Theoretical determination of the regularities of the plane motion of the grain in the non-uniform air flow of the horizontal pneumatic channel of the aerodynamic separator

Abstract

Annotation Purpose. Improving the mathematical description of the motion of the dynamics of grain motion in the horizontal non-uniform air flow of aerodynamic separators. Methods. Theoretical determination of the regularities of the plane motion of the grain in an uneven air flow determines the analytical method of research based on the compilation and analysis of the equations of motion of the grains in the form of a sphere in the air flow of the horizontal pneumatic channel of the separator. The mathematical model is formulated by obtaining differential equations of motion of the components of the grain material, which are represented by a material point and a complex indicator of aerodynamic properties – the coefficient of vitality (sail). Results. The flat motion of the grain in the uneven air flow of the horizontal pneumatic channel of the aerodynamic separator through the sieve surface with cracks in the axial direction of air is absorbed. The obtained equation of grain motion during horizontal air flow allows to determine the dependence of grain velocity in air-grain medium on a number of factors: geometric parameters of the separator, feed angle, initial kinematic mode of the material, and grain vitality coefficient. Conclusions 1. An improved mathematical model of the dynamics of the motion of a solid particle in a horizontal air flow is formulated, which differs from those known in that it reproduces the action of unaccounted factors (non-uniformity of the velocity field, action of lateral forces, material concentration). It is established that the change of the sign of the air flow gradient in the cross section leads to a change in the direction of the trajectories of the light fraction KZM, which increases the completeness of the removal of the feed fraction to 90% and increases the separation of the seed fraction by 15-20%. up to 2-3%. Changing the diagram of the air velocity in the horizontal channel increases the velocity in the wall area, which increases the clarity of the division by 18-24%. 2. The solution of the system of nonlinear differential equations with initial conditions is performed in the MathCad software environment in the form of grain motion trajectories in horizontal air flow, which allows calculating grain motion trajectories differing in vitality coefficients and determining rational values of pneumatic gravity separators. Keywords: variable air velocity, trajectory, lateral force, fractions, horizontal air flow, fractionation process, grain.