CN103116667A - Method of obtaining fusion reactor experimental covering module neutronics parameters - Google Patents

Abstract

The invention discloses a method of obtaining fusion reactor experimental covering module neutronics parameters. The method of obtaining fusion reactor experimental covering module neutronics parameters adopts a two-step method. The first step, according to axial geometry features of a fusion reactor experimental covering module, portions which are the same in the geometry and materials in an axial direction can be cut in an identical area. The covering module can be cut into a plurality of model lattice cells. Characteristic lines can be utilized to calculate a module to solve a neutron-transport equation in each lattice cell to obtain a thin crowd neutron-flux distribution. The obtained neutron-flux distribution can be utilized in each lattice cell, and homogenization modules can be adopted to be in homogenization to obtain thick crowd section parameters according to the weight of influx volume. The second step, the thick crowd section parameters of each model lattice cell can be used as known parameters to calculate the neutron-flux distribution of the fusion reactor experimental covering module in the entire fusion reactor experimental covering modules, wherein the thick crowd section parameters of each model lattice cell are obtained for the first step. Further, each item neutronics parameters can be calculated. The method of obtaining fusion reactor experimental covering module neutronics parameters has the advantages of being high in efficiency and precision so as to provide a result with a guiding and reference significance for a constructing design of a fusion reactor.

Description

A kind of method of obtaining thermonuclear reactor experiment cladding modular neutronics parameter

Technical field

The present invention relates to thermonuclear reactor experiment cladding modular Test Blanket Module(TBM) the Neutronics analysis field, be specifically related to a kind of method of obtaining thermonuclear reactor experiment cladding modular neutronics parameter.

Background technology

Fusion reactor is to utilize controllable nuclear fusion to continue the device of output energy.In the middle of present design, the agent structure of fusion reactor is covering, is comprised of hundreds of independent cladding modulars (TBM), and deuterium and tritium are completed the controllable nuclear fusion reaction and released energy in the cavity that covering surrounds.The correlation parameters such as TBM Neutron flux distribution and product tritium raito (T.R) (TBR), product tritium rate, neutron irradiation damage DPA, wind-puff is swollen are called the neutronics parameter, and the process of obtaining these parameters claims Neutronics analysis, and Neutronics analysis is significant to the design-build of fusion reactor.Due to fusion reactor still the design in the middle of, so present stage can only obtain TBM Neutronics analysis result by numerical computation method.

At present both at home and abroad to experiment cladding modular carry out Neutronics analysis the most widely instrument be based on the MCNP program of covering Taka sieve method.It is a kind of take the numerical method of Probability Statistics Theory as instructing covering Taka sieve method, uses random number to solve computational problem.The MCNP program is utilized the random physical process of computing machine direct modeling neutron and atomic nucleus effect to cover Taka sieve method as the basis.Carry out neutron position, speed and direction after the random sampling effect according to the probability of mechanism, after simulating so a large amount of neutron behaviors, just can obtain the distribution situation of neutron in material through statistics.Therefore, the result of MCNP program and the sample number of statistics are closely related, need to drop into a large amount of neutron numbers, just can obtain result comparatively accurately, and this makes the counting yield of MCNP program very low.And present stage to the construction of fusion reactor and Physical Mechanism analysis in early stage often need in a large number, repeatedly Neutronics analysis calculates, and under present design conditions, uses the MCNP program to carry out these calculating still very consuming time; The MCNP program also is more difficult to get neutron flux space distribution and angular distribution meticulous in object simultaneously.

Based on this, be necessary to provide a kind of high-level efficiency, high-precision Neutronics analysis method.Simultaneously because characteristics and the fusion reactor neutron anisotropy of TBM complex geometry are stronger, this method also should have high geometric compliance and anisotropic scattering cross section processing power simultaneously.

Summary of the invention

For addressing the above problem, the invention provides a kind of method of obtaining thermonuclear reactor experiment cladding modular neutronics parameter, can access every neutronics parameter of TBM inside: Neutron flux distribution, TBR, product tritium rate, the gentle swelling of DPA, efficient is high, precision is high; Thereby the construction design to fusion reactor provides the result with guidance, reference significance.

In order to achieve the above object, the present invention adopts following technical scheme:

A kind of method of obtaining thermonuclear reactor experiment cladding modular neutronics parameter adopts two-step approach, and concrete grammar is as follows:

Step 1: with thermonuclear reactor experiment cladding modular according to its axial geometrical feature, be divided into same district with axially going up how much, part that material is identical, cladding modular can be divided into several " typical cells " like this, utilize the characteristic curve computing module to find the solution neutron-transport equation on each " typical cell ", obtain thin group's Neutron flux distribution, then utilize the Neutron flux distribution that obtains to adopt the homogenising module to carry out homogenising according to the flux volume weighted in each " typical cell ", obtain the coarse-group cross section parameter;

Step 2: each coarse-group cross section parameter of " typical cell " that step 1 is obtained is calculated the Neutron flux distribution of full thermonuclear reactor experiment cladding modular, and is further calculated every neutronics parameter as known parameters on whole thermonuclear reactor experiment cladding modular size.

The described characteristic curve computing module of step 1 adopts characteristic line method MOC to find the solution neutron-transport equation, can process the P1 scattering cross-section, utilizes AUTOCAD Software Create characteristic curve information.

The formula that the described homogenising module of step 1 adopts is as shown in the formula (1)～(5):

$S_G^e=\underset{g\∈G}{\mathrm{\Σ}}{S}_g^e---\left(1\right)$

${\mathrm{\Σ}}_{a,G}=\frac{\underset{g\∈G}{\mathrm{\Σ}}{\mathrm{\Σ}}_{a,g}{\mathrm{\φ}}_g}{\underset{g\∈G}{\mathrm{\Σ}}{\mathrm{\φ}}_g}---\left(2\right)$

${\mathrm{\Σ}}_{f,G}=\frac{\underset{g\∈G}{\mathrm{\Σ}}{\mathrm{\Σ}}_{f,g}{\mathrm{\φ}}_g}{\underset{g\∈G}{\mathrm{\Σ}}{\mathrm{\φ}}_g}---\left(3\right)$

${\mathrm{\&Sigma;}}_{\mathrm{<figure-callout\; id="0"\; label="s"\; filenames="HDA00002771338600033.png"\; state="\{\{state\}\}">s</figure-callout>}0,G->G^{\&prime;}}=\frac{\underset{g^{\&prime;}\&Element;G^{\&prime;}}{\mathrm{\&Sigma;}}\underset{g\&Element;G}{\mathrm{\&Sigma;}}{\mathrm{\&Sigma;}}_{\mathrm{<figure-callout\; id="0"\; label="s"\; filenames="HDA00002771338600033.png"\; state="\{\{state\}\}">s</figure-callout>}0,g->g^{\&prime;}}{\mathrm{\&phi;}}_g}{\underset{g\&Element;G}{\mathrm{\&Sigma;}}{\mathrm{\&phi;}}_g}---\left(4\right)$

${\mathrm{\&Sigma;}}_{s1,G->G^{\&prime;}}=\frac{\underset{g^{\&prime;}\&Element;G^{\&prime;}}{\mathrm{\&Sigma;}}\underset{g\&Element;G}{\mathrm{\&Sigma;}}{\mathrm{\&Sigma;}}_{s,g->g^{\&prime;}}{J}_g}{\underset{g\&Element;G}{\mathrm{\&Sigma;}}{J}_g}---\left(5\right)$

In formula (1)～(5),

Be g thin group's stationary source intensity, unit is every cubic centimetre of per second, ncm ^-3S ^-1

Be G thick group's stationary source intensity, unit is every cubic centimetre of per second, ncm ^-3S ^-1

φ _gBe g thin group's neutron-flux density, unit is every square centimeter of per second, ncm ^-2S ^-1

∑ _{A, g}Be g thin group's absorption cross section, unit is every centimetre, cm ^-1

∑ _{A, G}Be G thick group's absorption cross section, unit is every centimetre, cm ^-1

∑ _{F, g}Be g thin group's fission cross section, unit is every centimetre, cm ^-1

∑ _{F, G}Be G thick group's fission cross section, unit is every centimetre, cm ^-1

∑ _{S0, g-＞g'}Be g group to g ' group's isotropic scatterning cross section, unit is every centimetre, cm ^-1

∑ _{S0, G-＞G'}Be G group to G ' group's isotropic scatterning cross section, unit is every centimetre, cm ^-1

∑ _{S1, g-＞g'}Be g group to g ' group's anisotropic scattering cross section, unit is every centimetre, cm ^-1

∑ _{S1, G-＞G'}Be G group to G ' group's anisotropic scattering cross section, unit is every centimetre, cm ^-1

J _gBe g group's neutron-current density, unit is every square centimeter of per second, ncm ^-2S ^-1

Subsequently, with the anisotropic scattering cross section ∑ that obtains _{S1, G-＞G'}To isotropic scatterning cross section ∑ _{S0, G-＞G '}Do transporting correction, obtain revised scattering cross-section, as shown in the formula (6) and (7):

∑ ' _{S0, G-＞G '}=∑ _{S0, G-＞G'}, when G ≠ G' (6)

${\mathrm{\&Sigma;}}_{s,G->G}^{\&prime;}={\mathrm{\&Sigma;}}_{\mathrm{<figure-callout\; id="0"\; label="s"\; filenames="HDA00002771338600033.png"\; state="\{\{state\}\}">s</figure-callout>}0,G->G}-\underset{G^{\&prime;}=1}{\mathrm{\&Sigma;}}{\mathrm{\&Sigma;}}_{s1,G->G^{\&prime;}}---\left(7\right)$

Coarse-group cross section after processing through above homogenising will be used as the parameter that step 2 is calculated.

The Neutron flux distribution of the full thermonuclear reactor experiment cladding modular of the described calculating of step 2 adopts Simplified spherical harmonics method SPN, is specially: at first neutron-transport equation spherical-harmonic expansion under the dull and stereotyped geometry of one dimension, and then with the differentiating operator in equation

Directly replace with the gradient under three-dimensional coordinate

Obtain three rank SPN system of equations SP3 under three-dimensional cartesian coordinate system, to wherein odd-order equation cancellation, the even-order equation become partial differential equation of second order simultaneously by mathematic(al) manipulation again, make the partial differential equation of second order of two couplings that obtain identical with diffusion equation on mathematics by distortion.

The described every neutronics parameter of step 2 comprises TBR, product tritium rate, DPA, wind-puff is swollen, and its computing formula is as follows:

TBR refers to consume the triton number that a source neutron can produce, computing formula following formula (8):

$\mathrm{TBR}=\frac{\underset{g=1}{\mathrm{\&Sigma;}}\&Integral;{\mathrm{\&phi;}}_g\&CenterDot;{\mathrm{\&Sigma;}}_{\mathrm{tr},g}\mathrm{dv}}{S},---\left(8\right)$

In formula:

φ _gBe g group's flux, unit is every square centimeter of per second, ncm ^-2S ^-1

∑ _{Tr, g}Be g group's product tritium cross section, unit is every centimetre, cm ^-1

S is source strength, and unit is every cubic centimetre of per second, ncm ^-3S ^-1

Produce the tritium rate and refer to the total amount of the tritium that produces in the unit interval, computing formula is as shown in the formula (9):

In formula:

φ _gBe g group's flux, unit is every square centimeter of per second, ncm ^-2S ^-1

∑ _{Tr, g}Be g group's product tritium cross section, unit is every centimetre, cm ^-1

DPA weighs in fusion reactor, and the atom of high-energy neutron and material lattice reacts, and causes a kind of sign of lattice imperfection, and computing formula is as shown in the formula (10):

$\mathrm{DPA}=\frac{T\&times;\underset{g=1}{\mathrm{\&Sigma;}}\&Integral;{\mathrm{\&phi;}}_g\&CenterDot;{\mathrm{\&Sigma;}}_{\mathrm{DPA},g}\mathrm{dv}}{\mathrm{NA}}---\left(10\right)$

In formula:

T is the time that material is received irradiation altogether, and unit is second, s;

φ _gBe g group's flux, unit is every square centimeter of per second, ncm ^-2S ^-1

∑ _{DPA, g}Be g group's DPA cross section, unit is every centimetre, cm ^-1

NA is the nucleon number in material, and unit is individual every cubic centimetre, ncm ^-3

The calculating wind-puff is swollen: weigh the swollen parameter of wind-puff and be on average helium generation rate and hydrogen generation rate on an atom, computing formula is as shown in the formula (11) and (12):

In formula:

T is the time that material is received irradiation altogether, and unit is second, s;

φ _gBe g group's flux, unit is every square centimeter of per second, ncm ^-2S ^-1

∑ _{α, g}Be (n, α) cross section of g group, unit is every centimetre, cm ^-1

∑ _{P, g}Be the cross section of g group (n, p), unit is every centimetre, cm ^-1

NA is the nucleon number in material, and unit is individual every cubic centimetre, ncm ^-3

Compared to the prior art the present invention has following advantage:

1. due to the computing method that adopted " two-step approach ", for few group cross-section information, make the multigroup cross section Information Compression counting yield greatly improve;

2. owing to adopting characteristic line method to find the solution transport equation, make this method have higher geometric compliance;

3. because characteristic line method of the present invention adopts the modular characteristics line technology, the object that will calculate is discrete is a lot of geometry module and extraction typical geometry module wherein, choose specific polar angle and argument, only store the characteristic curve information in typical geometry module, therefore can significantly reduce the required memory headroom of characteristic curve storage; Simultaneously, the modular characteristics line technology is completed by the VBA script based on the AUTOCAD secondary development, and automaticity is very high.

4. because the characteristic line method in the present invention can be processed P1 scattering cross-section information, make the present invention have the ability that anisotropic scattering is processed, therefore have higher computational accuracy;

Description of drawings

Fig. 1 is the calculation process schematic diagram of " two-step approach ";

Fig. 2 is a TBM modular structure schematic diagram;

Fig. 3 is the schematic diagram of " typical cell 1 " after TBM is divided;

Fig. 4 is the schematic diagram of " typical cell 2 " after TBM is divided;

Fig. 5 is the situation that a kind of argument is chosen;

Fig. 6 is the situation that a kind of polar angle is chosen;

Fig. 7 is the schematic diagram that characteristic curve is connected on the lattice cell interface.

Embodiment

Below in conjunction with the drawings and specific embodiments, structure of the present invention is elaborated.

As shown in Figure 1, a kind of method of obtaining thermonuclear reactor experiment cladding modular neutronics parameter of the present invention adopts two-step approach, and concrete grammar is as follows:

Step 1: with thermonuclear reactor experiment cladding modular according to its axial geometrical feature, be divided into same district with axially going up how much, part that material is identical, cladding modular can be divided into several " typical cells " like this, utilize the characteristic curve computing module to find the solution neutron-transport equation on each " typical cell ", obtain thin group's Neutron flux distribution, then utilize the Neutron flux distribution that obtains to adopt the homogenising module to carry out homogenising according to the flux volume weighted in each " typical cell ", obtain the coarse-group cross section parameter, these parameters will be as the input of step 2;

Step 2: each coarse-group cross section parameter of " typical cell " that step 1 is obtained is as known parameters, carry out modeling on whole thermonuclear reactor experiment cladding modular size, calculate the Neutron flux distribution of full thermonuclear reactor experiment cladding modular, and further obtain every neutronics parameter.

The below is elaborated:

Step 1:

At first with thermonuclear reactor experiment cladding modular discrete according to geometrical feature be several " typical cells ".Fig. 2 is a kind of structural representation of thermonuclear reactor experiment cladding modular, and the physical dimension of this thermonuclear reactor experiment cladding modular TBM is footpath 480mm * ring 32mm * utmost point 1832mm.It consists of firm box-packed structure by Be district, the first wall (FW), dividing plate 1, dividing plate 2, footpath utmost point dividing plate (RP dividing plate) and backboard; Outwards be divided into diametrically by plasma: the radial arrangement of Be district, the first wall, increment district, helium header.The increment district is divided into 3rd district by dividing plate 1 and dividing plate 2, and the helium header is surrounded 3rd district by 4 backboards.Select the RAFM steel as structured material.Shade in Fig. 2 is depicted as " typical cell " schematic diagram after discrete.

Be illustrated in figure 3 as the schematic diagram of " typical cell 1 " in Fig. 2, i.e. typical cell shown in top shade in Fig. 2 Figure 4 shows that the schematic diagram of " typical cell 2 " in Fig. 2, i.e. typical cell shown in the shade of Fig. 2 middle and lower part.Utilize characteristic line method to calculate Neutron flux distribution on each " typical cell ".Characteristic line method in the present invention has the technical characterstic that the modular characteristics line generates storage and can utilize P1 Cross section calculation anisotropic scattering source.The fundamental equation of characteristic line method is as shown in the formula (13):

$\frac{d{\mathrm{\&phi;}}_g(r,\mathrm{\&Omega;})}{\mathrm{ds}}+{\mathrm{\&Sigma;}}_{t,g}\left(r\right){\mathrm{\&phi;}}_g(r,\mathrm{\&Omega;})=Q_g(r,\mathrm{\&Omega;})---\left(13\right)$

In formula:

R is the polar coordinates position of neutron;

Ω is the direction of neutron operation;

G=1,2 ..., G, expression energy group number;

φ _g(r, Ω) is illustrated in r place, position neutron angular flux density, and unit is every square centimeter of per second, ncm ^-2S ^-1

∑ _{T, g}(r) gross section of expression neutron and material effect, unit is every centimetre, cm ^-1

Q _g(r, Ω) is illustrated in r place, position, and direction is Ω, and the total source strength in the unit space unit solid angle, unit are every cubic centimetre of per second, ncm ^-3S ^-1

Then, the processing in anisotropic scattering source in characteristic line method elaborated.Source item Q in formula (13) _g(r, Ω) can be expressed as follows formula (14):

$Q_g(r,\mathrm{\&Omega;})=Q_{f,g}\left(r\right)+Q_{s,g}^{\mathrm{iso}}\left(r\right)+Q_{s,g}^{\mathrm{aniso}}(r,\mathrm{\&Omega;})+S_g\left(r\right)---\left(14\right)$

In formula:

$Q_{f,g}\left(r\right)=\frac{{\mathrm{\&chi;}}_{\mathrm{<figure-callout\; id="4"\; label="g"\; filenames="HDA00002771338600033.png"\; state="\{\{state\}\}">g</figure-callout>}}}{4\mathrm{\&pi;}{k}_{\mathrm{eff}}}\underset{g^{\&prime;}=1}{\overset{G}{\mathrm{\&Sigma;}}}{\left(v{\mathrm{\&Sigma;}}_f\left(r\right)\right)}_{g^{\&prime;}}{\mathrm{\&phi;}}_{g^{\&prime;}}\left(r\right)---(14-1)$

$Q_{s,g}^{\mathrm{iso}}\left(r\right)=\frac{1}{4\mathrm{\&pi;}}\underset{g^{\&prime;}=1}{\overset{G}{\mathrm{\&Sigma;}}}{\mathrm{\&Sigma;}}_{\mathrm{<figure-callout\; id="0"\; label="s"\; filenames="HDA00002771338600033.png"\; state="\{\{state\}\}">s</figure-callout>}0,g^{\&prime;}\&RightArrow;g}\left(r\right){\mathrm{\&phi;}}_{g^{\&prime;}}\left(r\right)---(14-2)$

$Q_{s,g}^{\mathrm{aniso}}(r,\mathrm{\&Omega;})=\frac{3}{4\mathrm{\&pi;}}\mathrm{\&Omega;}\&CenterDot;\underset{g^{\&prime;}=1}{\overset{G}{\mathrm{\&Sigma;}}}{\mathrm{\&Sigma;}}_{s1,g^{\&prime;}\&RightArrow;g}\left(r\right)\underset{4\mathrm{\&pi;}}{\&Integral;}{J}_{g^{\&prime;}}(r,{\mathrm{\&Omega;}}^{\&prime;})d{\mathrm{\&Omega;}}^{\&prime;}---(14-3)$

(14) formula and (14-1)-(14-3) each variable physical meaning in formula is as follows:

Q _f,g(r) be g group's fission source strength, unit is every cubic centimetre of per second, ncm ^-3S ^-1

χ _gIt is g group's fission spectrum;

∑ _fBe fission cross section, unit is every centimetre, cm ^-1

Be g group's isotropic scatterning source item, unit is every cubic centimetre of per second, ncm ^-3S ^-1

∑ _{S0, g ' → g}(r) be g ' group to g group's isotropic scatterning cross section, unit is every centimetre, cm ^-1

Be g group's anisotropic scattering source item, unit is every cubic centimetre of per second, ncm ^-3S ^-1

∑ _{S1, g ' → g}(r) be g ' group to g group's anisotropic scattering cross section, unit is every centimetre, cm ^-1

J _g′(r, Ω ') is the neutron-current density along Ω ' direction, and unit is every square centimeter of per second, ncm ^-2S ^-1

S _g(r) be the r g group's of place fixedly source strength, unit is every cubic centimetre of per second, ncm ^-3S ^-1

For integration

Adopt the Discrete Ordinate method to carry out the discrete rear numerical integration approximate representation of using, i.e. following formula (15) to angle:

$\underset{4\mathrm{\&pi;}}{\&Integral;}{J}_{g^{\&prime;}}(r,{\mathrm{\&Omega;}}^{\&prime;})d{\mathrm{\&Omega;}}^{\&prime;}=\underset{n}{\mathrm{\&Sigma;}}{\mathrm{\&omega;}}_n{\mathrm{\&Omega;}}_n{\mathrm{\&phi;}}_{g^{\&prime;}}(r,{\mathrm{\&Omega;}}_n)---\left(15\right)$

Ω wherein _nBe n direction after discrete, ω _nIt is the weight of n direction.

(15) formula is brought in (14-3) formula, can be at solid angle Ω=Ω _mThe anisotropic scattering source item of direction is following formula (16):

$Q_{s,g}^{\mathrm{aniso}}(r,{\mathrm{\&Omega;}}_m)=\frac{3}{4\mathrm{\&pi;}}\underset{g^{\&prime;}=1}{\overset{G}{\mathrm{\&Sigma;}}}{\mathrm{\&Sigma;}}_{s1,g^{\&prime;}\&RightArrow;g}\left(r\right)\underset{n}{\mathrm{\&Sigma;}}{\mathrm{\&omega;}}_n({\mathrm{\&Omega;}}_m\&CenterDot;{\mathrm{\&Omega;}}_n){\mathrm{\&phi;}}_{g^{\&prime;}}(r,{\mathrm{\&Omega;}}_n)---\left(16\right)$

Due to solid angle variable Ω _iCan be expressed as following formula (17):

Wherein, θ is polar angle,

Be the position angle.So following formula (18) is arranged:

So final, the anisotropic scattering source item of characteristic line method can be expressed as following formula (19):

The main bugbear that characteristic line method runs into when being applied to three-dimensional computations is that the characteristic curve geometrical information is large, and is still unacceptable under the active computer hardware condition.In order to address this problem, MOC method of the present invention has proposed three-dimensional module characteristic curve technology to reduce the characteristic curve quantity of information.The modular characteristics line technology is split into lattice cell with the geometry of Solve problems, proposes typical cell, only stores the characteristic curve information in typical cell, thereby reaches the purpose that reduces the characteristic curve quantity of information.

In the modular characteristics line technology, argument and polar angle be no longer to choose arbitrarily, but determined by specific formulation.Argument is chosen by following formula (20-1) with (20-2) and is determined:

In formula, Δ x is the length of typical cell x direction, and Δ y is the length of y direction, and nx is segments on Δ x limit, and ny is the segments on Δ y limit.

Fig. 5 has represented a kind of situation of choosing of argument.A wherein, c, e, b, d are according to formula (20-1), (20-2) selected stack features line on the x-y plane, and they are also the sections perpendicular to the x-y plane in 3D solid simultaneously.

The thought of processing argument can be applicable to process polar angle equally, and polar angle is determined by following formula (21-1)～(21-3):

In formula,

All sections are along the total length of argument direction; s _kBe the length of section k along the argument direction, the i.e. length of oblique line section; Δ z be typical cell z to length; Nz is the waypoint on middle Δ z limit;

Be the limit On segments.

Fig. 6 has represented the situation that a kind of polar angle is chosen.At first with the section a in Fig. 5, b, c, d, e be according to a, c, and e, b, d is linked in sequence, and then according to formula (21-1), (21-2) and (21-3) chooses the characteristic curve on polar angle, then the serial number that is connected on interface according to the different characteristic line.

The edge

The area of section of direction is following formula (22):

Finally, by choosing of specific polar angle and argument, the subdivision of typical cell and extraction make characteristic curve information in identical lattice cell identical and can realize connecting on interface, thereby can only need the characteristic curve information in how much lattice cells of storage typical case, reach the purpose that reduces memory space.Characteristic curve in the connection of different lattice cell interfaces as shown in Figure 7.

In the present invention, how much subdivisions, the typical cell in the modular characteristics line technology extracts, the explement polar angle is chosen, characteristic curve production is by completing based on the VBA script of AUTOCAD program secondary development, and automaticity is very high.

It is more than the explanation of characteristic curve computing module and related art features in the present invention.Nearly 175 groups of cross section information in the international fusion database FENDL-2.1 database that uses in Neutronics analysis, energy group number is too much, if whole 175 group cross-sections are used for the calculating that transports of whole TBM, counting yield will be very low.Therefore, the characteristic curve computing module complete transport calculating after, carry out homogenising by the homogenising module according to the thin group energy spectrum that obtains and calculate, with the few group database of 175 group database boil down tos, thereby reach the purpose that improves counting yield.The also group that the homogenising module is used also distinguishes shown in formula following formula (1)～(5):

$S_G^e=\underset{g\&Element;G}{\mathrm{\&Sigma;}}{S}_g^e---\left(1\right)$

${\mathrm{\&Sigma;}}_{a,G}=\frac{\underset{g\&Element;G}{\mathrm{\&Sigma;}}{\mathrm{\&Sigma;}}_{a,g}{\mathrm{\&phi;}}_g}{\underset{g\&Element;G}{\mathrm{\&Sigma;}}{\mathrm{\&phi;}}_g}---\left(2\right)$

${\mathrm{\&Sigma;}}_{f,G}=\frac{\underset{g\&Element;G}{\mathrm{\&Sigma;}}{\mathrm{\&Sigma;}}_{f,g}{\mathrm{\&phi;}}_g}{\underset{g\&Element;G}{\mathrm{\&Sigma;}}{\mathrm{\&phi;}}_g}---\left(3\right)$

${\mathrm{\&Sigma;}}_{\mathrm{<figure-callout\; id="0"\; label="s"\; filenames="HDA00002771338600033.png"\; state="\{\{state\}\}">s</figure-callout>}0,G->G^{\&prime;}}=\frac{\underset{g^{\&prime;}\&Element;G^{\&prime;}}{\mathrm{\&Sigma;}}\underset{g\&Element;G}{\mathrm{\&Sigma;}}{\mathrm{\&Sigma;}}_{\mathrm{<figure-callout\; id="0"\; label="s"\; filenames="HDA00002771338600033.png"\; state="\{\{state\}\}">s</figure-callout>}0,g->g^{\&prime;}}{\mathrm{\&phi;}}_g}{\underset{g\&Element;G}{\mathrm{\&Sigma;}}{\mathrm{\&phi;}}_g}---\left(4\right)$

${\mathrm{\&Sigma;}}_{s1,G->G^{\&prime;}}=\frac{\underset{g^{\&prime;}\&Element;G^{\&prime;}}{\mathrm{\&Sigma;}}\underset{g\&Element;G}{\mathrm{\&Sigma;}}{\mathrm{\&Sigma;}}_{s,g->g^{\&prime;}}{J}_g}{\underset{g\&Element;G}{\mathrm{\&Sigma;}}{J}_g}---\left(5\right)$

In formula (1)～(5),

Be g thin group's stationary source intensity, unit is every cubic centimetre of per second, ncm ^-3S ^-1

Be G thick group's stationary source intensity, unit is every cubic centimetre of per second, ncm ^-3S ^-1

φ _gBe g thin group's neutron-flux density, unit is every square centimeter of per second, ncm ^-2S ^-1

∑ _{A, g}Be g thin group's absorption cross section, unit is every centimetre, cm ^-1

∑ _{A, G}Be G thick group's absorption cross section, unit is every centimetre, cm ^-1

∑ _{F, g}Be g thin group's fission cross section, unit is every centimetre, cm ^-1

∑ _{F, G}Be G thick group's fission cross section, unit is every centimetre, cm ^-1

∑ _{S0, g-＞g'}Be g group to g ' group's isotropic scatterning cross section, unit is every centimetre, cm ^-1

∑ _{S0, G-＞G'}Be G group to G ' group's isotropic scatterning cross section, unit is every centimetre, cm ^-1

∑ _{S1, g-＞g'}Be g group to g ' group's anisotropic scattering cross section, unit is every centimetre, cm ^-1

∑ _{S1, G-＞G'}Be G group to G ' group's anisotropic scattering cross section, unit is every centimetre, cm ^-1

J _gBe g group's neutron-current density, unit is every square centimeter of per second, ncm ^-2S ^-1

Subsequently, with the anisotropic scattering cross section ∑ that obtains _{S1, G-＞G '}To isotropic scatterning cross section ∑ _{S0, G-＞G '}Do transporting correction, obtain revised scattering cross-section, shown in (6) and (7):

∑ ' _{S0, G-＞G '}=∑ _{S0, G-＞G '}, when G ≠ G' (6)

${\mathrm{\&Sigma;}}_{s,G->G}^{\&prime;}={\mathrm{\&Sigma;}}_{s0,G->G}-\underset{G^{\&prime;}=1}{\mathrm{\&Sigma;}}{\mathrm{\&Sigma;}}_{s1,G->G^{\&prime;}}---\left(7\right)$

Coarse-group cross section after processing through above homogenising will be used as the parameter that second step calculates

Step 2:

In step 2, at first utilize the cross section information on each " typical cell " that the first step obtains, transport calculating on full thermonuclear reactor experiment cladding modular, obtain the Neutron flux distribution of thermonuclear reactor experiment cladding modular; Utilize subsequently the Neutron flux distribution that obtains further to calculate the result of calculation of each Neutronics analysis parameter.

The Neutron flux distribution that calculates full thermonuclear reactor experiment cladding modular adopts Simplified spherical harmonics method (SPN) to carry out numerical solution to neutron-transport equation, and the characteristics of the method are that counting yield is high, and speed is fast.At first neutron-transport equation spherical-harmonic expansion under the dull and stereotyped geometry of one dimension is then with the differentiating operator in equation

Directly replace with the gradient under three-dimensional coordinate

Obtain three rank SPN system of equations (SP3) under three-dimensional cartesian coordinate system, to wherein odd-order equation cancellation, the even-order equation become partial differential equation of second order simultaneously by mathematic(al) manipulation again, make the partial differential equation of second order of two couplings that obtain identical with diffusion equation on mathematics by distortion.

After utilizing the SP3 method to obtain the Neutron flux distribution of full TBM, can further obtain each neutronics parameter result, each parameter calculation formula is described as follows:

Calculate TBR:TBR and refer to consume the triton number that a source neutron can produce, computing formula is as shown in the formula (8):

$\mathrm{TBR}=\frac{\underset{g=1}{\mathrm{\&Sigma;}}\&Integral;{\mathrm{\&phi;}}_g\&CenterDot;{\mathrm{\&Sigma;}}_{\mathrm{tr},g}\mathrm{dv}}{S},---\left(8\right)$

In formula:

φ _gBe g group's flux, unit is every square centimeter of per second, ncm ^-2S ^-1

∑ _{Tr, g}Be g group's product tritium cross section, unit is every centimetre, cm ^-1

S is source strength, and unit is every cubic centimetre of per second, ncm ^-3S ^-1

Calculate to produce the tritium rate: produce the total amount that the tritium rate refers to the tritium that produces in the unit interval, computing formula is as shown in the formula (9):

In formula:

φ _gBe g group's flux, unit is every square centimeter of per second, ncm ^-2S ^-1

∑ _{Tr, g}Be g group's product tritium cross section, unit is every centimetre, cm ^-1

Calculate DPA: in fusion reactor, the atom of high-energy neutron and material lattice reacts, and causes lattice imperfection, affects the materials'use life-span.DPA is a kind of sign of weighing this defective, and computing formula is as shown in the formula (10):

$\mathrm{DPA}=\frac{T\&times;\underset{g=1}{\mathrm{\&Sigma;}}\&Integral;{\mathrm{\&phi;}}_g\&CenterDot;{\mathrm{\&Sigma;}}_{\mathrm{DPA},g}\mathrm{dv}}{\mathrm{NA}}---\left(10\right)$

In formula:

T is the time that material is received irradiation altogether, and unit is second, s;

φ _gBe g group's flux, unit is every square centimeter of per second, ncm ^-2S ^-1

∑ _{DPA, g}Be g group's DPA cross section, unit is every centimetre, cm ^-1

NA is the nucleon number in material, and unit is individual every cubic centimetre, ncm ^-3

The calculating wind-puff is swollen: in fusion reactor, the nucleon in high-energy neutron and structured material is as Fe ⁵⁶Deng (n, p) can occur, reactions such as (n, α), the helion of generation and proton are built up in material lattice, can form cavity, affect structured material serviceable life.Weigh the swollen parameter of wind-puff and be on average helium generation rate and hydrogen generation rate on an atom, computing formula is as shown in the formula (11) and (12):

In formula:

T is the time that material is received irradiation altogether, and unit is second, s;

φ _gBe g group's flux, unit is every square centimeter of per second, ncm ^-2S ^-1

∑ _{α, g}Be (n, α) cross section of g group, unit is every centimetre, cm ^-1

∑ _{P, g}Be the cross section of g group (n, p), unit is every centimetre, cm ^-1

NA is the nucleon number in material, and unit is individual every cubic centimetre, ncm ^-3

Through above step, just can finally try to achieve Neutron flux distribution and neutronics parameter in TBM.

Result of calculation of the present invention has the computational accuracy suitable with the Monte Carlo, but counting yield significantly improves, under same hardware condition and computing environment, the counting yield of " two-step approach " computing method that the present invention proposes can improve more than 10 than monte carlo method.Simultaneously owing to having adopted the AUTOCAD secondary development, the mistake of having avoided artificial treatment to bring, automaticity is high; Adopt the modular characteristics line technology, significantly reduce memory space, and can process the anisotropic scattering source, can obtain more accurate result than isotropic scatterning source.Therefore, relatively be fit to have complex geometry, large scale and have the problem of strong external source condition to carry out Neutronics analysis TBM is this.

Claims (5)

1. method of obtaining thermonuclear reactor experiment cladding modular neutronics parameter is characterized in that: adopt two-step approach, concrete grammar is as follows:

Step 1: with thermonuclear reactor experiment cladding modular according to its axial geometrical feature, be divided into same district with axially going up how much, part that material is identical, cladding modular can be divided into several " typical cells " like this, utilize the characteristic curve computing module to find the solution neutron-transport equation on each " typical cell ", obtain thin group's Neutron flux distribution, then utilize the Neutron flux distribution that obtains to adopt the homogenising module to carry out homogenising according to the flux volume weighted in each " typical cell ", obtain the coarse-group cross section parameter;

Step 2: each coarse-group cross section parameter of " typical cell " that step 1 is obtained is calculated the Neutron flux distribution of full thermonuclear reactor experiment cladding modular, and is further calculated every neutronics parameter as known parameters on whole thermonuclear reactor experiment cladding modular size.

2. a kind of method of obtaining thermonuclear reactor experiment cladding modular neutronics parameter according to claim 1, it is characterized in that: the described characteristic curve computing module of step 1 adopts characteristic line method MOC to find the solution neutron-transport equation, can process the P1 scattering cross-section, utilize AUTOCAD Software Create characteristic curve information.

3. a kind of method of obtaining thermonuclear reactor experiment cladding modular neutronics parameter according to claim 1 is characterized in that: the formula that the described homogenising module of step 1 adopts is as shown in the formula (1)～(5):

$S_G^e=\underset{g\&Element;G}{\mathrm{\&Sigma;}}{S}_g^e---\left(1\right)$

${\mathrm{\&Sigma;}}_{a,G}=\frac{\underset{g\&Element;G}{\mathrm{\&Sigma;}}{\mathrm{\&Sigma;}}_{a,g}{\mathrm{\&phi;}}_g}{\underset{g\&Element;G}{\mathrm{\&Sigma;}}{\mathrm{\&phi;}}_g}---\left(2\right)$

${\mathrm{\&Sigma;}}_{f,G}=\frac{\underset{g\&Element;G}{\mathrm{\&Sigma;}}{\mathrm{\&Sigma;}}_{f,g}{\mathrm{\&phi;}}_g}{\underset{g\&Element;G}{\mathrm{\&Sigma;}}{\mathrm{\&phi;}}_g}---\left(3\right)$

${\mathrm{\&Sigma;}}_{s0,G->G^{\&prime;}}=\frac{\underset{g^{\&prime;}\&Element;G^{\&prime;}}{\mathrm{\&Sigma;}}\underset{g\&Element;G}{\mathrm{\&Sigma;}}{\mathrm{\&Sigma;}}_{s0,g->g^{\&prime;}}{\mathrm{\&phi;}}_g}{\underset{g\&Element;G}{\mathrm{\&Sigma;}}{\mathrm{\&phi;}}_g}---\left(4\right)$

${\mathrm{\&Sigma;}}_{s1,G->G^{\&prime;}}=\frac{\underset{g^{\&prime;}\&Element;G^{\&prime;}}{\mathrm{\&Sigma;}}\underset{g\&Element;G}{\mathrm{\&Sigma;}}{\mathrm{\&Sigma;}}_{s,g->g^{\&prime;}}{J}_g}{\underset{g\&Element;G}{\mathrm{\&Sigma;}}{J}_g}---\left(5\right)$

In formula (1)～(5),

Be g thin group's stationary source intensity, unit is every cubic centimetre of per second, ncm ^-3S ^-1

Be G thick group's stationary source intensity, unit is every cubic centimetre of per second, ncm ^-3S ^-1

φ _gBe g thin group's neutron-flux density, unit is every square centimeter of per second, ncm ^-2S ^-1

∑ _{A, g}Be g thin group's absorption cross section, unit is every centimetre, cm ^-1

∑ _{A, G}Be G thick group's absorption cross section, unit is every centimetre, cm ^-1

∑ _{F, g}Be g thin group's fission cross section, unit is every centimetre, cm ^-1

∑ _{F, G}Be G thick group's fission cross section, unit is every centimetre, cm ^-1

∑ _{S0, g-＞g'}Be g group to g ' group's isotropic scatterning cross section, unit is every centimetre, cm ^-1

∑ _{S0, G-＞G'}Be G group to G ' group's isotropic scatterning cross section, unit is every centimetre, cm ^-1

∑ _{S1, g-＞g'}Be g group to g ' group's anisotropic scattering cross section, unit is every centimetre, cm ^-1

∑ _{S1, G-＞G'}Be G group to G ' group's anisotropic scattering cross section, unit is every centimetre, cm ^-1

J _gBe g group's neutron-current density, unit is every square centimeter of per second, ncm ^-2S ^-1

Subsequently, with the anisotropic scattering cross section ∑ that obtains _{S1, G-＞G'}To isotropic scatterning cross section ∑ _{S0, G-＞G '}Do transporting correction, obtain revised scattering cross-section, as shown in the formula (6) and (7):

Ε ' _{S0, G-＞G '}=∑ _{S0, G-＞G'}, when G ≠ G' (6)

${\mathrm{\&Sigma;}}_{s,G->G}^{\&prime;}={\mathrm{\&Sigma;}}_{s0,G->G}-\underset{G^{\&prime;}=1}{\mathrm{\&Sigma;}}{\mathrm{\&Sigma;}}_{s1,G->G^{\&prime;}}---\left(7\right)$

Coarse-group cross section after processing through above homogenising will be used as the parameter that step 2 is calculated.

4. a kind of method of obtaining thermonuclear reactor experiment cladding modular neutronics parameter according to claim 1, it is characterized in that: the Neutron flux distribution of the full thermonuclear reactor experiment cladding modular of the described calculating of step 2 adopts Simplified spherical harmonics method SPN, be specially: at first neutron-transport equation spherical-harmonic expansion under the dull and stereotyped geometry of one dimension, then with the differentiating operator in equation

Directly replace with the gradient under three-dimensional coordinate

Obtain three rank SPN system of equations SP3 under three-dimensional cartesian coordinate system, to wherein odd-order equation cancellation, the even-order equation become partial differential equation of second order simultaneously by mathematic(al) manipulation again, make the partial differential equation of second order of two couplings that obtain identical with diffusion equation on mathematics by distortion.

5. a kind of method of obtaining thermonuclear reactor experiment cladding modular neutronics parameter according to claim 1 is characterized in that: the described every neutronics parameter of step 2 comprises TBR, produces the tritium rate, DPA, wind-puff is swollen, and its computing formula is as follows:

TBR refers to consume the triton number that a source neutron can produce, computing formula following formula (8):

$\mathrm{TBR}=\frac{\underset{g=1}{\mathrm{\&Sigma;}}\&Integral;{\mathrm{\&phi;}}_g\&CenterDot;{\mathrm{\&Sigma;}}_{\mathrm{tr},g}\mathrm{dv}}{S},---\left(8\right)$

In formula:

φ _gBe g group's flux, unit is every square centimeter of per second, ncm ^-2S ^-1

∑ _{Tr, g}Be g group's product tritium cross section, unit is every centimetre, cm ^-1

S is source strength, and unit is every cubic centimetre of per second, ncm ^-3S ^-1

Produce the tritium rate and refer to the total amount of the tritium that produces in the unit interval, computing formula is as shown in the formula (9):

In formula:

φ _gBe g group's flux, unit is every square centimeter of per second, ncm ^-2S ^-1

∑ _{Tr, g}Be g group's product tritium cross section, unit is every centimetre, cm ^-1

DPA weighs in fusion reactor, and the atom of high-energy neutron and material lattice reacts, and causes a kind of sign of lattice imperfection, and computing formula is as shown in the formula (10):

$\mathrm{DPA}=\frac{T\&times;\underset{g=1}{\mathrm{\&Sigma;}}\&Integral;{\mathrm{\&phi;}}_g\&CenterDot;{\mathrm{\&Sigma;}}_{\mathrm{DPA},g}\mathrm{dv}}{\mathrm{NA}}---\left(10\right)$

In formula:

T is the time that material is received irradiation altogether, and unit is second, s;

φ _gBe g group's flux, unit is every square centimeter of per second, ncm ^-2S ^-1

∑ _{DPA, g}Be g group's DPA cross section, unit is every centimetre, cm ^-1

NA is the nucleon number in material, and unit is individual every cubic centimetre, ncm ^-3

The calculating wind-puff is swollen: weigh the swollen parameter of wind-puff and be on average helium generation rate and hydrogen generation rate on an atom, computing formula is as shown in the formula (11) and (12):

In formula:

T is the time that material is received irradiation altogether, and unit is second, s;

φ _gBe g group's flux, unit is every square centimeter of per second, ncm ^-2S ^-1

∑ _{α, g}Be (n, α) cross section of g group, unit is every centimetre, cm ^-1

∑ _{P, g}Be the cross section of g group (n, p), unit is every centimetre, cm ^-1

NA is the nucleon number in material, and unit is individual every cubic centimetre, ncm ^-3

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