A virtual grid-based solution reactor core thermal-hydraulic calculation method

Abstract

The application discloses a kind of based on virtual grid's solution stack core thermal-hydraulic calculation method, including the following steps, to reduce the number of calculation grid by adopting the mode of virtual grid to helical coil, accurate, fast calculation solution of solution stack core thermal-hydraulic is realized.Specific steps are as follows:1, core three-dimensional grid division;2, identify helical coil virtual grid and record grid index;3, fluid, tube wall physical field initialization;4, calculate fission gas mass source term and fission energy source term;5, three-dimensional field calculation fluid dynamics solution;6, respectively construct and solve tube wall and in-pipe fluid temperature calculation matrix, and iteratively calculate helical coil temperature;7, coupling solution energy equation;8, if meeting convergence requirement, then time step is advanced, until end time.

Description

Technical Field

[0001] This invention relates to the field of nuclear reactor thermal-hydraulic technology, specifically to a method for calculating the thermal-hydraulic properties of a solution reactor core based on a virtual grid. Background Technology

[0002] Production reactors are one of the important sources of medical isotopes. Solution reactors, as a means of producing medical isotopes, refer to reactors that use aqueous solutions of fissile salts as fuel. Compared with the traditional method of producing medical isotopes by irradiating targets in solid-fuel reactors, solution reactors have advantages such as greater flexibility in core design, inherent safety, high neutron utilization, no target operation, less waste generation, effective acquisition of multiple medical isotopes, lower construction costs, and lower operating costs.

[0003] The complex geometry of a solution-fueled reactor core necessitates the arrangement of multiple sets of helical cooling coils within a relatively small core to dissipate heat generated by nuclear fission and to increase the heat transfer area for enhanced heat transfer capacity. This geometric complexity significantly increases the computational burden of core thermal-hydraulic calculations. For instance, in the detailed modeling and solution of computational fluid dynamics for solution-fueled reactor cores, meticulous modeling of the helical coils results in a massive mesh size, severely impacting computational speed. Therefore, a computational method is urgently needed for the thermal-hydraulic calculation of solution-fueled reactor cores that can satisfy computational speed requirements while enabling coupled solution of the helical coils and core thermal-hydraulic processes. 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 solution reactor core thermal-hydraulic calculation method based on virtual grid. This method uses virtual grid for the spiral coil to effectively reduce the number of grids, and can couple the solution of the spiral coil with the core thermal-hydraulic, while ensuring the accuracy and speed of the calculation.

[0005] To achieve the above objectives, the present invention adopts the following technical solution:

[0006] A method for calculating the thermal-hydraulic properties of a solution reactor core based on a virtual grid includes the following steps:

[0007] Step 1, 3D mesh generation of the solution reactor core: Perform geometric modeling of the solution reactor core to be determined, ignoring the existence of the spiral coil, and mesh the core with hexahedrons;

[0008] Step 2, Identify the virtual grid of the spiral coil: Based on the grid divided in Step 1, identify the grid of the spiral coil position according to the spiral coil position coordinates and grid size, and record the grid index according to the fluid flow direction inside the spiral coil.

[0009] Step 3, Initialization of fluid and pipe wall physical fields: Initialize the temperature field, velocity field and pressure of the fluid inside the core and spiral coil, as well as the temperature field of the pipe wall, to serve as initial values ​​for the three-dimensional thermal hydraulic solution;

[0010] Step 4: Calculate the fission gas mass source term and fission energy source term. Calculate the fission gas mass source term and fission energy source term corresponding to each fluid grid based on the spatial distribution of fission gas and the fission energy distribution.

[0011] Step 5, Three-dimensional field computational fluid dynamics solution: The three-dimensional field of the reactor core is solved using computational fluid dynamics methods, including turbulence model calculation, pressure-velocity coupled solution, and energy equation correction;

[0012] Step 6, Iterative calculation of spiral coil temperature:

[0013] Sub-step 1: Construct the pipe wall temperature solution matrix

[0014] Assuming the dimensions of the spiral coil do not change over time, its geometry is axisymmetric, the wall temperature and flow conditions on the outer surface are also axisymmetric, and the axial temperature gradient is negligible compared to the radial temperature gradient, and the thermophysical properties of density, heat capacity, and thermal conductivity are constant and uniform over time; therefore, a simplified equation for the wall temperature is obtained.

[0015]

[0016] In the formula: ρ w —Pipe wall density / kg·m -3 ;c pw Specific heat of pipe wall / J·kg -1 ·K -1 ;T w —Pipe wall temperature / K; κ w —Pipe wall thermal conductivity / W·m -1 ·K -1 t — time / s;

[0017] The finite volume method was used to discretize equation (1). The time term was discretized using the back Euler method, and the diffusion term was discretized using the central difference scheme, resulting in the following discretized equation of the pipe wall.

[0018]

[0019] In the formula: r i —Coordinates of the i-th pipe wall grid / m; and — Coordinates of the front and rear boundaries of the i-th pipe wall grid (in meters); and — These represent the tube wall grid temperatures (in K) at the (i-1), i, and i+1th time steps, respectively. —Temperature of the i-th pipe wall grid at the previous time step / K; Δr —Radial grid length / m; Δt —Time step / s;

[0020] The pipe wall is divided into N virtual grids in the radial direction. Each group of pipe wall virtual grids corresponds to the spiral coil virtual grid identified in step two. An N×N tridiagonal matrix is ​​constructed according to equation (2), which is the pipe wall temperature solution matrix.

[0021] Sub-step 2: Solve for the tube wall temperature

[0022] The pipe wall temperature matrix constructed in sub-step 1 is solved using the Gaussian elimination method to obtain the pipe wall temperature distribution;

[0023] Sub-step 3: Construct the solution matrix for the fluid temperature inside the pipe.

[0024] Assuming the fluid inside the spiral coil is incompressible, a temperature equation for the fluid inside the spiral coil is established. It is further assumed that the spiral coil geometry is axisymmetric, the flow conditions on the inner surface are also axisymmetric, axial heat conduction is negligible, and the thermophysical properties of density, heat capacity, and thermal conductivity are constant and homogeneous over time. Therefore, a simplified temperature equation for the fluid inside the coil is obtained.

[0025]

[0026] In the formula: ρ f — Fluid density / kg·m -3 ;c pf Specific heat of fluid / J·kg -1 ·K -1 ;T f — Fluid temperature / K; q — Heat exchange between fluid and pipe wall / W·m -2 ·s -1 u—Flow velocity in the pipe / m·s -1 ;

[0027] The finite volume method was used to discretize equation (3). The time term was discretized using the back Euler method, and the convection term was discretized using the central difference scheme, resulting in the following discretized equation.

[0028]

[0029] In the formula: and — These represent the temperatures (in K) of the fluid grid at time steps j+1, j, and j-1, respectively. — Temperature of the j-th fluid grid at the previous time step (K); Δz — Axial grid length (m); h 2,j —Heat transfer coefficient between the j-th fluid grid and the inner wall of the pipe / W·m -2 ·K -1 ;T wall，j—Pipe wall temperature corresponding to the j-th fluid grid / K -1 r—inner diameter of pipe wall / m;

[0030] Assuming that step two identifies M virtual grids of spiral coils, construct an M×M tridiagonal matrix according to the flow direction based on equation (4), which is the solution matrix for the fluid temperature inside the pipe;

[0031] Sub-step 4: Solve for the temperature of the fluid inside the pipe.

[0032] The number of virtual grids is related to the length of the spiral coil and the grid size. In order to improve the calculation speed, the chasing method is used to solve the M×M tridiagonal matrix constructed in sub-step 3.

[0033] After the solution is completed, return to sub-step 1 until the relative temperature deviation of the spiral coil is less than 10. -5 ;

[0034] Step 7, Coupled Solution of Energy Equations: After the spiral coil temperature calculation is completed, the heat transfer of the spiral coil is added as a source term to the three-dimensional energy equation calculation, that is, the last term on the right side of equation (5). The core three-dimensional field is coupled with the spiral coil to solve the energy equation as follows:

[0035]

[0036] Where: ρ — density / kg·m -3 h — Enthalpy / J·kg -1 ; —— Velocity vector / m·s -1 p – Pressure / Pa; κ – Thermal conductivity / W·m -1 ·K -1 S—Source Term / J·m -3 ·s -1 ;

[0037] Step 8: If the convergence requirement is met, i.e., the relative error of the pressure field, velocity field, and enthalpy field is less than 10... -5 If the time step is successful, the time step is advanced; otherwise, the enthalpy is updated, and the process returns to step four to continue iterative calculation at the current time step until the end time is reached.

[0038] Compared with the prior art, the present invention has the following advantages:

[0039] 1. Convenience. The virtual mesh-based thermal-hydraulic calculation method for solution reactor core proposed in this invention has a simple modeling approach. A virtual mesh is used for the calculation of the helical coil, which is automatically identified by simply inputting the helical coil's position coordinates. Therefore, detailed modeling and mesh refinement of the helical coil are unnecessary during mesh generation, effectively reducing the workload of pre-processing. The temperature distribution of the helical coil wall and the fluid inside the coil is a separate virtual mesh temperature field, which can be output separately after calculation. It is not necessary to extract the temperature of each node on the wall and the fluid inside the coil based on their coordinate positions, effectively reducing the workload of post-processing.

[0040] 2. Speed. The solution reactor core thermal-hydraulic calculation method based on virtual mesh proposed in this invention has a fast calculation speed. Since the tube wall and the fluid inside the spiral coil are simulated using a virtual mesh, there is no need to mesh the spiral coil. Moreover, since the diameter of the spiral coil is small, traditional fine modeling and calculation methods require a large number of meshes. Therefore, the virtual mesh method greatly reduces the number of meshes, reduces the amount of calculation, and effectively improves the calculation speed.

[0041] 3. Accuracy. The virtual mesh-based helical coil thermal-hydraulic calculation method proposed in this invention provides detailed processing of heat and mass transfer in the core of a solution reactor. It considers the mass and energy of fission gas and the heat transfer of the helical coil in the core of the solution reactor, and simulates important thermal-hydraulic phenomena in the core of the solution reactor. It has drag models, heat transfer models, turbulence models, etc., and the constitutive model for flow heat transfer calculation is comprehensive, which can realize accurate calculation of thermal-hydraulic phenomena in the core of the solution reactor. Attached Figure Description

[0042] Figure 1 This is a block diagram of a solution reactor core thermal-hydraulic algorithm based on a virtual mesh.

[0043] Figure 2 This is a schematic diagram showing the generation of the real and virtual meshes in the solution reactor core. Detailed Implementation

[0044] The following is combined Figure 1 and Figure 2 This paper provides a detailed explanation of the solution reactor core thermal-hydraulic calculation method based on virtual grid proposed in this invention.

[0045] like Figure 1 As shown, the present invention provides a method for calculating the thermal-hydraulic properties of a solution-cooled reactor core based on a virtual grid, comprising the following steps:

[0046] Step 1: 3D Mesh Generation of the Solution Reactor Core: Geometric modeling of the solution reactor core is performed, ignoring the presence of the spiral coils. The core portion is then meshed using hexahedral meshes (see attached diagram). Figure 2 (as shown);

[0047] Step 2, Identify the virtual mesh of the spiral coil: Based on the mesh divided in Step 1, identify the mesh for the spiral coil position according to the spiral coil position coordinates and mesh size (as shown in the attached image). Figure 2 (as shown), and record the grid index according to the direction of fluid flow inside the spiral coil;

[0048] Step 3, Initialization of fluid and pipe wall physical fields: Initialize the temperature field, velocity field and pressure of the fluid inside the core and spiral coil, as well as the temperature field of the pipe wall, to serve as initial values ​​for the three-dimensional thermal hydraulic solution;

[0049] Step 4: Calculate the fission gas mass source term and fission energy source term. Based on the spatial distribution of fission gas and the distribution of fission energy, calculate the fission gas mass source term and fission energy source term corresponding to each fluid grid, and perform explicit processing on the source terms.

[0050] Step 5, Three-dimensional field computational fluid dynamics solution: The three-dimensional field of the reactor core is solved using computational fluid dynamics methods, including turbulence model calculation, pressure-velocity coupled solution, and energy equation correction;

[0051] Step 6, Iterative calculation of spiral coil temperature:

[0052] Sub-step 1: Construct the pipe wall temperature solution matrix

[0053] Assuming the dimensions of the spiral coil do not change over time, its geometry is axisymmetric, the wall temperature and flow conditions on the outer surface are also axisymmetric, and the axial temperature gradient is negligible compared to the radial temperature gradient, and its thermophysical properties such as density, heat capacity, and thermal conductivity are constant and uniform over time, a simplified equation for the wall temperature is obtained.

[0054]

[0055] In the formula: ρ w —Pipe wall density / kg·m -3 ;c pw Specific heat of pipe wall / J·kg -1 ·K -1 ;T w —Pipe wall temperature / K; κ w —Pipe wall thermal conductivity / W·m -1 ·K -1 t — time / s;

[0056] The finite volume method was used to discretize equation (1). The time term was discretized using the back Euler method, and the diffusion term was discretized using the central difference scheme, resulting in the following discretized equation of the pipe wall.

[0057]

[0058] In the formula r i—Coordinates of the i-th pipe wall grid / m; and — Coordinates of the front and rear boundaries of the i-th pipe wall grid (in meters); and — These represent the tube wall grid temperatures (in K) at the (i-1), i, and i+1th time steps, respectively; T i o —Temperature of the i-th pipe wall grid at the previous time step / K; Δr —Radial grid length / m; Δt —Time step / s;

[0059] The tube wall is divided into N virtual grids in the radial direction, and each group of tube wall virtual grids corresponds to the spiral coil virtual grids identified in step two. The convection heat transfer coefficients inside and outside the tube at each virtual grid position in the core three-dimensional field are obtained, as well as the tube wall temperature field at the previous time step. An N×N tridiagonal matrix is ​​constructed according to equation (2), which is the tube wall temperature solution matrix.

[0060] Sub-step 2: Solving for pipe wall temperature

[0061] The spiral coil has a thinner wall and the number of radial nodes N is usually small, so the matrix solution is not computationally intensive. Therefore, the Gaussian elimination method is used to solve the wall temperature matrix constructed in sub-step 1 to obtain the wall temperature distribution.

[0062] Sub-step 3: Construct the solution matrix for the fluid temperature inside the pipe

[0063] Assuming the fluid inside the spiral coil is incompressible, a temperature equation for the fluid inside the spiral coil is established. The geometry is axisymmetric, and the flow conditions on the inner surface are also axisymmetric. Axial heat conduction is negligible, and thermophysical properties such as density, heat capacity, and thermal conductivity are constant and homogeneous over time. Therefore, a simplified temperature equation for the fluid inside the coil is obtained.

[0064]

[0065] In the formula: ρ f — Fluid density / kg·m -3 ;c pf Specific heat of fluid / J·kg -1 ·K -1 ;T f — Fluid temperature / K; q — Heat exchange between fluid and pipe wall / W·m -2 ·s -1 u—Flow velocity in the pipe / m·s -1 ;

[0066] The finite volume method was used to discretize equation (3). The time term was discretized using the back Euler method, and the convection term was discretized using the central difference scheme, resulting in the following discretized equation.

[0067]

[0068] In the formula — These represent the temperatures (in K) of the fluid grid at time steps j+1, j, and j-1, respectively. — Temperature of the j-th fluid grid at the previous time step (K); Δz — Axial grid length (m); h 2,j —Heat transfer coefficient between the j-th fluid grid and the inner wall of the pipe / W·m -2 ·K -1 ;T wall，j —Pipe wall temperature corresponding to the j-th fluid grid / K -1 r—inner diameter of pipe wall / m;

[0069] Assuming that step two identifies M virtual grids of spiral coils, the convective heat transfer coefficients of each virtual grid position in the core three-dimensional field are obtained, as well as the fluid temperature field of the previous time step. According to the flow direction, an M×M tridiagonal matrix is ​​constructed based on equation (4), which is the solution matrix for the fluid temperature inside the tube.

[0070] Sub-step 4: Solve for the temperature of the fluid inside the pipe

[0071] The number of virtual grids is related to the length of the spiral coil and the grid size. When the number is large, the chasing method is used to solve the M×M tridiagonal matrix constructed in sub-step 3 in order to improve the calculation speed.

[0072] After the solution is completed, return to sub-step 1 until the relative temperature deviation of the spiral coil is less than 10. -5 ;

[0073] Step 7: Solve the energy equation: After the temperature calculation of the spiral coil is completed, the heat exchange of the spiral coil is added as a source term to the calculation of the three-dimensional energy equation, that is, the last term on the right side of equation (5). The three-dimensional field of the reactor core is coupled with the spiral coil to solve the energy equation as follows:

[0074]

[0075] Where: ρ — density / kg·m -3 h — Enthalpy / J·kg -1 ; —— Velocity vector / m·s -1 p – Pressure / Pa; κ – Thermal conductivity / W·m -1 ·K -1 S—Source Term / J·m -3 ·s -1 ;

[0076] Step 7: If the convergence requirement is met, i.e., the relative error of the pressure field, velocity field, and enthalpy field is less than 10... -5If the time step is successful, the time step is advanced; otherwise, the enthalpy is updated, and the process returns to step four to continue iterative calculation at the current time step until the end time is reached.

Claims

1. A method for calculating the thermal-hydraulic properties of a solution-cooled reactor core based on a virtual grid, characterized in that, Includes the following steps: Step 1, 3D mesh generation of the solution reactor core: Perform geometric modeling of the solution reactor core to be determined, ignoring the existence of the spiral coil, and mesh the core with hexahedrons; Step 2, Identify the virtual grid of the spiral coil: Based on the grid divided in Step 1, identify the grid of the spiral coil position according to the spiral coil position coordinates and grid size, and record the grid index according to the fluid flow direction inside the spiral coil. Step 3, Initialization of fluid and pipe wall physical fields: Initialize the temperature field, velocity field and pressure of the fluid inside the core and spiral coil, as well as the temperature field of the pipe wall, to serve as initial values ​​for the three-dimensional thermal hydraulic solution; Step 4: Calculate the fission gas mass source term and fission energy source term. Calculate the fission gas mass source term and fission energy source term corresponding to each fluid grid based on the spatial distribution of fission gas and the fission energy distribution. Step 5, Three-dimensional field computational fluid dynamics solution: The three-dimensional field of the reactor core is solved using computational fluid dynamics methods, including turbulence model calculation, pressure-velocity coupled solution, and energy equation correction; Step 6, Iterative calculation of spiral coil temperature: Sub-step 1: Construct the pipe wall temperature solution matrix Assuming the dimensions of the spiral coil do not change over time, its geometry is axisymmetric, the wall temperature and flow conditions on the outer surface are also axisymmetric, and the axial temperature gradient is negligible compared to the radial temperature gradient, and the thermophysical properties of density, heat capacity, and thermal conductivity are constant and uniform over time; therefore, a simplified equation for the wall temperature is obtained. In the formula: ρ w —Pipe wall density / kg·m -3 c pw Specific heat of pipe wall / J·kg -1 ·K -1 ;T w —Pipe wall temperature / K; κ w —Pipe wall thermal conductivity / W·m -1 ·K -1 t — time / s; The finite volume method was used to discretize equation (1). The time term was discretized using the back Euler method, and the diffusion term was discretized using the central difference scheme, resulting in the following discretized equation of the pipe wall. In the formula: r i —Coordinates of the i-th pipe wall grid / m; and — Coordinates of the front and rear boundaries of the i-th pipe wall grid (in meters); and — These represent the tube wall grid temperatures (in K) at the (i-1), i, and i+1th time steps, respectively. —Temperature of the i-th pipe wall grid at the previous time step / K; Δr —Radial grid length / m; Δt —Time step / s; The pipe wall is divided into N virtual grids in the radial direction. Each group of pipe wall virtual grids corresponds to the spiral coil virtual grid identified in step two. An N×N tridiagonal matrix is ​​constructed according to equation (2), which is the pipe wall temperature solution matrix. Sub-step 2: Solve for the tube wall temperature The pipe wall temperature matrix constructed in sub-step 1 is solved using the Gaussian elimination method to obtain the pipe wall temperature distribution; Sub-step 3: Construct the solution matrix for the fluid temperature inside the pipe. Assuming the fluid inside the spiral coil is incompressible, a temperature equation for the fluid inside the spiral coil is established. It is further assumed that the spiral coil geometry is axisymmetric, the flow conditions on the inner surface are also axisymmetric, axial heat conduction is negligible, and the thermophysical properties of density, heat capacity, and thermal conductivity are constant and homogeneous over time. Therefore, a simplified temperature equation for the fluid inside the coil is obtained. In the formula: ρ f — Fluid density / kg·m -3 c pf Specific heat of fluid / J·kg -1 ·K -1 ;T f — Fluid temperature / K; q — Heat exchange between fluid and pipe wall / W·m -2 ·s -1 u — Flow velocity in the pipe / m·s -1 ; The finite volume method was used to discretize equation (3). The time term was discretized using the back Euler method, and the convection term was discretized using the central difference scheme, resulting in the following discretized equation. In the formula: and — These represent the temperatures (in K) of the fluid grid at time steps j+1, j, and j-1, respectively. — Temperature of the j-th fluid grid at the previous time step (K); Δz — Axial grid length (m); h 2,j —Heat transfer coefficient between the j-th fluid grid and the inner wall of the pipe / W·m -2 ·K -1 ;T wall，j —Pipe wall temperature corresponding to the j-th fluid grid / K -1 r—inner diameter of pipe wall / m; Assuming that step two identifies M virtual grids of spiral coils, construct an M×M tridiagonal matrix according to the flow direction based on equation (4), which is the solution matrix for the fluid temperature inside the pipe; Sub-step 4: Solve for the temperature of the fluid inside the pipe. The number of virtual grids is related to the length of the spiral coil and the grid size. In order to improve the calculation speed, the chasing method is used to solve the M×M tridiagonal matrix constructed in sub-step 3. After the solution is completed, return to sub-step 1 until the relative temperature deviation of the spiral coil is less than 10. -5 ; Step 7, Coupled Solution of Energy Equations: After the temperature calculation of the spiral coil is completed, the heat transfer of the spiral coil is added as a source term to the calculation of the three-dimensional energy equation, that is, the last term on the right side of equation (5). The three-dimensional field of the reactor core is coupled with the spiral coil to solve the energy equation as follows: Where: ρ — density / kg·m -3 h — Enthalpy / J·kg -1 ; —— Velocity vector / m·s -1 p – Pressure / Pa; κ – Thermal conductivity / W·m -1 ·K -1 S—Source Term / J·m -3 ·s -1 ; Step 8: If the convergence requirement is met, advance the time step; otherwise, update the specific enthalpy and return to Step 4 to continue iterative calculation at the current time step until the end time is reached.

2. The method for calculating the thermal-hydraulic properties of a solution reactor core based on a virtual grid, as described in claim 1, is characterized in that... The convergence requirement in step eight is that the relative errors of the pressure field, velocity field, and enthalpy field are less than 10. -5 .

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