temperature.

[0106] The evaporative heat flux density is the heat carried away by the coolant as it changes from the water phase to the gas phase, and its expression is as follows:

[0107]

[0108] in, V represents the evaporative heat flux density. d N represents the volume of the bubble that has been removed from the air. ω ρ represents the density of nucleation sites. v h represents the gas phase density. fv denoted as latent heat of vaporization, and f represents the bubble detachment frequency.

[0109] Therefore, the three main influencing parameters in the RPI model are bubble detachment diameter, bubble detachment frequency, and nucleation site density. Thus, the heat transfer parameters of CRUD calculated above mainly include thermal conductivity, bubble detachment diameter, bubble detachment frequency, and nucleation site density. The specific thermal conductivity can be calculated according to formula (11).

[0110] For the calculation of bubble detachment diameter, bubble detachment frequency, and nucleation site density, the calculation models mentioned above include: the KI (Kocamustafaogullari and Ishii) model, the Cole model, and the YK (Yang and Kim) model; the corresponding second parameters include: liquid phase density, gas phase density, contact angle, gravitational acceleration, surface tension, cavity density, cavity opening radius, maximum bubble cavity radius, minimum bubble cavity radius, and cavity cone angle; the specific calculation process is as follows:

[0111] (B1) The bubble detachment diameter is calculated based on the liquid phase density, gas phase density, contact angle, gravitational acceleration, surface tension, and the KI model.

[0112] The expression for the KI model is as follows:

[0113]

[0114] Among them, D w Indicates the diameter of the bubble detachment, ρ f ρ represents the density of the liquid phase. v σ represents the gas phase density, θ represents the surface tension, and σ represents the surface density. w denoted by , where represents the contact angle, and g represents the gravitational acceleration.

[0115] (B2) The bubble detachment frequency is calculated based on the bubble detachment diameter, liquid phase density, gas phase density, gravitational acceleration, and Cole model.

[0116] The expression for the Cole model is as follows:

[0117]

[0118] Where f represents the bubble detachment frequency, g represents the gravitational acceleration, and ρ f ρ represents the density of the liquid phase. v D represents the gas phase density. w This indicates the diameter at which the bubble detaches.

[0119] (B3) The nucleation site density is calculated based on the cavity density, contact angle, cavity cone angle, cavity opening radius, maximum cavity radius of the bubble, minimum cavity radius of the bubble, and the YK model.

[0120] The expression for the YK model is as follows:

[0121]

[0122] Where, N ω N represents the density of nucleation sites. s Represents the cavity density, θ w Represents the contact angle, r max r represents the maximum cavity radius of the bubble. min Let θ represent the minimum cavity radius of the bubble, β represent the cavity cone angle, and r represent the cavity opening radius. It should be noted that the contact angle θ mentioned above... w The cavity density N can be obtained by diagonally scanning the probe liquid remaining on the CURD surface. s The probability density functions f(β) of the cavity cone angle β and f(r) of the cavity opening radius r can be obtained by testing the CRUD sample using SEM (Scanning Electron Microscopy) and AFM-3D (Atomic Force Microscopy), and then performing distribution fitting. SEM testing of the sample surface yields nanoscale surface morphology images. ImageJ image processing software is used to analyze the images based on contrast differences to obtain the number of cavities per unit area of ​​the sample surface and the radius dimensions of all cavity openings. MATLAB is used to perform distribution fitting on the cavity opening radius dimensions to obtain the probability density function of the cavity opening radius. AFM testing of the sample surface yields three-dimensional surface morphology images. The accompanying analysis software is used to analyze the morphology to obtain the cavity opening radius and depth, thus obtaining the cavity cone angle dimensions. MATLAB is used to perform distribution fitting on the cavity cone angle dimensions to obtain the probability density function of the cavity cone angle.

[0123] In summary, the heat transfer parameters of CRUD can be calculated using formulas (11) and (16)-(18).

[0124] Step S108: The contact temperature is calculated based on the heat transfer parameters; wherein, the contact temperature is used to characterize the temperature between the CRUD and the fuel rod cladding, and there is also an oxide layer between the CRUD and the fuel rod cladding.

[0125] Specifically, the CFD program models the geometry of the simulated object, generates a spatially discretized mesh, sets initial and boundary conditions such as temperature, flow rate, pressure, and heat source for the simulated working conditions, and discretizes the governing equations using the finite volume method after initialization to obtain a set of algebraic equations. The equations are then iteratively solved to obtain the fluid flow and temperature field distribution at different times, thereby obtaining the temperature between the CRUD and the fuel rod cladding, i.e., the contact temperature.

[0126] Step S110: Obtain the third parameter and calculate the oxide layer thickness based on the third parameter and the contact temperature;

[0127] Specifically, an oxide layer exists between the CRUD and the fuel rod cladding. When the CRUD is thick and has low porosity, a large temperature gradient is generated between the CRUD and the fuel rod cladding, leading to localized overheating. These localized overheating points caused by the CRUD can provide initiation points for oxidation corrosion, causing it to occur prematurely and resulting in fuel rod cladding damage and radioactive material leakage. Therefore, the evaluation of CILC in this embodiment of the invention starts with the growth thickness of the oxide layer. Oxide layer growth is affected by the temperature of the contact surface between the CRUD and the cladding, as well as the irradiation intensity. Oxide layer growth is divided into two different oxidation rate equations with the transition thickness as the boundary. Before the oxide layer thickness reaches the transition thickness, the oxide thickness increases cubically; after reaching the transition thickness, the oxide thickness increases linearly.

[0128] The third parameter includes multiple constant coefficients. The process of calculating the oxide layer thickness based on the third parameter and the contact temperature is as follows: the transition thickness is calculated based on the third parameter and the contact temperature; if the oxide layer thickness is less than the transition thickness, the oxide layer thickness is calculated according to the first thickness calculation model based on the third parameter and the contact temperature; or, if the oxide layer thickness is greater than the transition thickness, the oxide layer thickness is calculated according to the second thickness calculation model based on the third parameter and the contact temperature.

[0129] The expression for the first thickness calculation model is as follows:

[0130]

[0131] Among them, S ox The oxide layer thickness is represented by k1, Q1, and R. omIndicates the contact temperature.

[0132] In addition, the third parameter also includes the irradiation enhancement factor and the reactor fast neutron flux; the expression for the second thickness calculation model is as follows:

[0133]

[0134] Among them, S ox The oxide layer thickness is represented by k2, the constant coefficient is represented by Q1, the constant coefficient is represented by R, and the constant coefficient is represented by T. om Indicates the contact temperature, C0 represents the constant coefficient, and f OX denoted by irradiation enhancement factor, M by constant coefficient, Φ by reactor fast neutron flux, and Po by constant coefficient.

[0135] Furthermore, the transition thickness is calculated based on the third parameter and the contact temperature using the following formula:

[0136]

[0137] Among them, S trans Indicates the transition thickness; D3, Q3, E3, and R all represent constant coefficients; T om Indicates the contact temperature.

[0138] Step S112: Generate local corrosion results of the oxide layer based on the oxide layer thickness.

[0139] The oxide layer thickness S obtained from the above calculations ox Then, based on the oxide layer thickness S ox Analyze and assess the corrosion and failure status of the fuel rod cladding, and generate localized corrosion results based on the analysis; for example, when the oxide layer thickness S... ox When the oxide layer thickness exceeds the threshold, it is considered to be severely corroded, which will affect the normal use of the reactor core. In this case, localized corrosion results in severe localized corrosion. Conversely, when the oxide layer thickness S is below the threshold, the corrosion is considered severe. ox When the thickness is below the threshold, the oxide layer is considered to be less corroded, resulting in less localized corrosion.

[0140] Furthermore, regarding the aforementioned CFD numerical simulation process, such as Figure 5As shown, geometric modeling and meshing are performed based on the simulated object. While considering computational efficiency, accuracy is ensured. The governing equations are discretized using the finite volume method, resulting in a set of algebraic equations. Initial and boundary conditions are set according to the simulated operating conditions, and the equations are substituted into the system for iterative calculation to obtain the flow and temperature field distributions. This yields the near-wall fluid temperature and the mainstream velocity. These are then substituted into the growth and heat transfer models to further calculate the CRUD thickness. Changes in CRUD thickness lead to changes in thermal and hydraulic parameters such as CRUD thermal resistance and flow resistance. These changes are substituted into the governing equations to iteratively calculate the flow and temperature fields after the CRUD changes until convergence is achieved. For example, convergence is considered achieved when the residual is less than 1E-3 and the inlet and outlet velocities are balanced and stable. After convergence, it is determined whether the CRUD has grown to the expected thickness. If not, a new flow and temperature field distribution and CRUD thickness are used to replace the initial conditions, and the CRUD growth calculation continues. If the desired thickness is achieved, CILC risk prediction is performed. It should be noted that the specific calculation process described above can be referred to in the aforementioned embodiments, and the embodiments of this invention will not be described in detail here.

[0141] In summary, the method for predicting the growth of oxidation corrosion products (CRUD) and localized corrosion (CILC) provided in this invention uses a dynamic balance between the deposition rate of CRUD on the fuel rod cladding and the erosion rate of the deposited layer by the coolant to determine the formation of CRUD. Based on the temperature of the contact surface between the generated CRUD and the fuel cladding, the thickness of the oxide layer outside the cladding is obtained, and the CILC caused by CRUD is evaluated. This invention takes into account both the influence of supercooled boiling on corrosion product deposition and the influence of the loose and porous morphology of the CRUD on heat transfer. By coupling CRUD growth and heat transfer through CRUD thickness and cladding surface temperature, and obtaining the cladding oxide layer thickness, it is of great value for predicting fuel rod integrity, preventing radioactive material leakage, and ensuring reactor safety. Furthermore, through numerical simulation technology, the growth and localized corrosion characteristics of CRUD under multiple operating conditions can be quickly predicted, significantly reducing time costs compared to existing experimental methods.

[0142] Furthermore, due to the high radioactivity within the reactor core, it is difficult to directly remove fuel assemblies from the reactor and analyze CRUD growth and localized corrosion. Therefore, the most mature approach currently is to establish a test simulation system similar to the reactor's primary loop, using experimental methods to simulate CRUD growth and its impact on localized corrosion. For example, a WALT (Westing House Advanced Loop Tester) simulation test system can be constructed. By controlling the water chemistry conditions of the WALT test system, an oxide corrosion product deposition layer can be formed on the surface of electrically heated rods (simulating fuel rods). However, simulation tests typically require a long time (usually 2000 hours), and the test conditions need to be precisely controlled over a long period to accurately obtain the CRUD growth and localized corrosion characteristics. Therefore, the numerical prediction technology constructed in this embodiment of the invention can also significantly save on experimental costs and time, and can quickly obtain the CRUD growth and localized corrosion characteristics under multiple operating conditions.

[0143] 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 the growth of oxidation corrosion products and localized corrosion, characterized in that, The method includes: The first parameter is obtained, and the growth rate of corrosion products per unit area is calculated based on the first parameter and the growth model; wherein, the first parameter includes the temperature and flow rate of the fluid near the wall, as well as multiple growth condition calculation parameters; The target thickness of the corrosion product deposition layer CRUD is calculated based on the growth rate per unit area of ​​the corrosion products; wherein, the target thickness of the deposition layer is used to characterize the thickness of the deposition layer obtained by the combined action of deposition and erosion of the corrosion products at any time. A second parameter is obtained, and the heat transfer parameters of the CRUD are calculated based on the second parameter and the calculation model. The heat transfer parameters include: thermal conductivity, bubble detachment diameter, bubble detachment frequency, and nucleation site density. The calculation model includes: KI model, Cole model, and YK model. The second parameter includes: liquid phase density, gas phase density, contact angle, gravitational acceleration, surface tension, cavity density, cavity orifice radius, maximum bubble cavity radius, minimum bubble cavity radius, and cavity cone angle. The bubble detachment diameter is calculated based on the liquid phase density, gas phase density, contact angle, gravitational acceleration, surface tension, and the KI model. The bubble detachment frequency is calculated based on the bubble detachment diameter, liquid phase density, gas phase density, gravitational acceleration, and the Cole model. The nucleation site density is calculated based on the cavity density, contact angle, cavity cone angle, cavity orifice radius, maximum bubble cavity radius, minimum bubble cavity radius, and the YK model. The contact temperature is calculated based on the heat transfer parameters; wherein the contact temperature is used to characterize the temperature between the CRUD and the fuel rod cladding, and an oxide layer also exists between the CRUD and the fuel rod cladding; A third parameter is obtained, and the oxide layer thickness is calculated based on the third parameter and the contact temperature; wherein the third parameter includes: multiple constant coefficients; a transition thickness is calculated based on the third parameter and the contact temperature; if the oxide layer thickness is less than the transition thickness, the oxide layer thickness is calculated according to a first thickness calculation model based on the third parameter and the contact temperature; or, if the oxide layer thickness is greater than the transition thickness, the oxide layer thickness is calculated according to a second thickness calculation model based on the third parameter and the contact temperature. The localized corrosion results of the oxide layer are generated based on the oxide layer thickness.

2. The method according to claim 1, characterized in that, The corrosion products include dissolution corrosion products and particulate corrosion products. The growth model includes a dissolution growth model, a particulate growth model, and an erosion model. The growth condition calculation parameters include: dissolution growth condition parameters, particulate growth condition parameters, and erosion condition parameters. The step of calculating the growth rate per unit area of ​​corrosion products based on the first parameter and the growth model includes: The deposition rate of dissolution corrosion products per unit area was calculated based on the dissolution growth condition parameters and the dissolution growth model. The deposition rate of particle corrosion products per unit area was calculated based on the particle growth operating parameters and the particle growth model. The corrosion rate per unit area of ​​corrosion products was calculated based on the corrosion condition parameters and the corrosion model. The growth rate of the corrosion products per unit area is calculated based on the deposition rate of the dissolved corrosion products per unit area, the deposition rate of the particulate corrosion products per unit area, and the erosion rate of the corrosion products per unit area.

3. The method according to claim 1, characterized in that, The step of calculating the bubble detachment diameter based on the liquid phase density, the gas phase density, the contact angle, the gravitational acceleration, the surface tension, and the KI model includes: The expression for the KI model is as follows: in, This indicates the diameter of the bubble's detachment. This indicates the density of the liquid phase. This represents the gas phase density. This represents the surface tension. Indicates the contact angle, This represents the acceleration due to gravity.

4. The method according to claim 1, characterized in that, The step of calculating the bubble escape frequency based on the bubble escape diameter, the liquid phase density, the gas phase density, the gravitational acceleration, and the Cole model includes: The expression for the Cole model is as follows: in, This indicates the frequency at which the bubble detaches. This represents the acceleration due to gravity. This indicates the density of the liquid phase. This represents the gas phase density. This indicates the diameter at which the bubble detaches.

5. The method according to claim 1, characterized in that, The step of calculating the nucleation site density based on the cavity density, the cavity opening radius, the contact angle, the cavity cone angle, the maximum cavity radius of the bubble, the minimum cavity radius of the bubble, and the YK model includes: The expression for the YK model is as follows: in, This indicates the density of the nucleation sites. This indicates the cavity density. Indicates the contact angle, This indicates the maximum cavity radius of the bubble. This represents the minimum cavity radius of the bubble. Indicates the cone angle of the cavity. This represents the radius of the cavity opening.

6. The method according to claim 1, characterized in that, The step of calculating the transition thickness based on the third parameter and the contact temperature includes: The transition thickness is calculated based on the third parameter and the contact temperature using the following formula: in, This indicates the transition thickness. , , and All of these represent the constant coefficients. This indicates the contact temperature.

7. The method according to claim 6, characterized in that, The step of calculating the oxide layer thickness according to the third parameter and the contact temperature using the first thickness calculation model includes: The expression for the first thickness calculation model is as follows: in, This indicates the thickness of the oxide layer. , and All of these represent the constant coefficients. This indicates the contact temperature.

8. The method according to claim 7, characterized in that, The third parameter also includes the irradiation enhancement factor and the reactor fast neutron flux; the step of calculating the oxide layer thickness according to the third parameter and the contact temperature using the second thickness calculation model includes: The expression for the second thickness calculation model is as follows: in, This indicates the thickness of the oxide layer. , , , , and All of these represent the constant coefficients. This indicates the contact temperature. This represents the irradiation enhancement factor. This represents the fast neutron flux of the reactor.

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