CN114117870B - Feedback type radiation shielding analysis method, system, terminal and medium - Google Patents

Feedback type radiation shielding analysis method, system, terminal and medium Download PDF

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CN114117870B
CN114117870B CN202111561423.7A CN202111561423A CN114117870B CN 114117870 B CN114117870 B CN 114117870B CN 202111561423 A CN202111561423 A CN 202111561423A CN 114117870 B CN114117870 B CN 114117870B
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CN114117870A (en
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杨俊云
柴晓明
余红星
李兰
王金雨
吕焕文
唐松乾
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Nuclear Power Institute of China
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Abstract

The application discloses a feedback type radiation shielding analysis method, a system, a terminal and a medium, which relate to the technical field of radiation screens and have the technical scheme that: acquiring a forward solution of forward transport of the radiation area and a concomitant solution of concomitant transport by a deterministic method based on the initial multi-group cross-section library; determining a variance reduction parameter required by MC method calculation according to a forward solution and an accompanying solution of a radiation area; counting and analyzing counts in forward transportation of the MC method to generate nuclear reaction macroscopic cross sections of the materials in each space region, feeding back to the initial multi-group cross section library, and forming an updated multi-group cross section library in the same format; and (3) carrying out forward transport and accompanying transport calculation again according to the updated multi-group section library, and outputting a radiation field spatial distribution result obtained by MC method forward transport calculation after iteration for many times. The method can avoid the problems of rough calculation result caused by singly using the definite theory method and no counting or technical non-convergence in the deep penetration problem caused by singly using the MC method.

Description

Feedback type radiation shielding analysis method, system, terminal and medium
Technical Field
The application relates to the technical field of radiation screens, in particular to a feedback type radiation shielding analysis method, a feedback type radiation shielding analysis system, a feedback type radiation shielding analysis terminal and a feedback type radiation shielding analysis medium.
Background
In the fields of scientific research and engineering practice, the accurate and efficient radiation shielding analysis method has important research value and engineering application value. For the deep penetration radiation shielding problem, the calculation result is rough due to the accuracy problem of the multi-group section library in the deterministic method, the calculation result of the continuous energy Monte Carlo (MC) simulation method is accurate, but the problem that the area of interest is not counted or the counting is not converged can occur in solving the deep penetration problem. In order to realize accurate deep penetration radiation shielding analysis, a great deal of research work is carried out in the field at home and abroad.
In 1963, kalos indicated that there was a significance function that could guide MC sampling to zero variance in statistics. Based on different understanding of the importance function, several important degradation techniques are proposed: (1) In 1998, wagner et al proposed a CADIS method, which is applicable to source-detector problems and source-local solution problems, and calculated the accompanying function of the problems by a deterministic method, and designed corresponding weight window parameters to guide the accelerated convergence of MC simulation at the detector; (2) In 2001, cooper proposed a flat sampling technique for global solution problem, which considers that statistics are to be converged in all phase space cells, and requires that the MC particle density in the cells be high enough and controls the dispersion of the weight of the particles in the cells; (3) In 2007, wagner et al combined the Cooper's global variance-reducing idea with the CADIS method, and proposed a FW-CADIS method applicable to the global solution problem; (4) In 2009, becker puts forward a Global Flux Weight Window (GFWW) method and a Global Response Weight Window (GRWW) method based on a definite forward calculation result, and extends the global variance reduction method of Cooper from a standard flux to an energy-space cell layer; (5) In the same year, becker estimates a target weight window through particle value flow calculated by a definitive theory, makes assumption that the standard flux is positively related to the particle density, and develops flux deviation flattening and response deviation flattening technologies; (6) In 2016, the university of Berkeley generalized the FW-caddis method from energy-space cells to energy-space-angle cell level, which is both high in memory requirements and computational cost.
The above described hybrid calculation covariance techniques have a common theoretical basis, namely using deterministic calculations to produce importance functions that can be used to guide MC calculations. In practice, however, the deterministic method can only use multiple groups of section parameters, and the parameters have a certain difference from the MC method using the nuclear section with continuous energy, so that an importance function generated by the deterministic calculation is not matched with a MC method calculation model, and the calculation accuracy and the analysis capability of the hybrid method in deep penetration shielding are limited.
Disclosure of Invention
In order to solve the defects in the prior art, the application aims to provide a feedback type radiation shielding analysis method, a system, a terminal and a medium.
The technical aim of the application is realized by the following technical scheme:
in a first aspect, a feedback radiation shielding analysis method is provided, comprising the steps of:
acquiring a forward solution of forward transport of the radiation area and a concomitant solution of concomitant transport by a deterministic method based on the initial multi-group cross-section library;
determining a variance reduction parameter required by MC method calculation according to a forward solution and an accompanying solution of a radiation area;
counting and analyzing counts in forward transportation of the MC method to generate nuclear reaction macroscopic cross sections of the materials in each space region, feeding back to the initial multi-group cross section library, and forming an updated multi-group cross section library in the same format;
and (3) carrying out forward transportation and accompanying transportation calculation again according to the updated multi-group section library until the continuous section library used by the MC method is repeatedly updated for multiple times, reducing the difference between the continuous section library used by the MC method and the multi-group section library used by the deterministic method, and outputting a radiation field space distribution result obtained by the forward transportation calculation of the MC method.
Further, the forward transport solving equation is specifically:
wherein H represents a neutron forward transport operator;indicating neutron fluence rate; />Representing neutron state phase space; q represents the source intensity of the external neutrons; />Representing a spatial gradient operator; />A unit vector indicating a neutron motion direction after collision; />Representing the spatial location; e represents neutron energy after collision; />Representing the total cross-section of neutron interaction with the medium; />A scattering cross section representing neutron interaction with a medium; />Representing neutron energy before collision; />A unit vector representing the direction of neutron motion prior to collision.
Further, the accompanying solution acquisition process of the accompanying transport specifically includes: and solving and obtaining by a deterministic method based on the initial multi-group cross-section library and the forward solution of the radiation area.
Further, the solution equation of the concomitant transport is specifically:
wherein, the liquid crystal display device comprises a liquid crystal display device,representing neutron companion transport operators; />Representing neutron concomitant fluence rate; />Representing neutron state phase space; />Indicating the intensity of the accompanying neutron source; />Representing a spatial gradient operator; />A unit vector indicating a neutron motion direction after collision; />Representing the spatial location; e represents neutron energy after collision; />Representing the total cross-section of neutron interaction with the medium; />A scattering cross section representing neutron interaction with a medium; />Representing neutron energy before collision; />A unit vector representing the direction of neutron motion prior to collision.
Further, the deterministic method is a discrete ordinate method S N Spherical harmonic method R N Any one of a characteristic line method MOC, a penetration probability method TPM, a collision probability method CPM and a finite element method.
Further, the variance reduction parameters required for the MC method calculation include a source bias parameter and a weight window parameter.
Further, the macroscopic section of the nuclear reaction comprises a total section, an absorption section and a scattering section, and the calculation formulas of the total section, the absorption section and the scattering section are specifically as follows:
wherein, the liquid crystal display device comprises a liquid crystal display device,represents a nuclear reaction cross section; />Representing the type of nuclear reaction cross section, including total cross section, absorption cross section, scattering cross section; d represents the spatial region; g represents neutron n energy group number; />For summation compliance, subscript i represents the ith neutron history, subscript j represents the jth trace in the history, and the jth free flight; />A weight representing the j-th neutron trajectory; />The energy representing the j-th neutron trajectory; />A track length representing the ith neutron j track; />As an indication function, neutrons take a value of 1 when the energy group number is g in the space D, otherwise, 0.
In a second aspect, there is provided a feedback radiation shielded analysis system comprising:
the solving and calculating module is used for acquiring a forward solution of forward transportation of the radiation area and an accompanying solution of accompanying transportation based on the initial multi-group section library by a deterministic method;
the parameter determining module is used for determining a variance reduction parameter required by MC method calculation according to the forward solution and the accompanying solution of the radiation area;
the iteration updating module is used for counting and analyzing counts in forward transportation of the MC method, generating nuclear reaction macroscopic cross sections of the materials in each space region, feeding back to the initial multi-group cross section library, and forming an updated multi-group cross section library in the same format;
and the updating calculation module is used for carrying out forward transportation and accompanying transportation calculation again according to the updated multi-group section library until the continuous section library used by the MC method is repeatedly updated for multiple times, and outputting a radiation field space distribution result obtained by the forward transportation calculation of the MC method after the difference between the continuous section library used by the MC method and the multi-group section library used by the definite method is reduced.
In a third aspect, a computer terminal is provided, comprising a memory, a processor and a computer program stored in the memory and executable on the processor, the processor implementing a feedback radiation shielding analysis method according to any one of the first aspects when executing the program.
In a fourth aspect, a computer readable medium is provided, on which a computer program is stored, characterized in that the computer program is executed by a processor to implement a feedback radiation shielding analysis method according to any one of the first aspects.
Compared with the prior art, the application has the following beneficial effects:
1. the feedback type radiation shielding analysis method provided by the application can avoid the problems of rough calculation result caused by independently using the definite theory method and no counting or technical non-convergence in the deep penetration problem caused by independently using the MC method;
2. the method can break through the limitation of non-convergence of the shielding calculation result caused by the inconsistency of the multi-group database and the continuous energy database;
3. the application can realize the self-adaptive calculation of deep penetration shielding analysis;
4. the application can effectively meet the requirements of large-scale, deep penetration and high-precision radiation shielding analysis in scientific research and engineering.
Drawings
The accompanying drawings, which are included to provide a further understanding of embodiments of the application and are incorporated in and constitute a part of this specification, illustrate embodiments of the application and together with the description serve to explain the principles of the application. In the drawings:
FIG. 1 is a flow chart in an embodiment of the application;
fig. 2 is a system block diagram in an embodiment of the application.
Detailed Description
For the purpose of making apparent the objects, technical solutions and advantages of the present application, the present application will be further described in detail with reference to the following examples and the accompanying drawings, wherein the exemplary embodiments of the present application and the descriptions thereof are for illustrating the present application only and are not to be construed as limiting the present application.
Example 1: a feedback radiation shielding analysis method, as shown in fig. 1, comprises the following steps:
s1: acquiring a forward solution of forward transport of the radiation area and a concomitant solution of concomitant transport by a deterministic method based on the initial multi-group cross-section library;
s2: determining the required variance reduction parameters of MC method calculation by combining the forward solution and the accompanying solution of the radiation area through a variance reduction parameter manufacturing program; the MC method calculates required variance reduction parameters including a source bias parameter and a weight window parameter;
s3: counting and analyzing counts in forward transportation of the MC method to generate nuclear reaction macroscopic cross sections of the materials in each space region, feeding back to the initial multi-group cross section library, and forming an updated multi-group cross section library in the same format; after simulation of source particles with a certain number of samples, the macroscopic cross section of the nuclear reaction of each material is accurately obtained;
s4: and (3) carrying out forward transportation and accompanying transportation calculation again according to the updated multi-group section library until iterative updating is carried out for N-1 (N is a natural number, and N is more than or equal to 1) times, so that the difference between the continuous section library used by the MC method and the multi-group section library used by the deterministic method is reduced, and outputting a radiation field space distribution result obtained by the forward transportation calculation of the MC method after the N-th iteration is finished.
The forward transport solving equation is specifically:
wherein H represents a neutron forward transport operator;indicating neutron fluence rate; />Representing neutron state phase space; q represents the source intensity of the external neutrons; />Representing a spatial gradient operator; />A unit vector indicating a neutron motion direction after collision; />Representing the spatial location; e represents neutron energy after collision; />Representing the total cross-section of neutron interaction with the medium; />The scattering cross section of the neutron acting with the medium is shown.
In addition, the concomitant solution acquisition of the concomitant transport is obtained by solving in a deterministic method based on the initial multi-group cross-sectional library and the forward solution of the radiation region.
The solution equation for the concomitant transport is specifically:
wherein, the liquid crystal display device comprises a liquid crystal display device,representing neutron companion transport operators; />Representing neutron concomitant fluence rate; />Indicating that the companion neutron source is strong.
In the present embodiment, the deterministic method is the discrete ordinate method S N Spherical harmonic method R N Any one of a characteristic line method MOC, a penetration probability method TPM, a collision probability method CPM and a finite element method.
The macroscopic section of the nuclear reaction comprises a total section, an absorption section and a scattering section, and the calculation formulas of the total section, the absorption section and the scattering section are specifically as follows:
wherein, the liquid crystal display device comprises a liquid crystal display device,represents a nuclear reaction cross section; />Representing the type of nuclear reaction cross section, including total cross section, absorption cross section, scattering cross section; d represents the spatial region; g represents neutron n energy group number; />For summation compliance, subscript i represents the ith neutron history, subscript j represents the jth trace in the history, and the jth free flight; />A weight representing the j-th neutron trajectory; />The energy representing the j-th neutron trajectory; />A track length representing the ith neutron j track; />As an indication function, neutrons take a value of 1 when the energy group number is g in the space D, otherwise, 0.
Example 2: a feedback type radiation shielding analysis system, as shown in figure 2, comprises a solving calculation module, a parameter determination module, an iteration update module and an update calculation module.
The solution calculation module is used for acquiring a forward solution of forward transport of the radiation area and an accompanying solution of accompanying transport based on an initial multi-group section library by a deterministic method; the parameter determining module is used for determining a variance reduction parameter required by MC method calculation according to the forward solution and the accompanying solution of the radiation area; the iteration updating module is used for counting and analyzing counts in forward transportation of the MC method, generating nuclear reaction macroscopic cross sections of the materials in each space region, feeding back to the initial multi-group cross section library, and forming an updated multi-group cross section library in the same format; and the updating calculation module is used for carrying out forward transportation and accompanying transportation calculation again according to the updated multi-group section library until the continuous section library used by the MC method is repeatedly updated for multiple times, and outputting a radiation field space distribution result obtained by the forward transportation calculation of the MC method after the difference between the continuous section library used by the MC method and the multi-group section library used by the definite method is reduced.
Working principle: the application provides a feedback type radiation shielding analysis method combining a definite theory method and a Monte Carlo (MC) method, which is characterized in that forward solutions and accompanying solutions of a concerned radiation area are solved through the definite theory method, forward transport calculation model parameters for the MC method are established, a plurality of cross section libraries used by the definite theory method are further subjected to iterative updating through the MC method, new forward transport calculation model parameters of the MC method are established through the updated plurality of cross section libraries, and finally, a calculation result is obtained through continuous energy MC forward transport calculation.
It will be appreciated by those skilled in the art that embodiments of the present application may be provided as a method, system, or computer program product. Accordingly, the present application may take the form of an entirely hardware embodiment, an entirely software embodiment or an embodiment combining software and hardware aspects. Furthermore, the present application may take the form of a computer program product embodied on one or more computer-usable storage media (including, but not limited to, disk storage, CD-ROM, optical storage, and the like) having computer-usable program code embodied therein.
The present application is described with reference to flowchart illustrations and/or block diagrams of methods, apparatus (systems) and computer program products according to embodiments of the application. It will be understood that each flow and/or block of the flowchart illustrations and/or block diagrams, and combinations of flows and/or blocks in the flowchart illustrations and/or block diagrams, can be implemented by computer program instructions. These computer program instructions may be provided to a processor of a general purpose computer, special purpose computer, embedded processor, or other programmable data processing apparatus to produce a machine, such that the instructions, which execute via the processor of the computer or other programmable data processing apparatus, create means for implementing the functions specified in the flowchart flow or flows and/or block diagram block or blocks.
These computer program instructions may also be stored in a computer-readable memory that can direct a computer or other programmable data processing apparatus to function in a particular manner, such that the instructions stored in the computer-readable memory produce an article of manufacture including instruction means which implement the function specified in the flowchart flow or flows and/or block diagram block or blocks.
These computer program instructions may also be loaded onto a computer or other programmable data processing apparatus to cause a series of operational steps to be performed on the computer or other programmable apparatus to produce a computer implemented process such that the instructions which execute on the computer or other programmable apparatus provide steps for implementing the functions specified in the flowchart flow or flows and/or block diagram block or blocks.
The foregoing detailed description of the application has been presented for purposes of illustration and description, and it should be understood that the application is not limited to the particular embodiments disclosed, but is intended to cover all modifications, equivalents, alternatives, and improvements within the spirit and principles of the application.

Claims (8)

1. A feedback radiation shielding analysis method, comprising the steps of:
acquiring a forward solution of forward transport of the radiation area and a concomitant solution of concomitant transport by a deterministic method based on the initial multi-group cross-section library;
determining a variance reduction parameter required by MC method calculation according to a forward solution and an accompanying solution of a radiation area;
counting and analyzing counts in forward transportation of the MC method to generate nuclear reaction macroscopic cross sections of the materials in each space region, feeding back to the initial multi-group cross section library, and forming an updated multi-group cross section library in the same format;
forward transport and accompanying transport calculation are carried out again according to the updated multi-group section library until the continuous section library used by the MC method is repeatedly updated and the difference between the continuous section library used by the MC method and the multi-group section library used by the definite theory method is reduced, and then a radiation field space distribution result obtained by the forward transport calculation of the MC method is output;
the forward transport solving equation is specifically:
wherein H represents a neutron forward transport operator; phi represents neutron fluence rate;representing neutron state phase space; q represents the source intensity of the external neutrons; />Representing a spatial gradient operator; omega represents a unit vector of neutron motion direction after collision; />Representing the spatial location; e represents neutron energy after collision; sigma (sigma) t Representing the total cross-section of neutron interaction with the medium; sigma (sigma) s A scattering cross section representing neutron interaction with a medium; e' represents neutron energy before collision; omega' represents a unit vector of neutron motion direction before collision;
the solution equation of the concomitant transport is specifically as follows:
wherein H is + Representing neutron companion transport operators; phi (phi) + Representing neutron concomitant fluence rate;representing neutron state phase space; q + Indicating the intensity of the accompanying neutron source; />Representing a spatial gradient operator; omega represents a unit vector of neutron motion direction after collision; />Representing the spatial location; e represents neutron energy after collision; sigma (sigma) t Representing the total cross-section of neutron interaction with the medium; sigma (sigma) s A scattering cross section representing neutron interaction with a medium; e' represents neutron energy before collision; Ω' represents a unit vector of the neutron motion direction before collision.
2. The feedback radiation shielding analysis method according to claim 1, wherein the accompanying solution acquisition process of the accompanying transport specifically comprises: and solving and obtaining by a deterministic method based on the initial multi-group cross-section library and the forward solution of the radiation area.
3. A feedback radiation shielding analysis method according to any of claims 1-2, wherein said deterministic method is the discrete ordinate method S N Spherical harmonic method R N Any one of a characteristic line method MOC, a penetration probability method TPM, a collision probability method CPM and a finite element method.
4. A feedback radiation-shielding analysis method according to any of claims 1-2, wherein the parameters of the variance reduction required for the calculation of the MC method comprise source bias parameters and weight window parameters.
5. The feedback radiation shielding analysis method according to any one of claims 1-2, wherein the macroscopic section of the nuclear reaction comprises a total section, an absorption section and a scattering section, and the calculation formulas of the total section, the absorption section and the scattering section are specifically as follows:
wherein σ represents a nuclear reaction cross section; x represents the nuclear reaction cross-section type, including total cross-section, absorption cross-section, scattering cross-section; d represents the spatial region; g represents neutron n energy group number; sigma (sigma) i，j For summation compliance, subscript i represents the ith neutron history, subscript j represents the jth trace in the history, and the jth free flight; WTL (WTL) i，j A weight representing the j-th neutron trajectory; e (E) i，j The energy representing the j-th neutron trajectory; iota (iota) i，j A track length representing the ith neutron j track; zeta type toy D，g As an indication function, neutrons take a value of 1 when the energy group number is g in the space D, otherwise, 0.
6. A feedback radiation shielding analysis system, comprising:
the solving and calculating module is used for acquiring a forward solution of forward transportation of the radiation area and an accompanying solution of accompanying transportation based on the initial multi-group section library by a deterministic method;
the parameter determining module is used for determining a variance reduction parameter required by MC method calculation according to the forward solution and the accompanying solution of the radiation area;
the iteration updating module is used for counting and analyzing counts in forward transportation of the MC method, generating nuclear reaction macroscopic cross sections of the materials in each space region, feeding back to the initial multi-group cross section library, and forming an updated multi-group cross section library in the same format;
the updating calculation module is used for carrying out forward transportation and accompanying transportation calculation again according to the updated multi-group section library until the continuous section library used by the MC method is iteratively updated for a plurality of times, and outputting a radiation field space distribution result obtained by the forward transportation calculation of the MC method after the difference between the continuous section library used by the MC method and the multi-group section library used by the definite theory method is reduced;
the forward transport solving equation is specifically:
wherein H represents a neutron forward transport operator; phi represents neutron fluence rate;representation ofNeutron state phase space; q represents the source intensity of the external neutrons; />Representing a spatial gradient operator; omega represents a unit vector of neutron motion direction after collision; />Representing the spatial location; e represents neutron energy after collision; sigma (sigma) t Representing the total cross-section of neutron interaction with the medium; sigma (sigma) s A scattering cross section representing neutron interaction with a medium; e' represents neutron energy before collision; omega' represents a unit vector of neutron motion direction before collision;
the solution equation of the concomitant transport is specifically as follows:
wherein H is + Representing neutron companion transport operators; phi (phi) + Representing neutron concomitant fluence rate;representing neutron state phase space; q + Indicating the intensity of the accompanying neutron source; />Representing a spatial gradient operator; omega represents a unit vector of neutron motion direction after collision; />Representing the spatial location; e represents neutron energy after collision; sigma (sigma) t Representing the total cross-section of neutron interaction with the medium; sigma (sigma) s Indicating neutron interaction with the mediumIs a scattering cross section of (2); e' represents neutron energy before collision; Ω' represents a unit vector of the neutron motion direction before collision.
7. A computer terminal comprising a memory, a processor and a computer program stored in the memory and executable on the processor, wherein the processor implements a feedback radiation shielding analysis method according to any one of claims 1-5 when executing the program.
8. A computer readable medium having stored thereon a computer program, wherein the computer program is executable by a processor to implement a feedback radiation shielding analysis method as claimed in any one of claims 1-5.
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CN104376217A (en) * 2014-11-20 2015-02-25 中国科学院合肥物质科学研究院 Radiation shielding calculation method based on monte carlo self-adaptive variance reduction
CN108549753A (en) * 2018-03-28 2018-09-18 中国船舶重工集团公司第七〇九研究所 A kind of radiation shield computational methods that Point- kernel integral method is coupled with Monte Carlo method
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