CN106202867B - A method of calculating fast neutron reactor component axial direction swelling effect - Google Patents
A method of calculating fast neutron reactor component axial direction swelling effect Download PDFInfo
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Abstract
A method of fast neutron reactor component axial direction swelling effect is calculated, is comprised the steps of：1, calculating grid will be transported to detach with burnup calculating grid, calculating grid is transported and remained unchanged in entire calculate, and burnup calculating grid is with the growth of fuel assembly axial direction swelling holding same ratio；2, it is based on variation Nodal method, constructs the weak form of neutron-transport equation solution, locking nub middle section is and the relevant function in spatial position so that transport to calculate allows multiple material occur inside locking nub；3, Flux Expansion is solved into Flux Expansion square, to obtain the Flux Distribution of each locking nub using response matrix method using spheric harmonic function and orthogonal space multinomial；4, the burn-up level of the locking nub is calculated according to the mean power of burnup locking nub, the Homogenized cross sections of burnup locking nub are obtained according to burnup interpolation, the Homogenized cross sections inside burnup locking nub are adjusted according to component axial elongation, and then obtain calculating the required nonuniform section in locking nub.
Description
Technical field
The present invention relates to nuclear reactor design and security technology areas, and in particular to a kind of calculating fast neutron reactor component
The method of axial swelling effect.
Background technology
Fissilenuclide can be converted into fissile nuclide by fast neutron reactor so that the utilization rate of uranium resource is significantly
It improves, has great importance for the sustainable development of nuclear energy.Currently, fast reactor also in experiment and the design phase, accurately
It carries out numerical simulation and puts into extensive commercialization for fast reactor to be essential link.
It is different from existing commercialization presurized water reactor, in order to keep power spectrum harder, better cultivation effect is obtained, fast reactor is usually used
Metallic uranium zircaloy is as fuel.Metal fuel has larger temperature expansion coefficient, while while being irradiated also is easy to happen
Swelling deforms.In reactor core, the temperature of component present position is different, while the irradiation suffered by component is also different, these
Factor makes different components axial elongation under some burnup also be different.In traditional two-step method calculates, locking nub
Method is that reactor core calculates common method.Fuel assembly axial elongation effect can make occur two kinds of different combustions in calculating locking nub
The material of consumption.One material calculated comprising two kinds of different burnups in locking nub means in the calculating locking nub that section is not uniform
's.It is similarly to control rod pointed tooth effect, different place is in almost all of calculating locking nub to include two kinds of sections.
Traditionally the method for processing pointed tooth effect can not be well on calculating axial swelling effect.First, adaptive
It answers grid method that can make occur meticulous grid in reactor core locking nub, not only considerably increases calculation amount, while but also locking nub
Flux is difficult to restrain.It then needs each locking nub to calculate Homogenized cross sections using the calculating of homogenization method again, considerably increases calculating
Amount.As it can be seen that if computation module axial direction swelling effect that can be rapidly and efficiently, needs a kind of locking nub that can directly calculate heterogeneous material
Method.
Invention content
In order to overcome the above-mentioned problems of the prior art, the object of the present invention is to provide one kind capable of quickly calculating fast reactor
Variation Nodal method based on non-homogeneous locking nub is applied and is calculated in three-dimensional reactor core by the method for component axial direction swelling effect, this method
In, it enables to transport the material for calculating and including two kinds of burnups in locking nub, axial so as to effectively calculate fast pile component
Swelling effect.
To achieve the goals above, this invention takes following technical schemes to be practiced：
A method of fast neutron reactor component axial direction swelling effect being calculated, this approach includes the following steps：
Step 1 carries out mesh generation to domain, and radially a hexagonal assembly is a locking nub, axis standing root
Several grids are divided according to particular problem, with conventional method the difference is that the calculating grid in axial direction, which is divided into, transports calculating grid
With burnup grid, at burnup initial stage, two sets calculate grid and overlap, and with the variation of burnup, fuel assembly axial elongation transports meter
Grid is calculated to remain unchanged, and burnup grid is elongated with component axial elongation, transport calculate material in grid be not it is uniform,
And material is uniform in burnup grid；
Step 2 is based on variation Nodal method VNM, establishes global functional in domain, constructs three-dimensional even symmetry shape
The weak form of formula neutron-transport equation solution, the not uniform constant in section in locking nub local functional, with spatial position phase
The function of pass, this to transport to calculate allows multiple material occur inside locking nub；
Step 3, using spheric harmonic function and orthogonal space multinomial by inside hexagon locking nub even flux and boundary
The linear algebraic equation that expansion square is obtained in functional and to expansion square derivation is brought in Lagrange multiplier item expansion at face into
Group solves Flux Expansion square, to obtain the flux of each locking nub using response matrix method and four coloured chess disk scanning algorithm
Distribution, at this moment solves the mean power of burnup locking nub；
Step 4 can calculate the burn-up level of the locking nub according to the mean power of burnup locking nub, according to burnup interpolation
The Homogenized cross sections of burnup locking nub are obtained, the Homogenized cross sections inside burnup locking nub are adjusted according to component axial elongation, in turn
It obtains calculating the required nonuniform section in locking nub.
Compared with prior art, the present invention has following outstanding advantages：
It is orthogonal polynomial form 1. transporting and calculating Flux Expansion inside locking nub, calculating can be straight after Flux Expansion square
Locking nub inside Flux Distribution is obtained to obtain, power reconstruct is not needed.
2. due to that can directly obtain Flux Distribution in locking nub, this method, which may be implemented to transport, calculates grid and burnup grid
Separation, to accurately calculate the section of next step burnup.
Two or more materials can be considered 3. transporting and calculating locking nub, calculating need not be homogenized again, to significantly
Improve computational efficiency.
Description of the drawings
Fig. 1 is component axial elongation effect schematic diagram.
Fig. 2 program computational flow figures.
Specific implementation mode
Invention is further described in detail with reference to the accompanying drawings and detailed description：
The method of the present invention applies the variation Nodal method based on non-homogeneous locking nub in the calculating of three-dimensional reactor core, will transport
It calculates grid to separate with burnup grid, transports the material for calculating and may include different burnups in grid, include equal in burnup grid
Even material, reactor core locking nub computational methods use non-homogeneous variation Nodal method, and it includes two kinds that it, which enables to calculate in locking nub,
The material of burnup.After calculating and completing, according to Flux Expansion square, can in the hope of power in locking nub in axial distribution, to
The average flux in burnup locking nub is found out, and then the section of next burnup step can be obtained.
Entire calculate specifically includes following steps：
Step 1 carries out mesh generation to domain, and radially a hexagonal assembly is a locking nub, axis standing root
Several grids are divided according to particular problem, with conventional method the difference is that grid, which is divided into, calculates grid and burnup grid, are being fired
At consumption initial stage, two sets calculate grid and overlap, and with the variation of burnup, fuel assembly axial elongation transports calculating grid and remains unchanged,
And burnup grid is elongated with component axial elongation, it is not uniform to transport and calculate material in grid, and material in burnup grid
Material is uniform；
Step 2, the solution of non-homogeneous locking nub neutron-transport equation
The neutron-transport equation of single energy can be written as form：
R --- spatial position variable；
Ω --- angle variables；
φg--- g can group's neutron angular flux density；
G --- it can group identification；
Σt,g--- the total cross section of g energy groups；
--- the self-scattering section of g energy groups；
Qg--- the neutron-transport equation source item of g energy groups, including source item and fission source term are scattered between group,
It is assumed that scattering is isotropic,
Define odd even flux：
ψ --- even flux density；
χ --- strange flux density；
Equation (1) can be write as the neutron-transport equation of even symmetry form：
Φ --- neutron scalar flux density；
It enables
Jγ(r, Ω)=nγ·Ωχγ(r,Ω) (4)
nγ--- it is the borderline exterior normal directions locking nub γ；
χγ--- it is the borderline strange flux of locking nub γ；
If the variable carries out integral to angle and can be obtained the borderline net neutron-currents of γ：
NJ (r)=∫ d Ω Jγ(r,Ω) (5)
Global functional is established to the region solved, global functional is the adduction form of each locking nub local functional.
Wherein local functional is
I [ψ, J] is boundary integral item, for inner boundary
Ii[ψ, J]=2 ∫ΓidΓ∫dΩψ(r,Ω)J(r,Ω) (8)
For vacuum boundary
Ij[ψ, J]=∫ΓjdΓ∫N Ω < 0dΩ|n·Ω|ψ2(r,Ω) (9)
Then, the problem of solving neutron-transport equation then converts to solve the variational problem of global functional minimum, and
The solution of variational problem is the Solution of Weak Formulation of second order parity equation.
(8) J (r, Ω) is Lagrange multiplier item in formula, and effect is the constraint eliminated boundary condition and brought, and passes through drawing
Ge Lang multiplier items add boundary condition in functional, to realize the coupling between locking nub；
The angle item of even flux and Lagrange multiplier item is launched into the form of spheric harmonic function, space exhibition by step 3
It is split into the form of orthogonal basis function：
Wherein g (Ω)=[Y0,0,Y2,-2,Y2,-1,Y2,0,Y2,1,Y2,2...]TFor the normalized spheric harmonic function of even order.f
(r)=[f1,f2,f3...]TFor the orthogonal polynomial being defined on inside locking nub v, h (r)=[h1,h2...]TTo be defined on locking nub v
The orthogonal polynomial of boundary.VectorAnd ξ is expansion coefficient, and square is referred to as unfolded
(10) formula, which is brought into, can convert functional to a function about expansion square in functional (7).
Wherein
M=[M1 M2 … Mγ …] (12)
Function fvDerivative about even Flux Expansion square is zero, i.e.,：
It can obtain
Overall situation function is zero about Lagrange multiplier items expansion square derivative, can obtain equation
Wherein subscript v and v' represents two adjacent locking nubs, and γ and γ ' represents the interface of two locking nubs.
It notices that Lagrange multiplier items include normal direction, there is Jv'γ'=-Jvγ, and its basic function is completely the same, therefore
Square is unfolded to meet：
ξv'γ'=-ξvγ (19)
I.e.：
To obtain：
In boundary ΓγPlace is continuous.
Square is unfolded in the shunting for defining the faces γ：
Understand that bias current expansion square is continuous in locking nub boundary.
It is retouched using four coloured chess sweeping on the strategy for solving expansion square and the computational methods of response matrix, response matrix is public
Formula is as follows：
j+=Bs+Rj- (22)
Wherein
B=[G+I]-1CT (24)
R=[G+I]-1[G-I] (25)
H=A-1 (28)
Four response matrix R H C B and the material in locking nub, geometry and energy group are relevant, are being iterated
Before calculating, response matrix can be calculated in advance.According to (22) formula, can the locking nub be obtained by the incident bias current square of some locking nub
It is emitted bias current square.All locking nubs of reactor core are scanned using the locking nub scanning algorithm of four coloured chess disk, until all locking nubs is inclined
Stream expansion square convergence, bias current expansion square, which is brought into formula (23), can obtain Flux Expansion square, this process is inner iteration process.Have logical
Scattering source needs to be iterated if containing upper scattering in collision matrix in whole process between the i.e. renewable group of amount expansion square,
Iterative strategy is using Gauss Saden that iteration.It is all characteristic value k to may be updated after the Flux Expansion square convergence of groupeff, fission
Source item also updates therewith, this process is known as fission source iteration, and calculation process is as shown in Figure 2.
Step 4, due to burnup grid with transport calculate grid it is inconsistent, need to calculate grid carry out power reconstruct, from
And obtain the average power density of burnup grid.Variation Nodal method is calculating inside locking nub directly to flux progress multinomial exhibition
It opens, therefore can easily obtain the power distribution in locking nub after iteratively solving out Flux Expansion square.
Wherein following table v indicates v-th of calculating locking nub, and 1 indicates that square is unfolded in first spheric harmonic expansion square, i.e. scalar flux, and g is indicated
It can group.
The power of burnup locking nub can be obtained by following formula：
κgΣfgFor the energy production section of neutron
Square is unfolded for 0 rank netron-flux density of v1 locking nub g groups, i.e. square is unfolded in scalar flux.
ha,l,hbFor range of integration, indicates burnup locking nub and transport the location information of locking nub.
Homogenized cross sections in burnup locking nub are obtained according to current burn-up level interpolation.Due to fuel assembly axial elongation
It is to change with burnup, different burnups can correspond to different elongations, therefore section needs to make corresponding adjustment.Assuming that combustion
Expect that the axial tension of component is uniform, it is respectively l to stretch front and back length1With l2, then the section of next step burnup calculating is carried out
For：
After obtaining the nonuniform section of calculating locking nub, you can the burnup for carrying out next step calculates.
Claims (1)
1. a kind of method calculating fast neutron reactor component axial direction swelling effect, it is characterised in that：This approach includes the following steps：
Step 1 carries out mesh generation to domain, and radially hexagonal assembly is a locking nub, it is axial on according to tool
Body problem divides several grids, with conventional method the difference is that the calculating grid in axial direction, which is divided into transporting, calculates grid and combustion
Grid is consumed, at burnup initial stage, two sets calculate grid and overlap, and with the variation of burnup, fuel assembly axial elongation transports calculating net
Lattice remain unchanged, and burnup grid is elongated with component axial elongation, and it is not uniform to transport and calculate material in grid, and is fired
It is uniform to consume material in grid；
Step 2 is based on variation Nodal method VNM, establishes global functional in domain, constructs in three-dimensional even symmetry form
The weak form of sub- transport equation solution, the not uniform constant in section in locking nub local functional are relevant with spatial position
Function, this to transport to calculate allows multiple material occur inside locking nub；
Step 3, will be at the even flux and interface inside hexagon locking nub using spheric harmonic function and orthogonal space multinomial
The expansion of Lagrange multiplier item, bring into locking nub local functional and obtain the linear algebra side that square is unfolded to expansion square derivation
Journey group solves Flux Expansion square using response matrix method and four coloured chess disk scanning algorithm, to obtain the logical of each locking nub
Amount distribution, at this moment solves the mean power of burnup locking nub；
Step 4 can calculate the burn-up level of the locking nub according to the mean power of burnup locking nub, according to burn-up level interpolation
The Homogenized cross sections of burnup locking nub are obtained, the Homogenized cross sections inside burnup locking nub are adjusted according to component axial elongation, in turn
It obtains calculating the required nonuniform section in locking nub.
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Families Citing this family (4)
| Publication number | Priority date | Publication date | Assignee | Title |
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| CN107145657B (en) * | 2017-04-27 | 2020-02-14 | 西安交通大学 | Non-uniform geometric variable block method for reactor neutron diffusion equation |
| CN107066751B (en) * | 2017-04-27 | 2020-06-12 | 西安交通大学 | Flat source acceleration method for non-uniform geometric variable block method |
| CN112393699A (en) * | 2019-08-13 | 2021-02-23 | 中核核电运行管理有限公司 | Method for measuring and calculating axial elongation of heavy water reactor fuel channel |
| CN112199851A (en) * | 2020-10-19 | 2021-01-08 | 中国核动力研究设计院 | Method, device and equipment for acquiring fuel consumption of fuel containing gadolinium based on Lagrange interpolation |
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| CN105426657A (en) * | 2015-10-30 | 2016-03-23 | 西安交通大学 | Method for eliminating control rod tine effect in reactor core calculation |
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| CN105426657A (en) * | 2015-10-30 | 2016-03-23 | 西安交通大学 | Method for eliminating control rod tine effect in reactor core calculation |
Non-Patent Citations (4)
| Title |
|---|
| Impacts of Burnup-Dependent Swelling of Metallic Fuel on the Performance of a Compact Breed-and-Burn Fast Reactor;Donny Hartanto et al.;《Nuclear Engineering and Technology》;20160121;第48卷;第330-338页 * |
| 变分节块法求解中子扩散方程;王永平 等;《现代应用物理》;20140930;第5卷(第3期);第174-176、181页 * |
| 基于六角形节块法的行波堆燃耗程序HANDF-E;孙伟 等;《原子能科学技术》;20130630;第47卷;第376-380页 * |
| 快堆三维节块法程序燃耗模块的开发;杨晓燕 等;《核科学与工程》;20100930;第30卷(第3期);第228-233页 * |
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