Efficient mineral mining and processing using innovations is inseparable from safety. Mine turbo machines feature high energy consumption due to insufficient aerodynamic stability. Using the Cauchy integrals theory of residues as well as Zhukovsky’s and Chaplygin’s approaches, the vortex theory is modified with regard to circular gratings, and the mathematic model is constructed for engineering aerodynamically stable turbo machinery for mines. Considering the reduced wave equation and the conformal mapping method, the integral equation of energy balance in the turbo machine–mine ventilation network system is obtained. The equation defines conditions for stable air feed in mine given essential fluctuations of drag in the mine ventilation system. Furthermore, the equations are obtained for additional circulation in an aerodynamically stable circular grating to compensate variation in drag in the mine ventilation system. It is found that aerodynamic coupling of a turbo machine frame with vortex chambers in the impeller blades, through the functional connection of energetic of vortex sources and the mine ventilation performance, ensures the aerodynamic stability of the circular grating of blade cascade at the preset geometry. Based on the modified vortex theory for circular gratings of aero-gas-dynamic blade cascades, the radial aerodynamic configuration of improved stability is developed, and the main pathways toward persistent upgrading of nature-like turbo machinery design procedure are formulated. The tests of fan model VRVP-12U prove feasibility of stable air feed in ventilation systems of blind tunnels in mines under the change in the air resistance by up to 12%. The ventilation economy is improved by not less than 7% in this case at the sustained aero-gas-dynamic safety.

For citation: Makarov N. V., Makarov V. N., Lifanov A. V., Tauger V. M., Ugol'nikov A. V. Modification of vortex theory for engineering aerodynamically stable circular gratings for turbo machines. MIAB. Mining Inf. Anal. Bull. 2019;(9):184-194. [In Russ]. DOI: 10.25018/0236-1493-2019-09-0-184-194.



Turbo machine, stable vortex source, adaptivity, additive mathematical model, circulation, residues, air drag.

Issue number: 9
Year: 2019
ISBN: 0236-1493
UDK: 62-137
DOI: 10.25018/0236-1493-2019-09-0-184-194
Authors: Makarov N. V., Makarov V. N., Lifanov A. V., Tauger V. M., Ugol'nikov A. V.

About authors: N.V. Makarov, Cand. Sci. (Eng.), Head of Chair, V.N. Makarov, Dr. Sci. (Eng.), Professor, A.V. Lifanov, General Director, e-mail:, Scientific-Production Complex «OylGazMash», Podolsk, Russia, V.M. Tauger, Cand. Sci. (Eng.), Head of Chair, A.V. Ugol'nikov, Cand. Sci. (Eng.), Head of Chair, Ural State Mining University, 620144, Ekaterinburg, Russia. Corresponding author: N.V. Makarov, e-mail:


1.     Makarov V. N., Patrakeeva I. Yu., Makarov N. V. Genesis of perfection local ventilation fans. Gornyy informatsionno-analiticheskiy byulleten’. 2016, no 4, pp. 54—61. [In Russ].

2.     Torshizi S. A. M., Benisi A. H., Durali M. Multilevel Optimization of the Splitter Blade Profile in the Impeller of a Centrifugal Compressor. Scientia Iranica. 2017. Vol. 24. Pp. 707—714.

3.     Galerkin YU. B., Rekstin A. F., Soldatova K. V., Drozdov A. A. Radial and axial-and-radial impellers of centrifugal flow compressors—advantages, disadvantages, application ranges. Compressor equipment and pneumatics. Kompressornaya tekhnika i pnevmatika. 2015, no 7, pp. 23—32. [In Russ].

4.     Podbolotov S. V., Kol'ga A. D. Gidravlicheskie poteri v elementakh turbomashin. Dobycha, obrabotka i primenenie pridorozhnogo kamnya. Sbornik nauchnykh trudov. Pod red. G. D. Pershina [Hydraulic losses in elements of turbo machines. Roadside stone production and use. Collection of scientific papers. Pershin G. D. (Ed.). Issue 16. Magnitogorsk, Izd-vo MGTU im. G.I. Nosova, 2016, pp. 134—138.

5.     Makarov N. V., Makarov V. N., Yasakov S. E. Patent RU 2557818, 27.05.2015.

6.     Makarov V. N., Makarov N. V., Vakulin V. E., Soldatenko A. A. Modification of hydrodynamic theory for circular gratings of mine turbo machines. Sbornik statey XV Mezhdunarodnoy nauchno-tekhnicheskoy konferentsii. Chteniya pamyati V.R. Kubacheka. Ekaterinburg, 2018, pp. 251—

254. [In Russ].

7.     Petrov N. N., Kaygorodov Yu. M. Evolution of ventilation systems in mines in Kuzbass. Avtomaticheskoe upravlenie v gornom dele. Novosibirsk, IGD SO AN SSSR, 1974, pp. 50—57.

8.     Wang P. Mulyi-Objective desing of a transonic turbocharger compressor with reduced Noise and increased efficiency. Ph.D. Thesis, UCL University, London. 2017.

9.     Loytsyanskiy L. G. Mekhanika zhidkosti i gaza. Uchebnik dlya vuzov. 7-e izd. [Mechanics of fluids and gas. Textbook for high schools. 7th edition. Moscow, Drofa, 2003, 840 p.

10.     Mao Y. F. Numerical Study of Correlation between the Surge of Centrifugal Compressor and the Piping System. PhD Thesis, Xi’an Jiaotong University, Xi’an. 2016. (In Chinese).

11.     Kosarev N. P., Makarov V.N., Makarov N. V., Sveridov K. K., Ugol'nikov A. V., Lifanov A.V. Engineering adaptable local ventilation fans based on the modified additive mathematical model. Izvestiya Ural’skogo gosudarstvennogo gornogo universiteta. 2018, no 3 (51), pp. 114—119. [In Russ].

12.     Kofman V. M. Determining operating performance factors of compressor and fan of gas turbine engine by the nonuniform air flow parameters. Vestnik Ufimskogo gosudarstvennogo aviatsionnogo tekhnicheskogo universiteta. 2010. Т. 15, no 5(40), pp. 27—37. [In Russ].

13.     Torshizi S. A. M., Benisi A. H., Durali M. Numerical Optimization and Manufacturing of the Impeller of a Centrifugal Compressor by Variation of Splitter Blades. ASME Turbo Expo 2016: Turbomachinery Technical Conference and Exposition, Seoul, 13—17 June 2016, 1—7.

14.     Petrov A. P. Using fans to measure air flow through cooling system radiator. Izvestiya Samarskogo nauchnogo tsentra Rossiyskoy akademii nauk. 2013. Vol. 15, no 4(2), pp. 534—537.

15.     Kabin Wang, Xin Ai, Ruizi Zang, Jingyin Li. Optimization of a Centrifugal Impeller with the Constraint on Efficiency at the Stall Point. DOI: 10.4236/ojfd.2018.81002.

Subscribe for our dispatch