Sodium-cooled fast reactor pool type sodium fire calculation method based on finite volume method

Abstract

The invention discloses a sodium-cooled fast reactor pool type sodium fire calculation method based on a finite volume method. The method comprises the following steps: 1, dividing a pool type sodium fire space calculation domain to be analyzed into unstructured grids; 2, inputting and reading calculated operation parameters and calculation parameters; 3, calculating the mass fraction and density of sodium and air; 4, calculating the temperature of sodium and air; 5, solving velocity divergence; 6, calculating the air velocity; and 7, if the current time is equal to the combustion transient calculation time, outputting a calculation result, otherwise, returning to the step 3, and calculating again until the calculation is finished. According to the method, a finite volume frame and an unstructured grid data format are adopted, calculation objects of any geometrical shape are adapted, physical processes such as surface oxidation, gas-phase combustion, one-dimensional heat conduction, gas flow and heat transmission of pool type sodium fire combustion are considered, modeling of complex geometry and calculation of key physical quantities in three-dimensional space-time are achieved, and the method has the advantages of being simple in structure and high in calculation efficiency. And the physical quantity at the key position in the solution domain is accurately obtained, so that the consequence of the sodium-cooled fast reactor pool type sodium fire accident is evaluated more comprehensively and effectively, and the design of a sodium fire extinguishing system is guided.

Description

Technical Field

[0001] This invention belongs to the field of nuclear energy development and nuclear reactor safety technology, specifically relating to a calculation method for sodium fire in a pool-type sodium-cooled fast reactor based on the finite volume method. Background Technology

[0002] Sodium-cooled fast reactors (SNCRs) are the most mature reactor type, with over 400 reactor-years of operational experience to date, making them one of the most likely fourth-generation nuclear energy systems to be widely deployed first. In my country, SNCRs have also successfully progressed from experimental reactors and prototype reactors to commercial reactors. However, SNCRs use liquid metallic sodium as a coolant, and due to sodium's highly reactive chemical properties, it poses a significant fire hazard. Damage to the sodium system boundary can cause sodium leakage and subsequent combustion, making sodium fire one of the most critical safety issues in fast reactors. Generally, sodium fires are classified into three types: pool fires, jet fires, and mixed fires. Combustion produces dense white smoke, primarily composed of sodium oxide and sodium peroxide. The thermodynamic consequences of a sodium fire directly manifest as increased temperature and pressure within the fire chamber, potentially endangering safety equipment and systems within the chamber, as well as the building structure. Therefore, sodium fire accident analysis and evaluation of sodium fire protection are crucial components of fast reactor safety analysis.

[0003] Previous sodium fire analysis programs mostly used the lumped parameter method, which has certain shortcomings in sodium fire simulation and analysis. For example, after an accident occurs, it is impossible to perform three-dimensional spatiotemporal calculations on the physical parameters within the computational space, making it impossible to implement precise and effective control for sodium fire suppression. Therefore, it is necessary to develop a more accurate, practical, reliable, and user-friendly sodium fire calculation method to calculate, evaluate, and analyze changes in room temperature and pressure, smoke flow, and the impact of sodium fire protection measures under sodium fire accidents. This will facilitate the design of sodium leakage and sodium fire accident verification tests, analysis of test data, design of protective measures, and better achievement of sodium fire protection tasks. Summary of the Invention

[0004] To overcome the problems existing in the prior art, the present invention aims to provide a pool-type sodium fire calculation method based on the finite volume method. This method develops a finite volume framework, defines unstructured mesh writing rules, generates an unstructured mesh for the computational domain, defines the total computation time and time step, and considers physical processes such as surface oxidation, gas-phase combustion, one-dimensional heat conduction, gas flow, and heat transfer in pool-type sodium fire combustion. It calculates the mass changes of sodium and gas using the mass equation, gas transport using the momentum equation, heat transfer using the energy equation, and chemical combustion component changes using the component transport equation, thereby obtaining the spatiotemporal changes of temperature, pressure, velocity, oxygen concentration, and sodium mass in three-dimensional space. The method of the present invention can simulate the three-dimensional spatiotemporal distribution of key physical quantities such as temperature, pressure, and oxygen concentration in space under severe pool-type sodium fire accidents, providing theoretical guidance for the safety analysis and assessment of sodium-cooled fast reactors and the design of sodium fire suppression systems.

[0005] To achieve the above objectives, the present invention adopts the following technical solution: A pool-type sodium fire calculation method based on the finite volume method includes the following steps: Step 1: Divide the computational domain of the pool-type sodium fire space to be analyzed into an unstructured finite volume grid: First, divide the computational domain of the sodium-cooled fast reactor to be analyzed into an unstructured finite volume grid, including the overall grid cell number and face index file of the computational domain, the grid face number and node index file, and the total number of faces and face index file of the pressure region and boundary region. Step 2: Input and read the calculation parameters and operating parameters: Store the mesh information by reading the mesh format files obtained in Step 1, such as mesh cell number and face index files, mesh face number and node index files, and the total number of faces and face index files contained in the pressure region and boundary region. Operating parameters include the total combustion time, time step, gas introduction and exhaust time, initial mass, initial temperature and thickness of the liquid sodium pool, initial ambient temperature and initial oxygen concentration of the computational domain, volumetric flow rate and temperature of the oxygen supply, exhaust rate of the ventilation system, physical properties of liquid sodium, area of ​​the liquid sodium pool, area and material properties of the walls, area of ​​the vents and exhaust vents, and the relationship between sodium and air in the combustion reaction. Calculation parameters include the temperature and mass change rate of the liquid sodium pool, ambient temperature of the computational domain, oxygen concentration, air velocity, and pressure. Initialize the program based on the operating parameters to obtain the initial values ​​for the entire computational domain. Step 3: Calculate the mass fraction and density of sodium and air: Introduce the source and diffusion terms of each substance in sodium and air into the mass conservation equation shown in equation (1) to obtain the grid numbered... The mass conservation equation for the continuity of components (2), (1) (2) In the formula, : Components, representing sodium vapor, oxygen, and nitrogen; Components density / ; Air speed / ; :time / ; Components The mass fraction; Components diffusion coefficient / ; : Mass change due to the evaporation of liquid sodium per unit volume / ; : Mass change per unit volume due to the combustion of liquid sodium / The superscripts n and n+1 represent time n and time n+1, respectively; the subscript ijk represents the ijk-th grid cell. The sum of all components in the continuity equation (2) satisfies The sum of the mass changes caused by the evaporation of liquid sodium per unit volume satisfies The component continuity equation (2) directly relates to Solve as a whole, according to The density of the substance, including all its components, was calculated, i.e., the total density of sodium vapor, oxygen, and nitrogen, based on... Calculated components The mass fraction; Step 4: Calculate the temperature of sodium and air: The combustion process of liquid sodium is divided into a pre-combustion stage and a combustion stage. Each process involves oxidation and evaporation, and is related to the density, specific heat, and heat release of vaporization of liquid sodium. Equations (3), (4), and (5) represent the density, specific heat, and heat release of vaporization of liquid sodium, respectively: (3) (4) (5) In the formula, Density of liquid sodium / ; : Temperature of liquid sodium in K; Specific heat of liquid sodium / ; The heat released during the vaporization of liquid sodium / ; Critical temperature of liquid sodium / ; The mass combustion rate of liquid sodium during the pre-combustion stage is: (6) In the formula, Mass combustion rate of liquid sodium during the pre-combustion stage / ; Atmospheric density ; Oxygen diffusion coefficient / ; Oxygen mole fraction; Sodium droplet diameter / m; The mass ratio of oxygen to sodium in the reaction; Schmidt number , kinematic viscosity / ; Reynolds number, ,in The relative velocity between the droplet and the air / ; During the combustion phase, the evaporation of liquid sodium causes a decrease in the mass of the liquid pool. The evaporation rate during combustion is: (7) In the formula, Mean pressure / Pa; Evaporation rate of liquid sodium within a single time step / ; Mass transfer coefficient between liquid sodium and air / ; Molar mass of liquid sodium / ; Universal gas constant / ; Temperature of the gas near the surface of liquid sodium (°C); : Volume fraction of sodium vapor near the surface of liquid sodium; : Volume fraction of liquid sodium; by solving for the sum of the evaporation of liquid sodium in the pre-combustion stage and the combustion stage at different times, the mass change rate of liquid sodium at different times is obtained; Combustion of liquid sodium occurs at specific oxygen concentrations and liquid sodium temperatures. An extinction model incorporating both oxygen concentration and liquid sodium temperature is established based on the critical flame temperature. If either condition fails, no chemical reaction occurs. If the liquid sodium temperature is lower than the ignition temperature of sodium, combustion is inhibited. The extinction model incorporating oxygen concentration and liquid sodium temperature is as follows: (8) In the formula, Mass fraction of liquid sodium; : Mass fraction of air; Mass fraction of combustion products; Critical temperature of liquid sodium / °C; Enthalpy of liquid sodium at temperature T / ; Enthalpy change of liquid sodium / ; Enthalpy of air at temperature T / ; Enthalpy of combustion products at temperature T / ; Liquid sodium in enthalpy value at time / ; Air in enthalpy value at time / ; Combustion products in enthalpy value at time / ; For a liquid sodium pool with a length-to-width ratio greater than 10, it is considered as one-dimensional heat conduction, and its one-dimensional transient heat conduction equation is: (9) In the formula, Thermal diffusivity of liquid sodium / ; Time / s; : Distance between the inside of the sodium pool and the upper surface of the sodium pool / m; Temperature of liquid sodium in the vertical direction / °C; The temperature of liquid sodium can be calculated using the one-dimensional transient heat conduction equation; For the temperature of the air, the ideal gas law shown in equation (10) is used to solve the problem: (10) In the formula, Air pressure / Pa; The total density of sodium vapor, oxygen, and nitrogen obtained from step 3 / ; Universal gas constant / ; Air temperature / K; air molar mass / ; Calculate air temperature using the ideal gas law. ; Step 5: Solve for the velocity divergence: After determining the density, mass fraction, and temperature of each component, the velocity divergence at the nth time step can be calculated. : (11) In the formula, Heat release rate per unit volume of liquid sodium combustion / ; Energy of liquid sodium droplets / ; : Conduction, diffusion and radiation heat flux of liquid sodium and air / ; Background pressure (Pa); Enthalpy / ; Step 6: Calculate air velocity: Based on the velocity divergence obtained in step 5, solve the pressure Poisson equation: (12) In the formula, Stagnation energy per unit mass / F: Stress term; n and n+1 represent the nth and (n+1)th time steps, respectively; Therefore, the velocity at the (n+1)th time step is calculated based on the velocity at the nth time step in step 5: (13) In the formula, and Represent the air velocity at time steps n and (n+1) respectively. ; : The stress term at the nth time step; The stagnation energy gradient per unit mass at the nth time step; Step 7: Add the time step to the calculated time to get the current time, return to step 3 to continue the calculation until the current time equals the total combustion time set in step 2, then end the calculation; output curves or contour maps of the temperature and mass change rate of liquid sodium, ambient temperature of the calculation domain, oxygen concentration, air velocity and pressure.

[0006] Compared with the prior art, the present invention has the following advantages: The computational method of this invention employs a finite volume framework, supporting unstructured meshes adapted to computational objects of arbitrary geometric shapes. Compared to previous computational methods based on lumped parameter methods, it can achieve modeling of complex geometries and calculation of key physical quantities in three-dimensional spacetime, accurately obtaining physical quantities at key locations within the solution domain. Specific advantages are as follows: 1. The method of the present invention supports reading and storing unstructured finite volume mesh information. By compiling and identifying the mesh element number and surface index file, the mesh surface number and node index file, the total number of surfaces and surface index file contained in the pressure region and the boundary region, different functions can be divided into different regions in three-dimensional space and different attributes can be set. 2. The method of this invention supports setting the liquid sodium mass, initial temperature, oxygen supply time and location, and exhaust system flow rate and location for pool-type sodium fires. By solving partial differential equations and combustion equations in three-dimensional spacetime, it achieves condition settings similar to those of real pool-type sodium fires in three-dimensional space. Compared with existing methods that use lumped parameter methods to solve for the average value of the entire field, the method of this invention can truly reflect the changes of physical quantities such as temperature, pressure, velocity, and oxygen concentration at different spatial locations over time. This allows for a more comprehensive and effective assessment of the consequences of pool-type sodium fire accidents in sodium-cooled fast reactors, providing a theoretical reference for sodium fire fire protection design and optimization. Attached Figure Description

[0007] Figure 1 This is a flowchart of a pool-type sodium fire calculation method based on the finite volume method provided in a specific embodiment of the present invention.

[0008] Figure 2 It is the geometric domain of liquid sodium pool combustion.

[0009] Figure 3 It is a temperature curve at the monitoring point within the calculation domain.

[0010] Figure 4 This is a temperature contour map of the central cross-section of a liquid sodium pool. Detailed Implementation

[0011] This invention provides a pool-type sodium fire calculation method based on the finite volume method. The invention will be described in detail below with reference to the accompanying drawings and embodiments.

[0012] like Figure 1 As shown, this invention discloses a pool-type sodium fire calculation method based on the finite volume method, comprising the following seven steps: 1. Dividing the spatial computational domain of the pool-type sodium fire to be analyzed into an unstructured mesh; 2. Inputting and reading the calculation operation parameters and calculation parameters; 3. Solving the mass equation to calculate the mass fraction and density of sodium and air; 4. Calculating the temperature of sodium and air; 5. Solving the velocity divergence; 6. Solving the pressure Poisson equation to calculate the air velocity; 7. If the current time is equal to the combustion transient calculation time, outputting the calculation result; otherwise, returning to step 3 and recalculating until the calculation ends.

[0013] Step 1: Divide the pool-type sodium fire space computational domain into an unstructured mesh: First, divide the computational domain of the sodium-cooled fast reactor to be analyzed into an unstructured finite volume mesh, including the overall mesh cell number and face index file of the computational domain, the mesh face number and node index file, and the total number of faces and face index file of the pressure region and boundary region. Step 2: Input and read the calculation parameters: Store the mesh information by reading the mesh format files obtained in Step 1, such as mesh cell number and face index files, mesh face number and node index files, and the total number of faces and face index files contained in the pressure region and boundary region. The operating parameters include the total combustion time, time step, gas introduction and exhaust time, initial mass, initial temperature and thickness of the liquid sodium pool, initial ambient temperature and initial oxygen concentration of the computational domain, volumetric flow rate and temperature of the oxygen supply, exhaust rate of the ventilation system, physical properties of liquid sodium, area of ​​the liquid sodium pool, area and material properties of the walls, area of ​​the vents and exhaust vents, and the relationship between sodium and air in the combustion reaction. The calculation parameters include the temperature and mass change rate of the liquid sodium pool, ambient temperature of the computational domain, oxygen concentration, air velocity, and pressure. Initialize the program based on the operating parameters to obtain the initial values ​​for the entire computational domain. Step 3: Calculate the mass fraction and density of sodium and air: Introduce the source and diffusion terms of each substance in sodium and air into the mass conservation equation shown in equation (1) to obtain the grid numbered... The mass conservation equation for the continuity of components (2), (1) (2) In the formula, : Components, representing sodium vapor, oxygen, and nitrogen; Components density / ; Air speed / ; :time / ; Components The mass fraction; Components diffusion coefficient / ; : Mass change due to the evaporation of liquid sodium per unit volume / ; : Mass change per unit volume due to the combustion of liquid sodium / The superscripts n and n+1 represent time n and time n+1, respectively; the subscript ijk represents the ijk-th grid cell. The sum of all components in the continuity equation (2) satisfies The sum of the mass changes caused by the evaporation of liquid sodium per unit volume satisfies The component continuity equation (2) directly relates to Solve as a whole, according to The density of the substance, including all its components, was calculated, i.e., the total density of sodium vapor, oxygen, and nitrogen, based on... Calculated components The mass fraction; Step 4: Calculate the temperature of sodium and air: The combustion process of liquid sodium is divided into a pre-combustion stage and a combustion stage. Each process involves oxidation and evaporation, and is related to the density, specific heat, and heat release of vaporization of liquid sodium. Equations (3), (4), and (5) represent the density, specific heat, and heat release of vaporization of liquid sodium, respectively: (3) (4) (5) In the formula, Density of liquid sodium / ; : Temperature of liquid sodium in K; Specific heat of liquid sodium / ; The heat released during the vaporization of liquid sodium / ; Critical temperature of liquid sodium / ; The mass combustion rate of liquid sodium during the pre-combustion stage is: (6) In the formula, Mass combustion rate of liquid sodium during the pre-combustion stage / ; Atmospheric density ; Oxygen diffusion coefficient / ; Oxygen mole fraction; Sodium droplet diameter / m; The mass ratio of oxygen to sodium in the reaction; Schmidt number , kinematic viscosity / ; Reynolds number, ,in The relative velocity between the droplet and the air / ; During the combustion phase, the evaporation of liquid sodium causes a decrease in the mass of the liquid pool. The evaporation rate during combustion is: (7) In the formula, Mean pressure / Pa; Evaporation rate of liquid sodium within a single time step / ; Mass transfer coefficient between liquid sodium and air / ; Molar mass of liquid sodium / ; Universal gas constant / ; Temperature of the gas near the surface of liquid sodium (°C); : Volume fraction of sodium vapor near the surface of liquid sodium; : Volume fraction of liquid sodium; by solving for the sum of the evaporation of liquid sodium in the pre-combustion stage and the combustion stage at different times, the mass change rate of liquid sodium at different times is obtained; Combustion of liquid sodium occurs at specific oxygen concentrations and liquid sodium temperatures. An extinction model incorporating both oxygen concentration and liquid sodium temperature is established based on the critical flame temperature. If either condition fails, no chemical reaction occurs. If the liquid sodium temperature is lower than the ignition temperature of sodium, combustion is inhibited. The extinction model incorporating oxygen concentration and liquid sodium temperature is as follows: (8) In the formula, Mass fraction of liquid sodium; : Mass fraction of air; Mass fraction of combustion products; Critical temperature of liquid sodium / °C; Enthalpy of liquid sodium at temperature T / ; Enthalpy change of liquid sodium / ; Enthalpy of air at temperature T / ; Enthalpy of combustion products at temperature T / ; Liquid sodium in enthalpy value at time / ; Air in enthalpy value at time / ; Combustion products in enthalpy value at time / ; For a liquid sodium pool with a length-to-width ratio greater than 10, it is considered as one-dimensional heat conduction, and its one-dimensional transient heat conduction equation is: (9) In the formula, Thermal diffusivity of liquid sodium / ; Time / s; : Distance between the inside of the sodium pool and the upper surface of the sodium pool / m; Temperature of liquid sodium in the vertical direction / °C; The temperature of liquid sodium can be calculated using the one-dimensional transient heat conduction equation; For the temperature of the air, the ideal gas law shown in equation (10) is used to solve the problem: (10) In the formula, Air pressure / Pa; The total density of sodium vapor, oxygen, and nitrogen obtained from step 3 / ; Universal gas constant / ; Air temperature / K; air molar mass / ; Calculate air temperature using the ideal gas law. ; Step 5: Solve for the velocity divergence: After determining the density, mass fraction, and temperature of each component, the velocity divergence at the nth time step can be calculated. : (11) In the formula, Heat release rate per unit volume of liquid sodium combustion / ; Energy of liquid sodium droplets / ; : Conduction, diffusion and radiation heat flux of liquid sodium and air / ; Background pressure (Pa); Enthalpy / ; Step 6: Calculate air velocity: Based on the velocity divergence obtained in step 5, solve the pressure Poisson equation: (12) In the formula, Stagnation energy per unit mass / F: Stress term; n and n+1 represent the nth and (n+1)th time steps, respectively; Therefore, the velocity at the (n+1)th time step is calculated based on the velocity at the nth time step in step 5: (13) In the formula, and Represent the air velocity at time steps n and (n+1) respectively. ; : The stress term at the nth time step; The stagnation energy gradient per unit mass at the nth time step; Step 7: Add the time step to the calculated time to get the current time, return to step 3 to continue the calculation until the current time equals the total combustion time set in step 2, then end the calculation; output curves or contour maps of the temperature and mass change rate of liquid sodium, ambient temperature of the calculation domain, oxygen concentration, air velocity and pressure.

[0014] The effects of this invention will be explained below with reference to specific computational objects. Figure 2 Taking the liquid sodium pool combustion geometry as an example, in the figure: 1 is the first oxygen supply channel, 2 is the second oxygen supply channel, 3 is the third oxygen supply channel, 4 is the fourth oxygen supply channel, 5 is the wall, 6 is the vent, and 7 is the liquid sodium pool. First, the pool-type sodium fire spatial computational domain is divided into an unstructured finite volume mesh. The mesh element numbers and surface index files, mesh surface numbers and node index files, and the total number of surfaces and surface index files contained in the pressure region and boundary region are read. The mesh information is stored in the program, and the operating parameters are set, such as a total combustion time of 240 minutes, a time step of 0.01s, and oxygen at a rate of 0.0017 at 0s. Oxygen is supplied into the computational domain through channels 1-4. Ventilation is initiated from the vents at 0 seconds using natural circulation. The initial mass of the liquid sodium pool is 550 kg, the initial temperature is 505 °C, and the thickness is 0.25 m. The initial ambient temperature of the computational domain is 55 °C, the initial oxygen concentration is 21% (Vol%), and the area of ​​the liquid sodium pool is 0.1 m. The total area of ​​all walls is 1. The wall surface is covered with a layer 0.003m thick and has a thermal conductivity of 53.498. Specific heat is 0.46 The density is 7830. The relationship between the combustion reaction of stainless steel plate, sodium, and air is as follows: The coefficients in this formula are automatically calculated by the program based on temperature and oxygen concentration. Steps 2-7 above can be used to calculate the combustion phenomena, gas transport, heat conduction, and oxygen consumption during the pool-type sodium combustion process. Figure 3The graph shows the temperature changes over time at several monitoring points set in the computational domain in this specific embodiment. The temperature changes exhibit a trend of first increasing to a peak over time, and then slowly decreasing, demonstrating the excellent computational effect of this invention on the temperature change characteristics during pool-type sodium combustion. Figure 4 The invention presents a temperature cloud map of the central section of a liquid sodium pool, demonstrating its excellent computational performance for physical quantities in three-dimensional space. This provides a basis for a more comprehensive and effective assessment of the safety of sodium-cooled fast reactors and the design of sodium fire suppression systems.

[0015] The above description is a further detailed explanation of the present invention in conjunction with specific preferred embodiments. It should not be considered that the specific embodiments of the present invention are limited to this. For those skilled in the art, several simple deductions or substitutions can be made without departing from the concept of the present invention, and all such deductions or substitutions should be considered to fall within the scope of patent protection determined by the submitted claims.

Claims

1. A calculation method for sodium-cooled fast reactor pool-type sodium fire based on the finite volume method, characterized in that: Includes the following steps: Step 1: Divide the computational domain of the pool-type sodium fire space to be analyzed into an unstructured finite volume grid: First, divide the computational domain of the sodium-cooled fast reactor to be analyzed into an unstructured finite volume grid, including the overall grid cell number and face index file of the computational domain, the grid face number and node index file, and the total number of faces and face index file of the pressure region and boundary region. Step 2: Input and read the calculation parameters and operating parameters: Store the mesh information by reading the mesh format files obtained in Step 1, namely the mesh cell number and face index file, the mesh face number and node index file, and the total number of faces and face index files contained in the pressure region and boundary region. Operating parameters include the total combustion time, time step, gas introduction and exhaust time, initial mass, initial temperature and thickness of the liquid sodium pool, initial ambient temperature and initial oxygen concentration of the computational domain, volumetric flow rate and temperature of the oxygen supply, exhaust rate of the ventilation system, physical properties of liquid sodium, area of ​​the liquid sodium pool, area and material properties of the walls, area of ​​the vents and exhaust vents, and the relationship between sodium and air in the combustion reaction. Calculation parameters include the temperature and mass change rate of the liquid sodium pool, ambient temperature of the computational domain, oxygen concentration, air velocity, and pressure. Initialize the program based on the operating parameters to obtain the initial values ​​for the entire computational domain. Step 3: Calculate the mass fraction and density of sodium and air: Introduce the source and diffusion terms of each substance in sodium and air into the mass conservation equation shown in equation (1) to obtain the grid numbered... The mass conservation equation for the continuity of components (2), (1) (2) In the formula, : Components, representing sodium vapor, oxygen, and nitrogen; Components density / ; Air speed / ; :time / ; Components The mass fraction; Components diffusion coefficient / ; : Mass change due to the evaporation of liquid sodium per unit volume / ; : Mass change per unit volume due to the combustion of liquid sodium / The superscripts n and n+1 represent time n and time (n+1) respectively; the subscripts... ijk Indicates the first ijk One grid cell; The sum of all components in the continuity equation (2) satisfies The sum of the mass changes caused by the evaporation of liquid sodium per unit volume satisfies The component continuity equation (2) directly relates to Solve as a whole, according to The density of the substance, including all its components, was calculated, i.e., the total density of sodium vapor, oxygen, and nitrogen, based on... Calculated components The mass fraction; Step 4: Calculate the temperature of sodium and air: The combustion process of liquid sodium is divided into a pre-combustion stage and a combustion stage. Each process involves oxidation and evaporation, and is related to the density, specific heat, and heat release of vaporization of liquid sodium. Equations (3), (4), and (5) represent the density, specific heat, and heat release of vaporization of liquid sodium, respectively: (3) (4) (5) In the formula, Density of liquid sodium / ; : Temperature of liquid sodium in K; Specific heat of liquid sodium / ; The heat released during the vaporization of liquid sodium / ; Critical temperature of liquid sodium / ; The mass combustion rate of liquid sodium during the pre-combustion stage is: (6) In the formula, Mass combustion rate of liquid sodium during the pre-combustion stage / ; Atmospheric density ; Oxygen diffusion coefficient / ; Oxygen mole fraction; Sodium droplet diameter / m; The mass ratio of oxygen to sodium in the reaction; Schmidt number , kinematic viscosity / ; Reynolds number, ,in The relative velocity between the droplet and the air / ; During the combustion phase, the evaporation of liquid sodium causes a decrease in the mass of the liquid pool. The evaporation rate during combustion is: (7) In the formula, Mean pressure / Pa; : Evaporation rate of liquid sodium within a single time step / ; Mass transfer coefficient between liquid sodium and air / ; Molar mass of liquid sodium / ; Universal gas constant / ; : Temperature of the gas near the surface of liquid sodium / °C; : Volume fraction of sodium vapor near the surface of liquid sodium; : Volume fraction of liquid sodium; by solving for the sum of the evaporation of liquid sodium in the pre-combustion stage and the combustion stage at different times, the mass change rate of liquid sodium at different times is obtained; Combustion of liquid sodium occurs at specific oxygen concentrations and liquid sodium temperatures. An extinction model incorporating both oxygen concentration and liquid sodium temperature is established based on the critical flame temperature. If either condition fails, no chemical reaction occurs. If the liquid sodium temperature is lower than the ignition temperature of sodium, combustion is inhibited. The extinction model incorporating oxygen concentration and liquid sodium temperature is as follows: (8) In the formula, Mass fraction of liquid sodium; : Mass fraction of air; Mass fraction of combustion products; Critical temperature of liquid sodium / °C; Enthalpy of liquid sodium at temperature T / ; Enthalpy change of liquid sodium / ; Enthalpy of air at temperature T / ; Enthalpy of combustion products at temperature T / ; Liquid sodium in enthalpy value at time / ; Air in enthalpy value at time / ; Combustion products in enthalpy value at time / ; For a liquid sodium pool with a length-to-width ratio greater than 10, it is considered as one-dimensional heat conduction, and its one-dimensional transient heat conduction equation is: (9) In the formula, Thermal diffusivity of liquid sodium / ; Time / s; : Distance between the inside of the sodium pool and the upper surface of the sodium pool / m; Temperature of liquid sodium in the vertical direction / °C; The temperature of liquid sodium can be calculated using the one-dimensional transient heat conduction equation; For the temperature of the air, the ideal gas law shown in equation (10) is used to solve the problem: (10) In the formula, Air pressure / Pa; The total density of sodium vapor, oxygen, and nitrogen obtained from step 3 / ; Universal gas constant / ; Air temperature / K; air molar mass / ; Calculate air temperature using the ideal gas law. ; Step 5: Solve for the velocity divergence: After determining the density, mass fraction, and temperature of each component, the velocity divergence at the nth time step can be calculated. : (11) In the formula, Heat release rate per unit volume of liquid sodium combustion / ; Energy of liquid sodium droplets / ; : Conduction, diffusion and radiation heat flux of liquid sodium and air / ; Background pressure (Pa); Enthalpy / ; Step 6: Calculate air velocity: Based on the velocity divergence obtained in step 5, solve the pressure Poisson equation: (12) In the formula, Stagnation energy per unit mass / ; F: Stress term; n and n +1 respectively represent the first n and the n +1 time step; Therefore, the velocity at the (n+1)th time step is calculated based on the velocity at the nth time step in step 5: (13) In the formula, and They represent the first n and the n +1 time step air speed / ; : No. n Stress terms at each time step; : No. n The stagnation energy gradient per unit mass at each time step; Step 7: Add the time step to the calculated time to get the current time, return to step 3 to continue the calculation until the current time equals the total combustion time set in step 2, then end the calculation; output curves or contour maps of the temperature and mass change rate of liquid sodium, ambient temperature of the calculation domain, oxygen concentration, air velocity and pressure.

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