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Mathematical model of melt flow channel granulator

https://doi.org/10.20914/2310-1202-2016-1-11-15

Abstract

Granulation of carbohydrate-vitamin-mineral supplements based on molasses is performed at a high humidity (26 %), so for a stable operation of granulator it is necessary to reveal its melt flow pattern. To describe melt non-isothermal flow in the granulator a mathematical model with following initial equations: continuity equation, motion equation and rheological equation – was developed. The following assumptions were adopted: the melt flow in the granulator is a steady laminar flow; inertial and gravity forces can be ignored; melt is an incompressible fluid; velocity gradient in the flow direction is much smaller than in the transverse direction; the pressure gradient over the cross section of the channel is constant; the flow is hydrodynamically fully developed; effects impact on the channel inlet and outlet may be neglected. Due to the assumptions adopted, it can be considered that in this granulator only velocity components in the x-direction are significant and all the members of the equation with the components and their derivatives with respect to the coordinates y and z can be neglected. The resulting solutions were obtained: the equation for the mean velocity, the equation for determining the volume flow, the formula for calculating of mean time of the melt being in the granulator, the equation for determining the shear stress, the equation for determining the shear rate and the equation for determining the pressure loss. The results of calculations of the equations obtained are in complete agreement with the experimental data; deviation range is 16–19 %. The findings about the melt movement pattern in granulator allowed developing a methodology for calculating a rational design of the granulator molding unit.

About the Authors

A. A. Kiselev
Voronezh state university of engineering technologies
Russian Federation
applicant, Department of technlogy of bread, confectionery, macaroni and grain processing industries. phone (473) 255–65–11


A. A. Anikin
Voronezh state university of engineering technologies
Russian Federation
applicant, Department of technlogy of bread, confectionery, macaroni and grain processing industries. phone (473) 255–65–11


Y. V. Chernukhin
Voronezh state university of engineering technologies
Russian Federation
associate professor, Department of technlogy of bread, confectionery, macaroni and grain processing industries. phone (473) 255–65–11


References

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2. 2 Ostrikov A.N., Abramov O.V., Vasilen ko V.N., Popov A.S. Matematicheskoe modelirovanie techeniya anomal’no-vyazkikh sred v kanalakh ekstrudera [Mathematical modeling of abnormally viscous media channels extruders]. Voronezh, Izdatel’stvo VGU, 2010. 237 p. (In Russ.).

3. 3 Michaeli W. Extrusion heads for plastics and rubber. The design and technical calculations. Saint-Petersburg, Profession, 2007. 472 p.

4. 4 Rauwendaal C. Polymer extrusion: 2, repr. ed. Munich, Hanser, Cop. 1990. 568 p.

5. 5 Schenkel G. Zur Extrusion von Kunststoffen aus Rechteck-Kanalen. Kunststoffe, 1981, no. 74 (8), pp. 479–484.


Review

For citations:


Kiselev A.A., Anikin A.A., Chernukhin Y.V. Mathematical model of melt flow channel granulator. Proceedings of the Voronezh State University of Engineering Technologies. 2016;(1):11-15. (In Russ.) https://doi.org/10.20914/2310-1202-2016-1-11-15

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ISSN 2226-910X (Print)
ISSN 2310-1202 (Online)