CN106128518A - A kind of method obtaining the few group cross-section of high-precision fast neutron reaction pile component - Google Patents

A kind of method obtaining the few group cross-section of high-precision fast neutron reaction pile component Download PDF

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Publication number
CN106128518A
CN106128518A CN201610472890.5A CN201610472890A CN106128518A CN 106128518 A CN106128518 A CN 106128518A CN 201610472890 A CN201610472890 A CN 201610472890A CN 106128518 A CN106128518 A CN 106128518A
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section
group
cross
formula
nucleic
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郑友琦
杜夏楠
曹良志
李云召
吴宏春
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Xian Jiaotong University
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    • G—PHYSICS
    • G21—NUCLEAR PHYSICS; NUCLEAR ENGINEERING
    • G21C—NUCLEAR REACTORS
    • G21C5/00—Moderator or core structure; Selection of materials for use as moderator
    • G—PHYSICS
    • G21—NUCLEAR PHYSICS; NUCLEAR ENGINEERING
    • G21C—NUCLEAR REACTORS
    • G21C1/00—Reactor types
    • G21C1/02—Fast fission reactors, i.e. reactors not using a moderator ; Metal cooled reactors; Fast breeders
    • Y—GENERAL TAGGING OF NEW TECHNOLOGICAL DEVELOPMENTS; GENERAL TAGGING OF CROSS-SECTIONAL TECHNOLOGIES SPANNING OVER SEVERAL SECTIONS OF THE IPC; TECHNICAL SUBJECTS COVERED BY FORMER USPC CROSS-REFERENCE ART COLLECTIONS [XRACs] AND DIGESTS
    • Y02—TECHNOLOGIES OR APPLICATIONS FOR MITIGATION OR ADAPTATION AGAINST CLIMATE CHANGE
    • Y02E—REDUCTION OF GREENHOUSE GAS [GHG] EMISSIONS, RELATED TO ENERGY GENERATION, TRANSMISSION OR DISTRIBUTION
    • Y02E30/00—Energy generation of nuclear origin
    • Y02E30/30—Nuclear fission reactors

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  • Engineering & Computer Science (AREA)
  • Plasma & Fusion (AREA)
  • General Engineering & Computer Science (AREA)
  • High Energy & Nuclear Physics (AREA)
  • Monitoring And Testing Of Nuclear Reactors (AREA)

Abstract

A kind of method obtaining the few group cross-section of high-precision fast neutron reaction pile component, the thin group cross-section of fast neutron reactor assembly is calculated by the way of using some cross-section data and Multi-group data to combine, at line computation elastic scattering matrix, and use thin group cross-section solve neutron-transport equation obtain thin group's netron-flux density, and with this merger energy group thus obtain the Few group parameter of fast pile component；Directly use a cross-section data due to the method, elastic scattering resonance effect and the resonance interference method effect of all nucleic that mean quality nucleic is had accurately are considered；Employing the netron-flux density of real system during energy group's merger, merger result is the most accurate；The inventive method calculated fast neutron reaction pile component Few group parameter is compared with reference value, and error is overall within 1%, has higher precision.

Description

A kind of method obtaining the few group cross-section of high-precision fast neutron reaction pile component
Technical field
The present invention relates to nuclear reactor design and nuclear reactor physical computing field, be specifically related to a kind of acquisition high-precision The method of the few group cross-section of the fast neutron reaction pile component of degree.
Background technology
The development of fast reactor at present is in the pre-designed and experimental stage, in order to solve reactor core neutronics parameter quickly and accurately, Method based on " two-step method " becomes the main method of fast reactor engineering calculation.So-called " two-step method ", the first step is each to heap in-core Kind assembly material carries out multigroup neutron transport calculating, it is thus achieved that the netron-flux density in assembly is distributed thus merger goes out to lack group uniform Change group cross-section；Second step is by back calculated homogenization parameter, reactor core to be carried out few group of neutron-transport equations to ask Solve, obtain the physical quantity such as reactor core Effective multiplication factor, core power distribution.
In fast reactor, the material such as rustless steel, liquid metal sodium is relatively conventional and the material that exists in a large number, these nucleic Elastic scattering cross-section there is extremely strong elastic scattering resonance effect.The fastest owing to there is the energy area of elastic scattering resonance The region that the distribution of neutron reactor netron-flux density is concentrated, it is necessary to accurately consider this effect.Additionally, due to cause fission reaction For fast neutron, and threshold energy reaction has the cross section value with elastic scattering cross-section same order, and threshold energy is reacted and also should be paid attention to；? After, not only heavy nucleus have resonance effect, and the nucleic of medium atomic mass also has resonance effect, and in material, the resonance of many nucleic is done Relating to effect also answers emphasis to consider.So-called resonance interference method effect, refers to two or more nucleic with resonance effect, its The overlapped impact caused of formant.
On the other hand, fast neutron has longer mean free path, and its non-uniformed effect is the most weak, in the power spectrum of assembly Calculating considering, uniformity problem is obtained with sufficiently high precision.So-called heterogeneous effect, refers to be situated between due to different in space Matter such as fuel is different with the cross section of coolant value, and in different medium, Neutron flux distribution has significant difference.
At present, " two-step method " has been widely used at thermal reactor (such as presurized water reactor) and has obtained the accreditation of industrial quarters, and has very Ripe software for calculation.But owing to fast reactor and thermal reactor exist greatly difference, the method that these programs are used on neutrons characteristic It is the calculating being unsuitable for fast neutron reactor, it is therefore desirable to exploitation one can obtain the few group of high-precision fast neutron reactor The method in cross section.
Summary of the invention
For the problem overcoming above-mentioned prior art to exist, it is an object of the invention to provide a kind of acquisition high-precision soon The method of the few group cross-section of neutron reaction pile component, in order to obtain the few group cross-section of accurate fast neutron reactor assembly, the inventive method will It is distributed based on netron-flux density in a cross section information computation module, carries out group's merger to obtain few group cross-section parameter with this, it The parameter of the few group cross-section of assembly can be calculated efficiently, accurately, provide reliable data for reactor core Neutronics calculation.
In order to realize object above, the present invention takes following technical scheme:
A kind of method obtaining the few group cross-section of high-precision fast neutron reaction pile component, comprises the steps:
Step 1: for the arbitrary fast pile component of required calculating, reads information in Multi-group data storehouse, including total cross section, non-ballistic Property scattering section matrix, neutron fission spectrum, every time fission release neutron population, the macroscopic view utilizing formula (2) computation module is non-resilient Collision matrix, utilizes formula (3) to calculate the dilution cross section value of each nucleic；
In formula:
G group is to macroscopical inelastic scattering cross section matrix of g ' group
NiThe nucleon density of the nucleic
The nucleic g group is to the inelastic scattering cross section matrix of g ' group
The thin group energy group identification number of g g '
In formula:
The dilution cross section of nucleic
Nucleic microcosmic total cross section
NjThe nucleon density of nucleic
Step 2: for the arbitrary fast pile component of required calculating, reads some library of cross section information, including total cross section, elasticity Scattering section, fission cross section and can not differentiate the interpolation table of resonance region, the microcosmic utilizing formula (5) to calculate thin group the most always cuts Face, microcosmic average proof resilience scattering section, microcosmic Average Fission cross section, utilize the dilute of calculated each nucleic in step 1 The interpolation table that releasing cross section provides according to data base carries out interpolation；
In formula:
The averga cross section of g group, x is response type
ΣtThe volumic total cross-section of system
ΔEgG group's can group interval
Step 3: the microcosmic average proof resilience scattering section of each nucleic provided by step 2, utilizes formula (8) to calculate each The elastic scattering cross-section matrix of individual nucleic, utilizes formula (10) to calculate macroscopic view elastic scattering cross-section matrix, and calculates with step 1 To macroscopical inelastic scattering cross section matrix add and, utilize formula (11) to calculate macroscopic scattering cross section matrix；
In formula:
L rank are scattered to the elastic scattering cross-section of g ' group by g group
σs,gThe elastic scattering cross-section of g group
α——(A-1)2/(A+1)2, A is the atomic mass of nucleic
μcAngle of scattering cosine value under geocentric coordinate system
f(E,μc) probability of scattering function
Pl(μs) about μsRank Legnedre polynomial
μsAngle of scattering cosine value under laboratory coordinate
In formula:
L rank g group is to macroscopical elastic scattering cross-section matrix of g ' group
L rank the nucleic g group is to the elastic scattering cross-section matrix of g ' group
In formula:
L rank g group is to the macroscopic scattering cross section matrix of g ' group
Step 4: obtained the average total cross section of microcosmic of fast pile component, macroscopic scattering cross section matrix, micro-by step 2 and step 3 See Average Fission cross section, utilize formula (12) to carry out solving of neutron-transport equation, it is thus achieved that the Neutron flux distribution of thin group, utilize The Neutron flux distribution tried to achieve uses formula (13) and (14) to carry out energy group's merger in cross section, it is thus achieved that has high-precision few group and cuts Face amount；
In formula:
The critical buckling of B system
χgThe neutron fission spectrum of g group
υ fissions release neutron population every time
keffThe Effective multiplication factor of system
G order of a group netron-flux density is distributed
A n = b n - 1 + a n A n + 1
a n = n + 1 2 n + 1 n + 1 2 ( n + 1 ) + 1 B 2
b n = Σ t - Σ s n + 1
In formula:
The few group energy group identification number of G
Belong to the thin group g of the few group of G.
Compared with prior art, the present invention has a following prominent advantage:
1. utilize the flow process of the thin group cross-section of the some library of cross section fast pile component of making, finely consider mean quality nucleic The elastic scattering resonance effect strongly that exists in middle high-energy interval and all nucleic are all can being total to of having of section Shake interference effect.
2. when being thin group cross-section by a cross-section aggregation, it is provided that the real netron-flux density of this problem is distributed.
3. calculate thin group's netron-flux density distribution of fast pile component and with this merger cross section, i.e. save the calculating time, again There is enough precision.
Accompanying drawing explanation
Fig. 1 is the flow chart utilizing the few group cross-section of some Cross section calculation.
Fig. 2 is that iterative nucleic dilutes schematic cross-section.
Fig. 3 is 26 groups of volumic total cross-sections and error thereof.
Detailed description of the invention
With detailed description of the invention, the present invention is described in further detail below in conjunction with the accompanying drawings:
The present invention, by directly using some cross-section file, finely considers resonance effect present in fast pile component, carries out all Solving of even problem neutron-transport equation, it is thus achieved that the true Neutron flux distribution of assembly, carries out energy group's merger with this, thus obtains Accurate group cross-section parameter less, as it is shown in figure 1, this invention comprises the steps:
Step 1: for the arbitrary fast pile component of required calculating, reads information in Multi-group data storehouse, including total cross section, non-ballistic Property scattering section, neutron fission spectrum, every time fission release neutron population, first pair cross-section carry out temperature interpolation, wherein, cross section Temperature interpolation follow regularity, as shown in formula (1):
In formula:
σ cross section
X response type, such as total cross section
T temperature
Subscript 3 is interpolated temperature spot
Subscript 1,2 interpolated temperature point
Utilize the inelastic scattering matrix of each nucleic under the specified temp that interpolation obtains, utilize formula (2) to be calculated group Macroscopical inelastic scattering matrix of part.
In formula:
G group is to macroscopical inelastic scattering cross section matrix of g ' group
NiThe nucleon density of the nucleic
The nucleic g group is to the inelastic scattering cross section matrix of g ' group
Subsequently, calculating the dilution cross section value of each nucleic, for nucleic, its dilution cross section is defined by formula (3).
In formula:
The dilution cross section of nucleic
Nucleic microcosmic total cross section
NjThe nucleon density of nucleic
In formula (3), dilution cross section is to be determined by the total cross section of other nucleic, and after the dilution cross section of this nucleic determines Can retrieve again the total cross section value under this dilution cross section, whole process needs to be iterated calculating, total when this problem final Iteration convergence is thought when macroscopic cross section changes hardly.Dilute the iterative process of Cross section calculation as shown in Figure 2:
1) initialize the initial value in the dilution cross section of all nucleic, enter according to formula (4) according to this Initial dilution cross section value Row interpolation calculates, and obtains the total cross section value of each nucleic；
2) according to the new total cross section value of each nucleic, recycling formula (3) calculates the dilution cross section value that all nucleic are new；
3) again by newly generated dilution cross section according to formula (4) calculate total cross section value；
4) think that when the total cross section relative deviation of twice calculating is less than 0.000001 calculating restrains, and otherwise proceeds Calculate.
Formula (4) provides log-log interpolation rule.
In formula:
σxThe cross section of a certain reaction, such as total cross section
σ0Dilution cross section
Subscript 3 interpolated point
Subscript 1,2 interpolation point
Step 2: for the arbitrary fast pile component of required calculating, reads some library of cross section information, including total cross section, elasticity Scattering section, fission cross section and the interpolation table of resonance region can not be differentiated；For being positioned at the cross section that can not differentiate resonance region, utilize step The dilution cross section of each nucleic obtained after rapid 1 calculating convergence, can calculate each nucleic inseparable by the way of interpolation Distinguish the total cross section of resonance region, fission cross section, elastic scattering cross-section, thus obtain the some cross section information of the all-round section of all nucleic. Owing in each nucleic point cross section, the number of energy point differs, therefore the some cross section of each nucleic all can section carried out linearly Interpolation calculation, obtains the some cross section value under equal energy point.Based on narrow resonance approximation, the multigroup cross section of each nucleic can be by formula (5) determine.So-called narrow resonance approximation, refers to that the width of formant is sufficiently narrow, is too narrow to lose less than after neutron generation elastic scattering Energy width.
In formula:
The averga cross section of g group, x is response type, such as total cross section etc.
ΣtThe volumic total cross-section of system
ΔEgG group's can group interval
Utilize formula (5) can calculate the average total cross section of thin group, average proof resilience scattering section, Average Fission cut Face；
Step 3: the microcosmic average proof resilience scattering section value of each nucleic provided by step 2, utilizes formula (8) to calculate The elastic scattering cross-section matrix of each nucleic, utilizes formula (10) to calculate macroscopical elastic scattering cross-section matrix of this problem, and with Step 1 calculated macroscopic view inelastic scattering cross section matrix add and, utilize formula (11) to calculate macroscopic scattering cross section matrix；
General, after the neutron generation elastic scattering reaction that projectile energy is, when outgoing neutron energy is, scattering section can Determined by following formula:
In formula:
σs(E → E ') is scattered to the elastic scattering cross-section of energy point E ' by energy point E
α——(A-1)2/(A+1)2, A is the atomic mass of nucleic
μcAngle of scattering cosine value under geocentric coordinate system
f(E,μc) probability of scattering function
Formula (6) is carried out the integration on energy group, i.e. can get the group elastic scattering cross-section to group, such as following formula:
In formula:
φgThe netron-flux density distribution of g group
Strict solution formula (7), by consuming the more time, on the basis of the many group structures of thin group, can introduce approximation, recognize Constant for netron-flux density and cross section on a certain energy group, then formula (7) can be reduced to:
In formula:
σs(g → g ') is scattered to the elastic scattering cross-section of g ' group by g group
σs,gThe elastic scattering cross-section of g group
After elastic scattering cross-section is according to Legendre polynomial expansion, the scattering section on its each rank is represented by:
In formula:
Rank scattering section
Pl(μs) about μsRank Legnedre polynomial
μsAngle of scattering cosine value under laboratory coordinate
Final according to formula (9), elastic scattering cross-section, each rank matrix of all nucleic can be obtained, thus utilize formula (10) Calculate macroscopic view elastic scattering cross-section, each rank matrix of system, add and cut by step 2 calculated macroscopic view inelastic scattering Face matrix, utilizes formula (11) i.e. to can get the macroscopic scattering cross section matrix of system.
In formula:
L rank g group is to macroscopical elastic scattering cross-section matrix of g ' group
L rank the nucleic g group is to the elastic scattering cross-section matrix of g ' group
In formula:
L rank g group is to the macroscopic scattering cross section matrix of g ' group
Step 4: obtained the average total cross section of microcosmic of fast pile component, macroscopic scattering cross section matrix, micro-by step 2 and step 3 See Average Fission cross section, for the fast pile component calculated, utilize formula (12) to solve multigroup neutron-transport equation the most available Thin group's multigroup netron-flux density distribution of this problem:
In formula:
The critical buckling of B system
χgThe neutron fission spectrum of g group
υ fissions release neutron population every time
keffThe Effective multiplication factor of system
G order of a group netron-flux density is distributed
A n = b n - 1 + a n A n + 1
a n = n + 1 2 n + 1 n + 1 2 ( n + 1 ) + 1 B 2
b n = Σ t - Σ s n + 1
After obtaining netron-flux density distribution, then through energy group's merger, finally can obtain few group part of this fast pile component Cross section parameter.Utilize netron-flux density can be drawn by formula (13), (14) as the calculating of weight merger few group cross-section parameter. Wherein, formula (13) is used for merger total cross section, neutron production cross section, and formula (14) is used for the collision matrix on merger rank.
In formula:
The few group energy group identification number of G
Belong to the thin group g of the few group of G
Fig. 3 illustrates and utilizes the present invention calculated one 26 groups of volumic total cross-sections of fast pile component and use Monte Carlo side 26 group cross-sections that method calculates and error between the two.Preliminary result of calculation shows, utilizes the present invention calculated Few group cross-section is with compared with solution, and the cross section relative error of almost all energy group is within 1%, at indivedual energy that energy is relatively low Group, error control is within 3%.Owing to the netron-flux density of energy lower is distributed the lowest, this error is acceptable 's.Utilize accurately lack group cross-section, it is possible to carry out the various Neutronics calculations of fast reactor reactor core, as stable state calculate, burnup calculate, Transient state calculating etc..The present invention both the highest available precision, computational efficiency Monte Carlo method to be significantly larger than, can be applicable to reality simultaneously In the middle of the engineering calculation on border.

Claims (1)

1. the method obtaining the few group cross-section of high-precision fast neutron reaction pile component, it is characterised in that: comprise the steps:
Step 1: for the arbitrary fast pile component of required calculating, reads information in Multi-group data storehouse, including total cross section, non-resilient dissipates Penetrate cross section matrix, neutron fission spectrum, every time fission release neutron population, utilize macroscopical inelastic scattering of formula (2) computation module Matrix, utilizes formula (3) to calculate the dilution cross section value of each nucleic；
In formula:
G group is to macroscopical inelastic scattering cross section matrix of g ' group
NiThe nucleon density of the nucleic
The nucleic g group is to the inelastic scattering cross section matrix of g ' group
G g' thin group energy group identification number
In formula:
The dilution cross section of nucleic
Nucleic microcosmic total cross section
NjThe nucleon density of nucleic
Step 2: for the arbitrary fast pile component of required calculating, reads some library of cross section information, including total cross section, elastic scattering Cross section, fission cross section and the interpolation table of resonance region can not be differentiated, utilize formula (5) calculate thin group the average total cross section of microcosmic, Microcosmic average proof resilience scattering section, microcosmic Average Fission cross section, utilize the dilution of calculated each nucleic in step 1 to cut The interpolation table that face provides according to data base carries out interpolation；
In formula:
The averga cross section of g group, x is response type
ΣtThe volumic total cross-section of system
ΔEgG group's can group interval
Step 3: the microcosmic average proof resilience scattering section of each nucleic provided by step 2, utilizes formula (8) to calculate each core The elastic scattering cross-section matrix of element, utilizes formula (10) to calculate macroscopic view elastic scattering cross-section matrix, and calculated with step 1 Macroscopic view inelastic scattering cross section matrix add and, utilize formula (11) to calculate macroscopic scattering cross section matrix；
In formula:
L rank are scattered to the elastic scattering cross-section σ of g ' group by g groups,gThe elasticity of g group dissipates Penetrate cross section
α——(A-1)2/(A+1)2, A is the atomic mass of nucleic
μcAngle of scattering cosine value under geocentric coordinate system
f(E,μc) probability of scattering function
Pl(μs) about μsRank Legnedre polynomial
μsAngle of scattering cosine value under laboratory coordinate
In formula:
L rank g group is to macroscopical elastic scattering cross-section matrix of g ' group
L rank the nucleic g group is to the elastic scattering cross-section matrix of g ' group
In formula:
L rank g group is to the macroscopic scattering cross section matrix of g ' group
Step 4: obtained the average total cross section of microcosmic of fast pile component by step 2 and step 3, macroscopic scattering cross section matrix, microcosmic are put down All fission cross section, utilizes formula (12) to carry out solving of neutron-transport equation, it is thus achieved that the Neutron flux distribution of thin group, utilization is tried to achieve Neutron flux distribution use that formula (13) and (14) carries out cross section can group's merger, it is thus achieved that there is high-precision few group cross-section Value；
iBφ 1 g + Σ t g φ 0 g = Σ g ′ Σ s , 0 g ′ → g φ 0 g ′ + χ g k e f f Σ g ′ υΣ f g ′ φ 0 g ′
φ l g = - 1 ( 2 l + 1 ) A l g iBφ l - 1 g , l = 2 , 3 , ... , N
In formula:
The critical buckling of B system
χgThe neutron fission spectrum of g group
υ fissions release neutron population every time
keffThe Effective multiplication factor of system
G order of a group netron-flux density is distributed
A n = b n - 1 + a n A n + 1
a n = n + 1 2 n + 1 n + 1 2 ( n + 1 ) + 1 B 2
b n = Σ t - Σ s n + 1
In formula:
The few group energy group identification number of G
Belong to the thin group g of the few group of G.
CN201610472890.5A 2016-06-24 2016-06-24 A kind of method obtaining the few group cross-section of high-precision fast neutron reaction pile component Pending CN106128518A (en)

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CN113326648A (en) * 2021-06-17 2021-08-31 中国核动力研究设计院 Cell homogenization constant calculation method and system considering environmental effect and terminal
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Application publication date: 20161116