A method for predicting core impurity deposition

Abstract

The application discloses a kind of reactor core impurity deposition prediction methods, steps are as follows:1, establish coolant flow heat exchange model and fuel rod heat conduction analysis model;2, establish corrosion product deposition amount model;3, establish deposit thermal resistance model and is coupled with fuel rod heat conduction analysis model;4, establish deposit multi-physics field coupling solution method, obtain the reactor core coolant flow field and temperature field under the influence of impurity deposit at a time;5, carry out the calculation of multiple deposition time results.This method simplifies the geometry structure in the reactor core of pressurized water reactor, considers the influence of deposit on the internal physical quantity of reactor core by establishing the deposit model of reactor core cladding corrosion product, and solves multiple physical models, realizes the accurate prediction of multi-physics field under the condition of full-scale, long-period deposition state of reactor core, and has the advantages of fast calculation speed and less resource consumption.The calculation result can provide an efficient and accurate computational fluid dynamics method for long-term prediction of pressurized water reactor full reactor core and full life cycle.

Description

Technical Field

[0001] This invention belongs to the field of nuclear reactor safety analysis technology, specifically relating to a method for predicting impurity deposition in pressurized water reactor cores, which can achieve accurate prediction of multiple physical fields under full-scale and long-period deposition conditions in the reactor core. Background Technology

[0002] Pressurized water reactor (PWR) nuclear power plants are the most widely used commercial reactor type today, with system materials operating under high temperature, high pressure, and radioactive conditions for extended periods. During reactor operation, the core internals and fuel rods are corroded by the high-temperature, high-pressure coolant, resulting in corrosion products. The amount of corrosion products increases continuously with core operation time and accumulates in various locations. The corrosion deposits (Chalk River Unidentified Deposit, CRUD) deposited on the surface of the fuel element cladding have various physicochemical forms, mainly composed of elements such as Ni and Fe. CRUD has high thermal resistance, hindering heat exchange between the fuel cladding and the coolant. Its loose structure facilitates the deposition of other solutes, further accelerating material corrosion and causing boron enrichment, leading to axial offset anomaly (AOA). CRUD migration also increases the radiation dose in the primary circuit, adversely affecting the safe and stable operation of the primary circuit.

[0003] Due to the complexity of corrosion product deposition models, most related research methods employ one-dimensional system programs or sub-channel programs. CFD calculation methods, on the other hand, are limited by computational resources, and the research objects are mostly limited to single bars or partial components. It is difficult to carry out detailed modeling and calculation of the entire reactor core, and it is also impossible to obtain the distribution characteristics of corrosion products of the entire reactor core. At present, there are very few studies on corrosion deposition simulation and thermal-hydraulic effects of the entire reactor core, both domestically and internationally. Summary of the Invention

[0004] In order to overcome the problems existing in the prior art, the purpose of this invention is to provide a method for predicting core impurity deposition. This invention provides a method with low computational resource consumption and high computational accuracy for analyzing and predicting corrosion deposition characteristics of pressurized water reactors at the whole core scale and over long periods.

[0005] The technical solution adopted by this invention to solve this technical problem is as follows:

[0006] A computational fluid dynamics-based method for analyzing and predicting impurity deposition in the core of a pressurized water reactor (PWR) is proposed. The complex geometry within the reactor is simplified, and a coolant flow heat transfer analysis model and a fuel rod thermal conductivity analysis model are established and coupled to calculate the core's thermal-hydraulic parameters. Then, the deposition thermal resistance is obtained using a corrosion product deposition model and a deposition thermal resistance model, and this thermal resistance is coupled to the fuel rod thermal conductivity analysis model using a fluid-structure interaction method. Finally, by iterating and updating the deposition time, the corrosion deposition characteristics of the entire PWR core over long periods can be analyzed and predicted.

[0007] A method for predicting core impurity deposition specifically includes the following steps:

[0008] Step 1: Establish a multi-control volume mesh analysis model for the reactor core. Based on this model, establish a coolant flow heat transfer analysis model and a fuel rod thermal conductivity analysis model. Finally, couple the coolant flow heat transfer analysis model and the fuel rod thermal conductivity analysis model to obtain the fuel rod and coolant information for the reactor core control volume. This process involves the following steps:

[0009] Step 1-1: Based on the core structure, divide the core multi-control volume mesh. For the three-dimensional geometric model of the pressurized water reactor core, simplify the fuel rods, control rods and structural elements in the core, ignore their actual geometric structure, and simplify them into a fluid domain calculation model composed of multiple regular hexahedrons, forming a set of regular-shaped multi-control volumes, thus obtaining the core multi-control volume mesh analysis model.

[0010] Step 1-2: Establish a coolant flow heat transfer analysis model to obtain the velocity and temperature field distributions of the coolant inside the reactor core. The specific steps for establishing the model are as follows: Based on the multi-control volume mesh analysis model of the reactor core, and considering the coolant flow characteristics of the pressurized water reactor core, establish the mass, momentum, and energy conservation equations for the coolant for a set of regularly shaped multi-control volumes. By solving these three conservation equations, the velocity and temperature field distributions inside the pressurized water reactor core are obtained, thus yielding the coolant flow heat transfer analysis model. The mass, momentum, and energy conservation equations for the coolant are as follows:

[0011] The mass conservation equation for coolant is:

[0012]

[0013] In the formula, Coolant density / , Coolant flow rate / , For time / ;

[0014] The equation for the conservation of coolant momentum is:

[0015]

[0016] In the formula, Coolant pressure / , The dynamic viscosity coefficient of the coolant / , This represents the momentum exchange caused by turbulent mixing. acceleration due to gravity / , The momentum source term is introduced for rod bundles and wire winding structures; the physical quantities with arrows in the above equation are vectors;

[0017] The energy conservation equation for coolant is:

[0018]

[0019] In the formula, Enthalpy of coolant / , This represents the energy exchange between channels caused by turbulent mixing. , Energy source terms introduced for heat exchange on the surface of fuel rods / , For heat flux / ;

[0020] Steps 1-3: Establish a fuel rod thermal conductivity analysis model to describe the temperature characteristics of the fuel rods within the control body. The fuel rod thermal conductivity analysis model consists of two parts: a fuel rod node thermal conductivity model and a fuel rod cladding surface convective heat transfer model. These two sub-models are combined to form the fuel rod thermal conductivity analysis model. The specific steps for establishing the fuel rod node thermal conductivity model and the fuel rod cladding surface convective heat transfer model are as follows:

[0021] Step 1-3-1: Establish the thermal conductivity model of the fuel rod nodes. The specific establishment process is as follows: Consider the power share distribution of different fuel rods, and divide the fuel rods into N nodes radially according to their structural characteristics, including the cladding, air gap, and different material structures of the fuel pellets; the nodes extend outward from the center region of the pellets, and the last three nodes fall on the outer surface of the fuel pellet, the inner surface of the fuel cladding, and the outer surface of the fuel cladding, respectively; neglecting the axial thermal conductivity of the fuel rods, according to the law of conservation of energy, the following thermal conductivity equation exists for node n, which is the thermal conductivity model of the fuel rod nodes:

[0022]

[0023] In the formula, The material density at node n / , Specific heat capacity of the material at node n / , The equivalent volume at node n / , The heat transferred from node n-1 to node n / , The heat transferred from node n+1 to node n / , The heat release rate per unit volume at node n / , Temperature at node n / ;

[0024] Step 1-3-2: Establish the convective heat transfer model of the fuel rod cladding surface. The specific process is as follows: Assuming that all fuel rods in a single control volume have the same geometric properties and thermal state, and that the fuel rods and control rods are uniformly distributed within the core, the heat transfer relationship between the coolant and the fuel rods, i.e., the convective heat transfer model of the fuel rod cladding surface, is as follows:

[0025]

[0026] In the formula, Surface heat transfer coefficient / , Heat transfer area per unit length , For the mainstream temperature of the fluid / , Temperature of the outermost node in the fuel rod node thermal conductivity model / , For the heat exchange between fuel rods and coolant fluid / ;

[0027] Steps 1-4: Couple the thermal conductivity analysis model of fuel rods in Step 1-3 with the heat transfer analysis model of core coolant flow in Step 1-2 for calculation; the coupled calculation is based on the heat transfer coefficient. Therefore, the calculation of the heat transfer coefficient needs to be introduced before the coupling calculation begins;

[0028] Heat transfer coefficient between fuel rods and coolant Nusel number Find:

[0029]

[0030] In the formula, Thermal conductivity of coolant , Equivalent hydraulic diameter ;

[0031] Nusel number Depend on Formula calculation:

[0032]

[0033] In the formula, The Reynolds number is... It is a Prandtl number;

[0034] and The expression is:

[0035]

[0036] In the formula, Density of coolant / , fluid velocity / , The dynamic viscosity coefficient of the coolant / , Specific heat capacity of coolant / , Thermal conductivity of coolant / ;

[0037] At the start of formal coupling, the coolant flow field and temperature field are first initialized. After initialization, the following procedures are performed: 1. The fuel rod temperature distribution is calculated using the fuel rod thermal conductivity analysis model; 2. Based on... The formula yields the heat transfer coefficient between the fuel rods and the coolant; 3. The convective heat transfer is incorporated into the core coolant flow heat transfer analysis model to obtain new thermal properties, flow rate, and temperature of the coolant;

[0038] Repeat the process from 1-1 to 1-3 above until convergence, and the coupled calculation of the core coolant flow heat transfer analysis model and the fuel rod thermal conductivity analysis model can be realized, and the fuel rod and coolant information of the core control body can be obtained.

[0039] Step 2: Establish a corrosion product concentration model, then calculate the deposition rate of various corrosion products based on the corrosion product concentration model, and finally obtain the corrosion product deposition amount through the corrosion product deposition amount model. This is specifically divided into the following steps:

[0040] Step 2-1: Establish a corrosion product concentration model. The specific process is as follows: Assuming the corrosion product concentration in the coolant is saturated, the corrosion product concentration in the reactor core is equal to the saturated solubility under the corresponding water chemistry conditions. The corrosion product elements are divided into three types: Fe, Cr, and Ni. The saturated solubility of each element is obtained by relevant water chemistry functions or by coupling with a solubility solver. The corrosion product concentration model is as follows:

[0041]

[0042]

[0043]

[0044] In the formula, , and These represent the solubility of corrosion products / , Hydrogen pressure / , Hydrogen ion concentration / , The universal activation coefficient for neutral ions. The universal activation coefficient for first-order cations. Solution temperature / ;

[0045] Step 2-2: Calculate the deposition rate of dissolved corrosion products based on the corrosion product concentration model in Step 2-1. Deposition rate of particulate corrosion products and coolant erosion rate The specific calculations are as follows:

[0046] The corrosion deposition process on the core cladding surface is described using the mass transfer principle, and the deposition rate of dissolved corrosion products is... The calculation formula is as follows:

[0047]

[0048] In the formula, Deposition rate of dissolved corrosion products / , The mass transfer coefficient is . For wet period / , For control body height / , and These represent the solubility of the mainstream coolant within the same control volume and the solubility at the wall surface, respectively. , and These are the temperatures of the mainstream coolant and the wall surface within the same control cell, respectively. ;

[0049] The deposition of particulate corrosion products satisfies the conditions for Brownian motion. The particles are small in size. Assuming the particles adhere uniformly to the wall surface, the deposition rate of particulate corrosion products is... The calculation formula is:

[0050]

[0051] In the formula, The mass transfer coefficient of particulate matter. Mainstream coolant particulate matter concentration;

[0052] The flowing coolant exerts shear force on the corrosion products on the core cladding surface, causing erosion. The amount of erosion is directly proportional to the shear force applied by the coolant, and the coolant erosion rate is... Calculated from the coolant flow intensity function:

[0053]

[0054] In the formula, For the erosion rate, As the impact factor, For shear stress, For the adhesion of the sedimentary layer, This represents the amount of erosion impact.

[0055] Step 2-3: Establish a corrosion product deposition model; based on the deposition rate of dissolved corrosion products, the deposition rate of particulate corrosion products, and the coolant erosion rate from Step 2-2, combined with the deposition time, the sediment mass can be obtained. The specific calculation formula, i.e. the corrosion product deposition model, is as follows:

[0056]

[0057] In the formula, For sediment mass / , Deposition rate of dissolved corrosion products / , Deposition rate of particulate corrosion products / , Erosion rate / , For deposition time / ;

[0058] Step 3: Based on the sediment mass obtained in Step 2, first calculate the sediment thickness, then establish a sediment thermal resistance model to calculate the sediment thermal resistance, and finally couple the sediment thermal resistance to the fuel rod node thermal conductivity model to achieve coupling between the sediment thermal resistance and the fuel rod thermal conductivity analysis model; the specific steps are as follows:

[0059] Step 3-1: Based on sediment quality Calculate sediment thickness The specific calculation formula is as follows:

[0060]

[0061] In the formula, sediment thickness / , For sediment mass / , Sediment density / ;

[0062] Step 3-2: Establish a sediment thermal resistance model, dividing the heat transfer process between the sediment and the coolant into solid and fluid regions, and calculate the heat transfer process between the solid and liquid phases separately. The specific calculation formula is as follows:

[0063] The heat transfer processes in the fluid region and the solid region are respectively represented as follows:

[0064]

[0065]

[0066] In the formula, Heat flux density of the fluid region / , Heat flux density of the solid region / , Equivalent heat transfer coefficient / , Thermal conductivity of the solid region / , Temperature difference of sedimentary layer / , sediment thickness / , To influence regional factors, The heat flux density of the sedimentary layer;

[0067] The specific calculation formula for the sediment thermal resistance calculation model is as follows:

[0068]

[0069] In the formula, For the thermal resistance of sediments / , Thermal resistance of the fluid region / , Thermal resistance of solid region / , For regional factors;

[0070] Step 3-3: Couple the sediment thermal resistance calculation model to the fuel rod node thermal conductivity model from Step 1-3; add a sediment node to the outermost node of the fuel rod node thermal conductivity model from Step 1-3-1, bringing the total number of nodes to N+1. Couple the sediment thermal resistance with the fuel rod thermal conductivity analysis model by listing the calculation relationship at this point. The calculation relationship for the thermal conductivity node at point N+1 is then:

[0071]

[0072] In the formula, Sediment density / , Specific heat capacity of sediment / , Equivalent volume of sediment / , Temperature at the surface of the casing / , Sediment temperature / , For the thermal resistance of the sediment, Coolant temperature / , Surface heat transfer coefficient / , Heat transfer area per unit length ;

[0073] Step 4: Perform multiphysics coupling calculations on the sediments to obtain the coolant flow field and temperature field under the influence of impurity sediments at a certain moment. The specific steps are as follows:

[0074] Step 4-1: Calculation of core thermal-hydraulic parameters; At the beginning of the calculation, the parameters of the core coolant flow heat transfer analysis model and the fuel rod thermal conductivity analysis model are initialized, and then iterative calculations are performed on the core coolant flow heat transfer analysis model and the fuel rod thermal conductivity analysis model; the fuel rod thermal conductivity analysis model is... The convective heat transfer coefficient of the fuel rod surface is obtained by analyzing the core coolant flow field and temperature field at a given time, and this is used as the boundary condition to complete the process. The calculation of time yields The calculation results of the fuel rod temperature distribution at any given time are used. Similarly, based on the calculated fuel rod temperature distribution, the core coolant flow heat transfer analysis model obtains the convective heat transfer on the fuel rod surface and adds it to the source term of the coolant energy conservation equation for solution, yielding the result. The coolant flow field and temperature field at any given time are thus determined, thus completing the coupled solution of the thermal-hydraulic parameters;

[0075] Step 4-2: Impurity Deposition Calculation; After obtaining stable core thermal-hydraulic parameters, the iterative calculation of Step 2 begins; First, based on the obtained thermal-hydraulic parameters and the corrosion product concentration model, the deposition rate of dissolved corrosion products, the deposition rate of particulate corrosion products, and the coolant erosion rate are calculated. Then, the deposition mass is obtained through the corrosion product deposition amount calculation model; After completing Step 2, Step 3 first calculates the deposition thickness based on the deposition mass obtained in Step 2, and then calculates the deposition thermal resistance through the deposition thermal resistance model. The deposition thermal resistance is coupled to the fuel rod node thermal conduction model to complete Step 3, thus completing the coupled solution of impurity deposition;

[0076] Step 4-3: After completing Step 4-2, repeat Step 4-1, iteratively calculating Step 4-1 and Step 4-2 repeatedly. Determine if the residuals of coolant flow rate, temperature, fuel rod internal temperature, and deposit thickness are less than preset residual values. If they are less, convergence is achieved, and the impurity deposition coupling calculation is complete, yielding the result. The coolant flow field and temperature field are constantly affected by impurity deposits;

[0077] Step 5: Perform calculations for multiple deposition times to obtain the coolant flow field and temperature field under the influence of impurity deposits at multiple time points: After completing Step 4-3, increase the deposition time of Step 2-3. new sediment volume was obtained. Since the deposition rate has changed, the calculation of the fuel rod thermal conductivity analysis model will be affected. Therefore, a new iterative cycle will be started according to step 4, and the result will be obtained after convergence at the new time step. The coolant flow field and temperature field are constantly affected by impurity deposits. By repeating the above operation, the calculation results of fuel rod temperature distribution, coolant flow field and temperature field and deposition amount in pressurized water reactor core at multiple time steps after considering corrosion product deposition can be obtained, realizing accurate prediction of multi-physics field under full-scale and long-period deposition state of reactor core.

[0078] The present invention has the following advantages and effects:

[0079] 1. The complex structures such as fuel rods in the reactor core have been simplified, thus avoiding the need to establish a complex geometric model of the reactor core. Through the channel-level coolant flow heat transfer model, fuel rod heat conduction model and coupling model, the full core parameters of the pressurized water reactor are accurately simulated.

[0080] 2. A core deposition calculation model was established. The deposition amount was calculated by simulating the operating parameters of the entire reactor. The results can accurately reflect the deposition distribution characteristics in a real reactor.

[0081] 3. A deposition thermal resistance model was established. By coupling it to the heat conduction of fuel rods, the influence of sediments on the core thermal-hydraulic properties was accurately considered, thus obtaining the precise core thermal-hydraulic parameter characteristics under the influence of sediments.

[0082] 4. Because the impact of sediments on the core can be accurately considered, the calculable sedimentation timescale is greatly expanded, enabling long-term analysis and research on sedimentation distribution characteristics and core thermal-hydraulic characteristics over multiple sedimentation time steps.

[0083] This invention has been experimentally proven to accurately obtain the distribution of core sediment characteristics and the distribution of the influence of sedimentation amount on core thermal-hydraulic properties. The corrosion deposition characteristic analysis method based on computational fluid dynamics proposed in this invention can be applied to three-dimensional computational fluid dynamics numerical simulation. It can achieve full-scale, long-term impurity deposition characteristic analysis while significantly reducing the consumption of computational resources. It has the characteristics of simple modeling and fast calculation speed. Attached Figure Description

[0084] Figure 1 This is a schematic diagram of the pressurized water reactor fuel rods, components, and core.

[0085] Figure 2 A schematic diagram showing the fuel rod node division considering deposition thermal resistance.

[0086] Figure 3 This is a schematic diagram of iterative calculations for corrosion deposition characteristic analysis.

[0087] Figure 4 A flowchart illustrating the analysis method for corrosion deposition characteristics of pressurized water reactor core cladding. Detailed Implementation

[0088] The following combination Figure 4 The method block diagram shown provides a further detailed description of the present invention.

[0089] This paper proposes a fluid dynamics-based method for analyzing the corrosion deposition on the core cladding of pressurized water reactors and its impact on thermal-hydraulic parameters. The specific implementation method is as follows:

[0090] Step 1: Establish a multi-control volume mesh analysis model for the reactor core. Based on this model, establish a coolant flow heat transfer analysis model and a fuel rod thermal conductivity analysis model. Finally, couple the coolant flow heat transfer analysis model and the fuel rod thermal conductivity analysis model to obtain the fuel rod and coolant information for the reactor core control volume. This process involves the following steps:

[0091] Step 1-1: First, based on the specific core structure to be studied, simplify the fuel rods, control rods, and structural elements in the core, ignoring their actual geometry. Then, use 3D CAD modeling software such as SpaceClaim or UG to create a 3D geometric model of the pressurized water reactor core. Modeling begins with fuel rod grids, then assembles them into fuel assemblies and splices them into the entire core. Figure 1 As shown, the core multi-control volume mesh analysis model is obtained by dividing it into multiple hexahedral combinations using mesh generation software such as ICEM or MESHING, forming a set of regularly shaped control volumes.

[0092] Step 1-2: Establish a coolant flow heat transfer analysis model to obtain the velocity and temperature field distributions of the coolant inside the reactor core. The specific steps for establishing the model are as follows: Based on the multi-control volume mesh analysis model of the reactor core, and considering the coolant flow characteristics of the pressurized water reactor core, establish the mass, momentum, and energy conservation equations for the coolant for a set of regularly shaped multi-control volumes. By solving these three conservation equations, the velocity and temperature field distributions inside the pressurized water reactor core are obtained, thus yielding the coolant flow heat transfer analysis model. The mass, momentum, and energy conservation equations for the coolant are as follows:

[0093] The mass conservation equation for coolant is:

[0094]

[0095] In the formula, Coolant density / , Coolant flow rate / , For time / ;

[0096] The equation for the conservation of coolant momentum is:

[0097]

[0098] In the formula, Coolant pressure / , The dynamic viscosity coefficient of the coolant / , This represents the momentum exchange caused by turbulent mixing. acceleration due to gravity / , The momentum source term is introduced for rod bundles and wire winding structures; the physical quantities with arrows in the above equation are vectors;

[0099] The energy conservation equation for coolant is:

[0100]

[0101] In the formula, Enthalpy of coolant / , This represents the energy exchange between channels caused by turbulent mixing. , Energy source terms introduced for heat exchange on the surface of fuel rods / , For heat flux / ;

[0102] Steps 1-3: Establish a fuel rod thermal conductivity analysis model to describe the temperature characteristics of the fuel rods within the control body. This model consists of two parts: a fuel rod nodal thermal conductivity model and a fuel rod cladding surface convective heat transfer model. These two sub-models are combined to form the fuel rod thermal conductivity analysis model. The specific steps for establishing the fuel rod nodal thermal conductivity model and the fuel rod cladding surface convective heat transfer model are as follows:

[0103] Step 1-3-1: Establish the thermal conductivity model of the fuel rod nodes. The specific establishment process is as follows: Considering the power share distribution of different fuel rods, different power is given for different fuel rods, and N nodes are divided radially according to the structural characteristics of the fuel rods, including the cladding, air gap, and different material structure regions of the fuel pellet; the nodes extend outward from the center region of the pellet, and the last three nodes fall on the outer surface of the fuel pellet, the inner surface of the fuel cladding, and the outer surface of the fuel cladding, respectively; ignoring the axial thermal conductivity of the fuel rods, according to the law of conservation of energy, the following thermal conductivity equation exists for node n, which is the thermal conductivity model of the fuel rod nodes:

[0104]

[0105] In the formula, The material density at node n / , Specific heat capacity of the material at node n / , The equivalent volume at node n / , The heat transferred from node n-1 to node n / , The heat transferred from node n+1 to node n / , The heat release rate per unit volume at node n / , Temperature at node n / ;

[0106] Step 1-3-2: Establish the convective heat transfer model of the fuel rod cladding surface. The specific process is as follows: Assuming that all fuel rods in a single control volume have the same geometric properties and thermal state, and that the fuel rods and control rods are uniformly distributed within the core, the heat transfer relationship between the coolant and the fuel rods, i.e., the convective heat transfer model of the fuel rod cladding surface, is as follows:

[0107]

[0108] In the formula, Surface heat transfer coefficient / , Heat transfer area per unit length , For the mainstream temperature of the fluid / , Temperature of the outermost node in the fuel rod node thermal conductivity model / , For the heat exchange between fuel rods and coolant fluid / ;

[0109] Steps 1-4: Couple the thermal conductivity analysis model of fuel rods in Step 1-3 with the heat transfer analysis model of core coolant flow in Step 1-2 for calculation; the coupled calculation is based on the heat transfer coefficient. Therefore, the calculation of the heat transfer coefficient needs to be introduced before the coupling calculation begins;

[0110] Heat transfer coefficient between fuel rods and coolant Nusel number Find:

[0111]

[0112] In the formula, Thermal conductivity of coolant , Equivalent hydraulic diameter ;

[0113] Nusel number Depend on Formula calculation:

[0114]

[0115] In the formula, The Reynolds number is... It is a Prandtl number;

[0116] and The expression is:

[0117]

[0118] In the formula, Density of coolant / , fluid velocity / , The dynamic viscosity coefficient of the coolant / , Specific heat capacity of coolant / , Thermal conductivity of coolant / ;

[0119] At the start of formal coupling, the coolant flow field and temperature field are first initialized. After initialization, the following procedures are performed: 1. The fuel rod temperature distribution is calculated using the fuel rod thermal conductivity analysis model; 2. Based on... The formula yields the heat transfer coefficient between the fuel rods and the coolant; 3. The convective heat transfer is incorporated into the core coolant flow heat transfer analysis model to obtain new thermal properties, flow rate, and temperature of the coolant;

[0120] Repeating steps 1 to 3 above until convergence will enable the coupled calculation of the core coolant flow heat transfer analysis model and the fuel rod thermal conductivity analysis model, and obtain the fuel rod and coolant information of the core control body at this time.

[0121] Step 2: Establish a corrosion product concentration model, then calculate the deposition rate of various corrosion products based on the corrosion product concentration model, and finally obtain the corrosion product deposition amount through the corrosion product deposition amount model. This is specifically divided into the following steps:

[0122] Step 2-1: Establish a corrosion product concentration model. The specific process is as follows: Assuming the corrosion product concentration in the coolant is saturated, the corrosion product concentration in the reactor core is equal to the saturated solubility under the corresponding water chemistry conditions. The corrosion product elements are divided into three types: Fe, Cr, and Ni. The saturated solubility of each element is obtained by relevant water chemistry functions or by coupling with a solubility solver. The corrosion product concentration model is as follows:

[0123]

[0124]

[0125]

[0126] In the formula, , and These represent the solubility of corrosion products / , Hydrogen pressure / , Hydrogen ion concentration / , The universal activation coefficient for neutral ions. The universal activation coefficient for first-order cations, Solution temperature / ;

[0127] Step 2-2: Calculate the deposition rate of dissolved corrosion products based on the corrosion product concentration model in Step 2-1. Deposition rate of particulate corrosion products and coolant erosion rate The specific calculations are as follows:

[0128] The corrosion deposition process on the core cladding surface is described using the mass transfer principle, and the deposition rate of dissolved corrosion products is... The calculation formula is as follows:

[0129]

[0130] In the formula, Deposition rate of dissolved corrosion products / , The mass transfer coefficient is . For wet period / , For control body height / , and These represent the solubility of the mainstream coolant within the same control volume and the solubility at the wall surface, respectively. , and These are the temperatures of the mainstream coolant and the wall surface within the same control cell, respectively. ;

[0131] The deposition of particulate corrosion products satisfies the conditions for Brownian motion. The particles are small in size. Assuming the particles adhere uniformly to the wall surface, the deposition rate of particulate corrosion products is... The calculation formula is:

[0132]

[0133] In the formula, The mass transfer coefficient of particulate matter. Mainstream coolant particulate matter concentration;

[0134] The flowing coolant exerts shear force on the corrosion products on the core cladding surface, causing erosion. The amount of erosion is directly proportional to the shear force applied by the coolant, and the coolant erosion rate is... Calculated from the coolant flow intensity function:

[0135]

[0136] In the formula, For the erosion rate, As the impact factor, For shear stress, For the adhesion of the sedimentary layer, This represents the amount of erosion impact.

[0137] Step 2-3: Establish a corrosion product deposition model; based on the deposition rate of dissolved corrosion products, the deposition rate of particulate corrosion products, and the coolant erosion rate from Step 2-2, combined with the deposition time, the sediment mass can be obtained. The specific calculation formula, i.e. the corrosion product deposition model, is as follows:

[0138]

[0139] In the formula, For sediment mass / , Deposition rate of dissolved corrosion products / , Deposition rate of particulate corrosion products / , Erosion rate / , For deposition time / ;

[0140] Step 3: Based on the sediment mass obtained in Step 2, first calculate the sediment thickness, then establish a sediment thermal resistance model to calculate the sediment thermal resistance, and finally couple the sediment thermal resistance to the fuel rod node thermal conductivity model to achieve coupling between the sediment thermal resistance and the fuel rod thermal conductivity analysis model; the specific steps are as follows:

[0141] Step 3-1: Based on sediment quality Calculate sediment thickness The specific calculation formula is as follows:

[0142]

[0143] In the formula, sediment thickness / , For sediment mass / , Sediment density / ;

[0144] Step 3-2: Establish a sediment thermal resistance model, dividing the heat transfer process between the sediment and the coolant into solid and fluid regions, and calculate the heat transfer process between the solid and liquid phases separately. The specific calculation formula is as follows:

[0145] The heat transfer processes in the fluid region and the solid region are respectively represented as follows:

[0146]

[0147]

[0148] In the formula, Heat flux density of the fluid region / , Heat flux density of the solid region / , Equivalent heat transfer coefficient / , Thermal conductivity of the solid region / , Temperature difference of sedimentary layer / , sediment thickness / , To influence regional factors, The heat flux density of the sedimentary layer;

[0149] The specific calculation formula for the sediment thermal resistance calculation model is as follows:

[0150]

[0151] In the formula, For the thermal resistance of sediments / , Thermal resistance of the fluid region / , Thermal resistance of solid region / , For regional factors;

[0152] Step 3-3: Couple the sediment thermal resistance calculation model to the fuel rod node thermal conductivity model of Step 1-3; add a sediment node to the outermost node of the fuel rod node thermal conductivity model in Step 1-3-1, and the final total number of nodes becomes N+1, as follows. Figure 2 As shown; by listing the calculation relationship at point N+1, the deposition thermal resistance and fuel rod thermal conductivity analysis model are coupled. The calculation relationship for the thermal conductivity node at point N+1 is as follows:

[0153]

[0154] In the formula, Sediment density / , Specific heat capacity of sediment / , Equivalent volume of sediment / , Temperature at the surface of the casing / , Sediment temperature / , For the thermal resistance of the sediment, Coolant temperature / , Surface heat transfer coefficient / , Heat transfer area per unit length ;

[0155] Step 4: Perform multiphysics coupled solution calculations on the sediments to obtain the coolant flow field and temperature field under the influence of impurity sediments at a certain moment. This includes the calculation of core thermal-hydraulic parameters and impurity deposition. The coupled solution steps are as follows: Figure 3 As shown, the specific calculation steps are as follows:

[0156] Step 4-1: Calculation of core thermal-hydraulic parameters; At the beginning of the calculation, the parameters of the core coolant flow heat transfer analysis model and the fuel rod thermal conductivity analysis model are initialized, and then iterative calculations are performed on the core coolant flow heat transfer analysis model and the fuel rod thermal conductivity analysis model; the fuel rod thermal conductivity analysis model is... The convective heat transfer coefficient of the fuel rod surface is obtained by analyzing the core coolant flow field and temperature field at a given time, and this is used as the boundary condition to complete the process. The calculation of time yields The calculation results of the fuel rod temperature distribution at any given time are used. Similarly, based on the calculated fuel rod temperature distribution, the core coolant flow heat transfer analysis model obtains the convective heat transfer on the fuel rod surface and adds it to the source term of the coolant energy conservation equation for solution, yielding the result. The coolant flow field and temperature field at any given time are thus determined, thus completing the coupled solution of the thermal-hydraulic parameters;

[0157] Step 4-2: Impurity Deposition Calculation; After obtaining stable core thermal-hydraulic parameters, the iterative calculation of Step 2 begins; First, based on the obtained thermal-hydraulic parameters and the corrosion product concentration model, the deposition rate of dissolved corrosion products, the deposition rate of particulate corrosion products, and the coolant erosion rate are calculated. Then, the deposition mass is obtained through the corrosion product deposition amount calculation model; After completing Step 2, Step 3 first calculates the deposition thickness based on the deposition mass obtained in Step 2, and then calculates the deposition thermal resistance through the deposition thermal resistance model. The deposition thermal resistance is coupled to the fuel rod node thermal conduction model to complete Step 3, thus completing the coupled solution of impurity deposition;

[0158] Step 4-3: After completing Step 4-2, repeat Step 4-1, iteratively calculating Step 4-1 and Step 4-2 repeatedly. Determine if the residuals of coolant flow rate, temperature, fuel rod internal temperature, and deposit thickness are less than preset residual values. If they are less, convergence is achieved, and the impurity deposition coupling calculation is complete, yielding the result. The coolant flow field and temperature field are constantly affected by impurity deposits;

[0159] Step 5: Perform calculations for multiple deposition times to obtain the coolant flow field and temperature field under the influence of impurity deposits at multiple time points: After completing Step 4-3, increase the deposition time of Step 2-3. ,Right now Figure 3 In At this point, the corrosion product deposition model will calculate the new deposition amount. Since the deposition rate has changed, the calculation of the fuel rod thermal conductivity analysis model will be affected. Therefore, a new iterative cycle needs to be started according to step 4, and the result will be obtained after convergence at the new time step. The coolant flow field and temperature field are constantly affected by impurity deposits. By repeating the above operation, the calculation results of fuel rod temperature distribution, coolant flow field and temperature field and deposition amount in pressurized water reactor core at multiple time steps after considering corrosion product deposition can be obtained, realizing accurate prediction of multi-physics field under full-scale and long-period deposition state of reactor core.

Claims

1. A method for predicting core impurity deposition, characterized in that: Includes the following steps: Step 1: Establish a multi-control volume mesh analysis model for the reactor core. Based on this model, establish a coolant flow heat transfer analysis model and a fuel rod thermal conductivity analysis model. Finally, couple the coolant flow heat transfer analysis model and the fuel rod thermal conductivity analysis model to obtain the fuel rod and coolant information for the reactor core control volume. This process involves the following steps: Step 1-1: Based on the core structure, divide the core multi-control volume mesh. For the three-dimensional geometric model of the pressurized water reactor core, simplify the fuel rods, control rods and structural elements in the core, ignore their actual geometric structure, and simplify them into a fluid domain calculation model composed of multiple regular hexahedrons, forming a set of regular-shaped multi-control volumes, thus obtaining the core multi-control volume mesh analysis model. Step 1-2: Establish a coolant flow heat transfer analysis model to obtain the velocity and temperature field distributions of the coolant inside the reactor core. The specific steps for establishing the model are as follows: Based on the multi-control volume mesh analysis model of the reactor core, and considering the coolant flow characteristics of the pressurized water reactor core, establish the mass, momentum, and energy conservation equations for the coolant for a set of regularly shaped multi-control volumes. By solving these three conservation equations, the velocity and temperature field distributions inside the pressurized water reactor core are obtained, thus yielding the coolant flow heat transfer analysis model. The mass, momentum, and energy conservation equations for the coolant are as follows: The mass conservation equation for coolant is: In the formula, Coolant density / , Coolant flow rate / , For time / ; The equation for the conservation of coolant momentum is: In the formula, Coolant pressure / , The dynamic viscosity coefficient of the coolant / , This represents the momentum exchange caused by turbulent mixing. acceleration due to gravity / , The momentum source term is introduced for rod bundles and wire winding structures; the physical quantities with arrows in the above equation are vectors; The energy conservation equation for coolant is: In the formula, Enthalpy of coolant / , This represents the energy exchange between channels caused by turbulent mixing. , Energy source terms introduced for heat exchange on the surface of fuel rods / , For heat flux / ; Steps 1-3: Establish a fuel rod thermal conductivity analysis model to describe the temperature characteristics of the fuel rods within the control body. The fuel rod thermal conductivity analysis model consists of two parts: a fuel rod node thermal conductivity model and a fuel rod cladding surface convective heat transfer model. These two sub-models are combined to form the fuel rod thermal conductivity analysis model. The specific steps for establishing the fuel rod node thermal conductivity model and the fuel rod cladding surface convective heat transfer model are as follows: Step 1-3-1: Establish the thermal conductivity model of the fuel rod nodes. The specific establishment process is as follows: Consider the power share distribution of different fuel rods, and divide the fuel rods into N nodes radially according to their structural characteristics, including the cladding, air gap, and different material structures of the fuel pellets; the nodes extend outward from the center region of the pellets, and the last three nodes fall on the outer surface of the fuel pellet, the inner surface of the fuel cladding, and the outer surface of the fuel cladding, respectively; neglecting the axial thermal conductivity of the fuel rods, according to the law of conservation of energy, the following thermal conductivity equation exists for node n, which is the thermal conductivity model of the fuel rod nodes: In the formula, The material density at node n / , Specific heat capacity of the material at node n / , The equivalent volume at node n / , The heat transferred from node n-1 to node n / , The heat transferred from node n+1 to node n / , The heat release rate per unit volume at node n / , Temperature at node n / ; Step 1-3-2: Establish the convective heat transfer model of the fuel rod cladding surface. The specific process is as follows: Assuming that all fuel rods in a single control volume have the same geometric properties and thermal state, and that the fuel rods and control rods are uniformly distributed within the core, the heat transfer relationship between the coolant and the fuel rods, i.e., the convective heat transfer model of the fuel rod cladding surface, is as follows: In the formula, Surface heat transfer coefficient / , Heat transfer area per unit length , For the mainstream temperature of the fluid / , Temperature of the outermost node in the fuel rod node thermal conductivity model / , For the heat exchange between fuel rods and coolant fluid / ; Steps 1-4: Couple the fuel rod thermal conductivity analysis model from Step 1-3 with the coolant flow heat transfer analysis model from Step 1-2; the coupled calculation is based on the heat transfer coefficient. Therefore, the calculation of the heat transfer coefficient needs to be introduced before the coupling calculation begins; Heat transfer coefficient between fuel rods and coolant Nusel number Find: In the formula, Thermal conductivity of coolant , Equivalent hydraulic diameter ; Nusel number Depend on Formula calculation: In the formula, Let Reynolds number be 1. It is a Prandtl number; and The expression is: In the formula, Density of coolant / , fluid velocity / , The dynamic viscosity coefficient of the coolant / , Specific heat capacity of coolant / , Thermal conductivity of coolant / ; At the start of formal coupling, the coolant flow field and temperature field are first initialized. After initialization, the following procedures are performed:

1. The fuel rod temperature distribution is calculated using the fuel rod thermal conductivity analysis model; 2. Based on... The formula yields the heat transfer coefficient between the fuel rod and the coolant; 3. Incorporate the convective heat transfer into the coolant flow heat transfer analysis model to obtain new thermal properties, flow rate, and temperature of the coolant; Repeat the process from 1-1 to 1-3 above until convergence, that is, realize the coupled calculation of the core coolant flow heat transfer analysis model and the fuel rod heat conduction analysis model, and obtain the fuel rod and coolant information of the core control body; Step 2: Establish a corrosion product concentration model, then calculate the deposition rate of various corrosion products based on the corrosion product concentration model, and finally obtain the corrosion product deposition amount through the corrosion product deposition amount model. This is specifically divided into the following steps: Step 2-1: Establish a corrosion product concentration model. The specific process is as follows: Assuming the corrosion product concentration in the coolant is saturated, the corrosion product concentration in the reactor core is equal to the saturated solubility under the corresponding water chemistry conditions. The corrosion product elements are divided into three types: Fe, Cr, and Ni. The saturated solubility of each element is obtained by relevant water chemistry functions or by coupling with a solubility solver. The corrosion product concentration model is as follows: In the formula, , and The solubility of corrosion products / , Hydrogen pressure / , Hydrogen ion concentration / , The activation coefficient of neutral ions. The activation coefficient of the first-order cation is... Solution temperature / ; Step 2-2: Calculate the deposition rate of dissolved corrosion products based on the corrosion product concentration model in Step 2-1. Deposition rate of particulate corrosion products and coolant erosion rate The specific calculations are as follows: The corrosion deposition process on the core cladding surface is described using the mass transfer principle, and the deposition rate of dissolved corrosion products is... The calculation formula is as follows: In the formula, Deposition rate of dissolved corrosion products / , The mass transfer coefficient is . For wet period / , For control body height / , and These represent the solubility of the mainstream coolant within the same control volume and the solubility at the wall surface, respectively. , and These are the temperatures of the mainstream coolant and the wall surface within the same control cell, respectively. ; The deposition of particulate corrosion products satisfies the conditions for Brownian motion. The particles are small in size. Assuming the particles adhere uniformly to the wall surface, the deposition rate of particulate corrosion products is... The calculation formula is: In the formula, The mass transfer coefficient of particulate matter. Mainstream coolant particulate matter concentration; The flowing coolant exerts shear force on the corrosion products on the core cladding surface, causing erosion. The amount of erosion is directly proportional to the shear force applied by the coolant, and the coolant erosion rate is... Calculated from the coolant flow intensity function: In the formula, For the erosion rate, As the impact factor, For shear stress, For the adhesion of the sedimentary layer, This represents the amount of erosion impact. Step 2-3: Establish a corrosion product deposition model; based on the deposition rate of dissolved corrosion products, the deposition rate of particulate corrosion products, and the coolant erosion rate from Step 2-2, combined with the deposition time, the sediment mass can be obtained. The specific calculation formula, i.e. the corrosion product deposition model, is as follows: In the formula, For sediment mass / , Deposition rate of dissolved corrosion products / , Deposition rate of particulate corrosion products / , Erosion rate / , For deposition time / ; Step 3: Based on the sediment mass obtained in Step 2, first calculate the sediment thickness, then establish a sediment thermal resistance model to calculate the sediment thermal resistance, and finally couple the sediment thermal resistance to the fuel rod node thermal conductivity model to achieve coupling between the sediment thermal resistance and the fuel rod thermal conductivity analysis model; the specific steps are as follows: Step 3-1: Based on sediment quality Calculate sediment thickness The specific calculation formula is as follows: In the formula, sediment thickness / , For sediment mass / , Sediment density / ; Step 3-2: Establish a sediment thermal resistance model, dividing the heat transfer process between the sediment and the coolant into solid and fluid regions, and calculate the heat transfer process between the solid and liquid phases separately. The specific calculation formula is as follows: The heat flux densities of the fluid region and the solid region are expressed as follows: In the formula, Heat flux density of the fluid region / , Heat flux density of the solid region / , Equivalent heat transfer coefficient / , Thermal conductivity of the solid region / , Temperature difference of sedimentary layer / , sediment thickness / , To influence regional factors, The heat flux density of the sedimentary layer; The specific calculation formula for the sediment thermal resistance calculation model is as follows: In the formula, For the thermal resistance of sediments / , Thermal resistance of the fluid region / , Thermal resistance of solid region / , For regional factors; Step 3-3: Couple the sediment thermal resistance calculation model to the fuel rod node thermal conductivity model in Step 1-3-1; add a sediment node to the outermost node of the fuel rod node thermal conductivity model in Step 1-3-1, bringing the total number of nodes to N+1. Couple the sediment thermal resistance with the fuel rod thermal conductivity analysis model by listing the calculation formula for the sediment node N+1. The calculation formula for the thermal conductivity node at N+1 is then: In the formula, Sediment density / , Specific heat capacity of sediment / , Equivalent volume of sediment / , Temperature at the surface of the casing / , Sediment temperature / , For the thermal resistance of the sediment, Coolant temperature / , Surface heat transfer coefficient / , Heat transfer area per unit length ; Step 4: Perform multiphysics coupling calculations on the sediments to obtain the coolant flow field and temperature field under the influence of impurity sediments at a certain moment. The specific steps are as follows: Step 4-1: Calculation of core thermal-hydraulic parameters; At the beginning of the calculation, the parameters of the coolant flow heat transfer analysis model and the fuel rod thermal conductivity analysis model are initialized, and then iterative calculations are performed on the core coolant flow heat transfer analysis model and the fuel rod thermal conductivity analysis model; the fuel rod thermal conductivity analysis model is... The convective heat transfer coefficient of the fuel rod surface is obtained by analyzing the core coolant flow field and temperature field at a given time, and this is used as the boundary condition to complete the process. The calculation of time yields The calculation results of the fuel rod temperature distribution at any given time are used; similarly, the coolant flow heat transfer analysis model obtains the convective heat transfer on the fuel rod surface based on the calculated fuel rod temperature distribution, and adds it to the source term of the coolant energy conservation equation for solution, resulting in... The coolant flow field and temperature field at any given time are thus determined, thus completing the coupled solution of the thermal-hydraulic parameters; Step 4-2: Impurity Deposition Calculation; After obtaining stable core thermal-hydraulic parameters, the iterative calculation of Step 2 begins; First, based on the obtained thermal-hydraulic parameters and the corrosion product concentration model, the deposition rate of dissolved corrosion products, the deposition rate of particulate corrosion products, and the coolant erosion rate are calculated. Then, the deposition mass is obtained through the corrosion product deposition amount calculation model; After completing Step 2, Step 3 calculates the deposition thickness based on the deposition mass obtained in Step 2, and then calculates the deposition thermal resistance through the deposition thermal resistance model. The deposition thermal resistance is coupled to the fuel rod node thermal conductivity model, completing Step 3. This completes the coupled solution of impurity deposition. Step 4-3: After completing Step 4-2, repeat Step 4-1, iteratively calculating Step 4-1 and Step 4-2 repeatedly. Determine if the residuals of coolant flow rate, temperature, fuel rod internal temperature, and deposit thickness are less than preset residual values. If they are less, convergence is achieved, and the impurity deposition coupling calculation is complete, yielding the result. The coolant flow field and temperature field are constantly affected by impurity deposits; Step 5: Perform calculations for multiple deposition times to obtain the coolant flow field and temperature field under the influence of impurity deposits at multiple time points: After completing Step 4-3, increase the deposition time of Step 2-3. new sediment volume was obtained. Since the deposition rate has changed, the calculation of the fuel rod thermal conductivity analysis model will be affected. Therefore, a new iterative cycle will be started according to step 4, and the result will be obtained after convergence at the new time step. The coolant flow field and temperature field are constantly affected by impurity deposits. After repeating steps 2-3 and following the operation in step 4, the calculation results of the fuel rod temperature distribution, coolant flow field and temperature field, and deposition amount in the pressurized water reactor core at multiple time steps after considering the deposition of corrosion products are obtained, realizing accurate prediction of multi-physics fields under the full-scale and long-period deposition state of the reactor core.

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