Mathematical modeling of grain fractionation process in pneumogravity separator
DOI:
https://doi.org/10.31734/agroengineering2021.25.012Keywords:
aspiration channel, pneumatic gravity separator, grain, variable speed, trajectory, grain rotation, sailability coefficientAbstract
The work is devoted to development of the mathematical models of grain motion as a part of grain material components (GMC) in the separator’s aspiration channel. The trajectories of grain movement in the aspiration channel of the separator with different values of sailability coefficients are obtained. The equation of grain motion under the action of additional forces is obtained, which allows determining dependence of the material velocity in the GMC layer on the angular velocity of the grain, the coefficient of sail (sail), geometric parameters of the aspiration channel. The process of grain material movement in the separator’s aspiration channel is substantiated, which allows determining the rational parameters of GMC introduction into the aspiration channel of the separator and its uniform distribution in the channel with the subsequent possibility of its fractionation. The dependence of the function of the grain flow rate in the aspiration channel of the separator is obtained, which allows determining the parameters of distribution of the grain material by the cross-sectional area of the separator aspiration channel. The absolute velocity of grain material in the aspiration channel of the separator is estimated on the basis of a mathematical model built by analogy with the hydrodynamic model, which in its turn allows analyzing the recombination of grains by the thickness of the grain material layer. According to the established mathematical models, the graphical dependences of the absolute velocity of grain on time, the trajectory of the mass of particles, the calculated trajectories of particles of grain material, which are fed into the pneumatic channel under constant initial conditions. A mathematical model has been developed that differs from the known as it reproduces the action of previously unaccounted for factors: the unevenness of the velocity field, the action of transverse forces such as Zhukovsky and Magnus, the density of grains. Analysis of the grain trajectories made it possible in the first approximation to estimate the possibility of separation of grain material components in downward - countercurrent grain movement in the vertical channel, as well as to establish the influence of individual forces and pneumatic separation modes on the magnitude of branching trajectories. It was found that to compensate or prevent the negative impact of transverse forces, it is necessary to ensure a uniform air flow in the cross section of the pneumatic channel or artificially change the air velocity distribution in the channel so that the maximum air speed in the channel was in the wall area.
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