CN114077796B - High-adaptability multiphase particle dispersion type fuel element temperature field calculation method - Google Patents
High-adaptability multiphase particle dispersion type fuel element temperature field calculation method Download PDFInfo
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- 239000000446 fuel Substances 0.000 title claims abstract description 130
- 239000006185 dispersion Substances 0.000 title claims abstract description 64
- 239000002245 particle Substances 0.000 title claims abstract description 63
- 238000004364 calculation method Methods 0.000 title claims abstract description 22
- 238000004088 simulation Methods 0.000 claims abstract description 43
- 238000000034 method Methods 0.000 claims abstract description 17
- 239000011159 matrix material Substances 0.000 claims abstract description 14
- 230000005540 biological transmission Effects 0.000 claims abstract 2
- 239000000463 material Substances 0.000 claims description 18
- 238000012546 transfer Methods 0.000 claims description 9
- 239000002131 composite material Substances 0.000 claims description 8
- 238000013461 design Methods 0.000 claims description 7
- 230000000704 physical effect Effects 0.000 claims description 4
- 230000008878 coupling Effects 0.000 claims description 2
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- 230000006399 behavior Effects 0.000 description 8
- 230000009471 action Effects 0.000 description 3
- 230000008901 benefit Effects 0.000 description 2
- 238000010586 diagram Methods 0.000 description 2
- 238000002474 experimental method Methods 0.000 description 2
- 230000004992 fission Effects 0.000 description 2
- 230000003993 interaction Effects 0.000 description 2
- 238000011160 research Methods 0.000 description 2
- OKTJSMMVPCPJKN-UHFFFAOYSA-N Carbon Chemical compound [C] OKTJSMMVPCPJKN-UHFFFAOYSA-N 0.000 description 1
- 229910052770 Uranium Inorganic materials 0.000 description 1
- 230000003044 adaptive effect Effects 0.000 description 1
- 239000000919 ceramic Substances 0.000 description 1
- 230000008859 change Effects 0.000 description 1
- 238000000280 densification Methods 0.000 description 1
- 238000009792 diffusion process Methods 0.000 description 1
- 229910002804 graphite Inorganic materials 0.000 description 1
- 239000010439 graphite Substances 0.000 description 1
- 230000007246 mechanism Effects 0.000 description 1
- 229910052751 metal Inorganic materials 0.000 description 1
- 239000002184 metal Substances 0.000 description 1
- 239000000203 mixture Substances 0.000 description 1
- 238000012986 modification Methods 0.000 description 1
- 230000004048 modification Effects 0.000 description 1
- 230000008569 process Effects 0.000 description 1
- 230000006903 response to temperature Effects 0.000 description 1
- 239000012798 spherical particle Substances 0.000 description 1
- 238000012360 testing method Methods 0.000 description 1
- JFALSRSLKYAFGM-UHFFFAOYSA-N uranium(0) Chemical compound [U] JFALSRSLKYAFGM-UHFFFAOYSA-N 0.000 description 1
- 239000002699 waste material Substances 0.000 description 1
- XLYOFNOQVPJJNP-UHFFFAOYSA-N water Substances O XLYOFNOQVPJJNP-UHFFFAOYSA-N 0.000 description 1
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Abstract
A method for calculating the temperature field of a high-adaptability multiphase particle dispersion type fuel element mainly comprises the following steps: 1. establishing and setting a geometric simulation model of the fuel element and the multiphase dispersion particles; 2. the control flow engineering software imports the geometrical simulation model after the setting; 3. calculating the element temperature field at the current moment; 4. dividing the element subregions; 5. calculating and storing the average temperature of each subarea; 6. numerical simulation software modifies the representative particle parameters and calculates the temperature field; 7. storing the thermal conductivity of the particles and the matrix material of each subarea; 8. calculating the equivalent heat conductivity of the fuel area of the element by using a theoretical model; 9. correcting the element heat conduction parameters; 10. repeating the steps 3-9 until the end of the moment. The high-adaptability calculation method can establish a connection between the element temperature field and the dispersed particle temperature field, realize mutual transmission of real-time parameters, and update data of the element heat conductivity, thereby more effectively and accurately evaluating the fuel element temperature field.
Description
Technical Field
The invention relates to the field of performance analysis of multiphase dispersion type fuel elements of nuclear reactors, in particular to a high-adaptability multiphase particle dispersion type fuel element temperature field calculation method.
Background
The multiphase dispersion type fuel element is a novel fuel form formed by dispersing and distributing nuclear fission materials in metal, ceramic or graphite matrixes, has the advantages of high uranium utilization efficiency, good thermal conductivity, wide material selection range and the like, is used for researching and testing reactors, pebble bed type high-temperature gas cooled reactors and pressurized water reactors, and is expected to be applied to the field of nuclear waste treatment.
Because the composition of each structure of the multiphase dispersion type fuel element is greatly different in response to temperature and irradiation; at the same time, the internal thermal conductivity of the component is affected by the matrix material and the mass of dispersed particles. Considering the interaction of heat transfer between multiphase dispersion particles and fuel elements is important to determine the equivalent heat conductivity of the fuel elements, and has important significance for analyzing the conditions of the fuel elements and the heat exchange conditions in the reactor.
The complex structure of the multiphase dispersion type fuel element is a fuel area containing dispersion particles, and according to the related theory of the composite material, the equivalent heat conductivity of the material is mainly determined by the heat conductivity of the dispersoid, the heat conductivity of the matrix and the volume fraction of the dispersoid in the matrix. At present, the research on the equivalent thermal conductivity of the composite material is divided into theoretical research, experiments and numerical simulation. Theoretical studies on equivalent physical properties of composite materials include theoretical models and analytical solutions. A large number of theoretical models are limited to the normal two-phase composite material, and have respective application ranges; for an analytic solution for solving a specific problem, when a physical equation contains variable physical parameters, the equation is difficult to solve; furthermore, due to the particularities of nuclear reactors, there are few experiments involved and the subject cannot be concerned with all dispersive fuel element designs. In the numerical simulation, most of the numerical simulation is focused on mechanism analysis, and mainly the influence of single variables such as volume share and the like on equivalent thermal conductivity is studied. In order to determine the equivalent heat conductivity of the fuel area of the multiphase dispersion type fuel element, the influence of physical parameters of multiphase dispersion particles in the pile on the overall heat conductivity of the fuel area under the combined action of multiple factors such as temperature, irradiation, burnup and the like is required to be studied, and the overall heat conductivity of the fuel area is related to the state of the multiphase dispersion particles, so that the heat transfer analysis of two dimensions is required to be coupled, and the equivalent heat conductivity of the fuel element is more comprehensively and accurately studied.
Disclosure of Invention
In order to overcome the problems of the prior art, the object of the present invention is to provide a highly adaptive calculation method for determining the temperature field of a multiphase dispersion fuel element. According to the method, temperature field calculation is firstly carried out on the fuel element at the initial moment, the division mode of the fuel element subareas is determined according to the predefined power level and the fuel element form, the fuel element subareas are divided into subareas, and the subareas correspond to the space positions inside the fuel element and are numbered. Determining the temperature profile of each subarea according to the space position of each subarea, storing the data, determining the average temperature of each subarea by an arithmetic average method, then determining the average temperature of each subarea as the boundary condition of heat transfer calculation of the representative multiphase dispersion particles of each subarea (as a plurality of particles are dispersed in each subarea, the average heat conduction parameter of the multiphase dispersion particles calculated by the average temperature of each subarea can be used as the average property of the multiphase dispersion particles in each subarea, taking the particles with the average heat conduction property of the multiphase dispersion particles in each subarea as the representative multiphase dispersion particles in each subarea), performing temperature field calculation of the representative multiphase dispersion particles, determining the equivalent heat conductivity of the representative multiphase dispersion particles in each subarea at the moment by using a Fourier law, determining the heat conductivity of a matrix material in each subarea by using a theoretical model of the equivalent heat conductivity of a two-phase composite material, then fitting the functional relation between the equivalent heat conductivity of each subarea and the subarea, and the numerical simulation software correcting the heat conduction coefficient definition of a fuel element by using the obtained function as the physical parameter of the fuel element before calculation until the moment is finished.
In order to achieve the above purpose, the invention adopts the following technical scheme:
a method for calculating the temperature field of a high-adaptability multiphase particle dispersion type fuel element comprises the following steps:
step 1: determining the form, the internal structure and the geometric parameters of the fuel element, determining the form, the arrangement mode and the geometric parameters of multiphase dispersion particles, and establishing a fuel element geometric simulation model and a multiphase dispersion particle geometric simulation model by using numerical simulation software;
step 2: determining the type and design parameters of a researched reactor, determining a physical parameter model of a multiphase material according to the type and design parameters of the reactor, determining an irradiation behavior model of the multiphase material, determining a physical parameter model of a matrix material, and completing the operations of physical parameter model, irradiation behavior model, physical field boundary condition and source item setting of a geometric simulation model of a fuel element in numerical simulation software to complete the operations of physical parameter model, irradiation behavior model, physical field boundary condition and source item setting of the multiphase dispersion particle geometric simulation model;
step 3: the control flow engineering software is led into a fuel element geometric simulation model and a multiphase dispersion particle geometric simulation model;
step 4: the control flow engineering software determines regular and uniform subarea geometric shapes which are not overlapped in a crossing way according to the symmetry of the geometric simulation model of the fuel element, determines the number n of dividing subareas, completes subarea division, and completes subarea numbering according to the space position of the subarea corresponding to the geometric simulation model of the fuel element;
step 5: the control flow engineering software calls a geometric simulation model of the fuel element, and carries out heat transfer calculation of the fuel element at the initial moment to obtain a temperature profile of the fuel element;
step 6: the control flow engineering software determines the temperature molded line of each subarea of the fuel element at the corresponding space position according to the space position of each subarea of the fuel element in the geometric simulation model of the fuel element, obtains the temperature data in each subarea of the fuel element, determines the boundary temperature of each subarea of the fuel element, determines the average temperature of each subarea of the fuel element according to an arithmetic average method, and stores the average temperature data of each subarea of the fuel element according to the number of each subarea of the fuel element;
step 7: the control flow engineering software calls a multiphase dispersion particle geometric simulation model, and average temperature data of a subarea number 1 at the initial moment is called as a temperature boundary condition of representative multiphase dispersion particle heat transfer calculation of the subarea number 1;
step 8: calculating the temperature field of the representative multiphase dispersion particles with the subarea number 1 by the numerical simulation software, calculating the equivalent heat conductivity of the representative multiphase dispersion particles with the subarea number 1 according to the Fourier law, controlling the flow engineering software to extract the equivalent heat conductivity of the representative multiphase dispersion particles with the subarea number 1 and storing data according to the subarea number;
step 9: the control flow engineering software calls the average temperature data of the subarea number 1, and calculates the heat conductivity of the base material in the subarea number 1 by using the base material physical property parameter model determined in the step 2;
step 10: the control flow engineering software calls a theoretical model of the equivalent heat conductivity of the composite material, and calculates the whole equivalent heat conductivity of the subarea serial number 1;
step 11: the control flow engineering software stores the whole equivalent heat conductivity of the subarea serial number 1 according to the subarea serial number;
step 12: the control flow engineering software repeats the steps 7-11 for the rest subarea serial numbers except the subarea serial number 1;
step 13: the control flow engineering software completes the whole equivalent heat conductivity of each subarea of the fuel element, fits the whole equivalent heat conductivity of each subarea according to the relation between the length of the subarea and the radius of the fuel element, and obtains the functional relation between the equivalent heat conductivity of the fuel element and the radius as the updated equivalent heat conductivity of the fuel element;
step 14: the control flow engineering software transmits the updated equivalent heat conductivity of the fuel element to the numerical simulation software, and the numerical simulation software modifies the heat conduction parameters of the geometric simulation model of the fuel element;
step 15: and at the next moment, the control flow engineering software judges whether the final moment of calculation setting is reached, if the final moment is not reached, the program repeats the steps 5-14, and if the final moment is reached, the control flow engineering software calculation is ended.
Compared with the prior art, the invention has the following advantages:
1. the method allows for the interaction of the multiphase dispersion fuel element and the multiphase dispersion particles.
2. The method does not limit the geometry of the dispersion type fuel element.
3. The method can consider the combined action of multiple factors such as temperature, burnup, irradiation and the like.
4. The method can solve other equivalent physical parameters of the material.
5. The method is comprehensive and accurate and is easy to implement.
Drawings
FIG. 1 is a flow chart of a method of calculating equivalent thermal conductivity of a multiphase dispersion fuel element.
Fig. 2 is a volume fraction of 9% fuel zone thermal conductivity (for example, spherical fuel elements).
Fig. 3 shows the temperature distribution of a fuel zone with a volume fraction of 9% (for example spherical fuel elements).
Fig. 4 is a schematic structural view of a multiphase dispersion particle.
Fig. 5 is a schematic diagram of a multiphase dispersion fuel element configuration (spherical fuel elements are taken as an example).
Detailed Description
The process according to the invention is described in further detail in the following with reference to the specific embodiments of the drawings,
as shown in FIG. 1, the method for calculating the temperature field of the high-adaptability multiphase particle dispersion type fuel element comprises the following steps:
step 1: determining the form, the internal structure and the geometric parameters of the fuel element, determining the form, the arrangement mode and the geometric parameters of multiphase dispersion particles, and establishing a spherical fuel element geometric simulation model and a multiphase dispersion particle geometric simulation model by using numerical simulation software, wherein the multiphase dispersion particles are multi-layer coated spherical particles, the fuel element is spherical, the dispersion mode of the multiphase dispersion particles in a fuel sphere fuel zone is random dispersion, and the multiphase dispersion particles are in a spherical shape as shown in the structural schematic diagrams of the multiphase dispersion particles and the spherical fuel element shown in fig. 4 and 5;
step 2: determining the type and design parameters of a reactor to be researched, determining a physical parameter model of a multiphase material according to the type and design parameters of the reactor, determining an irradiation behavior model of the multiphase material, and determining a physical parameter model of a matrix material, wherein the physical parameter model of the material comprises thermal and force parameters which change along with burnup, temperature and neutron fluence rate, the irradiation behavior model of the material comprises behaviors of densification, irradiation deformation, irradiation creep, fission product release and diffusion, and the operations of the physical parameter model, the irradiation behavior model, physical field boundary conditions and source setting of a geometric simulation model of a fuel element are completed in numerical simulation software, and the operations of the physical parameter model, the irradiation behavior model, the physical field boundary conditions and the source setting of the multiphase dispersion particle geometric simulation model are completed;
step 3: the control flow engineering software is led into a fuel element geometric simulation model and a multiphase dispersion particle geometric simulation model;
step 4: the control flow engineering software determines regular and uniform subarea geometric shapes which are not overlapped in a crossing way according to the symmetry of the geometric simulation model of the fuel element, determines the number n of dividing subareas, completes subarea division, and completes subarea numbering according to the space position of the subarea corresponding to the geometric simulation model of the fuel element;
step 5: the control flow engineering software calls a geometric simulation model of the fuel element, and carries out heat transfer calculation of the fuel element at the initial moment to obtain a temperature profile of the fuel element;
step 6: the control flow engineering software determines the temperature molded line of each subarea of the fuel element at the corresponding space position according to the space position of each subarea of the fuel element in the geometric simulation model of the fuel element, obtains the temperature data in each subarea of the fuel element, determines the boundary temperature of each subarea of the fuel element, determines the average temperature of each subarea of the fuel element according to an arithmetic average method, and stores the average temperature data of each subarea of the fuel element according to the number of each subarea of the fuel element;
step 7: the control flow engineering software calls a multiphase dispersion particle geometric simulation model, and average temperature data of a subarea number 1 at the initial moment is called as a temperature boundary condition of representative multiphase dispersion particle heat transfer calculation of the subarea number 1;
step 8: calculating the temperature field of the representative multiphase dispersion particles with the subarea number 1 by the numerical simulation software, calculating the equivalent heat conductivity of the representative multiphase dispersion particles with the subarea number 1 according to the Fourier law, controlling the flow engineering software to extract the equivalent heat conductivity of the representative multiphase dispersion particles with the subarea number 1 and storing data according to the subarea number;
step 9: the control flow engineering software calls the average temperature data of the subarea number 1, and calculates the heat conductivity of the base material in the subarea number 1 by using the base material physical property parameter model determined in the step 2;
step 10: the control flow engineering software calls a theoretical model of the equivalent thermal conductivity of the composite material, such as a Maxwell model (formula (1)), and calculates the overall equivalent thermal conductivity of the subarea number 1:
wherein:
k fr -thermal conductivity of the fuel element fuel zone/(W/m·k);
kappa-ratio of multiphase dispersed particles to matrix material thermal conductivity/1;
k c -thermal conductivity of the matrix material/(W/m·k);
phi-the volume fraction/% of the dispersoid in the matrix material;
step 11: the control flow engineering software stores the whole equivalent heat conductivity of the subarea serial number 1 according to the subarea serial number;
step 12: the control flow engineering software repeats the steps 7-11 for the rest subarea serial numbers except the subarea serial number 1;
step 13: the control flow engineering software completes the whole equivalent heat conductivity of each subarea of the fuel element, fits the whole equivalent heat conductivity of each subarea according to the relation between the length of the subarea and the radius of the fuel element, and obtains the functional relation between the equivalent heat conductivity of the fuel element and the radius as the updated equivalent heat conductivity of the fuel element;
step 14: the control flow engineering software transmits the updated equivalent heat conductivity of the fuel element to the numerical simulation software, and the numerical simulation software modifies the heat conduction parameters of the geometric simulation model of the fuel element;
step 15: and at the next moment, the control flow engineering software judges whether the final moment of calculation setting is reached, if the final moment is not reached, the program repeats the steps 5-14, and if the final moment is reached, the control flow engineering software calculation is ended.
The results obtained according to this calculation method are shown in fig. 2 and 3, from which it can be seen that: the equivalent thermal conductivity of the fuel zone of the spherical fuel element increases along the radius at the initial stage of burnup, remains substantially unchanged along the radial direction at the final stage of burnup, and the maximum temperature within the fuel sphere increases with burnup. The result shows that the equivalent heat conductivity of the spherical fuel element can be accurately and comprehensively determined by coupling the multiphase coated particles and the temperature field of the spherical fuel element under the combined action of multiple factors such as temperature, burnup, irradiation and the like. The calculation method proposed by the invention can also be applied to plate-shaped or rod-shaped dispersion-type fuel elements.
While the invention has been described in connection with what is presently considered to be the most practical and preferred embodiment, it is to be understood that the invention is not limited to the disclosed embodiment, but on the contrary, is intended to cover various modifications and equivalent arrangements included within the spirit and scope of the appended claims.
Claims (2)
1. A high-adaptability multiphase particle dispersion type fuel element temperature field calculation method is characterized in that: aiming at the calculation problem of the temperature field of the dispersed fuel element, the parameter transmission of the geometric simulation model of the fuel element and the geometric simulation model of the dispersed particles is realized by using control flow engineering software, the coupling between the models is realized, the equivalent heat conductivity of the dispersed fuel element is accurately and comprehensively determined, and the temperature field of the dispersed fuel element is calculated;
the method comprises the following steps:
step 1: determining the form, the internal structure and the geometric parameters of the fuel element, determining the form, the arrangement mode and the geometric parameters of multiphase dispersion particles, and establishing a fuel element geometric simulation model and a multiphase dispersion particle geometric simulation model by using numerical simulation software;
step 2: determining the type and design parameters of a researched reactor, determining a physical parameter model of a multiphase material according to the type and design parameters of the reactor, determining an irradiation behavior model of the multiphase material, determining a physical parameter model of a matrix material, and completing the operations of physical parameter model, irradiation behavior model, physical field boundary condition and source item setting of a geometric simulation model of a fuel element in numerical simulation software to complete the operations of physical parameter model, irradiation behavior model, physical field boundary condition and source item setting of the multiphase dispersion particle geometric simulation model;
step 3: the control flow engineering software is led into a fuel element geometric simulation model and a multiphase dispersion particle geometric simulation model;
step 4: the control flow engineering software determines regular and uniform subarea geometric shapes which are not overlapped in a crossing way according to the symmetry of the geometric simulation model of the fuel element, determines the number n of dividing subareas, completes subarea division, and completes subarea numbering according to the space position of the subarea corresponding to the geometric simulation model of the fuel element;
step 5: the control flow engineering software calls a geometric simulation model of the fuel element, and carries out heat transfer calculation of the fuel element at the initial moment to obtain a temperature profile of the fuel element;
step 6: the control flow engineering software determines the temperature molded line of each subarea of the fuel element at the corresponding space position according to the space position of each subarea of the fuel element in the geometric simulation model of the fuel element, obtains the temperature data in each subarea of the fuel element, determines the boundary temperature of each subarea of the fuel element, determines the average temperature of each subarea of the fuel element according to an arithmetic average method, and stores the average temperature data of each subarea of the fuel element according to the number of each subarea of the fuel element;
step 7: the control flow engineering software calls a multiphase dispersion particle geometric simulation model, and average temperature data of a subarea number 1 at the initial moment is called as a temperature boundary condition of representative multiphase dispersion particle heat transfer calculation of the subarea number 1;
step 8: calculating the temperature field of the representative multiphase dispersion particles with the subarea number 1 by the numerical simulation software, calculating the equivalent heat conductivity of the representative multiphase dispersion particles with the subarea number 1 according to the Fourier law, controlling the flow engineering software to extract the equivalent heat conductivity of the representative multiphase dispersion particles with the subarea number 1 and storing data according to the subarea number;
step 9: the control flow engineering software calls the average temperature data of the subarea number 1, and calculates the heat conductivity of the base material in the subarea number 1 by using the base material physical property parameter model determined in the step 2;
step 10: the control flow engineering software calls a theoretical model of the equivalent heat conductivity of the composite material, namely a Maxwell model is shown in a formula (1), and the whole equivalent heat conductivity of a subarea number 1 is calculated:
wherein:
k fr -thermal conductivity of the fuel element fuel zone/(W/m·k);
kappa-ratio of multiphase dispersed particles to matrix material thermal conductivity/1;
k c -thermal conductivity of the matrix material/(W/m·k);
phi-the volume fraction/% of the dispersoid in the matrix material;
step 11: the control flow engineering software stores the whole equivalent heat conductivity of the subarea serial number 1 according to the subarea serial number;
step 12: the control flow engineering software repeats the steps 7-11 for the rest subarea serial numbers except the subarea serial number 1;
step 13: the control flow engineering software completes the whole equivalent heat conductivity of each subarea of the fuel element, fits the whole equivalent heat conductivity of each subarea according to the relation between the length of the subarea and the radius of the fuel element, and obtains the functional relation between the equivalent heat conductivity of the fuel element and the radius as the updated equivalent heat conductivity of the fuel element;
step 14: the control flow engineering software transmits the updated equivalent heat conductivity of the fuel element to the numerical simulation software, and the numerical simulation software modifies the heat conduction parameters of the geometric simulation model of the fuel element;
step 15: and at the next moment, the control flow engineering software judges whether the final moment of calculation setting is reached, if the final moment is not reached, the program repeats the steps 5-14, and if the final moment is reached, the control flow engineering software calculation is ended.
2. A method of calculating a temperature field for a highly adaptable multiphase particle dispersed fuel element as recited in claim 1, wherein: the numerical simulation software adopts COMSOL, ANSYS or ABAQUS software; the control flow engineering software adopts MATLAB, mathmatics or FORTRAN software.
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