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ArticleName Improved deterministic physico-mathematical model of gas-dynamic separation of granular materials
DOI 10.17580/tsm.2023.05.01
ArticleAuthor Tyukin A. P.

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:


Previously, the author developed and researched the process of gas-dynamic separation. The author also developed a mathematical model of the above process. The model was then optimized. It simulates the dynamic motion of a particle that is following a ballistic path while moving through gas after it has left the acceleration channel and when it is moving in a plane turbulent gas jet and starts to lower under gravity. This last idea is the key one. The model enables to set the mean sphericity factor and diameter dispersions, as well as the friction coefficient of each component of the mixture. It is possible to set the fall height of particles after they exit from the acceleration channel, the free fall acceleration (such set-up capability is necessary for calculating the parameters of gas-dynamic separation of the lunar regolith in a tight low-pressure chamber, or the Mars regolith in a similar chamber or in the atmosphere) and the variable cross-section of the acceleration channel. At the first stage, the programme calculates the current gas velocity in the acceleration channel. Once the particle has passed a distance exceeding the specified length of the acceleration channel, the programme switches over and starts to calculate the parameters of the particle moving along the ballistic path. The model of a plane turbulent jet in the farfield was chosen as the basic model, the conditions of which are satisfied with high accuracy in the problem under consideration. The author carried out mathematical transformations based on hydrodynamics laws and presented a visualization showing the distribution of velocities and directions in which gas moves through the space in front of the acceleration channel. The shape of the plane turbulent jet is shown, and the expected gas motion paths are confirmed in each point of the space. The physico-mathematical model is still iterative in nature, as it recalculates the dynamic gas pressure on the particle at equal intervals of the horizontal distance, as well as the position of the particle in space allowing for the changing horizontal and vertical acceleration. It was established that after leaving the acceleration channel, in which lighter particles acquire, on average, a higher speed due to lower inertia, each particle moves through the medium and the horizontal component of its velocity decreases as the result of the medium resistance. As it is free flying in the plane turbulent jet and further through the medium, the lighter particle slows down more rapidly and can be caught into the corresponding receiving container at a closer distance than a heavy one, as it has less inertia. This paper proposes the following fundamental options for implementing the technology of gas-dynamic separation of mineral and metallized materials, including those designed for rarefied environments. Problems are formulated for the subsequent research stages concerning the calibration of the physico-mathematical model based on deterministic and stochastic components.

keywords Hydrodynamics, gas dynamics, dry separation, gas, concentration, minerals, metals, rarefaction, vacuum, pressure, Moon, Mars, regolith

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