Method, apparatus, and device for heat and mass transfer analysis of nuclear reactor corrosion products

Abstract

This application relates to a method, apparatus, computer equipment, storage medium, and computer program product for analyzing the heat and mass transfer of corrosion products in nuclear reactors. It includes: obtaining the average thermal conductivity of the corrosion products and determining the temperature distribution of the corrosion products in coolant saturation, nucleation boiling, and evaporation states based on the average thermal conductivity; determining the coolant flow rate distribution in the corrosion products based on the pressure distribution; obtaining the concentration relationship between the boric acid concentration and the concentrations of other soluble substances in the coolant, and determining the concentration distribution of other soluble substances based on the concentration relationship and the boric acid concentration; analyzing the internal heat and mass transfer of the corrosion products based on the temperature distribution, flow rate distribution, and concentration distribution of soluble substances to obtain the concentration of boron enriched within the corrosion products, and obtaining the total boron deposition based on the enriched concentration. This method can accurately analyze the heat and mass transfer of corrosion products in nuclear reactors.

Description

Technical Field

[0001] This application relates to the field of heat and mass transfer analysis technology, and in particular to a method, apparatus, computer equipment, storage medium and computer program product for analyzing the heat and mass transfer of corrosion products in nuclear reactors. Background Technology

[0002] During operation, pressurized water reactors generate a large amount of oxidation and corrosion products, primarily composed of iron ions, nickel ions, and their oxides. These corrosion products, under the influence of supercooled nucleus boiling, deposit on the surface of the fuel cladding in the upper part of the core, forming a thin, loose, porous scale layer known as corrosion products. The presence of corrosion products increases the thermal resistance of the fuel rods, leading to a deterioration in heat transfer performance. Furthermore, due to the loose, porous chimney structure, boron tends to accumulate more within the corrosion products, resulting in uneven axial distribution of boron in the fuel rods and potentially inducing core power drift.

[0003] Currently, the heat and mass transfer process inside corrosion products is mainly analyzed by calculating the temperature, flow rate, pressure, and solute concentration distribution within the deposition layer. However, due to the limited number of parameters used, the accuracy of the heat and mass transfer analysis is reduced. Summary of the Invention

[0004] Therefore, it is necessary to provide a method, apparatus, computer equipment, computer-readable storage medium, and computer program product for analyzing the heat and mass transfer of nuclear reactor corrosion products, which can accurately analyze heat and mass transfer, in order to address the above-mentioned technical problems.

[0005] In a first aspect, this application provides a method for analyzing the heat and mass transfer of corrosion products in nuclear reactors, the method comprising:

[0006] The average thermal conductivity of corrosion products in a nuclear reactor is obtained, and the temperature distribution of the corrosion products is determined based on the average thermal conductivity when the coolant is saturated, in a nucleating boiling state, and in a dry state.

[0007] The flow rate distribution of the coolant in the corrosion products is determined based on the pressure distribution in the corrosion products;

[0008] Obtain the concentration relationship between the boric acid concentration and the concentrations of other soluble substances in the coolant, and determine the concentration distribution of the other soluble substances based on the concentration relationship and the boric acid concentration.

[0009] Based on the temperature distribution, the flow rate distribution, and the concentration distribution of soluble substances, the heat and mass transfer process inside the corrosion products is analyzed to obtain the concentration of boron after enrichment inside the corrosion products, and the total amount of boron deposition is obtained based on the enriched concentration; the soluble substances include boric acid and other soluble substances.

[0010] In one embodiment, obtaining the average thermal conductivity of the corrosion products includes:

[0011] The porosity of the corrosion products, the solid thermal conductivity of the corrosion products, and the liquid thermal conductivity of the coolant in the corrosion products are obtained.

[0012] The average thermal conductivity of the corrosion products is determined based on the porosity, the solid thermal conductivity, and the liquid thermal conductivity.

[0013] In one embodiment, determining the temperature distribution of the corrosion products when the coolant is saturated, based on the average thermal conductivity, includes:

[0014] Obtain the thickness of the corrosion product;

[0015] Based on the average thermal conductivity and the thickness, the saturation temperature distribution of the corrosion products is determined when the coolant is saturated; the temperature distribution includes the saturation temperature distribution.

[0016] In one embodiment, determining the internal temperature distribution of the corrosion products when the coolant is in a nucleation boiling state, based on the average thermal conductivity, includes:

[0017] Obtain the wick boiling relationship, which characterizes the relationship between the thickness of the corrosion products and the internal temperature of the corrosion products when the coolant is in a nucleation boiling state;

[0018] Based on the relationship between the thickness distribution of the corrosion products and the boiling of the wick, the internal temperature distribution of the corrosion products in the bubbling boiling state is determined; the temperature distribution includes the temperature distribution in the bubbling boiling state.

[0019] In one embodiment, the method further includes:

[0020] Determine the temperature relationship characterizing the relationship between the thickness of the corrosion products and the temperature of the corrosion products, the flow rate relationship characterizing the relationship between the pressure in the corrosion products and the flow rate of the coolant, and the concentration relationship.

[0021] Based on the temperature relationship and the thickness of the corrosion product, the nth temperature distribution of the corrosion product in the nth iteration step and the (n+1)th temperature distribution of the corrosion product in the (n+1)th iteration step are determined, and the temperature difference between the nth temperature distribution and the (n+1)th temperature distribution is determined; the nth iteration step and the (n+1)th iteration step are adjacent iteration steps; n is a positive integer.

[0022] Based on the flow rate relationship and the pressure in the corrosion products, the nth flow rate distribution of the coolant in the nth iteration step and the n+1th flow rate distribution of the coolant in the n+1th iteration step are determined, and the flow rate difference between the nth flow rate distribution and the n+1th flow rate distribution is determined.

[0023] Based on the concentration relationship and the boric acid concentration in the coolant, the concentration distribution of the other soluble substances at the nth iteration step and the concentration distribution of the coolant at the (n+1)th iteration step are determined, and the concentration difference between the nth concentration distribution and the (n+1)th concentration distribution is determined.

[0024] The maximum difference among the temperature difference, the flow rate difference, and the concentration difference is determined. If the maximum difference is less than a preset difference threshold, the nth flow rate distribution is determined as the flow rate distribution, the nth temperature distribution is determined as the temperature distribution, and the nth concentration distribution is determined as the concentration distribution of the other soluble substances.

[0025] In one embodiment, determining the temperature distribution of the corrosion products when the coolant is in a dry state based on the average thermal conductivity includes:

[0026] Obtain a three-dimensional coordinate system formula characterizing the relationship between the thickness of the corrosion products and the temperature of the corrosion products when the coolant is evaporated to dryness;

[0027] Based on the relationship between the thickness of the corrosion products and the three-dimensional coordinate system, the evaporation temperature distribution of the corrosion products is determined; the temperature distribution includes the evaporation temperature distribution.

[0028] Secondly, this application provides a heat and mass transfer analysis device for nuclear reactor corrosion products, the device comprising:

[0029] The temperature distribution determination module is used to obtain the average thermal conductivity of the corrosion products of the nuclear reactor, and to determine the temperature distribution of the corrosion products in the coolant saturation state, the nucleation boiling state, and the evaporation state based on the average thermal conductivity.

[0030] A flow rate distribution determination module is used to determine the flow rate distribution of the coolant in the corrosion products based on the pressure distribution in the corrosion products;

[0031] The concentration distribution determination module is used to obtain the concentration relationship between the concentration of boric acid and the concentration of other soluble substances in the coolant, and to determine the concentration distribution of the other soluble substances based on the concentration relationship and the concentration of boric acid.

[0032] The analysis module is used to analyze the heat and mass transfer process of the corrosion products based on the temperature distribution, the flow rate distribution, and the concentration distribution of soluble substances, to obtain the concentration of boron after enrichment inside the corrosion products, and to obtain the total amount of boron deposition based on the enriched concentration; the soluble substances include boric acid and other soluble substances.

[0033] Thirdly, this application provides a computer device, including a memory and a processor, wherein the memory stores a computer program, and the processor executes the computer program to implement the steps of the above-described method.

[0034] Fourthly, this application provides a computer-readable storage medium having a computer program stored thereon, which, when executed by a processor, implements the steps of the above-described method.

[0035] Fifthly, this application provides a computer program product, including a computer program that, when executed by a processor, implements the steps of the above-described method.

[0036] The aforementioned methods, apparatus, computer equipment, storage media, and computer program products for analyzing the heat and mass transfer of nuclear reactor corrosion products analyze the temperature distribution of corrosion products based on their average thermal conductivity under saturated, bubbling, and dried-out coolant conditions. This allows for a comprehensive analysis of the heat transfer of corrosion products by understanding the influence of the coolant's state on the heat transfer of the corrosion products. Furthermore, by determining the coolant flow rate distribution based on the pressure distribution within the corrosion products, and by determining the concentrations of other soluble substances in the corrosion products based on concentration relationships and the boric acid concentration, the analysis combines temperature distribution, flow rate distribution, and soluble substance concentration distribution. This approach considers the coupling relationship between these factors, enabling a comprehensive analysis of the heat and mass transfer process. The resulting accurate concentration of boron enriched within the corrosion products allows for the determination of the total boron deposition. Attached Figure Description

[0037] Figure 1 This is a diagram illustrating the application environment of a heat and mass transfer analysis method for nuclear reactor corrosion products in one embodiment.

[0038] Figure 2 This is a flowchart illustrating a method for analyzing the heat and mass transfer of corrosion products in a nuclear reactor, as described in one embodiment.

[0039] Figure 3 This is a flowchart illustrating a method for analyzing the heat and mass transfer of nuclear reactor corrosion products in another embodiment.

[0040] Figure 4This is a structural block diagram of a heat and mass transfer analysis device for nuclear reactor corrosion products in one embodiment.

[0041] Figure 5 This is an internal structural diagram of a computer device in one embodiment. Detailed Implementation

[0042] To make the objectives, technical solutions, and advantages of this application clearer, the following detailed description is provided in conjunction with the accompanying drawings and embodiments. It should be understood that the specific embodiments described herein are merely illustrative and not intended to limit the scope of this application.

[0043] The heat and mass transfer analysis method for nuclear reactor corrosion products provided in this application can be applied to, for example... Figure 1 The application environment is shown. Terminal 102 communicates with server 104 via a network. A data storage system can store the data that server 104 needs to process. The data storage system can be integrated onto server 104 or placed on a cloud or other network server. Server 104 obtains the average thermal conductivity of corrosion products in the nuclear reactor and determines the temperature distribution of the corrosion products under coolant saturation, bubbling boiling, and evaporation states based on the average thermal conductivity. Server 104 determines the coolant flow rate distribution inside the corrosion products based on the pressure distribution within the corrosion products. Server 104 obtains a concentration relationship formula characterizing the relationship between the concentration of boric acid and other soluble substances in the coolant, and then determines the concentration distribution of other soluble substances based on the concentration relationship formula and the boric acid concentration. Server 104 analyzes the heat and mass transfer inside the corrosion products based on the obtained temperature distribution, flow rate distribution, soluble substance concentration distribution, and the total amount of boron deposited in the corrosion products, obtaining the analysis results. Terminal 102 can be, but is not limited to, various personal computers, laptops, tablets, IoT devices, etc. Server 104 can be implemented using a standalone server or a server cluster consisting of multiple servers.

[0044] In one embodiment, such as Figure 2 As shown, a method for analyzing the heat and mass transfer of corrosion products in nuclear reactors is provided, and this method is applied to... Figure 1 Taking server 104 as an example, the following steps are included:

[0045] Step 202: Obtain the average thermal conductivity of the corrosion products in the nuclear reactor, and determine the temperature distribution of the corrosion products in the coolant saturation state, nucleation boiling state, and dry state based on the average thermal conductivity.

[0046] Corrosion products refer to a thin, loose, and porous scale layer formed on the fuel cladding surface by the deposition of oxidative corrosion products, mainly iron ions, nickel ions, and their oxides, under the action of supercooled nucleation boiling. For example, CRUD (chalk river unidentified deposit).

[0047] Average thermal conductivity, also known as thermal conductivity coefficient, is the inherent ability to transfer or conduct heat. It is derived from the solid thermal conductivity of corrosion products and the fluid thermal conductivity of coolants. Temperature distribution refers to the variation of temperature with spatial location within a given region at a given time. For example, at the current time point, within region A, there are locations a and b. The temperature at location a is x, and the temperature at location b is y. Combining the temperatures at these two locations, we can obtain the temperature distribution of region A at the current time point.

[0048] A saturated state refers to a state where the number of molecules entering the space per unit time is equal to the number of molecules returning to the liquid, and evaporation and condensation are in dynamic equilibrium. Although evaporation and condensation continue, the density of vapor molecules in the space no longer increases; this state is called a saturated state. When the coolant is saturated, the porous areas of corrosion products are filled with liquid, and the heat transferred from the cladding surface to the fuel rods is transferred to the coolant through the corrosion products via thermal conduction. Temperature analysis in a saturated state allows for early prediction of temperature distribution, preventing localized overheating that could lead to fuel damage. The nucleation boiling state refers to a state where superheat increases, and bubbles are continuously generated on the wall surface, rising and growing in the liquid. As heat transfer continues, when the CRUD cladding interface temperature reaches the nucleation boiling initiation temperature, nucleation boiling begins from the bottom of the CRUD layer, filling the CRUD with coolant and vapor. The coolant fills the small pore areas, and the vapor fills the large pore areas, i.e., the chimney area. The coolant and steam flow along a low-resistance path. Under capillary action, the coolant is drawn to the bottom of the CRUD, where it contacts the fuel cladding, forming bubbles and further generating steam. The steam escapes through the chimney and enters the coolant, subsequently being carried away by the coolant flow. Nucleus boiling enhances heat transfer within the CRUD, significantly increasing the overall heat transfer coefficient between the fuel rods and the coolant. The dry-out state occurs when the coolant required for nucleus boiling exceeds the coolant supplied by capillary action. In this case, the liquid-gas separation in the steam chimney breaks down, and the coolant dries at the interface between corrosion products and the cladding, forming a gas film that reduces the overall heat transfer coefficient of the CRUD.

[0049] Optionally, the server first determines the average thermal conductivity of the corrosion products based on the solid thermal conductivity of the corrosion products and the fluid thermal conductivity of the coolant. Then, it determines the temperature distribution of the corrosion products when the coolant is saturated, the temperature distribution of the corrosion products when the coolant is in a bubbling boiling state, and the temperature distribution of the corrosion products when the coolant is in a dry state.

[0050] Step 204: Determine the flow rate distribution of coolant in the corrosion products based on the pressure distribution in the corrosion products.

[0051] The pressure distribution is obtained through the pressure control equation and the boundary conditions for that equation. The velocity distribution is obtained after obtaining the pressure distribution, based on the relationship between pressure and velocity determined by Darcy's law. That is, the pressure distribution is treated as the independent variable, the velocity distribution as the dependent variable, and other parameters are known, thus yielding the velocity distribution of the coolant at various locations within the corrosion products. The pressure distribution refers to the set of specific pressure values ​​at various locations within the corrosion products of a nuclear reactor. For example, at the current time point, in region A, there are locations a and b. The pressure at location a is x, and the pressure at location b is y. Combining the pressures at these two locations, the pressure distribution of region A at the current time point can be obtained. The velocity distribution refers to the set of specific velocity values ​​of the coolant at various locations within the corrosion products of a nuclear reactor. At different time points, the pressure or velocity at the same location may be the same or different.

[0052] The pressure control equation is The boundary conditions for the pressure control equation are as follows: p| x＝0 =p f and Where, ρ w The density of the coolant is expressed in kg / m³. 3 κ represents the permeability of corrosion products, i.e., CRUD permeability; μ w This indicates the dynamic viscosity of the coolant, expressed in N·s / m³. 2 ;p f The pressure in the mainstream coolant zone is expressed in MPa; p and ▽p both represent the pressure inside the corrosion products; φ represents the porosity of the corrosion products; T represents the temperature of the corrosion products, which is a variable; r c The denoting factor represents the average pore radius, r represents the pore radius (a variable), x represents the depth of a specific location within the corrosion products, and δ represents the depth of the corrosion products. c h represents the average thickness of the CRUD in the deposition area. fg This represents the latent heat of vaporization of the coolant, expressed in kJ / mol.

[0053] The magnitude of CRUD permeability κ is mainly determined by the nth fractal dimension D. f and the (n+1)th fractal dimension D T Sure: Where d E λ represents the effective hydraulic diameter, in μm. min and λ max φ represents the minimum and maximum pore diameters, respectively, in μm; φ represents the porosity of the corrosion products; L represents the thickness of the coolant bubble growth; and τ represents the tortuosity of the coolant flow across the CRUD surface.

[0054] According to Darcy's law, the flow rate of coolant in corrosion products... The relationship between pressure ▽p and the expression is: The pressure ▽p is substituted as the independent variable into the relational expression to solve for the flow velocity.

[0055] Optionally, the server determines an expression characterizing the relationship between pressure and flow rate based on Darcy's law, then solves for the pressure distribution of coolant in the corrosion products according to the pressure control equation and the boundary conditions for the pressure control equation, and finally determines the flow rate distribution of coolant in the corrosion products based on the pressure distribution and the expression relating flow rate and pressure.

[0056] Step 206: Obtain the concentration relationship of soluble substances in the coolant, and determine the concentration distribution of other soluble substances based on the concentration relationship and the boric acid concentration.

[0057] The boric acid concentration in the coolant is obtained by explicitly solving the kinetic equations. The concentrations of other soluble substances refer to the concentrations of soluble substances in the coolant other than boric acid. These concentrations can be calculated using the boric acid concentration and ordinary differential equations or algebraic calculations. The concentration distribution of soluble substances refers to the set of specific concentration values ​​of soluble substances in the coolant at various locations within the nuclear reactor. The formula for calculating the concentration of each soluble substance is as follows: Among them, C i C represents the concentration of the i-th soluble substance, in mol / L; i,source C refers to the concentration of the i-th soluble substance formed. i,sink D represents the deposition concentration of the i-th soluble substance, in mol / L. i τ represents the diffusion coefficient of the i-th soluble substance as a function of the coolant temperature; τ represents the tortuosity of the coolant flow across the CRUD surface. Represents the vector depth at a specific location in CRUD operations; This represents the vector velocity of the coolant at a specific location in the CRUD. The boundary conditions for calculating the concentrations of other soluble substances are: Ci | x＝0 =C i,coolant , Among them, C i,coolant Let be the saturation concentration of the i-th soluble substance in the coolant, and x represent the depth of a certain position in the CRUD.

[0058] Optionally, the server explicitly solves for the boric acid concentration in the corrosion products based on the kinetic equations, and the concentration relationship formula characterizing the relationship between the boric acid concentration and the concentrations of other soluble substances in the coolant. Based on the concentration relationship formula and the boric acid concentration, the server calculates the concentrations of other soluble substances in the corrosion products, thereby obtaining the concentration distribution of other soluble substances in the coolant.

[0059] Step 208 involves analyzing the heat and mass transfer processes within the corrosion products based on temperature distribution, flow rate distribution, and the concentration distribution of soluble substances. This yields the concentration of boron enriched within the corrosion products, and the total boron deposition is calculated based on this enriched concentration. Soluble substances include boric acid and other soluble compounds.

[0060] Here, heat transfer and mass transfer refer to heat transfer and mass transfer, respectively. Total boron deposition m B The total mass of corrosion products and the concentration of boron after enrichment within the corrosion products can be used to calculate the concentration. The calculation formula is: m B =C adsorp ρ c A d δ c C adsorp ρ represents the adsorption capacity of corrosion products for boron per unit mass, expressed in g / g; c The density of the coolant is expressed in kg / m³. 3 ;δ c This represents the average thickness of the CRUD in the deposition area. C adsorp The calculation formula is C adsorp =9×10 -9 ·C clad +2×10 -4 C clad This indicates the concentration of boron after it has accumulated within the corrosion products, expressed in ppm. clad The calculation formula is Where CF represents the concentration factor, which is a dimensionless number; m e The boiling rate is represented by C, obtained from thermal engineering software. bulk This indicates the concentration of boric acid in the coolant, expressed in ppm; D B ρ represents the diffusion coefficient of boron, with units of cm / s; s This indicates the density of the coolant at saturation, expressed in g / cm³. 3φ represents the porosity of the corrosion products. (From C) clad Calculation formula It is known that concentration enrichment only occurs when corrosion products are present and occur in the supercooled nucleus boiling region. In the region of concentration enrichment, the concentration distribution of corrosion products along the thickness direction exhibits an exponential relationship; as the thickness increases, C... clad As the concentration increases, the concentration difference between the bottom of the corrosion products and the mainstream increases.

[0061] Optionally, the server analyzes the heat and mass transfer process of the corrosion products based on the temperature distribution, coolant flow rate distribution, and concentration distribution of soluble substances in the coolant, to obtain the concentration of boron enriched inside the corrosion products, and based on the concentration of boron enriched inside the corrosion products, obtains the total amount of boron deposited in the heat and mass transfer process inside the corrosion products.

[0062] In the aforementioned method for analyzing the heat and mass transfer of nuclear reactor corrosion products, the temperature distribution of the corrosion products is analyzed based on their average thermal conductivity under three conditions: saturated coolant, bubbling boiling, and dry-state coolant. This analysis reveals the influence of the coolant's state on the heat transfer of the corrosion products, allowing for a comprehensive analysis of the heat transfer. Furthermore, the flow rate distribution of the coolant is determined based on the pressure distribution within the corrosion products. The concentrations of other soluble substances in the corrosion products are determined using concentration relationships and the boric acid concentration. Combining these factors with the temperature distribution, flow rate distribution, and soluble substance concentration distribution allows for a comprehensive analysis of the heat and mass transfer process. This provides a more accurate estimate of the boron concentration after enrichment within the corrosion products, ultimately leading to the total boron deposition.

[0063] In one embodiment, obtaining the average thermal conductivity of the corrosion products includes:

[0064] The porosity of the corrosion products, the solid thermal conductivity of the corrosion products, and the liquid thermal conductivity of the coolant in the corrosion products were obtained.

[0065] The average thermal conductivity of corrosion products is determined based on porosity, solid thermal conductivity, and liquid thermal conductivity.

[0066] Porosity refers to the percentage of pore volume in a bulk material to the total volume of the material in its natural state. For example, the porosity of CRUD. Thermal conductivity, also known as the thermal conductivity coefficient, reflects a material's ability to conduct heat. According to Fourier's law, it is defined as the amount of heat transferred per unit temperature gradient per unit time through a unit conductive surface. Average thermal conductivity k... m The calculation formula is k m =(1-φ)k s+φk f Where φ represents porosity; k s k is the thermal conductivity of the solid. f k is the thermal conductivity of the liquid. s The solution can be obtained from the relationship between the proportion of each substance in the coolant and temperature: k s,i v represents the thermal conductivity of the i-th material in Table 1. f,i Let k be the volume fraction of the i-th substance in Table 1, and n be the quantity of the substance. f The solution formula is: k f =0.686 + 7.3 * 10 -10 P + 5.87 * 10 -6 (Ts-415) 2 P represents pressure, with the unit being Pa; Ts represents the coolant saturation temperature, with the unit being K.

[0067] Table 1. Heat transfer coefficients and proportions of each component.

[0068]

[0069]

[0070] Optionally, the server obtains the fluid thermal conductivity of the coolant based on the relationship between the proportion of each substance in the coolant and temperature, and obtains the solid thermal conductivity of the corrosion products using the formula for calculating solid thermal conductivity. Simultaneously, it also obtains the porosity of the corrosion products. Based on the solid thermal conductivity, fluid thermal conductivity, and porosity, the server uses formula k... m =(1-φ)k s +φk f The average thermal conductivity of the corrosion products is obtained by solving.

[0071] In this embodiment, by obtaining porosity, solid thermal conductivity, and fluid thermal conductivity, the average thermal conductivity of the corrosion products can be calculated, and the temperature distribution of the corrosion products can be determined based on the average thermal conductivity.

[0072] In one embodiment, determining the internal temperature distribution of corrosion products when the coolant is saturated, based on average thermal conductivity, includes:

[0073] Obtain the thickness of the corrosion products.

[0074] Based on the average thermal conductivity and thickness, the saturation temperature distribution of corrosion products in a saturated state of coolant is determined; the temperature distribution includes the saturation temperature distribution.

[0075] Thickness refers to the thickness of the material conducting heat under stable heat transfer conditions. For example, if the thickness of a CRUD is 1 meter when the coolant is saturated, then 1 meter is the thickness.

[0076] The saturation temperature distribution is determined by the product of thickness and average thermal conductivity. In other words, the saturation temperature distribution of corrosion products when the coolant is saturated is obtained by multiplying the thickness of the corrosion products by the average thermal conductivity.

[0077] Optionally, the server obtains the thickness of the corrosion products and then determines the saturation temperature distribution of the corrosion products when the coolant is saturated, based on the product between the thickness and the average thermal conductivity.

[0078] In this embodiment, by analyzing heat transfer under saturated coolant conditions, the temperature distribution of corrosion products at future moments can be predicted in advance, thereby avoiding localized overheating that could lead to fuel damage in the nuclear reactor.

[0079] In one embodiment, determining the temperature distribution of corrosion products when the coolant is in a nucleation boiling state based on average thermal conductivity includes:

[0080] Obtain the wick boiling relationship, which characterizes the relationship between the thickness of the corrosion products and the internal temperature of the corrosion products under the condition of nucleation boiling in the coolant.

[0081] Based on the relationship between the thickness distribution of corrosion products and wick boiling, the internal temperature distribution of the corrosion products in the nucleation boiling state is determined. This temperature distribution includes the temperature distribution during the nucleation boiling state.

[0082] The specific form of the wick boiling relationship is as follows: The boiling relationship of the wick can be obtained by combining the heat transfer process formula ∫ shell q c dA+∫ chimney q b The expression relating dA=0, internal temperature Tx of the CRUD, and CRUD thickness x is as follows: And boundary conditions: T x＝0 =T0, We obtain: Ts and T0 represent the coolant saturation temperature and the main fluid temperature, respectively, in K; x represents the depth of a certain location in the CRUD, in μm; Tx represents the temperature at depth x in the CRUD; and N represents the pore density, in cells / cm³. 2 ;r c The pore size represents the average radius in cm; f represents the CRUD effective heat transfer area coefficient. k m q represents the average thermal conductivity of CRUD, expressed in W / (m·K);b This represents the boiling heat flux density, with units of W / m³. 2 ;q c This refers to the heat flux density A within the CRUD, which represents the evaporation coefficient; δ c The average thickness of the CRUD in the deposition area is expressed in cm; chimney refers to the chimney channel in the corrosion products; shell refers to the integral along the entire cladding surface; h c Indicates the evaporative heat transfer coefficient;

[0083] Optionally, by combining the heat transfer process formula, the relationship between the internal temperature Tx and the thickness x of the CRUD, and the boundary conditions, the server can obtain the wick boiling relationship, which characterizes the relationship between the thickness and temperature of the corrosion products when the coolant is in a nucleation boiling state. Based on the thickness of each location in the corrosion products and the obtained wick boiling relationship, the server obtains the nucleation boiling temperature distribution representing the temperature of each location in the corrosion products.

[0084] In this embodiment, by obtaining the wick boiling relation, which characterizes the relationship between the thickness of the corrosion product and the internal temperature of the corrosion product, under the condition that the coolant is in a bubbling boiling state, the internal temperature distribution of the corrosion product can be solved based on the wick boiling relation and the thickness distribution of the corrosion product, thereby obtaining the temperature distribution of the corrosion product under the condition that the coolant is in a bubbling boiling state.

[0085] In one embodiment, such as Figure 3 As shown, the methods for analyzing the heat and mass transfer of nuclear reactor corrosion products include:

[0086] Step 302: Determine the temperature relationship, which characterizes the relationship between the thickness of the corrosion products and the temperature of the corrosion products; the flow rate relationship, which characterizes the relationship between the pressure in the corrosion products and the flow rate of the coolant; and the concentration relationship.

[0087] The temperature relationship refers to the temperature relationship of the coolant in three states: saturation, nucleation boiling, and evaporation. The flow rate relationship is derived from Darcy's law, characterizing the flow rate of the coolant in the corrosion products. The relationship between pressure ▽p and expression Concentration relationship refers to the formula for calculating the concentration of soluble substances.

[0088] Optionally, the server determines the temperature relationship of the coolant in three states: saturation, nucleation boiling, and evaporation. It also determines the relationship between the flow rate and pressure of the coolant in the corrosion products based on Darcy's law, and the concentration relationship between the concentration of boric acid and the concentration of other soluble substances in the coolant.

[0089] Step 304: Based on the temperature relationship and the thickness of the corrosion products, determine the nth temperature distribution of the corrosion products in the nth iteration step and the (n+1)th temperature distribution of the corrosion products in the (n+1)th iteration step, and determine the temperature difference between the nth and (n+1)th temperature distributions. The nth and (n+1)th iteration steps are adjacent iteration steps. n is a positive integer.

[0090] In this context, iteration refers to the activity of a repeated feedback process. The nth iteration step can be understood as the activity of the repeated feedback process at time A, and the (n+1)th iteration step can be understood as the activity of the repeated feedback process at time B. Time A and time B are adjacent, meaning there are no other iteration steps between the nth and (n+1)th iteration steps. When calculating the temperature distribution, the temperature calculated in the previous iteration step is used for the calculation in the next iteration step.

[0091] If the temperature difference between the temperature distribution obtained in the nth iteration step and the temperature distribution obtained in the (n+1)th iteration step is less than a pre-set difference threshold, it indicates that the temperature relationship has converged. The converged relationship can then be used to calculate the (n+2)th temperature distribution in the (n+2)th iteration step again. Alternatively, the nth temperature distribution or the (n+1)th temperature distribution can be directly output as the final temperature distribution used to analyze the heat and mass transfer process of the corrosion products.

[0092] Optionally, the server calculates the temperature distribution of corrosion products at the nth iteration step and the (n+1)th iteration step based on the formula for calculating temperature distribution of the coolant in the saturated state; calculates the temperature distribution of corrosion products at the nth iteration step and the (n+1)th iteration step based on the formula for calculating temperature distribution of the coolant in the nucleation boiling state; calculates the temperature distribution of corrosion products at the nth iteration step and the (n+1)th iteration step based on the formula for calculating temperature distribution of the coolant in the dried state; calculates the temperature difference between the nth and (n+1)th temperature distributions obtained in the saturated state, the nucleation boiling state, and the dried state.

[0093] Step 306: Based on the flow velocity relationship and the pressure in the corrosion products, determine the nth flow velocity distribution of the coolant in the nth iteration step and the n+1th flow velocity distribution of the coolant in the n+1th iteration step, and determine the flow velocity difference between the nth flow velocity distribution and the n+1th flow velocity distribution.

[0094] The nth velocity distribution and the (n+1)th velocity distribution are based on the velocity relationship formula. The flow velocity distribution is obtained by considering the specific values ​​of the pressure distribution. In other words, if all the parameters on the right-hand side of the flow velocity equation are known, the flow velocity distribution of the coolant can be obtained. The specific values ​​of the flow velocity distribution used in each iteration step may be the same or different. When calculating the flow velocity distribution, the flow velocity calculated in the previous iteration step is used for the calculation in the next iteration step.

[0095] Optionally, the server calculates the nth velocity distribution of the coolant at the nth iteration step and the (n+1)th velocity distribution at the (n+1)th iteration step, based on the velocity expression characterizing the relationship between velocity and pressure, and the pressure distributions at the nth iteration step and the (n+1)th iteration step. The server then calculates the velocity difference of the coolant based on the obtained nth and (n+1)th velocity distributions.

[0096] Step 308: Based on the concentration relationship and the boric acid concentration in the coolant, determine the concentration distribution of other soluble substances in the nth iteration step and the concentration distribution of the coolant in the (n+1)th iteration step, and determine the concentration difference between the nth concentration distribution and the (n+1)th concentration distribution.

[0097] The concentration relationship refers to

[0098] Optionally, the server calculates the nth concentration distribution in the coolant at the nth iteration step and the (n+1)th concentration distribution at the (n+1)th iteration step, based on the concentration expression characterizing the relationship between the concentrations of boric acid and other soluble chemicals, and the boric acid concentration distributions at the nth iteration step and the (n+1)th iteration step. The server then calculates the concentration difference for other soluble chemicals in the coolant based on the obtained nth and (n+1)th concentration distributions.

[0099] Step 310: Determine the maximum difference among the temperature difference, flow rate difference, and concentration difference. If the maximum difference is less than a preset difference threshold, determine the nth flow rate distribution as the flow rate distribution, the nth temperature distribution as the temperature distribution, and the nth concentration distribution as the concentration distribution of other soluble substances.

[0100] Optionally, the maximum difference refers to the largest difference among temperature, flow rate, and concentration. A maximum difference less than a preset difference threshold indicates that all relationships have converged. If the maximum difference is less than the preset difference threshold, the (n+1)th flow rate distribution can be determined as the flow rate distribution for heat and mass transfer analysis, the (n+1)th temperature distribution can be determined as the temperature distribution for heat and mass transfer analysis, and the (n+1)th concentration distribution can be determined as the concentration distribution of other soluble substances for heat and mass transfer analysis. Furthermore, based on the converged relationships, the (n+2)th temperature distribution, (n+2)th flow rate distribution, and (n+2)th concentration distribution of the (n+2)th iteration step can be calculated.

[0101] In one embodiment, a temperature difference threshold can be set for the temperature distribution, a flow rate difference threshold can be set for the flow rate distribution, and a concentration difference threshold can be set for the concentration distribution. It is set so that no further iteration is needed only when the temperature difference is less than the temperature difference threshold, the flow rate difference is less than the flow rate difference threshold, and the concentration difference is less than the concentration difference threshold. That is, the final determined relation is used to determine the temperature distribution, flow rate distribution, and concentration distribution for heat and mass transfer analysis of corrosion products only when all relations are converged.

[0102] In this embodiment, by setting a difference threshold and determining the convergence of each relation only when the maximum difference is less than the preset difference threshold, the temperature distribution, concentration distribution, and flow rate distribution obtained based on each relation can be more accurate, thereby making the heat and mass transfer analysis results obtained based on the temperature distribution, concentration distribution, and flow rate distribution more accurate.

[0103] In one embodiment, the average thermal conductivity determines the temperature distribution of corrosion products when the coolant is in a dry state, including:

[0104] Obtain a three-dimensional coordinate system formula characterizing the relationship between the thickness of corrosion products and the temperature of corrosion products when the coolant is evaporated.

[0105] Based on the relationship between the thickness of the corrosion products and the three-dimensional coordinate system, the evaporation temperature distribution of the corrosion products is determined. The temperature distribution includes the evaporation temperature distribution.

[0106] Three-dimensional coordinate systems are coordinate systems used for positioning in three dimensions and can be established using three-dimensional CFD (Computational Fluid Dynamics) software. Examples include cylindrical coordinate systems, geodetic coordinate systems, and spherical coordinate systems. The specific form of a cylindrical coordinate system is as follows: Under steady-state conditions, constant physical properties, and without internal heat sources, the cylindrical coordinate system relationship can be rewritten as: Boundary conditions are Where R c The distance from the center of the chimney to the unit boundary in the corrosion products is expressed in μm; C p,f ρ represents the specific heat of the coolant at the corresponding pressure; f h represents the density of the coolant. c Indicates the evaporative heat transfer coefficient; T and Ts both represent temperature; q w This represents the heat flux density at the interface between the fuel cladding and corrosion products, expressed in W / m³. 2 ;k w L represents the thickness of the thermal boundary layer, expressed in W / (m·K). b The thickness of the bubble growth is indicated by the unit μm. The angle is represented by Φ, which is an unknown parameter; r represents the pore radius.

[0107] Optionally, the server obtains a cylindrical coordinate system formula characterizing the relationship between the thickness of the corrosion products and the temperature of the corrosion products when the coolant is in a state of complete evaporation. And rewritten under steady-state, constant physical properties, and no internal heat source conditions, we obtain... The server is based on the rewritten... Solve for the evaporation temperature distribution of corrosion products in three dimensions, and solve for the evaporation temperature distribution while satisfying the boundary conditions.

[0108] In this embodiment, by determining the three-dimensional coordinate system relationship between the thickness of the corrosion products and the temperature of the corrosion products when the coolant is in a dried state, the temperature distribution within the corrosion products can be observed more intuitively, thereby making the heat and mass transfer analysis results obtained based on the temperature distribution more accurate.

[0109] This application also provides an application scenario in which the aforementioned method for analyzing the heat and mass transfer of nuclear reactor corrosion products is applied. Specifically, the application of this method in this scenario is as follows: The server obtains the fluid thermal conductivity of the coolant based on the relationship between the proportion of each substance in the coolant and temperature. It then obtains the solid thermal conductivity of the corrosion products using the formula for calculating solid thermal conductivity, and also acquires the porosity of the corrosion products. Based on the solid thermal conductivity, fluid thermal conductivity, and porosity, the server uses a formula to calculate the average thermal conductivity of the corrosion products. Finally, based on the product of the average thermal conductivity and the thickness of the corrosion products, the server determines the temperature distribution of the corrosion products when the coolant is saturated.

[0110] The server calculates the temperature distribution of corrosion products at the nth iteration step and the (n+1)th iteration step based on the formula for calculating temperature distribution of the coolant in the nucleation boiling state. It then calculates the same formula for calculating temperature distribution of corrosion products in the (nth)th iteration step and the (n+1)th iteration step. Finally, it calculates the temperature difference between the nth and (n+1)th temperature distributions obtained when the coolant is saturated, in the nucleation boiling state, and in the dry state. The server determines that the formula for calculating temperature distribution has converged if all temperature differences are less than a temperature difference threshold, and then designates the (n+1)th temperature distribution as the temperature distribution used for heat and mass transfer analysis.

[0111] The server calculates the nth velocity distribution of the coolant at the nth iteration step and the (n+1th)th velocity distribution at the (n+1th)th iteration step, based on the velocity expression representing the relationship between velocity and pressure, and the pressure distributions at the nth and (n+1th)th iteration steps. The server then calculates the velocity difference for the coolant based on the obtained nth and (n+1th)th velocity distributions. If both velocity differences are less than a velocity difference threshold, the server determines that the equation for calculating the velocity distributions has converged and designates the (n+1th)th velocity distribution as the velocity distribution used for heat and mass transfer analysis.

[0112] The server calculates the nth and (n+1)th concentration distributions in the coolant based on the concentration expression characterizing the relationship between boric acid concentration and the concentrations of other soluble substances, as well as the boric acid concentration distributions at the nth and (n+1)th iteration steps. Using the obtained nth and (n+1)th concentration distributions, the server calculates the concentration difference for soluble substances in the coolant. If the concentration difference is less than a concentration difference threshold, the server determines that the formula for calculating the concentration distributions has converged and designates the (n+1)th concentration distribution as the concentration distribution used for heat and mass transfer analysis. The server calculates the total boron deposition based on the total mass of corrosion products, thus obtaining the total boron deposition in the corrosion products.

[0113] Finally, based on the temperature distribution in the corrosion products, the flow rate distribution of the coolant, the concentration distribution of soluble substances in the coolant, and the total amount of boron deposited in the corrosion products, the server analyzes the heat and mass transfer process of the corrosion products, thereby obtaining the heat and mass transfer analysis results for the corrosion products.

[0114] It should be understood that although the steps in the flowcharts of the embodiments described above are shown sequentially according to the arrows, these steps are not necessarily executed in the order indicated by the arrows. Unless explicitly stated herein, there is no strict order restriction on the execution of these steps, and they can be executed in other orders. Moreover, at least some steps in the flowcharts of the embodiments described above may include multiple steps or multiple stages. These steps or stages are not necessarily completed at the same time, but can be executed at different times. The execution order of these steps or stages is not necessarily sequential, but can be performed alternately or in turn with other steps or at least some of the steps or stages of other steps.

[0115] Based on the same inventive concept, this application also provides a heat and mass transfer analysis apparatus for nuclear reactor corrosion products, used to implement the heat and mass transfer analysis method for nuclear reactor corrosion products described above. The solution provided by this apparatus is similar to the solution described in the above method. Therefore, the specific limitations of one or more embodiments of the heat and mass transfer analysis apparatus for nuclear reactor corrosion products provided below can be found in the limitations of the heat and mass transfer analysis method for nuclear reactor corrosion products described above, and will not be repeated here.

[0116] In one embodiment, such as Figure 4 As shown, a heat and mass transfer analysis device for nuclear reactor corrosion products is provided, comprising:

[0117] Temperature distribution determination module 402 is used to obtain the average thermal conductivity of corrosion products in the nuclear reactor, and to determine the temperature distribution of corrosion products in the coolant saturation state, nucleation boiling state and dry state based on the average thermal conductivity.

[0118] The velocity distribution determination module 404 is used to determine the velocity distribution of coolant in corrosion products based on the pressure distribution in the corrosion products.

[0119] The concentration distribution determination module 406 is used to obtain the concentration relationship between the concentration of boric acid and the concentration of other soluble substances in the coolant, and to determine the concentration distribution of other soluble substances based on the concentration relationship and the concentration of boric acid.

[0120] Analysis module 408 is used to analyze the heat and mass transfer processes within the corrosion products based on temperature distribution, flow rate distribution, and concentration distribution of soluble substances. This analysis yields the concentration of boron enriched within the corrosion products and calculates the total boron deposition based on this enriched concentration. Soluble substances include boric acid and other soluble compounds.

[0121] In one embodiment, the temperature distribution determination module includes:

[0122] The first data determination unit is used to obtain the porosity of the corrosion products, the solid thermal conductivity of the corrosion products, and the liquid thermal conductivity of the coolant in the corrosion products.

[0123] The second data determination unit is used to determine the average thermal conductivity of corrosion products based on porosity, solid thermal conductivity, and liquid thermal conductivity.

[0124] In one embodiment, the temperature distribution determination module includes:

[0125] The length acquisition unit is used to obtain the thickness of the corrosion products.

[0126] The saturation temperature distribution determination unit is used to determine the saturation temperature distribution of corrosion products when the coolant is saturated, based on the average thermal conductivity and thickness. The temperature distribution includes the saturation temperature distribution.

[0127] In one embodiment, the temperature distribution determination module includes:

[0128] The first relational determination unit is used to obtain the wick boiling relation, which characterizes the relationship between the thickness of the corrosion products and the temperature of the corrosion products when the coolant is in the nucleation boiling state.

[0129] The bubbling boiling temperature distribution determination unit is used to determine the temperature distribution inside the corrosion products in the bubbling boiling state based on the relationship between the thickness distribution of the corrosion products and the wick boiling. The temperature distribution includes the temperature distribution in the bubbling boiling state.

[0130] In one embodiment, the heat and mass transfer analysis apparatus for nuclear reactor corrosion products further includes:

[0131] The second relationship determination unit is used to determine the temperature relationship characterizing the relationship between the thickness of the corrosion products and the temperature of the corrosion products, the flow rate relationship characterizing the relationship between the pressure in the corrosion products and the flow rate of the coolant, and the concentration relationship.

[0132] The temperature difference determination unit is used to determine the nth temperature distribution of the corrosion products in the nth iteration step and the (n+1)th temperature distribution of the corrosion products in the (n+1)th iteration step, based on the temperature relationship and the thickness of the corrosion products, and to determine the temperature difference between the nth and (n+1)th temperature distributions. The nth and (n+1)th iteration steps are adjacent iteration steps.

[0133] The velocity difference determination unit is used to determine the nth velocity distribution of the coolant in the nth iteration step and the n+1th velocity distribution of the coolant in the n+1th iteration step based on the velocity relationship and the pressure in the corrosion products, and to determine the velocity difference between the nth velocity distribution and the n+1th velocity distribution.

[0134] The concentration difference determination unit is used to determine the concentration distribution of other soluble substances in the nth iteration step and the concentration distribution of the coolant in the (n+1)th iteration step based on the concentration relationship and the boric acid concentration in the coolant, and to determine the concentration difference between the nth concentration distribution and the (n+1)th concentration distribution.

[0135] The (n+2)th data determination unit is used to determine the maximum difference among the temperature difference, flow rate difference, and concentration difference. If the maximum difference is less than a preset difference threshold, the nth flow rate distribution is determined as the flow rate distribution, the nth temperature distribution is determined as the temperature distribution, and the nth concentration distribution is determined as the concentration distribution of soluble substances.

[0136] In one embodiment, the temperature distribution determination module includes:

[0137] The third relational determination unit is used to obtain a three-dimensional coordinate system relational expression characterizing the relationship between the thickness of the corrosion products and the temperature of the corrosion products when the coolant is in a state of evaporation.

[0138] The unit for determining the evaporation temperature distribution is used to determine the evaporation temperature distribution of corrosion products based on the relationship between the thickness of the corrosion products and the three-dimensional coordinate system. The temperature distribution includes the evaporation temperature distribution.

[0139] Each module in the aforementioned heat and mass transfer analysis device for nuclear reactor corrosion products can be implemented entirely or partially through software, hardware, or a combination thereof. These modules can be embedded in or independent of the processor in a computer device, or stored in the computer device's memory as software, so that the processor can call and execute the corresponding operations of each module.

[0140] In one embodiment, a computer device is provided, which may be a server, and its internal structure diagram may be as follows: Figure 5As shown, this computer device includes a processor, memory, input / output (I / O) interfaces, and a communication interface. The processor, memory, and I / O interfaces are connected via a system bus, and the communication interface is also connected to the system bus via the I / O interfaces. The processor provides computational and control capabilities. The memory includes non-volatile storage media and internal memory. The non-volatile storage media stores the operating system, computer programs, and a database. The internal memory provides the environment for the operation of the operating system and computer programs stored in the non-volatile storage media. The database stores data on average thermal conductivity, temperature distribution, pressure distribution, flow rate distribution, boric acid concentration, concentration distribution of other soluble substances, total boron deposition, and total boron deposition. The I / O interfaces are used for information exchange between the processor and external devices. The communication interface is used for communication with external terminals via a network connection. When executed by the processor, the computer program implements a method for analyzing the heat and mass transfer of corrosion products in a nuclear reactor.

[0141] Those skilled in the art will understand that Figure 5 The structure shown is merely a block diagram of a portion of the structure related to the present application and does not constitute a limitation on the computer device to which the present application is applied. Specific computer devices may include more or fewer components than those shown in the figure, or combine certain components, or have different component arrangements.

[0142] In one embodiment, a computer device is provided, including a memory and a processor, wherein the memory stores a computer program, and the processor executes the computer program to perform the following steps:

[0143] The average thermal conductivity of corrosion products in a nuclear reactor is obtained, and the temperature distribution of these products under coolant saturation, nucleation boiling, and evaporation states is determined based on this average thermal conductivity. The flow rate distribution of the coolant within the corrosion products is determined based on the pressure distribution. The concentration relationship between boric acid and other soluble substances in the coolant is obtained, and the concentration distribution of other soluble substances is determined based on this relationship and the boric acid concentration. The heat and mass transfer process of the corrosion products is analyzed based on the temperature, flow rate, and soluble substance concentration distributions to obtain the concentration of boron enriched within the corrosion products, and the total boron deposition is calculated based on this enriched concentration. Soluble substances include boric acid and other soluble compounds.

[0144] In one embodiment, the processor, when executing a computer program, also performs the following steps:

[0145] The porosity of the corrosion products, the solid thermal conductivity of the corrosion products, and the liquid thermal conductivity of the coolant in the corrosion products are obtained; based on the porosity, solid thermal conductivity, and liquid thermal conductivity, the average thermal conductivity of the corrosion products is determined.

[0146] In one embodiment, the processor, when executing a computer program, also performs the following steps:

[0147] Obtain the thickness of the corrosion products; based on the average thermal conductivity and thickness, determine the saturation temperature distribution of the corrosion products when the coolant is saturated; the temperature distribution includes the saturation temperature distribution.

[0148] In one embodiment, the processor, when executing a computer program, also performs the following steps:

[0149] Obtain the wick boiling relation, which characterizes the relationship between the thickness of the corrosion products and the internal temperature of the corrosion products under the wick boiling state of the coolant; based on the thickness distribution of the corrosion products and the wick boiling relation, determine the temperature distribution inside the corrosion products under the wick boiling state; the temperature distribution includes the temperature distribution under the wick boiling state.

[0150] In one embodiment, the processor, when executing a computer program, also performs the following steps:

[0151] This paper establishes a temperature relationship characterizing the relationship between the thickness and temperature of corrosion products, a flow rate relationship characterizing the relationship between the pressure in the corrosion products and the flow rate of the coolant, and a concentration relationship. Based on the temperature relationships and the thickness of the corrosion products, it determines the nth temperature distribution of the corrosion products in the nth iteration step and the (n+1)th temperature distribution of the corrosion products in the (n+1)th iteration step, and determines the temperature difference between the nth and (n+1)th temperature distributions. The nth and (n+1)th iteration steps are considered adjacent iteration steps. Based on the flow rate relationships and the pressure in the corrosion products, it determines the nth flow rate distribution of the coolant in the nth iteration step and the (n+1)th flow rate distribution of the coolant in the (n+1)th iteration step. The flow rate distribution at step n+1 is determined, and the flow rate difference between the nth flow rate distribution and the (n+1)th flow rate distribution is determined. Based on the concentration relationship and the boric acid concentration in the coolant, the concentration distribution of other soluble substances at step n and the concentration distribution of the coolant at step n+1 are determined, and the concentration difference between the nth and (n+1)th concentration distributions is determined. The maximum difference among the temperature difference, flow rate difference, and concentration difference is determined, and if the maximum difference is less than a preset difference threshold, the nth flow rate distribution is determined as the flow rate distribution, the nth temperature distribution is determined as the temperature distribution, and the nth concentration distribution is determined as the concentration distribution of other soluble substances.

[0152] In one embodiment, the processor, when executing a computer program, also performs the following steps:

[0153] Obtain a three-dimensional coordinate system formula characterizing the relationship between the thickness and temperature of corrosion products when the coolant is in a state of evaporation; based on the relationship between the thickness and the three-dimensional coordinate system formula, determine the evaporation temperature distribution of the corrosion products; the temperature distribution includes the evaporation temperature distribution.

[0154] In one embodiment, a computer-readable storage medium is provided having a computer program stored thereon, the computer program performing the following steps when executed by a processor:

[0155] The average thermal conductivity of corrosion products in a nuclear reactor is obtained, and the temperature distribution of these products under coolant saturation, nucleation boiling, and evaporation states is determined based on this average thermal conductivity. The flow rate distribution of the coolant within the corrosion products is determined based on the pressure distribution. The concentration relationship between boric acid and other soluble substances in the coolant is obtained, and the concentration distribution of other soluble substances is determined based on this relationship and the boric acid concentration. The heat and mass transfer process of the corrosion products is analyzed based on the temperature, flow rate, and soluble substance concentration distributions to obtain the concentration of boron enriched within the corrosion products, and the total boron deposition is calculated based on this enriched concentration. Soluble substances include boric acid and other soluble compounds.

[0156] In one embodiment, the processor, when executing a computer program, also performs the following steps:

[0157] The porosity of the corrosion products, the solid thermal conductivity of the corrosion products, and the liquid thermal conductivity of the coolant in the corrosion products are obtained; based on the porosity, solid thermal conductivity, and liquid thermal conductivity, the average thermal conductivity of the corrosion products is determined.

[0158] In one embodiment, the processor, when executing a computer program, also performs the following steps:

[0159] Obtain the thickness of the corrosion products; based on the average thermal conductivity and thickness, determine the saturation temperature distribution of the corrosion products when the coolant is saturated; the temperature distribution includes the saturation temperature distribution.

[0160] In one embodiment, the processor, when executing a computer program, also performs the following steps:

[0161] Obtain the wick boiling relationship, which characterizes the relationship between the thickness of the corrosion products and the internal temperature of the corrosion products under the condition of nucleation boiling in the coolant; based on the thickness distribution of the corrosion products and the wick boiling relationship, determine the temperature distribution inside the corrosion products under the condition of nucleation boiling; the temperature distribution includes the temperature distribution under the condition of nucleation boiling.

[0162] In one embodiment, the processor, when executing a computer program, also performs the following steps:

[0163] This paper establishes a temperature relationship characterizing the relationship between the thickness and temperature of corrosion products, a flow rate relationship characterizing the relationship between the pressure in the corrosion products and the flow rate of the coolant, and a concentration relationship. Based on the temperature relationships and the thickness of the corrosion products, it determines the nth temperature distribution of the corrosion products in the nth iteration step and the (n+1)th temperature distribution of the corrosion products in the (n+1)th iteration step, and determines the temperature difference between the nth and (n+1)th temperature distributions. The nth and (n+1)th iteration steps are considered adjacent iteration steps. Based on the flow rate relationships and the pressure in the corrosion products, it determines the nth flow rate distribution of the coolant in the nth iteration step and the (n+1)th flow rate distribution of the coolant in the (n+1)th iteration step. The flow rate distribution at step n+1 is determined, and the flow rate difference between the nth flow rate distribution and the (n+1)th flow rate distribution is determined. Based on the concentration relationship and the boric acid concentration in the coolant, the concentration distribution of other soluble substances at step n and the concentration distribution of the coolant at step n+1 are determined, and the concentration difference between the nth and (n+1)th concentration distributions is determined. The maximum difference among the temperature difference, flow rate difference, and concentration difference is determined, and if the maximum difference is less than a preset difference threshold, the nth flow rate distribution is determined as the flow rate distribution, the nth temperature distribution is determined as the temperature distribution, and the nth concentration distribution is determined as the concentration distribution of other soluble substances.

[0164] In one embodiment, the processor, when executing a computer program, also performs the following steps:

[0165] Obtain a three-dimensional coordinate system formula characterizing the relationship between the thickness and temperature of corrosion products when the coolant is in a state of evaporation; based on the relationship between the thickness and the three-dimensional coordinate system formula, determine the evaporation temperature distribution of the corrosion products; the temperature distribution includes the evaporation temperature distribution.

[0166] In one embodiment, a computer program product is provided, including a computer program that, when executed by a processor, performs the following steps:

[0167] The average thermal conductivity of corrosion products in a nuclear reactor is obtained, and the temperature distribution of these products under coolant saturation, nucleation boiling, and evaporation states is determined based on this average thermal conductivity. The flow rate distribution of the coolant within the corrosion products is determined based on the pressure distribution. The concentration relationship between boric acid and other soluble substances in the coolant is obtained, and the concentration distribution of other soluble substances is determined based on this relationship and the boric acid concentration. The heat and mass transfer process of the corrosion products is analyzed based on the temperature, flow rate, and soluble substance concentration distributions to obtain the concentration of boron enriched within the corrosion products, and the total boron deposition is calculated based on this enriched concentration. Soluble substances include boric acid and other soluble compounds.

[0168] In one embodiment, the processor, when executing a computer program, also performs the following steps:

[0169] The porosity of the corrosion products, the solid thermal conductivity of the corrosion products, and the liquid thermal conductivity of the coolant in the corrosion products are obtained; based on the porosity, solid thermal conductivity, and liquid thermal conductivity, the average thermal conductivity of the corrosion products is determined.

[0170] In one embodiment, the processor, when executing a computer program, also performs the following steps:

[0171] Obtain the thickness of the corrosion products; based on the average thermal conductivity and thickness, determine the saturation temperature distribution of the corrosion products when the coolant is saturated; the temperature distribution includes the saturation temperature distribution.

[0172] In one embodiment, the processor, when executing a computer program, also performs the following steps:

[0173] Obtain the wick boiling relationship, which characterizes the relationship between the thickness and temperature of corrosion products when the coolant is in the nucleation boiling state; based on the thickness distribution of corrosion products and the wick boiling relationship, determine the temperature distribution of corrosion products in the nucleation boiling state; the temperature distribution includes the temperature distribution in the nucleation boiling state.

[0174] In one embodiment, the processor, when executing a computer program, also performs the following steps:

[0175] This paper establishes a temperature relationship characterizing the relationship between the thickness and temperature of corrosion products, a flow rate relationship characterizing the relationship between the pressure in the corrosion products and the flow rate of the coolant, and a concentration relationship. Based on the temperature relationships and the thickness of the corrosion products, it determines the nth temperature distribution of the corrosion products in the nth iteration step and the (n+1)th temperature distribution of the corrosion products in the (n+1)th iteration step, and determines the temperature difference between the nth and (n+1)th temperature distributions. The nth and (n+1)th iteration steps are considered adjacent iteration steps. Based on the flow rate relationships and the pressure in the corrosion products, it determines the nth flow rate distribution of the coolant in the nth iteration step and the flow rate distribution of the coolant in the (n+1)th iteration step. The flow rate distribution at the (n+1)th step is determined, and the flow rate difference between the nth and (n+1)th flow rate distributions is determined. Based on the concentration relationship and the boric acid concentration in the coolant, the concentration distributions of other soluble substances at the nth iteration step and the (n+1)th concentration distribution of the coolant at the (n+1)th iteration step are determined, and the concentration difference between the nth and (n+1)th concentration distributions is determined. The maximum difference among the temperature difference, flow rate difference, and concentration difference is determined, and if the maximum difference is less than a preset difference threshold, the nth flow rate distribution is determined as the flow rate distribution, the nth temperature distribution is determined as the temperature distribution, and the nth concentration distribution is determined as the concentration distribution of soluble substances.

[0176] In one embodiment, the processor, when executing a computer program, also performs the following steps:

[0177] Obtain a three-dimensional coordinate system formula characterizing the relationship between the thickness and temperature of corrosion products when the coolant is in a state of evaporation; based on the relationship between the thickness and the three-dimensional coordinate system formula, determine the evaporation temperature distribution of the corrosion products; the temperature distribution includes the evaporation temperature distribution.

[0178] It should be noted that the user information (including but not limited to user device information, user personal information, etc.) and data (including but not limited to data used for analysis, data stored, data displayed, etc.) involved in this application are all information and data authorized by the user or fully authorized by all parties, and the collection, use and processing of the relevant data shall comply with the relevant laws, regulations and standards of the relevant countries and regions.

[0179] Those skilled in the art will understand that all or part of the processes in the methods of the above embodiments can be implemented by a computer program instructing related hardware. The computer program can be stored in a non-volatile computer-readable storage medium, and when executed, it can include the processes of the embodiments of the above methods. Any references to memory, databases, or other media used in the embodiments provided in this application can include at least one of non-volatile and volatile memory. Non-volatile memory can include read-only memory (ROM), magnetic tape, floppy disk, flash memory, optical memory, high-density embedded non-volatile memory, resistive random access memory (ReRAM), magnetic random access memory (MRAM), ferroelectric random access memory (FRAM), phase change memory (PCM), graphene memory, etc. Volatile memory can include random access memory (RAM) or external cache memory, etc. By way of illustration and not limitation, RAM can take many forms, such as Static Random Access Memory (SRAM) or Dynamic Random Access Memory (DRAM). The databases involved in the embodiments provided in this application may include at least one type of relational database and non-relational database. Non-relational databases may include, but are not limited to, blockchain-based distributed databases. The processors involved in the embodiments provided in this application may be general-purpose processors, central processing units, graphics processing units, digital signal processors, programmable logic devices, quantum computing-based data processing logic devices, etc., and are not limited to these.

[0180] The technical features of the above embodiments can be combined in any way. For the sake of brevity, not all possible combinations of the technical features in the above embodiments are described. However, as long as there is no contradiction in the combination of these technical features, they should be considered to be within the scope of this specification.

[0181] The embodiments described above are merely illustrative of several implementation methods of this application, and while the descriptions are specific and detailed, they should not be construed as limiting the scope of this patent application. It should be noted that those skilled in the art can make various modifications and improvements without departing from the concept of this application, and these all fall within the protection scope of this application. Therefore, the protection scope of this application should be determined by the appended claims.

Claims

1. A method for heat and mass transfer analysis of corrosion products of a nuclear reactor, characterized by, The method includes: The average thermal conductivity of corrosion products in a nuclear reactor is obtained, and the temperature distribution of the corrosion products is determined based on the average thermal conductivity when the coolant is saturated, in a nucleating boiling state, and in a dry state. The flow rate distribution of the coolant in the corrosion products is determined based on the pressure distribution in the corrosion products; Obtain the concentration relationship between the boric acid concentration and the concentrations of other soluble substances in the coolant, and determine the concentration distribution of the other soluble substances based on the concentration relationship and the boric acid concentration. Based on the temperature distribution, the flow rate distribution, and the concentration distribution of soluble substances, the heat and mass transfer process inside the corrosion products is analyzed to obtain the concentration of boron after enrichment inside the corrosion products, and the total amount of boron deposition is obtained based on the enriched concentration; the soluble substances include boric acid and other soluble substances.

2. The method according to claim 1, characterized in that, The process of obtaining the average thermal conductivity of the corrosion products includes: The porosity of the corrosion products, the solid thermal conductivity of the corrosion products, and the liquid thermal conductivity of the coolant in the corrosion products are obtained. The average thermal conductivity of the corrosion products is determined based on the porosity, the solid thermal conductivity, and the liquid thermal conductivity.

3. The method according to claim 1, characterized in that, Determining the internal temperature distribution of the corrosion products when the coolant is saturated, based on the average thermal conductivity, includes: Obtain the thickness of the corrosion product; Based on the average thermal conductivity and the thickness, the saturation temperature distribution of the corrosion products is determined when the coolant is saturated; the temperature distribution includes the saturation temperature distribution.

4. The method according to claim 1, characterized in that, Determining the temperature distribution of the corrosion products in the coolant nucleation boiling state based on the average thermal conductivity includes: Obtain the wick boiling relationship, which characterizes the relationship between the thickness of the corrosion products and the internal temperature of the corrosion products when the coolant is in a nucleation boiling state. Based on the relationship between the thickness distribution of the corrosion products and the boiling of the wick, the internal temperature distribution of the corrosion products in the bubbling boiling state is determined; the temperature distribution includes the temperature distribution in the bubbling boiling state.

5. The method according to claim 1, characterized in that, The method further includes: Determine the temperature relationship characterizing the relationship between the thickness of the corrosion products and the temperature of the corrosion products, the flow rate relationship characterizing the relationship between the pressure in the corrosion products and the flow rate of the coolant, and the concentration relationship. Based on the temperature relationship and the thickness of the corrosion product, the nth temperature distribution of the corrosion product in the nth iteration step and the (n+1)th temperature distribution of the corrosion product in the (n+1)th iteration step are determined, and the temperature difference between the nth temperature distribution and the (n+1)th temperature distribution is determined; the nth iteration step and the (n+1)th iteration step are adjacent iteration steps; n is a positive integer. Based on the flow rate relationship and the pressure in the corrosion products, the nth flow rate distribution of the coolant in the nth iteration step and the n+1th flow rate distribution of the coolant in the n+1th iteration step are determined, and the flow rate difference between the nth flow rate distribution and the n+1th flow rate distribution is determined. Based on the concentration relationship and the boric acid concentration in the coolant, the concentration distribution of the other soluble substances at the nth iteration step and the concentration distribution of the coolant at the (n+1)th iteration step are determined, and the concentration difference between the nth concentration distribution and the (n+1)th concentration distribution is determined. The maximum difference among the temperature difference, the flow rate difference, and the concentration difference is determined. If the maximum difference is less than a preset difference threshold, the nth flow rate distribution is determined as the flow rate distribution, the nth temperature distribution is determined as the temperature distribution, and the nth concentration distribution is determined as the concentration distribution of the other soluble substances.

6. The method according to claim 1, characterized in that, Determining the temperature distribution of the corrosion products when the coolant is in a dry state based on the average thermal conductivity includes: Obtain a three-dimensional coordinate system formula characterizing the relationship between the thickness of the corrosion products and the temperature of the corrosion products when the coolant is evaporated to dryness; Based on the relationship between the thickness of the corrosion products and the three-dimensional coordinate system, the evaporation temperature distribution of the corrosion products is determined; the temperature distribution includes the evaporation temperature distribution.

7. A heat and mass transfer analysis device for corrosion products of nuclear reactors, characterized in that, The device includes: The temperature distribution determination module is used to obtain the average thermal conductivity of corrosion products in the nuclear reactor, and to determine the temperature distribution of the corrosion products in the coolant saturation state, the nucleation boiling state, and the evaporation state based on the average thermal conductivity. A flow rate distribution determination module is used to determine the flow rate distribution of the coolant in the corrosion products based on the pressure distribution in the corrosion products; The concentration distribution determination module is used to obtain the concentration relationship between the concentration of boric acid and the concentration of other soluble substances in the coolant, and to determine the concentration distribution of the other soluble substances based on the concentration relationship and the concentration of boric acid. The analysis module is used to analyze the heat and mass transfer process inside the corrosion products based on the temperature distribution, the flow rate distribution, and the concentration distribution of soluble substances, to obtain the concentration of boron after enrichment inside the corrosion products, and to obtain the total amount of boron deposition based on the enriched concentration; the soluble substances include boric acid and other soluble substances.

8. A computer device comprising a memory and a processor, wherein the memory stores a computer program, characterized in that, When the processor executes the computer program, it implements the steps of the method according to any one of claims 1 to 6.

9. A computer-readable storage medium having a computer program stored thereon, characterized in that, When the computer program is executed by a processor, it implements the steps of the method according to any one of claims 1 to 6.

10. A computer program product, comprising a computer program, characterized in that, When the computer program is executed by a processor, it implements the steps of the method according to any one of claims 1 to 6.

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