Kemerovo, Kemerovo, Russian Federation
A method of modeling the continuous process of the mixing of bulk materials on the basis of cybernetic analysis with some elements of automatic control theory (ACT) [6, 9] has been considered. In this case, a mixing unit (MU) is represented in the form of a dynamic system, which is characterized by the known topology of the motion of material flows and subjected to various external disturbances. The two developed mathematical models allow us to determine the degree of the smoothening of input material flow fluctuations from volumetric dosers by the mixers incorporated into a MU. The obtained numerical values of smoothability indicate that it is reasonable to equip the studied mixers of new design with volumetric dosers. This allows us to meet the requirements to MUs from both the engineering and economical viewpoints.
centrifugal mixer, time-and-frequency analysis, bulk materials, combined food products, modeling, cybernetic analysis
INTRODUCTION
The contemporary state of the market of food industry equipment is characterized by a considerable increase in the demand for machines and apparatuses that allow the production of high-quality food products of increased nutritional value (enriched with vitamins and biologically essential components) at low expenditures. In particular, the population should have new combined food products that compensate the deficient of different food components and micronutrients in its ration due to considerable ecological disturbances in different regions of Russia and other countries.
Since the content of many food additives in the major product is small (1% and lower), the key problem consists in their uniform distribution over the entire volume. Using the results of studies, it has been revealed that continuous centrifugal mixers (CCMs) [2, 5] characterized by a high intensity of mixing due to the targeted organization of the motion of thin disperse layers are most promising for the solution of this problem. Centrifugal mixers enable the production of good-quality mixtures at a component ratio of 1:100 [2]. However, a single CCM is usually insufficient at higher ratios. In this connection, we propose to incorporate two serially arranged centrifugal mixers with a good smoothability into a single MU. In this case, it is possible to use volumetric dosers with certain advantages (high material feed rate, small dimensions, low cost and maintenance expenditures) for the preparation of mixtures with high ratios of mixed components. For this reason, the objective of our work is to compare the operational efficiencies of two centrifugal MU of new design (differ from each other by the set of equipment incorporated in them), in which it is possible to obtain dry combined food products with a high ratio of mixed components, using cybernetic analysis and some ACT elements [6, 7, 9].
When studying the operation of certain mixing equipment, we artificially imposed a disturbance of one or another kind onto the input feed flow and then analyzed its consequences at the output of an apparatus (plotted a response curve) [10]. The function determined from the given curve for the residence time distribution of particles in centrifugal mixers was used in combination with the accepted flow pattern of mixed materials in an apparatus to predict the process of mixing in it [1, 8].
A number of scientific works [1, 6, 8, 13,15] are devoted to the problems of the modeling of mixing processes. In our work, we have detailed the questions of the creation of a MU mathematical model, which would allow us to match the time-and- frequency characteristics of CCMs and dosers incorporated into a MU in the interactive operational mode of a computer. As a result, this provides the possibility of decreasing the amplitude of fluctuations in the output material flow of a mixer and improving the quality of a ready mixture.
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2. Borodulin, D.M. and Ivanets, V.N., Razvitie smesitel’nogo oborudovaniya tsentrobezhnogo tipa dlya polycheniya sukhikh i uvlazhnennykh kombinirovannykh produktov (Development of Centrifugal Mixing Equipment for the Preparation of Dry and Wetted Combined Food Products), Kemerovo: KemTIPP, 2012.
3. Gel’man, M.I. and Kirsanova, N.V., Praktikum po fizicheskoi khimii. Uchebnoe posobie (Workshop on Physical Chemistry: Tutorials), St. Petersburg: Lan’, 2004.
4. Ivanets, V.N., Smesiteli poroshkoobraznykh materialov dlya vitaminizatsii pishchevykh i kormovykh productov (Mixers of powder-like materials for the vitaminization of food and fodder products), Izvestiya Vysshikh Uchebnykh Zavedenii. Pishchevaya Tekhnologiya (News of Institutes of Higher Education. Food Technology), 1988, no. 1, pp.89-97.
5. Ivanets, V.N. and Poznyakovskii, V.M., Gigienicheskie aspekty, tekhnologiya, i apparaturnoe oformlenie vitaminizatsii pishchevykh produktov (Hygienic Aspects, Technology, and Equipment Implementation of Food Product Vitaminization), Kemerovo: KemTIPP, 1991.
6. Ivanets, V.N. and Fedosenkov, B.A., Protsessy dozirovaniya sypuchikh materialov v smeseprigotovitel’nykh agregatakh nepreryvnogo deistviya: obobshchennaya teoriya i analiz (Bulk Material Dosing Processes in Continuous Mixture Preparing Units: Generalized Theory and Analysis), Kemerovo: KemTIPP, 2002.
7. Ivanets, V.N., Zhukov, A.N., and Borodulin, D.M., Analiz chastotno-vremennykh kharakteristik smesitelya nepreryvnogo deistviya tsentrobezhnogo tipa (Analysis of the time-and-frequency characteristics of a continuous centrifugal mixer), Khranenie i Pererabotka Sel’khozsyr’ya (Storage and Processing of Farm Products), 2004, no. 2, pp. 52-54.
8. Kafarov, V.V. and Dorokhov, I.N. Sistemnyi analiz protsessov khimicheskoi Tekhnologii (System Analysis of Chemical Engineering Processes), Moscow: Nauka, 1976.
9. Lazareva, T.Ya. and Martem’yanov, Yu.F., Osnovy teorii avtomaticheskogo upravleniya. Uchebnoe posobie (Foundations of Automatic Control Theory: Textbook), Tambov: Izd. Tambov. Gos. Univ., 2004.
10. Makarov, Yu.I., Apparaty dlya smesheniya sypuchikh materialov (Apparatuses for the Mixing of Bulk Materials), Moscow: Mashinostroenie, 1973.
11. RF Patent 2361653, Byull. Izobret., 2009, no 20.
12. RF Patent 2207186, Byull. Izobret., 2003, no. 18.
13. Dehling, H.G., Hoffmann, A.C., and Stuut, H.W., Stochastic models for transport in a fluidized bed, SIAM Journal on Applied Mathematics, 1999, vol. 60, no. 1, r. 337-358.
14. Hoffmann, A.C. and Paarhuis, H.I., A study of the particle residence time distribution in continuous fluidized beds, Institution of Chemical Engineers Symposium Series, 1990, vol. 121, r. 37-49.
15. Salahudeen, S.A. and AlOthman, O., Optimization of rotor speed based on stretching, efficiency, and viscous heating in nonintermeshing internal batch mixer: simulation and experimental verification, Journal of Applied Polymer Science, 2013, vol. 127, no. 4, pp. 2739-2748.
