Development of an Algorithm for Random Packing of Multi-Sized Spherical Particles
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Development of an Algorithm for Random Packing of Multi-Sized Spherical Particles H. de la Garza-Gutiérrez 1,2, G. Plascencia-Barrera1 and S.D. de la Torre1 1 Instituto Politécnico Nacional. Centro de Investigación e Innovación Tecnológica CIITEC-IPN. Cerrada CECATI S/N. Col. Santa Catarina. Azcapotzalco, C.P.02250, México D.F. Mexico. 2 Instituto Tecnológico de Chih.-II, Av. de las Industrias 11101, Comp. Ind. Chihuahua, Mexico.
ABSTRACT A new computational algorithm is introduced for packing simulation of spherical elements/particles into an imaginary container with three main possible geometries, cubic, cylindrical and spherical. The performance of the algorithm depends directly on the strategy or logic considered to solve the problem and the quality of its computational implementation. The combination of these two factors let the packing algorithm here presented and named as Octant Packing Random Algorithm (OPRA) to reduce the computation time between 2 and 127 times, when compared with the simplest or classical Packing Algorithm. OPRA is designed to reduce the number of comparisons needed to accept or reject a new position for an element/particle to be allocated into the virtual container. OPRA considers the container as if it were divided into 8 equal cells or octants limiting the overlap detection for a new position. INTRODUCTION In many industrial fields, particles with different size distribution are used. Among these industries are: catalysts, cement, mineral processing, grain storage, etc. In order to accommodate these particles into containers or processing units, it is necessary to understand how such particles are susceptible to utilize the volume destined to their storage/processing. In this paper we propose an algorithm based in random allocation and for this reason, it is useful for systems with low relation solid/volume. To do so, the algorithm takes a particle and transforms it into an element, which can be traced as it accommodates in a given container. When a system to be modeled involves small particles and/or solid elements placed inside a container, it is convenient to represent both the vessel and the set of elements in a computational arrangement for study. It is then required to specify at least a number of conditions; namely, the size and geometry of the container, the system of used coordinates, the specification of the system’s origin and/or spatial location, the geometry of the elements (particles) as well as the number and size of each interacting element, especially when different particle sizes are considered simultaneously. As for each element and/or particle placed into the vessel concerns, there should be a virtual counterpart allocated inside the system model. The ideal allocation process implies to find out a valid position for each element, where none of it replaces the space occupied by the other. This task is defined to as the packing stage. In order to conduct it, one can opt for developing an original algorithm and/or to choose between some available in the corresponding
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