JP2010107314A - Simulation method and device - Google Patents

Abstract

<P>PROBLEM TO BE SOLVED: To provide a simulation method and a simulation device capable of simulating behavior of all platinum group particles in a glass fusion furnace in an actual time. <P>SOLUTION: This simulation method for analyzing behavior of a plurality of platinum group particles by applying operation processing based on a discrete element method to analysis object data showing the state of a solid-liquid mixed phase flow comprising liquid-phase glass and the plurality of solid-phase platinum group particles by using a computer, includes a coarsely-visualized model generation process for applying to the analysis object data, coarsely visualizing processing for modeling a group constituted of several platinum group particles as coarsely-visualized particles having respective larger particle sizes than those of the platinum group particles, and adopts a constitution wherein the operation processing based on the discrete element method is applied to coarsely-visualized model data acquired in the coarsely-visualized model generation process. <P>COPYRIGHT: (C)2010,JPO&INPIT

Description

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

As a method for treating high-level radioactive liquid waste, as disclosed in Patent Document 1 below, a high-level radioactive liquid waste is melted together with glass raw materials in a glass melting furnace to produce molten glass,
Thereafter, a technique for solidifying is known.

  Depending on the operating conditions of the glass melting furnace, metal components contained in the high-level radioactive liquid waste, particularly platinum group particles (ruthenium (Ru), rhodium (Rh), palladium (Pd), etc.) are deposited inside the glass melting furnace, There is a possibility of depositing inside the glass melting furnace. In the glass melting furnace, an electric current is passed between electrodes provided in the glass melting furnace, and the glass raw material is melted by the generated heat (Joule heat). 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. In order to suppress the occurrence of such problems, it is necessary to grasp the behavior of platinum group particles in a solid-liquid mixed phase flow with molten glass and to optimize the operating conditions of the glass melting furnace.

Upon elucidation of the internal mechanism of the solid-liquid multiphase flow, in a large system that handles high-level radioactive waste liquid such as a glass melting furnace, it is not easy to measure the moving distance of the density and the constituent particles, approach experiments difficult Therefore, an approach based on numerical simulation 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 yet been established practically, and there remain problems such as application to a large-scale system such as a glass melting furnace. 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, a simulation of a large-scale system (for example, the volume in the glass melting furnace is about 1 cubic meter), which is said to require more than 1 billion particles such as platinum group particles in the glass melting furnace, is realistic. Could not calculate in time. Therefore, the conventional method has a problem that the behavior of all platinum group particles in the glass melting furnace is not simulated.

  The present invention has been made in view of the above problems, and an object thereof is to provide a simulation method and a simulation apparatus capable of simulating the behavior of all platinum group particles in a glass melting furnace in a realistic time. And

In order to solve the above-described problems, the present invention provides an 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 glass and a plurality of solid phase platinum group particles. Is performed by using a computer to analyze the behavior of the plurality of platinum group particles, and the group consisting of some of the platinum group particles has a particle size larger than the particle size of the platinum group particles. A coarse-grained model generation step for performing coarse-graining processing on the analysis target data to be modeled as large coarse-grained particles, and the discrete element is included in the coarse-grained model data obtained by the coarse-grained model generation step A configuration is adopted in which arithmetic processing based on the law is performed.
By adopting such a configuration, the present invention models a group of platinum group particles and simulates the platinum group particle system by using coarse particles coarsely calculated. It becomes possible to analyze the behavior of platinum group particles in the melting furnace.

In the coarse-grained model generation step, the present invention applies the predetermined force acting depending on the particle size in the solid-liquid mixed phase flow to the coarse-grained particles having a large particle size and the coarse-grained particles. A configuration is adopted in which modeling is performed so as to match the plurality of platinum group particles having a small particle diameter constituting the structured particles.
By adopting such a configuration, in the present invention, a predetermined force such as a fluid force or a contact force acting depending on the size of the particle diameter is applied between the group of platinum group particles and the coarse-grained particles. Therefore, the actual behavior of the platinum group particles can be accurately simulated with the coarse-grained particles.

Further, the present invention employs a configuration in which the predetermined force includes a van der Waals force.
By adopting such a configuration, in the present invention, the van der Waals force is taken into account, and the adhesion force between the platinum group particles is modeled, so that the behavior of the aggregation and deposition of the platinum group particles in the molten glass is controlled. It becomes possible to analyze.

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白金族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 present invention models the platinum group particles and the coarse-grained particles in a spherical shape, and the coarse-grained particles have a particle size L smaller than the platinum-group particle size. When the coarse-grained particles are composed of L ³ platinum group particles, the van der Waals force acting on the coarse-grained particles is F _{VW i,} and the platinum constituting the coarse-grained particles When the van der Waals force acting on each of the group particles is F _{VW O} , a configuration that satisfies the relationship of the following formula (a) is adopted.

By adopting such a configuration, the present invention balances the van der Waals force acting on the coarse-grained particles and the van der Waals force acting on the plurality of platinum group particles constituting the coarse-grained particles. be able to.

Further, the present invention employs a configuration in which the predetermined force includes an electric double layer force.
By adopting such a configuration, the present invention analyzes the behavior of aggregation and deposition of platinum group particles in molten glass by modeling the repulsive force between platinum group particles in consideration of the electric double layer force. It becomes possible to do.

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電気二重層力と粗視化粒子を構成する複数の白金族粒子に作用する電気二重層力とのバランスをとることができる。 In the coarse-grained model generation step, the present invention models the platinum group particles and the coarse-grained particles in a spherical shape, and the coarse-grained particles have a particle size L smaller than the platinum-group particle size. fold increase, when constituting the coarse-grained particles with L ³ of the aforementioned platinum group particles, an electric double layer forces acting on the coarse-grained particles and F _{e i,} the platinum constituting the coarse grained particles When the electric double layer force acting on each of the group particles is F _{e O} , a configuration that satisfies the relationship is adopted.

By adopting such a configuration, the present invention balances the electric double layer force acting on the coarse-grained particles and the electric double layer force acting on a plurality of platinum group particles constituting the coarse-grained particles. be able to.

In addition, the present invention applies calculation processing based on the discrete element method to data to be analyzed that indicates a state of a solid-liquid mixed phase flow composed of glass as a liquid phase and a plurality of platinum group particles as a solid phase. A simulation apparatus for analyzing the behavior of the plurality of platinum group particles by using a group consisting of some of the platinum group particles as a coarse-grained particle having a particle size larger than that of the platinum group particles A coarse-grained model generating means for applying the coarse-graining process to the analysis target data, and performing the arithmetic processing based on the discrete element method on the coarse-grained model data obtained by the coarse-grained model generating means The configuration is adopted.
By adopting such a configuration, the present invention models a group of platinum group particles and simulates the platinum group particle system by using coarse particles coarsely calculated. It becomes possible to analyze the behavior of platinum group particles in the melting furnace.

According to the present invention, calculation processing based on the discrete element method is performed using a computer on analysis target data indicating the state of a solid-liquid mixed phase flow composed of glass as a liquid phase and a plurality of platinum group particles as a solid phase. A simulation method for analyzing the behavior of the plurality of platinum group particles by using a group consisting of some of the platinum group particles as a coarse-grained particle having a particle size larger than that of the platinum group particles A coarse-grained model generation step for performing coarse-graining processing on the analysis target data, and performing arithmetic processing based on the discrete element method on the coarse-grained model data obtained by the coarse-grained model generation step By adopting the configuration, the group of platinum group particles is modeled, and the platinum group particle system is simulated using coarse particles that are computationally large, so the number of particles in the glass melting furnace is smaller than the actual number. It is possible to analyze the behavior of the gold group particle.
Therefore, the present invention has an effect of providing a simulation method capable of simulating the behavior of all platinum group particles in the glass melting furnace in a realistic time.

Hereinafter, an embodiment of the present invention will be described based on the drawings and mathematical formulas. First, the outline of the configuration of the simulation apparatus and the flow of the simulation method in the present invention will be briefly described, and then the modeling and calculation method of platinum group particles 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 glass as a liquid phase inside a glass melting furnace and a plurality of platinum group particles as a solid phase. It has the apparatus 2, the output device 3, the memory | storage device 4, and CPU5.

  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, a group composed of several platinum group particles is modeled as coarse-grained particles having a particle size larger than that of the platinum group particles. Visualization processing is performed on the analysis target data (step ST1: coarse-grained model generation step). In the simulation apparatus 1, the CPU 5 that has received the analysis command of the solid-liquid mixed phase flow from the input device 2 extracts the solid phase data of the platinum group particles included in the analysis target data of the storage device 4 and executes the coarse-grained program. Thus, coarse-grained model data is obtained.
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, by outputting the simulation result to the output device 3, the behavior of the solid-liquid mixed phase flow composed of the solid phase platinum group particles and the liquid phase molten glass is analyzed (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, the liquid phase may be described as a Moving Particle Semi-implicit method (hereinafter referred to as MPS method) that simulates the behavior of a plurality of fluid particles (hereinafter also referred to as liquid phase particles). A DEM that simulates the behavior of the solid phase by a plurality of solid particles (hereinafter sometimes referred to as solid phase particles) is applied to the solid phase. 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 perform analysis of a large-scale system of a glass melting furnace in a DEM simulation of a solid phase, since there is a large calculation load and a limit on the number of particles by a computer memory, in this embodiment, platinum group particles (hereinafter, A coarse-graining process is performed in which a group of particles that may be referred to as original particles) 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 all platinum group particles in the glass melting furnace in a realistic time, it is necessary to model the solid particles so that the scale of the solid particles is 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, the force such as the adhesion force and the repulsive force (predetermined force) depends on the particle size of the solid particles. Therefore, in order to accurately simulate the behavior of platinum group particles having a small particle size of about submicron with coarse-grained particles having a large particle size, 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). Furthermore, it is necessary to make the magnitude of repulsive force the same between the coarse-grained particles and the original particles and to balance them.

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 of a glass melting furnace, the discretization scale of 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 liquid phase particles and solid phase particles.
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.

(repulsive force)
In this embodiment, repulsive force (electric double layer force) is considered. The repulsive force acting on the coarse-grained solid particle i is given by the following equation (24).

  However, (gamma) and (kappa) are given like the following Formula (25) and the following Formula (26), respectively.

Here, r _s , n, k _b , T, h, z, e, ε ₀ , ε _r and ψ ₀ are the particle radius, electrolyte ion number density, Boltzmann constant, liquid phase solvent temperature, particle surface, respectively. Distance, electrolyte valence, unit charge, vacuum dielectric constant, solvent dielectric constant and potential.

As described above, by modeling the contact force, adhesion force, and repulsive force (electric double layer force) between the fluid force and the solid particles, for systems with different liquid phase and solid phase space discretization scales In calculation, both can be handled on the same scale.
However, in the case of high salt concentration or low temperature, the electric double layer becomes thin, and the electric double layer force becomes small, so that the repulsive force may be negligible.
In addition, the structure which considers random force in addition to the said force here may be sufficient.

  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 (27) and the following formula (28).

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 (29).

  The speed correction amount is expressed by the following equation (30).

  The corrected speed and position are expressed by the following formula (31) and the following formula (32), respectively.

The particle number density is represented by the following formula (33).

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 (34).

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 The angular displacement is calculated explicitly as in the following formula (35) to the following formula (38), respectively.

However, the bold letters u _s ^* and x _s ^* are expressed by the following equations (39) and (40) using the results of the second phase of the liquid phase, as in equations (31) and (32). To be corrected.

  Δt in the coarse-grained model of DEM is the following formula (41), 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, the calculation processing based on the discrete element method is applied to the analysis target data indicating the state of the solid-liquid mixed phase flow including the liquid phase glass and the solid phase plural platinum group particles. A simulation method for analyzing the behavior of the plurality of platinum group particles by applying a coarse particle having a particle size larger than the particle size of the platinum group particles. A coarse-grained model generation step for performing coarse-graining processing on the data to be analyzed, which is modeled as visualized particles, and the coarse-grained model data obtained by the coarse-grained model generation step is converted into the discrete element method. By adopting a configuration that performs arithmetic processing based on the model, a group of platinum group particles is modeled, and the coarser particles in the calculation are used to simulate the platinum group particle system. It is possible to analyze the behavior of the platinum group particles in the glass melting furnace in a few.
Therefore, this embodiment has an effect of providing a simulation method that can simulate the behavior of all platinum group particles in the glass melting furnace in a realistic time.

  In the present embodiment, in the coarse-grained model generation step, fluid force, contact force, adhesion force (Van der Waals force) and repulsive force (depending on the size of the particle diameter in the solid-liquid mixed phase flow) By applying modeling to match the electric double layer force) between the coarse-grained particles having a large particle diameter and a plurality of the platinum group particles having a small particle diameter constituting the coarse-grained particles, The behavior of the actual platinum group particles can be accurately simulated with the coarse-grained particles by balancing the predetermined force acting depending on the size of the platinum group particles and the coarse-grained particles. It becomes possible.

  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.

Further, for example, in the above-described embodiment, in the coarse-grained model generation step, fluid force, contact force, and adhesion force (Van der Waals force) acting depending on the particle size in the solid-liquid mixed phase flow. And the repulsive force (electric double layer force) is explained to be modeled to match the coarse-grained particles having a large particle diameter and the plural platinum group particles having a small particle diameter constituting the coarse-grained particles. However, the structure which adds a random force here may be sufficient. The random force (R ² ) is expressed as in the following formula (42).

Here, ξ is a Stokes resistance coefficient.

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 (12)

A plurality of platinum groups are obtained by performing arithmetic processing based on a discrete element method on data to be analyzed indicating a state of a solid-liquid mixed phase flow composed of a glass that is a liquid phase and a plurality of platinum group particles that are a solid phase. A simulation method for analyzing the behavior of particles,
Coarse-grained model generation for subjecting the analysis target data to a coarse-grained process for modeling a group composed of some of the platinum-group particles as coarse-grained particles having a particle size larger than that of the platinum-group particles Having a process,
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, a predetermined force acting depending on the size of the particle diameter in the solid-liquid mixed phase flow is used to form the coarse-grained particles having a large particle diameter and the particles constituting the coarse-grained particles. The simulation method according to claim 1, wherein modeling is performed to match the plurality of platinum group particles having a small diameter.   The simulation method according to claim 2, wherein the predetermined force includes a van der Waals force. In the coarse-grained model generation step, the platinum group particles and the coarse-grained particles are modeled in a spherical shape, and the coarse-grained particles have a particle size that is L times larger than the platinum-group particles. When the coarse particles are composed of L ³ platinum group particles, the van der Waals force acting on the coarse-grained particles is F _{VW i} and acts on each of the platinum-group particles constituting the coarse-grained particles. When the van der Waals force is F _{VW O} ,

The simulation method according to claim 3, wherein the relationship is satisfied.   The simulation method according to claim 2, wherein the predetermined force includes an electric double layer force. In the coarse-grained model generation step, the platinum group particles and the coarse-grained particles are modeled in a spherical shape, and the coarse-grained particles have a particle size that is L times larger than the platinum-group particles. In the case where the particles are composed of L ³ platinum group particles, the electric double layer force acting on the coarse-grained particles is defined as Fe _i and acts on each of the platinum group particles constituting the coarse-grained particles. When the electric double layer force is F _{e O} ,

The simulation method according to claim 5, wherein the relationship is satisfied. A plurality of platinum groups are obtained by performing arithmetic processing based on a discrete element method on data to be analyzed indicating a state of a solid-liquid mixed phase flow composed of a glass that is a liquid phase and a plurality of platinum group particles that are a solid phase. A simulation device for analyzing the behavior of particles,
Coarse-grained model generation for subjecting the analysis target data to a coarse-grained process for modeling a group composed of some of the platinum-group particles as coarse-grained particles having a particle size larger than that of the platinum-group particles Having means,
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, a predetermined force acting depending on the size of the particle diameter in the solid-liquid mixed phase flow is applied to the coarse-grained particles having a large particle diameter and the particles constituting the coarse-grained particles. The simulation apparatus according to claim 7, wherein modeling is performed to match the plurality of platinum group particles having a small diameter.   The simulation apparatus according to claim 8, wherein the predetermined force includes a van der Waals force. In the coarse-grained model generation means, the platinum group 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 platinum-group particles, When the coarse particles are composed of L ³ platinum group particles, the van der Waals force acting on the coarse-grained particles is F _{VW i} and acts on each of the platinum-group particles constituting the coarse-grained particles. When the van der Waals force is F _{VW O} ,

The simulation apparatus according to claim 9, wherein the relationship is satisfied.   The simulation apparatus according to claim 8, wherein the predetermined force includes an electric double layer force. In the coarse-grained model generation means, the platinum group 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 platinum-group particles, In the case where the particles are composed of L ³ platinum group particles, the electric double layer force acting on the coarse-grained particles is defined as Fe _i and acts on each of the platinum group particles constituting the coarse-grained particles. When the electric double layer force is F _{e O} ,

The simulation apparatus according to claim 11, wherein the relationship is satisfied.

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