CN107301314A - A kind of computational methods searched for for fast neutron reactor balanced recycle - Google Patents
A kind of computational methods searched for for fast neutron reactor balanced recycle Download PDFInfo
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Abstract
A kind of computational methods searched for for fast neutron reactor balanced recycle, 1, fuel management scheme is expressed as a plurality of fuel management path；2nd, fuel recycle process is equivalent to approximate equilibrium circulation；3rd, pairing approximation balanced recycle, the neutron transport burnup coupling for carrying out heap interior circulation is calculated, and obtains the transmuting matrix in each fuel management path each stage；4th, repeat step 2 and 3, until the nucleon density vector convergence in each fuel management path each stage, obtain heap interior circulation pattern；5th, to length of the cycle linear interpolation or extrapolation, search is met the heap interior circulation pattern of discharge burn-up depth requirements；6th, calculate spentnuclear fuel post processing recovery and fresh fuel remanufactures process, according to transmuting matrix, the burnup that the sub- intensity vector of new loading fuel kernel carries out heap interior circulation is calculated, repetition said process newly loads the sub- intensity vector convergence of fuel kernel until each fuel management path；7th, the new target effective proliferation factor for loading fuel enrichment, realizing specified time point is adjusted.
Description
Technical field
The present invention relates to nuclear reactor fuel cycle art, be it is a kind of by fast neutron reactor balanced recycle search based on
Calculation method.
Background technology
The fuel recycle of nuclear reactor be related to burnup in heap of the manufacture of nuclear fuel, nuclear fuel and unloaded out of heap it is weary
The complex process of circulation is reclaimed in fuel post processing.The fuel recycle simulation of nuclear reactor, can calculate and obtain nuclear fuel in heap
With the quality stream in heap outer loop process, and the Effective multiplication factor k of evaluation response heapeff, core power distribution etc. parameter, be
Nuclear reactor designs analyze the basis with Economic Evaluation.The balanced recycle of nuclear reactor is that the representativeness of reactor operation is followed
Ring, the determination of the parameter such as its length of the cycle, fuel enrichment is the committed step of reactor design analysis.
Existing fast neutron reactor fuel recycle computational methods are based primarily upon square or the neutron of hexagon locking nub is defeated
Fortune or diffusion computational methods, and microcosmic burnup computational methods are coupled, according to given fuel management scheme, circulation one by one is counted
Calculate until balanced recycle.In above-mentioned fast neutron reactor fuel recycle computational methods balanced recycle is searched for by cycle calculations one by one
Computational efficiency it is relatively low, it is difficult to meet fast neutron reactor design analysis actual demand.Therefore, a kind of fast neutron of research is needed badly
The fuel recycle process of the computational methods, quick and precisely simulation fast neutron reactor of the search of reactor balanced recycle, and search for
Balanced recycle, the parameter such as length of the cycle and fuel enrichment to determine balanced recycle.
The content of the invention
In order to overcome the problem of above-mentioned prior art is present, it is used for fast neutron reaction it is an object of the invention to provide one kind
The computational methods of heap balanced recycle search, realize the fuel recycle simulation of fast neutron reactor and the quick of balanced recycle is searched
Rope.
In order to achieve the above object, the present invention is adopted the following technical scheme that：
A kind of computational methods searched for for fast neutron reactor balanced recycle, comprise the following steps：
Step 1：Repeated fuel management scheme applied to fast neutron reactor is expressed as a plurality of cartridge line of reasoning
Footpath, every fuel management path description fuel assembly is from loading reactor core and the locus in heap residing for each combustion cycle
The whole process for setting out reactor core is finally unloaded, the combustion cycle that fuel assembly undergoes in heap is defined as a stage；
For the fast neutron reactor using batch turning formula refuelling scheme, the difference that same fuel assembly is undergone in heap in-core diverse location
Stage definitions are a fuel management path；For the fast neutron reactor using scattered refueling scheme, by each fuel stack
Part is respectively defined as separate fuel management path in the different phase that heap in-core same position undergoes；If reactor core includes K
Individual fuel assembly position, r1,r2,…,rK, fuel management scheme includes L bar fuel managements path, fuel management path l descriptions
One fuel assembly is from loading reactor core and in heap undergoing multiple combustion cycles and finally unload the process of reactor core of setting out, wherein firing
Expect that locus of the component in heap is defined by regional number r, it is 1 that the new fuel assembly for loading reactor core, which defines its stage No., in heap
The stage No. of the fuel assembly of τ combustion cycle of interior experience is τ+1, the combustion cycle number of times that fuel assembly undergoes altogether in heap
For Sl, therefore when stage No. reaches SlWhen+1, fuel assembly will unload and set out reactor core；
Step 2：For the fast neutron reactor using batch turning formula or scattered refueling scheme, according to different equivalence sides
Formula, the reactor core combustion cycle by repeatability is approximately balanced recycle.For using scattered refueling scheme reactor, using point
Scattered formula is reloaded approximately, the nucleon density vector in each stage in fuel management path is mixed, then by mixed nucleon density
Corresponding fuel assembly during DUAL PROBLEMS OF VECTOR MAPPING is circulated to approximate equilibrium；, will be same for the reactor using batch turning formula refuelling scheme
Fuel assembly is mapped to corresponding fuel assembly in approximate equilibrium circulation in the nucleon density vector of the different phase of heap in-core；
Define Nr(t) be moment t when positioned at region r fuel assembly average nucleon intensity vector, its calculation formula is such as
Formula (1)：
In formula：
Nl,τ(t) --- fuel management path l description fuel assembly be in nucleon densities of the stage τ in moment t to
Amount；
Vl--- the volume of the fuel assembly of fuel management path l descriptions；
Step 3：For approximate equilibrium circulation, the neutron transport burnup coupling for carrying out burnup cyclic process in heap is calculated, by
Formula (2) calculates the transmuting matrix for obtaining that stage τ burnup process is represented in the l of fuel management pathBased on transmuting
MatrixThe l fuel assemblies described in fuel management path are calculated in stage τ burnup process；
In formula：
L --- fuel management path number；
τ --- the burnup cycle stage numbers in heap；
T --- combustion cycle length；
E --- the new enrichment for loading fuel；
--- the new nucleon density vector for loading fuel；
--- each burnup nucleic mutually converts pass during representing stage τ burnup in the l of fuel management path
The burnup matrix of system；
If enrichment is the e new sub- intensity vector of loading fuel kernelLoad reactor core in first S circulation, by length of the cycle
The post processing of S heap interior circulation and spentnuclear fuel for T and fresh fuel remanufacture process, will produce identical and newly load fuel
Nucleon density vectorNow reactor core is in poised state, while meeting the discharge burn-up depth requirements that user specifies；To fuel
Manage the fuel assembly and its residing stage τ (1≤τ≤S of path l descriptionsl), there is transmuting matrixCan be by fuel
The nucleon density vector of component is unloaded when end is circulated from stage τ burnup to stage τ+1, then to be set out the nucleon density vector of reactor core and is,
In formula：
Sl--- the combustion cycle number of times that the fuel assembly of fuel management path l descriptions undergoes altogether in heap；
--- the fuel assembly of fuel management path l descriptions each burnup nucleic phase during stage τ burnup
The transmuting matrix mutually converted；
--- nucleon density vector of the fuel assembly of fuel management path l descriptions when initially loading reactor core；
L --- the fuel management number of passes included in fuel management scheme；
The fuel assembly of fuel management path l descriptions is represented by public affairs from loading reactor core to unloading the burnup process that sets out reactor core
Transmuting matrix in formula (4)
In formula：
Sl--- the combustion cycle number of times that the fuel assembly of fuel management path l descriptions undergoes altogether in heap；
--- the fuel assembly of fuel management path l descriptions each burnup nucleic during stage τ burnup
The transmuting matrix mutually converted；
The fuel assembly for the L bar fuel management path descriptions that fuel management scheme is included sets out reactor core from loading reactor core to unloading
Burnup process be represented by transmuting matrix in formula (5)
In formula：
Diag --- represent the diagonal element of matrix in block form；
--- represent the fuel assembly of the description of fuel management path 1 from reactor core is loaded to unloading the combustion that sets out reactor core
The transmuting matrix of material process, by that analogy；
To all fuel management paths, unloaded during circulation end and set out the nucleon density vector of reactor core and can be written as following compact shape
Formula,
In formula：
--- the fuel assembly for the L bar fuel management path descriptions that fuel management scheme is included from load reactor core
To the transmuting matrix for unloading the burnup process for setting out reactor core；
--- the L bar fuel managements path included to fuel management scheme, the new nucleon density vector for loading fuel；
Step 4：Repeat step 2 and 3, untill the nucleon density vector convergence in each fuel management path each stage, from
And obtain heap interior circulation pattern；Core during the fuel management path l stages τ burnup end that convergent criterion obtains for twice adjacent calculation
The norm of relative error 2 of sub- intensity vector is less than the convergence criterion value that user specifies, and calculation formula is as follows；
E=| | N(q)-N(q-1)||2Formula (7)
The relative of nucleon density vector is missed when the fuel management path l stages τ burnup that e --- twice adjacent calculation is obtained is last
Poor 2 norm；
N(q)--- nucleon density vector when the fuel management path l stages τ burnup that the q times calculating is obtained is last；
N(q-1)--- nucleon density vector when the fuel management path l stages τ burnup that the q-1 times calculating is obtained is last；
Step 5：According to heap interior circulation pattern, the average discharge burn-up depth for obtaining reactor core can be calculated, will to meet user
The discharge burn-up depth b asked0, linear interpolation or extrapolation are carried out to length of the cycle as shown in formula (8), and re-search for following in heap
Ring mode, untill being met the heap interior circulation pattern for the discharge burn-up depth requirements that user specifies；
In formula：
T1--- the combustion cycle length assumed in balanced recycle search procedure；
b(T1) --- combustion cycle length takes T1When the average discharge burn-up depth of obtained reactor core；
T2--- the combustion cycle length assumed in balanced recycle search procedure；
b(T2) --- combustion cycle length takes T2When the average discharge burn-up depth of obtained reactor core；
b0--- the target discharge burn-up depth in balanced recycle search procedure；
Step 6：On the basis of the heap interior circulation pattern of discharge burn-up depth requirements is met, it is considered to heap outer circulation, calculate weary
The nucleon density vector for remanufacturing process, obtaining new loading fuel with fresh fuel is reclaimed in the post processing of fuelSuch as formula (9)
It is shown：
In formula：
Qr(N) --- the matrix that the post processing recovery coefficient of different nucleic is constituted in unloading spentnuclear fuel (will provide variable whole
Body implication)；
N --- the vector that the nucleon density vector unloaded from each fuel management path is constituted；
Qf(N) --- the matrix that the distribution share of external complement nucleic is constituted；
Nf--- the nucleon density vector of external complement nucleic；
The transmuting matrix in each fuel management path each stage obtained according to heap interior circulation mode computation, fuel is loaded to new
Nucleon density vectorLoad reactor core to fuel assembly from fuel assembly and unload and set out the burnup process of reactor core and calculated, obtain
The nucleon density vector for setting out reactor core is unloaded in each fuel management path, is repeated said process and is newly loaded until in each fuel management path
The nucleon density vector of fuelUntill convergence, so as to obtain the unrestricted balanced recycle pattern of Effective multiplication factor；
Ignore transmuting matrixWith length of the cycle and the new nucleon density vector for loading fuelCorrelation, tool
Body iterative process is as follows,
In formula：
N(v)--- the v times iterate to calculate obtain from each fuel management path unload nucleon density vector constitute to
Amount；
--- the fuel assembly for the L bar fuel management path descriptions that fuel management scheme is included from load reactor core
To the transmuting matrix for unloading the burnup process for setting out reactor core；
--- the v times iterative calculation when each fuel management path newly load fuel nucleon density vector constitute to
Amount；
--- each fuel management path newly loads the nucleon density vector composition of fuel during the v+1 times iterative calculation
Vector；
Qr(N(v)) --- the matrix that the post processing recovery coefficient of different nucleic is constituted in unloading spentnuclear fuel；
Qf(N(v)) --- the matrix that the distribution share of external complement nucleic is constituted；
Nf--- the nucleon density vector of external complement nucleic；
N(v+1)--- what the nucleon density vector unloaded from each fuel management path that the v+1 times iterative calculation is obtained was constituted
Vector；
--- each fuel management path newly loads the nucleon density vector composition of fuel during the v+2 times iterative calculation
Vector；
Qr(N(v+1)) --- the matrix that the post processing recovery coefficient of different nucleic is constituted in unloading spentnuclear fuel；
Qf(N(v+1)) --- the matrix that the distribution share of external complement nucleic is constituted；
Using changeless length of the cycle T and enrichment e, above-mentioned iterative process is repeated, the core until newly loading fuel
Sub- intensity vectorUntill convergence；
Step 7：Based on obtained unrestricted balanced recycle pattern, by the new enrichment e for loading fuel of adjustment, realizing will
Effective multiplication factor k in the combustion cycle asked during time point α T0, so as to obtain final limited balanced recycle pattern；Using
Convergent transmuting matrixThe convergent new nucleon density vector for loading fuelWith length of the cycle T, calculate then
Between point α T when Effective multiplication factor k；Assuming that Effective multiplication factor k is on the new linear function for loading fuel enrichment, it is
Effective multiplication factor k during α T at the time of satisfaction is required0, linear interpolation is carried out to enrichment or extrapolation is as follows,
In formula：
e1--- the new loading fuel enrichment assumed in balanced recycle search procedure；
k(e1) --- the new fuel enrichment that loads takes e1When obtained reactor core Effective multiplication factor；
e2--- the new loading fuel enrichment assumed in balanced recycle search procedure；
k(e2) --- the new fuel enrichment that loads takes e2When obtained reactor core Effective multiplication factor；
k0--- the target effective proliferation factor in balanced recycle search procedure；
According to the new enrichment e of estimation3, re-search for meeting the heap interior circulation pattern of discharge burn-up requirement and unrestricted flat
Weigh circulation pattern, and calculates Effective multiplication factor k when obtaining α T, steps be repeated alternatively until effective when being met moment α T
Proliferation factor is k0Limited balanced recycle.
Compared with traditional balanced recycle searching method simulated based on direct circulation, the present invention has following outstanding advantages：
1. the present invention is while search is balanced circulation, it is determined that balanced recycle newly loads the enrichment of fuel and followed
Ring length, the requirement of reactor core Effective multiplication factor when meeting discharge burn-up depth that user specifies and sometime putting；
2. searching for during balanced recycle, compared to direct circulation analogy method, amount of calculation needed for the present invention is significantly reduced, and is counted
Efficiency is calculated to significantly improve.
Brief description of the drawings
Fig. 1 balanced recycle search routine figures.
The iterative process figure of Fig. 2 heap interior circulation patterns.
Embodiment
The present invention proposes a set of computational methods searched for suitable for fast neutron reactor balanced recycle, realizes fast neutron
The fuel recycle simulation of reactor and the fast search of balanced recycle, and determine the length of the cycle and fuel enrichment of balanced recycle
Etc. parameter with the Effective multiplication factor requirement when discharge burn-up depth for meeting reactor core and specified time point.
The present invention includes following aspect：
1) neutron that each stage burnup analysis in every fuel management path needs in the fuel management scheme that will be repeated
Transport to calculate with burnup and be compressed to approximate equilibrium circulation, fuel management path each stage is obtained according to approximate equilibrium cycle calculations
Transmuting matrix, repeats said process untill the nucleon density vector convergence in each fuel management path each stage, obtains in heap
Circulation pattern；
2) adjust the length of the cycle of combustion cycle and calculate heap interior circulation pattern again, until being met user's sound
The length of the cycle of bright discharge burn-up depth requirements, further considers heap outer circulation, and the post processing for calculating spentnuclear fuel is reclaimed and new
Fuel remanufactures process, and obtains heap interior circulation pattern, repeats said process and loads combustion until new in each fuel management path
Untill the nucleon density vector convergence of material, unrestricted balanced recycle pattern is obtained；
3) it can be calculated according to unrestricted balanced recycle pattern and obtain during balanced recycle k at sometime pointeff, no
Disconnected adjustment is new to be loaded in fuel the easily enrichment of fissioner and re-searches for unrestricted balanced recycle pattern, is met balance
Sometime user specifies k at point in cyclic processeffIt is required that limited balanced recycle pattern.
As shown in figure 1, the embodiment of balanced recycle searching method is as follows：
Step 1：Repeated fuel management scheme applied to fast neutron reactor is expressed as a plurality of cartridge line of reasoning
Footpath, every fuel management path description fuel assembly is from loading reactor core and the locus in heap residing for each combustion cycle
The whole process for setting out reactor core is finally unloaded, the combustion cycle that fuel assembly undergoes in heap is defined as a stage.
For the fast neutron reactor using batch turning formula refuelling scheme, the difference that same fuel assembly is undergone in heap in-core diverse location
Stage definitions are a fuel management path.For the fast neutron reactor using scattered refueling scheme, by each fuel stack
Part is respectively defined as separate fuel management path in the different phase that heap in-core same position undergoes.If reactor core includes K
Individual fuel assembly position, r1,r2,…,rK, fuel management scheme includes L bar fuel managements path, fuel management path l descriptions
One fuel assembly is from loading reactor core and in heap undergoing multiple combustion cycles and finally unload the process of reactor core of setting out, wherein firing
Expect that locus of the component in heap is defined by regional number r, it is 1 that the new fuel assembly for loading reactor core, which defines its stage No., in heap
The stage No. of the fuel assembly of τ combustion cycle of interior experience is τ+1, the combustion cycle number of times that fuel assembly undergoes altogether in heap
For Sl, therefore when stage No. reaches SlWhen+1, fuel assembly will unload and set out reactor core.
Step 2：For the fast neutron reactor using batch turning formula or scattered refueling scheme, according to different equivalence sides
Formula, the reactor core combustion cycle by repeatability is approximately balanced recycle.For using scattered refueling scheme reactor, using point
Scattered formula is reloaded approximately, the nucleon density vector in each stage in fuel management path is mixed, then by mixed nucleon density
Corresponding fuel assembly during DUAL PROBLEMS OF VECTOR MAPPING is circulated to approximate equilibrium；, will be same for the reactor using batch turning formula refuelling scheme
Fuel assembly is mapped to corresponding fuel assembly in approximate equilibrium circulation in the nucleon density vector of the different phase of heap in-core.
Define Nr(t) be moment t when positioned at region r fuel assembly average nucleon intensity vector, its calculation formula is such as
Formula (1)：
In formula：
Nl,τ(t) --- fuel management path l description fuel assembly be in nucleon densities of the stage τ in moment t to
Amount；
Vl--- the volume of the fuel assembly of fuel management path l descriptions；
Step 3：For approximate equilibrium circulation, the neutron transport burnup coupling for carrying out burnup cyclic process in heap is calculated, will
Burnup cyclic process is temporally divided into some burnup steps in heap, to each burnup step using such as region nucleon density iteration side
Method, neutron transport and burnup calculating process to combustion cycle in heap are iterated, each fuel of heap in-core when burnup walks end
Component axially each section nucleon density vector convergence position；Calculated by formula (2) and obtain representing stage τ in the l of fuel management path
The transmuting matrix of burnup processBased on transmuting matrixThe fuel stack described to fuel management path l
Part is calculated in stage τ burnup process, and burnup, which is calculated, can use the matrix exponetial algorithm based on Chebyshev's rational approximation.
In formula：
L --- fuel management path number；
τ --- the burnup cycle stage numbers in heap；
T --- combustion cycle length；
E --- the new enrichment for loading fuel；
--- the new nucleon density vector for loading fuel；
--- each burnup nucleic mutually converts pass during representing stage τ burnup in the l of fuel management path
The burnup matrix of system；
If enrichment is the e new sub- intensity vector of loading fuel kernelLoad reactor core in first S circulation, by length of the cycle
The post processing of S heap interior circulation and spentnuclear fuel for T and fresh fuel remanufacture process, will produce identical and newly load fuel
Nucleon density vectorNow reactor core is in poised state, while meeting the discharge burn-up depth requirements that user specifies.To fuel
Manage the fuel assembly and its residing stage τ (1≤τ≤S of path l descriptionsl), there is transmuting matrixCan be by fuel
The nucleon density vector of component is unloaded when end is circulated from stage τ burnup to stage τ+1, then to be set out the nucleon density vector of reactor core and is,
In formula：
Sl--- the combustion cycle number of times that the fuel assembly of fuel management path l descriptions undergoes altogether in heap；
--- the fuel assembly of fuel management path l descriptions each burnup nucleic phase during stage τ burnup
The transmuting matrix mutually converted；
--- nucleon density vector of the fuel assembly of fuel management path l descriptions when initially loading reactor core；
L --- the fuel management number of passes included in fuel management scheme；
The fuel assembly of fuel management path l descriptions is represented by public affairs from loading reactor core to unloading the burnup process that sets out reactor core
Transmuting matrix in formula (4)
In formula：
Sl--- the combustion cycle number of times that the fuel assembly of fuel management path l descriptions undergoes altogether in heap；
--- the fuel assembly of fuel management path l descriptions each burnup nucleic during stage τ burnup
The transmuting matrix mutually converted；
The fuel assembly for the L bar fuel management path descriptions that fuel management scheme is included sets out reactor core from loading reactor core to unloading
Burnup process be represented by transmuting matrix in formula (5)
In formula：
Diag --- represent the diagonal element of matrix in block form；
--- represent the fuel assembly of the description of fuel management path 1 from reactor core is loaded to unloading the combustion that sets out reactor core
The transmuting matrix of material process, by that analogy；
To all fuel management paths, unloaded during circulation end and set out the nucleon density vector of reactor core and can be written as following compact shape
Formula,
In formula：
--- the fuel assembly for the L bar fuel management path descriptions that fuel management scheme is included from load reactor core
To the transmuting matrix for unloading the burnup process for setting out reactor core；
--- the L bar fuel managements path included to fuel management scheme, the new nucleon density vector for loading fuel；
Step 4：As shown in Fig. 2 repeat step 2 and 3, until the nucleon density vector in each fuel management path each stage is received
Untill holding back, so as to obtain heap interior circulation pattern；Convergent criterion is the fuel management path l stages τ that twice adjacent calculation is obtained
The norm of relative error 2 of nucleon density vector is less than the convergence criterion value that user specifies when burnup is last, and calculation formula is as follows；
E=| | N(q)-N(q-1)||2Formula (7)
The relative of nucleon density vector is missed when the fuel management path l stages τ burnup that e --- twice adjacent calculation is obtained is last
Poor 2 norm；
N(q)--- nucleon density vector when the fuel management path l stages τ burnup that the q times calculating is obtained is last；
N(q-1)--- nucleon density vector when the fuel management path l stages τ burnup that the q-1 times calculating is obtained is last；
Step 5：According to heap interior circulation pattern, the average discharge burn-up depth for obtaining reactor core can be calculated, will to meet user
The discharge burn-up depth b asked0, linear interpolation or extrapolation are carried out to length of the cycle as shown in formula (8), and re-search for following in heap
Ring mode, untill being met the heap interior circulation pattern for the discharge burn-up depth requirements that user specifies；
In formula：
T1--- the combustion cycle length assumed in balanced recycle search procedure；
b(T1) --- combustion cycle length takes T1When the average discharge burn-up depth of obtained reactor core；
T2--- the combustion cycle length assumed in balanced recycle search procedure；
b(T2) --- combustion cycle length takes T2When the average discharge burn-up depth of obtained reactor core；
b0--- the target discharge burn-up depth in balanced recycle search procedure；
Step 6：On the basis of the heap interior circulation pattern of discharge burn-up depth requirements is met, it is considered to heap outer circulation, calculate weary
The nucleon density vector for remanufacturing process, obtaining new loading fuel with fresh fuel is reclaimed in the post processing of fuelSuch as formula (9)
It is shown：
In formula：
Qr(N) --- the matrix that the post processing recovery coefficient of different nucleic is constituted in unloading spentnuclear fuel (will provide variable whole
Body implication)；
N --- the vector that the nucleon density vector unloaded from each fuel management path is constituted；
Qf(N) --- the matrix that the distribution share of external complement nucleic is constituted；
Nf--- the nucleon density vector of external complement nucleic；
The transmuting matrix in each fuel management path each stage obtained according to heap interior circulation mode computation, fuel is loaded to new
Nucleon density vectorLoad reactor core to fuel assembly from fuel assembly and unload and set out the burnup process of reactor core and calculated, obtain
The nucleon density vector for setting out reactor core is unloaded in each fuel management path, is repeated said process and is newly loaded until in each fuel management path
The nucleon density vector of fuelUntill convergence, so as to obtain the unrestricted balanced recycle pattern of Effective multiplication factor；
Ignore transmuting matrixWith length of the cycle and the new nucleon density vector for loading fuelCorrelation, tool
Body iterative process is as follows,
In formula：
N(v)--- the v times iterate to calculate obtain from each fuel management path unload nucleon density vector constitute to
Amount；
--- the fuel assembly for the L bar fuel management path descriptions that fuel management scheme is included from load reactor core
To the transmuting matrix for unloading the burnup process for setting out reactor core；
--- the v times iterative calculation when each fuel management path newly load fuel nucleon density vector constitute to
Amount；
--- each fuel management path newly loads the nucleon density vector composition of fuel during the v+1 times iterative calculation
Vector；
Qr(N(v)) --- the matrix that the post processing recovery coefficient of different nucleic is constituted in unloading spentnuclear fuel；
Qf(N(v)) --- the matrix that the distribution share of external complement nucleic is constituted；
Nf--- the nucleon density vector of external complement nucleic；
N(v+1)--- what the nucleon density vector unloaded from each fuel management path that the v+1 times iterative calculation is obtained was constituted
Vector；
--- each fuel management path newly loads the nucleon density vector composition of fuel during the v+2 times iterative calculation
Vector；
Qr(N(v+1)) --- the matrix that the post processing recovery coefficient of different nucleic is constituted in unloading spentnuclear fuel；
Qf(N(v+1)) --- the matrix that the distribution share of external complement nucleic is constituted；
Using changeless length of the cycle T and enrichment e, above-mentioned iterative process is repeated, the core until newly loading fuel
Sub- intensity vectorUntill convergence.
Step 7：Based on obtained unrestricted balanced recycle pattern, by the new enrichment e for loading fuel of adjustment, realizing will
Effective multiplication factor k in the combustion cycle asked during time point α T0, so as to obtain final limited balanced recycle pattern.Using
Convergent transmuting matrixThe convergent new nucleon density vector for loading fuelWith length of the cycle T, calculate then
Between point α T when Effective multiplication factor k.Assuming that Effective multiplication factor k is on the new linear function for loading fuel enrichment, it is
Effective multiplication factor k during α T at the time of satisfaction is required0, linear interpolation is carried out to enrichment or extrapolation is as follows,
In formula：
e1--- the new loading fuel enrichment assumed in balanced recycle search procedure；
k(e1) --- the new fuel enrichment that loads takes e1When obtained reactor core Effective multiplication factor；
e2--- the new loading fuel enrichment assumed in balanced recycle search procedure；
k(e2) --- the new fuel enrichment that loads takes e2When obtained reactor core Effective multiplication factor；
k0--- the target effective proliferation factor in balanced recycle search procedure；
According to the new enrichment e of estimation3, re-search for meeting the heap interior circulation pattern of discharge burn-up requirement and unrestricted flat
Weigh circulation pattern, and calculates Effective multiplication factor k when obtaining α T, steps be repeated alternatively until effective when being met moment α T
Proliferation factor is k0Limited balanced recycle.
Claims (1)
1. a kind of computational methods searched for for fast neutron reactor balanced recycle, it is characterised in that：Comprise the following steps：
Step 1：Repeated fuel management scheme applied to fast neutron reactor is expressed as a plurality of fuel management path, often
Bar fuel management path description fuel assembly is from loading reactor core and locus in heap residing for each combustion cycle and most
The whole process for setting out reactor core is unloaded eventually, and the combustion cycle that fuel assembly undergoes in heap is defined as a stage；For
Using the fast neutron reactor of batch turning formula refuelling scheme, the different phase that same fuel assembly is undergone in heap in-core diverse location
It is defined as a fuel management path；For the fast neutron reactor using scattered refueling scheme, each fuel assembly is existed
The different phase of heap in-core same position experience is respectively defined as separate fuel management path；If reactor core includes K combustion
Expect module position, r1,r2,…,rK, fuel management scheme includes L bar fuel managements path, and fuel management path l describes one
Individual fuel assembly is from loading reactor core and undergo multiple combustion cycles in heap and finally unload the process of reactor core of setting out, wherein fuel stack
Locus of the part in heap is defined by regional number r, and it is 1 that the new fuel assembly for loading reactor core, which defines its stage No., is passed through in heap
The stage No. for going through the fuel assembly of τ combustion cycle is τ+1, and the combustion cycle number of times that fuel assembly undergoes altogether in heap is
Sl, therefore when stage No. reaches SlWhen+1, fuel assembly will unload and set out reactor core；
Step 2：, will according to different equivalents for the fast neutron reactor using batch turning formula or scattered refueling scheme
The reactor core combustion cycle of repeatability is approximately balanced recycle；For the reactor using scattered refueling scheme, using distributing
Reload approximate, the nucleon density vector in each stage in fuel management path is mixed, then by mixed nucleon density vector
Map to corresponding fuel assembly in approximate equilibrium circulation；For the reactor using batch turning formula refuelling scheme, by same fuel
Component is mapped to corresponding fuel assembly in approximate equilibrium circulation in the nucleon density vector of the different phase of heap in-core；
Define Nr(t) be moment t when positioned at region r fuel assembly average nucleon intensity vector, its calculation formula such as formula (1)：
In formula：
Nl,τ(t) --- the fuel assembly of fuel management path l descriptions is in nucleon density vectors of the stage τ in moment t；
Vl--- the volume of the fuel assembly of fuel management path l descriptions；
Step 3：For approximate equilibrium circulation, the neutron transport burnup coupling for carrying out burnup cyclic process in heap is calculated, by formula
(2) the transmuting matrix for obtaining that stage τ burnup process is represented in the l of fuel management path is calculatedBased on transmuting matrixThe l fuel assemblies described in fuel management path are calculated in stage τ burnup process；
In formula：
L --- fuel management path number；
τ --- the burnup cycle stage numbers in heap；
T --- combustion cycle length；
E --- the new enrichment for loading fuel；
--- the new nucleon density vector for loading fuel；
--- the combustion of each mutual transforming relationship of burnup nucleic during stage τ burnup is represented in the l of fuel management path
Consume matrix；
If enrichment is the e new sub- intensity vector of loading fuel kernelLoad reactor core in first S circulation, be T by length of the cycle
S heap interior circulation and the post processing of spentnuclear fuel and fresh fuel remanufacture process, identical will be produced and newly load fuel kernel
Sub- intensity vectorNow reactor core is in poised state, while meeting the discharge burn-up depth requirements that user specifies；To cartridge
The fuel assembly and its residing stage τ (1≤τ≤S of line of reasoning footpath l descriptionsl), there is transmuting matrixBy fuel assembly
Nucleon density vector unload when end is circulated from stage τ burnup to stage τ+1, then and set out the nucleon density vector of reactor core and be,
In formula：
Sl--- the combustion cycle number of times that the fuel assembly of fuel management path l descriptions undergoes altogether in heap；
--- the fuel assembly of fuel management path l descriptions each burnup nucleic during stage τ burnup mutually turns
The transmuting matrix of change；
--- nucleon density vector of the fuel assembly of fuel management path l descriptions when initially loading reactor core；
L --- the fuel management number of passes included in fuel management scheme；
Fuel management path l description fuel assembly from load reactor core to unload set out reactor core burnup procedural representation be formula (4)
In transmuting matrix
In formula：
Sl--- the combustion cycle number of times that the fuel assembly of fuel management path l descriptions undergoes altogether in heap；
--- the fuel assembly of fuel management path l descriptions each burnup nucleic during stage τ burnup mutually turns
The transmuting matrix of change；
The fuel assembly for the L bar fuel management path descriptions that fuel management scheme is included is from reactor core is loaded to unloading the combustion that sets out reactor core
Consumption process is represented by the transmuting matrix in formula (5)
In formula：
Diag --- represent the diagonal element of matrix in block form；
--- represent the fuel assembly of the description of fuel management path 1 from reactor core is loaded to unloading the fuel mistake that sets out reactor core
The transmuting matrix of journey, by that analogy；
To all fuel management paths, unloaded during circulation end and set out the nucleon density vector of reactor core and be written as following compact form,
In formula：
--- the fuel assembly for the L bar fuel management path descriptions that fuel management scheme is included is from reactor core is loaded to unloading
Set out the transmuting matrix of the burnup process of reactor core；
--- the L bar fuel managements path included to fuel management scheme, the new nucleon density vector for loading fuel；
Step 4：Repeat step 2 and 3, untill the nucleon density vector convergence in each fuel management path each stage, so that
To heap interior circulation pattern；Nucleon is close during the fuel management path l stages τ burnup end that convergent criterion obtains for twice adjacent calculation
The norm of relative error 2 of degree vector is less than the convergence criterion value that user specifies, and calculation formula is as follows；
E=| | N(q)-N(q-1)||2Formula (7)
The relative error 2 of nucleon density vector when the fuel management path l stages τ burnup that e --- twice adjacent calculation is obtained is last
Norm；
N(q)--- nucleon density vector when the fuel management path l stages τ burnup that the q times calculating is obtained is last；
N(q-1)--- nucleon density vector when the fuel management path l stages τ burnup that the q-1 times calculating is obtained is last；
Step 5：According to heap interior circulation pattern, the average discharge burn-up depth for obtaining reactor core is calculated, to meet unloading for user's requirement
Expect burn-up level b0, linear interpolation or extrapolation are carried out to length of the cycle as shown in formula (8), and re-search for heap interior circulation mould
Formula, untill being met the heap interior circulation pattern for the discharge burn-up depth requirements that user specifies；
In formula：
T1--- the combustion cycle length assumed in balanced recycle search procedure；
b(T1) --- combustion cycle length takes T1When the average discharge burn-up depth of obtained reactor core；
T2--- the combustion cycle length assumed in balanced recycle search procedure；
b(T2) --- combustion cycle length takes T2When the average discharge burn-up depth of obtained reactor core；
b0--- the target discharge burn-up depth in balanced recycle search procedure；
Step 6：On the basis of the heap interior circulation pattern of discharge burn-up depth requirements is met, it is considered to heap outer circulation, spentnuclear fuel is calculated
Post processing reclaim and fresh fuel remanufactures process, obtain the new nucleon density vector for loading fuelAs shown in formula (9)：
In formula：
Qr(N) --- the matrix that the post processing recovery coefficient of different nucleic is constituted in unloading spentnuclear fuel；
N --- the vector that the nucleon density vector unloaded from each fuel management path is constituted；
Qf(N) --- the matrix that the distribution share of external complement nucleic is constituted；
Nf--- the nucleon density vector of external complement nucleic；
The transmuting matrix in each fuel management path each stage obtained according to heap interior circulation mode computation, to the new core for loading fuel
Sub- intensity vectorLoad reactor core to fuel assembly from fuel assembly and unload and set out the burnup process of reactor core and calculated, obtain each combustion
The nucleon density vector for setting out reactor core is unloaded in expects pipe line of reasoning footpath, is repeated said process and is loaded fuel until new in each fuel management path
Nucleon density vectorUntill convergence, so as to obtain the unrestricted balanced recycle pattern of Effective multiplication factor；
Ignore transmuting matrixWith length of the cycle and the new nucleon density vector for loading fuelCorrelation, it is specific repeatedly
It is as follows for flow,
In formula：
N(v)--- the vector that the nucleon density vector unloaded from each fuel management path that the v times iterative calculation is obtained is constituted；
--- the fuel assembly for the L bar fuel management path descriptions that fuel management scheme is included is from reactor core is loaded to unloading
Set out the transmuting matrix of the burnup process of reactor core；
--- each fuel management path newly loads the vector that the nucleon density vector of fuel is constituted during the v times iterative calculation；
--- the v+1 times iterative calculation when each fuel management path newly load fuel nucleon density vector constitute to
Amount；
Qr(N(v)) --- the matrix that the post processing recovery coefficient of different nucleic is constituted in unloading spentnuclear fuel；
Qf(N(v)) --- the matrix that the distribution share of external complement nucleic is constituted；
Nf--- the nucleon density vector of external complement nucleic；
N(v+1)--- the v+1 times iterate to calculate obtain from each fuel management path unload nucleon density vector constitute to
Amount；
--- the v+2 times iterative calculation when each fuel management path newly load fuel nucleon density vector constitute to
Amount；
Qr(N(v+1)) --- the matrix that the post processing recovery coefficient of different nucleic is constituted in unloading spentnuclear fuel；
Qf(N(v+1)) --- the matrix that the distribution share of external complement nucleic is constituted；
Using changeless length of the cycle T and enrichment e, above-mentioned iterative process is repeated, until the nucleon for newly loading fuel is close
Degree vectorUntill convergence；
Step 7：Based on obtained unrestricted balanced recycle pattern, by the new enrichment e for loading fuel of adjustment, realize what is required
Effective multiplication factor k in combustion cycle during time point α T0, so as to obtain final limited balanced recycle pattern；Using convergence
Transmuting matrixThe convergent new nucleon density vector for loading fuelWith length of the cycle T, calculate to time point
Effective multiplication factor k during α T；Assuming that Effective multiplication factor k is on the new linear function for loading fuel enrichment, to meet
It is required that at the time of α T when Effective multiplication factor k0, linear interpolation is carried out to enrichment or extrapolation is as follows,
In formula：
e1--- the new loading fuel enrichment assumed in balanced recycle search procedure；
k(e1) --- the new fuel enrichment that loads takes e1When obtained reactor core Effective multiplication factor；
e2--- the new loading fuel enrichment assumed in balanced recycle search procedure；
k(e2) --- the new fuel enrichment that loads takes e2When obtained reactor core Effective multiplication factor；
k0--- the target effective proliferation factor in balanced recycle search procedure；
According to the new enrichment e of estimation3, the heap interior circulation pattern and unrestricted balance for re-searching for meeting discharge burn-up requirement follow
Ring mode, and calculate Effective multiplication factor k when obtaining α T, steps be repeated alternatively until Effective multiplication when being met moment α T
The factor is k0Limited balanced recycle.
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| CN115424747A (en) * | 2022-07-20 | 2022-12-02 | 上海核工程研究设计院有限公司 | Reactor core loading scheme local searching method and system |
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| CN108664714A (en) * | 2018-04-26 | 2018-10-16 | 华南理工大学 | Krylov subspace accelerates to solve the numerical computation method of burn up equation |
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