JP2009193110A - Solid-gas two-phase flow simulation program using grid-free method, storage medium with the program stored, and solid-gas two-phase flow simulation device - Google Patents

Abstract

<P>PROBLEM TO BE SOLVED: To provide a solid-gas two-phase flow simulation program using a grid-free method, a storage medium with the program stored, and a solid-gas two-phase flow simulation device, for precisely analyzing an analytic region without dividing it into calculation grids with a solid-gas two-phase flow in which particles coexist in an air flow as an object. <P>SOLUTION: This analytic method by the grid-free method includes: discretizing by a plurality of vortex elements, focusing attention on the vorticity field of a solid-gas two-phase flow in which micro-fine solid particles disperse in an air flow and flow while intereacting with the air flow; deriving a vorticity equation from a momentum conservation relation in consideration of the force of particles affecting the air flow; and calculating the behavior of vortex elements by the Lagrangian calculation of the vorticity equation, thus dispensing with division of the analytic region into calculation grids. <P>COPYRIGHT: (C)2009,JPO&INPIT

Description

  The present invention relates to a solid-gas two-phase flow simulation program using a grid-free method and a method for analyzing the behavior of a solid-gas two-phase flow in which minute solid particles are dispersed in an air flow and interact with each other. It relates to a storage medium storing it and a solid-gas two-phase flow simulation device.

  Solid-gas two-phase flow in which fine solid particles are dispersed in an air stream and interact with each other is observed in various industrial equipment such as pulverized coal combustion equipment, solid rocket engines, and sandblasting equipment. Therefore, the establishment of a rational numerical analysis method for the behavior of this solid-gas two-phase flow is desired.

  For numerical analysis of solid-gas two-phase flow, Euler-type methods such as the difference method and the finite volume method have been widely used. In these analyses, it is necessary to divide the analysis area into a number of grids (grids) as preprocessing. The grid covers the entire analysis area in a mesh and is called a calculation grid. The shape of each grid is generally rectangular. Flow variables (velocity, pressure, etc.) are defined at the vertices of each grid and calculated by the above solution. Fig. 1 (a) shows the liquid flow field (analysis region) around a cylinder when the cylinder is installed in a cylindrical container filled with liquid. Fig. 1 (b) shows an example of grid division. Since the analysis accuracy depends on the state of grid division, to ensure high accuracy, the region where the flow is expected to change sharply needs to be divided into many fine grids. It must also satisfy the geometric requirement that there should be no overlap or gaps between the grids. Therefore, in engineering practical simulations dealing with flow fields with complex geometric shapes, careful attention and a great deal of work were required for grid division, which caused the analysis to be complicated.

  In the conventional analysis method described above, velocity and pressure were used as flow variables, multiple partial differential equations governing them were analyzed, and flow variables were calculated at the top of the calculation grid. These partial differential equations can be replaced by algebraic equations by approximating the differential with a difference. However, since the nonlinear term has numerical instability, if the Reynolds number of the solid-gas two-phase flow is high, the calculation process There is a risk of divergence. In particular, solid-gas two-phase flows found in industrial equipment often have high Reynolds numbers, and there is a problem that high-precision analysis cannot be performed.

By the way, the vortex method has been used effectively for the analysis of single-phase flow with only gas or liquid. Here, the vortex method is a Lagrangian method for tracking the vortex elements with vorticity and obtaining the temporal change of the vorticity field. The vortex structure can be used to form and deform large-scale vortices without using a computational grid. It has the feature that the development process of can be calculated well. Non-Patent Documents 1 to 8 below disclose techniques for analyzing the behavior of solid-gas two-phase flow using this vortex method.
Chung, JN and Troutt, TR, Simulation of particle dispersion in an axisymmetric jet, J. Fluid Mech., 186 (1988), 199-222. Tomomi Uchiyama and two others, Numerical solution of solid-gas two-phase free turbulence by the vortex method (numerical model and application to two-dimensional mixed layer), Transactions of the Japan Society of Mechanical Engineers (B), 66-651 (2000), 2853-2860. Tomomi Uchiyama and Masaaki Naruse, Numerical analysis of solid-gas two-phase free turbulence by the Vortex in Cell method, Transactions of the Japan Society of Mechanical Engineers (B), Vol.69, No.686 (2003), 2200-2207. Tomomi Uchiyama and Akihito Fukase, Numerical analysis of a solid-gas two-axis circular jet by the three-dimensional vortex method, Transactions of the Japan Society of Mechanical Engineers (Part B), Volume 70, No. 696 (2004), 1957-1964. Tomomi Uchiyama and Yoshinobu Kitano, Numerical Analysis of Particle Jets Formed by Free-Falling Particles, Transactions of the Japan Society of Mechanical Engineers (Part B), 69, 684 (2003), 1737-1745. Uchiyama, T. and Yagami, H., Numerical Analysis of Gas-Particle Two-Phase Wake Flow by Vortex Method, Powder Technol., 149 (2005), 112-120. Uchiyama, T. and Fukase, A., Three-Dimensional Vortex Simulation of Particle-Laden Air Jet, Chem. Eng. Sci., 61 (2006), 1767-1778. Tomomi Uchiyama and Masaaki Naruse, Three-dimensional vortex analysis of particle jets formed by free-falling particles, Transactions of the Japan Society of Mechanical Engineers (B), 71 707 (2005), 1738-1745. JP 2004-126925 A JP 2006-85603 A JP 2007-308916 A JP 2007-286955 A JP 2007-286514 A JP 2007-17380 A JP 2006-259911 A JP 2006-77288 A JP 2000-214134 A JP-A-7-84992

  However, the technique described in Non-Patent Document 1 first calculates the airflow when there is no particle by the vortex method, and then calculates the motion of the particle placed in the airflow. The effect on the gas flow was ignored, and the behavior of solid-gas two-phase flow could not be analyzed accurately.

  The technologies described in Non-Patent Documents 2 and 3 relate to the simulation of solid-gas two-phase flow by the vortex method, which is the subject of this application. However, we use a method that divides the analysis area into calculation grids (grids) when calculating the effect of particles on the airflow. Therefore, the method that does not use the calculation grid (grid-free method) targeted by this application has not been introduced. The grid-free methods of this application are completely different from the equations and algorithms described in Non-Patent Documents 2 and 3 above, so these methods cannot be applied.

  The technique described in Non-Patent Document 4 is an extension of the technique described in Non-Patent Document 2 for three-dimensional analysis. Similar to the technique of Non-Patent Document 2, the analysis region is a calculation grid (grid). The method of dividing into two is used. Therefore, the method that does not use the calculation grid (grid-free method) targeted by this application has not been introduced. In addition, since the grid-free method of this application is completely different from the equations and algorithms described in Non-Patent Document 4, these methods cannot be applied.

  The non-patent documents 5 to 8 describe the analysis results when various solid-gas two-phase flows are analyzed using the simulation technique described in any of the non-patent documents 2 to 4. Therefore, it is not related to the grid-free method of this application.

The technique of Patent Document 1 analyzes fluid flow using the vortex method, but analyzes single-phase flow such as water or air. Phase flow cannot be analyzed.
The technique of Patent Document 2 relates to an analysis method by a vortex method for a bubble flow in which bubbles dispersed in a liquid interact and interact with each other. Not applicable to.

  Patent Documents 3 to 10 disclose techniques for analyzing the motion of solid particles from their governing equations by calculation, but all use a grid-free technique that does not use the calculation grid that is the subject of this application. It is not a solution based on the vortex method, nor is it related to particles moving in an air stream.

In other words, the technology of Patent Document 3 is intended to simulate the movement phenomenon caused by beach currents for the sand and sand thrown into the seabed, and is not related to the air flow containing solid particles, that is, the solid-gas two-phase flow.
The technique of Patent Document 4 relates to the behavioral simulation of particles in a container, but is not a solution based on the vortex method.

The technology of Patent Document 5 provides a particle behavior simulation apparatus, a particle behavior simulation method, and a computer program by the discrete particle method, and is related to calculation of collision and contact between particles. Not targeted.
The technique of Patent Document 6 relates to a simulation for collision between particles when a large number of particles exist, and does not cover fluid calculation.

The technique of Patent Document 7 relates to an analysis method and a computer program that consider the influence between particles using the discrete element method, and is not treated as a solid-gas two-phase flow.
The technique of Patent Document 8 provides a method for predicting the combustion phenomenon in consideration of the collision and growth phenomenon of concentrate particles in the flash furnace, and omits the gas flow.

The technique of Patent Document 9 is a simulation based on the amount of static electricity generated by the mixing and agitation operation using the agitation member in the container containing the granular material, not the simulation relating to the flow.
The technique of Patent Document 10 relates to the prediction of particle behavior in a rotating mixing vessel, analyzes the motion due to collision between particles, and does not deal with particle behavior due to fluid motion.

  The present invention has been completed based on the above-described circumstances, and is intended for a solid-gas two-phase flow in which particles are mixed in an air current, and without being divided into calculation grids (grids) with high accuracy. The purpose is to provide a solid-gas two-phase flow simulation program using a grid-free method, a storage medium storing it, and a solid-gas two-phase flow simulation device.

As a means for achieving the above object, a solid-gas two-phase flow simulation program using a grid-free method relating to the invention of claim 1 is used to analyze a solid-gas two-phase flow including minute solid particles in an air flow. This is a solid-gas two-phase flow simulation program for causing a computer to execute the following steps (a) to (i) and analyzing the behavior of the solid-gas two-phase flow.
(A) calculating a velocity of each particle existing in the analysis region in a Lagrangian manner.
(B) A step of calculating the position of each particle in a Lagrangian manner.
(C) placing four square cells around each particle;
(D) calculating a fluid drag acting on each particle based on the velocity calculated in the step (a).
(E) Based on the fluid drag calculated in step (d), the amount of change in circulation in each cell is calculated based on the vorticity equation derived from the momentum conservation equation of airflow and the Reynolds transport theorem. Step to do.
(F) Based on the circulation change amount in each cell calculated in the step (e), the circulation of each vortex element in the cell is calculated, and the position and circulation of each vortex element are stored in the storage means (1). Saving step.
(G) A step of calculating the core radius of each vortex element in a Lagrangian manner and storing it in the storage means (2).
(H) The position, circulation and core radius data of each vortex element stored in the step (f) and the step (g) are read, and the advection, that is, the position of each vortex element is calculated in a Lagrangian manner. Storing the position, circulation and core radius of the memory in the storage means (3).
(I) The position, circulation and core radius data of each vortex element stored in the step (h) is read out, the gas velocity at the evaluation point is calculated using the Biosavart equation, and stored in the storage means (4) Saving step.

  The invention of claim 2 is a storage medium storing a solid-gas two-phase flow simulation program using the grid-free method of claim 1. As the storage medium, floppy (registered trademark) disk, CD-ROM, etc. are suitable.

A solid-gas two-phase flow simulation apparatus according to claim 3 is a solid-gas two-phase flow simulation apparatus using a grid-free method for analyzing a solid-gas two-phase flow including minute solid particles in an air flow, The following means (a) to (i) are provided, and these means are executed to analyze the behavior of the solid-gas two-phase flow.
(A) A means for calculating the velocity of each particle existing in the analysis region in a Lagrangian manner.
(B) Means for calculating the position of each particle in a Lagrangian manner.
(C) means for arranging four square cells around each particle;
(D) Means for calculating the fluid drag acting on each particle based on the velocity calculated by the means (a).
(E) Based on the fluid drag calculated by the means (d), the amount of change in circulation in each cell is calculated based on the vorticity equation derived from the momentum conservation equation of airflow and the Reynolds transport theorem. Means to do.
(F) Based on the circulation change amount in each cell calculated by the means (e), the circulation of each vortex element in the cell is calculated, and the position and circulation of each vortex element are stored in the storage means (1). Means for storage.
(G) Means for calculating the core radius of each vortex element in a Lagrangian manner and storing it in the storage means (2).
(H) The position, circulation and core radius data of each vortex element stored by the means (f) and the means (g) are read out, and the advection, that is, the position of each vortex element is calculated in a Lagrangian manner. Means for storing the position, circulation and core radius of the memory in the storage means (3).
(I) The position, circulation and core radius data of each vortex element stored by the means (h) is read out, the gas velocity at the evaluation point is calculated using the Biosavart equation, and stored in the storage means (4) Means for storage.

The present invention focuses on the vorticity field of a solid-gas two-phase flow in which minute solid particles are dispersed in an air flow and interact with each other, and are discretized by a plurality of vortex elements, and The vorticity equation is derived from the momentum conservation relation considering the force, and the behavior of the vortex element is obtained by Lagrange calculation of this vorticity equation.
This is an analysis method that does not require the analysis area to be divided into grids. Since the size and arrangement of the grid influence the analysis accuracy, careful attention and a great deal of work are required for grid division. Therefore, this grid-free method, which can omit the grid division work, is extremely useful for analysis of flow fields with complicated geometric shapes such as in industrial equipment.

  In addition, since the nonlinear term does not appear in the Lagrangian calculation of the vorticity transport equation, it is possible to perform a stable and highly accurate analysis of a solid-phase two-phase flow with a high Reynolds number without depending on the Reynolds number. In addition, the high vorticity region has the feature that vortex elements are actively concentrated, so that high analysis accuracy can be automatically secured.

  Furthermore, when calculating the vorticity, it is desirable to apply a core spreading method that increases the core radius of the vortex element over time. In this way, the attenuation of vorticity due to viscous diffusion is taken into account, and an appropriate vorticity can be obtained.

<Theory>
The following theory of the present invention will be described.
1. Symbols In the present invention, the following symbols are defined as follows.
A: Area per cell installed around the particle
C _D : Particle resistance coefficient
d: Particle diameter
F _D : Force that a unit volume of gas receives from particles
f _D : Fluid drag acting on particles
g: Gravity acceleration
L: Length of one side of the square cell
N _v : Number of vortex elements in the analysis region
p: Pressure
t: time
u: Speed
v _p : Relative velocity of particles relative to gas = u _p -u _g
x, y: spatial coordinates
Γ: Circulation
ν: Kinematic viscosity of gas
ρ: Density
σ: Core radius of vortex element
ω: Vorticity = ∇ x u _g
Subscript
g: Gas
p: Particle

2. Assumptions The present invention assumes the following assumptions.
(A) The gas is incompressible.
(B) The density of particles is sufficiently larger than that of gas.
(C) The particles are spherical and have a uniform diameter.
(D) The impact of interparticle collisions on the entire flow field is small and can be ignored.

3. Basic Expression In the present invention, conditions necessary for the calculation are set based on predetermined setting data (input data described later), and the calculation is executed based on the basic equation of flow. The basic flow equations used in the calculation are explained below.

(1) Gas governing equation The gas mass and momentum conservation equations are expressed by the following equations, assuming the above assumptions (a) to (d).

ここで，mは粒子の質量であり，流体抗力f_Dは次式で与えられる．

ただし，dは粒子直径であり，抗力係数C_Dは次式で定められる．

ここで，Re_p=d|u_g-u_p|/νである． (2) The governing equation of particles The prevailing forces acting on the particles are the fluid drag and gravity, assuming the above assumptions (a) to (d), and are given by the following equation.

Where m is the mass of the particle and the fluid drag f _D is given by

Where d is the particle diameter and drag coefficient _CD is determined by the following equation.

Here, Re _p = d | u _g -u _p | / ν.

一方，任意の位置xにおける気体の速度は次のビオサバールの式により求められる．

ここで，u_g0は一様流またはポテンシャル流れの速度を表す． (3) Discretization of the vorticity field by the vortex element If the analysis target is a two-dimensional flow field, the vorticity equation of the gas is obtained by substituting the above equation 1 by rotating the equation 2 above. expressed.

On the other hand, the velocity of the gas at an arbitrary position x can be obtained by the following biosavart equation.

Here, u _g0 represents the velocity of uniform flow or potential flow.

ここで，コア関数fは次式で与えられる．

Next, the vorticity field is discretized by many vortex elements. A vortex element model for single-phase flow analysis is applied and a vortex element with a core structure is introduced. If the circulation of the vortex element α is Γ _α , the core radius is σ _{α and the} position vector is x ^α _, the vorticity of the position x by the vortex element α is given by

Here, the core function f is given by the following equation.

ここで，kは渦度ベクトルと同一方向の単位ベクトルであり，関数gは次式で与えられる．

If the vorticity field is discretized with N _v vortex elements, the velocity of the gas can be expressed by the following equation obtained from Equation 7 and Equation 8 above.

Here, k is a unit vector in the same direction as the vorticity vector, and the function g is given by

Moreover, since the vortex element is advected at the air velocity, it can be calculated from the following Lagrangian analysis.

なお，Core spreading法は，Leonard, A., Vortex methods for flow simulation, J. Comput. Phys., 37(1980), 289-335. に記載されている． (4) Change in core radius due to viscous diffusion Vorticity is attenuated by viscous diffusion. Here, in the single-phase flow analysis with only liquid or gas, it is considered by the core spreading method that increases the core radius with time. Therefore, in the present invention, this is applied mutatis mutandis, and the time change of the core radius is obtained by Lagrangian analysis of the following equation.

The Core spreading method is described in Leonard, A., Vortex methods for flow simulation, J. Comput. Phys., 37 (1980), 289-335.

上記数式１４にレイノルズの輸送定理を適用したのち，上記数式１と上記数式２を代入し，変形すれば次式を得る．

ここで，drは線素ベクトルである．また，粘性拡散項は，上記数式１３で考慮されているので，代入に際し無視している． (5) Change in circulation due to particle motion The time change rate of the circulation Γ around an arbitrary closed curve is expressed by the following equation.

After applying Reynolds' transport theorem to the above formula 14, substituting the above formula 1 and the above formula 2, we can obtain the following formula.

Where dr is a line element vector. In addition, the viscous diffusion term is taken into account in the above equation 13, so it is ignored in the substitution.

ここで，Δzはx-y平面に垂直方向（図２で紙面奥行方向）に粒子が等間隔で分布するもと仮定したときの分布間隔である．
セル頂点７の間でF_Dが線形変化するものと仮定し，４つのセル１，２，３，４に上記数式１５を適用すれば，セル１，２，３，４の循環変化ΔΓ₁，ΔΓ₂，ΔΓ₃，ΔΓ₄は次式で表される．

(6) Calculation method of circulation change due to particle motion As shown in FIG. 2, four square cells 6 are provided around the particle P. Cell 6 can be easily placed if the position of the particle is known. Therefore, the work required for the placement is significantly easier than the conventional technology that divides the analysis area into a large number of grids. In particular, a special effect appears when an analysis region having a complicated geometric shape is targeted. Cell 6 is along the coordinate axes x and y, and the length of one side is L. If the relative velocity of the particle with respect to the gas G is v _p (= u _p -u _g ), the fluid drag f _D acts in the -v _p direction. Let θ be the angle that f _D makes with the x-axis. In this case, the x-direction component F _Dx and y-direction components F _Dy of F _D acting on the cell vertex O to position particles P, are respectively given by the following equation.

Here, Δz is the distribution interval when the particles are assumed to be distributed at regular intervals in the direction perpendicular to the xy plane (the depth direction in FIG. 2).
Assuming that F _D between the cell vertices 7 is linearly changed, by applying the above equation 15 into four cells 1, 2, 3, 4, circulatory changes [Delta] [gamma] ₁ of the cell 1, 2, 3, 4, ΔΓ ₂ , ΔΓ ₃ , and ΔΓ ₄ are expressed by the following equations.

When n _v vortex elements exist in the cell β (β = 1, 2, 3, 4) for four cells installed around each particle P, the circulation per vortex element is expressed as ΔΓ. Let _β / n _v . When there is no vortex element, one vortex element with circulation ΔΓ _β is generated from the cell center.

  Let us consider a case where a new vortex element 5 is generated from four cells 6 one by one by particle motion. When θ = 90 °, as shown in FIG. 3A, the arrangement of the vortex elements 5 is symmetrical with respect to the moving direction of the particles P with respect to the airflow. Furthermore, as can be seen from Equation 17, the absolute value of the circulation is also symmetric. The airflow around the particle P induced by the four vortex elements 5 is calculated as shown in FIG. 3B, and the airflow is also symmetrical with respect to the direction of particle motion. Since the particles are spherical and the shape is axisymmetric with respect to the direction of travel, the flow resulting from the motion must be line-symmetric or symmetric about the axis in the case of two-dimensional analysis. Therefore, a reasonable velocity field is required in Fig. 3 (b). Similar airflow velocities are obtained when θ = 0 °, 180 °, and 270 °.

  On the other hand, when the value of θ is not 0 °, 90 °, 180 °, or 270 °, the arrangement of the vortex elements 5 and the absolute value of circulation are not symmetric with respect to the particle traveling direction as shown in FIG. For example, when the airflow when θ = 65 ° is obtained, an asymmetric velocity distribution is obtained as shown in FIG. 4B, and an appropriate result cannot be obtained.

Therefore, as shown in FIG. 5, to place the four cells 6 so that the vector from the particle location (cell vertex O) in the cell vertex N coincides with always f _D. Since this cell arrangement corresponds to the arrangement in Fig. 3 (a), a symmetrical airflow around the particle can be accurately calculated [see Fig. 3 (b)].

(7) Analysis procedure If the flow of particles and gas at time t = t is known, the flow at time t = t + Δt can be calculated by the following procedure, for example. In addition, as shown in FIG. 6, the vortex element 5 and the particle P exist in the analysis region H, and the evaluation point 8 for calculating the gas velocity is arranged in advance.
(A) The motion of the particle P is obtained from Equation 3.
(B) Four square cells 6 are installed around the particle P, and the circulation variation amounts ΔΓ _{1 to} ΔΓ ₄ in each cell 6 are obtained as θ = 90 ° in Equation 17.
(C) The circulation variation amounts ΔΓ _{1 to} ΔΓ ₄ in each cell 6 are given to the circulation of the vortex element in the cell 6. If there is no vortex element in the cell, one vortex element with circulation equal to the circulation variation is generated from the center of the cell.
(D) The core radius σ of the vortex element 5 is obtained from Equation 13.
(E) The position of the vortex element 5 is obtained from Equation 12.
(F) determining the velocity u _g of the airflow at the evaluation point 8 from Equation 10.

  By repeating this procedure at predetermined time intervals, it is possible to analyze solid-gas two-phase flow with high accuracy without using a grid (grid-free).

  Hereinafter, an embodiment of the present invention will be described with reference to the above-described theory and FIGS.

  A solid-gas two-phase flow simulation program using the grid-free method according to the present embodiment is recorded in an information storage device 16 to be described later and introduced into a personal computer (hereinafter referred to as “computer 11”). This is to execute the analysis step of the behavior of solid-gas two-phase flow described later.

1. Configuration of Computer and its Peripheral Equipment Figure 7 shows the configuration of the computer 11 and its peripheral equipment. The computer 11 includes a central processing unit 12 for performing arithmetic operations and controlling peripheral devices, an I / O interface 13 for connecting the central processing unit 12 and peripheral devices, and a display device 14 which is a peripheral device. , A printing device 15, an information storage device 16, and an input device 17 are connected.

  In addition to the cathode ray tube (CRT), the display device 14 includes a liquid crystal device, a liquid crystal projector, and the like. The printing device 15 does not need to be directly connected to the computer 11 but may be connected via a network such as a LAN. The input device 17 is a console such as a keyboard or a mouse, for example, and can input coordinate position data for setting the boundary of the analysis region H, input data for setting fluid characteristics, and the like by operation here.

  Although details of the central processing unit 12 are not shown, the central processing unit 12 includes a ROM, various RAMs, a chip set, and the like in addition to a central processing unit (CPU). The information storage device 6 is a hard disk, floppy (registered trademark) disk, MO, CD-ROM, or the like, and can read or record programs and various data of the computer 1.

2. Analysis of Solid-Gas Two-Phase Flow Now, the operation of this embodiment will be described with reference to a flowchart of a solid-gas two-phase flow simulation program executed by the central processing unit 12.

(1) Input of input data necessary for calculation and setting of boundary condition First, input data necessary for calculation is input by operating the input device 17. Here, as input data, the density ρ _g and kinematic viscosity ν _g of the gas G, the density ρ _p and diameter d of the solid particles P, the number of inflows of particles P per unit time at the entrance of the analysis region H, the analysis region H Geometric shape and dimensions, analysis time, analysis time timing Δt.

(1) Condition setting In this embodiment, it is a numerical analysis with respect to the air flow (solid-gas two-phase flow) containing the particle P in the free space not surrounded by the wall surface. More specifically, as shown in FIG. 8, the particles P fall into still air, the falling particles induce a flow of gas G (air flow) around them, and the particles P and the gas G interact with each other. The analysis target is a solid-gas two-phase flow flowing together.

(2) Analysis processing After setting the above conditions, the computer 11 repeatedly executes the processing of the flowchart shown in FIG. 9 at the above analysis time timing Δt, and numerically analyzes the behavior of the solid-gas two-phase flow.

To determine what happened to the analysis time timing in step S1, when it is analysis time timing ( "Y" in step S1), the velocity u _p of the particles P in step S2, is calculated from Equation 3. That is, a process corresponding to “calculate the velocity of each particle existing in the analysis region in a Lagrangian manner” in “step (a)” and “means (a)” described in the claims of the present invention is executed. More specifically, Euler's forward difference method is applied to Equation 3, and each particle P in the analysis region H is tracked by Lagrangian analysis. In this case, although the f _D of Equation 3 is given by Equation 4, the velocity of the gas G and the particles P of the right side of Equation 4 is to use a rate calculated in the previous analysis time timing. Note that the velocity of the gas G is determined by interpolation of the velocity at the evaluation point 8 arranged in advance in the analysis region H. For interpolation, select the neighboring point 8 of the position to be evaluated and use the interpolation method.

In step S3, the position of the particle P is calculated by the Lagrangian method based on the velocity _p of the particle P calculated in step S2. That is, a process corresponding to “calculate the position of each particle in a Lagrangian manner” in “step (b)” and “means (b)” described in the claims of the present invention is executed. More specifically, if the velocity is known, the position can be obtained by integration over time, so it is calculated by Euler's forward difference method as in the case of the particle velocity.

In step S4, four square cells 6 are arranged around each particle. That is, processing corresponding to “place four square cells around each particle” in “step (c)” and “means (c)” described in the claims of the present invention is executed. Vector More specifically, the relative velocity v _p of the particles _P (= u _p -u _g) was calculated to gas G, as shown in FIG. 5, directed from the particle location (cell vertex O) to the cell vertex N Place cell 6 so that matches with v _p .

In step S5, the fluid drag force f _D acting on each particle is calculated from Equation 4 using the velocity u _{g of the} gas G calculated at the previous analysis time timing and the velocity u _p of the particle P calculated in step S1. calculate. That is, the “fluid drag acting on each particle” in “step (d)” and “means (d)” described in the claims of the present invention is set to the speed calculated in step (a) or means (a). The process corresponding to “Calculate based on” is executed. Incidentally, the speed u _g of the gas G is to be determined from the interpolation of the speed of advance arrangement the evaluation points in the analysis region H.

In step S6, the circulating amount of change ΔΓ ₁ ~ΔΓ ₄ in four cells around each particle, based on the fluid drag force acting on each particle calculated in step S5, calculated from Equation 17. That is, based on the fluid drag calculated in “step (d)” or “means (d)” in “step (e)” and “means (e)” described in the claims of the present invention, the circulation in each cell The process corresponding to "Calculate the amount of change based on the vorticity equation derived from the momentum conservation equation of airflow and the Reynolds transport theorem" is executed. In addition, from the arrangement of the cells in step S4, the calculation is performed with θ = 90 ° in Equation 17.

In step S7, based on the circulation variation data of each cell calculated in step S6, the circulation of the vortex element existing in each cell is calculated, and the position and circulation of each vortex element are determined by, for example, the information recording device. The data is stored in 16 predetermined storage areas or a predetermined area of RAM. That is, the cyclic change data in each cell stored by “step (e)” or “means (e)” in “step (f)” and “means (f)” described in the claims of the present invention is read out. , Calculate the circulation of each vortex element in the cell, and execute the process corresponding to “save the position and circulation of each vortex element in the storage means (1)”. Specifically, if there are n _v vortex elements in a cell with a circulation change of ΔΓ, the change of circulation of each vortex element is ΔΓ / n _v . If there is no vortex element, a new vortex element with circulation ΔΓ is generated.

  In step S8, the core radius σ of the time-varying vortex element is calculated from Equation 13, and stored in, for example, a predetermined storage area of the information recording device 16 or a predetermined area of the RAM. That is, it corresponds to “the core radius of each vortex element is calculated in a Lagrangian manner and stored in the storage means (2)” in “step (g)” and “means (g)” recited in the claims of the present invention. Execute the process. Euler's forward difference method can be applied to this Lagrangian calculation.

  In step S9, the advection of the vortex element 5 is calculated from Equation 12, and stored in, for example, a predetermined storage area of the information recording device 16 or a predetermined area of the RAM. That is, the vortex stored by “step (f) and step (g)” or “means (f) and means (g)” in “step (h)” and “means (h)” described in the claims of the present invention. Processing corresponding to “reading element position, circulation and core radius data, calculating advection, ie position, of each vortex element in a Lagrangian manner, and storing the position, circulation and core radius of each vortex element in storage means (3)” Execute More specifically, the position of the vortex element 16 in the analysis region H is tracked by analyzing Formula 12 by the Euler forward difference method as in the case of the motion calculation of the particle P.

  In step S10, the position, circulation and core radius of the vortex element calculated in steps S7 to S9 are substituted into Equation 10, and the velocity of the gas G at the evaluation point preset in the analysis region is calculated. Store in 16 predetermined storage areas or in a predetermined area of RAM. That is, the position, circulation, and core radius data of each vortex element stored by “step (h) or means (h)” in “step (i)” and “means (i)” described in the claims of the present invention , And the gas velocity at the evaluation point is calculated using the Biosavart equation, and the process corresponding to “save in the storage means (4)” is executed. If the analysis is continued in step 12 (“Y” in step S12), the process returns to step S1.

By repeatedly executing the above steps, the flow of particles P and gas G, that is, the time change of the solid-gas two-phase flow can be simulated. When the above calculation is completed, the computer 11 delivers the analysis data to, for example, the display device 14 or the printing device 15. The analysis data are the speeds u _p and u _g of the particle P and gas G, the position coordinates of the particle P and the vortex element 5, and can be displayed in vector or contour by using generally available visualization software.

  FIG. 10 shows an example of the calculation result, which shows the behavior of particles, vortex elements and air currents generated when the particles P freely fall in the air. Based on the analysis data, the particles P and vortex elements 6. The velocity vector of the airflow is displayed.

3. Advantages of this embodiment The methods used in the past for analysis of solid-gas two-phase flows, without exception, need to divide the analysis region into calculation grids (grids) as preprocessing of the analysis. The grid covers the entire analysis area in a mesh and is called a calculation grid. The shape of each grid is generally rectangular. Flow variables (velocity, pressure, etc.) are defined at the vertices of each grid and calculated by the above solution. Since the analysis accuracy depends on the state of grid division, to ensure high accuracy, the region where the flow is expected to change sharply needs to be divided into many fine grids. It must also satisfy the geometric requirement that there should be no overlap or gaps between the grids. Therefore, in practical simulations used in the design of industrial equipment, flow fields with complex geometries are often the subject of analysis, and a great deal of work has been required for grid division. In the solid-gas two-phase flow analysis method according to this embodiment, it is not necessary to divide the analysis region into calculation grids. This grid-free technology greatly simplifies the preprocessing of analysis and brings about rationalization of practical simulation.

In the analysis method according to this embodiment, it is not necessary to approximate the differential term of the governing equation by difference. For this reason, the conventional analysis method can be applied to the analysis of high Reynolds number flows where the calculation fails due to numerical instability.
In addition, since the vortex element actively advects to the region with high vorticity, high analysis accuracy can be secured.

Furthermore, in the conventional analysis method in which the velocity and pressure of the fluid are unknown variables, the use of the turbulent flow model was indispensable. However, in the analysis method of this embodiment, the solid-gas two-phase flow is not used without using the turbulent flow model. Can be analyzed.
<Other embodiments>
The present invention is not limited to the embodiments described with reference to the above description and drawings. For example, the following embodiments are also included in the technical scope of the present invention, and are within the scope not departing from the gist other than the following. Various changes can be made with.
(1) In the above embodiment, the example in which the two-dimensional analysis is performed on the analysis region H has been described. However, the present invention can also be applied to the three-dimensional analysis.

  (2) In the above-described embodiment, the particles P are spherical. However, the present invention is not limited to this, and may be, for example, an elliptical sphere from the viewpoint of achieving high functionality. In this case, for example, the input device 17 may select a plurality of types of shapes for the particles P, and the calculation may be performed for the plurality of types of particles.

Diagram for explaining analysis area and calculation grid in fluid analysis The figure for demonstrating the cell installed around the particle | grains of this invention The figure when the cell of this invention is installed appropriately, and the figure for explaining the gas velocity which is obtained The figure when the cell of this invention is installed improperly and the figure for explaining the gas velocity which is obtained The figure for demonstrating arrangement | positioning of the cell installed around the particle | grains of this invention The figure for demonstrating the vortex element of this invention, a solid particle, and a gas velocity evaluation point The figure which shows the computer and peripheral device in which the solid-gas two-phase flow simulation program which concerns on one Embodiment of this invention is introduce | transduced The figure for demonstrating the solid-gas two-phase flow which calculation of this invention makes object Flow chart showing processing contents by computer The figure which shows the analysis result by this embodiment

Explanation of symbols

DESCRIPTION OF SYMBOLS 5 ... Vortex element 6 ... Cell 7 ... Cell vertex 8 ... Evaluation point of gas velocity 11 ... Computer 12 ... Central processing part 16 ... Information recording device (storage means)
G ... Gas H ... Analysis area P ... Solid particles

Claims (3)

A solid-gas two-phase flow simulation program using a grid-free method for analyzing a solid-gas two-phase flow including minute solid particles in an air current, and the computer performs the following steps (a) to (i) This is a solid-gas two-phase flow simulation program that analyzes the position and velocity of particles in the analysis region and the velocity of airflow at the evaluation points set in advance in the analysis region.
(A) calculating a velocity of each particle existing in the analysis region in a Lagrangian manner.
(B) A step of calculating the position of each particle in a Lagrangian manner.
(C) placing four square cells around each particle;
(D) calculating a fluid drag acting on each particle based on the velocity calculated in the step (a).
(E) Based on the fluid drag calculated in step (d), the amount of change in circulation in each cell is calculated based on the vorticity equation derived from the momentum conservation equation of airflow and the Reynolds transport theorem. Step to do.
(F) Based on the circulation change amount in each cell calculated in the step (e), the circulation of each vortex element in the cell is calculated, and the position and circulation of each vortex element are stored in the storage means (1). Saving step.
(G) A step of calculating the core radius of each vortex element in a Lagrangian manner and storing it in the storage means (2).
(H) The position, circulation and core radius data of each vortex element stored in the step (f) and the step (g) are read, and the advection, that is, the position of each vortex element is calculated in a Lagrangian manner. Storing the position, circulation and core radius of the memory in the storage means (3).
(I) The position, circulation and core radius data of each vortex element stored in the step (h) is read out, the gas velocity at the evaluation point is calculated using the Biosavart equation, and stored in the storage means (4) Saving step. A storage medium storing a solid-gas two-phase flow simulation program using the grid-free method according to claim 1. A solid-gas two-phase flow simulation apparatus for analyzing a solid-gas two-phase flow containing minute solid particles in an air flow, comprising the following means (a) to (i), and executing these means: , A solid-gas two-phase flow simulation device that analyzes the position and velocity of particles in the analysis region, and the velocity of the airflow at the evaluation points set in advance in the analysis region.
(A) A means for calculating the velocity of each particle existing in the analysis region in a Lagrangian manner.
(B) Means for calculating the position of each particle in a Lagrangian manner.
(C) means for arranging four square cells around each particle;
(D) Means for calculating the fluid drag acting on each particle based on the velocity calculated by the means (a).
(E) Based on the fluid drag calculated by the means (d), the amount of change in circulation in each cell is calculated based on the vorticity equation derived from the momentum conservation equation of airflow and the Reynolds transport theorem. Means to do.
(F) Based on the circulation change amount in each cell calculated by the means (e), the circulation of each vortex element in the cell is calculated, and the position and circulation of each vortex element are stored in the storage means (1). Means for storage.
(G) Means for calculating the core radius of each vortex element in a Lagrangian manner and storing it in the storage means (2).
(H) The position, circulation and core radius data of each vortex element stored by the means (f) and the means (g) are read out, and the advection, that is, the position of each vortex element is calculated in a Lagrangian manner. Means for storing the position, circulation and core radius of the memory in the storage means (3).
(I) The position, circulation and core radius data of each vortex element stored by the means (h) is read out, the gas velocity at the evaluation point is calculated using the Biosavart equation, and stored in the storage means (4) Means for storage.

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