CN111145924B - Power density distribution statistical method for porous hexagonal prism type nuclear fuel element - Google Patents
Power density distribution statistical method for porous hexagonal prism type nuclear fuel element Download PDFInfo
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Abstract
The invention discloses a power density distribution statistical method for a porous hexagonal prism type nuclear fuel element, which comprises the following steps: 1. dividing a rhombic grid in the cross section of one symmetrical area of the fuel element; 2. uniformly selecting sampling points in the diamond grid and determining relative coordinates of the sampling points; 3. calculating the absolute coordinates of sampling points in each grid according to the position of each grid; 4. obtaining the number of effective sampling points positioned in the fuel matrix in each grid according to the absolute coordinates of the sampling points; 5. calculating the area of each grid; 6. calculating the corresponding power statistical unit volume of each grid; 7. calculating the thermal deposition value in each power statistical unit; 8. and calculating the power density of each power statistical unit, and finishing the calculation. The method can obtain fine power density distribution of the porous hexagonal prism type fuel element irregular-shaped fuel matrix, and can provide reference for design optimization and safety analysis of the nuclear thermal propulsion reactor.
Description
Technical Field
The invention relates to the field of nuclear reactor design and safety analysis, in particular to a fine power density distribution statistical method for a porous hexagonal prism type nuclear fuel element.
Background
With the continuous improvement of the scale of human space exploration, the requirements on performance indexes such as flight time, flight load, flight acceleration and the like of the spacecraft are higher and higher. The traditional chemical energy propulsion technology has high technical maturity, the performance gradually approaches to the technical limit, but the characteristics of small specific impulse and low energy density are more and more difficult to adapt to the needs of future space activities, a chemical rocket supporting remote space flight must have very large initial payload mass of earth low orbit, the ground launching cost is greatly increased, and the bearable degree can be reached. Therefore, the development of more advanced space propulsion technology with high energy density and strong cruising ability has become a necessary choice. The nuclear reactor can provide energy for a long time, does not need external energy such as solar energy and the like, and is not sensitive to the radiation band on the surface of the outer space planet. Thus, nuclear thermal propulsion has irreplaceable advantages in performing long-time deep space exploration and interplanetary missions. Research shows that the nuclear thermal propulsion engine has the remarkable advantages of large thrust range, high specific impulse, long service life and multiple starting, and is ideal power for novel space propulsion systems such as future manned spaceflight and the like.
The power density of the nuclear thermal propulsion reactor and the outlet temperature of the propellant directly determine two key performance parameters of a nuclear thermal engine, namely a thrust-weight ratio and a specific impulse. Under the condition that the high-temperature resistance of the reactor core material is certain, the key point for improving the power density and the outlet temperature of the reactor core lies in the effort of improving the heat exchange capacity of the reactor core and reducing the heat exchange resistance of the reactor core. Core fuel element fine power distribution and temperature distribution are important matters of concern in the optimization process of reactor design. The fine physical-thermal coupling analysis aiming at the fuel elements is a necessary means for analyzing and optimizing the heat exchange capacity of the reactor core. The fuel elements of the nuclear thermal propulsion reactor are generally designed in a porous hexagonal prism mode, the fuel matrix part of the elements is in an irregular shape, and the elements are greatly different from regular cylindrical fuel rods of a traditional reactor, so that certain difficulty is brought to the fine power density distribution statistics inside the fuel elements. The fine power density distribution is the premise and the basis for performing fine physical thermal coupling analysis on the fuel elements, so that the development of a fine power density distribution statistical method of the porous hexagonal prism type nuclear fuel elements has important significance for the research and development of a nuclear thermal propulsion reactor.
Disclosure of Invention
The invention aims to conveniently carry out fine physical thermal coupling analysis on reactor core fuel elements in the design optimization process of a nuclear thermal propulsion reactor, and provides a fine power density distribution statistical method for porous hexagonal prism type nuclear fuel elements.
In order to achieve the purpose, the invention adopts the following technical scheme to implement:
a statistical method for power density distribution of a porous hexagonal prism type nuclear fuel element comprises the following steps:
step 1, dividing a hexagonal prism type nuclear fuel element substrate into six symmetrical regions, wherein the symmetrical regions are distributed in a rotational symmetry mode around the axis of the hexagonal prism type nuclear fuel element substrate; selecting one of the symmetrical regions, dividing a rhombic grid in the cross section of the symmetrical region, and enabling two adjacent sides of the grid to be parallel to two adjacent symmetrical sides of the cross section of the symmetrical region respectively;
step 2, determining the sampling point distance, and establishing a relative coordinate system ij in the rhombic grid of one of the cross sections of the symmetrical areas in the step 1, wherein the i and j axes of the relative coordinate system are respectively superposed with two diagonals of the rhombic grid; uniformly selecting a series of sampling points in the complete diamond grid, and determining the coordinate values of the sampling points in a relative coordinate system:
xrelative,d＝Qpi·md·s (1)
yrelative,d＝Qpj·nd·s (2)
in the above formula:
xrelative,d,yrelative,d-coordinate values of the d-th sampling point in the relative coordinate system;
Qpi,Qpj-the values of the sampling points are 1, 1 respectively in the first quadrant of the relative coordinate system; the values of the sampling points are respectively-1 and 1 in a second quadrant relative to the coordinate system; the values of the sampling points are respectively-1 and-1 in a third quadrant of the relative coordinate system; the sampling points respectively take values of 1 to 1 in the fourth quadrant of the relative coordinate system;
md-the d-th sample point is counted along the row in the direction of the horizontal axis of the relative coordinate system;
nd-the d-th sample point is counted along a column in the longitudinal direction of the relative coordinate system;
s-sampling point spacing;
step 3, establishing an absolute coordinate system xy in the cross section of the hexagonal prism type nuclear fuel element, wherein the origin of the absolute coordinate system is at the geometric center of the cross section of the hexagonal prism type nuclear fuel element, and the positive half shaft of the x axis is coincided with one symmetric side of the cross section of one symmetric region, so that the cross section of the symmetric region is completely located in the first quadrant of the absolute coordinate system; and calculating coordinate values of all grid sampling points under an absolute coordinate system:
xcentre,g＝(mg-0.5)·lg+(ng-0.5)·lgcos(60) (3)
ycentre,g＝(ng-0.5)·lgsin(60) (4)
xabsolute,g,d＝xcentre,g+xrelative,dcos(θi,x)+yrelative,dcos(θj,x) (5)
yabsolute,g,d＝ycentre,g+xrelative,dcos(θi,y)+yrelative,dcos(θj,y) (6)
in the above formula:
xabsolute,g,d,yabsolute,g,d-in the g-th grid, the coordinate value of the d-th sampling point in the absolute coordinate system;
xcentre,g,yabsolute,g,d-the coordinate value of the g-th grid center in the absolute coordinate system;
mg-counting matrix grid rows in the positive direction of the x-axis of the absolute coordinate system;
ng-counting the matrix grid rows along the direction of the symmetry edge adjacent to the x-axis of the absolute coordinate system;
lg-side length of the rhombus grid;
θi,xthe included angle between the horizontal axis of the relative coordinate system and the horizontal axis of the absolute coordinate system in the grid ranges from 0 to pi;
θj,x-the angle between the longitudinal axis of the relative coordinate system and the transverse axis of the absolute coordinate system in the grid ranges from 0 to pi;
θi,y-the angle between the horizontal axis of the relative coordinate system and the vertical axis of the absolute coordinate system in the grid ranges from 0 to pi;
θj,y-the angle between the longitudinal axis of the relative coordinate system and the longitudinal axis of the absolute coordinate system in the grid ranges from 0 to pi;
step 4, scanning sampling points in all grids, and judging whether the sampling points are positioned in the hexagonal prism type nuclear fuel element substrate or not according to absolute coordinate values of the sampling points; the inequality of judgment whether the sampling point is in the hexagonal prism type nuclear fuel element matrix is as follows:
A1·xabsolute,g,d+B1·yabsolute,g,d+C1≥0 (7)
A2·xabsolute,g,d+B2·yabsolute,g,d+C2≥0 (8)
A3·xabsolute,g,d+B3·yabsolute,g,d+C3≤0 (9)
in the above formula:
A1，B1，C1-the first side of the cross section of the symmetric region is related to the x-axis of the absolute coordinate systemLinear equation coefficients of coincident symmetrical edges;
A2，B2，C2-the second side of the cross section of the symmetric region is the linear equation coefficient of the symmetric side adjacent to the x-axis of the absolute coordinate system;
A3，B3，C3-linear equation coefficients of the third side of the cross section of the symmetric region, i.e. the asymmetric side;
xo,k，yo,k-the coordinate value of the center of the cross-section of the kth cooling channel in the symmetric region in the absolute coordinate system;
Do-fuel element cooling channel diameter;
No-the number of cooling channels in the symmetric region;
marking sampling points in the fuel matrix as effective sampling points;
step 5, calculating the areas of all grids in the symmetrical region and the volume of a power statistical unit corresponding to each grid, wherein the power statistical unit is a control body formed by stretching the grids for a certain length along the axial direction:
Vg＝SgL (12)
in the above formula:
Sg-the area of the individual meshes within the symmetric region;
Peffective，Psum-the number of valid samples and the total number of samples within a single grid;
a1，a2-two diagonal lengths of the complete diamond-shaped mesh;
l is the axial length of the power statistical unit;
Vg-the volume of the power statistics unit;
step 6, performing steady-state neutron analysis on the hexagonal prism type nuclear fuel element by adopting a Monte Carlo method to obtain a thermal deposition value of each power statistical unit;
and 7, dividing the thermal deposition value of each power statistical unit by the volume of the power statistical unit to obtain the power density of each power statistical unit, and finishing the calculation.
Compared with the prior art, the invention has the following outstanding advantages:
the invention can disperse irregular fuel matrixes of the porous hexagonal prism type fuel elements into a certain number of control bodies, calculate the volume of each control body, calculate and obtain the thermal deposition in each control body by combining a Monte Carlo method, obtain fine power density distribution data of the fuel matrixes and lay a foundation for subsequent fine fuel element physical-thermal coupling analysis.
Drawings
FIG. 1 is a schematic representation of fuel element matrix meshing.
Fig. 2 is a schematic diagram of absolute coordinates on a cross section of a fuel element.
FIG. 3 is a diagram of a complete diamond grid sampling point selection.
Fig. 4 is a flow chart of the method of the present invention.
Detailed Description
The method of the present invention is further described in detail below with reference to the following detailed description of the drawings:
as shown in fig. 4, the present invention is a fine power density distribution statistical method for a porous hexagonal prism nuclear fuel element, comprising the steps of:
step 1, dividing the hexagonal-prism nuclear fuel element substrate into six symmetrical regions as shown in fig. 1, wherein the symmetrical regions are distributed in a rotational symmetry manner around the axis of the hexagonal-prism nuclear fuel element substrate. One of the symmetric regions is selected (in this embodiment, the symmetric region 1 is selected as an example for explanation), a rhombic grid is divided in the cross section of the symmetric region, and two adjacent sides of the grid are respectively parallel to two adjacent symmetric sides (such as a boundary line 1 and a boundary line 2 shown in fig. 2) of the cross section of the symmetric region.
And 2, determining the sampling point distance, and establishing a relative coordinate system ij in the rhombic grid of the cross section of the symmetrical area 1 as shown in fig. 3, wherein the i and j axes of the relative coordinate system are respectively superposed with two diagonals of the rhombic grid. Uniformly selecting a series of sampling points in the complete diamond grid, and determining the coordinate values of the sampling points under a relative coordinate system:
xrelative,d＝Qpi·md·s (1)
yrelative,d＝Qpj·nd·s (2)
in the above formula:
xrelative,d,yrelative,d-coordinate values of the d-th sampling point in the relative coordinate system;
Qpi,Qpj-the values of the sampling points are 1, 1 respectively in the first quadrant of the relative coordinate system; the values of the sampling points are respectively-1 and 1 in a second quadrant relative to the coordinate system; the values of the sampling points are respectively-1 and-1 in a third quadrant of the relative coordinate system; the sampling points respectively take values of 1 to 1 in the fourth quadrant of the relative coordinate system;
md-the d-th sample point is counted along the row in the direction of the horizontal axis of the relative coordinate system;
nd-the row count of the d-th sample point along the direction relative to the longitudinal axis of the coordinate system;
s-sampling point spacing;
step 3, as shown in fig. 2, establishing an absolute coordinate system xy in the cross section of the hexagonal prism nuclear fuel element, wherein the origin of the absolute coordinate system is at the geometric center of the cross section of the hexagonal prism nuclear fuel element, and the positive half axis of the x axis is coincided with one symmetric edge of the cross section of the symmetric region 1, so that the cross section of the symmetric region 1 is completely located in the first quadrant of the absolute coordinate system; and calculating coordinate values of all grid sampling points under an absolute coordinate system:
xcentre,g＝(mg-0.5)·lg+(ng-0.5)·lgcos(60) (3)
ycentre,g＝(ng-0.5)·lgsin(60) (4)
xabsolute,g,d＝xcentre,g+xrelative,dcos(θi,x)+yrelative,dcos(θj,x) (5)
yabsolute,g,d＝ycentre,g+xrelative,dcos(θi,y)+yrelative,dcos(θj,y) (6)
in the above formula:
xabsolute,g,d,yabsolute,g,d-coordinate values in absolute coordinate system of the sample point of the d-th within the g-th grid;
xcentre,g,yabsolute,g,d-the coordinate value of the g-th grid center in the absolute coordinate system;
mg-matrix grid row count in the positive direction of the x-axis of the absolute coordinate system, as shown in figure 2 for the matrix grid row count in the direction of boundary 1;
ng-matrix grid row counting along the direction of the symmetry edge adjacent to the x-axis of the absolute coordinate system, as shown in fig. 2 for the boundary 2;
lg-side length of the rhombus grid;
θi,xthe included angle between the horizontal axis of the relative coordinate system and the horizontal axis of the absolute coordinate system in the grid ranges from 0 to pi;
θj,x-the angle between the longitudinal axis of the relative coordinate system and the transverse axis of the absolute coordinate system in the grid ranges from 0 to pi;
θi,y-the angle between the horizontal axis of the relative coordinate system and the vertical axis of the absolute coordinate system in the grid ranges from 0 to pi;
θj,y-the angle between the longitudinal axis of the relative coordinate system and the longitudinal axis of the absolute coordinate system in the grid ranges from 0 to pi;
and 4, scanning the sampling points in all the grids, and judging whether the sampling points are positioned in the hexagonal prism type nuclear fuel element substrate or not according to absolute coordinate values of the sampling points, wherein as shown in the figures 1 and 2, the cross section of a symmetrical area is formed by surrounding three boundary lines, namely boundary lines 1, 2 and 3, and a plurality of circular holes are dug in the middle of the cross section. The inequality of judgment whether the sampling point is in the hexagonal prism type nuclear fuel element matrix is as follows:
A1·xabsolute,g,d+B1·yabsolute,g,d+C1≥0 (7)
A2·xabsolute,g,d+B2·yabsolute,g,d+C2≥0 (8)
A3·xabsolute,g,d+B3·yabsolute,g,d+C3≤0 (9)
in the above formula:
A1，B1，C1the linear equation coefficient of the first side of the cross section of the symmetric region, i.e. the symmetric side coinciding with the x-axis of the absolute coordinate system, is shown in fig. 2 as the linear equation coefficient of the boundary line 1;
A2，B2，C2the linear equation coefficient of the second side of the cross section of the symmetric region, i.e. the symmetric side adjacent to the x-axis of the absolute coordinate system, is shown in fig. 2 as the linear equation coefficient of the boundary line 2;
A3，B3，C3the linear equation coefficient of the third side of the cross section of the symmetric region, i.e. the asymmetric side, is shown in fig. 2 as the linear equation coefficient of the boundary line 3;
xo,k，yo,k-the coordinate value of the center of the cross section of the kth cooling channel in the symmetric region in the absolute coordinate system;
Do-fuel element cooling channel diameter;
No-number of cooling channels in the symmetric region;
marking sampling points in the fuel matrix as effective sampling points;
step 5, calculating the areas of all grids in the symmetrical region and the volume of a power statistical unit corresponding to each grid, wherein the power statistical unit is a control body formed by stretching the grids for a certain length along the axial direction:
Vg＝SgL (12)
in the above formula:
Sg-the area of the individual meshes within the symmetric region;
Peffective，Psum-the number of valid samples and the total number of samples within a single grid;
a1，a2-two diagonal lengths of the complete diamond-shaped mesh;
l is the axial length of the power statistical unit;
Vg-the volume of the power statistics unit;
step 6, performing steady-state neutron analysis on the hexagonal prism type nuclear fuel element by adopting a Monte Carlo method to obtain a thermal deposition value of each power statistical unit;
and 7, dividing the thermal deposition value of each power statistical unit by the volume of the power statistical unit to obtain the power density of each power statistical unit, and finishing the calculation.
Claims (1)
1. A statistical method for power density distribution of a porous hexagonal prism type nuclear fuel element is characterized by comprising the following steps:
step 1, dividing a hexagonal prism type nuclear fuel element substrate into six symmetrical regions, wherein the symmetrical regions are distributed in a rotational symmetry mode around the axis of the hexagonal prism type nuclear fuel element substrate; selecting one of the symmetrical regions, dividing a rhombic grid in the cross section of the symmetrical region, and enabling two adjacent sides of the grid to be parallel to two adjacent symmetrical sides of the cross section of the symmetrical region respectively;
step 2, determining the sampling point distance, and establishing a relative coordinate system ij in the rhombic grid of one of the cross sections of the symmetrical areas in the step 1, wherein the i and j axes of the relative coordinate system are respectively superposed with two diagonals of the rhombic grid; uniformly selecting a series of sampling points in the complete diamond grid, and determining the coordinate values of the sampling points in a relative coordinate system:
xrelative,d＝Qpi·md·s (1)
yrelative,d＝Qpj·nd·s (2)
in the above formula:
xrelative,d,yrelative,d-coordinate values of the d-th sampling point in the relative coordinate system;
Qpi,Qpj-the values of the sampling points are 1, 1 respectively in the first quadrant of the relative coordinate system; the values of the sampling points are respectively-1 and 1 in a second quadrant relative to the coordinate system; the values of the sampling points are respectively-1 and-1 in a third quadrant of the relative coordinate system; the sampling points respectively take values of 1 to 1 in the fourth quadrant of the relative coordinate system;
md-the d-th sample point is counted along the row in the direction of the horizontal axis of the relative coordinate system;
nd-the d-th sample point is counted along a column in the longitudinal direction of the relative coordinate system;
s-sampling point spacing;
step 3, establishing an absolute coordinate system xy in the cross section of the hexagonal prism type nuclear fuel element, wherein the origin of the absolute coordinate system is at the geometric center of the cross section of the hexagonal prism type nuclear fuel element, and the positive half shaft of the x axis is coincided with one symmetric side of the cross section of one symmetric region, so that the cross section of the symmetric region is completely located in the first quadrant of the absolute coordinate system; and calculating coordinate values of all grid sampling points under an absolute coordinate system:
xcentre,g＝(mg-0.5)·lg+(ng-0.5)·lgcos(60) (3)
ycentre,g＝(ng-0.5)·lgsin(60) (4)
xabsolute,g,d＝xcentre,g+xrelative,dcos(θi,x)+yrelative,dcos(θj,x) (5)
yabsolute,g,d＝ycentre,g+xrelative,dcos(θi,y)+yrelative,dcos(θj,y) (6)
in the above formula:
xabsolute,g,d,yabsolute,g,dwithin the g grid, the d sampleCoordinate values of the points in an absolute coordinate system;
xcentre,g,yabsolute,g,d-the coordinate value of the g-th grid center in the absolute coordinate system;
mg-counting matrix grid rows in the positive direction of the x-axis of the absolute coordinate system;
ng-counting the matrix grid rows along the direction of the symmetry edge adjacent to the x-axis of the absolute coordinate system;
lg-side length of the rhombus grid;
θi,xthe included angle between the horizontal axis of the relative coordinate system and the horizontal axis of the absolute coordinate system in the grid ranges from 0 to pi;
θj,x-the angle between the longitudinal axis of the relative coordinate system and the transverse axis of the absolute coordinate system in the grid ranges from 0 to pi;
θi,y-the angle between the horizontal axis of the relative coordinate system and the vertical axis of the absolute coordinate system in the grid ranges from 0 to pi;
θj,y-the angle between the longitudinal axis of the relative coordinate system and the longitudinal axis of the absolute coordinate system in the grid ranges from 0 to pi;
step 4, scanning sampling points in all grids, and judging whether the sampling points are positioned in the hexagonal prism type nuclear fuel element substrate or not according to absolute coordinate values of the sampling points; the inequality of judgment whether the sampling point is in the hexagonal prism type nuclear fuel element matrix is as follows:
A1·xabsolute,g,d+B1·yabsolute,g,d+C1≥0 (7)
A2·xabsolute,g,d+B2·yabsolute,g,d+C2≥0 (8)
A3·xabsolute,g,d+B3·yabsolute,g,d+C3≤0 (9)
in the above formula:
A1，B1，C1-the first side of the cross section of the symmetric region is the linear equation coefficient of the symmetric side coinciding with the x-axis of the absolute coordinate system;
A2，B2，C2-the second side of the cross section of the symmetric region is the linear equation coefficient of the symmetric side adjacent to the x-axis of the absolute coordinate system;
A3，B3，C3-linear equation coefficients of the third side of the cross section of the symmetric region, i.e. the asymmetric side;
xo,k，yo,k-the coordinate value of the center of the cross-section of the kth cooling channel in the symmetric region in the absolute coordinate system;
Do-fuel element cooling channel diameter;
No-the number of cooling channels in the symmetric region;
marking sampling points in the fuel matrix as effective sampling points;
step 5, calculating the areas of all grids in the symmetrical region and the volume of a power statistical unit corresponding to each grid, wherein the power statistical unit is a control body formed by stretching the grids for a certain length along the axial direction:
Vg＝SgL (12)
in the above formula:
Sg-the area of the individual meshes within the symmetric region;
Peffective，Psum-the number of valid samples and the total number of samples within a single grid;
a1，a2-two diagonal lengths of the complete diamond-shaped mesh;
l is the axial length of the power statistical unit;
Vg-the volume of the power statistics unit;
step 6, performing steady-state neutron analysis on the hexagonal prism type nuclear fuel element by adopting a Monte Carlo method to obtain a thermal deposition value of each power statistical unit;
and 7, dividing the thermal deposition value of each power statistical unit by the volume of the power statistical unit to obtain the power density of each power statistical unit, and finishing the calculation.
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