CN113836683B - Intelligent acceleration method for improving tritium proliferation ratio of tritium-producing cladding of fusion reactor - Google Patents
Intelligent acceleration method for improving tritium proliferation ratio of tritium-producing cladding of fusion reactor Download PDFInfo
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Abstract
The invention discloses an intelligent acceleration method for improving the tritium proliferation ratio of a tritium-producing cladding of a fusion reactor, which comprises the steps of carrying out three-dimensional neutron transport calculation aiming at a cladding initial scheme, carrying out first-order and second-order perturbation calculation under 1% disturbance of the geometric boundary of each functional area based on the three-dimensional neutron transport calculation, and obtaining the initial scheme and the multi-group tritium proliferation ratio of each tritium proliferation area under each perturbation state; calculating first-order and second-order perturbation coefficients of each energy group of each tritium proliferation region in each perturbation state, and finally obtaining a multidimensional second-order analysis function of tritium proliferation ratio of the whole cladding module along with boundary perturbation quantity of each functional region; and (3) finding out a global optimal solution of the whole cladding module in a perturbation calculation effective interval based on a simulated annealing algorithm, repeating the process, iterating for a plurality of times until convergence, and rapidly finding out a tritium production performance optimal scheme of the fusion reactor tritium production cladding. The advantages are that: the method overcomes the defect that the neutron optimization of the tritium-producing cladding by adopting transport calculation is covered by the statistical fluctuation of the Monte Carlo program, greatly reduces the calculated amount and improves the optimization efficiency.
Description
Technical Field
The invention belongs to the field of fusion reactor tritium-producing cladding neutron science, and particularly relates to an intelligent acceleration method for improving the proliferation ratio of tritium in a fusion reactor tritium-producing cladding.
Background
In a fusion reactor, a tritium-producing cladding is a key for realizing the proliferation and thermoelectric conversion of fusion fuel tritium, and is one of the most important components of the fusion reactor. The tritium-producing cladding is positioned between the reactor core plasma and the vacuum chamber wall and directly faces the high-temperature plasma, 80% of energy released by the D-T fusion reaction appears in the form of neutron kinetic energy, and when various materials (facing plasma materials, structural materials, tritium breeder, neutron multiplier, coolant, neutron absorption moderator and the like) penetrating the cladding, neutrons are scattered and absorbed, and finally the functions of energy deposition, tritium production and the like are realized in the cladding. The tritium-producing cladding has the main functions of:
1) Energy which enters the cladding layer by fusion neutrons, core heat radiation and the like is deposited, carried by a cooling system and subjected to thermoelectric conversion.
2) And shielding fusion neutrons and gamma rays and protecting the safety of components and personnel.
3) Tritium required for fusion reactions is propagated in the cladding by nuclear reactions of fusion neutrons with tritium breeder agents.
Fusion stacks can cause tritium loss for a variety of engineering reasons, such as: 1. tritium retention of the tritium proliferation material in the tritium-producing cladding; 2. tritium permeation of tritium-producing cladding structure materials; 3. tritium loss in the tritium extraction system; 4. in the plasma operation process, the utilization rate of tritium is not high, and the process of repeated extraction, recovery, separation and recycling is carried out, so that considerable tritium loss is brought, and the tritium-producing cladding is difficult to meet the tritium self-sustaining requirement. Therefore, the tritium proliferation ratio of the tritium-producing cladding layer is improved as much as possible on the premise of ensuring the feasibility of engineering, and the method has important academic significance and engineering value.
The traditional tritium production cladding optimization is performed in a manner of independent analysis of neutrons, thermodynamic mechanics, thermomechanics and electromagnetics, and has low design and optimization efficiency and consumes a large amount of calculation resources and manpower. Thus, an automatic optimization procedure emerges therewith. And the automatic data transfer among a plurality of commercial programs is realized by writing an interface program. However, the existing fusion reactor tritium-producing cladding tritium proliferation ratio automatic optimization program is mostly based on multiple transport calculation and adopts a hill climbing algorithm, and the method is easy to realize and parallel. There are a number of bottlenecks:
(1) In each optimization step, the method only accepts the scheme optimized relative to the previous step. Therefore, the found optimization schemes are mostly local optimal solutions, and global optimal solutions cannot be found;
(2) The method is greatly dependent on the determination of the initial scheme and the selection of the optimization step size;
(3) In the multidimensional optimization problem, the phenomenon of oscillation back and forth between two extreme values easily occurs;
(4) When the optimization step length is smaller, the tritium proliferation ratio lifting value obtained through two transport calculation is easily covered by the statistical fluctuation of the Monte Carlo program;
(5) When the optimization step is small, a method of increasing the number of simulation examples is generally adopted to obtain higher calculation accuracy and lower statistical error. So that the optimization efficiency is greatly reduced.
(6) The geometric optimization process of tritium-producing cladding neutron is usually accompanied by small changes in the density of the proliferation region, which can cause disturbance to the tritium proliferation ratio of the whole cladding module. When the optimization step length is small, the optimization direction and the result are influenced.
Therefore, the intelligent optimization research of the fusion reactor tritium-producing cladding tritium proliferation ratio is developed, a global optimal scheme is searched, the optimization efficiency is improved, and a solid technical foundation is provided for the design and research of the CFETR tritium-producing cladding.
Disclosure of Invention
The invention aims to provide an intelligent calculation method for improving the tritium proliferation ratio of a tritium-producing cladding of a fusion reactor, which is based on a high-order neutron perturbation theory and a simulated annealing algorithm, and can quickly find a global optimal scheme by automatically adjusting the geometric boundary of a tritium-producing cladding functional region of the fusion reactor.
The technical scheme of the invention is as follows: an intelligent calculation method for improving the tritium proliferation ratio of a tritium-producing cladding of a fusion reactor is characterized by comprising the following steps:
step 1: and carrying out three-dimensional neutron transport calculation aiming at the cladding initial scheme, carrying out first-order and second-order perturbation calculation under the 1% disturbance of the geometric boundary of each functional region based on the three-dimensional neutron transport calculation, and obtaining the initial scheme and the multi-group tritium proliferation ratio of each tritium proliferation region under each perturbation state.
Step 2: and calculating the first-order perturbation coefficient and the second-order perturbation coefficient of each energy group of each tritium proliferation region under each perturbation state, and finally obtaining a multidimensional second-order analysis function of the tritium proliferation ratio of the whole cladding module along with the boundary perturbation quantity of each functional region.
Step 3: and (3) intelligently optimizing a calculation flow for the tritium proliferation ratio of the tritium-producing cladding of the fusion reactor.
In the step 1
Wherein: TBR (Tunnel boring machine) 0 Tritium proliferation ratio for the entire cladding module under the initial protocol;tritium proliferation ratio of the jth group of the ith tritium proliferation zone in the initial scheme; 1 TBR k tritium proliferation ratio of the whole cladding module when the kth functional area is disturbed under the first-order perturbation; />Tritium proliferation ratio of the jth group of the ith tritium proliferation zone when the kth functional zone is disturbed under the first-order perturbation; 2 TBR k tritium proliferation ratio of the whole cladding module when the kth functional area is disturbed under the second-order perturbation; />Tritium proliferation ratio of the jth group of the ith tritium proliferation zone in the disturbance of the kth functional zone under the second-order perturbation; n is the total number of tritium proliferation regions; g is the number of energy groups.
In the step 2
Wherein:a first-order perturbation coefficient of a j group of an i tritium proliferation region under the perturbation of a k functional region; />The second order perturbation coefficient of the j group of the i tritium proliferation area under the disturbance of the kth functional area; Δl isPerturbation quantity of geometric boundary of each functional area;
deducing a multidimensional second-order analytic function of tritium proliferation ratio of the whole cladding module along with boundary disturbance quantity of each functional area:
wherein: Δl k The disturbance quantity of the geometric boundary of the kth functional area; m is the total number of functional areas.
Said step 3 comprises
(1) First, the initial annealing temperature T is set 0 Annealing termination temperature T F Annealing temperature t=t 0 Chain length of Marshall Markov Annealing coefficient lambda.
(2) Generating a random disturbance to the geometrical boundary disturbance quantity of each functional area respectively:
wherein: Δl' k The disturbance quantity after the geometric boundary of the kth functional area is randomly disturbed;random disturbance quantity for the geometric boundary of the kth functional area;
substituting (6) to obtain the tritium proliferation ratio of the whole cladding module under random disturbance.
(3) The increase in tritium proliferation ratio after random perturbation was calculated:
ΔTBR＝TBR(Δl′ 1 ,Δl' 2 …Δl' m )-TBR(Δl 1 ,Δl 2 …Δl m ) (8)
wherein: delta TBR random perturbation followed by an increase in the tritium proliferation ratio of the entire cladding module.
(4) If delta TBR is more than or equal to 0, the disturbance is accepted, and the variable after the disturbance is used as the starting point of the disturbance in the next step:
Δl i ＝Δl′ i ,i＝1,2…m (9)
TBR(Δl 1 ,Δl 2 …Δl m )＝TBR(Δl′ 1 ,Δl' 2 …Δl' m ) (10)
if ΔTBR < 0, the probability e -ΔTBR/T And receiving the current disturbance, otherwise, taking the state before the disturbance as the starting point of the next disturbance.
(5) Performing a cyclic operation on the steps (2), (3) and (4) until the number of times of the state after no disturbance is accepted reaches l Markov Cooling after that:
T＝λT (11)。
(6) Performing the cyclic operation on the step (5) until T is less than T F Until that point. And searching the optimal solution of the geometric boundary disturbance quantity of each functional area in the effective area of perturbation calculation.
Repeating the steps 1, 2 and 3 for a plurality of iterations until convergence.
The invention has the beneficial effects that: and adopting a simulated annealing algorithm to intelligently optimize the tritium proliferation ratio of the tritium-producing cladding of the fusion reactor. The defect that the traditional automatic optimization algorithm can not find the global optimal solution is overcome. The high-order neutron perturbation theory is adopted to replace multiple neutron transport calculation, the defect that the neutron optimization of the tritium production cladding by adopting the transport calculation is covered by the statistical fluctuation of the Monte Carlo program is overcome, the calculated amount is greatly reduced, and the optimization efficiency is improved.
Detailed Description
The present invention will be described in further detail with reference to specific examples.
The invention is based on the existing Monte Carlo neutron transport algorithm, and adopts a high-order neutron perturbation theory and a simulated annealing algorithm to realize the intelligent acceleration of the fusion reactor tritium-producing cladding tritium proliferation ratio global optimal solution searching and calculating method. The intelligent acceleration method comprises the following steps:
(1) Carrying out three-dimensional neutron transport calculation aiming at a cladding initial scheme, carrying out first-order and second-order perturbation calculation under 1% disturbance of the geometric boundary of each functional area based on the three-dimensional neutron transport calculation, and obtaining a multi-group tritium proliferation ratio of each tritium proliferation area under the initial scheme and each perturbation state;
(2) Calculating first-order and second-order perturbation coefficients of each energy group of each tritium proliferation region in each perturbation state, and finally obtaining a multidimensional second-order analysis function of tritium proliferation ratio of the whole cladding module along with boundary perturbation quantity of each functional region;
(3) Finding out the global optimal solution (comprising the optimal disturbance quantity of the geometric boundary of each functional area and the tritium proliferation ratio under the optimal solution) of the whole cladding module in the perturbation calculation effective interval based on a simulated annealing algorithm; and repeating the process for multiple iterations until convergence, and rapidly finding out the optimal tritium production performance scheme of the tritium production cladding of the fusion reactor.
An intelligent calculation method for improving the tritium proliferation ratio of a tritium-producing cladding of a fusion reactor comprises the following steps:
step 1: and (3) carrying out three-dimensional neutron transport calculation aiming at the cladding initial scheme, carrying out first-order and second-order perturbation calculation under the 1% disturbance of the geometric boundary of each functional area based on the three-dimensional neutron transport calculation, and obtaining the initial scheme and the multi-group tritium proliferation ratio of each tritium proliferation area under each perturbation state, wherein the multi-group tritium proliferation ratio is shown in (1) to (3).
Wherein: TBR (Tunnel boring machine) 0 Tritium proliferation ratio for the entire cladding module under the initial protocol;tritium proliferation ratio of the jth group of the ith tritium proliferation zone in the initial scheme; 1 TBR k tritium proliferation ratio of the whole cladding module when the kth functional area is disturbed under the first-order perturbation; />Tritium proliferation ratio of the jth group of the ith tritium proliferation zone when the kth functional zone is disturbed under the first-order perturbation; 2 TBR k tritium proliferation ratio of the whole cladding module when the kth functional area is disturbed under the second-order perturbation; />Tritium proliferation ratio of the jth group of the ith tritium proliferation zone in the disturbance of the kth functional zone under the second-order perturbation; n is the total number of tritium proliferation regions; g is the number of energy groups.
Step 2: and calculating the first-order perturbation coefficient and the second-order perturbation coefficient of each energy group of each tritium proliferation region under each perturbation state, and finally obtaining a multidimensional second-order analysis function of the tritium proliferation ratio of the whole cladding module along with the boundary perturbation quantity of each functional region.
The first order perturbation coefficient is shown as (4), and the second order perturbation coefficient is shown as (5):
wherein:a first-order perturbation coefficient of a j group of an i tritium proliferation region under the perturbation of a k functional region; />The second order perturbation coefficient of the j group of the i tritium proliferation area under the disturbance of the kth functional area; Δl is the perturbation of the geometric boundaries of each functional region;
according to the perturbation coefficient, a multidimensional second-order analytic function of tritium proliferation ratio of the whole cladding module along with boundary perturbation quantity of each functional area can be deduced, and the multidimensional second-order analytic function is shown as (6):
wherein: Δl k The disturbance quantity of the geometric boundary of the kth functional area; m is the total number of functional areas;
step 3: finding out the global optimal solution (comprising the optimal disturbance quantity of the geometric boundary of each functional area and the tritium proliferation ratio under the optimal solution) of the whole cladding module in the perturbation calculation effective interval based on a simulated annealing algorithm;
(1) First, the initial annealing temperature T is set 0 Annealing termination temperature T F Annealing temperature t=t 0 Chain length of Marshall Markov Annealing coefficient lambda.
(2) Generating a random disturbance to the geometrical boundary disturbance quantity of each functional area respectively, as shown in (7):
wherein: Δl' k The disturbance quantity after the geometric boundary of the kth functional area is randomly disturbed;random disturbance quantity for the geometric boundary of the kth functional area;
substituting (6) to obtain the tritium proliferation ratio of the whole cladding module under random disturbance.
(3) The increase in tritium proliferation ratio after random perturbation was calculated as shown in (8):
ΔTBR＝TBR(Δl′ 1 ,Δl' 2 …Δl' m )-TBR(Δl 1 ,Δl 2 …Δl m ) (8)
wherein: delta TBR random disturbance is followed by an increase in tritium proliferation ratio of the entire cladding module;
(4) If Δtbr is greater than or equal to 0, the disturbance is accepted, and the variable after disturbance (the disturbance quantity of the geometric boundary and the tritium proliferation ratio) is taken as the starting point of the next disturbance, as shown in (9) and (10):
Δl i ＝Δl′ i ,i＝1,2…m (9)
TBR(Δl 1 ,Δl 2 …Δl m )＝TBR(Δl′ 1 ,Δl' 2 …Δl' m ) (10)
if ΔTBR < 0, the probability e -ΔTBRT And receiving the current disturbance, otherwise, taking the state before the disturbance as the starting point of the next disturbance.
(5) Performing a cyclic operation on the steps (2), (3) and (4) until the number of times of the state after no disturbance is accepted reaches l Markov Cooling is performed after that, as shown in (11):
T＝λT (11)
(6) Performing the cyclic operation on the step (5) until T is less than T F Until that point. And searching the optimal solution of the geometric boundary disturbance quantity of each functional area in the effective area of perturbation calculation.
Repeating the above processes (step 1, step 2 and step 3) for multiple iterations until convergence, and rapidly finding out the optimal tritium production performance scheme of the tritium production cladding of the fusion reactor.
Claims (1)
1. An intelligent calculation method for improving the tritium proliferation ratio of a tritium-producing cladding of a fusion reactor is characterized by comprising the following steps:
step 1: carrying out three-dimensional neutron transport calculation aiming at a cladding initial scheme, carrying out first-order and second-order perturbation calculation under 1% disturbance of the geometric boundary of each functional area based on the three-dimensional neutron transport calculation, and obtaining a multi-group tritium proliferation ratio of each tritium proliferation area under the initial scheme and each perturbation state;
step 2: calculating first-order and second-order perturbation coefficients of each energy group of each tritium proliferation region in each perturbation state, and finally obtaining a multidimensional second-order analysis function of tritium proliferation ratio of the whole cladding module along with boundary perturbation quantity of each functional region;
step 3: intelligent optimization calculation flow of tritium proliferation ratio of tritium-producing cladding of fusion reactor;
in the step 1
Wherein: TBR (Tunnel boring machine) 0 Tritium proliferation ratio for the entire cladding module under the initial protocol;tritium proliferation ratio of the jth group of the ith tritium proliferation zone in the initial scheme; 1 TBR k tritium proliferation ratio of the whole cladding module when the kth functional area is disturbed under the first-order perturbation; 2 TBR k tritium proliferation ratio of the whole cladding module when the kth functional area is disturbed under the second-order perturbation; />Tritium proliferation ratio of the jth group of the ith tritium proliferation zone when the kth functional zone is disturbed under the first-order perturbation; />Tritium proliferation ratio of the jth group of the ith tritium proliferation zone in the disturbance of the kth functional zone under the second-order perturbation; n is the total number of tritium proliferation regions; g is the number of energy groups;
in the step 2
Wherein:first order micro for the j group of the i tritium proliferation region under the disturbance of the k functional regionA disturbance coefficient; />The second order perturbation coefficient of the j group of the i tritium proliferation area under the disturbance of the kth functional area; Δl is the perturbation of the geometric boundaries of each functional region;
deducing a multidimensional second-order analytic function of tritium proliferation ratio of the whole cladding module along with boundary disturbance quantity of each functional area:
wherein: Δl k The disturbance quantity of the geometric boundary of the kth functional area; m is the total number of functional areas;
said step 3 comprises
(1) First, the initial annealing temperature T is set 0 Annealing termination temperature T F Annealing temperature t=t 0 Chain length of Marshall Markov An annealing coefficient lambda;
said step 3 comprises
(2) Generating a random disturbance to the geometrical boundary disturbance quantity of each functional area respectively:
wherein: Δl' k The disturbance quantity after the geometric boundary of the kth functional area is randomly disturbed;random disturbance quantity for the geometric boundary of the kth functional area;
substituting (6) to obtain the tritium proliferation ratio of the whole cladding module under random disturbance;
said step 3 comprises
(3) The increase in tritium proliferation ratio after random perturbation was calculated:
ΔTBR＝TBR(Δl′ 1 ,Δl' 2 …Δl' m )-TBR(Δl 1 ,Δl 2 …Δl m ) (8)
wherein: delta TBR random disturbance is followed by an increase in tritium proliferation ratio of the entire cladding module;
said step 3 comprises
(4) If delta TBR is more than or equal to 0, the disturbance is accepted, and the variable after the disturbance is used as the starting point of the disturbance in the next step:
Δl i ＝Δl′ i ,i＝1,2…m (9)
TBR(Δl 1 ,Δl 2 …Δl m )＝TBR(Δl′ 1 ,Δl' 2 …Δl' m ) (10)
if ΔTBR < 0, the probability e -ΔTBR/T Receiving the current disturbance, otherwise, taking the state before the disturbance as the starting point of the next disturbance;
said step 3 comprises
(5) Performing a cyclic operation on the steps (2), (3) and (4) until the number of times of the state after no disturbance is accepted reaches l Markov Cooling after that:
T＝λT (11)
said step 3 comprises
(6) Performing the cyclic operation on the step (5) until T is less than T F Until the completion, searching an optimal solution of the geometric boundary disturbance quantity of each functional area in the effective area of perturbation calculation;
repeating the steps 1, 2 and 3 for a plurality of iterations until convergence.
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