CN107092784A - A kind of method that burnup coupling is calculated that transports suitable for nuclear reactor - Google Patents
A kind of method that burnup coupling is calculated that transports suitable for nuclear reactor Download PDFInfo
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Abstract
A kind of method that burnup coupling is calculated that transports suitable for nuclear reactor, comprises the following steps：1st, walk first atom cuclear density by burnup to carry out transporting calculating, obtain coarse net parameter, microreaction rate；2nd, burnup calculating is carried out by microreaction rate and atom cuclear density, obtains the atom cuclear density that burnup step end is estimated；3rd, carry out transporting calculating by the atom cuclear density estimated, obtain coarse net parameter, microreaction rate；4th, burnup CMFD sub-steps, the coarse net parameter that linear interpolation is preserved are divided in burnup step；5th, by the coarse net parameter and the fine-structure mesh neutron flux of step 3 of step 4, the microreaction rate of burnup CMFD sub-steps is updated；6th, burnup calculating is carried out with the microreaction rate in burnup CMFD sub-steps, obtains burnup step end accurately atom cuclear density；7th, judge whether burnup step number mesh shows whether judgement calculating terminates with input value one；The inventive method expands the step-length that burnup is calculated on the premise of very high degree of precision is ensured, greatly, reduces the time calculated in the nuclear reactor whole phase in longevity.
Description
Technical field
The present invention relates to nuclear reactor physical computing technical field, and in particular to a kind of to transport combustion suitable for nuclear reactor
The method that consumption coupling is calculated.
Background technology
The today for requiring to improve constantly in design condition and computational accuracy, nuclear reactor designs field is wished by accurately building
Mould, and the approximate and error introduced in the nuclear reactor calculating process of upstream is farthest reduced, realize the reactor of high-fidelity
Physical computing, so as to carry out Accurate Analysis simulation to reactor.
The reactor physics of high-fidelity, which are calculated, mainly includes neutron transport calculating and burnup calculates two parts.Neutron transport meter
Calculate and netron-flux density is obtained according to atomic nucleus density field, temperature field etc., and then core power distribution is provided；Burnup calculates root
The microcosmic neutron reaction rate for calculating and obtaining is transported according to a certain moment, the atomic nucleus density field at the moment is obtained, so carried out continuous
Iteration, and then obtain power distribution of nuclear reactor etc. and change with time rule.
In the reactor physics of high-fidelity are calculated, neutron transport, which is calculated, extremely to be taken, therefore transports burnup couple strategy
It is most important.Outstanding transports burnup couple strategy, can efficiently reduce whole burnup on the premise of very high degree of precision is ensured
In phase in longevity, the number of times that neutron transport is calculated, and then greatly reduce the time that whole reactor physics are calculated.
In burnup calculating process, the most commonly seen burnup couple strategy that transports is starting point approximation method.So-called starting point is near
It is exactly to think the microreaction rate (microscopic cross of nucleic and the product of neutron scalar flux density) between two kinds of burnup steps like method
Keep constant, then calculated always from beginning of life to the end of term in longevity.Due to interim in the whole longevity, microreaction rate is being continually changing,
Obvious starting point approximately only divides superfine burnup step, could obtain an accurate result.On the basis of starting point is approximate, birth
The traditional neutron transport burnup couple strategy with Predictor Corrector is given birth to.Burnup couple strategy is transported with Predictor Corrector
Burnup step-length can significantly be expanded, and keep the precision of calculating, and the effect for transporting couple strategy of several Predictor Correctors
It is very close to.
With Predictor Corrector couple strategy is transported traditional, and a kind of the most frequently used Predictor Corrector transports burnup coupling plan
Slightly assume that the microreaction rate (microscopic cross of nucleic and the product of neutron scalar flux density) and original in current burnup step-length
Daughter nucleus density is linear changing relation：The atom cuclear density progress of burnup step initial time current first transports calculating and obtained initially
The microreaction rate at moment, the burn up equation then solved with the microreaction rate in current burnup step-length obtains burnup step-length end
Atom cuclear density, be referred to as the atom cuclear density for estimating step, then carry out transporting calculating again with the atom cuclear density for estimating step, obtain
To the microreaction rate at burnup step-length end, solve once the burn up equation of current burnup step again with the microreaction rate, fired
The atom cuclear density at step-length end is consumed, the atom cuclear density of step is referred to as corrected.By the atom cuclear density and the original of correction step of estimating step
The atom cuclear density that the average value of daughter nucleus density is walked as next burnup.
Traditional transports burnup couple strategy, when component or reactor core are covered with poisonous substance, it is necessary to by the step size controlling of burnup
In the value of very little, a preferable result could be obtained, but also therefore needs to carry out the calculating of neutron transport many times, this is in reality
High-fidelity reactor physics calculate in be extremely time-consuming, greatly extend the calculating time.
Predictor Corrector method in the conventional fuel assembly without burnable poison rod is calculated, precision be it is higher, still
When the fuel assembly with burnable poison rod or even reactor core calculating, in order to ensure the accuracy of Predictor Corrector method, it is necessary to will divide
Thinner burnup step, therefore in the burnup of whole phase in longevity is calculated, can carry out it is multiple transport calculating, when considerably increasing calculating
Between.
The content of the invention：
In order to overcome the problem of above-mentioned prior art is present, new to be applied to core anti-it is an object of the invention to provide a kind of
The method that burnup coupling is calculated that transports of heap is answered, on the premise of very high degree of precision is ensured, greatly expands the step-length that burnup is calculated,
The nuclear reactor physics for reducing high-fidelity transports the time of calculating, so as to reduce the time calculated in the nuclear reactor whole phase in longevity.
To achieve these goals, the present invention will take following technical scheme to be practiced：
A kind of method that burnup coupling is calculated that transports suitable for nuclear reactor, comprises the following steps:
Step 1：The geological information that atom cuclear density and input card according at the beginning of being walked burnup are provided carries out transporting calculating, defeated
It is CMFD accelerated methods that coarse net accelerated method is introduced when fortune is calculated, and preserves burnup and walks the coarse net ginseng obtained during just coarse net speed-up computation
Number, obtains the microreaction rate i.e. microscopic cross of the nucleic in each burnup area and corresponding burnup in each first burnup area of burnup step
The product of area's neutron scalar flux density, wherein fine-structure mesh neutron angular flux density, coarse net accelerated method energy can be obtained by transporting calculating
The neutron scalar flux density of coarse net is enough updated, to accelerate the iteration convergence of fine-structure mesh neutron angular flux density；Specifically include following step
Suddenly：
1) the original multigroup microscopic cross information of each nucleic is read from database；
2) nucleic atom cuclear density, temperature and the geological information included in material is read from input card；
1) and 2) 3) original multigroup microscopic cross, atom cuclear density and temperature information based on each nucleic obtained by,
Resonance self-shielding calculating is carried out using subgroup method, the multigroup of each nucleic is obtained effectively from screen section, specific calculation formula is such as
Under：
In formula：
σx,g,iso-- nucleic iso, energy group g, reaction channel χ section；
ΔEg-- the energy width of g groups；
σx,iso(E) -- the section of the reaction channel χ at nucleic iso, ENERGY E；
φ (E) -- energy is E netron-flux density；
4) neutron transport calculating is carried out using MOC characteristic line methods according to the information 3) obtained, obtained in regional
Sub- angular flax density, specific calculation formula is as follows：
In formula：
Ω --- angle direction；
--- gradient operator；
ψg(r, Ω) --- g can group region r, the neutron angular flux density of angle Ω；
G --- g can group；
G --- can group's sum；
Σt,g(r) --- the volumic total cross-section of g groups；
Qg(r, Ω) --- neutron-transport equation source item；
Thus the neutron angular flux density of each zoning is obtained；
5) full angle space upper integral is carried out to calculating obtained neutron angular flux density in formula (2), obtained on fine-structure mesh
Average neutron scalar flux densitySpecific calculation formula is as follows：
In formula：
M --- discrete direction sum；
ωm--- quadrature group
And have：
Thus the neutron scalar flux density of each zoning is obtained；6) when carrying out MOC iterative calculation, coarse net is solved
The corresponding coarse net difference equation of equilibrium equation, obtains coarse net flux, shown in calculation formula such as formula (4)；Pass through coarse net difference meter
Neutron scalar flux before and after calculating in the ratio between coarse grid average neutron scalar flux density synchronized update coarse grid on all refined nets is close
Degree, the source item of equation right-hand member, can speed up MOC iterative calculation, calculation formula such as formula during for updating MOC calculating next time
(5) shown in；After MOC calculating terminates, the parameter of now coarse net difference equation is preserved, specific calculation formula is as follows：
In formula：
N --- difference coarse net grid
U (u=x, y, z) --- direction signs；
--- mesh widths of the difference coarse net n on u (u=x, y, z) direction；
--- on coarse net grid n, g energy groups, direction is the net neutron current in u positive direction；
--- on coarse net grid n, g energy groups, direction is the net neutron current in u negative direction；
--- on coarse net grid n, g can group, r kind Homogenized cross sections；
--- on coarse net grid n, the netron-flux density on the coarse net of g energy groups；
--- on coarse net grid n, the generation section of g ' energy groups；
--- on coarse net grid n, the netron-flux density on the coarse net of g ' energy groups；
--- on coarse net grid n, the scattering section of g energy groups is scattered to from g ' energy groups；
χg--- the fission spectrum of g energy groups；
keff--- the characteristic value of neutron balance equation；
In formula：
--- the average scalar flux of thin area i g crowds of flat source after renewal, to update l+1 submatrixs MOC meters
The source item of calculation；
--- the CMFD after l submatrixs MOC calculating calculates obtained coarse net n g group mean scalar flux；
--- l submatrixs MOC calculates obtained coarse net n g groups of homogenization scalar flux；
--- l submatrixs MOC calculates resulting thin area i g crowds of flat source average scalar flux；
7) by the microscopic cross and respective regions neutron scalar flux density of each nucleic for 3), 4), 5) respectively obtaining needs
Product, i.e. each nucleic of regional microreaction rate；
Step 2：The first microreaction rate of obtained burnup step is calculated using step 1 and atom cuclear density carries out burnup meter
Calculate, when burnup is calculated, divide burnup sub-step in two burnup steps, burnup calculating is only carried out in each burnup sub-step, is not entered
Row transports calculating, carries out the renewal of microreaction rate, obtains the atom cuclear density at burnup step end, and the atom cuclear density is referred to as estimating
The atom cuclear density of step；Specifically include following steps：
1) the fission production of the decay coefficient of each nucleic, reaction channel branching ratio, fission nuclide is read from burnup database
The burnup data such as volume；
2) the atom cuclear density of each nucleic of the regional preserved in calculating is transported is read, and transports meter
The microreaction rate of obtained regional each nucleic；
3) according to the information 1), 2) obtained, burn up equation is solved using Chebyshev's rational approximation method, it is specific to calculate
Formula is as follows：
In formula：
N (t) -- expression formula of the atom cuclear density on the time；
The atom cuclear density of N (0) -- initial time
A-- burnup matrixes；
Γ -- curve is integrated, and is enclosed counterclockwise around all characteristic values one of matrix tA；
I-- unit matrixs；
I-- imaginary numbers；
Step 3：Carry out transporting calculating, calculation formula such as formula using the atom cuclear density for estimating step obtained in step 2
(1), formula (2) and formula (3) are shown, introduce coarse net accelerated method i.e. CMFD accelerated methods when transporting calculating, calculation formula is such as
Shown in formula (4) and formula (5), the coarse net parameter obtained when the last coarse net of burnup step is calculated is preserved, the microcosmic of burnup step end is obtained
Reactivity is product of the microscopic cross with neutron scalar flux density of nucleic, and wherein netron-flux density is the neutron mark on fine-structure mesh
Flux density；
Step 4：Burnup CMFD sub-steps are divided in the middle of two burnup steps, in each burnup CMFD sub-steps, burnup is walked
Just walk last coarse net parameter with burnup and carry out linear interpolation, obtain the coarse net parameter in each burnup CMFD sub-steps；
Step 5：In each burnup CMFD sub-steps, the coarse net parameter obtained using interpolation in step 4 is entered to formula (4)
Row is solved, and carries out coarse net calculating, updates the flux of coarse net, and the burnup obtained using step 3 walks the neutron mark on the fine-structure mesh at end
Flux density, the neutron scalar flux density on the fine-structure mesh in each burnup CMFD sub-steps is updated according to formula (5), and then update every
Microreaction rate in individual burnup CMFD sub-steps；
Step 6：Using the microreaction rate i.e. nucleic microscopic cross updated in step 5 in each burnup CMFD sub-steps and more
The product of neutron scalar flux density after new, is carried out between burnup calculating, and adjacent burnup CMFD sub-steps, together by formula (6)
Sample divides burnup sub-step and calculated, and finally gives the atom cuclear density at burnup step end, and the atom cuclear density is the burnup needed
The accurate atom cuclear density in step end；
Step 7：Judge whether burnup step number mesh is consistent with input value, if burnup step is consistent with input value, calculate knot
Beam；If inconsistent, step 1 is back to, the calculating of next burnup step is entered.
Compared with conventional method, the present invention has following outstanding advantages：
In burnup calculating process, it is constant value to no longer assume that the microreaction rate between two burnup steps.The inventive method exists
When correction step is calculated, by dividing burnup CMFD sub-steps, joined in each burnup CMFD sub-steps by linear interpolation coarse net parameter
Number, carries out coarse net calculating, have updated the netron-flux density in each burnup CMFD sub-steps, capture microreaction rate with combustion
The change of consumption, therefore the division of burnup step-length can be expanded, reduce the time that whole phase in longevity burnup is calculated.
Brief description of the drawings
Fig. 1 is the inventive method flow chart.
Embodiment：
The present invention is described in further details with reference to the accompanying drawings and detailed description：
As shown in figure 1, a kind of method that burnup coupling is calculated that transports suitable for nuclear reactor of the present invention, including following step
Suddenly:
Step 1：The geological information that atom cuclear density and input card according at the beginning of being walked burnup are provided carries out transporting calculating, defeated
It is CMFD accelerated methods that coarse net accelerated method is introduced when fortune is calculated, and preserves burnup and walks the coarse net ginseng obtained during just coarse net speed-up computation
Number, obtains the microreaction rate i.e. microscopic cross of the nucleic in each burnup area and corresponding burnup in each first burnup area of burnup step
The product of area's neutron scalar flux density, wherein fine-structure mesh neutron angular flux density, coarse net accelerated method energy can be obtained by transporting calculating
The neutron scalar flux density of coarse net is enough updated, to accelerate the iteration convergence of fine-structure mesh neutron angular flux density；Specifically include following step
Suddenly：
1) the original multigroup microscopic cross information of each nucleic is read from database；
2) nucleic atom cuclear density, temperature and the geological information included in material, input card are read from input card
In detailed domain mesh is carried out to the geometry of Solve problems, the radial zone for including fuel rod lattice cell is divided and circumferential area
Domain is divided, generally for conventional fuel rod lattice cell, and fuel region is radially divided into 3rd area, is circumferentially divided into 8th area；For
Fuel lattice cell with burnable poison Gd rods, because there is stronger space to be radially divided into 10 from effect, fuel region is shielded for it
Area, is circumferentially divided into 8th area, and it is burnup area to be marked with the region of fissioner；
1) and 2) 3) original multigroup microscopic cross, atom cuclear density and temperature letter based on each nucleic obtained by
Breath, Resonance self-shielding calculating is carried out using subgroup method, obtains the multigroup of each nucleic effectively from screen section, specific calculation formula
It is as follows：
In formula：
σx,g,iso-- nucleic iso, energy group g, reaction channel χ section；
ΔEg-- the energy width of g groups；
σx,iso(E) -- the section of the reaction channel χ at nucleic iso, ENERGY E；
φ (E) -- energy is E netron-flux density；
4) neutron transport calculating is carried out using MOC characteristic line methods according to the information 3) obtained, obtained in regional
Sub- angular flax density, specific calculation formula is as follows：
In formula：
Ω --- angle direction；
--- gradient operator；
ψg(r, Ω) --- g can group region r, the neutron angular flux density of angle Ω；
G --- g can group；
G --- can group's sum；
Σt,g(r) --- the volumic total cross-section of g groups；
Qg(r, Ω) --- neutron-transport equation source item；
Thus the neutron angular flux density of each zoning is obtained；
5) full angle space upper integral is carried out to calculating obtained neutron angular flux density in formula (2), obtained on fine-structure mesh
Average neutron scalar flux densitySpecific calculation formula is as follows：
In formula：
M --- discrete direction sum；
ωm--- quadrature group
And have：
Thus the neutron scalar flux density of each zoning is obtained；
6) when carrying out MOC iterative calculation, the corresponding coarse net difference equation of coarse net equilibrium equation is solved, coarse net is obtained and leads to
Amount, shown in calculation formula such as formula (4).It is synchronous by the ratio between coarse grid average neutron scalar flux density before and after coarse net Difference Calculation
The neutron scalar flux density on all refined nets in coarse grid is updated, the source of equation right-hand member during for updating MOC calculating next time
, MOC iterative calculation can be accelerated, shown in calculation formula such as formula (5).After MOC calculating terminates, now coarse net is preserved
The parameter of difference equation, specific calculation formula is as follows：
In formula：
N --- difference coarse net grid
U (u=x, y, z) --- direction signs；
--- mesh widths of the difference coarse net n on u (u=x, y, z) direction；
--- on coarse net grid n, g energy groups, direction is the net neutron current in u positive direction；
--- on coarse net grid n, g energy groups, direction is the net neutron current in u negative direction；
--- on coarse net grid n, g can group, r kind Homogenized cross sections；
--- on coarse net grid n, the netron-flux density on the coarse net of g energy groups；
--- on coarse net grid n, the generation section of g ' energy groups；
--- on coarse net grid n, the netron-flux density on the coarse net of g ' energy groups；
--- on coarse net grid n, the scattering section of g energy groups is scattered to from g ' energy groups；
χg--- the fission spectrum of g energy groups；
keff--- the characteristic value of neutron balance equation；
In formula：
--- the average scalar flux of thin area i g crowds of flat source after renewal, to update l+1 submatrixs MOC meters
The source item of calculation；
--- the CMFD after l submatrixs MOC calculating calculates obtained coarse net n g group mean scalar flux；
--- l submatrixs MOC calculates obtained coarse net n g groups of homogenization scalar flux；
--- l submatrixs MOC calculates resulting thin area i g crowds of flat source average scalar flux.
7) by the microscopic cross and respective regions neutron scalar flux density of each nucleic for 3), 4), 5) respectively obtaining needs
Product, i.e. each nucleic of regional microreaction rate；
Step 2：The first microreaction rate of obtained burnup step is calculated using step 1 and atom cuclear density carries out burnup meter
Calculate, when burnup is calculated, divide burnup sub-step in two burnup steps, burnup calculating is only carried out in each burnup sub-step, is not entered
Row transports calculating, carries out the renewal of microreaction rate, obtains the atom cuclear density at burnup step end, and the atom cuclear density is referred to as estimating
The atom cuclear density of step；Specifically include following steps：
1) the fission production of the decay coefficient of each nucleic, reaction channel branching ratio, fission nuclide is read from burnup database
The burnup data such as volume；
2) the atom cuclear density of each nucleic of the regional preserved in calculating is transported is read, and transports meter
The microreaction rate of obtained regional each nucleic；
3) according to the information 1), 2) obtained, burn up equation is solved using Chebyshev's rational approximation method, it is specific to calculate
Formula is as follows：
In formula：
N (t) -- expression formula of the atom cuclear density on the time；
The atom cuclear density of N (0) -- initial time
A-- burnup matrixes；
Γ -- curve is integrated, and is enclosed counterclockwise around all characteristic values one of matrix tA；
I-- unit matrixs；
I-- imaginary numbers；
Step 3：Carry out transporting calculating, calculation formula such as formula using the atom cuclear density for estimating step obtained in step 2
(1), formula (2) and formula (3) are shown, introduce coarse net accelerated method i.e. CMFD accelerated methods when transporting calculating, calculation formula is such as
Shown in formula (4) and formula (5), the coarse net parameter obtained when the last coarse net of burnup step is calculated is preserved, the microcosmic of burnup step end is obtained
Reactivity is product of the microscopic cross with neutron scalar flux density of nucleic, and wherein netron-flux density is the neutron mark on fine-structure mesh
Flux density；
Step 4：Burnup CMFD sub-steps are divided in the middle of two burnup steps, in each burnup CMFD sub-steps, burnup is walked
Just walk last coarse net parameter with burnup and carry out linear interpolation, obtain the coarse net parameter in each burnup CMFD sub-steps；
Step 5：In each burnup CMFD sub-steps, the coarse net parameter obtained using interpolation in step 4 is entered to formula (4)
Row is solved, and carries out coarse net calculating, updates the flux of coarse net, and the burnup obtained using step 3 walks the neutron mark on the fine-structure mesh at end
Flux density, the neutron scalar flux density on the fine-structure mesh in each burnup CMFD sub-steps is updated according to formula (5), and then update every
Microreaction rate in individual burnup CMFD sub-steps；
Step 6：Using the microreaction rate i.e. nucleic microscopic cross updated in step 5 in each burnup CMFD sub-steps and more
The product of neutron scalar flux density after new, is carried out between burnup calculating, and adjacent burnup CMFD sub-steps, together by formula (6)
Sample divides burnup sub-step and calculated, and finally gives the atom cuclear density at burnup step end, and the atom cuclear density is the burnup needed
The accurate atom cuclear density in step end；
Step 7：Judge whether burnup step number mesh is consistent with input value, if burnup step is consistent with input value, calculate knot
Beam；If inconsistent, step 1 is back to, the calculating of next burnup step is entered.
Claims (1)
1. a kind of method that burnup coupling is calculated that transports suitable for nuclear reactor, it is characterised in that：Comprise the following steps:
Step 1：The geological information that atom cuclear density and input card according at the beginning of being walked burnup are provided carries out transporting calculating, transports meter
It is CMFD accelerated methods that coarse net accelerated method is introduced during calculation, preserves burnup and walks the coarse net parameter obtained during just coarse net speed-up computation,
Obtain the microreaction rate i.e. microscopic cross of the nucleic in each burnup area in each first burnup area of burnup step and corresponding burnup area
The product of neutron scalar flux density, wherein fine-structure mesh neutron angular flux density can be obtained by transporting calculating, coarse net accelerated method can
The neutron scalar flux density of coarse net is updated, to accelerate the iteration convergence of fine-structure mesh neutron angular flux density；Specifically include following steps：
1) the original multigroup microscopic cross information of each nucleic is read from database；
2) nucleic atom cuclear density, temperature and the geological information included in material is read from input card；
1) and 2) 3) original multigroup microscopic cross, atom cuclear density and temperature information based on each nucleic obtained by, are used
Subgroup method carries out Resonance self-shielding calculating, obtains the multigroup of each nucleic effectively from screen section, specific calculation formula is as follows：
<mrow>
<msub>
<mi>&sigma;</mi>
<mrow>
<mi>x</mi>
<mo>,</mo>
<mi>g</mi>
<mo>,</mo>
<mi>i</mi>
<mi>s</mi>
<mi>o</mi>
</mrow>
</msub>
<mo>=</mo>
<mfrac>
<mrow>
<msub>
<mo>&Integral;</mo>
<mrow>
<msub>
<mi>&Delta;E</mi>
<mi>g</mi>
</msub>
</mrow>
</msub>
<msub>
<mi>&sigma;</mi>
<mrow>
<mi>x</mi>
<mo>,</mo>
<mi>i</mi>
<mi>s</mi>
<mi>o</mi>
</mrow>
</msub>
<mrow>
<mo>(</mo>
<mi>E</mi>
<mo>)</mo>
</mrow>
<mi>&phi;</mi>
<mrow>
<mo>(</mo>
<mi>E</mi>
<mo>)</mo>
</mrow>
<mi>d</mi>
<mi>E</mi>
</mrow>
<mrow>
<msub>
<mo>&Integral;</mo>
<mrow>
<msub>
<mi>&Delta;E</mi>
<mi>g</mi>
</msub>
</mrow>
</msub>
<msub>
<mi>&sigma;</mi>
<mrow>
<mi>x</mi>
<mo>,</mo>
<mi>i</mi>
<mi>s</mi>
<mi>o</mi>
</mrow>
</msub>
<mrow>
<mo>(</mo>
<mi>E</mi>
<mo>)</mo>
</mrow>
<mi>d</mi>
<mi>E</mi>
</mrow>
</mfrac>
<mo>-</mo>
<mo>-</mo>
<mo>-</mo>
<mrow>
<mo>(</mo>
<mn>1</mn>
<mo>)</mo>
</mrow>
</mrow>
In formula：
σx,g,iso-- nucleic iso, energy group g, reaction channel χ section；
ΔEg-- the energy width of g groups；
σx,iso(E) -- the section of the reaction channel χ at nucleic iso, ENERGY E；
φ (E) -- energy is E netron-flux density；
4) neutron transport calculating is carried out using MOC characteristic line methods according to the information 3) obtained, obtains the Neutron Angular of regional
Flux density, specific calculation formula is as follows：
<mrow>
<mi>&Omega;</mi>
<mo>&CenterDot;</mo>
<mo>&dtri;</mo>
<msub>
<mi>&psi;</mi>
<mi>g</mi>
</msub>
<mrow>
<mo>(</mo>
<mi>r</mi>
<mo>,</mo>
<mi>&Omega;</mi>
<mo>)</mo>
</mrow>
<mo>+</mo>
<msub>
<mi>&Sigma;</mi>
<mrow>
<mi>t</mi>
<mo>,</mo>
<mi>g</mi>
</mrow>
</msub>
<mrow>
<mo>(</mo>
<mi>r</mi>
<mo>)</mo>
</mrow>
<msub>
<mi>&psi;</mi>
<mi>g</mi>
</msub>
<mrow>
<mo>(</mo>
<mi>r</mi>
<mo>,</mo>
<mi>&Omega;</mi>
<mo>)</mo>
</mrow>
<mo>=</mo>
<msub>
<mi>Q</mi>
<mi>g</mi>
</msub>
<mrow>
<mo>(</mo>
<mi>r</mi>
<mo>,</mo>
<mi>&Omega;</mi>
<mo>)</mo>
</mrow>
<mo>,</mo>
<mi>g</mi>
<mo>=</mo>
<mn>1</mn>
<mo>,</mo>
<mo>...</mo>
<mo>,</mo>
<mi>G</mi>
<mo>-</mo>
<mo>-</mo>
<mo>-</mo>
<mrow>
<mo>(</mo>
<mn>2</mn>
<mo>)</mo>
</mrow>
</mrow>
In formula：
Ω --- angle direction；
--- gradient operator；
ψg(r, Ω) --- g can group region r, the neutron angular flux density of angle Ω；
G --- g can group；
G --- can group's sum；
Σt,g(r) --- the volumic total cross-section of g groups；
Qg(r, Ω) --- neutron-transport equation source item；
Thus the neutron angular flux density of each zoning is obtained；
5) full angle space upper integral is carried out to calculating obtained neutron angular flux density in formula (2), obtains flat on fine-structure mesh
Equal neutron scalar flux densitySpecific calculation formula is as follows：
<mrow>
<msub>
<mover>
<mi>&phi;</mi>
<mo>&OverBar;</mo>
</mover>
<mi>i</mi>
</msub>
<mo>=</mo>
<munder>
<mo>&Integral;</mo>
<mrow>
<mn>4</mn>
<mi>&pi;</mi>
</mrow>
</munder>
<msub>
<mover>
<mi>&psi;</mi>
<mo>&OverBar;</mo>
</mover>
<mi>i</mi>
</msub>
<mrow>
<mo>(</mo>
<mi>&Omega;</mi>
<mo>)</mo>
</mrow>
<mi>d</mi>
<mi>&Omega;</mi>
<mo>&ap;</mo>
<munderover>
<mo>&Sigma;</mo>
<mrow>
<mi>m</mi>
<mo>=</mo>
<mn>1</mn>
</mrow>
<mi>M</mi>
</munderover>
<msub>
<mi>&omega;</mi>
<mi>m</mi>
</msub>
<msub>
<mover>
<mi>&psi;</mi>
<mo>&OverBar;</mo>
</mover>
<mi>i</mi>
</msub>
<mrow>
<mo>(</mo>
<msub>
<mi>&Omega;</mi>
<mi>m</mi>
</msub>
<mo>)</mo>
</mrow>
<mo>-</mo>
<mo>-</mo>
<mo>-</mo>
<mrow>
<mo>(</mo>
<mn>3</mn>
<mo>)</mo>
</mrow>
</mrow>
In formula：
M --- discrete direction sum；
ωm--- quadrature group
And have：
<mrow>
<munderover>
<mo>&Sigma;</mo>
<mrow>
<mi>m</mi>
<mo>=</mo>
<mn>1</mn>
</mrow>
<mi>M</mi>
</munderover>
<msub>
<mi>&omega;</mi>
<mi>m</mi>
</msub>
<mo>=</mo>
<mn>4</mn>
<mi>&pi;</mi>
</mrow>
Thus the neutron scalar flux density of each zoning is obtained；
6) when carrying out MOC iterative calculation, the corresponding coarse net difference equation of coarse net equilibrium equation is solved, coarse net flux is obtained,
Shown in calculation formula such as formula (4)；It is synchronous more by the ratio between coarse grid average neutron scalar flux density before and after coarse net Difference Calculation
Neutron scalar flux density in new coarse grid on all refined nets, the source item of equation right-hand member during for updating MOC calculating next time,
MOC iterative calculation is can speed up, shown in calculation formula such as formula (5)；After MOC calculating terminates, now coarse net is preserved poor
Divide the parameter of equation, specific calculation formula is as follows：
<mrow>
<munder>
<mo>&Sigma;</mo>
<mrow>
<mi>u</mi>
<mo>=</mo>
<mi>x</mi>
<mo>,</mo>
<mi>y</mi>
<mo>,</mo>
<mi>z</mi>
</mrow>
</munder>
<mfrac>
<mn>1</mn>
<msubsup>
<mi>a</mi>
<mi>u</mi>
<mi>n</mi>
</msubsup>
</mfrac>
<mrow>
<mo>(</mo>
<msubsup>
<mi>J</mi>
<mrow>
<mi>u</mi>
<mi>g</mi>
<mo>+</mo>
</mrow>
<mi>n</mi>
</msubsup>
<mo>-</mo>
<msubsup>
<mi>J</mi>
<mrow>
<mi>u</mi>
<mi>g</mi>
<mo>-</mo>
</mrow>
<mi>n</mi>
</msubsup>
<mo>)</mo>
</mrow>
<mo>+</mo>
<msubsup>
<mover>
<mo>&Sigma;</mo>
<mo>&OverBar;</mo>
</mover>
<mrow>
<mi>r</mi>
<mo>,</mo>
<mi>g</mi>
</mrow>
<mi>n</mi>
</msubsup>
<msubsup>
<mover>
<mi>&phi;</mi>
<mo>&OverBar;</mo>
</mover>
<mi>g</mi>
<mi>n</mi>
</msubsup>
<mo>=</mo>
<mfrac>
<msub>
<mi>&chi;</mi>
<mi>g</mi>
</msub>
<msub>
<mi>k</mi>
<mrow>
<mi>e</mi>
<mi>f</mi>
<mi>f</mi>
</mrow>
</msub>
</mfrac>
<munderover>
<mo>&Sigma;</mo>
<mrow>
<msup>
<mi>g</mi>
<mo>&prime;</mo>
</msup>
<mo>=</mo>
<mn>1</mn>
</mrow>
<mi>G</mi>
</munderover>
<msubsup>
<mrow>
<mo>(</mo>
<mi>v</mi>
<msub>
<mover>
<mi>&Sigma;</mi>
<mo>&OverBar;</mo>
</mover>
<mi>f</mi>
</msub>
<mo>)</mo>
</mrow>
<msup>
<mi>g</mi>
<mo>&prime;</mo>
</msup>
<mi>n</mi>
</msubsup>
<msubsup>
<mover>
<mi>&phi;</mi>
<mo>&OverBar;</mo>
</mover>
<msup>
<mi>g</mi>
<mo>&prime;</mo>
</msup>
<mi>n</mi>
</msubsup>
<mo>+</mo>
<munderover>
<mo>&Sigma;</mo>
<munder>
<mrow>
<msup>
<mi>g</mi>
<mo>&prime;</mo>
</msup>
<mo>=</mo>
<mn>1</mn>
</mrow>
<mrow>
<msup>
<mi>g</mi>
<mo>&prime;</mo>
</msup>
<mo>&NotEqual;</mo>
<mi>g</mi>
</mrow>
</munder>
<mi>G</mi>
</munderover>
<msubsup>
<mover>
<mo>&Sigma;</mo>
<mo>&OverBar;</mo>
</mover>
<mrow>
<mi>s</mi>
<mo>,</mo>
<msup>
<mi>g</mi>
<mo>&prime;</mo>
</msup>
<mo>-</mo>
<mi>g</mi>
</mrow>
<mi>n</mi>
</msubsup>
<msubsup>
<mover>
<mi>&phi;</mi>
<mo>&OverBar;</mo>
</mover>
<msup>
<mi>g</mi>
<mo>&prime;</mo>
</msup>
<mi>n</mi>
</msubsup>
<mo>-</mo>
<mo>-</mo>
<mo>-</mo>
<mrow>
<mo>(</mo>
<mn>4</mn>
<mo>)</mo>
</mrow>
</mrow>
In formula：
N --- difference coarse net grid
U (u=x, y, z) --- direction signs；
--- mesh widths of the difference coarse net n on u (u=x, y, z) direction；
--- on coarse net grid n, g energy groups, direction is the net neutron current in u positive direction；
--- on coarse net grid n, g energy groups, direction is the net neutron current in u negative direction；
--- on coarse net grid n, g can group, r kind Homogenized cross sections；
--- on coarse net grid n, the netron-flux density on the coarse net of g energy groups；
--- on coarse net grid n, the generation section of g ' energy groups；
--- on coarse net grid n, the netron-flux density on the coarse net of g ' energy groups；
--- on coarse net grid n, the scattering section of g energy groups is scattered to from g ' energy groups；
χg--- the fission spectrum of g energy groups；
keff--- the characteristic value of neutron balance equation；
<mrow>
<msubsup>
<mi>&phi;</mi>
<mi>g</mi>
<mrow>
<mi>i</mi>
<mo>,</mo>
<mrow>
<mo>(</mo>
<mi>l</mi>
<mo>+</mo>
<mn>1</mn>
<mo>/</mo>
<mn>2</mn>
<mo>)</mo>
</mrow>
</mrow>
</msubsup>
<mo>=</mo>
<mfrac>
<msubsup>
<mover>
<mi>&phi;</mi>
<mo>&OverBar;</mo>
</mover>
<mi>g</mi>
<mrow>
<mi>n</mi>
<mo>,</mo>
<mrow>
<mo>(</mo>
<mi>l</mi>
<mo>+</mo>
<mn>1</mn>
<mo>/</mo>
<mn>2</mn>
<mo>)</mo>
</mrow>
</mrow>
</msubsup>
<msubsup>
<mover>
<mi>&phi;</mi>
<mo>&OverBar;</mo>
</mover>
<mi>g</mi>
<mrow>
<mi>n</mi>
<mo>,</mo>
<mrow>
<mo>(</mo>
<mi>l</mi>
<mo>)</mo>
</mrow>
</mrow>
</msubsup>
</mfrac>
<msubsup>
<mi>&phi;</mi>
<mi>g</mi>
<mrow>
<mi>i</mi>
<mo>,</mo>
<mrow>
<mo>(</mo>
<mi>l</mi>
<mo>)</mo>
</mrow>
</mrow>
</msubsup>
<mo>,</mo>
<mi>i</mi>
<mo>&Element;</mo>
<mi>n</mi>
<mo>-</mo>
<mo>-</mo>
<mo>-</mo>
<mrow>
<mo>(</mo>
<mn>5</mn>
<mo>)</mo>
</mrow>
</mrow>
In formula：
--- the average scalar flux of thin area i g crowds of flat source after renewal, to update l+1 submatrixs MOC calculating
Source item；
--- the CMFD after l submatrixs MOC calculating calculates obtained coarse net n g group mean scalar flux；
--- l submatrixs MOC calculates obtained coarse net n g groups of homogenization scalar flux；
--- l submatrixs MOC calculates resulting thin area i g crowds of flat source average scalar flux；
7) by the microscopic cross for each nucleic for 3), 4), 5) respectively obtaining needs and multiplying for respective regions neutron scalar flux density
Product, i.e. the microreaction rate of each nucleic of regional；
Step 2：The first microreaction rate of obtained burnup step is calculated using step 1 and atom cuclear density carries out burnup calculating, combustion
When consumption is calculated, burnup sub-step is divided in two burnup steps, burnup calculating is only carried out in each burnup sub-step, without transporting
Calculate, carry out the renewal of microreaction rate, obtain the atom cuclear density at burnup step end, the atom cuclear density is referred to as the original for estimating step
Daughter nucleus density；Specifically include following steps：
1) decay coefficient, reaction channel branching ratio, fission yield of fission nuclide of each nucleic etc. are read from burnup database
Burnup data；
2) read transport calculate in the atom cuclear density of each nucleic of regional that preserves, and transport and calculate
The microreaction rate of regional each nucleic arrived；
3) according to the information 1), 2) obtained, burn up equation, specific calculation formula are solved using Chebyshev's rational approximation method
It is as follows：
In formula：
N (t) -- expression formula of the atom cuclear density on the time；
The atom cuclear density of N (0) -- initial time
A-- burnup matrixes；
Γ -- curve is integrated, and is enclosed counterclockwise around all characteristic values one of matrix tA；
I-- unit matrixs；
I-- imaginary numbers；
Step 3：Carry out transporting calculating using the atom cuclear density for estimating step obtained in step 2, calculation formula such as formula (1),
Shown in formula (2) and formula (3), coarse net accelerated method i.e. CMFD accelerated methods, calculation formula such as formula is introduced when transporting calculating
(4) and shown in formula (5), the coarse net parameter obtained when the last coarse net of burnup step is calculated is preserved, the microreaction at burnup step end is obtained
Rate is product of the microscopic cross with neutron scalar flux density of nucleic, and wherein netron-flux density is the neutron scalar flux on fine-structure mesh
Density；
Step 4：Divide burnup CMFD sub-steps in the middle of two burnups step, in each burnup CMFD sub-steps, burnup is walked just and
The coarse net parameter at burnup step end carries out linear interpolation, obtains the coarse net parameter in each burnup CMFD sub-steps；
Step 5：In each burnup CMFD sub-steps, the coarse net parameter obtained using interpolation in step 4 is asked formula (4)
Solution, carries out coarse net calculating, updates the flux of coarse net, and the burnup obtained using step 3 walks the neutron scalar flux on the fine-structure mesh at end
Density, the neutron scalar flux density on the fine-structure mesh in each burnup CMFD sub-steps is updated according to formula (5), and then update each combustion
The microreaction rate consumed in CMFD sub-steps；
Step 6：After the microreaction rate i.e. nucleic microscopic cross and renewal updated in step 5 in each burnup CMFD sub-steps
Neutron scalar flux density product, carried out by formula (6) between burnup calculating, and adjacent burnup CMFD sub-steps, it is same to draw
Point burnup sub-step is calculated, and finally gives the atom cuclear density at burnup step end, and the atom cuclear density is the burnup step end needed
Accurate atom cuclear density；
Step 7：Judge whether burnup step number mesh is consistent with input value, if burnup step is consistent with input value, calculating terminates；Such as
It is really inconsistent, step 1 is back to, the calculating of next burnup step is entered.
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| CN110717254A (en) * | 2019-09-21 | 2020-01-21 | 哈尔滨工程大学 | Hybrid preprocessing method for rapidly predicting neutron flux distribution of digital reactor |
| CN112347645A (en) * | 2020-11-06 | 2021-02-09 | 中国核动力研究设计院 | Method and device for reconstructing burnup characteristics of reactor core grid cells |
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| CN108846190A (en) * | 2018-06-05 | 2018-11-20 | 哈尔滨工程大学 | A kind of nuclear heat coupling simulation method of PWR fuel assembly |
| CN109086506A (en) * | 2018-07-20 | 2018-12-25 | 西安交通大学 | A kind of burnup analysis calculation method suitable for liquid fuel molten salt reactor |
| CN109522510A (en) * | 2018-11-19 | 2019-03-26 | 西安交通大学 | A kind of molten salt reactor tritium transport property coupling calculation |
| 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 |
| CN110457802B (en) * | 2019-07-31 | 2021-08-20 | 上海交通大学 | Precision optimization implementation method for SFCOMPO fuel consumption experiment benchmark question check simulation |
| CN110717254A (en) * | 2019-09-21 | 2020-01-21 | 哈尔滨工程大学 | Hybrid preprocessing method for rapidly predicting neutron flux distribution of digital reactor |
| CN112347645B (en) * | 2020-11-06 | 2022-03-22 | 中国核动力研究设计院 | Method and device for reconstructing burnup characteristics of reactor core grid cells |
| CN112347645A (en) * | 2020-11-06 | 2021-02-09 | 中国核动力研究设计院 | Method and device for reconstructing burnup characteristics of reactor core grid cells |
| CN112800641A (en) * | 2020-12-21 | 2021-05-14 | 中国核动力研究设计院 | Generalized coarse net finite difference acceleration method based on region decomposition parallel |
| CN115099049A (en) * | 2022-07-08 | 2022-09-23 | 西安交通大学 | Fission yield data optimization method based on irradiated sample nuclide stock measured value |
| CN115099049B (en) * | 2022-07-08 | 2023-05-16 | 西安交通大学 | Fission yield data optimization method based on actual measured value of nuclide stock of irradiated sample |
| CN114913936A (en) * | 2022-07-18 | 2022-08-16 | 西安交通大学 | Multi-physical-fuel performance analysis method for uranium-plutonium mixed oxide fuel |
| CN114913936B (en) * | 2022-07-18 | 2022-10-25 | 西安交通大学 | Multi-physical fuel performance analysis method for uranium-plutonium mixed oxide fuel |
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