CN106991272A - A kind of accurate method for calculating nucleic atom cuclear density in calculating for burnup - Google Patents
A kind of accurate method for calculating nucleic atom cuclear density in calculating for burnup Download PDFInfo
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Abstract
A kind of accurate method for calculating nucleic atom cuclear density in calculating for burnup, step is as follows：1st, according to tnThe atom cuclear density N of moment various nucleicnSolve the netron-flux density that multigroup neutron-transport equation obtains various nucleicAnd calculate the microreaction rate R of each nucleicn；2nd, according to RnWith tn‑1Microreaction rate of the moment various nucleic by corrected correction stepCalculate tnThe moment corrected microreaction rate for estimating step3rd, t is calculated by solving burn up equationn+1Moment various nucleic estimate the atom cuclear density N of stepn+1(p)；4th, multigroup neutron-transport equation is solved again obtain tn+1The netron-flux density at momentWith the microreaction rate R of each nucleicn+1；5th, t is obtained using the method for linear interpolationn+1The corrected correction step microreaction rate of moment each nucleic6th, burn up equation is solved again calculate tn+1The atom cuclear density N of moment various nucleicn+1；The inventive method calculates obtained nucleic atom cuclear density closer to the atom cuclear density under time of day, so that the result that burnup is calculated is more accurate.
Description
Technical field
The present invention relates to nuclear reactor designs and reactor physics calculating field, and in particular to one kind is used in burnup calculating
The accurate method for calculating nucleic atom cuclear density.
Background technology
In the process of running, the fissile nuclide in nuclear fuel is continuous by the reaction such as fission or radiation capture for reactor
Ground is consumed, and fertile nuclide is such as238Fissile nuclide is converted to after U, capture neutron again239Pu, at the same time some fission products
(such as135I and135Xe) produce and disappearance reaches poised state, some are then constantly accumulated.In a word, the nuclide composition in fuel
It will be changed with burn-up level.In in-core fuel management calculating, the calculating that nuclear fuel composition changes with burn-up level
(i.e. burnup is calculated) is a very important content.In reactor design and fuel management are calculated, burnup, which is calculated, is often
One independent part, it mainly provides the atom cuclear density (nucleon number in unit volume) of various nucleic with the change of burn-up level
Change, calculate the new cross section parameter of various fuel assemblies, used for reactor core diffusion calculating.
In burnup calculating, microreaction rate is changed over time, it is necessary to solve burnup in certain burnup step-length
Equation obtains the atom cuclear density of all nucleic in burnup step-length end, due to needing to assume the burnup when solving burn up equation
Microreaction rate does not change over time (i.e. it is a constant) in step-length, so burnup step-length needs to obtain sufficiently small, ability
Enough precision for ensureing to calculate.The burnup computational methods of early stage are that burnup step-length is obtained into sufficiently small so that can be approximately with current
The microreaction rate of burnup step initial time is used as the microreaction rate in whole burnup step-length.It can so describe in fuel rod
Composition with the change of burnup, but its shortcoming is it is also obvious that need to spend considerably long calculating time.
Later, Predictor Corrector method was applied in burnup calculating process.The basic thought of Predictor Corrector：I.e. first basis is worked as
The atom cuclear density of preceding burnup step initial time carries out Neutronics calculation (solution neutron-transport equation) and obtains the micro- of initial time
Reactivity is seen, the atomic nucleus that the burn up equation then solved with the reactivity in current burnup step-length obtains burnup step-length end is close
Degree, is referred to as the atom cuclear density for estimating step, then solving a Neutronics calculation again with the atom cuclear density for estimating step is walked
The microreaction rate at long end, the burn up equation of current burnup step is solved once with the microreaction rate, burnup step-length end is obtained again
Atom cuclear density, referred to as correct the atom cuclear density of step.By the atom cuclear density and the atom cuclear density of correction step of estimating step
The atom cuclear density that is walked as next burnup of average value.Burnup meter can be carried out choosing larger burnup step-length by so doing
Calculate, computational efficiency can be improved.However, traditional Predictor Corrector burnup computational methods think that current burnup walks the original of initial time
Daughter nucleus density is the average value that back burnup calculates the atom cuclear density for obtaining Predictor Corrector step, and Predictor Corrector method is obtained
Current burnup step initial time atom cuclear density and its real atom cuclear density there is certain deviation, so traditional
Predictor Corrector method when the burnup for carrying out the burnable poison assembly with very strong neutron-absorbing effect is calculated, it is still desirable to
The precision that very thin burnup step-length just can guarantee that calculating is divided, i.e., still must spend the considerably long calculating time.
The content of the invention
In order to overcome the problem of above-mentioned prior art is present, the invention aims to avoid dividing when burnup is calculated
Thin burnup step-length expends the substantial amounts of calculating time and in order to choose big burnup on the premise of computational accuracy is ensured
There is provided the accurate method for calculating nucleic atom cuclear density, the party in a kind of calculating for burnup to improve computational efficiency for step-length
Method uses the parameter under existing burnup point, and the microreaction rate (including estimating step and correction step) walked to current burnup is repaiied
Just, it is specially that linear extrapolation is used to the microreaction rate for estimating step under current burnup step-length, to the microreaction of correction step
Rate is modified using the method for linear interpolation, makes the nucleic atom cuclear density that its calculating is obtained closer under time of day
Atom cuclear density, so that the result that burnup is calculated is more accurate.
To achieve these goals, it is practiced this invention takes following technical scheme：
A kind of accurate method for calculating nucleic atom cuclear density in calculating for burnup, step is as follows：
Step 1：First according to tnThe atom cuclear density N of various nucleic in moment materialnMultigroup neutron-transport equation is solved to obtain
To the netron-flux density of various nucleicIt is calculated as shown in formula (1), and according to obtained netron-flux densityThe microreaction rate R of each nucleic is calculated by formula (3)n；
In formula：
Ω --- angle direction；
--- gradient operator；
——tnAt moment space r, on Ω directions, the netron-flux density of g energy groups；
Σt,n,g(r)——tnAt moment space r, volumic total cross-section/cm of the material in g energy groups-1；
Qs,n,g(r,Ω)——tnAt moment space r, on Ω directions, the scattering source item of g energy groups；
Qf,n,g(r,Ω)——tnAt moment space r, on Ω directions, the fission source term of g energy groups；
Wherein tnAt moment space r, volumic total cross-section Σ of the material in g energy groupst,n,g(r) it is specific to calculate such as formula (2)：
In formula：
I --- nucleic is numbered；
I --- the nucleic sum in material；
σt,n,g,i——tnMicrocosmic total cross section/cm of moment nucleic i g energy groups-1；
Nn,i(r)——tnAt moment space r, nucleic i atom cuclear density；
Σt,n,g(r)——tnAt moment space r, volumic total cross-section/cm of the material in g energy groups-1；
In formula：
Rn——tnThe microreaction rate at moment；
σt,n,g——tnMicrocosmic total cross section/cm of moment g energy groups-1；
——tnThe netron-flux density of moment g energy groups；
Step 2：Obtained t is calculated according to step 1nThe microreaction rate R of various nucleic in the material at momentnWith tn-1Moment
Microreaction rate of the various nucleic by corrected correction step in materialCalculating tnDuring the parameter at moment, tn-1
The parameter at moment is known quantity, and t is calculated using the method for linear extrapolation by formula (4)nMoment is corrected to estimate the micro- of step
See reactivity
In formula：
——tnThe moment corrected microreaction rate for estimating step；
——tn-1The microreaction rate of moment corrected correction step；
Rn——tnThe microreaction rate at moment；
tp——tn-1The time step of moment burnup step；
t——tnThe time step of moment burnup step；
Step 3：Obtained t is calculated according to step 2nMoment estimates the micro- of step using the corrected various nucleic of linear extrapolation
See reactivityT is calculated by solving burn up equationn+1Moment various nucleic estimate the atom cuclear density N of stepn+1(p)；
Step 4：Obtained t is calculated according to step 3n+1Moment various nucleic estimate the atom cuclear density N of stepn+1(p) it is another
Secondary solution multigroup neutron-transport equation obtains tn+1The netron-flux density at momentWith the microreaction rate R of each nucleicn+1；
Step 5：T is obtained by step 4n+1The microreaction rate R of moment each nucleicn+1Afterwards, obtained using the method for linear interpolation
Obtain tn+1The corrected correction step microreaction rate of moment each nucleicIts specific calculating is as shown in formula (5)：
In formula：
——tn+1The microreaction rate of moment corrected correction step；
——tnThe moment corrected microreaction rate for estimating step；
Rn+1——tn+1The microreaction rate at moment；
Step 6：T is obtained by step 5n+1The corrected correction step microreaction rate of moment each nucleicAfterwards, further
Secondary solution burn up equation calculates tn+1The atom cuclear density N of moment various nucleicn+1。
Compared with prior art, the present invention has following outstanding advantages：
1. the present invention to the microreaction rate for estimating step under current burnup step-length by using linear extrapolation, correction is walked
Microreaction rate be modified using the method for linear interpolation, the more accurate atomic nucleus in current burnup step end can be obtained close
Degree.
2. relative to traditional Predictor Corrector burnup computational methods, the present invention is carried out to the microreaction rate that current burnup is walked
Amendment, makes it walk real microreaction rate closer to current burnup.So, when choosing identical burnup step-length, this hair
It is bright to obtain more accurate result of calculation, asked in particular for the burnable poison assembly with very strong neutron-absorbing effect
Topic.
Brief description of the drawings
Fig. 1 is the infinite multiplication factor relative deviation comparison diagram obtained by Predictor Corrector method and present invention calculating.
Embodiment
The present invention is described in further detail with reference to embodiment：
The present invention is adopted using the parameter under existing burnup point to the microreaction rate for estimating step under current burnup step-length
With linear extrapolation, the microreaction rate to correction step is modified using the method for linear interpolation, the result for obtaining its calculating
Atom cuclear density under closer to time of day, the present invention is a kind of to be used to accurately calculate nucleic atom cuclear density during burnup is calculated
Method, comprise the following steps：
Step 1：First according to tnThe atom cuclear density N of various nucleic in moment materialnMultigroup neutron-transport equation is solved to obtain
To the netron-flux density of various nucleicIt is calculated as shown in formula (1), and according to obtained netron-flux densityThe microreaction rate R of each nucleic is calculated by formula (3)n；
In formula：
Ω --- angle direction；
--- gradient operator；
——tnAt moment space r, on Ω directions, the netron-flux density of g energy groups；
Σt,n,g(r)——tnAt moment space r, volumic total cross-section/cm of the material in g energy groups-1；
Qs,n,g(r,Ω)——tnAt moment space r, on Ω directions, the scattering source item of g energy groups；
Qf,n,g(r,Ω)——tnAt moment space r, on Ω directions, the fission source term of g energy groups；
Wherein tnAt moment space r, volumic total cross-section Σ of the material in g energy groupst,n,g(r) it is specific to calculate such as formula (2)：
In formula：
I --- nucleic is numbered；
I --- the nucleic sum in material；
σt,n,g,i——tnMicrocosmic total cross section/cm of moment nucleic i g energy groups-1；
Nn,i(r)——tnAt moment space r, nucleic i atom cuclear density；
Σt,n,g(r)——tnAt moment space r, volumic total cross-section/cm of the material in g energy groups-1；
In formula：
Rn——tnThe microreaction rate at moment；
σt,n,g——tnMicrocosmic total cross section/cm of moment g energy groups-1；
——tnThe netron-flux density of moment g energy groups；
Step 2：Obtained t is calculated according to step 1nThe microreaction rate R of various nucleic in the material at momentnWith tn-1Moment
Microreaction rate of the various nucleic by corrected correction step in materialCalculating tnDuring the parameter at moment, tn-1
The parameter at moment is known quantity, and t is calculated using the method for linear extrapolation by formula (4)nMoment is corrected to estimate the micro- of step
See reactivity
In formula：
——tnThe moment corrected microreaction rate for estimating step；
——tn-1The microreaction rate of moment corrected correction step；
Rn——tnThe microreaction rate at moment；
tp——tn-1The time step of moment burnup step；
t——tnThe time step of moment burnup step；
Step 3：Obtained t is calculated according to step 2nMoment estimates the micro- of step using the corrected various nucleic of linear extrapolation
See reactivityT is calculated by solving burn up equationn+1Moment various nucleic estimate the atom cuclear density N of stepn+1(p)；
Step 4：Obtained t is calculated according to step 3n+1Moment various nucleic estimate the atom cuclear density N of stepn+1(p) it is another
Secondary solution multigroup neutron-transport equation obtains tn+1The netron-flux density at momentWith the microreaction rate R of each nucleicn+1；
Step 5：T is obtained by step 4n+1The microreaction rate R of moment each nucleicn+1Afterwards, obtained using the method for linear interpolation
Obtain tn+1The corrected correction step microreaction rate of moment each nucleicIts specific calculating is as shown in formula (5)：
In formula：
——tn+1The microreaction rate of moment corrected correction step；
——tnThe moment corrected microreaction rate for estimating step；
Rn+1——tn+1The microreaction rate at moment；
Step 6：T is obtained by step 5n+1The corrected correction step microreaction rate of moment each nucleicAfterwards, further
Secondary solution burn up equation calculates tn+1The atom cuclear density N of moment various nucleicn+1。
Illustrate effect of the present invention by taking UO2 fuel assemblies as an example below：
The present invention is adopted using the parameter under existing burnup point to the microreaction rate for estimating step under current burnup step-length
With linear extrapolation, the microreaction rate to correction step is modified using the method for linear interpolation, the nucleic for obtaining its calculating
Atom cuclear density is closer to the atom cuclear density under time of day.So relative to traditional Predictor Corrector burnup calculating side
Method, when choosing identical burnup step-length, the present invention can obtain more accurate result of calculation.Fig. 1 is to be directed to UO2 fuel stacks
Part is in the case where choosing identical burnup step-length (1.0GWd/tU), the unlimited increasing obtained by Predictor Corrector method with present invention calculating
The factor is grown relative to the relative deviation with reference to solution, as shown in figure 1, in the case where choosing identical burnup step-length, calculating knot of the invention
Fruit is more accurate than Predictor Corrector method.
Claims (1)
1. a kind of accurate method for calculating nucleic atom cuclear density in calculating for burnup, it is characterised in that：Step is as follows：
Step 1：First according to tnThe atom cuclear density N of various nucleic in moment materialnMultigroup neutron-transport equation is solved to obtain respectively
Plant the netron-flux density of nucleicIt is calculated as shown in formula (1), and according to obtained netron-flux densityIt is logical
Cross the microreaction rate R that formula (3) calculates each nucleicn；
In formula：
Ω --- angle direction；
--- gradient operator；
——tnAt moment space r, on Ω directions, the netron-flux density of g energy groups；
Σt,n,g(r)——tnAt moment space r, volumic total cross-section/cm of the material in g energy groups-1；
Qs,n,g(r,Ω)——tnAt moment space r, on Ω directions, the scattering source item of g energy groups；
Qf,n,g(r,Ω)——tnAt moment space r, on Ω directions, the fission source term of g energy groups；
Wherein tnAt moment space r, volumic total cross-section Σ of the material in g energy groupst,n,g(r) it is specific to calculate such as formula (2)：
In formula：
I --- nucleic is numbered；
I --- the nucleic sum in material；
σt,n,g,i——tnMicrocosmic total cross section/cm of moment nucleic i g energy groups-1；
Nn,i(r)——tnAt moment space r, nucleic i atom cuclear density；
Σt,n,g(r)——tnAt moment space r, volumic total cross-section/cm of the material in g energy groups-1；
In formula：
Rn——tnThe microreaction rate at moment；
σt,n,g——tnMicrocosmic total cross section/cm of moment g energy groups-1；
——tnThe netron-flux density of moment g energy groups；
Step 2：Obtained t is calculated according to step 1nThe microreaction rate R of various nucleic in the material at momentnWith tn-1Moment material
In various nucleic by it is corrected correction step microreaction rateCalculating tnDuring the parameter at moment, tn-1Moment
Parameter be known quantity, pass through formula (4) using linear extrapolation method calculate tnMoment is corrected to estimate the microcosmic anti-of step
Should rate
In formula：
——tnThe moment corrected microreaction rate for estimating step；
——tn-1The microreaction rate of moment corrected correction step；
Rn——tnThe microreaction rate at moment；
tp——tn-1The time step of moment burnup step；
t——tnThe time step of moment burnup step；
Step 3：Obtained t is calculated according to step 2nMoment estimates the microcosmic anti-of step using the corrected various nucleic of linear extrapolation
Should rateT is calculated by solving burn up equationn+1Moment various nucleic estimate the atom cuclear density N of stepn+1(p)；
Step 4：Obtained t is calculated according to step 3n+1Moment various nucleic estimate the atom cuclear density N of stepn+1(p) ask again
Solution multigroup neutron-transport equation obtains tn+1The netron-flux density at momentWith the microreaction rate R of each nucleicn+1；
Step 5：T is obtained by step 4n+1The microreaction rate R of moment each nucleicn+1Afterwards, t is obtained using the method for linear interpolationn+1
The corrected correction step microreaction rate of moment each nucleicIts specific calculating is as shown in formula (5)：
In formula：
——tn+1The microreaction rate of moment corrected correction step；
——tnThe moment corrected microreaction rate for estimating step；
Rn+1——tn+1The microreaction rate at moment；
Step 6：T is obtained by step 5n+1The corrected correction step microreaction rate of moment each nucleicAfterwards, solve again
Burn up equation calculates tn+1The atom cuclear density N of moment various nucleicn+1。
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| CN110457802A (en) * | 2019-07-31 | 2019-11-15 | 上海交通大学 | The precision optimizing implementation method of simulation is checked for SFCOMPO burnup experiment benchmark problem |
| CN112347632A (en) * | 2020-11-03 | 2021-02-09 | 中国核动力研究设计院 | Fuel burnup determination method and device based on nonlinear least square method |
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| Publication number | Priority date | Publication date | Assignee | Title |
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| CN110457802A (en) * | 2019-07-31 | 2019-11-15 | 上海交通大学 | The precision optimizing implementation method of simulation is checked for SFCOMPO burnup experiment benchmark problem |
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