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 BENEFICATION ArticleName Mathematical modelling of gas-dynamic separation processes DOI 10.17580/tsm.2020.07.01 ArticleAuthor Tyukin A. P., Yushina T. I. ArticleAuthorData National University of Science and Technology MISiS, Moscow, Russia: A. P. Tyukin, Applicant for a Doctoral Degree in Engineering, Department of Mineral Processing, Candidate of Technical Sciences, e-mail: TukinAP@yandex.ruT. I. Yushina, Head of the Department of Mineral Processing, Candidate of Technical Sciences, Associate Professor Abstract In gas dynamics, mathematical models are usually built to tackle highly specific applied problems which are mostly related to aircrafts and their aerodynamics. A specialized model is required to design a gas-dynamic separator for bulk solids. The purpose of separation was formulated, and the initial parameters of solid particles, gas and acceleration channel were defined. The final (resultant) concentration parameters were specified. They include concentrate output, concentration of the target component in the products, recovery of the valuable component into the concentrate, Hancock – Luyken criterion. Selecting the length of the acceleration channel and the linear gas speed to reach the best separation performance constitutes a practical task for the gas-dynamic separation model. The paper describes the derivation of a particle acceleration equation that forms the basis of the model. Possible solutions were analyzed and the optimum one was chosen – i.e. sampling. The paper describes how the model functions. The first module (‘Acceleration’) calculates the average particle speeds for each of the two separated components at every point on the acceleration path. The second module (‘Calculate SD of speed’) calculates the standard deviation of the particle speeds at the exit from the acceleration channel as a function of their properties, such as weight, diameter and spherical shape factor. The third module (‘Trapping’) calculates the lengthwise distribution of the product compositions after the mixture has exited from the acceleration channel and the particles have fallen down following a ballistic path. The fourth module (‘Achievable Performance’) calculates the achievable concentration performance (based on the Hancock – Luyken criterion) for different lengths of the acceleration channel while selecting optimum operating parameters. Using this mathematical model, it was calculated that the maximum achievable separation performance for a mixture of –0.4+0.2 mm fayalite and ilmenite within the acceleration channel length range of 200 to 1,000 mm is 0.25 to 0.27. The authors suggest areas for prospective research. The model can be applied to design gas-dynamic separators or their cascades. keywords Gravity concentration, gas-dynamic separator, aerodynamic flow, mathematical model, regolith, lunar soil, ilmenite References 1. Hancock R. T. Efficiency of classificating. Engineering and Mining Journal. 1920. No. 110. pp. 237–241.2. Luyken W. Determining the maximum process and economic efficiency of the mineral concentration process. Moscow : GONTI, 1932. 121 p.3. Akkerman Yu. E., Bukaty G. B., Kizevalter B. V. Reference book on ore concentration. Vol. 1. Ore preparation. Moscow : Nedra, 1982. 367 p.4. Dimitrioua I. Planar incompressible Navier-Stokes and Euler equations: A geometric formulation. Physics of Fluids. 2017. Vol. 29, No. 11. Id. 117101.5. Tyukin A. P. Developing a combination concentration process for granular material involving aerodynamic and shock separation. PhD dissertation. Moscow : MISiS, 2013. 151 p.6. Shelquist R. An Introduction to Air Density and Density Altitude Calculations. Available at: https://wahiduddin.net/calc/density_altitude.htm.7. Smits A. J., Dussauge J.-P. Turbulent shear layers in supersonic flow. New York : Springer, 2006.8. Liu M. B., Liu G. R., Zhou L. W., Chang J. Z. Dissipative particle dynamics (DPD): An overview and recent developments. Archives of Computational Meth ods in Engineering. 2015. Vol. 22, No. 4. pp. 529–556.9. Ye T., Pan D., Huang C., Liu M. Smoothed particle hydrodynamics (SPH) for complex fluid flows: Recent developments in methodology and applications. Physics of Fluids. 2019. Vol. 31, No. 1.10. Planovskiy A. N., Ramm V. M., Kagan S. Z. Processes and equipment of chemical technology. 2nd revised edition. Moscow : Gosudarstvennoe nauchnotekhnicheskoe izdatelstvo khimicheskoy literatury, 1962. 845 p.11. Cook L. W., Mishra A. A., Jarrett J. P., Willcox K. E., Iaccarino G. Optimization under turbulence model uncertainty for aerospace design. Physics of Fluids. 2019. Vol. 31, No. 10.12. Wachs C. A., Frigaard I. A. Inline motion and hydrodynamic interaction of 2D particles in a viscoplastic fluid. Physics of Fluids. 2018. Vol. 30.13. Ignatova A. M., Ignatov M. N. Developing the lunar surface through the use of regolith. Mezhdunarodnyy zhurnal eksperimentalnogo obrazovaniya. 2013. No. 11-2. pp. 101–110. Language of full-text russian Full content Buy
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