Features of calculation arch support with a splitting investigation of the final deposition rates in liquids of elongated rock particles

Wet gravity processes of ore separation are characterized by greater environmental friendliness compared to dry methods of enrichment. They allow you to separate rocks taking into account the size, density and shape of the grains. The practice of enrichment has shown that the grains of most ores after crushing and grinding differ significantly in shape from each other. Practically all the theoretical foundations of gravitational separation have been developed for spherical particles and, when applied to cylindrical forms, require clarification and appropriate corrections. The article provides an analysis of existing methods for determining the velocity of falling particles in a liquid. A method for determining the steady-state velocity of cylindrical particles of elongated shape taking into account the position of the particle is given. As a result of the research, it was found that for cylindrical particles, the area of the Mid-section varies depending on its position when falling randomly from the area of a circle to a rectangle. The results of experiments to determine the steady-state velocity of cylindrical particles of elongated shape in water, depending on the ratio of particle length to diameter, are presented. Graphs of the dependence of the velocity of falling particles with a density of 1.27 g/cm3 in water on the ratio of their length to diameter are given. The statistical dependence of the velocity of falling particles in water on the ratio of their length to diameter is found. The necessity of developing a simulation model of the process taking into account the random nature of particle sizes: length, diameter, as well as the angle between the longitudinal axis of symmetry of the particle and the velocity vector of the particle “α” is substantiated. Moreover, when developing a model, it is necessary to take into account the type of laws of distribution of random variables.

Keywords: the velocity of falling particles in a liquid, the Reynolds number, the diameter and length of the particle, the mid-section, the coefficient of resistance of the medium.
For citation:

Afanas’ev A. I., Potapov V. Ya., Uporov S. A., Potapov V. V. Features of calculation arch support with a splitting investigation of the final deposition rates in liquids of elongated rock particles. MIAB. Mining Inf. Anal. Bull. 2023;(12-1):5—16. [In Russ]. DOI: 10.25018/0236_1493_2023_121_0_5.

Issue number: 12
Year: 2023
Page number: 5-16
ISBN: 0236-1493
UDK: 622.5:621.928.46
DOI: 10.25018/0236_1493_2023_121_0_5
Article receipt date: 15.05.2023
Date of review receipt: 09.11.2023
Date of the editorial board′s decision on the article′s publishing: 10.11.2023
About authors:

Afanas’ev A. I.1, Dr. Sci. (Eng.), professor of the department of technical mechanics, http:// orcid.org/0000−0002−7869−9208 Е-mail: anatoly.afanasiev1948@yandex.ru
Potapov V. Ya.1, Dr. Sci. (Eng.), professor of the department of mining mechanics, http:// orcid.org/0009−0003−0305−5349, Е-mail: 2с1@inbox.ru
Uporov S. A.1, Cand. Sci. (Eng.), vice-rector for educational and methodological complex, http://orcid.org/0009−0008−8897−1480, Е-mail: UporovSA@m.ursmu.ru,
Potapov V. V.1, Cand. Sci. (Eng.), associate professor of the department of mining, http:// orcid.org/0000−0003−4862−523X Е-mail: actusprimo@gmail.com
1 Ural State Mining University, Russia, 620144, Yekaterinburg city, Kuibyshev st. 30.


For contacts:

1. Merinov N. F. Patterns of movement of mineral grains in a gravitational field. Enrichment of ores. 2006, no. 4, pp. 24–29. [In Russ].

2. Penkov P. M., Morozov Yu. P., Prokopyev S. A. Influence of viscosity resistance on the final velocles of stressed motion of particles. MIAB. Mining Inf. Anal. Bull. 2022, no. 11–1, pp. 119– 126. [In Russ]. DOI: 10.25018/0236149320221110119.

3. Filippov V. E., Lebedev I. F., Eremeeva N. G., Gavriliev D. M. Experimental studies of the behavior of mineral particles in hydroaerodynamic environment. Ed. A. I. Matveev, Novosibirsk, Academic Publishing House “Geo”, 2013, 85 p.

4. Tarasov V. K., Volgina L. V. Definition of hydraulic size solid particle non spherical form. Bulletin MSUCE. 2011, no. 8. pp. 111–115. [In Russ].

5. Matveev I. A., Matveev A. I., Grigoriev Yu. M., Eremeeva N. G. Experimental and theoretical study of the movement of particles in a water stream. MIAB. Mining Inf. Anal. Bull. 2018, no. 11, pp. 171–177. [In Russ]. DOI: 10.25018/0236−1493−2018−11−0-171−177.

6. Leonov R. E., Sosnovskaya D. V. S-model of ore purification in a thickener. MIAB. Mining Inf. Anal. Bull. 2022, no. 11−1, pp. 190–198. [In Russ]. DOI: 10.25018/0236−1493−2022−111−0-190.

7. Leonov R. E., Sosnovskaya D. V. Sedimentation of ore particles in the pulp. Materials of the International Scientific and Practical Conference, Yekaterinburg, April, 4 — 13, URSMU. 2022, pp. 445–446. [In Russ].

8. Starostin A. G., Fedotova O. A., Kobeleva A. R. Wastewater treatment from fine particles on a hydrocyclone. Vestnik Permskogo natsionalnogo issledovatelskogo politekhnicheskogo universiteta. 2020, no 1, pp. 99–112. [In Russ]. DOI: 10.15593/2224−9400/2020.1.08.

9. Ozan Kökkılıç, Ray Langlois, Kristian E. Waters. A design of experiments investigation into dry separation using a Knelson Concentrator. Minerals Engineering. 2015, vol. 72, pp. 73–86. DОI: 10.1016/j.mineng.2014.09.025.

10. Meng Zhou, Ozan Kökkılıç, Raymond Langlois, Kristian E. Waters. Size-by-size analysis of dry gravity separation using a 3-in. Knelson Concentrator. Minerals Engineering. 2016, vol. 91, pp. 42–54. DOI: 10.1016/j.mineng.2015.10.022.

11. Ghaffari A., Farzanegan A. An investigation on laboratory Knelson Concentrator separation performance: Part 1: Retained mass modelling. Minerals Engineering. 2017, vol. 112, pp. 57–67. DOI: 10.1016/j.mineng.2017.07.006.

12. Fatahi M. R., Farzanegan A. DEM simulation of laboratory Knelson concentrator to study the effects of feed properties and operating parameters. Advanced Powder Technology. 2017, vol. 28, pp. 1443−1458. DOI: 10.1016/j.apt.2017.03.011.

13. Divyamaan W., Prashant G., VedPrakash M. Chapter 7. Liquid–Solid Processes. Multiphase Flows for Process Industries. Fundamentals and Applications. 2022, vol. 2, pp. 359−475. DOI: 10.1002/9783527812066.

14. Potapov V. Ya., Makarov V. N., Anokhin P. M., Potapov V. V., Kostyuk P. A. Stepanenkov D. D. Study of aerodynamic characteristics of particles with windage in order to create pneumatic transport systems. MIAB. Mining Inf. Anal. Bull. 2017. no. 5, pp. 136–144. [In Russ].

15. Morozov Yu. P., Pen’kov P. M., Dmitriev V. T. Investigation of a method for increasing the technological parameters of centrifugal separation with pneumatic turbulence. Izvestiya vysshikh uchebnykh zavedenii. Gornyi zhurnal. 2020, no. 4, pp. 62–69. [In Russ]. DOI: 10.21440/0536−1028−2020−4-62−69.

16. Intogarova T. I., Valieva O. S., Morozov Yu. P., Tropnikov D. L. Improvement of the flotation process based on the enrichment of foam products in narrowing troughs. Gornyi zhurnal. 2019, no. 2, pp. 48–51. [In Russ]. DOI: 10.17580/gzh.2019.02.09.

17. Prokop’ev S. A., Pelevin A. E., Morozov Iu. P. Some features of mass transfer at spiral devices. Izvestiya vysshikh uchebnykh zavedenii. Gornyi zhurnal. 2018, no. 7, pp. 67–74. DOI: 10.21440/0536−1028−2018−7-67−74.

18. Kosarev N. P., Makarov V. N., Ugol’nikov A. V., Makarov N. V., Dyldin G. P. Mine aerology of dust aerosols in conditions of hydro vortex coagulation. Izvestiya Ural’skogo gosudarstvennogo gornogo universiteta. 2020, no. 4 (60), pp. 155–165. [In Russ]. DОI: 10.21440/2307−2091−2020−4-155−165.

19. Ji Li, Kuang Shibo, Yu Aibing. Numerical investigation of hydrocyclone feed inlet configurations for mitigating particle misplacement. Industrial and Engineering Chemistry Research. 2019, vol. 58, no. 36, pp. 16823–16833. DOI: 10.1021/acs.iecr.9B01203.

20. Anjos R. P., Andrade Medrono R. D., Suiden Klein T. Evaluation of turbulence models for single-phase cfd calculations of a liquid-liquid hydrocyclone using open foam. Turbulence log. 2021, vol. 22, no. 2, pp. 79–113. DOI: 10.1080/14685248.2020.1846050.

21. Geldenhuys S., Thiago Souza T., Filho L. L., Deglon D. Process evaluation of an iron ore operation using the floatability component model. Minerals. 2021, vol. 11, no. 6, p. 589. DOI: 10.3390/min11060589.

22. Yang Y., Ge L., He Y., Xie W., Ge Z. Mechanism and fine coal beneficiation of a pulsating airflow classifier. Int J Coal Prep Util. 2019, vol. 39(1), pp. 20–32. https://doi. org/10.10 80/19392699.2017.1288622.7.

Our partners

Подписка на рассылку

Раз в месяц Вы будете получать информацию о новом номере журнала, новых книгах издательства, а также о конференциях, форумах и других профессиональных мероприятиях.