Simulation mathematical model of the mixing process of bulk components in the mixer
https://doi.org/10.20914/2310-1202-2019-2-13-21
Abstract
The developed simulation model allows computer experiments on mixing components in which the parameters of the components of the mixture or mixer are changed, the nature of the influence of the parameter is established and recommendations for choosing the optimal values of the parameter are given. The model of the mixing process takes into account the size, shape and rheological properties of the components of the mixture, as well as the interaction of the bulk material with the working surfaces of the mixer (blades, blade struts, shafts, housing). The simulation mathematical model of the mixer has a high spatial resolution for the correct reproduction of the interaction of particles in the mixing process. In the framework of the finite element approximation, the bulk material is represented as a set of elements. The particle dynamics method was used to model the mechanical behavior of the mixture. Modeling is performed in three-dimensional Cartesian space. The state of each element is defined by six variables: the coordinates of its center and the velocity components. The solution of this system of differential equations of the second order are the functions that determine the trajectories of motion of the elements and allow to evaluate the efficiency of the mixing process. To solve differential equations of this kind, the second – order numerical method-Runge-Kutta is used. A computer program in the Object Pascal language in the Borland Delphi 7 integrated programming environment has been developed to implement the calculation according to the above formulas and to make it easier to conduct a series of computer experiments. The developed mathematical model of the process of mixing of bulk components allows to choose rational technological modes of mixing, which makes it possible to increase the homogeneity of mixing up to 98 %, and to calculate the kinematic mode of the mixing process in the mixer by creating a "quasi-weight" hydrodynamic mixing mode and a significant acceleration of the mixing process.
About the Authors
A. N. Ostrikov
Voronezh state university of engineering technologies
Russian Federation
Dr. Sci. (Engin.), professor, technology of fats, processes and apparatuses of chemical and food production department, Revolution Av., 19 Voronezh, 394036, Russia
Russian Federation
Dr. Sci. (Engin.), professor, technology of fats, processes and apparatuses of chemical and food production department, Revolution Av., 19 Voronezh, 394036, Russia
L. N. Frolova
Voronezh state university of engineering technologies
technology of fats, processes and devices of chemical and food production department, Revolution Av., 19 Voronezh, 394036, Russia
technology of fats, processes and devices of chemical and food production department, Revolution Av., 19 Voronezh, 394036, Russia
A. I. Aleksandrov
Voronezh state university of engineering technologies
extern, technology of fats, processes and devices of chemical and food production department, Revolution Av., 19 Voronezh, 394036, Russia
extern, technology of fats, processes and devices of chemical and food production department, Revolution Av., 19 Voronezh, 394036, Russia
V. V. Posmetiev
Affordable Robotics LLC
Cand. Sci. (Phys.-Math.), ,, Timiryazev St., 8, Voronezh, 394087, Russia
Cand. Sci. (Phys.-Math.), ,, Timiryazev St., 8, Voronezh, 394087, Russia
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Review
For citations:
Ostrikov A.N., Frolova L.N., Aleksandrov A.I., Posmetiev V.V. Simulation mathematical model of the mixing process of bulk components in the mixer. Proceedings of the Voronezh State University of Engineering Technologies. 2019;81(2):13-21. (In Russ.) https://doi.org/10.20914/2310-1202-2019-2-13-21
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