Modeling of particle motion in spiral pneumoseparator by statistical methods

  • Krylatova Sardaana R., tsubasasardaana@mail.ru M. K. Ammosov North-Eastern Federal University Institute of Physics and Technologies, 48 Kulakovsky Street, Yakutsk 677891, Russia
  • Matveev Andrey I., andrei.mati@yandex.ru Chersky Mining Institute of the North, 43 Lenin Avenue, Yakutsk 677980, Russia
  • Lebedev Ivan F., ivleb@mail.ru Chersky Mining Institute of the North, 43 Lenin Avenue, Yakutsk 677980, Russia
  • Yakovlev Boris V., b-yakovlev@mail.ru M. K. Ammosov North-Eastern Federal University Institute of Physics and Technologies, 48 Kulakovsky Street, Yakutsk 677891, Russia
Keywords: spiral separator, concentration, statistical method, motion equation, particle flow, enrichment, mathematical model

Abstract

In mathematical modeling of mineral processing, there arise problems of determining the probability of the particle presence on the working surfaces of devices. In the paper, we propose a statistical approach to solving such problem, i. e., the idea of the Gibbs method is used. We consider problems of modeling processes in an air spiral separator. A mathematical model of the spiral surface of a pneumoseparator, a model of particle motion, a flux of noninteracting particles along the separator working surface, and an algorithm for determining the particle flux concentration are developed. The calculated distribution of the noninteracting particles concentration on the working surface of the device is identified with the probability distribution of the location of one particle. The developed algorithm for determining the probability of position of a particle on the working surface of the pneumoseparator can be used as an element of a more complex mathematical model, for example, a model where interactions between particles are taken into account.

References


[1]
Matveev A. I., Filippov V. E., Fedorov F. M., Grigoriev A. N., Yakovlev V. B., Eremeeva N. G., Slepsova E. S., Gladyshev A. M., and Vinokurov V. P., Patent No. 2167005. 20.05.2001.

[2]
Hasankhoei A. R., Banisi S., and Mozafari P., “Designing a spiral splitter at the Zarand coal washing plant,” Indian J. Sci. Res., 1, No. 2, 151–156 (2014).

[3]
Shuvalov S. I. and Andreev A. A., “Mathematical description of motion of particles in a dynamic separator,” Vestn. Ivanovsk. Gos. Energ. Univ., 1, 25–28 (2005).

[4]
Matveev A. I., Lebedev I. F., Nikiforova L. V., and Yakolev B. V., “Modeling of motion of particles in a spiral pneumoseparator,” Mining Inform. Anal. Bull., 10, 172–178 (2014).

[5]
Barskii M. D., Revnivtsev V. I., and Sokolkin Y. V., Gravitatsionnaya Klassifikatsiya Zernistykh Materialov [in Russian], Nedra, Moscow (1974).

[6]
Filippov V. E., Lebedev I. F., Matveev A. I., and Grigoriev A. N., Patent No. 2194581 (2002).

[7]
Kapur P. C. and Meloy T. P., “Spirals observed,” Int. J. Mineral Process., 53, 15–28 (1998).

[8]
Das S. K., Godivalla K. M., Panda L., Bhattacharya K. K., Singh R., and Mehrotra S. P., “Mathematical modeling of separation characteristics of coal-washing spiral,” Int. J. Mineral Process., 84, 118–132 (2007).

[9]
Mishra B. K. and Alok Tripathy, “A preliminary study of particle separation in spiral concentrators using DEM,” Int. J. Mineral Process., 94, 192– 195 (2010).

[10]
Germanyuk G. Y., Mathematical Modeling of Particle Set Movement Using Canonical Method of Integration [in Russian], Diss. Kand. Fiz.-Mat. Nauk, Izhevsk (2010).

[11]
Gibbs J. W., Elementary Principles in Statistical Mechanics, Developed with Especial Reference to the Rational Foundation of Thermodynamics, Dover Publ., New York (1902).

[12]
Landau L. D. and Lifshitz E. M., Theoretical Physics. Vol. 5. Statistical Physics [in Russian], Nauka, Moscow (1976).

[13]
Karman T., Aerodynamics: Selected Topics in the Light of Their Historical Development, Cornell Univ. Press, Ithaca, NY (1954).

[14]
Frolov S. A., Nachertatelnaya Geometriya [in Russian], Mashinostroenie, Moscow (1983).

[15]
Sivukhin D. V., General Course of Physics. Vol. 1. Mechanics, Nauka, Moscow (1979).
How to Cite
Krylatova, S., Matveev, A., Lebedev, I. and Yakovlev, B. ( ) “Modeling of particle motion in spiral pneumoseparator by statistical methods”, Mathematical notes of NEFU, 25(1), pp. 90-97. doi: https://doi.org/10.25587/SVFU.2018.1.12771.
Section
Mathematical Modeling