JP2012194658A - Particle presence field analysis device, particle presence field analysis method, and computer program - Google Patents

Abstract

PROBLEM TO BE SOLVED: To calculate porosity of particles at high speed without remarkably lowering the calculation accuracy thereof even if the number of particles to be calculated increases.SOLUTION: After behavior of spherical particles in a two-dimensional area is analyzed by a DEM, a plurality of rectangular areas dividing the two-dimensional area is set. The length mean diameter of particles contained in the rectangular areas is individually calculated for each of the plurality of rectangular areas. Then, a plurality of cells 401 corresponding the plurality of rectangular areas are set. The cell 401 is a parallelepiped defined by a side in the x-axis direction of the rectangular area, a side in the z-axis direction, and a side in the y-axis direction having a length of the length mean diameter in the rectangular area, and a center position of the side in the y-axis direction is set at a position aligned with the center position of the spherical particle, both positions in the y-axis direction being aligned with each other. Then, the ratio of the particles contained in each cell 401 is obtained and a porosity ε in each rectangular area is calculated.

Description

  The present invention relates to a particle presence field analysis device, a particle presence field analysis method, and a computer program, and is particularly suitable for use in calculating the porosity of particles.

For example, in the ironmaking industry in the iron and steel industry, in order to stably produce high-quality hot metal, the behavior of particles such as sintered ore and coke in the blast furnace and the flow of gas in the blast furnace are analyzed. This is analyzed using a computer.
As such a technique, the discrete element method (discrete element method, which will be referred to as “DEM” in the following description) describing the discrete motion of particles, and the motion of gas (gas flow) are described. A technique for simulating a phenomenon in an actual blast furnace by coupling with the Navier-Stokes equation has been proposed (see Non-Patent Document 1). In this technology, the porosity of the particles is calculated from the arrangement of the particles in the three-dimensional region analyzed by DEM, and this porosity is given to the Navier-Stokes equation, so that the gas in the blast furnace in which the particles are charged is Analyzing the flow.

Written by Yuichi Yume, Toshihiko Umekage, Shinroku Matsuzaki, Masatomo Kadowaki, Kazuya Kunitomo, Masaaki Naito, Yuichi Ninagawa, Hitoshi Uehara, “The flow of multiphase (solid-gas powder) flow in an actual blast furnace aimed at CO2 emission minimum “Large-scale simulation”, 2008 Advanced Research Facility Shared Innovation Creation Project (use of industrial strategy) “Earth Simulator Industrial Strategy Use Program” use result report, Japan Agency for Marine-Earth Science and Technology, August 31, 2009, p. 15-25 Edited by the Society of Powder Technology, “Handbook of Powder Technology”, Nikkan Kogyo Shimbun, first edition, February 28, 1986, p. 15

  In the technique described in Non-Patent Document 1, analysis by DEM is performed to analyze the behavior of particles in a three-dimensional region. Therefore, in the technique of Non-Patent Document 1, an area having a quarter size of an actual blast furnace is used as a calculation area, and in reality, the number of particles existing in the hundreds of millions is increased to 10 million by increasing the particle diameter. Even if the calculation is performed using an earth simulator, the analysis by DEM requires several months of calculation time (In Non-Patent Document 1, the maximum number of particles to be calculated is 9 million. )

As described above, in the technique of handling the direct three-dimensional data described in Non-Patent Document 1 with the DEM, there is a problem that it takes an enormous time to calculate the porosity of the particles in the actual blast furnace. Therefore, it is also conceivable to perform particle analysis by DEM analysis in a two-dimensional region, and to calculate the porosity by two-dimensional calculation from the particle arrangement.
However, since the porosity of the particles is a three-dimensional index, the value of the particle porosity in the two-dimensional region is greatly different from the actual value of the porosity.
As described above, with the conventional technology, particularly when the number of particles to be calculated is large, it is difficult to calculate the porosity of the particles at high speed without greatly reducing the calculation accuracy. There was a point.

  The present invention has been made in view of the above problems, and even when the number of particles to be calculated increases, the void ratio of the particles is calculated at high speed without greatly reducing the calculation accuracy. For the purpose.

  The particle presence field analysis apparatus of the present invention includes a particle behavior analysis means for analyzing the behavior of particles in a two-dimensional region by a discrete element method with a spherical shape of the particles, and a plurality of rectangular regions that divide the two-dimensional region. A rectangular area setting means for setting a spherical particle in which all areas are contained in the rectangular area, and a rectangular particle in each of the plurality of rectangular areas set by the rectangular area setting means An average particle diameter calculating means for calculating an average diameter of spherical particles having a part of the region, and a spherical particle having a center position included in the rectangular region; A cell setting means for setting a plurality of cells corresponding to a rectangular area; a cell volume calculating means for calculating the volume of each of the cells; a volume of particles in which all the areas are contained in the cells; One in The volume of the cell calculated by the cell volume calculation means, the particle volume calculation means for calculating the sum of the volume of the areas included in the cell among the particle areas including the area of And, based on the total volume calculated by the particle volume calculation means, a void ratio calculation means for calculating the void ratio of the particles for each of the cells, the cell being the rectangular A first side that is a vertical side of the region, a second side that is a horizontal side of the rectangular region, a side perpendicular to the first side and the second side, and the rectangular region Is a parallelepiped defined by the third side having the length of the average diameter calculated by the average particle size calculating means, and in the direction along the third side at the center of the third side The positions are aligned in the direction along the third side. Characterized in that it is set to the center position and the aligned position of the particle that.

  The particle presence field analysis method of the present invention includes a particle behavior analysis step of analyzing the behavior of particles in a two-dimensional region by a discrete element method with the shape of the particles being spherical, and a plurality of rectangular regions dividing the two-dimensional region For each of the rectangular area setting step and the plurality of rectangular areas set by the rectangular area setting step, spherical particles in which all areas are contained in the rectangular area, and in the rectangular area An average particle diameter calculating step for calculating an average diameter of spherical particles having a part of the region, and a spherical particle having a center position included in the rectangular region; A cell setting step for setting a plurality of cells corresponding to a rectangular region, a cell volume calculating step for calculating the volume of each of the cells, a volume of particles in which all the regions are included in the cell, and the cell One in The volume of the cell calculated by the particle volume calculation step of calculating the sum of the volume of the region included in the cell of the particle region including the region of the cell, and the cell volume calculation step And a void ratio calculating step for calculating a void ratio of the particles for each of the cells based on the total volume calculated by the particle volume calculating step, and the cells are rectangular. A first side that is a vertical side of the region, a second side that is a horizontal side of the rectangular region, a side perpendicular to the first side and the second side, and the rectangular region Is a parallelepiped defined by a third side having a length of the average diameter calculated by the average particle size calculation step, and in a direction along the third side at the center of the third side The positions are aligned in the direction along the third side. Characterized in that it is set to the center position and the aligned position of the particle that.

  The computer program of the present invention causes a computer to function as each means of the particle presence field analyzer.

  According to the present invention, the behavior of particles in a two-dimensional region is analyzed by the discrete element method. And the average diameter of the spherical particle | grains contained in the said rectangular area is calculated separately about each of the several rectangular area which divides | segments the said two-dimensional area | region. Then, a plurality of cells corresponding to the plurality of rectangular areas are set. This cell has first and second sides which are vertical and horizontal sides of the rectangular region, and a side perpendicular to the first and second sides, and is an average calculated for the rectangular region. A parallelepiped defined by a third side having a length of a diameter, the position in the direction along the third side at the center of the third side is aligned with the position in the direction along the third side, respectively. It is set to a position aligned with the center position of the particles. Then, the porosity of the particles is calculated for each of these cells. Therefore, by calculating the particle porosity in the three-dimensional region by the discrete element method without calculating the particle behavior in the three-dimensional region, calculating a porosity close to the particle porosity. Can do. Therefore, the porosity of the particles can be calculated at high speed without greatly reducing the calculation accuracy.

It is a figure which shows an example of a functional structure of a particle presence field analyzer. It is a figure which shows notionally an example of the mode of two particle | grains which are contacting each other, and an example of the behavior of particle | grains. It is a figure which shows an example of the rectangular area | region set with respect to the two-dimensional area | region where each particle | grain is arrange | positioned. It is a figure which shows an example of the cell seen from the y-axis direction and the z-axis direction. It is a figure which shows the parameter of the calculation formula of the volume of the particle | grains in which all the area | regions are not contained in one cell. It is a figure which shows notionally an example of each particle | grain arrange | positioned in the area | region of calculation object by performing analysis by DEM. It is a figure which shows the particle size structure of each particle | grain in each area A, B, and C. FIG. It is a figure which shows the porosity calculated by varying the calculation method of the average diameter of the particle | grains contained in a rectangular area. It is a flowchart explaining an example of a process of a particle presence field analyzer. It is a flowchart explaining the particle | grain volume calculation process in a cell in step S906 of FIG.

Hereinafter, an embodiment of the present invention will be described with reference to the drawings.
FIG. 1 is a diagram illustrating an example of a functional configuration of the particle presence field analysis apparatus 100. The particle presence field analyzer 100 analyzes the behavior of particles (sintered or coke, etc.) charged into the blast furnace from, for example, a swirl chute for a bellless furnace top charging device of the blast furnace, and the result is obtained. This is used to analyze the gas flow in the blast furnace (fluid analysis). However, the object to be analyzed by the particle presence field analysis apparatus 100 is not limited to this.
The particle presence field analysis device 100 can be realized by using, for example, an information processing device (personal computer) including a CPU, ROM, RAM, HDD, various interfaces, a display, and the like.

(Particle behavior analysis unit 101)
The particle behavior analysis unit 101 analyzes the behavior of spherical particles in a two-dimensional region using a DEM. The particle behavior analysis unit 101 arranges each particle at a desired position based on particle information set based on, for example, a user interface operation by the user. Then, the particle behavior analysis unit 101 gives a condition for breaking the balance of forces generated between the particles, moves each particle, and determines whether each particle is in contact with other particles or structures. .
When the particles are in contact with other particles, the particle behavior analysis unit 101 obtains the repulsive force in the normal direction and the shear direction to solve the translational equation of motion, and obtains the moment of force around the center of gravity to rotate. The equation of motion is solved for each particle, and each particle is moved based on the result. On the other hand, when the particle is in contact with the structure, the particle behavior analysis unit 101 obtains the repulsive force in the normal direction and the shear direction, solves the translational equation of motion, and obtains the moment of force around the center of gravity. Solving the equation of motion of rotation is performed only for particles, not for structures.
The particle behavior analysis unit 101 performs the contact determination process and the movement process of each particle at predetermined time intervals. And the behavior in a predetermined period of each particle is obtained from the result.

Specifically, the particle behavior analysis unit 101 obtains the repulsive force F _{n, ij} in the normal direction in the contact region of the particles i and j by the following equation (1), for example, and by the following equation (2): The repulsive force F _{t, ij} in the shear direction in the contact region of the particles i and j is obtained, the translational equation of motion of the following equation (3) is solved, and the equation of rotation is solved by the following equation (4).

FIG. 2 is a diagram conceptually showing an example of the state of the two particles 201 and 202 that are in contact with each other (FIG. 2A) and an example of the behavior of the particle 203 (FIG. 2B). . The parameters of equations (1) to (4) will be described with reference to FIG.
In Equation (1), K _n is a spring constant in the normal direction, and can be set according to the distance H and δ _n in FIG. 2A, for example. However, K _n can be set to a predetermined constant value. Δu _{n, ij} is a relative translational displacement in the normal direction of the center of gravity between the two particles i and j. η _n is a viscosity constant in the normal direction and is set in advance. n _ij is a unit vector in the normal direction. Δt is a predetermined time interval and is set in advance.

In the equation (2), min [A, B] means that the smaller one of A and B is adopted. μ is a coefficient of friction and can be set to a preset value. However, μ can be varied depending on the state or the like. t _ij is a unit vector in the shear direction. K _t is a spring constant in the shear direction, and can be set according to, for example, the distance H, δ _n , or δ _t in FIG. However, K _t may also be a preset fixed value. Δut _{, ij} is the relative translational displacement in the shear direction of the center of gravity between the two particles i, j. Δφ _ij is a relative rotational displacement of the contact region caused by the rotation of the particle, and is represented by, for example, a difference between the rotational displacement φ _i of the particle 201 and the rotational displacement φ _j of the particle 202 in FIG. Can do. η _t is a viscosity constant in the shear direction and is set in advance. Δt is a predetermined time interval and is set in advance.

In equation (3), v is the velocity of the particles (see FIG. 2). The (dot) attached on v represents time differentiation. F is the total sum of the repulsive forces in the shear direction and the normal direction. m is the mass of the particles and is set in advance. g is a gravitational acceleration. When the particles are not in contact with other particles or structures, the first term on the right side of equation (3) is 0 (zero).
In the equation (4), ω is the angular velocity of the particles (see FIG. 2). * on ω indicates time differentiation. M is the total sum of moments of force, and is obtained from the repulsive forces F _{n, ij} and F _{t, ij in} the shear direction and the normal direction. I is a moment of inertia and is set in advance.

  In this embodiment, when analyzing the behavior of particles in a two-dimensional region by DEM, the particles are made spherical. This is because calculation is performed in consideration of an index having a three-dimensional component (such as a physical property value of particles). That is, when analyzing the behavior of particles in a two-dimensional region by DEM, the absolute value of the acting force acting on the particles is calculated as three-dimensional information, and the direction of the acting force acting on the particles is calculated as two-dimensional information. .

Further, when analyzing the behavior of the two-dimensional region of the particles charged into the blast furnace, the behavior of the two-dimensional region determined by the radial direction and the height direction of the blast furnace is analyzed. This is because the behavior of particles in the depth direction of the blast furnace has little influence on the analysis results. Therefore, when analyzing the behavior of the two-dimensional region of the particles charged into the blast furnace, the direction of the acting force acting on the particles is the in-plane direction of the cross section obtained by cutting the blast furnace along its axis.
As described above, the arrangement of each particle in the two-dimensional region to be calculated is obtained every predetermined time.

In addition, as the method for analyzing the behavior of particles (the analysis method executed by the particle behavior analysis unit 101), various known analysis methods for the behavior of particles in the DEM can be applied. The method is not limited to the method using the formula (4).
In the particle behavior analysis unit 101, for example, the CPU reads the particle information from the RAM or the like, executes the above-described arithmetic processing, obtains the coordinates in the two-dimensional region of each particle at each time, and stores the coordinates in the RAM or the like. Is realized.

(Rectangular area setting unit 102)
The rectangular area setting unit 102 sets a plurality of rectangular areas (so-called meshes) that divide the two-dimensional area whose particle behavior is analyzed by the particle behavior analysis unit 101. As described above, the particle behavior analysis unit 101 obtains the arrangement of each particle for each predetermined time in the two-dimensional region as the particle behavior. The rectangular area setting unit 102 sets a plurality of rectangular areas for the two-dimensional area in which the particles are arranged. When analyzing the behavior of the two-dimensional region of the particles charged into the blast furnace, the rectangular region setting unit 102, for example, information on the two-dimensional region in which each particle is arranged when the movement of each particle stops. And a plurality of rectangular areas are set for the two-dimensional area. However, it is not always necessary to set a plurality of rectangular areas for the two-dimensional area when the movement of each particle stops, and a plurality of rectangular areas can be set for the two-dimensional area at an arbitrary time.

FIG. 3 is a diagram illustrating an example of a rectangular region set for a two-dimensional region in which each particle is arranged. In addition, the two-dimensional area | region where each particle | grain is arrange | positioned is an area | region as shown to Fig.6 (a) mentioned later, for example.
As shown in FIG. 3, in this embodiment, a rectangular region having a length in the x-axis direction of dx and a length in the z-axis direction of dz in the two-dimensional region in which each particle is arranged is x It is set continuously in each of the axial direction and the z-axis direction. As shown in FIG. 3, some particles include all the regions in one rectangular region, and some particles exist across a plurality of rectangular regions.
When this two-dimensional region is a region in the blast furnace, the x-axis direction is the radial direction of the blast furnace, and the z-axis direction is the height direction of the blast furnace.

In the present embodiment, it is assumed that the sizes of all the rectangular areas are the same. In addition, it is preferable to determine the size of the rectangular area so that ten or more particles can enter one rectangular area. Furthermore, since the rectangular region can be set if the coordinates of the two-dimensional region to be analyzed by the particle behavior analysis unit 101 are known, the rectangular region is set before the analysis by the particle behavior analysis unit 101 is performed. May be.
The rectangular area setting unit 102 is realized, for example, when the CPU obtains coordinates (x-axis coordinates, z-axis coordinates) in a two-dimensional area (xz plane) of each rectangular area and stores them in a RAM or the like.

(Average particle size calculator 103)
The average particle diameter calculation unit 103 calculates the average diameter of spherical particles included in each of the plurality of rectangular areas set by the rectangular area setting unit 102. In this embodiment, the length average diameter is adopted as the most preferable average diameter. The reason for this will be described later.
Here, for particles in which all the regions are not included in one rectangular region, the length average diameter is calculated as belonging to the rectangular region in which the center of the particle is included.
The average particle diameter calculation unit 103 is realized, for example, when the CPU obtains the average length of spherical particles included in the rectangular area for all the rectangular areas and stores it in the RAM or the like.

(Cell setting unit 104)
The cell setting unit 104 includes “a side in the z-axis direction that is a vertical side of the rectangular region (a side having a length dz in FIG. 3)” and a “side in the x-axis direction that is a horizontal side in the rectangular region (FIG. 3). And the side in the y-axis direction perpendicular to the side in the z-axis direction and the side in the x-axis direction, and is calculated by the average particle diameter calculation unit 103 for the rectangular region. Y-axis direction side having the length of the average diameter of the length of the parallel hexahedron, wherein the y-axis direction position at the center of the y-axis direction side is the y-axis of the particle of the spherical field A plurality of parallelepipeds aligned with the center position of the direction are set. In the following description, this “parallelepiped” is referred to as “cell” as necessary.

FIG. 4 is a diagram illustrating an example of a cell viewed from the y-axis direction and the z-axis direction. In FIG. 4, for convenience of description, the number of particles contained in each of the cells 401a to 401c is 1 to 2, but actually, each of the cells 401a to 401c has more than this. Number of particles are included.
The cell setting unit 104 sets the “side in the z-axis direction (side of length dz in FIG. 3) and the side in the x-axis direction (side of length dx in FIG. 3) of the rectangular region set by the rectangular region setting unit 102. ) ”And the length average diameter information calculated by the average particle diameter calculation unit 103 for the rectangular region. Then, the cell setting unit 104 sets the “side of the rectangular area in the z-axis direction”, the “side of the rectangular area in the x-axis direction”, and the “vertex of the rectangular area as a central point, and the y-axis direction. A parallelepiped (a cuboid or a cube) defined by a side in the y-axis direction that extends to the left and right (equal to both the y-axis positive and negative directions) by the length of the length-average diameter set for the rectangular area All rectangular areas set by the setting unit 102 are determined.

In the example shown in FIG. 4, “the side in the y-axis direction with the vertex of the rectangular area as the center point and extended in the y-axis direction by the length of the length-average diameter set for the rectangular area” Are sides of length dy ₁ , dy ₂ , dy ₃ .
The parallelepipeds obtained in this way become cells 401a to 401c shown in FIG. 4, and the center position of each cell 401a to 401c in the y-axis direction is located on a plane 402 parallel to the x-axis and z-axis. .

Since the size and number of particles included in each rectangular region vary depending on the rectangular region, the average length diameter of the particles included in each rectangular region also varies depending on the rectangular region. Therefore, as shown in FIG. 4, the lengths dy ₁ to dy ₃ in the y-axis direction of the cells 401a to 401c are also different depending on the cells 401a to 401c (however, they may be the same).
In FIG. 4, only three cells 401 are shown, but the number of cells 401 set by the cell setting unit 104 is the same as the number of rectangular regions set by the rectangular region setting unit 102. Become.
The cell setting unit 104 is realized, for example, by the CPU obtaining three-dimensional coordinates (x-axis coordinates, y-axis coordinates, z-axis coordinates) of the cell 401 and storing them in a RAM or the like.

(Cell volume calculation unit 105)
The cell volume calculation unit 105 calculates the volume of each cell 401 set by the cell setting unit 104. As described above, since the shape of the cell is a parallelepiped (cuboid or cube), the volume of each cell 401 can be obtained by multiplying the lengths (dx, dy, dz) of each side. That is, the volume V _c of each cell 401 is obtained by the following equation (5).

  The cell volume calculation unit 105 is realized, for example, by the CPU obtaining the volume of each cell 401 and storing it in a RAM or the like.

(Particle volume calculation unit 106)
The particle volume calculation unit 106 calculates the volume of particles contained in the cell 401.
As shown in FIG. 4, the particle volume calculation unit 106 includes the center positions (coordinates) of the cells 401 a to 401 c in the y-axis direction and the positions of the centers 411 a to 415 a of the particles 411 to 415 in the y-axis direction. Are located on a plane 402 parallel to the x-axis and the z-axis, respectively.

  And the particle volume calculation part 106 calculates the volume of the particle | grains 411-415 contained in each cell 401a-401c.

The shape of each particle 411-415 is a sphere. Therefore, the particle volume calculation unit 106 calculates the volume V _p of the particles included in the cell 401 for the particles including all regions in the cell 401 by the following equation (6). calculate.

In the equation (6), D _p is the diameter of the particle (sphere). In the example shown in FIG. 4, the particles 413 to 415 correspond to such particles.
In addition, the particle volume calculation unit 106, for particles that do not include all the regions in one cell 401, out of the region of the particles, the volume of the region included in the cell 401, The volume V _p of the particles contained in the cell 401 is calculated.

FIG. 5 is a diagram illustrating parameters of calculation formulas for the volume of particles in which not all regions are included in one cell 401.
In FIG. 5, D _p is the diameter of the particle 416. a is the shortest distance between the center 416a of the particle 416 and the “side of the cell 401d on the xz plane” that the particle 416 straddles. When these D _p and a are used, the particle volume calculation unit 106 includes the particle 416 in which a part of the region is included in the cell 401, and is included in the cell 401d in the region of the particle 416. The volume of the area is calculated as the volume V _p of the particles contained in the cell 401d by the following equation (7).

In addition, for the particle 416 in which a part of the region is included in the cell 401, the particle volume calculation unit 106 calculates the volume of the region that is not included in the cell 401d out of the region of the particle 416. Is calculated by the following equation (8) as the volume V _p of the particles contained in the cell 401e to which.

In the example shown in FIG. 4, the particles 411 and 412 correspond to such particles.
In addition, the method (calculation formula) for calculating the volume of the region included in the cell 401 among the particle regions that do not include all the regions in one cell 401 is the above-described method ( It is not limited to (7) Formula and (8) Formula), but can be set as appropriate according to the positional relationship between the particles and the cell 401.
Then, the particle volume calculation unit 106 calculates “all of the particles in which at least a part of the region is included in one cell 401” by the expression (7) or (8). The total sum of the volume V _{p of the} particles is calculated.
The particle volume calculation unit 106 is realized, for example, when the CPU obtains a particle volume V _p contained in each cell 401 and stores it in a RAM or the like.

(Porosity calculation unit 107)
The void ratio calculation unit 107 calculates the “volume V _c of each cell 401” calculated by the cell volume calculation unit 105 and the “volume of particles contained in each cell 401 calculated by the particle volume calculation unit 106”. Based on the “total sum of V _p ”, the porosity of the particles is calculated for each of the plurality of cells 401 set by the cell setting unit 104.

  The porosity calculation unit 107 individually calculates the temporary porosity ε ′ [−] of the particles in each rectangular region by the following equation (9).

In Equation (9), n is the number of particle volumes V _p calculated by the particle volume calculation unit 106 as being included in the same cell 401. For example, in the example shown in FIG. 4, the number of the volume V _p of the particles calculated as being contained in the cell 401a is “2”, and the particles calculated as being contained in the cell 401b. the number of the volume V _p is "3", the number of the volume V _p of the calculated particles as contained in the cell 401c is "1".

Then, the porosity calculation unit 107 calculates a value obtained by adding a constant (= 0.02) to each of the calculated temporary porosity ε ′ of the particles in each rectangular region as the particle porosity ε in each rectangular region. . The reason for correcting the temporary void ratio ε ′ by adding a constant (= 0.02) will be described later.
The porosity calculation unit 107 is realized, for example, by the CPU obtaining the particle porosity ε in each cell 401 and storing it in a RAM, HDD, or the like.

(Fluid analysis unit 108)
The fluid analysis unit 108 uses the “particle porosity ε in each cell 401” calculated by the porosity calculation unit 107 to analyze the gas flow (fluid analysis) in the three-dimensional region where the particles are arranged. The result is displayed on the display. Since the method of fluid analysis is described in Non-Patent Document 1, for example, detailed description thereof is omitted here.
The fluid analysis unit 108 is realized, for example, when the CPU obtains a gas flow analysis result in a three-dimensional region where particles are arranged and outputs the data to a display.

(Reason for adopting length average diameter and reason for adjusting porosity)
In the present embodiment, the behavior of each particle in a two-dimensional region (two-dimensional calculation field) is calculated by DEM under the conditions having various particle size configurations shown below, and various average diameters are used from the calculation results. The porosity value was determined as described above, and the behavior of each particle in a three-dimensional region (three-dimensional calculation field) was calculated by DEM, and the porosity value was determined from each calculation result. As a result of comparing these porosity values, the method of setting the cell volume with the average particle diameter is three-dimensional even under conditions having various particle size configurations, as compared with the conventional method using a constant value. The value was close to the value, and it was found that any of the average diameters tried had sufficient accuracy for use in blast furnace gas flow analysis. Furthermore, among the various average diameters, it is preferable to adopt the length average diameter, and when adjusting the porosity value obtained using the length average diameter, a three-dimensional region (three-dimensional calculation field) It was found that a porosity very close to the value of the porosity determined in (1) was obtained. These are described in detail below.

  FIG. 6 is a diagram conceptually illustrating an example of each particle arranged in a calculation target region by performing an analysis by DEM. FIG. 6A is a diagram showing an arrangement of each particle obtained by analyzing the behavior of each particle in a two-dimensional region (two-dimensional calculation field). FIG. 6B is a diagram for comparison with FIG. 6A (this embodiment), and each particle obtained by analyzing the behavior of each particle in a three-dimensional region (three-dimensional calculation field). It is a figure which shows arrangement | positioning.

  As shown in FIG. 6A, when the behavior of each particle in the two-dimensional region is analyzed by DEM, the particles are not stacked in a direction (y-axis direction) orthogonal to the two-dimensional region (xz plane region). That is, spherical particles in which the center positions in the y-axis direction of the spherical field particles are all aligned are arranged on the xz plane. On the other hand, as shown in FIG. 6B, when the behavior of each particle in the three-dimensional region is analyzed by DEM, the spherical particles are arranged in the three-dimensional region (xyz space). They are also stacked in the y-axis direction.

FIG. 7 is a diagram showing a particle size configuration of each particle in each section A, B, and C shown in FIG. Specifically, FIG. 7A shows an area ratio of each particle in each section A, B, and C shown in FIG. 6A and each section in each of the sections A, B, and C shown in FIG. The volume ratio of the particles is shown. On the other hand, FIG. 7B shows the particle number ratio in each of the sections A, B, and C shown in FIGS. 6A and 6B.
In FIG. 6, in each of the sections A, B, and C, the particles are initially arranged so that they do not come into contact with each other, and the particles are gravity settled from above (in the direction of the arrow shown in FIG. 3), and the movement stops. The arrangement of each particle is shown. In FIG. 6, there is a gap between the particles for the convenience of description (in order to show that there is a void), but in reality, the particles are arranged more densely than in the state shown in FIG. Has been. As shown in FIG. 7, the particles dropped into the respective sections A, B, and C have three types of diameters (particle diameters) of 20.0 [mm], 37.5 [mm], and 55.0 [mm]. Particles.

  Here, the sections A, B, and C shown in FIG. 6A are two-dimensional areas, whereas the sections A, B, and C shown in FIG. 6B are three-dimensional areas. Therefore, in each of the sections A, B, and C, the ratios of these three types of particles are the sections A, B, and C shown in FIG. 6A and the sections A, B, and C shown in FIG. To be the same.

Specifically, as shown in FIG. 7A, the area ratio of each particle in each section A, B, C shown in FIG. 6A, and each section A shown in FIG. The volume ratio in B and C is made the same.
For example, as shown in FIG. 7 (a), “the total area of the particles having a particle diameter of 20.0 [mm]” in the section A shown in FIG. 6 (a) and the section B shown in FIG. 6 (a). The ratio of “total area of particles having a particle diameter of 20.0 [mm]” to “total area of particles having a particle diameter of 20.0 [mm]” in section C shown in FIG. Is “1: 1: 5”.
Therefore, as shown in FIG. 7 (b), “total volume of particles having a particle diameter of 20.0 [mm]” in section A shown in FIG. 6 (b) and section B shown in FIG. 6 (b). The ratio between the “total volume of particles having a particle diameter of 20.0 [mm]” and the “total volume of particles having a particle diameter of 20.0 [mm]” in the section C shown in FIG. Is “1: 1: 5”.

Further, the number ratio of each particle in each section A, B, C shown in FIG. 6B (particle number ratio) and the number ratio of each particle in each section A, B, C shown in FIG. The particle number ratio) is as shown in FIG.
For example, as shown in FIG. 7A, “the number of particles having a particle diameter of 20.0 [mm]” in the section A shown in FIG. 6A and “in the section B shown in FIG. The ratio between the “number of particles having a particle diameter of 20.0 [mm]” and the “number of particles having a particle diameter of 20.0 [mm]” in the section C shown in FIG. : 40 = 1: 1: 5 ”. On the other hand, “the number of particles having a particle diameter of 20.0 [mm]” in the section A shown in FIG. 6B and “the particle diameter of 20.0 [mm] in the section B shown in FIG. 6B”. The ratio between the “number of particles” and the “number of particles having a particle diameter of 20.0 [mm]” in the section C shown in FIG. 6B is also “21: 21: 105 = 1: 1: 5”. Become.

FIG. 8 is a diagram showing the porosity calculated by varying the calculation method of the average diameter of the particles contained in the rectangular region.
Each point shown in FIG. 8 indicates the void ratio of each rectangular region at the time when the particles stopped moving in the sections A, B, and C shown in FIG. 3 at the rate shown in FIG. Indicates the value of. In addition, six rectangular areas were set for each of the sections A, B, and C (this corresponds to the fact that there are six points in each of the sections A, B, and C in FIG. 8).

In FIG. 8, “3D” indicates the value of the porosity calculated from the result of analyzing the behavior of the particles in the three-dimensional region by DEM (see FIG. 3B). This value is the most reliable value.
The “fixed average diameter constant” indicates a porosity value calculated by fixing the length of the cell in the y-axis direction to 37.5 [mm] regardless of the rectangular area (the y-axis direction of the cell). The porosity is obtained by performing the same processing as in the present embodiment except that the length of the above is fixed (however, the porosity is calculated by the equation (9) and a constant is added. Absent)).

  In addition, “number average diameter”, “area average diameter”, “volume average diameter”, “average surface area diameter”, “average volume diameter” can be calculated using these average diameters instead of “length average diameter”. Indicates the value of the calculated porosity (except for the method of calculating the average diameter, the value of the porosity obtained by performing the same processing as in this embodiment (however, the porosity is calculated by the equation (9) And does not add a constant)).

The “length average diameter” is a void ratio (temporary void ratio ε ′ in equation (9)) before adding a constant.
Further, “length average diameter + 0.02” is a porosity obtained by performing the same processing as in the present embodiment.
The calculation method of “number average diameter”, “length average diameter”, “area average diameter”, “volume average diameter”, “average surface area diameter”, “average volume diameter” is described in Non-Patent Document 2. Has been. The “number average diameter”, “length average diameter”, “area average diameter”, and “volume average diameter” are “weighted number average diameter”, “weighted length average diameter”, and “weighted average diameter”, respectively. It may be referred to as “area average diameter” or “weighted volume average diameter”.

  As shown in FIG. 8, although there are differences in degree, “number average diameter”, “length average diameter”, “area average diameter”, “volume average diameter”, “average surface area diameter”, “average volume diameter” This graph is more similar to the “3D” graph than the “average diameter constant fixed” graph. In the sections A, B, and C, the composition ratios of the three types of particle diameters are extremely different (see FIG. 4). Therefore, in all the sections A, B, and C, if the shape and the value are close to the “3D” graph, the porosity is accurately calculated regardless of the condition of the particle diameter. You can say that you can. Therefore, it is understood that the porosity can be accurately calculated by calculating the average particle diameter for each rectangular region and determining the length of each cell in the y-axis direction based on the calculated average diameter.

In particular, the “average length diameter” graph is not only approximate but also close to the “3D” graph, indicating that it is particularly preferable. Therefore, in this embodiment, among these average diameters, the “length average diameter” is adopted.
In addition, the porosity calculated by adding a certain value to the porosity calculated using the “length average diameter” (“length average diameter” in FIG. 8), and the behavior of particles in a three-dimensional region were analyzed by DEM. In order to minimize the difference from the porosity value calculated from the result (“3D” in FIG. 8), the number of the constant values is calculated by the least square method. As a result, the fixed value was “0.02.” Therefore, in this example, if “0.02” is added as the constant value to the porosity value calculated using the “length average diameter”, the difference from the value of the “3D” graph is very large. A small porosity can be obtained. Therefore, in this embodiment, a value obtained by adding a constant value (= 0.02) to the void ratio (temporary void ratio ε ′) calculated using the “average length diameter” is adopted as the void ratio ε of each rectangular area. It was decided to.

  However, the result of analyzing the behavior of particles in the three-dimensional region by the DEM is the value of the porosity after adding or subtracting the constant value than the value of the porosity before adding or subtracting the constant value. If the difference from the value of the porosity calculated from the above is made small, it is not always necessary to calculate the constant value so that the difference from the value of the “3D” graph is minimized. In addition, the method used to calculate the constant value so that the difference from the value of the “3D” graph is minimized is not limited to the least square method.

  In addition, even with a porosity calculated using an average diameter other than the “length average diameter”, by adding or subtracting a constant value to the porosity, the value of the porosity obtained by adding or subtracting the constant value, Since the difference from the value of the “3D” graph can be reduced, this may be used. In particular, it is preferable to determine a constant value to be added to or subtracted from the value of the porosity so that the difference from the value of the “3D” graph is minimized. The calculation for obtaining a constant value that minimizes the difference from the value of the “3D” graph can be realized by using, for example, the least square method as described above.

(Operation flowchart)
Next, an example of processing of the particle presence field analysis apparatus 100 will be described with reference to the flowchart of FIG.
First, in step S901, the particle behavior analysis unit 101 analyzes the behavior of a spherical particle in a two-dimensional region using a DEM. Thereby, the arrangement | positioning of the particle | grains in a two-dimensional area | region is obtained for every predetermined time (refer Fig.3 (a)).
Next, in step S902, the rectangular area setting unit 102 sets a plurality of rectangular areas that divide the two-dimensional area in which the behavior of the particles is analyzed in step S901 (see FIG. 3).

Next, in step S903, the average particle diameter calculation unit 103 individually calculates the average length diameter of the spherical particles included in the rectangular area for each of the plurality of rectangular areas set in step S902.
Next, in step S904, the cell setting unit 104 sets each side of the “rectangular region” set in step S902 as an x-axis and z-axis direction side, and these x-axis and z-axis direction sides, and step S903. A parallelepiped determined by the side in the y-axis direction having a length of “the average length of the spherical particles included in the rectangular region” calculated in step 1, and the position of the center of the side in the y-axis direction is A plurality of parallelepipeds that are aligned respectively are set as cells 401 (see FIG. 4).

Next, in step S905, the cell volume calculation unit 105 calculates the volume of each cell set in step S904 (see equation (5)).
Next, in step S906, the particle volume calculation unit 106 executes an in-cell particle volume calculation process, and calculates the sum of the volume V _p of the particles contained in the cell 401 (equation (6) to (See equation (8)). Details of the in-cell particle volume calculation process will be described later with reference to FIG.

Next, in step S907, the void ratio calculation unit 107 calculates “volume V _c of each cell 401” calculated in step S905 and “calculation of particles contained in each cell 401 calculated in step S906”. Based on the volume V _p ”, the“ particle porosity ε ”in each of the plurality of cells 401 set in step S904 is calculated (the particle porosity ε is a constant equal to the temporary porosity ε ′ in the equation (9)). Is the value added).
Next, in step S908, the fluid analysis unit 108 uses the “particle porosity ε in each of the plurality of cells 401” calculated in step S907 to generate the gas in the three-dimensional region where the particles are arranged. Flow analysis (fluid analysis) is performed and the result is displayed on the display. And the process by the flowchart of FIG. 9 is complete | finished.

  Next, the in-cell particle volume calculation process in step S906 of FIG. 9 will be described in detail with reference to the flowchart of FIG. Note that the processing according to the flowchart of FIG. 10 is performed for all the cells set in step S904.

First, in step S <b> 1001, the particle volume calculation unit 106 selects one unselected particle among particles in which at least a partial region is included in the cell 401 to be calculated.
Next, in step S1002, the particle volume calculation unit 106 determines whether all the regions of the particles selected in step S1001 are included in the cell 401 to be calculated.

As a result of the determination, if all the regions of the particles selected in step S1001 are included in the cell 401 to be calculated, the process proceeds to step S1003.
In step S1003, the particle volume calculation unit 106 sets the total volume of the particles selected in step S1001 as the volume V _p of the particles contained in the cell 401 to be calculated according to equation (6). calculate.

On the other hand, if all the regions of the particles selected in step S1001 are not included in the cell 401 to be calculated, the process proceeds to step S1004.
In step S1004, the particle volume calculation unit 106 includes the volume of the region included in the cell 401 among the particle regions selected in step S1001 in the cell 401 to be calculated. The particle volume V _p is calculated by, for example, equation (7) or equation (8).

As described above, when the volume V _{p of the} particle contained in the cell 401 to be calculated is calculated for the particle selected in step S1001, the process proceeds to step S1005. In step S1005, the particle volume calculation unit 106 determines whether all the particles that include at least a part of the region in the cell 401 to be calculated have been selected. As a result of this determination, if all the particles that include at least a part of the region in the cell 401 to be calculated have not been selected, the process returns to step S1001. Steps are performed until the volume V _p of the particles included in the cell 401 to be calculated is calculated for all the particles in which at least a part of the region is included in the cell 401 to be calculated. The processes of S1001 to S1005 are repeated. Thereafter, the particle volume calculation unit 106 calculates the sum of the volume V _p of the particles contained in the cell 401 to be calculated.

(Summary)
As described above, in this embodiment, after analyzing the behavior of a spherical particle in a two-dimensional region by DEM, a plurality of rectangular regions that divide the two-dimensional region are set. For each of the plurality of rectangular regions, the length average diameter of the particles included in the rectangular region is individually calculated. Then, a plurality of cells 401 corresponding to the plurality of rectangular areas are set. This cell 401 is a parallelepiped that is defined by the x-axis and z-axis direction sides of the rectangular region and the y-axis direction side having the length of the length average diameter in the rectangular region. The position of the center of the side is set to a position that is aligned with the center position of the spherical particles whose positions in the y-axis direction are aligned. And the ratio of the particle | grains contained in each cell 401 is calculated | required, and the void ratio (epsilon) of the particle | grain in each rectangular area is calculated. Therefore, the porosity ε of a value close to the particle porosity ε obtained by calculating the particle behavior in the three-dimensional region can be calculated by the DEM without calculating the particle behavior in the three-dimensional region. Can do. For example, when the unloading from the top of the blast furnace to the tuyere is calculated by DEM in a three-dimensional calculation field, the calculation time is about two months, whereas when calculated by DEM in a two-dimensional calculation field, The time was about 5 days. In addition, the difference in the porosity ε in these was almost the same as the result shown in FIG. Therefore, even if the number of particles to be calculated increases, the porosity of the particles can be calculated at high speed without greatly reducing the calculation accuracy.

<Modification>
In the present embodiment, the fluid analysis is performed. However, if the particle porosity ε is calculated for each cell 401, the fluid analysis is not necessarily performed. Alternatively, the void ratio ε of the particles may be displayed on a display and presented to the user.

The embodiment of the present invention described above can be realized by a computer executing a program. Further, a means for supplying the program to the computer, for example, a computer-readable recording medium such as a CD-ROM recording such a program, or a transmission medium for transmitting such a program may be applied as an embodiment of the present invention. it can. A program product such as a computer-readable recording medium that records the program can also be applied as an embodiment of the present invention. The programs, computer-readable recording media, transmission media, and program products are included in the scope of the present invention.
In addition, the embodiments of the present invention described above are merely examples of implementation in carrying out the present invention, and the technical scope of the present invention should not be construed as being limited thereto. Is. That is, the present invention can be implemented in various forms without departing from the technical idea or the main features thereof.

DESCRIPTION OF SYMBOLS 100 Particle presence field analyzer 101 Particle behavior analysis part 102 Rectangular area | region setting part 103 Average particle diameter calculation part 104 Cell setting part 105 Cell volume calculation part 106 Particle volume calculation part 107 Porosity calculation part 108 Fluid analysis part 401 Cell 411-416 particle

Claims (11)

A particle behavior analysis means for analyzing the behavior of the particles in a two-dimensional region by using a discrete element method with a spherical shape of the particles;
Rectangular area setting means for setting a plurality of rectangular areas for dividing the two-dimensional area;
For each of the plurality of rectangular regions set by the rectangular region setting means, spherical particles in which all the regions are contained in the rectangular region, and spherical particles in which a part of the region is contained in the rectangular region Average particle diameter calculating means for calculating the average diameter of the spherical particles whose center position is included in the rectangular region, and
Cell setting means for setting a plurality of cells corresponding to the plurality of rectangular regions;
Cell volume calculating means for calculating the volume of each cell;
The volume of the particle that includes all the regions in the cell, and the volume of the region that is included in the cell among the regions of the particles that include a part of the region in the cell, Particle volume calculating means for calculating the sum of
Based on the volume of the cell calculated by the cell volume calculating means and the total volume calculated by the particle volume calculating means, the porosity of the particles is calculated for each of the cells. Calculating means,
The cell includes a first side that is a vertical side of the rectangular area, a second side that is a horizontal side of the rectangular area, and a side perpendicular to the first side and the second side. A parallelepiped defined by a third side having a length of an average diameter calculated by the average particle size calculation unit with respect to the rectangular region, and the third at the center of the third side. The particle presence field analyzer is characterized in that the position in the direction along the side of the particle is set to a position aligned with the center position of the particle in which the positions in the direction along the third side are aligned.   The average particle diameter calculating means calculates, for each of a plurality of rectangular areas set by the rectangular area setting means, a length average diameter of spherical particles contained in the rectangular area. The particle presence field analyzer described in 1.   3. The particle presence field analysis apparatus according to claim 1, further comprising porosity correction means for adding or subtracting a constant value to each of the particle porosity calculated by the porosity calculation means.   The particle presence field analysis apparatus according to any one of claims 1 to 3, further comprising fluid analysis means for performing fluid analysis in a three-dimensional region in which the particles exist using the porosity.   The particle presence field analyzer according to any one of claims 1 to 4, wherein the particles are particles charged into a blast furnace. A particle behavior analysis step of analyzing the behavior of the particles in a two-dimensional region by making the shape of the particles spherical, by a discrete element method,
A rectangular area setting step for setting a plurality of rectangular areas for dividing the two-dimensional area;
For each of a plurality of rectangular areas set by the rectangular area setting step, spherical particles in which all areas are included in the rectangular area, and spherical areas in which a part of the area is included in the rectangular area An average particle diameter calculating step for calculating an average diameter of the spherical particles whose center position is included in the rectangular region, and
A cell setting step for setting a plurality of cells corresponding to the plurality of rectangular regions;
A cell volume calculating step for calculating the volume of each of the cells;
The volume of the particle that includes all the regions in the cell, and the volume of the region that is included in the cell among the regions of the particles that include a part of the region in the cell, A particle volume calculation step for calculating the sum of
Based on the cell volume calculated by the cell volume calculating step and the total volume calculated by the particle volume calculating step, the porosity of the particles is calculated for each of the cells. A calculation step,
The cell includes a first side that is a vertical side of the rectangular area, a second side that is a horizontal side of the rectangular area, and a side perpendicular to the first side and the second side. A parallelepiped defined by a third side having a length of an average diameter calculated by the average particle size calculation step with respect to the rectangular region, and the third at the center of the third side. The particle presence field analysis method characterized in that the position in the direction along the side of the particle is set to a position aligned with the center position of the particle in which the positions in the direction along the third side are aligned.   The average particle diameter calculating step calculates a length average diameter of spherical particles included in the rectangular region for each of the plurality of rectangular regions set by the rectangular region setting step. 2. A particle presence field analysis method described in 1.   The particle presence field analysis method according to claim 6 or 7, further comprising a porosity correction step of adding or subtracting a constant value to each of the particle porosity calculated by the porosity calculation step.   9. The particle presence field analysis method according to claim 6, further comprising a fluid analysis step of performing fluid analysis in a three-dimensional region where the particles exist using the porosity.   The particle presence field analysis method according to any one of claims 6 to 9, wherein the particles are particles charged into a blast furnace.   A computer program for causing a computer to function as each means of the particle presence field analyzer according to any one of claims 1 to 5.

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