Diffuse type fuel rapid and fine burnup calculation method based on reaction rate equivalence

Abstract

The invention belongs to the technical field of nuclear reactor physics, and particularly relates to a fast and fine burnup calculation method for dispersive fuel based on reaction rate equivalence. Comprising the following steps: step 1, merging multi-group parameters; step 2, equivalently homogenizing the region; step 3, calculating burnup; and step 4, restarting calculation. The dispersion type fuel burn-up calculation method based on the reaction rate equivalence has the advantages that the efficiency of dispersion type fuel burn-up calculation is remarkably improved, meanwhile, high calculation precision is kept, and burn-up information of all layers in fuel particles is kept. The method provides an efficient and accurate calculation tool for design and safety analysis of the dispersion type fuel assembly.

Description

Technical Field

[0001] The present invention belongs to the technical field of nuclear reactor physics, and in particular relates to a method for calculating the rapid and precise burnup of dispersed fuel based on reaction rate equivalence. Background Art

[0002] Dispersed fuel, due to its excellent accident resistance, holds broad application prospects in advanced pressurized water reactors, research reactors, and space nuclear reactors. Unlike traditional homogeneous fuel, dispersed fuel consists of dispersed fuel particles (which may contain burnable poison particles) and a matrix material. This heterogeneous structure poses challenges to reactor physics calculations, particularly burnup calculations.

[0003] To accurately simulate the interaction between neutrons and fuel particles in detailed burnup calculations, the fuel particles are typically divided into multiple layers within a fine mesh. This fine spatial discretization significantly increases the number of computational grids and significantly prolongs burnup calculation time. Traditional burnup calculation methods directly perform calculations on each fine mesh, resulting in extremely high computational costs and difficulty meeting engineering design requirements. Summary of the Invention

[0004] To address the problems of long time consumption and high computing resource consumption in the burnup calculation of dispersed fuel, the present invention provides a method for rapid and precise burnup calculation of dispersed fuel based on reaction rate equivalence. While ensuring calculation accuracy, it significantly improves calculation efficiency and retains the burnup information of each layer within the fuel particles.

[0005] The technical solution of the present invention is as follows: a method for calculating the rapid and precise burnup of a dispersion fuel based on reaction rate equivalence, comprising the following steps:

[0006] Step 1: Merge multiple group parameters;

[0007] Step 2: Regional equivalent homogenization;

[0008] Step 3: Fuel consumption calculation;

[0009] Step 4: Restart the calculation.

[0010] In step 1, all energy groups in each burnup zone are combined, the microscopic cross section of each energy group of each nuclide is calculated, and the weighted average is performed using the neutron flux density to obtain the average microscopic cross section of each single group in each burnup zone, including the absorption cross section, effective fission cross section, fission cross section and capture cross section.

[0011] The specific merging process of step 1 is as follows:

[0012]

[0013] Among them, sg is the single energy group after merging; NG is the total number of energy groups; ireg is the current diffuse particle area, φig,ireg is the neutron flux of the ig energy group, φ sg,ireg is the neutron flux after the energy groups in region ireg are merged, σ ig (lnuc) is the microscopic cross section of the nuclide lnuc ig energy group, is the average microscopic cross section of the nuclide lnuc in the region ireg, n ireg (lnuc) is the nucleon density of the nuclide lnuc in the region ireg, σ snf,ireg (lnuc) is the microscopic effective fission cross section of the nuclide lnuc in the region ireg, R snf,ireg The effective fission reaction rate in the region ireg, σ sa,ireg (lnuc) is the microscopic absorption cross section of the nuclide lnuc in the region ireg, σ sf,ireg (lnuc) is the microscopic fission cross section of the nuclide lnuc in the region ireg, R cap,ireg The capture reaction rate within the region ireg.

[0014] The step 2 performs equivalent homogenization treatment on each layer of fuel particles and the matrix material in the dispersed fuel region as follows:

[0015] R grain =∑n grain ·V grain ·σ grain ·φ grain (5)

[0016]

[0017] The microscopic effective cross section of each nuclide in the dispersed particle fuel area is obtained by formula (7):

[0018]

[0019] φ ig,ireg =Volr grain ·φ grain,ig,ireg +Volr matirx ·φ matirx,ig,ireg (8)

[0020] Among them, R grain is the reaction rate within the particle, n grain is the nucleon density within the particle, V grain is the volume of the particle, σ grain is the microscopic cross section of the particle, φ grain is the neutron flux within the particle, is the average nucleon density in the region ireg, is the average microscopic cross section within the region ireg, φ sg,iregis the single energy group neutron flux in the region ireg, Volr grain is the volume fraction of particles, Volr matirx is the volume fraction of the matrix, φ grain,ig,ireg is the neutron flux of the ig energy group of particles in the region ireg, φ matirx,ig,ireg is the neutron flux of the ig-th energy group in the matrix within the region ireg.

[0021] In step 3, after obtaining the average microscopic cross-section and nuclide density of each burnup region, the fission heat release and capture heat release of each region are calculated:

[0022]

[0023] Based on the regional geometric information and energy group structure, the total neutron flux density, multi-group neutron flux density, reaction rate and power of each region are calculated.

[0024] In step 3, the prediction-correction method is used to calculate the burnup, calculate the multi-group merging and regional equivalent homogenization parameters, and update the material composition after each burnup step.

[0025] In step 3, the fuel consumption calculation program is called to perform fuel consumption calculation, including an estimation step and a correction step, as follows:

[0026] The estimation step is used to preliminarily estimate the nuclide density N at the end of the time step t(k+1) i (t(k+1)), using the neutron flux density and effective microscopic cross section at the beginning of the time step (t_k), for each nuclide i and each region ireg, calculate its total absorption rate, fission rate, capture rate, calculate the rate at which nuclide i is produced by other nuclides j, calculate the decay rate of nuclide i itself, and solve the differential equations for the variation of nuclide density with time based on the calculated constant reaction rate to obtain the estimated nuclide density at the end of the time step.

[0027] In step 4, a corresponding restart calculation input file is generated according to the burnup depth, boron concentration, moderator temperature and fuel temperature specified in the input card, the restart calculation input file is read in, initialized, the geometry and material information are matched, and stored in the corresponding array for subsequent calculation; then a resonance calculation is performed, and the macroscopic subgroup cross section in each particle layer and the matrix is ​​calculated using the online subgroup method, and the collision probability solution module is used to obtain the collision probability, escape probability and equivalent macroscopic subgroup cross section of the dispersed particle fuel area; a fixed source MOC calculation is performed, and the transport solver is used to iteratively solve to obtain the converged subgroup flux; under the intermediate resonance approximation, the multi-group microscopic self-screening cross section is obtained by merging and solving; finally, the MOC neutron transport calculation is performed in the full energy segment, and the fine flux information of each layer of particles in each region after convergence is obtained and stored through iterative solution.

[0028] Repeat steps 1 to 4 until the specified burnup depth or calculation time is reached.

[0029] The present invention provides a beneficial effect: the proposed method for calculating dispersed fuel burnup based on reactivity equivalence significantly improves the efficiency of dispersed fuel burnup calculations while maintaining high accuracy and preserving burnup information for each layer within the fuel particle. This method provides an efficient and accurate calculation tool for the design and safety analysis of dispersed fuel assemblies. BRIEF DESCRIPTION OF THE DRAWINGS

[0030] Figure 1 This is a flow chart of the method for calculating the burnup of a dispersed fuel based on reaction rate equivalence proposed by the present invention;

[0031] Figure 2 This is a schematic diagram of a single type of fuel particle grid element in a plate-shaped dispersed fuel assembly;

[0032] Figure 3 Schematic diagram of dual-type fuel particle grid elements in a plate-shaped dispersed fuel assembly;

[0033] Figure 4 The critical characteristic values ​​obtained by the burnup calculation of the plate-shaped dispersed fuel assembly using the method of the present invention are compared with the reference solution (Serpent program calculation results);

[0034] Figure 5 The key nuclides obtained by the burnup calculation of the plate-shaped dispersed fuel assembly using the method of the present invention are 235 U and 238 Comparison of the U nucleon density with the reference solution as it changes with burnup depth. DETAILED DESCRIPTION

[0035] The present invention will be further described in detail below with reference to the accompanying drawings and specific embodiments.

[0036] The present invention provides a method for rapid and precise burnup calculation of dispersed fuel based on reactivity equivalence. Based on the principle of reactivity conservation, after precise transport calculation, the macroscopic cross-section and nuclide density of each region within the dispersed fuel assembly (including each layer of fuel particles and matrix material) are subjected to equivalent homogenization processing to obtain an equivalent homogenized region. Then, a burnup calculation is performed on this equivalent homogenized region. Finally, based on the conservation relationship of nuclide number density, the nuclide density of each layer of the fuel particles is inversely solved.

[0037] This embodiment takes a plate-shaped dispersed fuel assembly as an example to illustrate the specific implementation steps of the burnup calculation method based on reactivity equivalence proposed by the present invention.

[0038] like Figure 1As shown in FIG, a method for calculating the rapid and precise burnup of a dispersion fuel based on reaction rate equivalence includes the following steps:

[0039] Step 1: Multi-group parameter merging

[0040] First, all energy groups in each burnup region are combined to calculate the microscopic cross section of each energy group for each nuclide. The weighted average is then taken using the neutron flux density to obtain the average microscopic cross section of each burnup region, including the absorption cross section, effective fission cross section, fission cross section, and capture cross section. Specifically, these are shown in formulas (1) to (4).

[0041]

[0042]

[0043] Among them, sg is the single energy group after merging; NG is the total number of energy groups; ireg is the current diffuse particle area. ig,ireg is the neutron flux of the ig energy group, φ sg,ireg is the neutron flux after the energy groups in region ireg are merged, σ ig (lnuc) is the microscopic cross section of the nuclide lnuc ig energy group, is the average microscopic cross section of the nuclide lnuc in the region ireg, n ireg (lnuc) is the nucleon density of the nuclide lnuc in the region ireg, σ snf,ireg (lnuc) is the microscopic effective fission cross section of the nuclide lnuc in the region ireg, R snf,ireg The effective fission reaction rate in the region ireg, σ sa,ireg (lnuc) is the microscopic absorption cross section of the nuclide lnuc in the region ireg, σ sf,ireg (lnuc) is the microscopic fission cross section of the nuclide lnuc in the region ireg, R cap,ireg The capture reaction rate within the region ireg.

[0044] Step 2: Regional equivalent homogenization

[0045] Based on the principle of conservation of reaction rate, each layer of fuel particles and the matrix material in the dispersed fuel area are treated with equivalent homogenization.

[0046] R grain =∑n grain ·V grain ·σ grain ·φ grain (5)

[0047]

[0048] Finally, the microscopic effective cross section of each nuclide in the dispersed particle fuel area can be obtained by formula (7):

[0049]

[0050] φ ig,ireg =Volr grain ·φ grain,ig,ireg +Volr matirx ·φ matirx,ig,ireg (8)

[0051] Among them, R grain is the reaction rate within the particle, n grain is the nucleon density within the particle, V grain is the volume of the particle, σ grain is the microscopic cross section of the particle, φ grain is the neutron flux within the particle, is the average nucleon density in the region ireg, is the average microscopic cross section within the region ireg, φ sg,ireg is the single energy group neutron flux in the region ireg, Volr grain is the volume fraction of particles, Volr matirx is the volume fraction of the matrix, φ grain,ig,ireg is the neutron flux of the ig energy group of particles in the region ireg, φ matirx,ig,ireg is the neutron flux of the ig-th energy group in the matrix within the region ireg.

[0052] Step 3: Fuel consumption calculation

[0053] After obtaining the average microscopic cross section and nuclide density of each burnup region, the fission heat release and capture heat release of each region are calculated:

[0054]

[0055] in, is the trapped heat release in the ireg region, R cap,ireg is the capture reaction rate in the ireg region, φ sg,ireg is the capture reaction rate in the ireg region, σ sa,ireg (lnuc) is the absorption cross section of the nuclide lnuc in the ireg region, σ sf,ireg (lnuc) is the fission cross section of the nuclide lnuc in the ireg region, φ sg,ireg is the neutron flux in the ireg region, n ireg (lnuc) is the nuclear number density of the nuclide lnuc in the ireg region, is the average number of neutrons produced by one fission in the ireg region, R fiss,ireg is the fission reaction rate in the ireg region, Vireg is the volume of the ireg region.

[0056] Subsequently, the total neutron flux density, multi-group neutron flux density, reactivity, and power are calculated for each region based on the regional geometry and energy group structure. For dispersed fuel, this calculation is performed separately for each layer of the fuel particles. Flux-volume weighting is then performed based on the regional geometry and energy group structure to calculate the equivalent homogenized macroscopic absorption cross section, macroscopic fission cross section, macroscopic neutron yield multiplied by the fission cross section, and scattering matrix.

[0057] This example uses the Predictor-Corrector method for burnup calculation. Before the calculation, multi-cluster merging and regional equivalent homogenization parameters must be calculated, and the material composition is updated after each burnup step. Using a collision probability method can effectively increase the burnup step size and shorten the burnup calculation time, especially for nuclides with rapidly varying reactivity over time.

[0058] The burnup calculation program (ERICA) is called to perform burnup calculation, including the estimation step and the correction step, which are briefly described as follows:

[0059] The estimation step is used to preliminarily estimate the nuclide density N at the end of the time step t(k+1) i (t(k+1)). Using the neutron flux density and effective microscopic cross section at the start of the time step (t_k), calculate the total absorption rate, fission rate, capture rate, etc. for each nuclide i and each region ireg. Calculate the rate at which nuclide i is produced by other nuclides j (via capture, (n,2n), decay, etc.). Calculate the decay rate of nuclide i itself. Based on the calculated constant reaction rate (i.e., assuming the reaction rate remains constant throughout Δt and is equal to the value at time t(k)), solve the system of differential equations for the time-varying nuclide density (the burnup chain equations) to obtain the estimated nuclide density at the end of the time step.

[0060] The correction step uses information from the prediction step to more accurately calculate the nuclide density at the end of the time step, t(k+1). Using the estimated nuclide density, the macroscopic cross section is updated, and a mid-transport calculation is performed to calculate the estimated flux spectrum and power distribution corresponding to the estimated end-state composition. The burnup equation is re-solved to calculate a more accurate final nuclide density. The nuclide composition of the material after burnup is updated.

[0061] Step 4: Restart the computer

[0062] First, the corresponding restart calculation input file is generated based on the burnup depth, boron concentration, moderator temperature and fuel temperature specified in the input card.

[0063] Then, the restart calculation input file is read in and initialized. The geometry (size / meshing of the calculation problem) and material (moderator, fuel cladding, matrix and fuel particles) information are mapped and stored in the corresponding array for subsequent calculations.

[0064] Then, a resonance calculation is performed, using an online subgroup method to calculate the macroscopic subgroup cross sections in each particle layer and the matrix. The collision probability solver module is used to obtain the collision probability, escape probability, and equivalent macroscopic subgroup cross sections in the dispersed particle fuel region. A fixed source MOC calculation (characteristic line method) is performed, and the transport solver is used to iteratively solve the converged subgroup flux. Under the intermediate resonance approximation, the multi-group microscopic self-screening cross sections are obtained by merging the solution.

[0065] Finally, the MOC neutron transport calculation is performed in the full energy range. Through iterative solution, the fine flux information of each particle layer in each region is obtained and stored after convergence. Iterative calculation: Steps 1-4 are repeated until the specified burnup depth or calculation time is reached.

[0066] This completes the fast and precise burnup calculation for dispersed fuels. Because the MOC transport calculation retains the neutron flux density information of each layer of fuel particles and the matrix, it can achieve precise layered burnup calculations for dispersed fuels.

[0067] The calculation results are as follows Figure 4 The calculated deviation of the characteristic value is between -50 and -378 pcm. When the maximum burnup depth is 100 MWd / kg, the maximum calculated deviation is -378 pcm.

[0068] In addition, the burnup nuclides were statistically analyzed. 235 U and 238 The calculated deviation of the nuclear density of U, such as Figure 5 As shown in the figure, the calculation deviation increases with the increase of burnup, with the maximum percentage deviation being -1.96% and 0.076% respectively. The above calculations show that the rapid and precise burnup calculation method for dispersed particle fuel has good numerical accuracy.

[0069] The present invention is not limited to the above-mentioned embodiments, and improvements and modifications are also considered to be within the scope of protection of the present invention. The contents not described in detail in this specification belong to the prior art known to professionals in this field.

Claims

1. A method for calculating the rapid and precise burnup of a dispersion fuel based on reaction rate equivalence, characterized in that: The steps include: Step 1: Merge multiple group parameters; Step 2: Regional equivalent homogenization; Step 3: Fuel consumption calculation; Step 4: Restart the calculation.

2. The method for calculating the rapid and precise burnup of a dispersion fuel based on reaction rate equivalence according to claim 1, characterized in that: In step 1, all energy groups in each burnup zone are combined, the microscopic cross section of each energy group of each nuclide is calculated, and the weighted average is performed using the neutron flux density to obtain the average microscopic cross section of each single group in each burnup zone, including the absorption cross section, effective fission cross section, fission cross section and capture cross section.

3. The method for calculating the rapid and precise burnup of a dispersion fuel based on reaction rate equivalence according to claim 2, wherein: The specific merging process of step 1 is as follows: Among them, sg is the single energy group after merging; NG is the total number of energy groups; ireg is the current diffuse particle area, φ ig,ireg is the neutron flux of the ig energy group, φ sg,ireg is the neutron flux after the energy groups in region ireg are merged, σ ig (lnuc) is the microscopic cross section of the nuclide lnuc ig energy group, is the average microscopic cross section of the nuclide lnuc in the region ireg, n ireg (lnuc) is the nucleon density of the nuclide lnuc in the region ireg, σ snf,ireg (lnuc) is the microscopic effective fission cross section of the nuclide lnuc in the region ireg, R snf,ireg The effective fission reaction rate in the region ireg, σ sa,ireg (lnuc) is the microscopic absorption cross section of the nuclide lnuc in the region ireg, σ sf,ireg (lnuc) is the microscopic fission cross section of the nuclide lnuc in the region ireg, R cap,ireg The capture reaction rate within the region ireg.

4. The method for calculating the rapid and precise burnup of a dispersion fuel based on reaction rate equivalence according to claim 1, wherein: The step 2 performs equivalent homogenization treatment on each layer of fuel particles and the matrix material in the dispersed fuel region as follows: R grain =∑n grain ·V grain ·s grain ·f grain (5) The microscopic effective cross section of each nuclide in the dispersed particle fuel area is obtained by formula (7): φ ig,ireg =Volr grain ·φ grain,ig,ireg +Full matirx ·φ matirx,ig,ireg (8) Among them, R grain is the reaction rate within the particle, n grain is the nucleon density within the particle, V grain is the volume of the particle, σ grain is the microscopic cross section of the particle, φ grain is the neutron flux within the particle, is the average nucleon density in the region ireg, is the average microscopic cross section within the region ireg, φ sg,ireg is the single energy group neutron flux in the region ireg, Volr grain is the volume fraction of particles, Volr matirx is the volume fraction of the matrix, φ grain,ig,ireg is the neutron flux of the ig energy group of particles in the region ireg, φ matirx,ig,ireg is the neutron flux of the ig-th energy group in the matrix within the region ireg.

5. The method for calculating the rapid and precise burnup of a dispersion fuel based on reaction rate equivalence according to claim 1, wherein: In step 3, after obtaining the average microscopic cross-section and nuclide density of each burnup region, the fission heat release and capture heat release of each region are calculated: Based on the regional geometric information and energy group structure, the total neutron flux density, multi-group neutron flux density, reaction rate and power of each region are calculated.

6. The method for calculating the rapid and precise burnup of a dispersion fuel based on reaction rate equivalence according to claim 5, characterized in that: In step 3, the prediction-correction method is used to calculate the burnup, calculate the multi-group merging and regional equivalent homogenization parameters, and update the material composition after each burnup step.

7. The method for calculating the rapid and precise burnup of a dispersion fuel based on reaction rate equivalence according to claim 6, wherein: In step 3, the fuel consumption calculation program is called to perform fuel consumption calculation, including an estimation step and a correction step, as follows: The estimation step is used to preliminarily estimate the nuclide density N at the end of the time step t(k+1) i (t(k+1)), using the neutron flux density and effective microscopic cross section at the beginning of the time step (t_k), for each nuclide i and each region ireg, calculate its total absorption rate, fission rate, capture rate, calculate the rate at which nuclide i is produced by other nuclides j, calculate the decay rate of nuclide i itself, and solve the differential equations for the variation of nuclide density with time based on the calculated constant reaction rate to obtain the estimated nuclide density at the end of the time step.

8. The method for calculating the rapid and precise burnup of a dispersion fuel based on reaction rate equivalence according to claim 1, characterized in that: In step 4, a corresponding restart calculation input file is generated according to the burnup depth, boron concentration, moderator temperature and fuel temperature specified in the input card, the restart calculation input file is read in, initialized, the geometry and material information are matched, and stored in the corresponding array for subsequent calculation; then a resonance calculation is performed, and the macroscopic subgroup cross section in each particle layer and the matrix is ​​calculated using the online subgroup method, and the collision probability solution module is used to obtain the collision probability, escape probability and equivalent macroscopic subgroup cross section of the dispersed particle fuel area; a fixed source MOC calculation is performed, and the transport solver is used to iteratively solve to obtain the converged subgroup flux; under the intermediate resonance approximation, the multi-group microscopic self-screening cross section is obtained by merging and solving; finally, the MOC neutron transport calculation is performed in the full energy segment, and the fine flux information of each layer of particles in each region after convergence is obtained and stored through iterative solution.

9. The method for calculating the rapid and precise burnup of a dispersion fuel based on reaction rate equivalence according to claim 1, characterized in that: Repeat steps 1 to 4 until the specified burnup depth or calculation time is reached.

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