JP2010108183A - Simulation method and simulation device - Google Patents

Abstract

<P>PROBLEM TO BE SOLVED: To provide a simulation method and a simulation device for simulating behaviors of particles of a large-scale system in a practical time including the flocculation of particles. <P>SOLUTION: The simulation method is provided for analyzing behavior of a plurality of particles by applying arithmetic processing, based on a discrete element method using a computer, to data to be analyzed showing the state of solid-liquid mixed phase including a plurality of particles in a liquid phase and a solid phase. The method includes a coarse graining model generation step for modeling a group configured of several particles as coarse graining particles whose particle diameters are larger than the particle diameters of the pertinent particles, and for performing coarse graining in which a predetermined force acting depending on the size of the particle diameter in the solid/liquid mixed phase is equalized between the coarse graining particles and the plurality of particles configuring the coarse graining particles, to the data to be analyzed. The predetermined force includes a van der Walls force. Arithmetic processing based on the discrete element method is applied to the coarse graining model data obtained by the coarse graining model generation step. <P>COPYRIGHT: (C)2010,JPO&INPIT

Description

  The present invention relates to a simulation method and a simulation apparatus.

  Research on solid-liquid mixed-phase flows ranges from natural phenomena such as debris flow, sand flow, and drift sand to stirring tanks, solid-liquid separation devices, and glass melting furnaces (see Patent Document 1) in mechanical and chemical engineering. In elucidating the internal mechanism of solid-liquid mixed phase flow, if the concentration of the solid phase increases, the measurement of the concentration and the distance traveled by the constituent particles may not be easy and the experimental approach may be difficult. It is expected (see, for example, Non-Patent Document 1 and Non-Patent Document 2).

As an analysis method for solid-liquid mixed-phase flow that has been developed so far, the Euler-Euler method is used to analyze the liquid phase and the solid phase, and the solid phase is analyzed using the Euler method. Euler-Lagrange method and Lagrange-Lagrange method for analyzing liquid and solid phases by Lagrangian method. So far, the behavior of the solid phase has mainly been studied in the liquid phase bulk region.
In solid-phase modeling, the discrete element method (DEM, hereinafter referred to as DEM), which is one of the Lagrangian methods, is used to accurately evaluate the contact force between solid particles ( For example, refer nonpatent literature 3).
JP 2002-71891 A Masayoshi Nakajima, Akihiko Miura, Kimiaki Tsuji, et al., “Development of analysis simulation system for vitrification melting furnace (1) Analysis method in simulation system”, Atomic Energy Society of Japan, Annual Meeting of the Atomic Energy Society of Japan, pp646 (2006) Akihiko Miura, Masayoshi Nakajima, Kimiaki Tsuji, et al., "Development of analytical simulation system for vitrification melting furnace (2) Physical behavior during TVF glass melting furnace operation", Atomic Energy Society of Japan, Proceedings of Annual Meeting of Japan Atomic Energy Society, pp646 (2006) Mikio Sakai and Seiichi Koshizuka, "Development of coarse-grained method of discrete element method in solid-gas multiphase flow", Powder Engineering Society, Journal of Powder Engineering Society, Volume 45, pp12 (2008)

  However, the discrete element method has not been established practically, and problems such as application to a large-scale system remain. One of the biggest challenges of application to large-scale systems is the number of computational particles. When calculating in realistic time using the latest PC (Personal Computer), the number of calculated particles is about several hundred thousand at most, and it is said that the number of hundreds of thousands of particles is equivalent to one sugar spoonful. It has been broken. For this reason, simulation of a large-scale system that is said to require more than 1 billion particles could not be calculated in a realistic time.

  In order to execute analysis of a large-scale system in DEM simulation, since the calculation load is large as described above and there is a limitation on the number of particles by computer memory, in recent years, a group of particles is larger than the particles. (Hereinafter, sometimes referred to as coarse-grained particles), and an approach of simulating an actual system by reducing the number of calculated particles as much as possible. However, fluid forces that are solid-liquid interaction forces and contact forces such as solid-solid interaction forces (predetermined forces) depend on the particle size. If it is increased, the behavior of particles having a small particle size cannot be evaluated with coarse-grained particles with high accuracy.

  Furthermore, in a large-scale system, particularly in a glass melting furnace, metal components contained in the high-level radioactive liquid waste that is the object to be treated, particularly platinum group particles (ruthenium (Ru), rhodium (Rh), palladium (Pd), etc.) May precipitate and agglomerate and accumulate at the bottom of the glass melting furnace. If platinum group particles are deposited inside the glass melting furnace, the platinum group particles may cause a short circuit or the like, which may hinder smooth melting processing of the glass melting furnace. Therefore, it is desired to develop a simulation method and a simulation apparatus that can grasp the behavior of aggregation like the platinum group particles.

  The present invention has been made in view of the above problems, and provides a simulation method and a simulation apparatus that can simulate the behavior of particles in a large-scale system in a realistic time including the aggregation of particles. Objective.

In order to solve the above problems, the present invention uses a computer to perform arithmetic processing based on a discrete element method on analysis target data indicating a state of a solid-liquid mixed phase flow composed of a liquid phase and a plurality of particles that are solid phases. A simulation method for analyzing the behavior of the plurality of particles by applying a model composed of some of the particles as coarse-grained particles having a particle size larger than the particle size of the particles, and The predetermined force acting depending on the size of the particle diameter in the solid-liquid mixed phase flow is obtained by combining the coarse-grained particles having a large particle diameter and the plurality of particles having a small particle diameter constituting the coarse-grained particles. A coarse-grained model generation step for performing coarse-graining processing on the analysis target data, and the predetermined force includes van der Waals force, and the coarse-grained model generation step includes the coarse-grained model generation step. Visualization model day It adopts a construction in applying operation based on the discrete element method.
By adopting such a configuration, in the present invention, a group of particles is modeled, and the particle system is simulated using coarse particles that are computationally large. It becomes possible to analyze the behavior of. In addition, in order to make a predetermined force such as fluid force or contact force acting depending on the size of the particle size coincide between the group of particles and the coarse-grained particles, the behavior of the actual particles is coarse-grained. Can be simulated with high accuracy. Furthermore, by considering the van der Waals force and modeling the adhesion force between particles, it is possible to analyze the behavior of particle aggregation / deposition.

このような構成を採用することによって、本発明では、粗視化粒子に作用するファンデルワールス力と粗視化粒子を構成する複数の粒子に作用するファンデルワールス力とのバランスをとることができる。 In the coarse-grained model generation step, the particles and the coarse-grained particles are modeled in a spherical shape, and the particle size of the coarse-grained particles is L times larger than the particle size of the particles. ^{In the case of three} particles, the van der Waals force acting on the coarse-grained particles is F _{VW i,} and the van der Waals force acting on each of the particles constituting the coarse-grained particles is F _{VW. When O} , a configuration that satisfies the relationship of the following formula (a) is adopted.

By adopting such a configuration, in the present invention, the van der Waals force acting on the coarse-grained particles and the van der Waals force acting on a plurality of particles constituting the coarse-grained particles can be balanced. it can.

Simulation that analyzes the behavior of multiple particles by applying computation processing based on the discrete element method to the data to be analyzed that indicates the state of the solid-liquid mixed phase flow consisting of a liquid phase and a plurality of solid particles A device that models a group of some of the particles as coarse-grained particles having a particle size larger than the particle size of the particles, and depends on the size of the particle size in the solid-liquid mixed phase flow The coarse-graining process for matching the predetermined force acting as the coarse-grained particle having a large particle diameter and the plurality of particles having a small particle diameter constituting the coarse-grained particle is the analysis target data. The coarse-grained model generation means to be applied to the above-mentioned predetermined force includes van der Waals force, and the coarse-grained model data obtained by the coarse-grained model generation means is subjected to arithmetic processing based on the discrete element method Apply A construction is adopted.
By adopting such a configuration, in the present invention, a group of particles is modeled, and the particle system is simulated using coarse particles that are computationally large. It becomes possible to analyze the behavior of. In addition, in order to make a predetermined force such as fluid force or contact force acting depending on the size of the particle size coincide between the group of particles and the coarse-grained particles, the behavior of the actual particles is coarse-grained. Can be simulated with high accuracy. Furthermore, by considering the van der Waals force and modeling the adhesion force between particles, it is possible to analyze the behavior of particle aggregation / deposition.

In the coarse-grained model generation means, the particles and the coarse-grained particles are modeled in a spherical shape, and the coarse-grained particles have a particle size L times larger than the particle size of the particles, and the coarse-grained particles are L ^{In the case of three} particles, the van der Waals force acting on the coarse-grained particles is F _{VW i,} and the van der Waals force acting on each of the particles constituting the coarse-grained particles is F _{VW. When O} , a configuration that satisfies the relationship of the above formula (a) is adopted.
By adopting such a configuration, in the present invention, the van der Waals force acting on the coarse-grained particles and the van der Waals force acting on a plurality of particles constituting the coarse-grained particles can be balanced. it can.

According to the present invention, the plurality of particles are obtained by performing arithmetic processing based on the discrete element method on the analysis target data indicating the state of the solid-liquid mixed phase flow composed of a liquid phase and a plurality of particles that are solid phases. A simulation method for analyzing the behavior of the particles, wherein a group composed of some of the particles is modeled as coarse-grained particles having a particle size larger than the particle size of the particles, and the particles in the solid-liquid mixed phase flow Coarse graining in which a predetermined force acting depending on the size of the diameter is matched between the coarse-grained particle having a large particle diameter and the plurality of particles having a small particle diameter constituting the coarse-grained particle. A coarse-grained model generation step for performing processing on the analysis target data, wherein the predetermined force includes van der Waals force, and the discrete-grained model data obtained by the coarse-grained model generation step includes the discrete Based on element method By adopting a configuration that performs arithmetic processing, the group of particles is modeled, and the particle system is simulated using coarse particles that are computationally large. It becomes possible to analyze the behavior. In addition, in order to make a predetermined force such as fluid force or contact force acting depending on the size of the particle size coincide between the group of particles and the coarse-grained particles, the behavior of the actual particles is coarse-grained. Can be simulated with high accuracy. Furthermore, by considering the van der Waals force and modeling the adhesion force between particles, it is possible to analyze the behavior of particle aggregation / deposition.
Therefore, the present invention has an effect of providing a simulation method capable of simulating the behavior of particles in a large-scale system in a realistic time including particle aggregation.

Hereinafter, an embodiment of the present invention will be described based on the drawings and mathematical formulas. First, the configuration of the simulation apparatus and the outline of the flow of the simulation method in the present invention will be briefly described, and then the particle modeling and calculation method according to the simulation method of the present invention will be described in detail.
FIG. 1 is a block diagram showing a schematic configuration of a simulation apparatus 1 according to an embodiment of the present invention. FIG. 2 is a flowchart showing a simulation method in the embodiment of the present invention.
As shown in FIG. 1, the simulation apparatus 1 is a computer system that analyzes the behavior of a solid-liquid mixed phase flow composed of a large-scale liquid phase and a plurality of solid particles, and includes an input device 2 and an output device 3. And a storage device 4 and a CPU 5.

  The input device 2 inputs data from the outside to the CPU 5 and includes a mouse, a keyboard, a communication device, and the like. The output device 3 outputs a simulation result output from the CPU 5 as an image, and includes a display device such as a monitor. The storage device 4 stores data and programs necessary for the simulation of the solid-liquid mixed phase flow, and includes a hard disk, a ROM, a RAM, and the like. This storage device 4 is obtained by analysis target data indicating the state of the solid-liquid mixed phase flow, a coarse-grained program (coarse-grained model generation means) that performs coarse-grain processing on the analysis target data, and coarse-grain processing. Coarse-grained model data and an analysis program for performing arithmetic processing on the coarse-grained model data based on the discrete element method are stored. The CPU 5 includes various input / output interface circuits that exchange data with the input device 2, the output device 3, and the storage device 4, and performs arithmetic processing for analyzing the behavior of the solid-liquid mixed phase flow. .

As shown in FIG. 2, in the simulation method of the present embodiment, first, coarse viewing in which a group composed of several solid phase particles is modeled as coarse-grained particles having a particle size larger than the particle size of the particles. Is applied to the analysis target data (step ST1: coarse-grained model generation step). In the simulation apparatus 1, the CPU 5 that has received a solid-liquid mixed phase flow analysis command from the input device 2 extracts the solid phase data of the particles included in the analysis target data of the storage device 4 and executes the coarse-grained program. To obtain coarse-grained model data.
Then, the CPU 5 executes an analysis program for performing arithmetic processing based on DEM on the coarse-grained model data obtained in the coarse-grained model generation step, and further performing arithmetic processing based on the MPS method (described later) on the liquid phase data. Then, the behavior of the solid-liquid mixed phase flow between the solid phase and the liquid phase is analyzed by outputting the simulation result to the output device 3 (step ST2: solid-liquid mixed phase flow analysis step).

Details of the simulation method will be described below.
In the simulation method of the present embodiment, a Lagrangian-Lagrange method is employed in which the liquid phase is analyzed using a Lagrangian method and the solid phase is analyzed using a Lagrangian method. Specifically, in the present embodiment, a moving particle semi-implicit method (hereinafter sometimes referred to as MPS method) that simulates the behavior of a plurality of fluid particles is applied to the liquid phase, and a plurality of solid phases are used. Apply DEM to simulate its behavior with solid particles. The MPS method is a Lagrangian calculation method and will be described later, but is disclosed in more detail in known technical documents (“particle method”, Seiichi Koshizuka, Maruzen (2005)) and the like. In the following description, an example in which the MPS method is applied to the liquid phase as described above will be described. However, an SPH method, a finite difference method, a finite volume method, or the like may be applied to the liquid phase.

  In order to execute analysis of a large-scale system in a solid-phase DEM simulation, there is a large calculation load and the number of particles due to computer memory is limited. Therefore, in this embodiment, solid-phase particles (hereinafter referred to as original particles) A coarse-graining process is performed in which a group of particles (which may be described) is represented by model particles larger than the original particles (hereinafter also referred to as coarse-grained particles). That is, in order to simulate the behavior of a large-scale system in a realistic time, it is necessary to make a model that handles the scale of solid particles larger than the original particles. At this time, the solid particles should not simply be enlarged. That is, the fluid force that is the interaction force between the solid phase and the liquid phase, the contact force that is the interaction force between the solid phase and the solid phase, and the force such as the adhesion force (predetermined force) depend on the particle size of the solid particles. Therefore, in order to accurately simulate the behavior of particles having a small particle diameter with coarse-grained particles having a large particle diameter, it is necessary to match the above forces between the two.

  3 to 5 are examples showing the difference in behavior between coarse-grained particles having a large particle size and a plurality of original particles having a small particle size constituting the particles. As shown in FIG. 3, when gas is sprayed in the direction of the arrow, the original particles shown in FIG. 3 (b) move more easily than the coarse-grained particles shown in FIG. 3 (a). Further, as shown in FIG. 4, when both particles having the same volume collide with the wall, the coarse-grained particles shown in FIG. 4 (a) and the original particles shown in FIG. And the energy dissipation of both is different. Further, as shown in FIG. 5, the coarse-grained particles shown in FIG. 5 (a) and the original particles shown in FIG. 5 (b) are different in the ease of aggregation of solid particles (adhesive force).

In addition, from the viewpoint of application of a Lagrangian-Lagrangian method to a large-scale system and computational efficiency, it is desirable to handle the discrete scales of both liquid and solid phases at the same scale in calculation. This is because, in a large-scale system, the discretization scale of the space between the liquid phase and the solid phase is different, and the scale of the solid phase is significantly smaller than that of the liquid phase.
Therefore, in this embodiment, the discrete scales of the liquid phase and the solid phase are treated as the same scale in the calculation, and the above-mentioned force depending on the size of the particle diameter is balanced between the original particles and the coarse-grained particles. The coarse-graining process is performed so as to take. A specific original particle modeling and calculation method will be described below.

In the solid-liquid multiphase flow of the Lagrangian-Lagrangian method, each particle constituting the solid-liquid multiphase flow belongs to either the liquid phase or the solid phase. Different from those with vectors and scalars. Therefore, in the Lagrangian / Lagrange-like method, it is necessary to calculate by giving respective equations of motion to the liquid phase and the solid phase.
The continuous equation and equation of motion of the liquid phase and the solid phase are respectively expressed by the following equations (1) to (5).

Here, bold u, p, [rho, mu, bold g, bold _F C, K, epsilon and m are each, velocity vector, pressure, density, viscosity, gravity, contact force, the fluid resistance coefficient, the volume fraction Rate and mass. Regarding the subscripts, l, ll, s, ss, and sl mean liquid phase, liquid phase-liquid phase, solid phase, solid phase-solid phase, and solid phase-liquid phase, respectively.
Details of the liquid phase and solid phase models are shown below.

[Liquid phase]
For the liquid phase, the pressure term, viscosity term, fluid force term and gravity term are calculated. The equation (2) of the liquid phase equation of motion includes gradient and Laplacian as differential operators. Furthermore, Laplacian also appears in the Poisson equation of pressure. The gradient model and Laplacian model of the MPS method are applied to these. Here, the outline of the gradient model and Laplacian model used in the pressure term and the viscosity term will be described. The MPS method is a Lagrangian calculation method for an incompressible flow. In the MPS method, advection is calculated by tracking the movement of particles, so that the influence of numerical diffusion can be eliminated. For this reason, the complicated change of the water surface shape can be calculated with high accuracy. Note that fluid force requires information on solid phase modeling, and will be described in the description of solid phase.

(Weight function)
In the MPS method, differential equations are discretized using an interparticle interaction model for differential operators such as gradient and Laplacian. The weight function w is introduced into the interparticle interaction model as shown in the following equation (6).

Here, x and r _e is the distance between particles and influence radius. Equation (6), x is from means to interact only when less than r _e.

(Particle number density)
The particle number density in the particle i is obtained from the following equation (7).

Here, bold x is a particle position vector. In the case of an incompressible flow, the particle number density must be the particle number density n ⁰ (constant value) defined in the initial state.

(Pressure term)
P at the position of the particle i is expressed by the following equation (8) using a gradient model.

  In the gradient model, a simple gradient vector is defined between a particle i and a neighboring particle j and multiplied by w to obtain an average. Here, D is the number of dimensions of the space.

(Viscosity term)
The viscosity term is calculated using the Laplacian model as shown in the following equation (9).

  According to the Laplacian model, the physical quantity of the particle i is distributed in the distribution of w to the neighboring particle j. Here, the coefficient λ is expressed as the following expression (10).

[Solid phase]
For the solid phase, the pressure term, fluid force term, contact force term, adhesion force term, repulsive force term and gravity term are calculated. The calculation procedure for the pressure term is the same as that for the liquid phase. Here, the contact force term, fluid force term, adhesion force term and repulsive force term will be described.
In the solid phase DEM simulation, the original particle group is represented by large coarse-grained particles for analysis. The coarse-grained model of the DEM models the force acting on the solid particles so that the coarse-grained particles can simulate the behavior of the original particle group. In the DEM, as shown in FIG. 6, the contact force acting between solid particles (indicated by reference numeral 10 in FIG. 6) is a spring 11 (spring constant k), a dashpot 12 (viscosity damping coefficient η), and a friction slider 13 (friction). The translational and rotational motions are evaluated using a model composed of the coefficient μ). For details of the coarse-grained model of DEM, see Non-Patent Document 3 described above.

(Contact force)
In this embodiment, spherical solid particles are handled. When coarse-grained particles that are L times larger than the original particles are used, the coarse-grained particles include L ³ original particles. For example, as shown in FIG. 7, when the particle size of the coarse-grained particles is twice as large as the particle size of the original particles, the coarse-grained particles include 8 original particles.
In the coarse-grained model, the contact force is formulated as the following equation (11), assuming that the kinetic energy of the coarse-grained particles and the original particle group (average) match.

Here, m _s , I, L, and bold ω are solid particle mass, moment of inertia, coarse-grained rate, and angular velocity vector, respectively. The subscripts CGM and O mean coarse-grained particles and original particles. For the translational motion, it is assumed that the coarse-grained particles and the original particles (average) match (see FIG. 7). Regarding the energy of the rotational motion, when the coarse-grained particles and the original particle group are matched, it is assumed that the original particles rotate at their center of gravity (see FIG. 8).

From equation (11), the contact force of L ³ times that of the original particles acts on the coarse-grained particles. In addition, particle-fluid interaction force, adhesion force, repulsive force term, and gravity are modeled so that these forces acting on the coarse-grained particles are balanced with those of the original particles in the coarse-grained particle region. To do. As a result, the equation of motion of the coarse-grained particles is expressed as the following equation (12).

Here, bold letters F _D , V _s , bold _letters F _VW , bold letters _Fe and bold letters F _g are fluid force, solid particle volume, van der Waals force, repulsive force (electric double layer force) and gravity, respectively. Expression (12) is expressed by the product of the number of original particles contained in the coarse-grained particles and the average interaction force thereof (corresponding to the sum of the interaction forces of the original particle groups contained in the coarse-grained particles). When solid particles i and j of coarse-grained particles collide with each other, all of the original particles included in the particles (that is, L ³ original particles per coarse-grained particle) collide with each other. (See FIG. 9).
Regarding the rotational motion, the relationship of the following formula (13) is established between the original particles and the coarse-grained particles.

Here, the bold letters T and r are the torque and the radius of the solid particles.
Regarding the relationship between the original particle system and the coarse-grained particle system, the expression (11) is satisfied by the expressions (12) and (13) that are assumed to be the same as the coarse-grained particles and the original particles (average). Also, the contact force acting on the coarse-grained model is based on the relationship between the original particle system and the coarse-grained particle system described above, the normal direction component, the tangential direction component when not sliding at the contact point, and the case of sliding at the contact point. The tangential direction components are respectively expressed as the following formula (14) to the following formula (16).

  Here, k, δ, η, and bold letter d are the spring constant, overlap width, viscous damping coefficient, and displacement due to translational motion, respectively. The subscripts n and t mean a vertical component and a tangential component. In the coarse-grained model, the physical property values of the original solid particles are used.

(Fluid force)
Regarding the fluid force between the particles and the fluid, the fluid force acting on the coarse-grained solid particle i is obtained from the following equation (17).

However, as shown in the following formula (18), the fluid particle velocity bold u _l is averaged based on the weight function.

  The fluid resistance coefficient is expressed by the following equation (19), and the original particle diameter is set. However, when the powder concentration is high, another coefficient (Ergun equation) may be used.

Here, C _D and d _s are drag coefficient and solid particle diameter, respectively. C _D is a function of the particle Reynolds number Re _p and is represented by the following equation (20).

Re _p is given by the following equation (21).

Using the original ones also particle size in the Re _p represented by equation (21).
The fluid force acting on the fluid particles is obtained by the same procedure, and two-way coupling is possible by considering the fluid force acting on the particles and the fluid.

(Adhesive force)
In this embodiment, Van der Waals force is considered as the adhesion force. Van der Waals force acting on the coarse-grained solid particle i is given by the following equation (22).

Here, H, X, and h are the Hammer car constant, the converted particle diameter, and the distance between the surfaces of the particles, respectively. X _O is given by the following equation (23).

X _Oi and X _Oj are particle sizes based on the original particle sizes contained in the coarse-grained solid particles i and solid particles j.

  Next, a calculation algorithm in the present embodiment will be described with reference to FIG. In addition, since the outline | summary of this calculation algorithm is disclosed by the said well-known technical document etc., it shall omit the detail.

[Liquid phase]
In the MPS method, in the time integration process of the equation of motion of the liquid phase, the SMAC method (refer to the publicly known technical literature of AAAmsden and FH Harlow: A Simplified MAC Technique for Incompressible Fluid Flow Calculations. J. Comp. Phys. 6, 322 (1970)). A two-stage solution is used, which is a semi-implicit algorithm similar to. Here, calculation of the flow at time step n will be described (steps ST21 to ST29). The first stage is the explicit process, the gravity term (step ST22), viscosity term (step ST23) and the fluid force based on (step ST24), the position of the bold _u ^{l *} and temporary speed of the temporary particles X _l ^* is obtained (step ST25). That is, u _l ^* and x _l ^* are expressed as in the following formula (24) and the following formula (25).

Since the particle number density n ^* at the stage where the explicit process is completed is not the initial particle number density n ⁰ , the law of conservation of mass is not satisfied. Therefore, in the second stage, the pressure is updated by implicitly calculating the Poisson equation of the pressure derived from the law of conservation of mass described by the pressure term and the particle number density (step ST26 to step ST28). The Poisson equation is expressed as the following equation (26).

  The speed correction amount is expressed by the following equation (27).

  The corrected speed and position are expressed by the following formula (28) and the following formula (29), respectively.

The particle number density is represented by the following formula (30).

Therefore, what time step n + 1, consistent with ^{n 0.}
In calculating the liquid phase, the time step Δt is set so as to satisfy the following equation (31).

Here, z ₀ , Cr _max and u _max are the initial interparticle distance, the upper limit value of the Courant number, and the maximum value of the fluid velocity.

[Solid phase]
The calculation of the flow at the time step n of the solid phase corresponds to the calculation of the flow at the time step n of the liquid phase (steps ST31 to ST39).
The calculation process of DEM is described. In calculating the equation of motion of the solid phase, the acceleration and angular acceleration based on the fluid force, particle-particle contact force and external force shown in Equation (4) are obtained, and the temporary velocity, temporary position, angular velocity and Angular displacements are calculated explicitly as in the following equations (32) to (35), respectively.

However, the bold letters u _s ^* and x _s ^* are expressed by the following equations (36) and (37) using the results of the second stage of the liquid phase, as in equations (28) and (29). To be corrected.

  Δt in the coarse-grained model of DEM is the following equation (38), which is the same as that of the original particle system. It is necessary to set the time step so that it can be analyzed stably.

Subsequently, a simulation result to which the present method is applied will be described with reference to FIGS. 11 and 12.
FIG. 11 is a diagram showing an initial arrangement of a solid-liquid mixed phase flow analysis system in the embodiment of the present invention. FIG. 12 is a simulation result showing a state of aggregation of solid particles in the embodiment of the present invention. 11 and 12, reference numeral 20 indicates a periodic boundary line, reference numeral 21 indicates a roughened solid particle, and reference numeral 22 indicates an original solid particle.
When the liquid phase flow is given to the solid particles initially arranged as shown in FIG. 11 in the direction of the arrow (the direction from the left side to the right side in FIG. 11), the solid particles are shown in FIG. Aggregation was confirmed. Therefore, by applying this method, the aggregation state of the coarse solid particles shown in FIG. 12B can qualitatively simulate the aggregation state of the original solid particles shown in FIG. It becomes.

Therefore, according to the above-described embodiment, arithmetic processing based on the discrete element method is performed on the analysis target data indicating the state of the solid-liquid mixed phase flow composed of the liquid phase and a plurality of particles that are the solid phase using a computer. A simulation method for analyzing the behavior of the plurality of particles by modeling a group composed of some of the particles as coarse-grained particles having a particle size larger than the particle size of the particles, and The predetermined force acting depending on the size of the particle diameter in the liquid multiphase flow is generated between the coarse-grained particles having a large particle diameter and the plurality of particles having a small particle diameter constituting the coarse-grained particles. A coarse-grained model generation step of performing a coarse-graining process for matching the analysis target data, wherein the predetermined force includes a van der Waals force, and the coarse-grained obtained by the coarse-grained model generation step Model day By adopting a configuration in which the calculation processing based on the above discrete element method is applied to the model, a group of particles is modeled, and the particle system is simulated using large coarse-grained particles in the calculation. It is possible to analyze the behavior of large-scale particles. In addition, in order to make a predetermined force such as fluid force or contact force acting depending on the size of the particle size coincide between the group of particles and the coarse-grained particles, the behavior of the actual particles is coarse-grained. Can be simulated with high accuracy. Furthermore, by considering the van der Waals force and modeling the adhesion force between particles, it is possible to analyze the behavior of particle aggregation / deposition.
Therefore, this embodiment has an effect of providing a simulation method and a simulation apparatus that can simulate the behavior of particles in a large-scale system in a realistic time including the aggregation of particles.

  As mentioned above, although preferred embodiment of this invention was described referring drawings, this invention is not limited to the said embodiment. Each configuration, combination, and the like shown in the above-described embodiments are examples, and various modifications can be made based on design requirements and the like without departing from the gist of the present invention.

For example, in the above-described embodiment, the coarse-grained model is applied to a Lagrangian-Lagrange method in which a solid phase is calculated by a Lagrangian method and a liquid phase is calculated by a Lagrangian method. It can also be applied to the Euler-Lagrange method of calculation.
For example, in the above-described embodiment, the MPS method is applied to the liquid phase, but the SPH method, the finite difference method, the finite volume method, or the like may be applied to the liquid phase.

It is a block diagram which shows schematic structure of the simulation apparatus in embodiment of this invention. It is a flowchart which shows the simulation method in embodiment of this invention. It is a figure which shows the difference in behavior of the coarse-grained particle | grains with a large particle diameter in embodiment of this invention, and the original particle group with a small particle diameter which comprises this particle | grain. It is a figure which shows the difference in behavior of the coarse-grained particle | grains with a large particle diameter in embodiment of this invention, and the original particle group with a small particle diameter which comprises this particle | grain. It is a figure which shows the difference in behavior of the coarse-grained particle | grains with a large particle diameter in embodiment of this invention, and the original particle group with a small particle diameter which comprises this particle | grain. It is a figure which shows the model of the contact force which acts on the solid particle in embodiment of this invention. It is a figure which shows the model of a coarse-grained particle and the model of an original particle group in the translational motion of the solid particle in embodiment of this invention. It is a figure which shows the model of a coarse-grained particle | grain and the model of an original particle group in the rotational motion of the solid particle in embodiment of this invention. It is a figure which shows the model of a coarse-grained particle and the model of an original particle group in the two-body collision of the solid particle in embodiment of this invention. It is a figure which shows the calculation algorithm of the simulation method in embodiment of this invention. It is a figure which shows the initial stage arrangement | positioning of the analysis system of the solid-liquid mixed phase flow in embodiment of this invention. It is a simulation result which shows the state of aggregation of the solid particle in embodiment of this invention.

Explanation of symbols

  1 ... simulation apparatus, ST1 ... step (coarse-grained model generation process)

Claims (4)

Simulation that analyzes the behavior of multiple particles by applying computation processing based on the discrete element method to the data to be analyzed, which shows the state of solid-liquid mixed phase flow consisting of a liquid phase and a plurality of solid particles A method,
A group composed of some of the particles is modeled as a coarse-grained particle having a particle size larger than the particle size of the particle, and the solid-liquid mixed phase flow acts depending on the size of the particle size. Coarse graining is performed on the data to be analyzed by performing a coarse graining process for matching the force between the coarse grained particle having a large particle diameter and the plurality of small particle diameters constituting the coarse grained particle. A model generation process,
The predetermined force includes van der Waals force,
A simulation method characterized by performing arithmetic processing based on the discrete element method on the coarse-grained model data obtained by the coarse-grained model generation step. In the coarse-grained model generation step, the particles and the coarse-grained particles are modeled in a spherical shape, and the particle diameter of the coarse-grained particles is L times larger than the particle diameter of the particles. ^When composed of ^three particles, the van der Waals force acting on the coarse-grained particles is F _{VW i,} and the van der Waals force acting on each of the particles constituting the coarse-grained particles is F _{VW. When O}

The simulation method according to claim 1, wherein the relationship is satisfied. Simulation that analyzes the behavior of multiple particles by applying computation processing based on the discrete element method to the data to be analyzed, which shows the state of solid-liquid mixed phase flow consisting of a liquid phase and a plurality of solid particles A device,
A group composed of some of the particles is modeled as a coarse-grained particle having a particle size larger than the particle size of the particle, and the solid-liquid mixed phase flow acts depending on the size of the particle size. Coarse graining is performed on the data to be analyzed by performing a coarse graining process for matching the force between the coarse grained particle having a large particle diameter and the plurality of small particle diameters constituting the coarse grained particle. Having model generation means;
The predetermined force includes van der Waals force,
A simulation apparatus characterized by performing arithmetic processing based on the discrete element method on the coarse-grained model data obtained by the coarse-grained model generation means. In the coarse-grained model generation means, the particles and the coarse-grained particles are modeled in a spherical shape, the coarse-grained particles have a particle size L times larger than the particle size of the particles, and the coarse-grained particles are L ^When composed of ^three particles, the van der Waals force acting on the coarse-grained particles is F _{VW i,} and the van der Waals force acting on each of the particles constituting the coarse-grained particles is F _{VW. When O}

The simulation apparatus according to claim 3, wherein the relationship is satisfied.

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