The effect of the filling degree of the tumbling mill chamber on the bifurcation value of the froude number

Keywords: tumbling mill, bifurcation value, Froude number, self-excitation of self-oscillations, filling degree, two-fraction loading

Abstract

The influence of the filling degree of the drum chamber on the bifurcation value of the Froude number in the case of self-excitation of self-oscillations of a two-fraction granular charge with a minimum swing is considered. Such a pulsating mode of the charge movement is used in the self-oscillating grinding process in a tumbling mill. The coarse fraction that simulated the milling bodies consisted of spherical particles of an incoherent granular material with a relative size in the chamber ψb=0.00733. The fine fraction, simulating the material to be ground, was cement with a relative particle size ψm≈0.092∙10-3. The value of the adopted analogue of the kinematic viscosity of the two-fraction granular loading approached the value of 10-3 m2/s. The main variable factor in experimental studies was the filling degree of the drum chamber with loading at rest κb=0.25, 0.35, and 0.45. An additional factor was the degree of filling the gaps between the spherical particles of the coarse fraction with particles of the fine fraction κb=0, 0.25, 0.5, and 1. The method of visual analysis through the transparent end wall of the chamber of transient processes of the loading behavior with a smooth change and fixation of the velocity was applied. The bifurcation minimum value of the rotation speed was recorded, at which the steady-state circulation mode of the load movement turns into a transient pulsation one with a minimum swing. A decrease in the bifurcation values of the Froude number Frb on the cylindrical surface of the chamber with an increase in κb has been established. An increase in the intensity of the decrease in Frb with an increase in κm was revealed. The recorded effect is due to an increase in the connected properties of a two-fraction loading during self-excitation of self-excited oscillations with an increase in κb and κm. The numerical values of the boundaries of the range of bifurcation values of the Froude number for a tumbling mill Frb=0.0484–1.17 have been determined. The obtained Frb range corresponds to the Reynolds value in the range Re=40–197. The maximum Frb value is obtained with coarse grinding. An increase in the likelihood of self-excitation of self-oscillations of the intra-chamber loading with a decrease in the fineness of grinding was revealed

Downloads

Download data is not yet available.

Author Biographies

Kateryna Deineka, National University of Water and Environmental Engineering

PhD

Technical College

Yurii Naumenko, National University of Water and Environmental Engineering

Doctor of Technical Sciences, Associate Professor

Department of Construction, Road, Reclamation, Agricultural Machines and Equipment

Tamara Myronenko, National University of Water and Environmental Engineering

Highest Category Lecturer

Technical College

References

Bouchard, J., LeBlanc, G., Levesque, M., Radziszewski, P., Georges-Filteau, D. (2019). Breaking down energy consumption in industrial grinding mills. CIM Journal, 10 (4), 157–164. doi: https://doi.org/10.15834/cimj.2019.18

Góralczyk, M., Krot, P., Zimroz, R., Ogonowski, S. (2020). Increasing Energy Efficiency and Productivity of the Comminution Process in Tumbling Mills by Indirect Measurements of Internal Dynamics – An Overview. Energies, 13 (24), 6735. doi: https://doi.org/10.3390/en13246735

Deineka, K., Naumenko, Y. (2019). Revealing the effect of decreased energy intensity of grinding in a tumbling mill during self-excitation of auto-oscillations of the intrachamber fill. Eastern-European Journal of Enterprise Technologies, 1 (1 (97)), 6–15. doi: https://doi.org/10.15587/1729-4061.2019.155461

Deineka, K. Y., Naumenko, Y. V. (2018). The tumbling mill rotation stability. Scientific Bulletin of National Mining University, 1, 60–68. doi: https://doi.org/10.29202/nvngu/2018-1/10

Lv, J., Wang, Z., Ma, S. (2020). Calculation method and its application for energy consumption of ball mills in ceramic industry based on power feature deployment. Advances in Applied Ceramics, 119 (4), 183–194. doi: https://doi.org/10.1080/17436753.2020.1732621

Deineka, K., Naumenko, Y. (2019). Establishing the effect of a decrease in power intensity of self-oscillating grinding in a tumbling mill with a reduction in an intrachamber fill. Eastern-European Journal of Enterprise Technologies, 6 (7 (102)), 43–52. doi: https://doi.org/10.15587/1729-4061.2019.183291

Deineka, K., Naumenko, Y. (2020). Establishing the effect of decreased power intensity of self-oscillatory grinding in a tumbling mill when the crushed material content in the intra-chamber fill is reduced. Eastern-European Journal of Enterprise Technologies, 4 (1 (106)), 39–48. doi: https://doi.org/10.15587/1729-4061.2020.209050

Deineka, K., Naumenko, Y. (2021). Establishing the effect of a simultaneous reduction in the filling load inside a chamber and in the content of the crushed material on the energy intensity of self-oscillatory grinding in a tumbling mill. Eastern-European Journal of Enterprise Technologies, 1 (1 (109)), 77–87. doi: https://doi.org/10.15587/1729-4061.2021.224948

Seiden, G., Thomas, P. J. (2011). Complexity, segregation, and pattern formation in rotating-drum flows. Reviews of Modern Physics, 83 (4), 1323–1365. doi: https://doi.org/10.1103/revmodphys.83.1323

Lee, W. B., Widjaja, E., Heng, P. W. S., Chan, L. W. (2020). The effect of rotation speed and particle size distribution variability on mixability: An avalanche rheological and multivariate image analytical approach. International Journal of Pharmaceutics, 579, 119128. doi: https://doi.org/10.1016/j.ijpharm.2020.119128

Trpělková, Ž., Hurychová, H., Kuentz, M., Vraníková, B., Šklubalová, Z. (2020). Introduction of the energy to break an avalanche as a promising parameter for powder flowability prediction. Powder Technology, 375, 33–41. doi: https://doi.org/10.1016/j.powtec.2020.07.095

Chen, J., Krengel, D., Matuttis, H.-G. (2021). Experimental study of particle shape dependence of avalanches inside a rotating drum. EPJ Web of Conferences, 249, 06001. doi: https://doi.org/10.1051/epjconf/202124906001

Preud’homme, N., Opsomer, E., Vandewalle, N., Lumay, G. (2021). Effect of grain shape on the dynamics of granular materials in 2D rotating drum. EPJ Web of Conferences, 249, 06002. doi: https://doi.org/10.1051/epjconf/202124906002

Han, R., Feng, J., Zhang, Y., Yang, H., Zivkovic, V., Li, R. (2021). Numerical simulation of avalanche propagation dynamics in a rotating drum. Powder Technology, 380, 199–204. doi: https://doi.org/10.1016/j.powtec.2020.11.016

Salinas, V., Quiñinao, C., González, S., Castillo, G. (2021). Triggering avalanches by transverse perturbations in a rotating drum. Scientific Reports, 11 (1). doi: https://doi.org/10.1038/s41598-021-93422-2

Han, R., Xin, Y., Wang, Z., Li, R., Yang, H., Chen, Q. (2021). Numerical simulation of particle velocity and coordination number under the slumping regime in a rotating drum. Powder Technology, 394, 775–781. doi: https://doi.org/10.1016/j.powtec.2021.09.021

asper, J. H., Magnanimo, V., de Jong, S. D. M., Beek, A., Jarray, A. (2021). Effect of viscosity on the avalanche dynamics and flow transition of wet granular matter. Particuology, 59, 64–75. doi: https://doi.org/10.1016/j.partic.2020.12.001

Pachón-Morales, J., Perré, P., Casalinho, J., Do, H., Schott, D., Puel, F., Colin, J. (2020). Potential of DEM for investigation of non-consolidated flow of cohesive and elongated biomass particles. Advanced Powder Technology, 31 (4), 1500–1515. doi: https://doi.org/10.1016/j.apt.2020.01.023

Pachón-Morales, J., Colin, J., Casalinho, J., Perré, P., Puel, F. (2020). Flowability characterization of torrefied biomass powders: Static and dynamic testing. Biomass and Bioenergy, 138, 105608. doi: https://doi.org/10.1016/j.biombioe.2020.105608

Li, R., Xiu, W., Liu, B., Zheng, G., Yang, H. (2021). Velocity distribution of rice particles in a rotating drum. Powder Technology, 386, 394–398. doi: https://doi.org/10.1016/j.powtec.2021.03.050

Moiseev, N. N. (2003). O needinstvennosti vozmozhnyh form ustanovivshihsya techeniy tyazheloy zhidkosti pri chislah Fruda, blizkih k edinice. Vol. 1. Gidrodinamika i mehanika. Optimizaciya, issledovanie operaciy i teoriya upravleniya. Moscow: Taydeks Ko, 115–123. Available at: http://www.ccas.ru/manbios/mois_trudi_v1.pdf

Deineka, K. Yu., Naumenko, Yu. V. (2016). The tumbling mill intrachamber filling self-oscillation parameters. Vibrations in engineering and technology, 3 (83), 29–34. Available at: http://vibrojournal.vsau.edu.ua/files/pdfa/3040.pdf

Deineka, K., Naumenko, Yu. (2018). Influence of structure of polydisperse fill of rotating drum on self-oscillation. Vibrations in engineering and technology, 3 (90), 75–82. Available at: http://vibrojournal.vsau.edu.ua/files/pdfa/4372.pdf

Naumenko, Y., Deineka, K. (2017). The rotating chamber degree of filling effect on granular fill selfoscillation. Vibrations in engineering and technology, 4 (87), 65–69. Available at: http://vibrojournal.vsau.edu.ua/files/pdfa/4044.pdf


👁 86
⬇ 68
Published
2021-12-22
How to Cite
Deineka, K., Naumenko, Y., & Myronenko, T. (2021). The effect of the filling degree of the tumbling mill chamber on the bifurcation value of the froude number. Technology Transfer: Fundamental Principles and Innovative Technical Solutions, 21-24. https://doi.org/10.21303/2585-6847.2021.002170