Mathematical model of local diffusion control in adaptable mine turbomachines

It is highly topical for the industry safety to implement mathematical modeling of energy transformation control in impellers of turbomachines, as well as their adaptability in the context of goal competitiveness of the Russian mining and metallurgy sector under conditions of globalization. The adaptability control dominator is proposed to be the hydrodynamic analog of local diffusion, namely, the change flow velocity on blade profile. Using conformal transformations and the Chaplygin points, the mathematical model of the local diffusion control by changing flow velocity through the agency of flow influence sources distributed on blade profiles. It is proven that the local diffusion control dominator is the power of the flow influence sources which govern the flow diffusion and, as a result, the change in the flow velocity around the blade profile. Using the proposed hypotheses, the mathematical model is created as a functional with its minimum to condition the optimal parameters of the flow influence sources, such that to ensure the highest increment in energy efficiency and cost-effective performance range of turbomachines. It is experimentally proved that profiles designed using the proposed procedure allow reduction in the profile drag factor of blades of impellers in turbomachines more than by 3 times, while their cost-effective performance range is expanded not less than by 47%.

Makarov V. N., Makarov N. V., Ugolnikov A. V., Churakov E. O., Molchanov M. V. Mathematical model of local diffusion control in adaptable mine turbomachines. MIAB. Mining Inf. Anal. Bull. 2021;(11-1):248—257. [In Russ]. DOI: 10.25018/0236_1493_2021_111_0_248.

Makarov V. N.¹, Dr. Sci. (Eng.), Professor at the Mining Mechanics Department;
Makarov N. V.¹, Cand. Sci. (Eng.), Associate Professor, Head of the Mining Mechanics Department;
Ugolnikov A. V.¹, Cand. Sci. (Eng.), Associate Professor, Head of the Electrical Engineering Department;
Churakov E. O.¹, Post-Graduate Student at the Mining Mechanics Department;
Molchanov M. V.², Strategic Mining Project Manager;
¹ Ural State Mining University, ul. Kuibysheva 30, Yekaterinburg, 620144 Russia;
² Uralmekhanobr, Yekaterinburg, Russia

Makarov N. V., e-mail: mnikolay84@mail.ru.

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