CN113609099B - Method for manufacturing fusion reactor multi-group shielding database based on Monte Carlo method - Google Patents
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Abstract
A method for manufacturing a fusion reactor multi-group shielding database based on a Monte Carlo method comprises the following steps: 1. processing the evaluation core database into an ACE (continuous energy ACE) format core database; 2. adding information in all scattering reaction channels of each nuclide in an ACE format database to obtain a continuous energy scattering response coefficient database; 3. designing a simplified one-dimensional model according to a real three-dimensional structure of a fusion reactor; 4. calculating a simplified model by adopting a Monte Carlo method based on an ACE format database and a continuous energy scattering response coefficient database; 5. obtaining a plurality of groups of high-order scattering cross sections according to the obtained low-order flux, high-order flux and high-order scattering reaction rate; 6. and combining the multiple groups of high-order scattering cross sections with a total cross section, a neutron generation cross section, an absorption cross section, a low-order scattering cross section and a response function library in the multiple groups of shielding databases to generate a new fusion reactor multiple groups of shielding databases. The data base enables the calculation of the radiation shielding of the fusion reactor to be more accurate and reduces the safety margin of the fusion reactor.
Description
Technical Field
The invention relates to the field of particle transport calculation and radiation shielding calculation, in particular to a method for manufacturing a fusion reactor multi-group shielding database based on a Monte Carlo method.
Background
In the design process of the fusion reactor, the calculation of radiation shielding of a reactor core and a factory building is a critical task. The current radiation shielding calculation adopts two main methods: a monte carlo method based on a continuous energy database; a determinism method based on multi-group shielding database. The basic idea of the determinism method is to disperse space, angle and energy, solve a particle transport equation after dispersion and approach continuous distribution by using discrete grid distribution.
When the determinism method is adopted to solve the particle transport equation, the emergent angle of the particles after each scattering can be processed according to a function expansion method. The zero-order expansion coefficient of the angular flux density in the particle transport equation is proved to be the particle flux density of the full-angle space integral, or called low-order flux; the higher order flux is when the expansion coefficient is greater than or equal to the first order. And performing function expansion on the scattering cross section, wherein the expansion coefficient is zero order, namely the low order scattering cross section, and the expansion coefficient is more than or equal to first order, namely the high order scattering cross section.
And a plurality of groups of shielding databases are databases which adopt weighted average of weight functions and are distributed discretely along with energy segments. The selection of the weighting function directly affects the accuracy of the multi-cluster masking database. When a multi-cluster shielding database is manufactured, a calculation model needs to be simplified to obtain a simplified model, then the simplified model is calculated, and flux density in the simplified model is used as a weight function to carry out weighted average. Methods for creating multi-cluster databases can be divided into two broad categories, depending on the method used in computing the simplified model. The first is a method for making a multi-group shielding database based on the determinism, and the second is a method for making a multi-group shielding database based on the statistics. A method for manufacturing a multi-group shielding database based on statistics is characterized in that a Monte Carlo method is adopted to calculate a simplified model, and flux density and reaction rates of various reactions, such as total reaction rate, absorption reaction rate, scattering reaction rate, high-order scattering reaction rate and the like, in the simplified model are obtained through statistics. The method is based on a continuous energy database, directly simulates the transportation process of particles, does not carry out equation dispersion, and avoids errors caused by dispersion.
However, the conventional statistical-based method for creating a multi-cluster mask database, which is referred to as a conventional statistical method, has some problems. First, the dimension of the higher order scattering reactivity is larger than the dimensions of other reactivity, and under the same calculation condition, the statistical fluctuation of the higher order scattering reactivity is larger and the convergence is more difficult. Secondly, theoretically, a high-order scattering cross section should be obtained based on high-order flux, but the high-order scattering cross section is still obtained based on low-order flux by the conventional statistical method at present, so that systematic deviation exists in the high-order scattering cross section obtained by the conventional statistical method, the manufactured fusion reactor multi-group shielding database is not accurate enough, more safety margins need to be considered during design of a fusion reactor radiation shielding, and the economy of the design of the fusion reactor radiation shielding is reduced.
Disclosure of Invention
In order to overcome the problems in the prior art, the invention aims to provide a method for manufacturing a fusion reactor multi-group shielding database based on a monte carlo method. And when Monte Carlo simulation of the fusion reactor simplified model is carried out, counting to obtain the high-order scattering reaction rate. The continuous energy scattering response coefficient database avoids the reaction channel sampling which is necessary for obtaining the high-order scattering reaction rate in the traditional statistical method, thereby reducing the statistical dimension of the high-order scattering reaction rate and reducing the statistical fluctuation of the high-order scattering reaction rate. Meanwhile, the method obtains a statistical formula of high-order flux based on infinite homogeneous medium approximation and zero-order curvature approximation, can directly obtain high-order flux while obtaining low-order flux, and can obtain multiple groups of high-order scattering cross sections by substituting the obtained high-order flux into a solving formula of the high-order scattering cross sections, thereby ensuring the consistency of program development and theoretical derivation.
In order to achieve the purpose, the invention adopts the following technical scheme to implement:
a method for manufacturing a fusion reactor multi-group shielding database based on a Monte Carlo method comprises the following steps:
step 1: processing the evaluation core database into an ACE (adaptive communication environment) format core database, which is called an ACE format database for short, by using core database processing software;
step 2: adding information in all scattering reaction channels of each nuclide in an ACE format database to obtain a continuous energy scattering response coefficient database, and recording the scattering response coefficient h of each nuclide with the expansion coefficient order of k, the number of i and the emergent energy group number of g of each energy point E i,k,g (E′)；
And step 3: according to the real three-dimensional structure of the fusion reactor, a simplified one-dimensional model is designed, namely the simplified model, and material regions of the simplified model are sequentially from left to right: stainless steel, vacuum, stainless steel, water, a multiplication plate, a neutron multiplication plate, vacuum, the neutron multiplication plate, the multiplication plate, water, stainless steel, vacuum, stainless steel and a coil, wherein the size of a material area in the simplified model is consistent with that of a material area corresponding to the real three-dimensional structure of the fusion reactor, and the material components of the material area are obtained by mixing materials in the material area corresponding to the real three-dimensional structure of the fusion reactor according to the principle of mass conservation and substance conservation;
and 4, step 4: calculating a simplified model by adopting a Monte Carlo method based on an ACE format database and a continuous energy scattering response coefficient database to obtain energy cluster-related low-order flux, high-order flux and high-order scattering reaction rate information; for the mth walk, the track length Deltal of the neutron in the material area is randomly extracted firstly m Counting the high-order flux and the high-order scattering reaction rate according to the track length; the statistical formula for the flux of the higher order is shown as formula (1), and the statistical formula for the reaction rate of the higher order scattering is shown as formula (2);
in the formula:
k-the order of the expansion coefficient;
g' - -incident energy group number;
φ k,g′ -a high order flux of the g' th energy group with an order of expansion coefficient k;
w- -the total weight of the initial neutrons;
n- - -the total number of initial neutrons;
n- - -the number of neutrons currently simulated;
M n -the total number of traces of the nth neutron;
m- - -the mth walk of the nth neutron;
wgt n,m -weight of mth walk of nth neutron;
Δl n,m -the trace length resulting from the mth walk of the nth neutron;
i-total number of species of nuclear in the fusion reactor material region;
i-numbering of nuclides in the fusion reactor material region;
D i -density of species i in the fusion reactor material region;
E m -the energy at the m-th walk of the nth neutron;
σ t,i (E m ) -the i-th nuclear species having an energy point E m A microscopic total cross-section of (a);
E g′-1 -the g' th lower energy band limit;
E g′ -the upper energy limit of the g' th energy cluster;
In the formula:
s- - -scattering cross section;
g- - -emergent energy group numbering;
R s,g′→g,k,i -a higher order scattering reactivity of the i nuclide scattered from the g 'th energy cluster to the g' th energy cluster with an expansion coefficient order of k;
h i,k,g (E m ) Incident energy of the ith nuclear species E m The number of the emergent energy group is g, and the order of the expansion coefficient is k;
And 5: obtaining a plurality of groups of high-order scattering cross sections according to the low-order flux, the high-order flux and the high-order scattering reaction rate obtained in the step (4), wherein a calculation formula is shown as a formula (3);
in the formula:
σ s,g′→g,k,i -a scattering cross section of the ith nuclear species scattering from the g 'th energy cluster to the g' th energy cluster with an expansion coefficient order of k;
and 6: and (4) combining the multiple groups of high-order scattering cross sections obtained in the step (5) with a total cross section, a neutron generation cross section, an absorption cross section, a low-order scattering cross section and a response function library in a multiple group shielding database to generate a new fusion reactor multiple group shielding database.
Compared with the prior art, the invention has the following advantages:
1. compared with a method for obtaining a plurality of groups of high-order scattering cross sections through low-order flux and high-order scattering reaction rate in the traditional statistical method, the method adopts the high-order flux and the high-order scattering reaction rate to obtain the plurality of groups of high-order scattering cross sections, and therefore consistency of program development and theoretical derivation is guaranteed.
2. The fusion reactor multi-group shielding database manufactured based on the method has higher calculation precision, so that the calculation result of the fusion reactor radiation shielding is more accurate, the safety margin of the fusion reactor radiation shielding is reduced, and the economy of the design of the fusion reactor radiation shielding is improved.
Drawings
FIG. 1 is a method for manufacturing a fusion reactor multi-group shielding database based on a Monte Carlo method.
FIG. 2 is a schematic diagram of a one-dimensional simplified model of a fusion reactor.
Detailed Description
The invention is described in further detail below with reference to the following figures and specific examples:
as shown in FIG. 1, the method for manufacturing the fusion reactor multi-group shielding database based on the Monte Carlo method comprises the following steps:
step 1: and processing an evaluation core database, such as an ENDF database, into a continuous energy database, namely an ACE format database, by utilizing core database processing software. The main work of general machining is divided into three parts. Firstly, compressing information in an evaluation kernel database on the premise of meeting linear interpolation; secondly, processing the data of the indistinguishable resonance area into a probability table; and finally, copying other data from the evaluation core database and storing the data into the ACE format database. In ACE format databases, the number of energy grids can reach tens or even hundreds of thousands. The ACE format database includes the following information: total cross section, elastic scattering cross section and absorption cross section under each energy point of different nuclides; the section of each neutron reaction channel changing along with energy, the type of the emergent particles, the energy distribution rule of the emergent particles and the angle distribution rule of the emergent particles; information blocks such as the energy distribution rule of delayed fission neutrons and the angle distribution rule of delayed fission neutrons.
And 2, step: and processing all scattering reaction channels of each nuclide according to data in the ACE format database, wherein the data comprises the section of the neutron reaction channel changing along with energy, the type of the emergent particle, the energy distribution rule of the emergent particle and the angle distribution rule of the emergent particle, and a continuous energy scattering response coefficient database is obtained. The processing formula is as shown in formula (4).
In the formula:
e' - -energy of incident neutrons;
e- -energy of the outgoing neutron;
E g-1 -the lower energy group;
E g -the upper energy limit of the g-th energy cluster;
h i,k,g (E ') - - - -scattering response coefficient value for the ith nuclide, for an incident energy E', an emergent energy group number g, and an expansion coefficient order k;
MT- - -number of scattering reaction channel;
Y i,MT -the neutron yield of the scattering reaction channel of the i-th nuclide, numbered MT;
σ i,MT (E ') - - -the reaction cross-section of the i-th nuclide with reaction channel number MT and incident energy E';
mu- - - -scattering angle, i.e. cosine value of the angle between the emergent direction and the incident direction;
f i,MT reaction cross section of (E '→ E, mu) - - -i-th nuclide, with reaction channel number MT, incident energy E' and emergent energy E, and scattering included angle mu;
P k a spherical harmonic value with the (mu) - - -expansion coefficient order of k and the scattering included angle of mu;
the scattering reaction channels can be divided into inelastic scattering reaction channels, elastic scattering reaction channels, and thermal scattering of molecules and crystals. For different inelastic scattering reaction channels, the ACE format database describes the energy distribution rule and the angle distribution rule of the emergent particles by using different rules. F of different scattering reaction channels i,MT (E' → E, μ) are different, but equation (4) ensures that the scatter information for each species, including the higher order scatter information, is not lost. Thus, the continuous energy scattering response coefficient database can be used to obtain higher order scattering responsivity.
And step 3: according to the real three-dimensional structure of the fusion reactor, a simplified one-dimensional model is designed, namely the simplified model, as shown in fig. 2, the material regions of the simplified model are as follows from left to right: the size of a material area in the simplified model is consistent with that of a material area corresponding to the real three-dimensional structure of the fusion reactor, and the material components of the material area are obtained by mixing materials of the material area corresponding to the real three-dimensional structure of the fusion reactor according to the principle of mass conservation and substance conservation. The blending formula is shown in formula (5).
In the formula:
z- - -feature region number of the simplified model;
k is the material area number in the real three-dimensional structure of the fusion reactor;
D i,z -the nuclear density of the ith species in the z-th characteristic region of the simplified model;
D i,k,z -nuclear density of the ith species in the kth material region in the true three-dimensional structure of the corresponding fusion reactor within the z-th characteristic region of the simplified model;
K z -the number of material regions in the true three-dimensional structure of the fusion reactor contained in the z-th characteristic region of the simplified model;
V k,z -simplifying the volume of the kth material region within the z-th characteristic region of the model;
S z -the area of the z-th feature region of the simplified model;
and 4, step 4: and calculating a simplified model by adopting a Monte Carlo method based on an ACE format database and a continuous energy scattering response coefficient database to obtain energy cluster-related low-order flux, high-order flux and high-order scattering reaction rate. By adopting the random walk idea, for the mth walk, the track length of the neutron in the material area is firstly randomly extracted, and the sampling formula is shown as formula (6). After extracting the track length of the neutron in the material area, moving the neutron along the motion direction of the neutron, and calculating the new position of the neutron according to the formula (7). And at the new position, extracting the reaction channels in which the reaction occurs according to the section information of each reaction channel stored in the ACE format database. And sampling the energy and the angle of the emergent neutrons according to the physical law of the extracted reaction channel. And carrying out the next wandering according to the energy and the angle of the emergent neutrons.
Δl n,m ＝-lnξ/∑ t (E m ) Formula (6)
In the formula:
ξ - -a pseudo-random number generated by a pseudo-random number generator;
∑ t (E m ) -neutron energy of E m The total cross section of the material;
in the formula:
in the process of simulating the migration of neutrons, different methods can be adopted to count the neutron flux and the reaction rate of various reactions. Taking the track length counting method as an example, the method is used for counting neutron flux, namely a formula for counting low-order flux is shown as a formula (8), a formula for counting high-order flux is shown as a formula (1), and a formula for counting high-order scattering reaction rate is shown as a formula (2).
In the formula:
φ 0,g′ - - -energy groupA plurality of groups of low order fluxes numbered g';
And 5: and (5) obtaining a plurality of groups of high-order scattering cross sections according to the low-order flux, the high-order flux and the high-order scattering reaction rate obtained in the step (4), wherein the calculation formula is shown as a formula (3).
In the formula:
σ s,g′→g,k,i -a scattering cross section of the ith nuclear species scattered from the g 'th energy cluster to the g' th energy cluster with an expansion coefficient order of k;
step 6: and (4) combining the multiple groups of high-order scattering cross sections obtained in the step (5) with a total cross section, a neutron generation cross section, an absorption cross section, a low-order scattering cross section and a response function library in a multiple group shielding database to generate a new fusion reactor multiple group shielding database. The multi-group shielding database can be used for subsequent fusion reactor shielding calculation based on a determinism method, and the shielding calculation precision of the multi-group shielding database is improved.
Claims (1)
1. A method for manufacturing a fusion reactor multi-group shielding database based on a Monte Carlo method is characterized by comprising the following steps: the method comprises the following steps:
step 1: processing the evaluation core database into an ACE (adaptive communication environment) format core database, which is called an ACE format database for short, by using core database processing software;
step 2: adding the information in all scattering reaction channels of each nuclide in an ACE format database to obtain a continuous energy scattering response coefficient database, wherein the expansion coefficient order of each energy point E' is k,The scattering response coefficient of a nuclide with the number i and the number g of the emergent energy group is recorded as h i,k,g (E′)；
And step 3: according to the real three-dimensional structure of the fusion reactor, a simplified one-dimensional model is designed, namely the simplified model, and material regions of the simplified model are sequentially from left to right: stainless steel, vacuum, stainless steel, water, a multiplication plate, a neutron multiplication plate, vacuum, the neutron multiplication plate, the multiplication plate, water, stainless steel, vacuum, stainless steel and a coil, wherein the size of a material area in the simplified model is consistent with that of a material area corresponding to the real three-dimensional structure of the fusion reactor, and the material components of the material area are obtained by mixing materials in the material area corresponding to the real three-dimensional structure of the fusion reactor according to the principle of mass conservation and substance conservation;
and 4, step 4: calculating a simplified model by adopting a Monte Carlo method based on an ACE format database and a continuous energy scattering response coefficient database to obtain energy cluster-related low-order flux, high-order flux and high-order scattering reaction rate information; for the mth walk, the track length Deltal of the neutron in the material area is randomly extracted firstly m Counting the high-order flux and the high-order scattering reaction rate according to the track length; the statistical formula for the flux of higher order is shown as formula (1), and the statistical formula for the reaction rate of higher order scattering is shown as formula (2);
in the formula:
k-the order of the expansion coefficient;
g' - -incident energy group number;
φ k,g′ -a high order flux of the g' th energy group with an order of expansion coefficient k;
w- -the total weight of the initial neutrons;
n- - -the total number of initial neutrons;
n- - -the number of neutrons currently simulated;
M n -the total number of traces of the nth neutron;
m- - -the mth walk of the nth neutron;
wgt n,m -the weight of the mth walk of the nth neutron;
Δl n,m -the trace length resulting from the mth walk of the nth neutron;
i-total number of species of nuclear in the fusion reactor material region;
i- - -numbering of nuclides in the fusion reactor material zone;
D i -density of species i in the fusion reactor material region;
E m -the energy at the m-th walk of the nth neutron;
σ t,i (E m ) -the i-th nuclear species having an energy point E m A microscopic total cross-section of;
E g′-1 -the g' th lower energy group boundary;
E g′ -the upper energy limit of the g' th energy cluster;
In the formula:
s- - -scattering cross section;
g- - -exit energy group numbering;
R s,g′→g,k,i -a higher order scattering reactivity of the i nuclide scattered from the g 'th energy cluster to the g' th energy cluster with an expansion coefficient order of k;
h i,k,g (E m ) Incident energy of the ith nuclear species E m Is emitted outA scattering response coefficient value with an energy group number of g and an expansion coefficient order of k;
And 5: obtaining a plurality of groups of high-order scattering cross sections according to the low-order flux, the high-order flux and the high-order scattering reaction rate obtained in the step (4), wherein a calculation formula is shown as a formula (3);
in the formula:
σ s,g′→g,k,i -a scattering cross section of the ith nuclear species scattered from the g 'th energy cluster to the g' th energy cluster with an expansion coefficient order of k;
step 6: and (4) combining the multiple groups of high-order scattering cross sections obtained in the step (5) with a total cross section, a neutron generation cross section, an absorption cross section, a low-order scattering cross section and a response function library in a multiple group shielding database to generate a new fusion reactor multiple group shielding database.
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