A207 CAによる可動容器中の粒子挙動シミュレーション(粒状体)

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In the present study, we performed granular flow simulation of particles inside moving container using Cellular Automata (CA). CA are the discrete system which consists of finite state variables arranged on uniform spatial grids (cells). State variable varies within a finite set of values in order to express the physical state of components of the system to be analyzed. Moreover, the states of each cell are updated synchronously according to the local interaction rules at every discrete time step. That is, the state of a cell at a given time step only depends on the previous state of itself and also that of nearby neighbor cells. Compared with the conventional method such as DEM, it is addressed that the modeling techniques with CA provide advantages on the point of computation efficiency and numerical stability due to the discrete treatment of time and space. It is also attractive for its simple strategy, however, rules must be defined along with physical consideration as carefully as we derive differential equations in the ordinary analysis. Likewise the state variables can be given certain physical quantities, on the other hand, regularly divided space into rectangle or triangle grids requires spatial averaging process. In the present CA model, the space is divided into triangular grids, where particles are distributed two dimensionally on cellular space. Three kinds of state variables are defined; The first one represents cell condition which distinguishes three kinds of physical state such as wall, particle and vacant space represented as integers 0, 1, 2 respectively. The second and the third variables apply additionally to the particle state cell, that are the moving direction vector and also the energy which apparently corresponds to kinetic energy of a particle. The triangular arrangement of cell grids allows six neighbors present around each cell. Therefore, the particles are movable into six directions, hence the identical variation of vector states exist. The traveling of particles is allowed only single cell distance per calculation step. The local interaction rules are defined so that the motion of particles can be expressed, incorporating moving vector reconfiguration and energy dissipation related to collisions of particle against particle, and also against wall. The simulation process consists of two parts. The first one demonstrates accumulation of falling particles on the floor that are dropped into the container from top wall, where the container is kept stationary. The effect of the energy dissipation rate d on the cumulation pattern is investigated for several d cases. The results showed that the particles piled up higher directly below the pouring position for the case energy is dissipated strongly, whereas the accumulation surface become flat for the case d is small. The second part deals with the simulation of granular flow of particles inside container for given sinusoidal excitation. The second simulation stage follows the first accumulation process, starting from the condition where the particles are stationary accumulated on the container floor. The simulated flow patterns are compared with experimental results for the case 20 particles are enclosed inside container. The simulation results coincide with experiment in a sense that particles gather and spread at a certain stage of container movement ; and the present CA model is verified in qualitative aspects.
一般社団法人日本機械学会の論文
2001-11-14

A207 CAによる可動容器中の粒子挙動シミュレーション(粒状体)

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