Improving the mechanical-mathematical model of pneumatic vibration centrifugal fractionation of grain materials based on their density

Abstract

This paper has substantiated the mechanical-mathematical modeling of the process of fractionation of grain material into fractions. It has been established that this could optimize the process parameters and would make it possible to design new or improve existing working surfaces of centrifugal separators. A mechanical-mathematical model of the pneumatic vibratory centrifugal separation of grain material by density has been improved. This research is based on the method of hydrodynamics of multiphase media. The improved mechanical-mathematical model takes into consideration the interaction between the discrete and continuous phases of grain material by introducing conditions of interaction at the interface of these phases. In the hydrodynamic modeling of the movement of the circular layer of seeds, the coefficient of dynamic viscosity of discrete and continuous phases was taken into consideration. It was established that the pneumatic vibratory centrifugal separation process parameters are critically affected by the circular frequency of rotation of the cylindrical working surface, the frequency and amplitude of its oscillations. As well as such process characteristics as the airflow rate, dynamic viscosity coefficient, the average thickness of a grain material layer, and the mean density of its particles. Rational values for the technical parameters of the grain material pneumatic vibratory centrifugal fractionation process in terms of density have been determined by using the improved mechanical-mathematical model. The amplitude and oscillation frequency of the working surface are in the ranges A=(35…50)·10–5 m, ω=15.0...15.6 rad/s. The circular rotation frequency of the working surface, ω=24...25 rad/s. The airflow rate, V=2 m/s. It was established that using the improved mechanical-mathematical model of fractionation makes it possible to improve the performance of a pneumatic vibratory centrifugal separator by 9 %. At the same time, the effectiveness of grain material separation could reach 100 %.