A method for analyzing oxide migration in a lead-bismuth reactor primary circuit
Patent Information
- Application Number
- CN202410334219.9
- Authority / Receiving Office
- CN · China
- Patent Type
- Patents(China)
- Current Assignee / Owner
- Filing Date
- 2024-03-22
- Publication Date
- 2026-10-09
- Estimated Expiration
- 2044-03-22
AI Technical Summary
这可能导致长期运行后流量和冷却能力下降
[0104] 1. The analytical method of this invention can calculate the typical oxide migration paths under the operating conditions of lead-bismuth reactors, filling the gap in existing computational needs;
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Abstract
Description
Technical Field
[0001] This invention relates to the field of lead-bismuth reactor design and corrosion oxygen control technology, specifically to a method for analyzing the migration of oxides in the primary loop of a lead-bismuth reactor. Background Technology
[0002] Liquid metal-cooled fast reactors are the main reactor type for fourth-generation advanced nuclear energy systems, possessing significant advantages such as high temperature, low pressure, breeder fuel, and transmutation of nuclear waste. Lead-bismuth alloys, due to their excellent neutronics and thermo-hydraulic properties, have become one of the main candidate materials for advanced nuclear energy systems such as fourth-generation nuclear reactors and accelerator-driven subcritical systems.
[0003] Under operating conditions, steel elements are continuously released into the lead-bismuth alloy through corrosion in lead-bismuth reactors and transported along with the coolant in the primary loop. These steel elements may subsequently deposit in the reactor loop or react with dissolved oxygen in the lead-bismuth alloy, generating impurities. Impurities with higher melting points cannot melt within the lead-bismuth alloy and exist as solid particles. The continuous deposition of corrosion products on cold surfaces and the accumulation of existing oxide particles can lead to blockages in narrow passages of the steam generator or fuel assemblies. These solid impurities, generated by the corrosion shedding of the lead-bismuth alloy, range in size from nanometers to hundreds of micrometers, ultimately forming a unique multiphase flow state in the flow channel system where the lead-bismuth alloy carries solid particles. This can lead to a decrease in flow rate and cooling capacity after long-term operation. Therefore, it is necessary to use numerical simulations to obtain information on the migration characteristics of oxide particles in the primary loop of lead-bismuth reactors, providing a basis for designing effective filtration systems. 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 analyzing the migration of oxide particles in the primary loop of a lead-bismuth reactor, which analyzes the migration law and distribution location of oxide particles in lead-bismuth alloys, and can calculate the typical oxide migration path under the operating conditions of a lead-bismuth reactor, thus filling the gap in existing calculation needs.
[0005] To achieve the above objectives, the present invention adopts the following technical solution:
[0006] A method for analyzing the migration of oxides in the primary loop of a lead-bismuth reactor, comprising the following steps:
[0007] Step 1: Perform closed-loop geometric modeling and mesh generation for the primary loop of the lead-bismuth reactor, and set the core and primary side of the steam generator as porous media;
[0008] Step 2: Considering fluid-structure conjugate heat transfer and Prandtl number correction for turbulence, obtain the steady-state flow field and temperature field of the entire primary loop of the lead-bismuth reactor;
[0009] Step 3: Based on the magnetite dissolution equilibrium model, oxide particles are injected at the peak of the temperature gradient change in the flow direction of the upper chamber.
[0010] Step 4: Use the DPM model to solve the migration of oxide particles of different sizes in the primary loop of the lead-bismuth reactor;
[0011] Step 5: For oxide particles that will enter the core, perform 3D CFD modeling of the wire winding assembly, and obtain the flow field and temperature field inside the assembly by giving the boundary.
[0012] Step 6: Add particle-wall interaction to the DPM model to solve the migration of oxide particles within the core wire-wound fuel assembly;
[0013] Within Fluent's default DPM model computation framework, a particle-wall interaction model is added to the discrete phase wall boundary conditions using a user-defined function. The specific description of the particle-wall interaction model is as follows:
[0014] If the normal velocity of the oxide particles colliding with the wall is less than the critical deposition velocity, the oxide particles are considered to have deposited. Otherwise, a restitution coefficient is applied to the velocity of the oxide particles, and the migration trajectory is solved until the oxide particles reach the specified boundary or the maximum number of iterations is reached, thereby obtaining the positional distribution information of the oxide particles after migration.
[0015] Preferably, in step 1: the porous media region of the reactor core is divided into a non-fuel assembly region and a fuel assembly region during modeling. A key setting parameter for the porous media in Fluent software is the drag coefficient f. For the porous media in the non-fuel assembly region, the drag coefficient f is set to a constant; for the porous media in the fuel assembly region, since the lead-bismuth alloy has low viscosity, viscous drag loss is ignored and only inertial loss is considered. The pressure drop of the reactor core is mainly determined by the fuel assemblies, and the inertial drag coefficient f adopts the Rehme relation:
[0016]
[0017] In the formula:
[0018] Re – Reynolds number for lead-bismuth alloys;
[0019] F – Geometric factor, fixed at 1.225;
[0020] N r —Number of fuel rods within the component;
[0021] D r —Outer diameter of fuel rod cladding / m;
[0022] D w —Wire diameter / m;
[0023] St — Wetting perimeter / m;
[0024] For the porous medium region on the primary side of the steam generator, a bulk heat source needs to be set up in Fluent software for heat transfer calculations. The Ushakov heat transfer equation suitable for liquid metal flowing through triangular or hexagonal rod bundles is used on the primary side:
[0025]
[0026]
[0027] In the formula:
[0028] Nu – Nusel number;
[0029] P—Heat transfer tube spacing / m;
[0030] D—Outer diameter of heat transfer tube / m;
[0031] Pe = Re·Pr — Berkeley number;
[0032] — Prandtl number;
[0033] μ——Kinetic viscosity of lead-bismuth alloy / Pa·s;
[0034] C P —Specific heat capacity of lead-bismuth composite / J·(kg·K) -1 ;
[0035] h e — Convective heat transfer coefficient on the lead-bismuth side / W·m -2 ·K -1 ;
[0036] λ — Thermal conductivity of lead-bismuth / W·m -1 ·K -1 ;
[0037] D H —Hydraulic diameter / m;
[0038] The overall heat transfer coefficient U on the primary and secondary sides and the volume heat source S in the porous medium region on the primary side of the steam generator. HX As shown in the following formula:
[0039]
[0040] S HX =UA exchange (TT water ) / V PHX
[0041] In the formula:
[0042] R—Thermal resistance of the heat transfer tubes inside the steam generator / W·m -2 ·K -1 ;
[0043] h i —Secondary side convective heat transfer coefficient / W·m -2 ·K -1 ;
[0044] A exchange ——Total heat transfer area of heat transfer tubes / m 2 ;
[0045] T—Temperature of lead-bismuth alloy in K;
[0046] T water —Temperature of saturated water inside the pipe / K;
[0047] V PHX ——Evaporator primary side volume / m 3 .
[0048] Preferably, in step 2: obtaining the steady-state flow field and temperature field of the entire lead-bismuth reactor primary loop requires three-dimensional CFD calculation using Fluent software. The calculation requires defining the material properties within the computational domain; the relationship between the properties of AISI 316L stainless steel in the solid region and the liquid lead-bismuth alloy is as follows:
[0049] ρ steel =8000 kg·m -3
[0050] λ steel =11.45+0.013T
[0051] C p,steel =500J·K -1 ·kg -1
[0052] ρ LBE =11096-1.3236T
[0053] λ LBE =3.61 + 1.517 × 10 -2 T-1.741×10 -6 T 2
[0054] C p,LBE =159 - 2.72 × 10 -2 T+7.12×10 -6 T 2
[0055]
[0056] In the formula:
[0057] T—Temperature of lead-bismuth alloy in K;
[0058] ρ steel — Density of stainless steel / kg·m -3 ;
[0059] λ steel — Stainless steel thermal conductivity / W·m -1 ·K -1 ;
[0060] C p,steel —Heat capacity of lead-bismuth alloy / J·K -1 ;
[0061] ρ LBE — Density of lead-bismuth alloy / kg·m -3 ;
[0062] λ LBE — Thermal conductivity of lead-bismuth alloy / W·m -1 ·K -1 ;
[0063] C p,LBE —Heat capacity of lead-bismuth alloy / J·K -1 ;
[0064] μ LBE —Kinetic viscosity of lead-bismuth alloy / N·s·m -2 ;
[0065] Because lead-bismuth coolant has a low Prandtl number, its molecular thermal conduction is dominant, and the development of the velocity and thermal boundary layers is not similar. Therefore, a modified turbulent Prandtl number model is introduced to optimize the heat transfer calculation of lead-bismuth coolant, as shown in the following equation:
[0066]
[0067]
[0068] Pe = ul / α
[0069] In the formula:
[0070] Pr t — Turbulent Prandtl number;
[0071] Pe – Berkeley number;
[0072] A – The intermediate variable has no practical significance;
[0073] u——Local flow velocity of lead-bismuth alloy / m·s -1 ;
[0074] l — Characteristic dimension of the lead-bismuth alloy flow field / m;
[0075] α—Thermal diffusivity of lead-bismuth alloy in the flow field / m 2 ·s -1 ;
[0076] By introducing the physical properties of AISI 316L stainless steel in the solid region, the physical property relationships of liquid lead-bismuth alloy, and the modified Prandtl number model for turbulence, the Navier-Stokes equations and energy equations can be solved to obtain the distribution of temperature T and flow velocity u in the primary loop of the lead-bismuth reactor, thereby obtaining the steady-state flow field and temperature field.
[0077] Preferably, in step 3: the magnetite dissolution equilibrium model is as follows:
[0078]
[0079]
[0080] In the formula:
[0081] K sp —Fe3O4 dissolution equilibrium constant;
[0082] C Fe(lbe) —Dissolved iron concentration in lead-bismuth alloys / wt%;
[0083] C O(lbe) —Dissolved oxygen concentration in lead-bismuth alloys / wt%;
[0084] T – Temperature of lead-bismuth alloy (K).
[0085] Preferably, in step 6, the critical deposition rate of particles is as follows:
[0086]
[0087] In the formula:
[0088]
[0089]
[0090] e t =0.998 - 1.16θ + 2.11θ 2 -0.67θ 3
[0091] e n =0.993-1.76θ+1.56θ 2 -0.49θ 3
[0092] v cr—Critical deposition rate of particles / m·s -1 ;
[0093] d p —Particle diameter / m;
[0094] K—Effective stiffness;
[0095] R a —The coefficient of restitution is usually taken as 1;
[0096] E s — Young's modulus of the wall surface / GPa;
[0097] E p —Particle Young's modulus / GPa;
[0098] v s —Poisson's ratio of the wall material;
[0099] v p —Particle Poisson's ratio;
[0100] e t —Particle tangential rebound recovery coefficient;
[0101] e n —Particle normal rebound recovery coefficient;
[0102] θ — Angle between the incident particle velocity and the contact surface / rad.
[0103] Compared with the prior art, the present invention has the following advantages:
[0104] 1. The analytical method of this invention can calculate the typical oxide migration paths under the operating conditions of lead-bismuth reactors, filling the gap in existing computational needs;
[0105] 2. The analysis method of the present invention introduces a more detailed inertial drag relationship in the core fuel assembly region, introduces a heat transfer relationship that takes into account the distribution shape of the steam generator heat exchange tubes, and considers conjugate heat transfer, which can more accurately calculate the coolant flow and heat transfer characteristics during the steady-state operation of the primary loop of the lead-bismuth reactor.
[0106] 3. The analytical method of this invention obtains the accurate location of oxide particle formation based on the steady-state temperature field using a magnetite dissolution equilibrium model, thereby ensuring the rationality of the injection location during migration calculation;
[0107] 4. The analytical method of this invention addresses the shortcomings of the modeling method for porous media in the reactor core, which cannot reflect the migration of oxides in this region. It introduces a method for fine modeling of lead-bismuth reactor wire-wound fuel assemblies to calculate the migration of oxides that will enter the reactor core. Attached Figure Description
[0108] Figure 1 This is a flowchart of the method of the present invention.
[0109] Figure 2 This is a schematic diagram of the primary loop structure of a certain lead-bismuth reactor. Detailed Implementation
[0110] The method of the present invention will be further described in detail below with reference to the accompanying drawings and specific embodiments:
[0111] like Figure 1 As shown, the present invention provides a method for analyzing the migration of oxides in the primary loop of a lead-bismuth reactor, comprising the following steps:
[0112] Step 1: Perform closed-loop geometric modeling and mesh generation for the primary loop of the lead-bismuth reactor, and set the core and primary side of the steam generator as porous media;
[0113] In the modeling of the porous media region of the reactor core, it is divided into non-fuel assembly region and fuel assembly region. A key setting parameter for the porous media in Fluent software is the drag coefficient f. For the porous media in the non-fuel assembly region, the drag coefficient f is set to a constant; for the porous media in the fuel assembly region, since the lead-bismuth alloy has low viscosity, viscous drag loss is ignored and only inertial loss is considered. The pressure drop of the reactor core is mainly determined by the fuel assemblies, and the inertial drag coefficient f adopts the Rehme relation:
[0114]
[0115] In the formula:
[0116] Re – Reynolds number for lead-bismuth alloys;
[0117] F – Geometric factor, fixed at 1.225;
[0118] N r —Number of fuel rods within the component;
[0119] D r —Outer diameter of fuel rod cladding / m;
[0120] D w —Wire diameter / m;
[0121] St — Wetting perimeter / m;
[0122] For the porous medium region on the primary side of the steam generator, a bulk heat source needs to be set up in Fluent software for heat transfer calculations. The Ushakov heat transfer equation suitable for liquid metal flowing through triangular or hexagonal rod bundles is used on the primary side:
[0123]
[0124]
[0125] In the formula:
[0126] Nu – Nusel number;
[0127] P—Heat transfer tube spacing / m;
[0128] D—Outer diameter of heat transfer tube / m;
[0129] Pe = Re·Pr — Berkeley number;
[0130] — Prandtl number;
[0131] μ——Kinetic viscosity of lead-bismuth alloy / Pa·s;
[0132] C P —Specific heat capacity of lead-bismuth composite / J·(kg·K) -1 ;
[0133] h e — Convective heat transfer coefficient on the lead-bismuth side / W·m -2 ·K -1 ;
[0134] λ — Thermal conductivity of lead-bismuth / W·m -1 ·K -1 ;
[0135] D H —Hydraulic diameter / m;
[0136] The overall heat transfer coefficient U on the primary and secondary sides and the volume heat source S in the porous medium region on the primary side of the steam generator. HX As shown in the following formula:
[0137]
[0138] S HX =UA exchange (TT water ) / V PHX
[0139] In the formula:
[0140] R—Thermal resistance of the heat transfer tubes inside the steam generator / W·m -2 ·K -1 ;
[0141] h i —Secondary side convective heat transfer coefficient / W·m -2 ·K -1 ;
[0142] A exchange ——Total heat transfer area of heat transfer tubes / m2 ;
[0143] T—Temperature of lead-bismuth alloy in K;
[0144] T water —Temperature of saturated water inside the pipe / K;
[0145] V PHX ——Evaporator primary side volume / m 3 .
[0146] Step 2: Considering fluid-structure conjugate heat transfer and Prandtl number correction for turbulence, obtain the steady-state flow field and temperature field of the entire primary loop of the lead-bismuth reactor;
[0147] Obtaining the steady-state flow field and temperature field of the entire primary loop of the lead-bismuth reactor requires three-dimensional CFD calculations using Fluent software. The calculations necessitate defining the material properties within the computational domain. The relationships between the properties of AISI 316L stainless steel in the solid region and the liquid lead-bismuth alloy are shown in the following equations:
[0148] ρ steel =8000 kg·m -3
[0149] λ steel =11.45+0.013T
[0150] C p,steel =500J·K -1 ·kg -1
[0151] ρ LBE =11096-1.3236T
[0152] λ LBE =3.61 + 1.517 × 10 -2 T-1.741×10 -6 T 2
[0153] C p,LBE =159 - 2.72 × 10 -2 T+7.12×10 -6 T 2
[0154]
[0155] In the formula:
[0156] T—Temperature of lead-bismuth alloy in K;
[0157] ρ steel — Density of stainless steel / kg·m -3 ;
[0158] λ steel — Stainless steel thermal conductivity / W·m -1 ·K -1 ;
[0159] C p,steel —Heat capacity of lead-bismuth alloy / J·K -1 ;
[0160] ρ LBE — Density of lead-bismuth alloy / kg·m -3 ;
[0161] λ LBE — Thermal conductivity of lead-bismuth alloy / W·m -1 ·K -1 ;
[0162] C p,LBE —Heat capacity of lead-bismuth alloy / J·K -1 ;
[0163] μ LBE —Kinetic viscosity of lead-bismuth alloy / N·s·m -2 ;
[0164] Because lead-bismuth coolant has a low Prandtl number, its molecular thermal conduction is dominant, and the development of the velocity and thermal boundary layers is not similar. Therefore, a modified turbulent Prandtl number model is introduced to optimize the heat transfer calculation of lead-bismuth coolant, as shown in the following equation:
[0165]
[0166]
[0167] Pe = ul / α
[0168] In the formula:
[0169] Pr t — Turbulent Prandtl number;
[0170] Pe – Berkeley number;
[0171] A – The intermediate variable has no practical significance;
[0172] u——Local flow velocity of lead-bismuth alloy / m·s -1 ;
[0173] l — Characteristic dimension of the lead-bismuth alloy flow field / m;
[0174] α—Thermal diffusivity of lead-bismuth alloy in the flow field / m 2 ·s -1 ;
[0175] By introducing the physical properties of AISI 316L stainless steel in the solid region, the physical property relationship of liquid lead-bismuth alloy, and the modified Prandtl number model of turbulence, the Navier-Stokes equation and energy equation can be solved to obtain the distribution of temperature T and flow velocity u in the primary loop of the lead-bismuth reactor, thereby obtaining the steady-state flow field and temperature field.
[0176] Step 3: Based on the magnetite dissolution equilibrium model, oxide particles are injected at the peak of the temperature gradient change in the flow direction of the upper chamber.
[0177] The magnetite dissolution equilibrium model is as follows:
[0178]
[0179]
[0180] In the formula:
[0181] K sp —Fe3O4 dissolution equilibrium constant;
[0182] C Fe(lbe) —Dissolved iron concentration in lead-bismuth alloys / wt%;
[0183] C O(lbe) —Dissolved oxygen concentration in lead-bismuth alloys / wt%;
[0184] T – Temperature of lead-bismuth alloy (K).
[0185] Step 4: Use the DPM model to solve the migration of oxide particles of different sizes in the primary loop of the lead-bismuth reactor.
[0186]
[0187]
[0188]
[0189] u p ——Particle velocity / m·s -1 ;
[0190] u—fluid velocity / m·s -1 ;
[0191] ρ p ——Particle density / kg·m -3 ;
[0192] ρ — fluid density / kg·m -3 ;
[0193] Re p —Particle Reynolds number;
[0194] d p —Particle diameter / m;
[0195] F D —The drag force on the particles;
[0196] C D —Drag coefficient;
[0197] F Vm —Virtual mass force / N;
[0198] —The velocity vector of the particle;
[0199] —The gradient of the velocity vector of the lead-bismuth alloy;
[0200] —The derivative of the particle velocity vector with time;
[0201] Step 5: For oxide particles that will enter the core, perform 3D CFD modeling of the wire winding assembly, and obtain the flow field and temperature field inside the assembly by giving the boundary.
[0202] Step 6: Add particle-wall interaction to the DPM model to solve the migration of oxide particles within the core wire-wound fuel assembly;
[0203] Within Fluent's default DPM model computation framework, a particle-wall interaction model is added to the discrete phase wall boundary conditions using a user-defined function. The specific description of the particle-wall interaction model is as follows:
[0204] If the normal velocity of the oxide particles colliding with the wall is less than the critical deposition velocity, the oxide particles are considered to have deposited. Otherwise, a restitution coefficient is applied to the velocity of the oxide particles, and the migration trajectory is solved again until the oxide particles reach the specified boundary or the maximum number of iterations is reached, thereby obtaining the positional distribution information of the oxide particles after migration.
[0205] The critical deposition rate of particles is as follows:
[0206]
[0207] In the formula:
[0208]
[0209]
[0210] e t =0.998 - 1.16θ + 2.11θ 2 -0.67θ 3
[0211] e n =0.993-1.76θ+1.56θ 2 -0.49θ 3
[0212] v cr —Critical deposition rate of particles / m·s -1 ;
[0213] d p —Particle diameter / m;
[0214] K—Effective stiffness;
[0215] R a —The coefficient of restitution is usually taken as 1;
[0216] E s — Young's modulus of the wall surface / GPa;
[0217] E p —Particle Young's modulus / GPa;
[0218] v s —Poisson's ratio of the wall material;
[0219] v p —Particle Poisson's ratio;
[0220] e t —Particle tangential rebound recovery coefficient;
[0221] e n —Particle normal rebound recovery coefficient;
[0222] θ — Angle between the incident particle velocity and the contact surface / rad.
[0223] The effects of this invention will be explained below with reference to specific computational objects. Figure 2Taking the schematic diagram of a lead-bismuth reactor primary loop as an example, step 1 involves performing closed-loop geometric modeling of the lead-bismuth reactor primary loop, including the core, main pump, steam generator, and upper, middle, and lower chambers, and meshing the model. The primary side regions of the core and steam generator are set as porous media. The flow within the entire computational domain is achieved by setting the pump (fan) boundary surface in the pump rotor region in Fluent software. Step 2 involves setting the physical properties of the fluid and solid materials respectively, considering fluid-structure conjugate heat transfer and Prandtl number correction for turbulence to obtain the steady-state flow field and temperature field of the entire reactor primary loop. Step 3 involves extracting the temperature obtained from the steady-state calculation along the axis in the flow direction of the upper chamber, and setting oxide particle injection in areas with large temperature gradient changes. The process involves several steps: Step 4 employs a surface injection method; Step 5 utilizes the DPM model from computational fluid dynamics, invoking its functions for calculating gravity, buoyancy, drag, turbulent diffusion, virtual mass force, and pressure gradient force to solve for the migration of oxide particles of different sizes within the reactor primary loop. The discrete phase wall conditions at the upper chamber free surface and core inlet are set to trap type, stopping trajectory calculation once the particles reach the free surface or core inlet; Step 6, based on the results of Step 4, performs 3D CFD modeling on the wire-wound fuel assembly for oxide particles that will enter the core, obtaining the flow and temperature fields within the assembly by defining boundaries; Step 7, adding particle-wall interactions to the DPM model to solve for the migration of oxide particles within the wire-wound fuel assembly in the core. This invention provides evaluation and guidance for the design of external filtration systems in lead-bismuth reactors.
Claims
1. A method for analyzing the migration of oxides in the primary loop of a lead-bismuth reactor, characterized in that: The steps are as follows: Step 1: Perform closed-loop geometric modeling and mesh generation for the primary loop of the lead-bismuth reactor, and set the core and primary side of the steam generator as porous media; Step 2: Considering fluid-structure conjugate heat transfer and Prandtl number correction for turbulence, obtain the steady-state flow field and temperature field of the entire primary loop of the lead-bismuth reactor; Step 3: Based on the magnetite dissolution equilibrium model, oxide particles are injected at the peak of the temperature gradient change in the flow direction of the upper chamber. Step 4: Use the DPM model to solve the migration of oxide particles of different sizes in the primary loop of the lead-bismuth reactor; Step 5: For oxide particles that will enter the core, perform 3D CFD modeling of the wire winding assembly, and obtain the flow field and temperature field inside the assembly by giving the boundary. Step 6: Add particle-wall interaction to the DPM model to solve the migration of oxide particles within the core wire-wound fuel assembly; Within the default DPM model calculation framework of Fluent software, the particle-wall interaction model is added to the discrete phase wall boundary conditions using a user-defined function. The specific description of the particle-wall interaction model is as follows: If the normal velocity of the oxide particles colliding with the wall is less than the critical deposition velocity, the oxide particles are considered to have deposited. Otherwise, a restitution coefficient is applied to the velocity of the oxide particles, and the migration trajectory is solved until the oxide particles reach the specified boundary or the maximum number of iterations is reached, thereby obtaining the positional distribution information of the oxide particles after migration.
2. The method for analyzing the migration of oxides in the primary loop of a lead-bismuth reactor according to claim 1, characterized in that: In step 1: the porous media region of the reactor core is divided into non-fuel assembly region and fuel assembly region during modeling. A key setting parameter for the porous media in Fluent software is the drag coefficient. f For porous media in non-fuel component regions, the drag coefficient f Set as a constant; for the porous medium in the fuel assembly region, due to the low viscosity of the lead-bismuth alloy, viscous drag loss is ignored, and only inertial loss is considered; the pressure drop in the core is mainly determined by the fuel assemblies, and the inertial drag coefficient is... f Using the Rehme relation: In the formula: —Reynolds number of lead-bismuth alloy; —Geometric factor, fixed at 1.225; —Number of fuel rods within the component; —Outer diameter of fuel rod cladding / m; —Wire diameter / m; —Wetting perimeter / m; For the porous medium region on the primary side of the steam generator, a bulk heat source needs to be set up in Fluent software for heat transfer calculations. The Ushakov heat transfer equation suitable for liquid metal flowing through triangular or hexagonal rod bundles is used on the primary side: In the formula: —Nusser number; —Heat transfer tube spacing / m; —Outer diameter of heat transfer tube / m; —Berkley number; — Prandtl number; —Kinetic viscosity of lead-bismuth alloy / ; Specific heat capacity of lead-bismuth composite / ; —Convection heat transfer coefficient on the lead-bismuth side / ; — Thermal conductivity of lead and bismuth / ; —Hydraulic diameter / m; Overall heat transfer coefficient of primary and secondary sides U and the bulk heat source of the porous medium region on the primary side of the steam generator SHX As shown in the following formula: In the formula: —Thermal resistance of heat transfer tubes inside the steam generator / ; —Secondary side convective heat transfer coefficient / ; —Total heat transfer area of heat transfer tubes / ; —Temperature of lead-bismuth alloy / K; —Temperature of saturated water inside the pipe / K; ——Evaporator primary side volume / .
3. The method for analyzing the migration of oxides in the primary loop of a lead-bismuth reactor according to claim 1, characterized in that: In step 2: Obtaining the steady-state flow field and temperature field of the entire lead-bismuth reactor primary loop requires three-dimensional CFD calculations using Fluent software. The calculations require defining the material properties within the computational domain. The relationships between the properties of AISI 316L stainless steel in the solid region and the liquid lead-bismuth alloy are as follows: In the formula: —Temperature of lead-bismuth alloy / K; —Stainless steel density / ; — Stainless steel thermal conductivity / ; —Heat capacity of lead-bismuth alloy / ; —Density of lead-bismuth alloy / ; — Thermal conductivity of lead-bismuth alloy / ; —Heat capacity of lead-bismuth alloy / ; —Kinetic viscosity of lead-bismuth alloy / ; Because lead-bismuth coolant has a low Prandtl number, its molecular thermal conduction is dominant, and the development of the velocity and thermal boundary layers is not similar. Therefore, a modified turbulent Prandtl number model is introduced to optimize the heat transfer calculation of lead-bismuth coolant, as shown in the following equation: In the formula: — Turbulent Prandtl number; —Berkley number; A —The intermediate variables have no practical significance; ——Local flow rate of lead-bismuth alloy / ; —Characteristic dimensions of the lead-bismuth alloy flow field / m; — Thermal diffusivity of lead-bismuth alloy flow field / ; By introducing the physical properties of AISI 316L stainless steel in the solid region, the physical property relationships of liquid lead-bismuth alloy, and the modified Prandtl number model for turbulence, the Navier-Stokes equations and energy equations can be solved to obtain the distribution of temperature T and flow velocity u in the primary loop of the lead-bismuth reactor, thereby obtaining the steady-state flow field and temperature field.
4. The method for analyzing the migration of oxides in the primary loop of a lead-bismuth reactor according to claim 1, characterized in that: In step 3: the magnetite dissolution equilibrium model is as follows: In the formula: —— Dissolution equilibrium constant; —Concentration of dissolved iron in lead-bismuth alloys / ; —Dissolved oxygen concentration in lead-bismuth alloys / ; —Temperature of lead-bismuth alloy / K.
5. The method for analyzing the migration of oxides in the primary loop of a lead-bismuth reactor according to claim 1, characterized in that: In step 6: the critical deposition rate of particles is as follows: In the formula: —Critical deposition rate of particles / ; —Particle diameter / ; —Effective stiffness; —Coefficient of recovery; — Young's modulus of the wall / ; —Particle Young's modulus / ; —Poisson's ratio of the wall material; —Particle Poisson's ratio; —Particle tangential rebound recovery coefficient; —Particle normal rebound recovery coefficient; —Angle between the incident particle velocity and the contact surface / rad.
Citation Information
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