Method for calculating surface temperatures of different batches of fuel spheres of pebble-bed high-temperature gas cooled reactor

Abstract

The invention discloses a method for calculating the surface temperature of different batches of fuel spheres of a pebble-bed high-temperature gas cooled reactor, which comprises the following steps of: performing grid division on the pebble-bed high-temperature gas cooled reactor, and calculating the helium temperature, the heat exchange coefficient and the grid power of the pebble-bed high-temperature gas cooled reactor; establishing the relationship between the average temperature of the grid and the surface temperature of the fuel balls by using a volume averaging method, calculating the power of the different batches of fuel balls in the grid according to the power ratio of the different batches of fuel balls in the grid, and obtaining the steady-state energy conservation equation of the different batches of fuel balls according to the steady-state energy conservation equation of the grid; compared with a widely used method for calculating the surface temperature of the fuel balls by solving the one-dimensional heat conduction equations of the fuel balls of different batches, the method for calculating the surface temperature of the fuel balls of different batches has the advantages that the calculation efficiency is higher; and meanwhile, certain calculation accuracy is guaranteed, and the requirement of engineering calculation can be met.

Description

Technical Field

[0001] The present invention relates to the field of thermal calculation technology for a pebble bed high temperature gas-cooled reactor, and in particular to a method for calculating the surface temperatures of fuel spheres of different batches in a pebble bed high temperature gas-cooled reactor. Background Art

[0002] Calculating the temperature distribution inside the core and fuel spheres of a pebble-bed high-temperature gas-cooled reactor is one of the key tasks in the thermal design and safety analysis of this type of reactor core. The fuel elements in a pebble-bed high-temperature gas-cooled reactor are irregularly stacked inside the core, and the position of the fuel elements changes during online refueling. The coolant flows through the gaps, flow channels, and flow conditions of the fuel elements in the core, which are very irregular. In order to accurately simulate the thermal hydraulics of the pebble-bed high-temperature gas-cooled reactor core, the pebble bed needs to be treated as a porous medium to study the flow and heat transfer of the coolant therein. Therefore, the thermal hydraulic calculation of the core requires the establishment and solution of the multi-dimensional porous medium field equations for the entire core. Under the porous medium model, the temperature distribution of the fuel spheres themselves requires a special model for additional solution.

[0003] When solving the temperature distribution of the fuel spheres themselves, the fuel spheres are divided into different batches within the computational grid according to their type and burnup depth; only the temperature distribution of the fuel spheres within each batch is calculated. The difficulty in solving the temperature distribution of different batches of fuel spheres lies in determining the outer boundary conditions of the fuel spheres. During the iterative process of the pebble bed temperature calculation, performing one-dimensional spherical coordinate heat conduction calculations on different batches of fuel spheres in different computational grids to determine the outer boundary conditions and temperature distribution of the fuel spheres is very time-consuming. How to quickly and accurately determine the surface temperature of different batches of fuel spheres to reduce the calculation time of the pebble bed temperature is a problem that needs to be solved. Summary of the Invention

[0004] In order to solve the problems existing in the above-mentioned prior art, the purpose of the present invention is to provide a method for accurately and efficiently calculating the surface temperature of fuel balls of different batches of pebble bed high-temperature gas-cooled reactors. Compared with the widely used method of calculating the surface temperature of fuel balls by solving the one-dimensional heat conduction equation of different batches of fuel balls, the method has higher calculation efficiency and also ensures a certain degree of calculation accuracy, which can meet the needs of engineering calculations.

[0005] In order to achieve the above object, the present invention adopts the following technical solutions:

[0006] A method for calculating the surface temperature of fuel spheres of different batches in a pebble-bed high-temperature gas-cooled reactor comprises:

[0007] Gridding the pebble-bed high-temperature gas-cooled reactor, establishing the pebble-bed high-temperature gas-cooled reactor grid control volume, and calculating the pebble-bed high-temperature gas-cooled reactor helium temperature, heat transfer coefficient, and grid power.

[0008] The volume averaging method is used to establish the relationship between the average temperature of the grid and the surface temperature of different batches of fuel balls in the grid;

[0009] The power of different batches of fuel balls in the grid is calculated based on the power proportion of different batches of fuel balls in the grid;

[0010] According to the grid steady-state energy conservation equation, the steady-state energy conservation equation of different batches of fuel balls in the grid is obtained;

[0011] The surface temperature of each batch of fuel balls in the grid is calculated based on the steady-state energy conservation equation of different batches of fuel balls in the grid.

[0012] Preferably, a pebble bed high temperature gas-cooled reactor grid control body is established according to a pebble bed high temperature gas-cooled reactor fluid temperature calculation program and a pebble bed high temperature gas-cooled reactor neutron physics calculation program, and the pebble bed high temperature gas-cooled reactor helium temperature, heat transfer coefficient, and grid power are obtained by calculation;

[0013] The relationship between the average temperature of the grid and the surface temperature of fuel balls of different batches is established based on the volume average on the control volume. The expression is:

[0014]

[0015] Where r is the radial coordinate of the grid center, z is the axial coordinate of the grid center, T(r,z) is the average temperature of the grid, k is the batch number of the fuel ball in the grid, num is the number of batches of fuel balls in the grid, F V,k (r, z) is the volume ratio of the kth batch of fuel balls in the grid, T surf,k (r,z) is the surface temperature of the kth batch of fuel balls in the grid.

[0016] Preferably, the power of different batches of fuel balls in the grid is calculated based on the power proportion of different batches of fuel balls in the grid, and the expression is:

[0017] P k (r,z)=F P,k (r,z)×P(r,z)

[0018] Where k is the batch number of the fuel ball in the grid, r is the radial coordinate of the grid center, z is the axial coordinate of the grid center, P k (r, z) is the power of the kth batch of fuel balls in the grid, F P,k (r,z) is the power proportion of the kth batch of fuel balls in the grid, and P(r,z) is the power of the grid.

[0019] Preferably, the grid steady-state energy conservation equation on the two-dimensional cylindrical geometry is expressed as:

[0020]

[0021] Where r is the radial coordinate of the grid center, z is the axial coordinate of the grid center, and λ e represents the thermal conductivity of the grid, T(r,z) is the average temperature of the grid, α(r,z) represents the convective heat transfer coefficient of the grid, T fluid (r, z) represents the temperature of the fluid flowing through the grid, and q(r, z) is the power density within the grid;

[0022] The power generated within a grid is derived from heat conduction between the grid and surrounding grids and from convection heat transfer with the fluid flowing through the grid. The power derived from heat conduction between the grid and surrounding grids is expressed as:

[0023]

[0024] Among them, Q cond is the power derived from the heat conduction between the grid and the surrounding grids, r is the radial coordinate of the grid center, z is the axial coordinate of the grid center, Δz is the length of the grid in the axial direction, and Δr is the length of the grid in the radial direction;

[0025] The power derived from the fluid flowing through the grid through convective heat transfer is expressed as:

[0026] Q conv =α(r,z)×V(r,z)×(T(r,z)-T fluid (r,z))

[0027] Among them, Q conv is the power derived from the fluid flowing through the grid by convection heat transfer, and V(r,z) is the volume of the grid;

[0028] From the above grid steady-state energy conservation equation, we can see that in steady-state conditions, the power generated in the grid is equal to the sum of the heat removed by the grid through heat conduction and convection. Therefore, the following expression is obtained:

[0029] P(r,z)=q(r,z)×V(r,z)

[0030] =Q cond +Q conv

[0031] Where P(r,z) is the power of the grid;

[0032] Substituting the relationship between the average temperature of the grid and the surface temperature of different batches of fuel balls in the grid into the equation for the power derived from the heat conduction between the grid and the surrounding grids, the expression is:

[0033]

[0034] Among them, i is the number of the surrounding grid of the grid at the (r, z) position, a i is the coefficient related to the heat conduction calculation of the corresponding surrounding grid, k is the batch number of the fuel ball in the grid, num is the batch number of the fuel ball in the grid, F V,k (r, z) is the volume ratio of the kth batch of fuel balls in the grid, T surf,k (r, z) is the surface temperature of the kth batch of fuel balls in the grid, T i (r,z) is the average temperature of the corresponding surrounding grid;

[0035] a i The expression is:

[0036]

[0037] Substituting the relationship between the average temperature of the grid and the surface temperature of different batches of fuel balls into the equation for the power derived from the convective heat transfer between the grid and the fluid flowing through the grid, the expression is:

[0038]

[0039] Combining the relationship between the power of different batches of fuel balls in a grid and the total power of the grid, as well as the relationship between the power of a grid and the heat removed by the grid through heat conduction and convection, the following expression is obtained:

[0040]

[0041] Therefore, the steady-state energy conservation equation of different batches of fuel balls in the grid can be obtained, which is expressed as:

[0042]

[0043] Preferably, the surface temperature of each batch of fuel balls in the grid is calculated based on the steady-state energy conservation equation of different batches of fuel balls in the grid, as follows:

[0044] The steady-state energy conservation equation of different batches of fuel balls in the grid is simplified to:

[0045] AT surf,k (r,z)-B=C

[0046] Among them, the expression of A is:

[0047]

[0048] The expression of B is:

[0049]

[0050] The expression of C is:

[0051] C=F P,k (r,z)×P(r,z)

[0052] Where r is the radial coordinate of the grid center, z is the axial coordinate of the grid center, k is the batch number of the fuel ball in the grid, T surf,k (r,z) is the surface temperature of the kth batch of fuel balls in the grid, a i is the coefficient related to the heat conduction calculation of the corresponding surrounding grid, F V,k (r, z) is the volume ratio of the kth batch of fuel balls in the grid, α(r, z) represents the convective heat transfer coefficient of the grid, V(r, z) is the volume of the grid, num is the number of batches of fuel balls in the grid, T fluid (r,z) represents the temperature of the fluid flowing through the grid, F P,k (r, z) is the power proportion of the kth batch of fuel balls in the grid, and P(r, z) is the power of the grid;

[0053] Therefore, the calculation relationship of the surface temperature of the kth batch of fuel balls in the grid is:

[0054]

[0055] Compared with the prior art, the present invention has the following advantages:

[0056] 1. Significantly improved computational efficiency: The fuel sphere surface temperature is directly solved from the steady-state energy conservation equation, avoiding the complex computational process of solving the fuel sphere's one-dimensional heat conduction equation in traditional methods, significantly reducing the number of calculation steps and the required computing resources.

[0057] 2. The algorithm is simple and efficient: Based on the grid energy conservation equation and the relationship between the volume and power proportions of each batch of fuel spheres, there is no need to construct and solve the partial differential equations for the internal temperature distribution of the fuel spheres and their boundary conditions. The algorithm logic is more direct and the implementation is simpler.

[0058] 3. The amount of calculation is greatly reduced: the traditional method eliminates the need to perform the spatial discretization and solution process of the temperature field inside the entire fuel ball in order to obtain the surface temperature. Under the same accuracy requirements, the overall amount of calculation is significantly reduced. BRIEF DESCRIPTION OF THE DRAWINGS

[0059] Figure 1 Schematic diagram of heat exchange when different batches of fuel balls exist in the grid.

[0060] Figure 2 Calculate the surface temperature of different fuel batches for a pebble-bed high-temperature gas-cooled reactor according to the present invention. Flowchart of the calculation method. DETAILED DESCRIPTION

[0061] The present invention will be further described in detail below with reference to the accompanying drawings and specific embodiments:

[0062] The invention divides a grid for establishing a pebble bed high temperature gas-cooled reactor, calculates the helium temperature, heat transfer coefficient and power of the grid of the pebble bed high temperature gas-cooled reactor, uses a volume averaging method to establish a relationship between the average temperature of the grid and the surface temperature of the fuel balls, calculates the power of different batches of fuel balls in the grid based on the power proportion of different batches of fuel balls in the grid, obtains the steady-state energy conservation equation of different batches of fuel balls based on the steady-state energy conservation equation of the grid, and calculates the surface temperature of each batch of fuel balls based on the energy conservation equation of different batches of fuel balls.

[0063] The following describes the calculation process of an accurate and efficient method for calculating the surface temperature of different batches of fuel balls in a core grid of a pebble bed high-temperature gas-cooled reactor, taking the calculation of the surface temperature of different batches of fuel balls in a pebble bed high-temperature gas-cooled reactor as an example. Figure 2 As shown, the specific steps include:

[0064] Step 1: Grid the pebble bed high temperature gas-cooled reactor according to the fluid temperature calculation program and the neutron physics calculation program, establish the pebble bed high temperature gas-cooled reactor grid control body, and obtain the pebble bed high temperature gas-cooled reactor helium temperature, heat transfer coefficient and grid power distribution through calculation.

[0065] Step 2: Based on the volume average, the relationship between the average temperature of the grid and the surface temperature of different batches of fuel balls in the grid is established on the control volume. The expression is:

[0066]

[0067] Where r is the radial coordinate of the grid center, z is the axial coordinate of the grid center, T(r,z) is the average temperature of the grid, k is the batch number of the fuel ball in the grid, num is the number of batches of fuel balls in the grid, F V,k (r, z) is the volume ratio of the kth batch of fuel balls in the grid, T surf,k (r,z) is the surface temperature of the kth batch of fuel balls in the grid.

[0068] Step 3: Calculate the power of different batches of fuel balls in the grid based on the power proportion of different batches of fuel balls in the grid. The expression is:

[0069] P k (r,z)=F P,k (r,z)×P(r,z)

[0070] Where k is the batch number of the fuel ball in the grid, r is the radial coordinate of the grid center, z is the axial coordinate of the grid center, P k (r, z) is the power of the kth batch of fuel balls in the grid, F P,k (r,z) is the power proportion of the kth batch of fuel balls in the grid, and P(r,z) is the power of the grid.

[0071] Step 4: The grid steady-state energy conservation equation on the two-dimensional cylindrical geometry is expressed as:

[0072]

[0073] Where r is the radial coordinate of the grid center, z is the axial coordinate of the grid center, and λ e represents the thermal conductivity of the grid, T(r,z) is the average temperature of the grid, α(r,z) represents the convective heat transfer coefficient of the grid, T fluid (r, z) represents the temperature of the fluid flowing through the grid, and q(r, z) is the power density within the grid.

[0074] The power generated in the grid is derived from heat conduction with the grids around it and convection heat transfer with the fluid flowing through the grid. The power derived from heat conduction between the grid and the surrounding grids is expressed as:

[0075]

[0076] Among them, Q cond is the power derived from the heat conduction between the grid and the surrounding grids, r is the radial coordinate of the grid center, z is the axial coordinate of the grid center, Δz is the axial length of the grid, and Δr is the radial length of the grid.

[0077] The power derived from the fluid flowing through the grid through convective heat transfer is expressed as:

[0078] Q conv =α(r,z)×V(r,z)×(T(r,z)-T fluid (r,z))

[0079] Among them, Q conv is the power derived from the fluid flowing through the grid by convection heat transfer, and V(r,z) is the volume of the grid.

[0080] From the above grid steady-state energy conservation equation, we can see that in steady-state conditions, the power generated within the grid is equal to the sum of the heat removed by the grid through heat conduction and convection. Therefore, the following expression can be obtained:

[0081] P(r,z)=q(r,z)×V(r,z)

[0082] =Q cond +Q conv

[0083] Where P(r,z) is the power of the grid.

[0084] Substituting the relationship between the average temperature of the grid and the surface temperature of different batches of fuel balls in the grid into the equation for the power derived from the heat conduction between the grid and the surrounding grids, the expression is:

[0085]

[0086] Among them, i is the number of the surrounding grid of the grid at the (r, z) position, a i is the coefficient related to the heat conduction calculation of the corresponding surrounding grid, k is the batch number of the fuel ball in the grid, num is the batch number of the fuel ball in the grid, F V,k (r, z) is the volume ratio of the kth batch of fuel balls in the grid, T surf,k (r, z) is the surface temperature of the kth batch of fuel balls in the grid, T i (r,z) is the average temperature of the corresponding surrounding grid.

[0087] a i The expression is:

[0088]

[0089] Substituting the relationship between the average temperature of the grid and the surface temperature of different batches of fuel balls into the equation for the power derived from the convective heat transfer between the grid and the fluid flowing through the grid, the expression is:

[0090]

[0091] Combining the relationship between the power of different batches of fuel balls in a grid and the total power of the grid, as well as the relationship between the power of a grid and the heat removed by the grid through heat conduction and convection, the following expression can be obtained:

[0092]

[0093] Therefore, the steady-state energy conservation equation of different batches of fuel balls in the grid can be obtained, which is expressed as:

[0094]

[0095] Step 5: Calculate the surface temperature of each batch of fuel balls in the grid based on the steady-state energy conservation equation of different batches of fuel balls in the grid.

[0096] The steady-state energy conservation equation of different batches of fuel balls in the grid is simplified to:

[0097] AT surf,k (r,z)-B=C

[0098] Among them, the expression of A is:

[0099]

[0100] The expression of B is:

[0101]

[0102] The expression of C is:

[0103] C=F P,k (r,z)×P(r,z)

[0104] Where r is the radial coordinate of the grid center, z is the axial coordinate of the grid center, k is the batch number of the fuel ball in the grid, T surf,k (r,z) is the surface temperature of the kth batch of fuel balls in the grid, a i is the coefficient related to the heat conduction calculation of the corresponding surrounding grid, F V,k (r, z) is the volume ratio of the kth batch of fuel balls in the grid, α(r, z) represents the convective heat transfer coefficient of the grid, V(r, z) is the volume of the grid, num is the number of batches of fuel balls in the grid, T fluid (r,z) represents the temperature of the fluid flowing through the grid, F P,k (r, z) is the power proportion of the kth batch of fuel balls in the grid, and P(r, z) is the power of the grid;

[0105] Therefore, the calculation relationship of the surface temperature of the kth batch of fuel balls in the grid is:

[0106]

[0107] In order to verify the feasibility of the method of the present invention, the Figure 1 The method was validated by calculating the surface temperature of different batches of fuel spheres within a specific grid in the core of the HTR-PM high-temperature gas-cooled reactor demonstration project. The fluid temperature, convective heat transfer coefficient, grid power, and other parameters for this grid were calculated using the pebble-bed high-temperature gas-cooled reactor fluid temperature calculation program and the neutron physics calculation program, as shown in Table 1. This grid contains 15 batches of fuel spheres, each with a volume fraction and power fraction of 0.067. Therefore, the surface temperature of each batch of fuel spheres calculated using the above method is 268.80°C.

[0108] Table 1 Calculation parameters

[0109]

[0110] The innovation of the method of the present invention lies in: starting from the energy conservation equation of the grid and the relationship between the average temperature of the grid and the surface temperature of different batches of fuel balls, the energy conservation equation of different batches of fuel balls is established, so that the surface temperature of the fuel balls is directly obtained without solving the heat conduction equation of one-dimensional spherical coordinate geometry. It can avoid repeated heat conduction calculations under one-dimensional spherical coordinate geometry for different batches of fuel balls in different grids when solving the temperature distribution of the core grid ball bed, thereby improving the calculation efficiency while meeting the calculation accuracy.

Claims

1. A method for calculating the surface temperature of different batches of fuel spheres in a pebble bed high temperature gas-cooled reactor, characterized in that: include: Gridding the pebble-bed high-temperature gas-cooled reactor, establishing the pebble-bed high-temperature gas-cooled reactor grid control volume, and calculating the pebble-bed high-temperature gas-cooled reactor helium temperature, heat transfer coefficient, and grid power. The volume averaging method is used to establish the relationship between the average temperature of the grid and the surface temperature of different batches of fuel balls in the grid; The power of different batches of fuel balls in the grid is calculated based on the power proportion of different batches of fuel balls in the grid; According to the grid steady-state energy conservation equation, the steady-state energy conservation equation of different batches of fuel balls in the grid is obtained; The surface temperature of each batch of fuel balls in the grid is calculated based on the steady-state energy conservation equation of different batches of fuel balls in the grid.

2. The method for calculating the surface temperature of different batches of fuel spheres for a pebble bed high temperature gas-cooled reactor according to claim 1, characterized in that: The pebble bed high temperature gas cooled reactor grid control volume was established based on the pebble bed high temperature gas cooled reactor fluid temperature calculation program and the pebble bed high temperature gas cooled reactor neutron physics calculation program, and the pebble bed high temperature gas cooled reactor helium temperature, heat transfer coefficient and grid power were obtained through calculation. The relationship between the average temperature of the grid and the surface temperature of fuel balls of different batches is established based on the volume average on the control volume. The expression is: Where r is the radial coordinate of the grid center, z is the axial coordinate of the grid center, T(r,z) is the average temperature of the grid, k is the batch number of the fuel ball in the grid, num is the number of batches of fuel balls in the grid, F V,k (r, z) is the volume ratio of the kth batch of fuel balls in the grid, T surf,k (r,z) is the surface temperature of the kth batch of fuel balls in the grid.

3. The method for calculating the surface temperature of different batches of fuel spheres for a pebble bed high temperature gas-cooled reactor according to claim 1, characterized in that: The power of different batches of fuel balls in the grid is calculated based on the power proportion of different batches of fuel balls in the grid, and the expression is: P k (r,z)=F P,k (r,z)×P(r,z) Where k is the batch number of the fuel ball in the grid, r is the radial coordinate of the grid center, z is the axial coordinate of the grid center, P k (r, z) is the power of the kth batch of fuel balls in the grid, F P,k (r,z) is the power proportion of the kth batch of fuel balls in the grid, and P(r,z) is the power of the grid.

4. The method for calculating the surface temperature of different batches of fuel spheres for a pebble bed high temperature gas-cooled reactor according to claim 1, characterized in that: The grid steady-state energy conservation equation on the two-dimensional cylindrical geometry is expressed as: Where r is the radial coordinate of the grid center, z is the axial coordinate of the grid center, and λ e represents the thermal conductivity of the grid, T(r,z) is the average temperature of the grid, α(r,z) represents the convective heat transfer coefficient of the grid, T fluid (r, z) represents the temperature of the fluid flowing through the grid, and q(r, z) is the power density within the grid; The power generated within a grid is derived from heat conduction between the grid and surrounding grids and from convection heat transfer with the fluid flowing through the grid. The power derived from heat conduction between the grid and surrounding grids is expressed as: Among them, Q cond is the power derived from the heat conduction between the grid and the surrounding grids, r is the radial coordinate of the grid center, z is the axial coordinate of the grid center, Δz is the length of the grid in the axial direction, and Δr is the length of the grid in the radial direction; The power derived from the fluid flowing through the grid through convective heat transfer is expressed as: Q conv =α(r,z)×V(r,z)×(T(r,z)-T fluid (r,z)) Among them, Q conv is the power derived from the fluid flowing through the grid by convection heat transfer, and V(r,z) is the volume of the grid; From the above grid steady-state energy conservation equation, we can see that in steady-state conditions, the power generated in the grid is equal to the sum of the heat removed by the grid through heat conduction and convection. Therefore, the following expression is obtained: P(r,z)=q(r,z)×V(r,z) =Q cond +Q conv Where P(r,z) is the power of the grid; Substituting the relationship between the average temperature of the grid and the surface temperature of different batches of fuel balls in the grid into the equation for the power derived from the heat conduction between the grid and the surrounding grids, the expression is: Among them, i is the number of the surrounding grid of the grid at the (r, z) position, a i is the coefficient related to the heat conduction calculation of the corresponding surrounding grid, k is the batch number of the fuel ball in the grid, num is the batch number of the fuel ball in the grid, F V,k (r, z) is the volume ratio of the kth batch of fuel balls in the grid, T surf,k (r, z) is the surface temperature of the kth batch of fuel balls in the grid, T i (r,z) is the average temperature of the corresponding surrounding grid; a i The expression is: Substituting the relationship between the average temperature of the grid and the surface temperature of different batches of fuel balls into the equation for the power derived from the convective heat transfer between the grid and the fluid flowing through the grid, the expression is: Combining the relationship between the power of different batches of fuel balls in a grid and the total power of the grid, as well as the relationship between the power of a grid and the heat removed by the grid through heat conduction and convection, the following expression is obtained: Therefore, the steady-state energy conservation equation of different batches of fuel balls in the grid can be obtained, which is expressed as:

5. The method for calculating the surface temperature of different batches of fuel spheres for a pebble bed high temperature gas-cooled reactor according to claim 1, characterized in that: The surface temperature of each batch of fuel balls in the grid is calculated based on the steady-state energy conservation equation of different batches of fuel balls in the grid, as follows: The steady-state energy conservation equation of different batches of fuel balls in the grid is simplified to: AT surf,k (r,z)-B=C Among them, the expression of A is: The expression of B is: The expression of C is: C=F P,k (r,z)×P(r,z) Where r is the radial coordinate of the grid center, z is the axial coordinate of the grid center, k is the batch number of the fuel ball in the grid, T surf,k (r,z) is the surface temperature of the kth batch of fuel balls in the grid, a i is the coefficient related to the heat conduction calculation of the corresponding surrounding grid, F V,k (r, z) is the volume ratio of the kth batch of fuel balls in the grid, α(r, z) represents the convective heat transfer coefficient of the grid, V(r, z) is the volume of the grid, num is the number of batches of fuel balls in the grid, T fluid (r,z) represents the temperature of the fluid flowing through the grid, F P,k (r, z) is the power proportion of the kth batch of fuel balls in the grid, and P(r, z) is the power of the grid; Therefore, the calculation relationship of the surface temperature of the kth batch of fuel balls in the grid is:

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