MATHEMATICAL MODELING OF THE BULK MATERIALS MIXING PROCESS IN A DRUM-BLADE MIXER

Abstract

A mathematical model of the bulk materials mixing process in a gravity-flow apparatus with additional mixing elements isproposed. The mixer includes a cylindrical housing rotating around a horizontal axis, inside of which there are steps with working blades and annular parti-tions, which provide both direct movement of material along the axis of rotation from the loading nozzle to the receiving hopper, and partial movement of material in the opposite direction, which makes it possible to increase the time stay of the mixture inside the device. To simulate the mixing process, the method of discrete elements is used, which is based on the representation of a bulk material in the form of a set of representative volumes containing a large number of particles in-teracting with each other and exposed to the action of the working bodies of the mixer and external force fields. The representative volumes sizes and masses are proportional to the sizes and masses of the particles of the mixture components. Their interaction includes the force of inelastic impact directed along the line connecting their centers, and the force of tangentialfriction lying in the plane perpendicular to this line and directed against the relative velocity projection onto the plane. The absolute values of these forces are proportional to the weight of the representative volumes, exponentially decrease when the centers of mass are removed from each other by a distance ex-ceeding the sum of their sizes, and exponentially increase when the centers approach, causing mu-tual overlap of the representative volumes. The force effect on the representative volumes when it comes into contact with the structural elements of the mixer is simulated in a similar way. To check the adequacy of the proposed model, full-scale experiments were carried out on mixing rapeseed and millet in the studied device. Comparison of the calculation results according to the proposed model with the data of experimental studies indicates their satisfactory convergence.