CN107038294B - For the Resonance self-shielding calculation method based on equivalent one-dimensional stick model of light water reactor - Google Patents
For the Resonance self-shielding calculation method based on equivalent one-dimensional stick model of light water reactor Download PDFInfo
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Abstract
For the Resonance self-shielding calculation method based on equivalent one-dimensional stick model of light water reactor, 1, for the Resonance self-shielding computational problem of light water reactor, the Dan Kefu modifying factor of each fuel rod is calculated using neutron current method；2, according to the functional relation of Dan Kefu modifying factor and one-dimensional stick moderator outer diameter, in the case where known Dan Kefu modifying factor, moderator outer diameter is obtained using binary chop method；3, equivalent one-dimensional fuel rod is calculated using subgroup method or ultra-fine group's method, obtain each circle of fuel rod effectively shields section certainly；Compared to traditional Resonance self-shielding calculation method, the problem of present invention can calculate complex geometry, there is higher computational efficiency, and can obtain space correlation effectively from screen section.
Description
Technical field
The present invention relates to nuclear reactor design and security technology areas, and in particular to it is a kind of for light water reactor based on
The Resonance self-shielding calculation method of equivalent one-dimensional stick model.
Background technique
Traditional light water reactor in-core fuel management calculates and generally uses two-step method, i.e., obtains few group by Assembly calculation first
Constant, then reactivity, critical boron concentration of reactor core etc. and the data such as power distribution are calculated by reactor core.But this method
The problems such as error and history effect of spatial homogenization can be introduced, therefore the high-fidelity of Whole core one-step method is calculated in recent years
Pay attention to.One-step method refers to the homogenization that do not do spatially, is directly calculated by the Resonance self-shielding of full heap scale, transports calculating and combustion
Reactivity, critical boron concentration etc. and the data such as power distribution is calculated in consumption.The precision of this method has very compared to two-step method
Big raising, but challenge is proposed to existing Resonance self-shielding calculation method simultaneously.The scale of heap complete first is very big, therefore it is required that
Resonance self-shielding calculation method efficiency with higher；Then the complex geometry being required in processing reactor core；It finally requires to obtain
Section is effectively shielded in accurate space correlation certainly, i.e., each circle of fuel rod is effective from screen section.
Existing Resonance self-shielding calculation method is broadly divided into equivalent theoretical, subgroup method and ultra-fine group's method three classes.It is of equal value
Theory is broadly divided into the calculating of lattice cell effective resonance integral and Dan Kefu corrects two steps.When calculating lattice cell effective resonance integral,
Scattering source item is simplified using narrow resonance approximation, rational approximation is used to the first collision probability of lattice cell, by the solution of lattice cell
Analysis power spectrum is write as form identical with the parsing power spectrum of homogeneous system, and then by the resonance integral equivalence of lattice cell at one or more
The sum of the weight of homogeneous system resonance integral.The resonance integral of homogeneous system can be made the form of table and be stored in multigroup number
According in library, when calculating, only needs to carry out interpolation according to coefficient, therefore has very high efficiency.Dan Kefu modifying factor is generally adopted
It is calculated with neutron current method, neutron current transports method for solving calculating using multigroup, the calculating suitable for complicated geometry.It is all total
Vibration energy group only uses a Dan Kefu modifying factor, and computational efficiency is higher, the calculating suitable for large scale problem.But reason of equal value
By the averga cross section for using Dan Kefu modifying factor amendment fuel rod, the section of space correlation can not be obtained.Subgroup method to cut
The division that face size carries out subgroup obtains subgroup stationary source equation by the integral to Continuous Energy transport equation on subgroup.
Since subgroup stationary source equation is similar to multigroup transport equation, method for solving can be transported using mature multigroup and it is solved,
Therefore the problem of theoretically subgroup method can be used for the calculating of full heap, be able to solve complex geometry and space correlation is obtained
Effectively from screen section.But since the multigroup of full heap scale transports, calculating is very time-consuming, and subgroup method needs to solve repeatedly
Multigroup transport equation, therefore the Resonance self-shielding computational efficiency that subgroup method is directly applied to full heap is lower.Ultra-fine group's method pair
Energy variable carries out the division of ultra-fine group, and moderation of neutrons equation is solved on the basis of ultra-fine group, has very high precision.But
Be ultra-fine group calculation amount it is very big, cannot be directly used to full heap Resonance self-shielding calculate.
Therefore the Resonance self-shielding that existing three kinds of methods all cannot be directly used to full heap calculates, it is necessary to study a kind of new
Resonance self-shielding calculation method solves challenge brought by one-step method.
Summary of the invention
In order to overcome the above-mentioned problems of the prior art, the purpose of the present invention is to provide a kind of bases for light water reactor
In the Resonance self-shielding calculation method of equivalent one-dimensional stick model, this method is transported solver using multigroup and is calculated using neutron current method
The Dan Kefu modifying factor of fuel rod；The equivalence defined with collision probability is defined using the neutron current of Dan Kefu modifying factor,
In the case where known fuel rod Dan Kefu modifying factor, according to Dan Kefuyin in Dan Kefu modifying factor collision probability definition
The functional relation of son and equivalent one-dimensional stick moderator outer diameter, obtains equivalent one-dimensional stick moderator outer diameter using binary chop method；
Equivalent one-dimensional stick problem is solved using subgroup method or ultra-fine group's method, obtain each circle of one-dimensional stick effectively shields section certainly.
To achieve the goals above, this invention takes following technical schemes to be practiced:
A kind of Resonance self-shielding calculation method based on equivalent one-dimensional stick model for light water reactor, this method includes following step
It is rapid:
Step 1: Resonance self-shielding computational problem is that known materials composition and geological information solve having for fuel region resonance nucleic
Effect is from screen section, and for light water reactor, it is infinitely great, scattering section zero that enable fuel region, which be black matrix i.e. absorption cross-section, source item zero,
Enabling on-fuel area scattering section is zero, and the value of absorption cross-section and source item is equal to elastic potential scattering section, transports solution using multigroup
Device solves following equation and obtains neutron angular flux:
Wherein Ω is angle,It is spatial position,It is angular flux,It is total cross section,It is that gesture elasticity dissipates
Penetrate section；The neutron scalar flux of each fuel rod is obtained using formula (2):
Wherein i is the number of fuel rod, φiIt is the scalar flux of i-th fuel rod；
Step 2: for each fuel rod, constructing corresponding isolated stick model is that fuel rod is placed in spatially infinity
In moderator, it is infinitely great, scattering section zero, source item zero, the scattering of on-fuel area that enable fuel region, which be black matrix i.e. absorption cross-section,
Section is zero, and the value of absorption cross-section and source item is equal to elastic potential scattering section, and solution formula (1) obtains neutron angular flux, is utilized
Neutron scalar flux is calculated in formula (2)；
Step 3: the Dan Kefu modifying factor of each fuel rod is calculated using formula (3):
Wherein CiIt is the Dan Kefu modifying factor of i-th fuel rod, φi,1And φi,2It is that step 1 and step 2 obtain respectively
I-th fuel rod scalar flux；
Step 4: the resonance of the corresponding equivalent one-dimensional stick of each fuel rod is constructed certainly according to Dan Kefu modifying factor conservation
Shielding computational problem, the material composition of equivalent one-dimensional stick and the radius of fuel rod are consistent with corresponding fuel rod, solve below etc.
Imitate the moderator outer diameter of one-dimensional stick, the functional relation such as formula (4) of Dan Kefu modifying factor and equivalent one-dimensional stick moderator outer diameter
It is shown:
Wherein CiIt is the Dan Kefu modifying factor for i-th fuel rod that step 3 obtains, R is one-dimensional stick moderator outer diameter,
Pe,iIt is the neutron escape probability of the corresponding isolated stick of i-th fuel rod, PmfIt (R) is the neutron of fuel region generation in one-dimensional stick at it
The probability of initial collision, ∑ occur in his regiontfIt is the total cross section of fuel region, enables it for infinity,It is being averaged for fuel region
Chord length obtains the corresponding equivalent one-dimensional stick moderator outer diameter of i-th fuel rod using binary chop method according to formula (4), until
This has obtained the material composition and geological information of equivalent one-dimensional stick；
Step 5: the Resonance self-shielding of the equivalent one-dimensional stick obtained using subgroup method or ultra-fine group's method solution procedure 4 is calculated
Problem, the resonant nucleus for obtaining all each circles of equivalent one-dimensional stick are known as effect from screen section, and the resonant nucleus of equivalent one-dimensional stick is known as effect
From screen section be correspond in light water reactor fuel rod resonant nucleus be known as effect from screen section, so far completion light water reactor Resonance self-shielding
It calculates.
Compared with prior art, the present invention has following outstanding advantages:
The present invention using neutron current method calculate fuel rod Dan Kefu modifying factor, all resonance energy groups only need using
One Dan Kefu modifying factor, it is only necessary to which the simple group of primary full heap transports calculating, and computational efficiency is higher；Solution is transported using multigroup
Device calculates neutron current, and Dan Kefu modifying factor can be obtained there are complex geometry；Using subgroup method or ultra-fine
Group method calculate equivalent one-dimensional stick, available space correlation effectively from screen section, i.e., each circle of fuel rod effectively from shield
Section.
Detailed description of the invention
Fig. 1 is the equivalent process schematic diagram of one-dimensional stick.
Fig. 2 is fuel assembly.
Specific embodiment
Invention is further described in detail with reference to the accompanying drawings and detailed description:
The present invention using neutron current method solve Dan Kefu modifying factor, according to Dan Kefu modifying factor neutron current definition and
The equivalence that collision probability defines obtains the moderator outer diameter of equivalent one-dimensional stick by binary chop method, finally uses subgroup
Method or ultra-fine group's method solve the Resonance self-shielding computational problem of equivalent one-dimensional stick, and obtain space correlation effectively shields section certainly.
The specific calculation process of this method includes following aspect:
1) Resonance self-shielding computational problem be known materials composition and geological information solve fuel region resonance nucleic effectively from
Shield section, for the Resonance self-shielding computational problem of light water reactor,
Enabling fuel region is black matrix (absorption cross-section is infinitely great, scattering section zero, source item zero), and the scattering of on-fuel area is cut
Face is zero, and the value of absorption cross-section and source item is equal to elastic potential scattering section, transports solver solution formula (1) using multigroup and obtains
Neutron angular flux；Since infinitely great section can not be taken in numerical value calculates, it is generally taken as 1E5barn；Obtain neutron
After angular flux, angular flux is integrated using formula (2), obtains the neutron scalar flux of each fuel rod；
2) for each fuel rod, corresponding isolated stick model is constructed, i.e., fuel rod is placed in the slow of spatially infinity
In agent, it is 10cm that the outer diameter of moderator is generally taken in numerical value calculating, and boundary condition is vacuum boundary；Enabling fuel region is black matrix,
I.e. absorption cross-section is 1E5barn, and scattering section zero, source item zero, on-fuel area scattering section is zero, absorption cross-section and source item
Value be equal to elastic potential scattering section, solution formula (1) obtains neutron angular flux, and it is logical that neutron mark is calculated using formula (2)
Amount；
3) the Dan Kefu modifying factor of each fuel rod is calculated using formula (3)；
4) since the neutron current of Dan Kefu modifying factor is defined, to define with collision probability be of equal value, the pellet of fuel rod
Can husband's factor flux can with formula (4) indicate, pass through the outer diameter of the available equivalent one-dimensional stick moderator of binary chop method；
As shown in Fig. 1, the corresponding equivalent one-dimensional stick of a fuel rod in grid, material composition and combustion are obtained through the above steps
The consistent of fuel rod is corresponded in the radius of charge bar and grid, the outer diameter of moderator is calculated by above-mentioned；
5) the Resonance self-shielding computational problem that equivalent one-dimensional stick is solved using subgroup method or ultra-fine group's method, obtains equivalent one
That ties up the space correlation of stick effectively shields section certainly；Method of the invention, subgroup method and ultra-fine group's method is respectively adopted and calculates Fig. 2
Shown in component, calculate the time be 18s, 426s and 775s respectively, compared to subgroup method and ultra-fine group's method, side of the invention
Method has higher computational efficiency.
Claims (1)
1. a kind of Resonance self-shielding calculation method based on equivalent one-dimensional stick model for light water reactor, it is characterised in that: this method
The following steps are included:
Step 1: Resonance self-shielding computational problem be known materials composition and geological information solve fuel region resonance nucleic effectively from
Shield section, for light water reactor, enable fuel region be black matrix i.e. absorption cross-section be it is infinitely great, scattering section zero, source item zero enables non-
Fuel region scattering section is zero, and the value of absorption cross-section and source item is equal to elastic potential scattering section, transports solver using multigroup and asks
Solution following equation obtains neutron angular flux:
Wherein Ω is angle,It is spatial position,It is angular flux,It is total cross section,It is that elastic potential scattering is cut
Face；The neutron scalar flux of each fuel rod is obtained using formula (2):
Wherein i is the number of fuel rod, φiIt is the scalar flux of i-th fuel rod；
Step 2: for each fuel rod, constructing corresponding isolated stick model is that fuel rod is placed in spatially infinitely great slowing down
In agent, it is infinitely great, scattering section zero, source item zero, on-fuel area scattering section that enable fuel region, which be black matrix i.e. absorption cross-section,
It is zero, the value of absorption cross-section and source item is equal to elastic potential scattering section, and solution formula (1) obtains neutron angular flux, utilizes formula
(2) neutron scalar flux is calculated；
Step 3: the Dan Kefu modifying factor of each fuel rod is calculated using formula (3):
Wherein CiIt is the Dan Kefu modifying factor of i-th fuel rod, φi,1And φi,2Be respectively step 1 and step 2 obtain i-th
The scalar flux of root fuel rod；
Step 4: the Resonance self-shielding meter of the corresponding equivalent one-dimensional stick of each fuel rod is constructed according to Dan Kefu modifying factor conservation
Calculation problem, the material composition of equivalent one-dimensional stick and the radius of fuel rod are consistent with corresponding fuel rod, solve equivalent one below
The moderator outer diameter of stick is tieed up, shown in functional relation such as formula (4) of the Dan Kefu modifying factor with equivalent one-dimensional stick moderator outer diameter:
Wherein CiIt is the Dan Kefu modifying factor for i-th fuel rod that step 3 obtains, R is one-dimensional stick moderator outer diameter, Pe,iIt is
The neutron escape probability of the corresponding isolated stick of i root fuel rod, PmfIt (R) is the neutron of fuel region generation in one-dimensional stick in other regions
The probability of initial collision, ∑ occurstfIt is the total cross section of fuel region, enables it for infinity,It is the mean chord of fuel region, according to
Formula (4) obtains the corresponding equivalent one-dimensional stick moderator outer diameter of i-th fuel rod using binary chop method, has so far obtained
Imitate the material composition and geological information of one-dimensional stick；
Step 5: the Resonance self-shielding calculating of the equivalent one-dimensional stick obtained using subgroup method or ultra-fine group's method solution procedure 4 is asked
It inscribes, the resonant nucleus for obtaining all each circles of equivalent one-dimensional stick is known as effect from screen section, and the resonant nucleus of equivalent one-dimensional stick is known as effect certainly
Screen section be correspond in light water reactor fuel rod resonant nucleus be known as effect from screen section, so far completion light water reactor Resonance self-shielding meter
It calculates.
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| CN110705054B (en) * | 2019-09-19 | 2021-06-11 | 西安交通大学 | Method for obtaining resonance group constant for neutron strong absorber |
| CN111914464B (en) * | 2020-08-12 | 2022-04-08 | 中国核动力研究设计院 | Method and system for optimizing multi-resonance nuclide resonance simulation subgroup of reactor assembly |
| CN111914463B (en) * | 2020-08-12 | 2022-02-22 | 中国核动力研究设计院 | Subgroup optimization method and system for reactor assembly resonance simulation |
| CN114491907B (en) * | 2020-10-27 | 2023-10-20 | 中国核动力研究设计院 | Optimal rational polynomial and ultra-fine group combined resonance algorithm based on vacuum boundary |
| CN112364555B (en) * | 2020-11-19 | 2022-03-25 | 中国核动力研究设计院 | Dual-heterogeneity space self-screening effect correction method, device, equipment and medium |
| CN114692062B (en) * | 2022-03-31 | 2024-04-09 | 西安交通大学 | Method for efficiently obtaining partial neutron flow discontinuity factors on surface of nuclear reactor fuel rod |
| CN114510861B (en) * | 2022-04-19 | 2022-07-15 | 西安交通大学 | Resonance calculation method for studying reactor based on equivalent geometric theory |
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