DOI: https://doi.org/10.15587/1729-4061.2020.206705

Features of mathematical modeling of electromagnetic processing of bulk materials

Yuri Zaporozhets, Nina Batechko, Sergey Shostak, Natalia Shkoda, Emilia Dibrivna

Abstract


The article notes the features of applying the general equations of mathematical physics of an elliptic type in problems of modeling specific phenomena of the interaction of electromagnetic fields with elements and particles of an inhomogeneous dispersed medium. Such phenomena take place in installations for the separation of organic and mineral raw materials or the electromagnetic treatment of grain, seeds, etc. This is relevant, because the usual approach to the formulation of mathematical models in these problems, which is mainly based on differential equations of field theory in a simplified form, does not always adequately reflect the physical essence of the mentioned phenomena. Therefore, it limits the possibilities of an in-depth study of the influence of many factors determining the final results of separation and electromagnetic processing (EMP) processes. In the present work, an alternative approach is proposed based on the use of integral equations of field theory, which is based on the concept of primary and secondary field sources and can significantly reduce the order of the system of equations for the numerical implementation of algorithms for solving EMP problems, and the total amount of necessary computing resources. With this approach, local parameters of the field in interaction with individual particles and their influence on one another become available for calculation. This aspect is essential for determining the technological characteristics of EMP production installations. The presented mathematical model, in contrast to the common simplified approaches to determining the field parameters and ponderomotive forces acting on the particles of matter in the field, adequately reflects the physical laws of the distribution of potentials and electric field strength of real charges and induced sources. Due to this, it clearly reproduces the mechanism of the formation of the main components of mechanical forces acting on the polarized body from the side of the electric field as a whole, through the densities of elementary forces with which the field acts on surface charges induced in dielectric bodies in the field of action of the fields. Such a mathematical model is a universal and compact tool for analysis, design, and optimization of various installations and devices that use an electric field and its electromechanical interaction with the medium and individual bodies

Keywords


electromagnetic treatment; dispersed materials; mathematical modeling; electric field; particles; substance; force

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References


Kyurchev, S., Kolodiy, A. (2013). The analysis of existing separators which are using for the separation of the seed. Мotrol. Сommission of motorization and energetics in agriculture, 15, 2, 197–204.

Dascalescu, L., Dragan, C., Bilici, M., Beleca, R., Hemery, Y., Rouau, X. (2010). Electrostatic Basis for Separation of Wheat Bran Tissues. IEEE Transactions on Industry Applications, 46 (2), 659–665. doi: https://doi.org/10.1109/tia.2010.2040050

Tarushkin, V. I. (2007). Dielektricheskaya separatsiya semyan. Vol. 1. Moscow, 401.

Korko, V. S., Gorodetskaya, E. A. (2013). Elektrofizicheskie metody stimulyatsii rastitel'nyh obektov. Minsk: BGATU, 232.

Kozlov, A. P. (2007). Bifilyarnaya obmotka dielektricheskogo separatora dlya sortirovaniya semyan zernovyh kul'tur. Moscow, 197.

Mayer Laigle, C., Barakat, A. (2017). Electrostatic Separation as an Entry into Environmentally Eco-Friendly Dry Biorefining of Plant Materials. Journal of Chemical Engineering & Process Technology, 08 (04). doi: https://doi.org/10.4172/2157-7048.1000354

Karmazin, V. V., Karmazin, V. I. (2005). Magnitnye, elektricheskie i spetsial'nye metody obogascheniya poleznyh iskopaemyh. Vol. 1. Moscow: Izdatel'stvo Moskovskogo gosudarstvennogo gornogo universiteta, 669.

Salama, A., Richard, G., Medles, K., Zeghloul, T., Dascalescu, L. (2018). Distinct recovery of copper and aluminum from waste electric wires using a roll-type electrostatic separator. Waste Management, 76, 207–216. doi: https://doi.org/10.1016/j.wasman.2018.03.036

Tilmatine, A., Medles, K., Younes, M., Bendaoud, A., Dascalescu, L. (2010). Roll-Type Versus Free-Fall Electrostatic Separation of Tribocharged Plastic Particles. IEEE Transactions on Industry Applications, 46 (4), 1564–1569. doi: https://doi.org/10.1109/tia.2010.2049553

Matsusaka, S., Maruyama, H., Matsuyama, T., Ghadiri, M. (2010). Triboelectric charging of powders: A review. Chemical Engineering Science, 65 (22), 5781–5807. doi: https://doi.org/10.1016/j.ces.2010.07.005

Ali Ebrahim, S. (2017). Biological Effects of Magnetic Water on Human and Animals. Biomedical Sciences, 3 (4), 78. doi: https://doi.org/10.11648/j.bs.20170304.12

Malkin, E. S., Furtat, I. E., Pryimak, O. V. (2009). Metodyka rozrakhunku ustanovok dlia pomiakshennia ta ochyshchennia vody v elektrychnykh i mahnitnykh poliakh. Nova Tema, 2, 26–29.

Lerman, L. B., Grischuk, O. Yu., Shkoda, N. G., Shostak, S. V. (2012). Features of Interaction of an Electromagnetic Radiation with Small Particles and Their Ensembles: Theoretical Aspects. Uspekhi fiziki metallov, 13 (1), 71–100.

Shkoda, N. H., Shostak, S. V., Kryvoruchko, Ya. S. (2012). Interaction of electromagnetic radiation and nanocoatings. Eastern-European Journal of Enterprise Technologies, 6 (5 (60)), 8–12. Available at: http://journals.uran.ua/eejet/article/view/5711/5156

Hnuchiy, Yu. B., Lerman, L. B., Shostak, S. V., Stetsenko, S. V. (2013). Pohlynannia elektromahnitnoho vyprominiuvannia bahatosharovymy kulovymy chastynkamy. Machinery and Energetics, 184, 142–149. Available at: http://journals.nubip.edu.ua/index.php/Tekhnica/article/view/1242/1196

Martynenko, I. I., Nikiforova, L. E. (2007). Innovatsionnaya tekhnologiya nizkoenergeticheskoy elektromagnitnoy obrabotki semyan. Energetika, ekonomika, tekhnologiya, ekologiya, 1, 89–92.

Li, J., Xu, Z., Zhou, Y. (2008). Theoretic model and computer simulation of separating mixture metal particles from waste printed circuit board by electrostatic separator. Journal of Hazardous Materials, 153 (3), 1308–1313. doi: https://doi.org/10.1016/j.jhazmat.2007.09.089

Pelevin, A. E. (2018). Magnetic and electrical enrichment methods. Magnetic enrichment methods. Yekaterinburg: Izd-vo UGGU, 296.

Kozyrskiy, V. V., Savchenko, V. V., Sinyavskiy, A. Y. (2019). Pre-Sowing Treatment of Leguminous Crop Seeds with a Magnetic Field. Agricultural Machinery and Technologies, 13 (1), 21–26. doi: https://doi.org/10.22314/2073-7599-2018-13-1-21-26

Mach, F., Kus, P., Karban, P., Doležel, I. (2012). Higher-Order Modeling of Electrostatic Separator of Plastic Particles. Przegląd elektrotechniczny, 12b, 74–76.

Kim, B., Han, O., Jeon, H., Baek, S., & Park, C. (2017). Trajectory Analysis of Copper and Glass Particles in Electrostatic Separation for the Recycling of ASR. Metals, 7 (10), 434. doi: https://doi.org/10.3390/met7100434

Nazarenko, I. (2013). Theoretical researches of co-operation of electric paul with dielectric suspension in systems of multielectrodes. Pratsi Tavriyskoho derzhavnoho ahrotekhnolohichnoho universytetu, 2 (13), 75–82.

Ciosk, K. (2012). Magnetic field and forces in a magnetic separator gap. Przegląd elektrotechniczny, 12b, 47–49.

Tarushkin, V. I. (2012). A mathematical model for improving dielectric separation devices. Bulletin of Moscow State Agrarian University named V.P. Goryachkina, 2, 7–9.

Prachukowska, A., Nowicki, M., Korobiichuk, I., Shewchyk, R., Salah, J. (2015). Modeling and validation of magnetic field distribution of permanent magnets. Eastern-European Journal of Enterprise Technologies, 6 (5 (78)), 4–11. doi: https://doi.org/10.15587/1729-4061.2015.55323

Volchenskov, V. I., Sobolev, V. A. (2013). On the features of modeling the magnetic circuit of a synchronous generator with permanent magnets. Engineering Bulletin, MGTU im. Baumana, 9, 635–644.

Blank, A. V. (2004). Analytical calculation of the excitation field of a synchronous machine based on one piecewise-continuous eigenfunction. Sbornik nauchnykh trudov NGTU, 4 (38), 3–8.

Meessen, K. J., Gysen, B., Paulides, J., Lomonova, E. A. (2008). Halbach Permanent Magnet Shape Selection for Slotless Tubular Actuators. IEEE Transactions on Magnetics, 44 (11), 4305–4308. doi: https://doi.org/10.1109/tmag.2008.2001536

Afonin, A. A. (2005). Elektromagnitnye nagruzki elektricheskih mashin s postoyannymi magnitami. Tekhnichna elektrodynamika, 1, 39–46.

Grinberg, G. A. (1948). Izbrannye voprosy matematicheskoy teorii elektricheskih i magnitnyh yavleniy. Moscow-Leningrad: Izd. AN SSSR, 733.

Mirolyubov, N. N., Kostenko, M. V. et. al. (1963). Metody rascheta elektrostaticheskih poley. Moscow: Vysshaya shkola, 415.

Sil'vester, P., Ferrari, R. (1986). Metod konechnyh elementov dlya radioinzhenerov i inzhenerov-elektrikov. Moscow: Mir, 229.

Zhang, Y. H., Xu, Y. Y., Ye, C. Y., Sheng, C., Sun, J., Wang, G. et. al. (2018). Relevance of electrical current distribution to the forced flow and grain refinement in solidified Al-Si hypoeutectic alloy. Scientific Reports, 8 (1). doi: https://doi.org/10.1038/s41598-018-21709-y

Tozoni, O. V. (1975). Metod vtorichnyh istochnikov v elektrotekhnike. Moscow: Energiya, 296.

Tihonov, A. N., Samarskiy, A. A. (1977). Uravneniya matematicheskoy fiziki. Moscow: Nauka, 735.

Verlan', A. F., Sizikov, V. S. (1978). Metody resheniya integral'nyh uravneniy s programmami dlya EVM. Kyiv: Naukova dumka, 219.

Tihonov, A. N., Arsenin, V. Ya. (1979). Metody resheniya nekorrektnyh zadach. Moscow: Nauka, 288.

Zaporozhets, Y., Ivanov, A., Kondratenko, Y. (2019). Geometrical Platform of Big Database Computing for Modeling of Complex Physical Phenomena in Electric Current Treatment of Liquid Metals. Data, 4 (4), 136. doi: https://doi.org/10.3390/data4040136

Govorkov, V. A. (1968). Elektricheskie i magnitnye polya. Moscow: Energiya, 488.

Tamm, I. E. (1976). Osnovy teorii elektrichestva. Moscow: Nauka, 616.

Polivanov, K. M. (1969). Teoreticheskie osnovy elektrotekhniki. Ch. ІІІ. Teoriya elektromagnitnogo polya. Moscow: «Energiya», 352.

Pavlovskyi, M. A. (2002). Teoretychna mekhanika. Kyiv: Tekhnika, 512.


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Copyright (c) 2020 Yuri Zaporozhets, Nina Batechko, Sergey Shostak, Natalia Shkoda, Emilia Dibrivna

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ISSN (print) 1729-3774, ISSN (on-line) 1729-4061