CN113314190A - Calculation method for radial power distribution of thorium-based mixed oxide fuel - Google Patents
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Abstract
The invention discloses a method for calculating radial power distribution of a thorium-based mixed oxide fuel, which is characterized in that the neutron flux and the change condition of the nuclear element in a fuel rod are calculated by adopting a Fick law and resonance capture empirical function coupling mode, the distribution condition of the flux is estimated by the Fick law, and the change condition of the fuel component is calculated according to the flux condition and the empirical function. The invention is based on the traditional UO2The radial power model of the fuel develops a radial power calculation model of the thorium-based mixed oxide and simultaneously considers232Th and238the resonance of the U is captured from the screen effect and therefore the fuel radial power distribution obtained using the present invention will be more accurate.
Description
Technical Field
The invention relates to the technical field of nuclear reactor power calculation, in particular to a method for calculating radial power distribution of a thorium-based mixed oxide fuel.
Background
The thorium-based fuel is operated in the reactor due to238The resonance capture of the epithermal neutrons by the U,239pu deposits on the outer surface of the fuel clad are significantly greater. This will result in a higher fuel power peakAnd therefore deeper burn-up of the fuel on the fuel surface. This can cause the radial power distribution of thorium-based fuels to differ significantly from that of conventional uranium dioxide fuels. Thus using the existing UO2Radial power modeling of fuels to simulate thorium-based mixed oxide fuels is clearly inadequate. At present, mixed oxides mainly based on thorium-based fuel are becoming the focus of research on accident-resistant fuel development, and the power distribution of the thorium-based fuel and the traditional UO are considered2Different fuels need to provide a stable, reliable and accurate calculation method of radial power distribution.
Disclosure of Invention
In order to overcome the defects and shortcomings in the prior art, the invention provides a calculation method of radial power distribution of a thorium-based mixed oxide fuel, which is used for calculating the neutron flux and the change condition of the nuclear element in a fuel rod by adopting a mode of coupling Fick's law and a resonance capture empirical function, and considers the change condition of the nuclear element in the fuel rod232Th and238the resonance of U is captured from the screen effect, has obtained more accurate fuel radial power distribution calculation result.
A second object of the invention is to provide a calculation system for the radial power distribution of a thorium-based mixed oxide fuel.
A third object of the present invention is to provide a storage medium.
It is a fourth object of the invention to provide a computing device.
In order to achieve the purpose, the invention adopts the following technical scheme:
a calculation method for radial power distribution of a thorium-based mixed oxide fuel adopts Fick's law to calculate neutron flux and adopts a mode of coupling a resonance capture empirical function to change the nuclear factor in a fuel rod, and specifically comprises the following steps:
calculating an initial nuclear density of the fuel within the fuel rod;
estimating the distribution condition of the current nuclear density flux based on the total section of the fuel rod and a Bessel function;
calculating the nuclear density change condition through a given burnup step length based on the initial nuclear density of the fuel in the fuel rod to obtain the nuclear density of each element of the fuel;
and calculating the radial power distribution curve of the current state according to the material composition and the flux distribution condition of the current state, and outputting the calculation result of the radial power distribution of the fuel.
As a preferred technical scheme, the initial nuclear density of the fuel in the fuel rod is calculated by the following specific calculation formula:
where ρ is the mass density of the fuel, A is the nuclear density of the fuel, M is the relative atomic mass of the fuel, and NAIs the Avogastron constant.
As a preferred technical scheme, the method further comprises a distribution coefficient setting step, and the specific steps comprise:
in calculating the nuclear density of the fuel, the fuel includes238U atom and232th atom of238U and232th is multiplied by a distribution coefficient, which is specifically expressed as:
in the calculation of232Th atom, the relevant parameters are as follows:
u1＝0.75
u2＝0.876×10-22×n232+0.925
u3＝0.75
in the calculation of238U, the relevant parameters are as follows:
u1＝1.613×10-22×n238+1.328
u2＝2.252×log(n238-3.8×1021)-45.289
u3＝-1.298×10-23×n238+0.757
wherein r isoutBeing fuelOuter radius, r being the currently calculated radius, n238Being fuel238Concentration of U atom, n232Being fuel232The concentration of Th atoms.
As a preferred technical scheme, the neutron flux is expressed by a general solution of a diffusion equation of a one-dimensional cylinder as follows:
Φ＝AI0×(Br)
wherein A is a constant, I0A Bessel function is modified for the zeroth order; b is the square of the total section Σ tot divided by the value of the diffusion coefficient, and r is the radius of the location.
As a preferred technical solution, the nuclear density variation is calculated to obtain the nuclear densities of various elements of the fuel, and the specific calculation formula is as follows:
for other nuclear species, including34U，235U，236U，239Pu，241Pu，242Pu, the specific calculation formula is:
wherein σaTo an absorption cross section, σcFor capturing the cross-section,. DELTA.bu is burnup, N is nuclear density, the subscript of N represents different nuclides, and α is a single speciesBit conversion factor, ρfuelWhich is the density of the fuel, x represents an isotope,f,kis a microscopic fission cross-section of the k-nuclear species,
is the nuclear density of the k species per volume.
As a preferred technical solution, the radial power distribution curve of the current state is calculated according to the material composition and the flux distribution condition of the current state, and the specific calculation formula is as follows:
PΦEfU235NU235+ΦEfPu239NPu239+ΦEfPu241NPu241
wherein E isfU235，EfPu239，EfPu241Are respectively as235U，239Pu，241Fission release energy, N, of PuU235，NPu239，NPu241Are respectively as235U，239Pu，241Nuclear density of Pu.
As a preferred technical solution, the flux and the nuclear density are functions of the radius, the radial power is calculated by taking the radius as a variable to obtain a radial power distribution curve, and the flux distribution when the current nuclear density is calculated is returned until the end of the life span is reached.
In order to achieve the second object, the present invention adopts the following technical solutions:
a system for calculating a radial power distribution of a thorium-based mixed oxide fuel, comprising: the system comprises an initial nuclear density calculation module, a flux distribution condition calculation module, a nuclear density change condition calculation module and a fuel radial power distribution calculation module;
the initial nuclear density calculation module is used for calculating the initial nuclear density of the fuel in the fuel rod;
the flux distribution condition calculation module is used for estimating the distribution condition of the current nuclear density flux based on the total cross section of the fuel rod and the Bezier function, and calculating the neutron flux by adopting Fick's law;
the nuclear density change condition calculation module is used for calculating the nuclear density change condition by adopting a mode of resonance capture empirical function coupling through a given burnup step length based on the initial nuclear density of the fuel in the fuel rod to obtain the nuclear density of various elements of the fuel;
the fuel radial power distribution calculation module is used for calculating a radial power distribution curve of the current state according to the material composition and the flux distribution condition of the current state and outputting a fuel radial power distribution calculation result.
In order to achieve the third object, the present invention adopts the following technical solutions:
a storage medium storing a program which, when executed by a processor, implements the method of calculating the radial power distribution of a thorium-based mixed oxide fuel as described above.
In order to achieve the fourth object, the present invention adopts the following technical means:
a computing device comprises a processor and a memory for storing a program executable by the processor, wherein the processor executes the program stored in the memory to realize the method for calculating the radial power distribution of the thorium-based mixed oxide fuel.
Compared with the prior art, the invention has the following advantages and beneficial effects:
(1) the invention adopts Fick's law and resonance capture empirical function coupling mode to calculate neutron flux and change condition of the nuclear element in the fuel rod, and considers232Th and238the resonance of U is captured from the screen effect, has obtained more accurate fuel radial power distribution calculation result.
(2) The invention uses the updated section data, so that the nuclear density change obtained by calculation is more accurate.
(3) The invention couples the burnup step length as the calculation factor of the nuclide change, and achieves the effects of improving the calculation precision and reducing the calculation time.
Drawings
FIG. 1 is a schematic flow chart of a method for calculating the radial power distribution of a thorium-based mixed oxide fuel according to the invention;
FIG. 2 is a calculated radial power distribution of a thorium-based mixed oxide fuel according to the inventionWith the conventional UO2Fuel radial power distribution contrast map;
FIG. 3 is a prior art radial power distribution of thorium-based fuel and conventional UO2Fuel radial power distribution versus map.
Detailed Description
In order to make the objects, technical solutions and advantages of the present invention more apparent, the present invention is described in further detail below with reference to the accompanying drawings and embodiments. It should be understood that the specific embodiments described herein are merely illustrative of the invention and are not intended to limit the invention.
Example 1
The embodiment provides a method for calculating radial power distribution of a thorium-based mixed oxide fuel, wherein the neutron flux and the change situation of the nuclear element in a fuel rod are calculated by adopting a mode of coupling Fick's law and a resonance capture empirical function, and the method comprises the following steps:
s1: firstly, according to the formulated conditions, passing through a formula
Calculating the initial nuclear density of the fuel in the fuel rod as the premise of processing, wherein A is the nuclear density of the fuel, rho is the mass density of the fuel, M is the relative atomic mass of the fuel, and NAIs an Avogastron constant;
s2: estimating the distribution condition of the current nuclear density flux based on the total section of the fuel rod and a Bessel function;
in the present embodiment, the normalized power distribution factor is calculated from the normalized neutron flux estimated by the bezier function;
due to the fact that238U and232the resonance self-shielding effect of Th is needed to calculate the next nuclear density238U and232th is multiplied by a distribution coefficient f (r) as follows:
for the232Relevant parameters of Th are as follows:
u1＝0.75
u2＝0.876×10-22×n232+0.925
u3＝0.75
for the238The U-related parameters are as follows:
u1＝1.613×10-22×n238+1.328
u2＝2.252×log(n238-3.8×1021)-45.289
u3＝-1.298×10-23×n238+0.757
wherein r isoutIs the outer radius of the fuel, r is the currently calculated radius, n238Being fuel238Concentration of U atom, n232Being fuel232The concentration of Th atoms.
According to feike's law, the normalized neutron flux in the radial direction can be calculated by the following general solution:
for the radial direction, the normalized neutron flux can be expressed in the general solution of the diffusion equation for a one-dimensional cylinder:
Φ＝AI0×(Br)
where A is a constant, determined from the fuel rod power, and can be set to a number 1 under the conditions of the method calculating the normalized value; i is0A Bessel function is modified for the zeroth order; b is the value of the square of the total section Σ tot divided by the value of the diffusion coefficient D; r is the radius of the location.
S3: calculating the nuclear density of each element of the fuel in the next step by inputting a given burnup step length according to the nuclear density of each element calculated in the previous step and a method for calculating the nuclear density change condition according to the following steps;
the nuclear density change of the nuclide can be calculated by the following method:
for other nuclides:234U，235U，236U，239Pu，241Pu，242pu has:
wherein σaTo an absorption cross section, σcTo capture the cross-section, Δ bu is burnup, N is the nuclear density, the subscript of N represents the different nuclides, a is calculated by:
where α is a unit conversion factor, ρfuelWhich is the density of the fuel, x represents an isotope,f,kis a microscopic fission cross-section of the k-nuclear species,
is the nuclear density of the k species per volume.
S4: the material composition and flux distribution condition according to the formula P phi E through the current statefU235NU235+ΦEfPu239NPu239+ΦEfPu241NPu241To calculate a radial power profile for the current state, where EfU235，EfPu239，EfPu241Are respectively as235U，239Pu，241Fission release energy, N, of PuU235，NPu239，NPu241Are respectively as235U，239Pu，241The nuclear density of Pu,. phi.is the flux, and the flux and nuclear density are halfThe function of the radius needs to calculate the radial power by taking the radius as a variable to obtain a radial power distribution curve, and returns to the step S2 to calculate until the end of the service life is reached;
the solution result obtained by the method of the embodiment can be used as a reference for researching the radial power distribution condition of the thorium-based mixed oxide fuel in detail.
As shown in FIGS. 2 and 3, the comparison of the two graphs shows that the radial power distribution rule and the magnitude of the thorium-based fuel calculated by the invention are consistent with the recorded results, and the radial power distribution rule and the magnitude are gradually increased along the radial direction, and the former stage and the UO are2The radial power distribution of the fuel is basically consistent, and the radial power is greatly increased near the outer surface of the fuel but is lower than UO2And (3) fuel.
Example 2
The present embodiment provides a calculation system for radial power distribution of a thorium-based mixed oxide fuel, including: the system comprises an initial nuclear density calculation module, a flux distribution condition calculation module, a nuclear density change condition calculation module and a fuel radial power distribution calculation module;
in the present embodiment, the initial nuclear density calculation module is configured to calculate an initial nuclear density of the fuel in the fuel rod;
calculating the initial nuclear density of the fuel in the fuel rod, wherein the specific calculation formula is as follows:
where ρ is the mass density of the fuel, A is the nuclear density of the fuel, M is the relative atomic mass of the fuel, and NAIs the Avogastron constant.
In the embodiment, the flux distribution condition calculation module is used for estimating the current distribution condition of the nuclear density flux based on the total cross section of the fuel rod and the Bezier function, and calculating the neutron flux by adopting Fick's law;
neutron flux is expressed as follows by using a general solution of a diffusion equation of a one-dimensional cylinder:
Φ＝AI0×(Br)
wherein A is a constant, I0A Bessel function is modified for the zeroth order; b is the square of the total section Σ tot divided by the value of the diffusion coefficient, and r is the radius of the location.
In this embodiment, the nuclear density change condition calculation module is configured to calculate the nuclear density change condition based on the initial nuclear density of the fuel in the fuel rod by a given burnup step length and in a mode of resonant capture empirical function coupling, so as to obtain the nuclear density of each element of the fuel;
in calculating the nuclear density of the fuel, the fuel includes238U atom and232th atom of238U and232th is multiplied by a distribution coefficient, which is specifically expressed as:
in the calculation of232Th atom, the relevant parameters are as follows:
u1＝0.75
u2＝0.876×10-22×n232+0.925
u3＝0.75
in the calculation of238U, the relevant parameters are as follows:
u1＝1.613×10-22×n238+1.328
u2＝2.252×log(n238-3.8×1021)-45.289
u3＝-1.298×10-23×n238+0.757
wherein r isoutIs the outer radius of the fuel, r is the currently calculated radius, n238Being fuel238Concentration of U atom, n232Being fuel232The concentration of Th atoms.
Calculating the nuclear density change condition to obtain the nuclear density of each element of the fuel, wherein the specific calculation formula is as follows:
for other nuclear species, including34U，235U，236U，239Pu，241Pu，242Pu, the specific calculation formula is:
wherein σaTo an absorption cross section, σcFor capturing the cross-section, Δ bu is burnup, N is nuclear density, the lower corner of N represents different nuclides, α is the unit conversion factor, ρfuelWhich is the density of the fuel, x represents an isotope,f,kis a microscopic fission cross-section of the k-nuclear species,
is the nuclear density of the k species per volume.
In the embodiment, the fuel radial power distribution calculation module is used for calculating the radial power distribution curve of the current state according to the material composition and the flux distribution condition of the current state, and outputting the calculation result of the fuel radial power distribution.
Calculating the radial power distribution curve of the current state according to the material composition and the flux distribution condition of the current state, wherein the specific calculation formula is as follows:
PΦEfU235NU235+ΦEfPu239NPu239+ΦEfPu241NPu241
wherein E isfU235，EfPu239，EfPu241Are respectively as235U，239Pu，241Fission release energy, N, of PuU235，NPu239，NPu241Are respectively as235U，239Pu，241Nuclear density of Pu.
The flux and the nuclear density are functions of the radius, the radial power is calculated by taking the radius as a variable to obtain a radial power distribution curve, and the flux distribution condition at the current nuclear density is calculated until the end of the service life is reached.
Example 3
This embodiment also provides a storage medium, which may be a storage medium such as a ROM, a RAM, a magnetic disk, an optical disk, etc., and the storage medium stores one or more programs, and when the programs are executed by a processor, the method for calculating the radial power distribution of the thorium-based mixed oxide fuel of embodiment 1 is implemented.
Example 4
The embodiment provides a computing device, which may be a desktop computer, a notebook computer, a smart phone, a PDA handheld terminal, a tablet computer, or other terminal device with a display function, and the computing device includes a processor and a memory, where the memory stores one or more programs, and when the processor executes the programs stored in the memory, the method for calculating the radial power distribution of the thorium-based mixed oxide fuel according to embodiment 1 is implemented.
The above embodiments are preferred embodiments of the present invention, but the present invention is not limited to the above embodiments, and any other changes, modifications, substitutions, combinations, and simplifications which do not depart from the spirit and principle of the present invention should be construed as equivalents thereof, and all such changes, modifications, substitutions, combinations, and simplifications are intended to be included in the scope of the present invention.
Claims (10)
1. A calculation method for radial power distribution of a thorium-based mixed oxide fuel is characterized by calculating neutron flux by Fick's law and changing the condition of the nuclear element in a fuel rod by coupling a resonance capture empirical function, and specifically comprises the following steps:
calculating an initial nuclear density of the fuel within the fuel rod;
estimating the distribution condition of the current nuclear density flux based on the total section of the fuel rod and a Bessel function;
calculating the nuclear density change condition through a given burnup step length based on the initial nuclear density of the fuel in the fuel rod to obtain the nuclear density of each element of the fuel;
and calculating the radial power distribution curve of the current state according to the material composition and the flux distribution condition of the current state, and outputting the calculation result of the radial power distribution of the fuel.
2. The method for calculating the radial power distribution of the thorium-based mixed oxide fuel as claimed in claim 1, wherein the initial nuclear density of the fuel in the fuel rod is calculated by the following specific formula:
where ρ is the mass density of the fuel, A is the nuclear density of the fuel, M is the relative atomic mass of the fuel, and NAIs the Avogastron constant.
3. The method for calculating the radial power distribution of the thorium-based mixed oxide fuel as claimed in claim 1, further comprising the step of setting the distribution coefficient, wherein the specific steps comprise:
in calculating the nuclear density of the fuel, the fuel includes238U atom and232th atom of238U and232th is multiplied by a distribution coefficient, which is specifically expressed as:
in the calculation of232Th atomThen, the relevant parameters are as follows:
u1＝0.75
u2＝0.876×10-22×n232+0.925
u3＝0.75
in the calculation of238U, the relevant parameters are as follows:
u1＝1.613×10-22×n238+1.328
u2＝2.252×log(n238-3.8×1021)-45.289
u3＝-1.298×10-23×n238+0.757
wherein r isoutIs the outer radius of the fuel, r is the currently calculated radius, n238Being fuel238Concentration of U atom, n232Being fuel232The concentration of Th atoms.
4. The method for calculating the radial power distribution of the thorium-based mixed oxide fuel according to claim 1, wherein the neutron flux is expressed by a general solution of a diffusion equation of a one-dimensional cylinder as:
Φ＝AI0×(Br)
wherein A is a constant, I0A Bessel function is modified for the zeroth order; b is the square of the total section Σ tot divided by the value of the diffusion coefficient, and r is the radius of the location.
5. The method for calculating the radial power distribution of the thorium-based mixed oxide fuel according to claim 1, wherein the nuclear density change condition is calculated to obtain the nuclear densities of various elements of the fuel, and the specific calculation formula is as follows:
for other nuclear species, including34U，235U，236U，239Pu，241Pu，242Pu, the specific calculation formula is:
wherein σaTo an absorption cross section, σcFor capturing the cross-section, Δ bu is burnup, N is nuclear density, the lower corner of N represents different nuclides, α is the unit conversion factor, ρfuelIs the density of the fuel, x represents the isotope, σf,kIs a microscopic fission cross-section of the k-nuclear species,
is the nuclear density of the k species per volume.
6. The method for calculating the radial power distribution of the thorium-based mixed oxide fuel as claimed in claim 1, wherein the radial power distribution curve of the current state is calculated according to the material composition and flux distribution condition of the current state, and the specific calculation formula is as follows:
P＝ΦEfU235NU235+ΦEfPu239NPu239+ΦEfPu241NPu241
wherein E isfU235，EfPu239，EfPu241Are respectively as235U，239Pu，241Fission release energy, N, of PuU235，NPu239，NPu241Are respectively as235U，239Pu，241Nuclear density of Pu.
7. The method for calculating the radial power distribution of the thorium-based mixed oxide fuel as claimed in claim 1, wherein the flux and the nuclear density are functions of radius, the radial power is calculated by taking the radius as a variable to obtain a radial power distribution curve, and the distribution of the flux when the current nuclear density is calculated is returned until the end of the service life is reached.
8. A system for calculating the radial power distribution of a thorium-based mixed oxide fuel, comprising: the system comprises an initial nuclear density calculation module, a flux distribution condition calculation module, a nuclear density change condition calculation module and a fuel radial power distribution calculation module;
the initial nuclear density calculation module is used for calculating the initial nuclear density of the fuel in the fuel rod;
the flux distribution condition calculation module is used for estimating the distribution condition of the current nuclear density flux based on the total cross section of the fuel rod and the Bezier function, and calculating the neutron flux by adopting Fick's law;
the nuclear density change condition calculation module is used for calculating the nuclear density change condition by adopting a mode of resonance capture empirical function coupling through a given burnup step length based on the initial nuclear density of the fuel in the fuel rod to obtain the nuclear density of various elements of the fuel;
the fuel radial power distribution calculation module is used for calculating a radial power distribution curve of the current state according to the material composition and the flux distribution condition of the current state and outputting a fuel radial power distribution calculation result.
9. A storage medium storing a program, characterized in that said program, when executed by a processor, implements the method of calculation of the radial power distribution of a thorium-based mixed oxide fuel as defined in any one of claims 1 to 7.
10. A computing device comprising a processor and a memory for storing a program executable by the processor, wherein the processor, when executing the program stored in the memory, implements the method for calculating the radial power distribution of a thorium-based mixed oxide fuel as defined in any one of claims 1 to 7.
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