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.ru
T. I. Yushina, Head of the Department of Mineral Processing, Candidate of Technical Sciences, Associate Professor

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.

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