CN117910282B - Method for calculating thermal conductivity of oxide-doped nuclear fuel - Google Patents
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- FCTBKIHDJGHPPO-UHFFFAOYSA-N uranium dioxide Inorganic materials O=[U]=O FCTBKIHDJGHPPO-UHFFFAOYSA-N 0.000 description 12
- OOAWCECZEHPMBX-UHFFFAOYSA-N oxygen(2-);uranium(4+) Chemical compound [O-2].[O-2].[U+4] OOAWCECZEHPMBX-UHFFFAOYSA-N 0.000 description 4
- -1 uranium ions Chemical class 0.000 description 4
- 229910010293 ceramic material Inorganic materials 0.000 description 3
- 229910052770 Uranium Inorganic materials 0.000 description 2
- 238000004458 analytical method Methods 0.000 description 2
- 230000009286 beneficial effect Effects 0.000 description 2
- 238000011161 development Methods 0.000 description 2
- 238000005516 engineering process Methods 0.000 description 2
- 229910052760 oxygen Inorganic materials 0.000 description 2
- 239000001301 oxygen Substances 0.000 description 2
- 238000011160 research Methods 0.000 description 2
- FRWYFWZENXDZMU-UHFFFAOYSA-N 2-iodoquinoline Chemical compound C1=CC=CC2=NC(I)=CC=C21 FRWYFWZENXDZMU-UHFFFAOYSA-N 0.000 description 1
- 229910052691 Erbium Inorganic materials 0.000 description 1
- GWEVSGVZZGPLCZ-UHFFFAOYSA-N Titan oxide Chemical compound O=[Ti]=O GWEVSGVZZGPLCZ-UHFFFAOYSA-N 0.000 description 1
- WGLPBDUCMAPZCE-UHFFFAOYSA-N Trioxochromium Chemical compound O=[Cr](=O)=O WGLPBDUCMAPZCE-UHFFFAOYSA-N 0.000 description 1
- QCWXUUIWCKQGHC-UHFFFAOYSA-N Zirconium Chemical compound [Zr] QCWXUUIWCKQGHC-UHFFFAOYSA-N 0.000 description 1
- 230000006399 behavior Effects 0.000 description 1
- LTPBRCUWZOMYOC-UHFFFAOYSA-N beryllium oxide Inorganic materials O=[Be] LTPBRCUWZOMYOC-UHFFFAOYSA-N 0.000 description 1
- 229910000423 chromium oxide Inorganic materials 0.000 description 1
- 230000010485 coping Effects 0.000 description 1
- 238000005336 cracking Methods 0.000 description 1
- 238000013461 design Methods 0.000 description 1
- 230000006866 deterioration Effects 0.000 description 1
- 238000009826 distribution Methods 0.000 description 1
- 230000007613 environmental effect Effects 0.000 description 1
- UYAHIZSMUZPPFV-UHFFFAOYSA-N erbium Chemical compound [Er] UYAHIZSMUZPPFV-UHFFFAOYSA-N 0.000 description 1
- CPLXHLVBOLITMK-UHFFFAOYSA-N magnesium oxide Inorganic materials [Mg]=O CPLXHLVBOLITMK-UHFFFAOYSA-N 0.000 description 1
- 239000000395 magnesium oxide Substances 0.000 description 1
- AXZKOIWUVFPNLO-UHFFFAOYSA-N magnesium;oxygen(2-) Chemical compound [O-2].[Mg+2] AXZKOIWUVFPNLO-UHFFFAOYSA-N 0.000 description 1
- 238000004519 manufacturing process Methods 0.000 description 1
- 238000012986 modification Methods 0.000 description 1
- 230000004048 modification Effects 0.000 description 1
- 230000000704 physical effect Effects 0.000 description 1
- 238000002360 preparation method Methods 0.000 description 1
- 230000005855 radiation Effects 0.000 description 1
- 238000012360 testing method Methods 0.000 description 1
- OGIDPMRJRNCKJF-UHFFFAOYSA-N titanium oxide Inorganic materials [Ti]=O OGIDPMRJRNCKJF-UHFFFAOYSA-N 0.000 description 1
- XLYOFNOQVPJJNP-UHFFFAOYSA-N water Substances O XLYOFNOQVPJJNP-UHFFFAOYSA-N 0.000 description 1
- 229910052726 zirconium Inorganic materials 0.000 description 1
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Abstract
The invention provides a method for calculating the thermal conductivity of oxide-doped nuclear fuel, which comprises the following steps: step 1, establishing a scattering coefficient calculation model of phonons in the heat conduction process by doping materials; the doping material forms an A xBy type solid solution material; step 2, respectively establishing phonon scattering coefficient calculation models generated by the class A lattice defects and the class B lattice defects in the doped material; step 3, establishing a phonon scattering coefficient model caused by calculating the substitute atoms; step 4, establishing a calculation method of each parameter in each phonon scattering coefficient model in the previous step; and 5, calculating the thermal conductivity of the doped material according to the result in the previous step. The invention can directly obtain the heat conductivity of the doped material through calculation based on the heat conductivity data of the doped oxide material, and does not need to separately prepare a standard-size sample required by heat conductivity experimental measurement, thereby being capable of rapidly reflecting the thermophysical property state of the researched material product, reducing the research and development cost of the new material and shortening the research and development period.
Description
Technical Field
The invention belongs to the technical field of nuclear energy, and particularly relates to a method for calculating the thermal conductivity of oxide-doped nuclear fuel.
Background
Nuclear power is a clean and efficient non-fossil energy source, and plays an extremely important role in coping with environmental deterioration and relieving energy crisis for many countries in the world in recent years. Safety and economy are two important aspects of particular concern for nuclear power development, the core of nuclear power technology is nuclear reactor technology, and nuclear fuel is a nuclear component of nuclear reactor, and is an energy source of the nuclear reactor, and the comprehensive performance of the nuclear reactor has important influence on ensuring and improving the safety and economy of nuclear energy. Uranium dioxide fuel, which is currently the most widely used light water reactor, has numerous advantages. However, as reactor fuel elements move toward longer life and higher safety, the inherent drawbacks of uranium dioxide fuels exposed in research and application, such as low thermal conductivity and non-ideal radiation resistance, are increasingly failing to meet the requirements of high performance fuels. Accordingly, in order to improve the overall performance of the existing uranium dioxide fuel, some scholars have conducted research on the performance of adding oxides such as magnesium oxide, beryllium oxide, titanium oxide, and chromium oxide to uranium dioxide fuel in recent years.
Deep knowledge and understanding of the thermophysical properties of fuel is of great importance for the design and manufacture of nuclear fuel elements and for understanding the irradiation behaviour within a reactor. For example, the thermal conductivity of fuel is one of the important properties that determine the internal temperature distribution of the fuel. Poor thermal conductivity will result in a large temperature gradient within the fuel, which can lead to cracking failure of the fuel during use. Therefore, how to quickly and accurately measure and evaluate the heat conduction performance of the fuel has great significance for the development of novel doped fuels.
However, aiming at the doped fuels with different components and under different process conditions, the accurate measurement of the thermal conductivity of the doped fuels requires preparation of experimental samples with uniform components and qualified sizes from the process, so that the cost is high, the time is long, and the rapid research and development of new fuels are seriously affected. Therefore, the invention provides a method for rapidly calculating and predicting the thermal conductivity of the nuclear fuel doped with the oxide material, which has very important significance for the research and development of novel doped fuel.
Disclosure of Invention
In view of the above, the present invention is directed to a method for calculating the thermal conductivity of a doped oxide nuclear fuel. Compared with the traditional material thermal conductivity testing method, the method can directly obtain the thermal conductivity of the doped material through calculation based on the thermal conductivity data of the oxide material before doping, and does not need to prepare a standard size sample required by thermal conductivity experimental measurement separately, so that the thermal physical property state of a researched material product can be reflected rapidly, the research and development cost of a new material can be reduced, and the research and development period is shortened.
The specific technical scheme of the invention is as follows:
A method for calculating the thermal conductivity of a doped oxide nuclear fuel, comprising:
Step 1: establishing a scattering coefficient calculation model of phonons in the heat conduction process by the doping material; the doping material forms an A xBy type solid solution material;
Step 2: respectively establishing phonon scattering coefficient calculation models generated by class A lattice defects and class B lattice defects in the doped material;
step 3: establishing a phonon scattering coefficient model caused by calculating the substitute atoms;
step 4: establishing a calculation method of each parameter in each phonon scattering coefficient model in the step 1, the step2 and the step 3;
Step 5: and calculating the thermal conductivity of the doped material according to the results in the steps 1 to 4.
Specifically, in step 1, the expression of the scattering coefficient calculation model of phonons in the heat conduction process by the doping material is:
In the above formula, Γ total represents the total phonon scattering coefficient due to doping; x and y each represent a chemical coefficient of the solid solution; m A and M B respectively represent the atomic average masses of class A lattice positions and class B lattice positions in the lattice of the material; m represents the average mass of all atoms in the lattice; Γ A and Γ B represent phonon scattering coefficients generated by class a lattice defects and class B lattice defects, respectively.
Specifically, in step 2, the expression of the phonon scattering coefficient calculation model generated by the class a lattice defect and the class B lattice defect in the material is:
ΓA＝xa·Γ'a+xb·Γ'b
ΓB＝xc·Γ'c+xd·Γ'd
in the above formula, subscripts a and b respectively represent elements corresponding to cations, and c and d respectively represent elements corresponding to anions or vacancies; x represents the share concentration of the element; Γ' represents the phonon scattering coefficient caused by the substitution atom.
Specifically, in step 3, the expression of the phonon scattering coefficient model caused by the substituted atoms is:
In the above formula, M i and r i represent the mass and ionic radius of such defects, respectively; And/> Respectively representing the average mass and the radius of atoms at the lattice position where the defect is located; epsilon represents the stress field factor, which mainly reflects the relative weights of mass differences and radius differences to phonon scattering.
Specifically, in the steps 1 to 3, the calculation method of each phonon scattering coefficient model parameter is as follows:
MA＝xa·Ma+xb·Mb
MB＝xc·Mc+xd·Md
rA＝xa·ra+xb·rb
rB＝xc·rc+xd·rd
In the above formulas, M a and M b respectively represent the atomic masses of the elements (or vacancies) corresponding to the two cations at the a-type lattice positions in the lattice of the material; m c and M d respectively represent the atomic masses of the elements (or vacancies) corresponding to the two anions at the B-type lattice positions in the lattice of the material; r a and r b respectively represent the ionic radii of the elements (or vacancies) corresponding to the two cations at the class A lattice positions in the lattice of the material; r c and r d respectively represent the ionic radii of the elements (or vacancies) corresponding to the two cations at the B-type lattice positions in the lattice of the material; alpha l represents the average linear expansion coefficient of the material; k T represents the isothermal bulk modulus of elasticity of the material; ρ represents the density of the material; c p represents the isobaric specific heat capacity of the material; μ is the poisson's ratio of the material.
Specifically, in step 5, the method for calculating the thermal conductivity of the doped oxide material is as follows:
in the above formula, k is the thermal conductivity of the doped oxide material; k 0 is the thermal conductivity of the undoped oxide material at the same temperature conditions as the doped oxide material.
The invention has the beneficial effects that:
according to the invention, the scattering coefficient of phonons in the heat conduction process of doping is calculated, and then the heat conductivity of the doped new material at different temperatures can be obtained based on the scattering coefficient and the heat conductivity of the main component material before doping, and a standard size sample required by heat conductivity experimental measurement is not required to be additionally and independently prepared, so that the heat conductivity of the researched material can be rapidly obtained, the research and development cost of the new material can be reduced, and the research and development period is shortened.
Drawings
FIG. 1 is a comparison of calculated values of thermal conductivity of Er 2O3-UO2 solid solutions at 500℃with experimental values.
FIG. 2 is a comparison of calculated thermal conductivity of ZrO 2-UO2 solid solution at 600℃with experimental values.
Detailed Description
In order to make the technical problems, technical schemes and beneficial effects to be solved more clear, the invention is further described in detail below with reference to the accompanying drawings and embodiments. It should be understood that the specific embodiments described herein are for purposes of illustration only and are not intended to limit the scope of the invention.
The invention mainly provides a method for calculating the thermal conductivity of oxide-doped nuclear fuel, and the following examples are listed according to specific oxide-doped materials.
Example 1:
The invention provides a method for calculating the thermal conductivity of oxide-doped nuclear fuel, which comprises the following steps:
(1) And establishing a scattering coefficient calculation model of phonons in the doping-to-heat conduction process. For an AB 2 type solid solution material formed by doping Er 2O3 with UO 2, the phonon scattering coefficient calculation expression is as follows:
(2) And respectively establishing phonon scattering coefficients generated by A-type lattice defects (erbium and uranium ions) and B-type lattice defects (oxygen ions or vacancies) in the material, wherein the expression of the model is as follows:
ΓA＝xEr·Γ'Er+(1-xEr)·Γ'U (8-2)
ΓB＝(2-xEr/2)·Γ'O+xEr/2·Γ' Vacancy, or both (8-3)
(3) And establishing a phonon scattering coefficient model caused by calculating the substituted atoms (or vacancies), wherein the expression of the model is as follows:
(4) The calculation method for establishing each parameter in the formulas (8-1) to (8-5) is as follows:
(5) The thermal conductivity calculation method of the solid solution formed by doping Er 2O3 with UO 2 under the condition of 500 ℃ is established:
In the formulas (8-1) to (8-9), M Er、MU、MO、M Vacancy, or both has values of 167.3amu, 238.0amu, 16.00amu and 0, respectively; the values of the oxide of r Er、rU、rO、r Vacancy, or both are respectively 0.088nm, 0.100nm, 0.074nm and 0; the other parameters are all values of UO 2 ceramic materials. Finally, according to the formula (8-10), the thermal conductivity of Er 2O3-UO2 solid solution formed after doping different Er 2O3 contents is calculated by combining thermal conductivity experimental data of UO 2 ceramic material at 500 ℃, and the thermal conductivity of the Er 2O3-UO2 solid solution at 500 ℃ is shown in figure 1.
Example 2:
The invention provides a method for calculating the thermal conductivity of oxide-doped nuclear fuel, which comprises the following steps of
(1) And establishing a scattering coefficient calculation model of phonons in the doping-to-heat conduction process. For the AB 2 type solid solution material formed by doping ZrO 2 with UO 2, the phonon scattering coefficient calculation expression is as follows:
(2) And respectively establishing phonon scattering coefficients generated by class A lattice defects (zirconium and uranium ions) and class B lattice defects (oxygen ions or vacancies) in the material, wherein the expression of the model is as follows:
ΓA＝xzr·Γ'zr+(1-xzr)·Γ'U (8-12)
ΓB＝2·Γ'O (8-13)
(3) And establishing a phonon scattering coefficient model caused by calculating the substituted atoms (or vacancies), wherein the expression of the model is as follows:
(4) The calculation method for establishing each parameter in the formulas (8-11) to (8-15) is as follows:
(5) The thermal conductivity calculation method of forming solid solution after ZrO 2 is doped with UO 2 is established under the condition of 600 ℃ is as follows:
In the formulas (8-11) to (8-19), M Zr、MU、MO、M Vacancy, or both takes the values 91.22amu, 238.0amu, 16.00amu and 0, respectively; the values of the oxide of r Zr、rU、rO、r Vacancy, or both are respectively 0.072nm, 0.100nm, 0.074nm and 0. Finally, according to the formula (8-20), the thermal conductivity of the ZrO 2-UO2 solid solution formed after doping with different ZrO 2 contents is calculated by combining thermal conductivity experimental data of the UO 2 ceramic material at 600 ℃, and the thermal conductivity of the ZrO 2-UO2 solid solution at 600 ℃ is shown in figure 2.
From the analysis of the comparison result of the calculated values and the experimental values in fig. 1 and 2, the maximum deviation between the calculated value and the experimental value of the thermal conductivity of the Er 2O3-UO2 solid solution obtained by calculation in the invention under the condition of 500 ℃ is 5.82%, and the maximum deviation between the calculated value and the experimental value of the thermal conductivity of the ZrO 2-UO2 solid solution under the condition of 600 ℃ is 7.26%, both of which are not more than 8%.
Based on the analysis, the method for calculating the thermal conductivity of the doped oxide nuclear fuel provided by the invention can be used for quickly calculating and predicting the thermal conductivity of the doped oxide solid solution material.
The foregoing description of the preferred embodiments of the invention is not intended to be limiting, but rather is intended to cover all modifications, equivalents, and alternatives falling within the spirit and principles of the invention.
Claims (1)
1. A method for calculating the thermal conductivity of oxide doped nuclear fuel is characterized in that: the method comprises the following steps:
Step 1: establishing a scattering coefficient calculation model of phonons in the heat conduction process by the doping material; the doped material forms an A xBy type solid solution material;
step 2: respectively establishing phonon scattering coefficient calculation models generated by class A lattice defects and class B lattice defects in the doped material;
step 3: establishing a phonon scattering coefficient model caused by calculating the substitute atoms;
step 4: establishing a calculation method of each parameter in each phonon scattering coefficient model in the step 1, the step 2 and the step 3;
step 5: calculating the thermal conductivity of the doped material according to the results in the steps 1 to 4;
in the step 1, the expression of the scattering coefficient calculation model of phonons in the heat conduction process by the doping material is as follows:
in the above formula, Γ total represents the total phonon scattering coefficient due to doping; x and y each represent a chemical coefficient of the solid solution; m A and M B respectively represent the atomic average masses of class A lattice positions and class B lattice positions in the lattice of the material; m represents the average mass of all atoms in the lattice; Γ A and Γ B represent phonon scattering coefficients generated by class a lattice defects and class B lattice defects, respectively;
in the step 2, the phonon scattering coefficient calculation model expression generated by the class a lattice defect and the class B lattice defect in the material is as follows:
ΓA＝xa·Γ'a+xb·Γ'b
ΓB＝xc·Γ'c+xd·Γ'd
In the above formula, subscripts a and b respectively represent elements corresponding to cations, and c and d respectively represent elements corresponding to anions or vacancies; x a、xb、xc and x d each represent the portion concentration of a different element or vacancy; Γ 'a、Γ'b、Γ'c and Γ' d represent phonon scattering coefficients caused by substitution of different types of atoms, respectively;
in the step 3, the expression of the phonon scattering coefficient model caused by the substituted atoms is as follows:
In the above formula, M i and r i represent the mass and ion radius of the defect, respectively; And/> Respectively representing the average mass and the radius of atoms at the lattice position where the defect is located; epsilon represents a stress field factor, which represents the relative weight of mass difference and radius difference to phonon scattering;
In the step1 to the step3, the calculation method of each parameter in each phonon scattering coefficient model is as follows:
MA＝xa·Ma+xb·Mb
MB＝xc·Mc+xd·Md
rA＝xa·ra+xb·rb
rB＝xc·rc+xd·rd
In the above formulas, M a and M b respectively represent the atomic masses of the elements corresponding to the two cations at the a-type lattice positions in the lattice of the material; m c and M d respectively represent the atomic masses of the elements corresponding to the two anions at the B-class lattice positions in the lattice of the material; r a and r b respectively represent the ionic radii of the elements corresponding to the two cations at the A-class lattice positions in the lattice of the material; r c and r d respectively represent the ionic radii of the elements corresponding to the two anions at the B-class lattice positions in the lattice of the material; alpha l represents the average linear expansion coefficient of the material; k T represents the isothermal bulk modulus of elasticity of the material; ρ represents the density of the material; c p represents the isobaric specific heat capacity of the material; μ is poisson's ratio of the material;
in the step 5, the method for calculating the thermal conductivity of the doped oxide material comprises the following steps:
in the above formula, k is the thermal conductivity of the doped oxide material; k 0 is the thermal conductivity of the undoped oxide material at the same temperature conditions as the doped oxide material.
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