High-precision rapid calculation method applied to pebble-bed high-temperature gas cooled reactor

Abstract

The invention discloses a high-precision rapid calculation method applied to a pebble-bed high-temperature gas cooled reactor, which comprises the following steps of: firstly, carrying out grid combination on a pebble-bed high-temperature gas cooled reactor fine net structure under each working condition, and combining circumferentially divided grids into one grid because circumferential materials of the pebble-bed high-temperature gas cooled reactor are uniformly distributed; due to the fact that the material distribution difference is large in the radial direction and the axial direction, when grid merging is carried out, grids made of the same material are evenly merged, and a coarse mesh structure is obtained; secondly, combining energy groups, applying the response contribution theory to few-group combination of the pebble-bed high-temperature gas cooled reactor, combining the existing six-group structures to obtain a wide-group structure, and shortening the calculation time and improving the calculation efficiency under the condition that the precision loss is within a specified range.

Description

Technical Field

[0001] The present invention belongs to the technical field of nuclear reactor engineering, and particularly relates to a high-precision and fast calculation method applied to a pebble bed high-temperature gas-cooled reactor. Background Art

[0002] The evaporator of the high-temperature gas-cooled reactor can reach 560 °C, greatly improving the power generation efficiency. The high-temperature gas-cooled reactor nuclear power plant has good inherent safety, which can ensure that the reactor does not experience core melting and a large release of radioactivity under any accident. The high-temperature gas-cooled reactor has advantages such as high thermal efficiency (40% - 41%), deep burnup (up to 20 MWd / t uranium at most), and high conversion ratio (0.7 - 0.8). Since helium has good chemical stability, good heat transfer performance, and low induced radioactivity, it can safely carry out the residual heat after shutdown, and has good safety performance.

[0003] The core feature of the high-temperature gas-cooled reactor technology is inherent safety, that is, there is no possibility of core melting and a large release of radioactive substances under any circumstances, so it will not have a major impact on the public and the environment. At the same time, it also has advantages such as high outlet temperature, high power generation efficiency, and wide applications, and can be widely used in non-electric fields such as high-temperature process heat supply and nuclear seawater desalination, and is internationally recognized as the fourth-generation advanced nuclear energy technology.

[0004] Using the transport theory or the diffusion theory under fine meshes and fine energy groups to solve the pebble bed high-temperature gas-cooled reactor can obtain a high-precision effective multiplication factor Keff solution, but the disadvantages are: whether using the transport method or the diffusion method under the conditions of fine meshes and fine energy groups to solve the pebble bed high-temperature gas-cooled reactor, the time spent is relatively long, affecting the engineering calculation efficiency. Summary of the Invention

[0005] To achieve the rapid calculation of the pebble bed high-temperature gas-cooled reactor, the purpose of the present invention is to provide a high-precision and fast calculation method applied to the pebble bed high-temperature gas-cooled reactor. This method greatly shortens the time required for diffusion calculation and improves the calculation efficiency by merging the number of meshes and performing energy group merging while ensuring the calculation accuracy. To achieve the above purpose, the present invention adopts the following technical solutions for implementation:

[0006] A high-precision and fast calculation method applied to a pebble bed high-temperature gas-cooled reactor first merges the meshes of the fine mesh structure to reduce the number of meshes, and then applies the response contribution theory to perform energy group merging, thereby reducing the time for diffusion calculation while ensuring the calculation accuracy. The specific steps are as follows:

[0007] Step 1: According to the characteristic of uniform circumferential material distribution in the pebble bed high-temperature gas-cooled reactor, first merge the circumferentially distributed meshes into one mesh. Secondly, for the axial distribution, the basic idea of merging is as follows: the meshes in the regions with the same material are uniformly merged; for the radial distribution, the pebble bed high-temperature gas-cooled reactor can be divided into 1 core and 8 reflector layers from the inside out. The method for merging the radial meshes is as follows: the reflector layer structure is divided into 8 meshes, that is, each reflector layer is one mesh, and the core part is equally spaced along the radial direction and divided into 5 - 10 meshes. As a result, multiple mesh merging results are generated. Perform diffusion calculations on each result, and use the effective multiplication factor Keff solution of NECP-Panda under the fine mesh structure as the reference solution. Select the mesh merging method whose deviation from the reference solution is within the specified range as the optimized coarse mesh structure;

[0008] Step 2: Apply the response contribution theory to the energy group merging of the pebble bed high-temperature gas-cooled reactor. First, calculate the contribution of neutrons in each energy group to the target response, and then use the idea of equal contribution sharing to perform energy group division; the equal contribution sharing of the response contribution theory is to equally divide the contribution according to three energy segments: fast group, resonance energy group, and thermal group; the contribution of wide group neutrons is obtained from the contribution of initial fine group neutrons. When dividing the wide group, the neutron contribution of the G-th group of the wide group is equal to the sum of the neutron contributions of the fine groups included in the G-th group of the wide group; in the finally obtained wide group structure, the neutron contributions of each wide group are equal;

[0009] Taking the 361-group fine group structure as the initial energy group structure, use this energy group merging method to merge the energy groups. Among the merging results, select the wide group structure whose deviation from the reference solution is within the specified range, combine it with the coarse mesh structure, and finally select the scheme whose deviation from the reference solution of the effective multiplication factor is within the specified range.

[0010] In Step 2, the contribution of neutrons in each energy group to the target response is calculated by the following formula:

[0011] C(E) = ∫ V dr∫ Ω dΩφ(r,E,Ω)φ * (r,E,Ω) (1)

[0012] In the formula:

[0013] C(E)——The contribution of neutrons with energy E per unit volume and per unit angle;

[0014] φ(r,E,Ω)——The forward flux of neutrons with energy E in the direction of Ω at r;

[0015] φ * (r,E,Ω)——The conjugate flux of neutrons with energy E in the direction of Ω at r;

[0016] The multigroup form of formula (1) is shown as the following formula:

[0017] C g = Vφ g φ *g (2)

[0018] In the formula:

[0019] C g —— Neutron contribution of the g-th group in the initial fine group;

[0020] V —— Volume of the material region;

[0021] φ g —— Forward flux of neutrons in the g-th group of the initial fine group per unit volume;

[0022] φ *g —— Conjugate flux of neutrons in the g-th group of the initial fine group per unit volume;

[0023] The forward flux and conjugate flux of the pebble bed high-temperature gas-cooled reactor in formula (2) are calculated by the volume weighting method using the forward flux and conjugate flux of each grid output by the diffusion solver.

[0024] In the second step, the wide-group neutron contribution is obtained from the initial fine-group neutron contribution. When dividing the wide groups, the neutron contribution of the G-th group in the wide group is equal to the sum of the neutron contributions of the fine groups included in the wide group G. The formula is as follows:

[0025]

[0026] g ∈ [E g , E g-1 , G ∈ [E G , E G-1 (4)

[0027] In the formula:

[0028] C G —— Neutron contribution of the G-th group in the finally obtained wide group;

[0029] —— Neutron contribution of each fine group included in the wide group;

[0030] E g —— Upper energy bound of the fine group;

[0031] E g-1 —— Lower energy bound of the fine group;

[0032] E G —— Upper energy bound of the wide group;

[0033] E G-1 —— Lower energy bound of the wide group.

[0034] Compared with the prior art, the present invention has the following advantages:

[0035] 1. Through grid merging, the number of grids is reduced, and the calculation efficiency is improved while the accuracy loss of the effective multiplication factor Keff is within the specified range.

[0036] 2. Through energy group merging, the number of energy groups is reduced, and the calculation efficiency is improved while the accuracy loss of the effective multiplication factor Keff is within the specified range. BRIEF DESCRIPTION OF THE DRAWINGS

[0037] Figure 1 is a flow chart of a high-precision and fast calculation method applied to a pebble bed high-temperature gas-cooled reactor.

[0038] Figure 2 is a simplified axial structure diagram of the pebble bed high-temperature gas-cooled reactor structure.

[0039] Figure 3 is a top view of the pebble bed high-temperature gas-cooled reactor.

[0040] Figure 4 is a structure diagram of the reflector of the pebble bed high-temperature gas-cooled reactor. DETAILED DESCRIPTION OF THE EMBODIMENTS

[0041] The present invention will be described in detail below in conjunction with the drawings and specific embodiments.

[0042] As Figure 1 shown, a high-precision and fast calculation method for a pebble bed high-temperature gas-cooled reactor according to the present invention first performs grid merging on a fine mesh structure to reduce the number of grids, and then applies the response contribution theory to perform energy group merging, thereby reducing the time of diffusion calculation while ensuring the calculation accuracy. The specific steps are as follows:

[0043] The first step: According to the characteristic that the circumferential material distribution of the pebble bed high-temperature gas-cooled reactor is uniform, first merge the circumferentially distributed grids into one grid. Secondly, for the axial distribution, the basic idea of merging is: the grids in the regions with the same material are uniformly merged; for the radial distribution, the pebble bed high-temperature gas-cooled reactor can be divided into 1 core and 8 reflector layer structures from the inside out. The radial grid merging method is: the reflector layer structure is divided into 8 grids, that is, each reflector layer is a grid, and the core part is equally divided into 5 - 10 grids along the radial direction. Thus, multiple grid merging results are generated. Perform diffusion calculations on each result, and use the effective multiplication factor Keff solution of NECP-Panda under the fine mesh structure as the reference solution, and select the grid merging method with a deviation within the specified range from the reference solution as the optimized coarse mesh structure;

[0044] Step 2: Apply the response contribution theory to the energy group merging of the pebble bed high-temperature gas-cooled reactor. First, calculate the contribution of neutrons in each energy group to the target response, and then use the idea of equal contribution sharing to perform energy group division. The equal contribution sharing of the response contribution theory divides the contribution equally into three energy segments according to the fast group, resonance energy group, and thermal group. The contribution of wide-group neutrons is obtained from the contribution of initial fine-group neutrons. When dividing wide groups, the neutron contribution of the G-th wide group is equal to the sum of the neutron contributions of the fine groups included in the G-th wide group. In the finally obtained wide-group structure, the neutron contributions of each wide group are equal.

[0045] As Figure 2 shown, the axial distribution of the pebble bed high-temperature gas-cooled reactor can be roughly divided from the bottom to the top into a bottom reflector region of 326.17 cm, a graphite pebble bed region of 605.0 cm, a mixed pebble bed region of 275 cm, a top cavity region of 287.33 cm, and a top reflector region of 186.5 cm. The basic idea of axial merging is: uniform merging of the regional grids in the same material region.

[0046] As Figure 3 shown, according to the relatively uniform circumferential material distribution characteristics of the pebble bed high-temperature gas-cooled reactor, the circumferential distributed grids are merged into one grid.

[0047] As Figure 4 shown, when considering the radial grid division of the reflector of the pebble bed high-temperature gas-cooled reactor, each layer of the reflector (with a certain height, based on the axial division method) is divided into one grid.

[0048] After the grid merging is completed, apply the response contribution theory to the energy group merging of the pebble bed high-temperature gas-cooled reactor. First, calculate the contribution of neutrons in each energy group to the target response, and then use the idea of equal contribution sharing to perform energy group division. The contribution of neutrons to a certain response can be calculated by the following formula:

[0049] C(E) = ∫ V dr ∫ Ω dΩ φ(r, E, Ω) φ * (r, E, Ω) (1)

[0050] In the formula:

[0051] C(E) —— The contribution of neutrons with energy E per unit volume and per unit angle;

[0052] φ(r, E, Ω) —— The forward flux of neutrons with energy E in the direction of Ω at r;

[0053] φ * (r, E, Ω) —— The conjugate flux of neutrons with energy E in the direction of Ω at r;

[0054] The multi-group form of formula (1) is shown as the following formula:

[0055] C g = Vφ g φ *g (2)

[0056] In the formula:

[0057] C g —— Particle contribution of the g-th group in the initial fine group;

[0058] V —— Volume of the material region;

[0059] φ g —— Forward flux of the g-th group in the initial fine group per unit volume;

[0060] φ *g —— Conjugate flux of the g-th group in the initial fine group per unit volume;

[0061] The forward flux and conjugate flux of the pebble bed high-temperature gas-cooled reactor in formula (2) can be calculated by the volume weighting method using the forward flux and conjugate flux of each grid output by the diffusion solver.

[0062] The response contribution theory equal contribution divides its contribution equally into three energy segments according to the fast group, resonance energy group, and thermal group. The wide group neutron contribution is obtained from the initial fine group neutron contribution. When dividing the wide group, the neutron contribution of the G-th group in the wide group is equal to the sum of the neutron contributions of the fine groups included in the wide group G:

[0063]

[0064] g ∈ [E g , E g-1 , G ∈ [E G , E G-1 (4)

[0065] In the formula:

[0066] C G —— Neutron contribution of the final obtained G-th group in the wide group;

[0067] —— Neutron contribution of each fine group included in the wide group;

[0068] E g —— Energy upper bound of the fine group;

[0069] E g-1 —— Energy lower bound of the fine group;

[0070] E G —— Energy upper bound of the wide group;

[0071] E G-1 —— Energy lower bound of the wide group;

[0072] In the finally obtained wide group structure, the neutron contributions of each wide group are equal.

[0073] Taking the fine group structure of 361 groups as the initial energy group structure, the energy groups are merged using this energy group merging method. Among the merging results, a wide group structure with a deviation within the specified range from the reference solution is selected and combined with the coarse mesh structure. Finally, a solution with a deviation within the specified range from the reference solution of the effective multiplication factor is selected.

[0074] Calculation result verification: Taking the calculation result of the effective multiplication factor Keff of the NECP-Panda six-group fine mesh structure (88 axial grids, 18 radial grids, 30 circumferential grids) as the reference solution, the deviation between the calculated effective multiplication factor Keff and the reference solution under different coarse mesh division methods is verified (the calculation result of the reference solution Keff is 0.99590, and the calculation time is 31.81 s):

[0075]

[0076]

[0077] As can be seen from the above table, after grid coarsening, the calculation time is greatly shortened, and the accuracy is within the specified range (the deviation from the reference solution is about 500 pcm or less).

[0078] The Keff of the six-group fine mesh structure (154 axial grids, 43 radial grids, 1 circumferential grid) is 0.99688 (the calculation time is 150.69 s). Using the response contribution theory, a four-group structure is obtained and compared with the reference solution:

[0079] Energy group structure Keff calculation result Calculation time (s) Keff deviation / pcm Four energy groups 0.99981 147.53 293

[0080] As can be seen from the above table, after energy group merging, the deviation of the effective multiplication factor Keff from the reference solution is also within the specified range (500 pcm), and the calculation efficiency is also improved.

Claims

1. A high-precision and fast calculation method applied to a pebble bed high-temperature gas-cooled reactor, characterized in that: First, perform mesh merging on the fine mesh structure to reduce the number of meshes. Then, apply the response contribution theory for energy group merging, thereby reducing the time for diffusion calculation while ensuring the calculation accuracy. The specific steps are as follows: The first step: According to the characteristic of uniform circumferential material distribution in the pebble bed high-temperature gas-cooled reactor, first merge the circumferentially distributed meshes into one mesh. Secondly, for the axial distribution, the basic idea of merging is as follows: The meshes in the areas with the same material are uniformly merged; for the radial distribution, the pebble bed high-temperature gas-cooled reactor can be divided into 1 core and 8 reflector layer structures from the inside out. The method for radial mesh merging is as follows: The reflector layer structure is divided into 8 meshes, that is, each reflector layer is one mesh, and the core part is equally divided into 5 - 10 meshes along the radial direction. Thus, multiple mesh merging results are generated. Perform diffusion calculation on each result. Using the effective multiplication factor Keff solution of NECP-Panda under the fine mesh structure as the reference solution, select the mesh merging method with a deviation within the specified range from the reference solution as the optimized coarse mesh structure; The second step: Apply the response contribution theory to the energy group merging of the pebble bed high-temperature gas-cooled reactor. First, calculate the contribution of neutrons in each energy group to the target response, and then use the idea of equal contribution distribution for energy group division; The equal contribution distribution of the response contribution theory is divided into three energy segments, namely the fast group, the resonance energy group, and the thermal group, to evenly distribute their contributions; The wide group neutron contribution is obtained from the initial fine group neutron contribution. When dividing the wide group, the neutron contribution of the G-th group of the wide group is equal to the sum of the neutron contributions of the fine groups included in the G-th group of the wide group; In the finally obtained wide group structure, the neutron contributions of each wide group are equal; Taking the 361-group fine group structure as the initial energy group structure, use this energy group merging method for energy group merging. Among the merging results, select the wide group structure with a deviation within the specified range from the reference solution, combine it with the coarse mesh structure, and finally select the solution with a deviation within the specified range from the effective multiplication factor reference solution.

2. The high-precision and fast calculation method applied to the pebble bed high-temperature gas-cooled reactor according to claim 1, characterized in that: In the second step, the contribution of neutrons in each energy group to the target response is calculated by the following formula: C(E) = ∫ V dr ∫ Ω dΩ φ(r, E, Ω) φ * (r, E, Ω) (1) In the formula: C(E) —— The contribution of neutrons with energy E per unit volume and unit angle; φ(r,E,Ω) —— The forward flux of neutrons with energy E in the direction of Ω at r; φ * (r, E, Ω) —— the conjugate flux of neutrons at r, in the direction of Ω, with energy E; The multi-group form of formula (1) is shown as the following formula: C g = Vφ g φ *g (2) In the formula: C g —— Neutron contribution of the g-th group of the initial fine groups; V —— The volume of the material region; φ g —— The forward flux of neutrons in the g-th group of the initial fine groups per unit volume; φ *g —— The conjugate flux of neutrons in the initial fine group g per unit volume; The forward flux and conjugate flux of the pebble bed high-temperature gas-cooled reactor in formula (2) are calculated by the volume weighting method using the forward flux and conjugate flux of each mesh output by the diffusion solver.

3. A high-precision and fast calculation method applied to a pebble bed high-temperature gas-cooled reactor according to claim 1, characterized in that: In the second step, the wide group neutron contribution is obtained from the initial fine group neutron contribution. When dividing the wide group, the neutron contribution of the G-th group of the wide group is equal to the sum of the neutron contributions of the fine groups included in the G-th group of the wide group. The formula is as follows: g ∈ [E g , E g-1 , G ∈ [E G , E G-1 In equation (4): C G —— Neutron contribution of the final resulting broad group G; —— Neutron contribution of each fine group included in the wide group E g —— upper bound of the energy of the fine group; E g-1 —— Lower bound of the energy of the fine group; E G —— upper bound of the energy of the wide group; E G-1 ——Lower energy bound of the wide group.

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