CN108549753B - Radiation shielding calculation method for coupling point kernel integration method and Monte Carlo method - Google Patents
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Abstract
The invention relates to the technical field of nuclear radiation protection, and provides a radiation shielding calculation method for coupling a point nuclear integration method and a Monte Carlo method, which comprises the steps of establishing a geometric part of a point nuclear integration sub-model; establishing a source item part of a point kernel integral model, and performing discrete processing on a source or a surface source; solving the attenuation of the source term in the point kernel integral submodel; solving a wide beam accumulation factor; solving a point kernel integral equation to obtain the dose rate or flux density of the shielded area; performing iterative computation according to variable parameters provided by a user; comparing all the calculated geometric information and dose rate/flux results to obtain an optimal model meeting the requirement; establishing a Monte Carlo submodel according to the optimal model; using a Monte Carlo calculation program to solve the Monte Carlo submodel; and comparing the calculation results of the Monte Carlo submodel and the point kernel integral submodel. The calculation method can evaluate the calculation correctness during iterative calculation, improve the calculation precision and obtain higher calculation efficiency.
Description
Technical Field
The invention relates to the technical field of nuclear radiation protection, in particular to a radiation shielding calculation method for coupling a point-kernel integration method and a Monte Carlo method.
Background
The radiation shielding calculation is to carry out particle transport simulation on the nuclear device through a radiation shielding calculation program so as to obtain the energy spectrum and the flux density of neutrons and gamma rays of the nuclear device in a shielding area, evaluate the radiation dose of personnel and equipment in the shielding area and guarantee the radiation safety of the personnel and the equipment.
The radiation shielding calculation procedures are generally classified into a point-kernel integration method, a deterministic theory method, and a monte carlo method.
The point-kernel integration method is a green function integration method, and is characterized in that the penetration behaviors of neutrons and gamma rays in a geometric space are calculated, an integral equation is calculated in a radiation shielding area to obtain an energy spectrum and neutron flux density of a concerned area, and for a complex area which cannot be solved, the complex area can be solved in a mode of performing space dispersion on a radiation source to enable the complex area to become a point source. The method has the advantages that the calculation speed is high, the method is suitable for calculating and processing the radiation shielding problem of the complex geometric space formed by various types of basic bodies, and the method is one of basic methods for designing the radiation shielding; the drawback is that the solution process requires a large number of empirical parameters, and the same problem may yield different results due to different understandings by different designers.
The deterministic method is a numerical analysis method, the problem to be solved is established into a mathematical model containing a plurality of groups of mathematical physical equations, and an approximate solution is obtained by using the analysis method. The determinism method has the advantages of high solving speed and the defect that a complex geometric model cannot be processed.
The Monte Carlo method is a calculation method based on probability and statistical theory, which links the problem to be solved with a certain probability model, and carries out random simulation on a computer to obtain the approximate solution of the problem. The Monte Carlo method has the advantages that the calculation result is accurate, accurate modeling of complex materials and complex geometry is supported, a large number of auxiliary modeling tools are available at present to realize three-dimensional visual modeling of a Monte Carlo calculation model, the simulation process of random sampling of the Monte Carlo method better accords with the characteristics of the actual transportation process of particles, and the Monte Carlo method is the best radiation safety calculation method confirmed by the international atomic energy Committee at present; the method has the disadvantages of low simulation speed, large time consumption for reaching a calculation result with small statistical error and low design efficiency during iterative design.
The traditional radiation shielding calculation method is generally a single method, and the radiation shielding design is mostly a repeated iteration process, so that each method has certain limitations. The point kernel integration method depends on design experience, and the correctness of a calculation result cannot be verified; the Monte Carlo method has accurate calculation results, but the iterative calculation process consumes a large amount of machines, so the design efficiency is low.
Disclosure of Invention
The invention aims to overcome the defects of the traditional radiation shielding calculation method in calculation correctness and calculation efficiency, and provides a radiation shielding calculation method in which a point kernel integration method and a Monte Carlo method are coupled, so that the calculation correctness is evaluated and the calculation efficiency is improved during iterative calculation.
The technical scheme adopted by the invention for solving the technical problems is as follows.
A radiation shielding calculation method for coupling a point kernel integration method and a Monte Carlo method comprises the following steps:
(1) establishing a geometric part of a point kernel integral model;
the point kernel integral submodel is composed of a plurality of areas, each area is composed of a uniform material, a user needs to give the size thickness and the used material (including information of density, element composition, mass proportion and the like) of each area, and variable parameters needing iterative computation are given, and the variable parameters comprise the size thickness and the used material of one or more areas and the like.
(2) Establishing a source item part of a point kernel integral model, and performing discrete processing on a source or a surface source;
wherein, the source term part of the point kernel integral submodel
Given by the user;
for a source or a surface source, spatial dispersion is performed using the following formula:
in the formula:
represents the source or the area source in
The total source intensity of the equivalent point sources at the position, J represents the number of discrete point sources, J represents the total number of discrete points,
representing discrete points
In that
The equivalent point source intensity of the location,
representing discrete points
The weighting factor of (2).
(3) Solving the attenuation of the source term in the point kernel integral submodel;
solving the attenuation effect of the source term in the point kernel integral model material by using the following formula:
in the formula: i represents the ith region of the point kernel integral submodel, I represents the total number of regions of the submodel,
representing discrete points
Equivalent point source to shielded area, mui(E) Representing the linear attenuation coefficient of the material used in the i-region.
(4) If the source item is a point source or the size of the source item can be regarded as the point source relative to the geometric model, turning to the step (6); if the source item is the source or the non-point source, go to step (5).
(5) Solving a wide beam accumulation factor;
solving for the wide-beam accumulation factor using the following equation:
in the formula: x represents the source-to-shielded region distance measured in mean free path, b represents the accumulation factor per mean free path, and Z represents the multiplication factor, which can be calculated by the following equation:
in the formula: a, c, d, XzFor the fitting parameters, fixed parameters are used which depend on the material and the source intensity energy E. Fitting parameters for typical materials can be found in reference [1]As a result, atypical materials can be derived by reference to typical material parameters based on material characteristics.
(6) Solving a point kernel integral equation to obtain the dose rate or flux density of the shielded area;
solving a point-kernel integral equation using:
in the formula: d represents the dose rate of the shielded area, CjkRepresenting energy as EkThe dose rate contributed by point source j to the shielded area;
in the formula: cjkRepresenting energy as EkThe flux-dose conversion factor of point source j is a fixed parameter that depends only on the source intensity energy E;
if only the flux density needs to be solved and no flux-dose conversion is needed, the calculation formula becomes:
the energy E can be directly obtained by the above two formulaskFlux density at the shielded area.
(7) And (3) starting iterative computation, and changing the geometric conditions and the source item conditions of the step (1) and the step (2) according to variable parameters provided by a user.
(8) And (5) repeating the steps (3) to (6).
(9) Repeating the step (7) and the step (8) for multiple times; and comparing all the calculated geometric information and dose rate/flux results so as to facilitate the user to screen an optimal model meeting the requirement.
(10) And establishing a Monte Carlo submodel according to the optimal model.
(11) The monte carlo submodel is solved using a monte carlo computer program.
(12) Comparing the calculation results of the Monte Carlo submodel and the point kernel integral submodel, and selecting one of the submodels to calculate the result if the error between the Monte Carlo submodel and the point kernel integral submodel is less than 10%; and (4) if the error between the two models is more than 10%, checking and comparing the difference between the two sub models, and repeating the step (6) and the step (11).
In the above technical solution, the number of times of repetition of step (9) may be calculated as follows: the user-provided variable parameters include L regions, M materials, N sizes, and the number of repetitions is L × M × N.
In the above solution, the monte carlo submodel in step (10) can be obtained by means of an auxiliary modeling tool.
The radiation shielding calculation method coupled with the point kernel integration method and the Monte Carlo method can evaluate the calculation correctness during iterative calculation, improve the calculation precision and obtain higher calculation efficiency.
Reference [1 ]: harma y.a adaptation of gamma-ray build factors by modified geological development [ J ]. Nuclear Science and Engineering, 1983, 983: 299-309.
Drawings
FIG. 1 is a schematic diagram of an embodiment of the present invention.
Wherein: 1.60co source, 2. iron, 3. lead.
Detailed Description
The invention is further described with reference to specific examples.
Examples
The technical problem to be solved is as follows:
source intensity is 106Of Bq60And the Co source wraps the iron and lead shielding material with the total thickness not more than 5cm on the surface, and when the surface dose rate is lower than 5 mu Sv/h, the total weight of the shielding body can be lightest by matching the thicknesses of the iron and the lead.
II, adopt
1. In this embodiment, a point kernel integration program rsc (radiation Shielding Analysis software)3.0 software developed by Atlantic Nuclear Services inc. is used to establish the point kernel integration sub-model shown in fig. 1, and a calculation process of the point kernel integration sub-model is completed to obtain a calculation result.
Table 1 shows the results of example calculations performed by the RSC3.0 routine.
TABLE 1
2. According to the calculation results of Table 1, the calculation result of No. 7 satisfies that the surface dose rate is less than 5. mu. Sv/h and the total weight of the shield is 9.03kg at the lightest.
3. In this embodiment, a Monte Carlo submodel is established by using Monte Carlo calculation program MCNP5(Monte Carlo N-Particle Transport Code, Version 5) software developed by Los Alamos laboratory, and the calculation process of the Monte Carlo submodel is completed, the number of sampling particles is 1E +08, and a calculation result is obtained (the statistical error is less than 1%).
Table 2 shows the calculation results of the MCNP5 program to obtain the example corresponding to number 7 in table 1.
TABLE 2
4. Comparing the calculation results in table 1 and table 2, the error of the two submodels is lower than 1.5%, which proves that the calculation results of the two submodels are both correct.
Third, the calculation time for the RSC3.0 program to complete the 20 submodels shown in Table 1 is 18min17 s. The MCNP5 program has a computation time of 21min32s for completing 1 sub-model shown in Table 2, and the estimated computation time of 430min for completing 20 sub-models.
Details not described in the present specification belong to the prior art known to those skilled in the art.
The above description is only for the purpose of illustrating the preferred embodiments of the present invention and is not to be construed as limiting the invention, and any modifications, equivalents, improvements and the like that fall within the spirit and principle of the present invention are intended to be included therein.
Claims (3)
1. A radiation shielding calculation method for coupling a point kernel integration method and a Monte Carlo method is characterized by comprising the following steps:
(1) establishing a geometric part of a point kernel integral model;
the point kernel integral submodel consists of a plurality of areas, each area consists of a uniform material, and a user needs to give the size thickness and the used material of each area and variable parameters needing iterative calculation;
(2) establishing a source item part of a point kernel integral model, and performing discrete processing on a source or a surface source;
wherein, the source term part of the point kernel integral submodel
Given by the user;
for a source or a surface source, spatial dispersion is performed using the following formula:
in the formula:
represents the source or the area source in
The total source intensity of the equivalent point sources at the position, J represents the number of discrete point sources, J represents the total number of discrete points,
representing discrete points
In that
The equivalent point source intensity of the location,
representing discrete points
The weighting factor of (1);
(3) solving the attenuation of the source term in the point kernel integral submodel;
solving the attenuation effect of the source term in the point kernel integral model material by using the following formula:
in the formula: i represents the ith region of the point kernel integral submodel, I represents the total number of regions of the submodel,
representing discrete points
Equivalent point source to shielded area, mui(E) Linear attenuation coefficient of the material used for the i area;
(4) if the source item is a point source or the size of the source item can be regarded as the point source relative to the geometric model, turning to the step (6); if the source item is a source or a non-point source, turning to the step (5);
(5) solving a wide beam accumulation factor;
solving for the wide-beam accumulation factor using the following equation:
in the formula: x represents the source-to-shielded region distance measured in mean free path, b represents the accumulation factor per mean free path, and Z represents the multiplication factor, which can be calculated by the following equation:
in the formula: a, c, d, XzAs fitting parameters, fixed parameters depending on the material and the source intensity energy E;
(6) solving a point kernel integral equation to obtain the dose rate or flux density of the shielded area;
solving a point-kernel integral equation using:
in the formula: d represents the dose rate of the shielded area,Djkrepresenting energy as EkThe dose rate contributed by point source j to the shielded area;
in the formula: cjkRepresenting energy as EkThe flux-dose conversion factor of point source j is a fixed parameter that depends only on the source intensity energy E;
if only the flux density needs to be solved and no flux-dose conversion is needed, the calculation formula becomes:
the energy E can be directly obtained by the above two formulaskFlux density at the shielded area;
(7) starting iterative computation, and changing the geometric conditions and the source item conditions of the step (1) and the step (2) according to variable parameters provided by a user;
(8) repeating the steps (3) to (6);
(9) repeating the step (7) and the step (8) for multiple times; comparing all the calculated geometric information and dose rate/flux results for a user to screen an optimal model meeting the requirement;
(10) establishing a Monte Carlo submodel according to the optimal model;
(11) using a Monte Carlo calculation program to solve the Monte Carlo submodel;
(12) comparing the calculation results of the Monte Carlo submodel and the point kernel integral submodel, and selecting one of the submodels to calculate the result if the error between the Monte Carlo submodel and the point kernel integral submodel is less than 10%; and (4) if the error between the two models is more than 10%, checking and comparing the difference between the two sub models, and repeating the step (6) and the step (11).
2. The method of claim 1, wherein the method comprises a radiation shielding calculation method in which a point-kernel integration method is coupled with a monte carlo method, wherein: the number of repetitions of step (9) may be calculated as follows: the user-provided variable parameters include L regions, M materials, N sizes, and the number of repetitions is L × M × N.
3. The method of claim 1, wherein the method comprises a radiation shielding calculation method in which a point-kernel integration method is coupled with a monte carlo method, wherein: the monte carlo submodel in step (10) may be obtained by means of an auxiliary modeling tool.
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