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HYDRAULICS. ENGINEERING HYDROLOGY. HYDRAULIC ENGINEERING

ANALYTICAL MODEL OF GROMEKA — BELTRAMI FLOW

Vestnik MGSU 4/2013
  • Zuykov Andrey L’vovich - Moscow State University of Civil Engineering (MGSU) Doctor of Technical Sciences, Chair, Department of Hydraulics; +7(495)287-49-14, ext. 14-18, Moscow State University of Civil Engineering (MGSU), 26 Yaroslavskoe shosse, Moscow, 129337, Russian Federation; This e-mail address is being protected from spambots. You need JavaScript enabled to view it .
  • Orekhov Genrikh Vasil’evich - Moscow State University of Civil Engineering (MGSU) Candidate of Technical Sciences, Associate Professor, Chair, Department of Hydroelectric Engineering and Use of Aquatic Resources; +7 (499) 182-99-58, Moscow State University of Civil Engineering (MGSU), 26 Yaroslavskoe shosse, Moscow, 129337, Russian Federation; This e-mail address is being protected from spambots. You need JavaScript enabled to view it .
  • Volshanik Valeriy Valentinovich - Moscow State University of Civil Engineering (MGSU) Doctor of Technical Sciences, Professor, Professor, Department of Hydroelectric Engineering and Use of Aquatic Resource, Moscow State University of Civil Engineering (MGSU), 26 Yaroslavskoe shosse, Moscow, 129337, Russian Federation; This e-mail address is being protected from spambots. You need JavaScript enabled to view it .

Pages 150-159

The authors provide a summarized overview of the analytical model of the Gromeka — Beltrami helical flow of nonviscous incompressible fluid in a cylindrical channel. The model is developed on the basis of the method of decomposition for Fourier — Bessel equations. The authors discuss the analytical distribution function for axial, azimuthal and radial fluid velocities and the flow function depending on the length and radius of the cylindrical channel. The analysis of the proposed solution demonstrates that the properties of the flows inside the channel depend on the value of the scalar coefficient. When the value of the coefficient is within the zero-order Bessel function of the first kind, the velocity distribution is characterized by significant reverse currents in the axial zone of the channel. The findings comply with the results of laboratory and field tests. The authors have identified that this type of flow has components of the wave. Similar flows have high angular velocity. The authors assume that these conditions correspond to the emergence of toroidal Taylor — Gertler vortices. Therefore, the analytical model of the Gromeka — Beltrami flow complies with the phenomena observed in the course of experiments and in the natural environment.

DOI: 10.22227/1997-0935.2013.4.150-159

References
  1. Gromeka I.S. Sobranie sochineniy [Collection of Works]. Moscow, AN SSSR Publ., 1952, 296 p.
  2. Loytsyanskiy L.G. Mekhanika zhidkosti i gaza [Fluid and Gas Mechanics]. Moscow, Drofa Publ., 2003, 840 p.
  3. Byushgens S.S. O vintovom potoke [About the Helical Flow]. Nauchnye zapiski MGMI [Proceedings of Moscow Institute of Hydraulic Reclamation of Land]. 1948, vol. 17, pp. 73—90.
  4. Korn G., Korn T. Spravochnik po matematike dlya nauchnykh rabotnikov i inzhenerov [Reference Book of Mathematics for Researchers and Engineers]. Moscow, Nauka Publ., 1970, 720 p.
  5. Gostintsev Yu.A., Pokhil P.F., Uspenskiy O.A. Potok Gromeki — Bel’trami v polubeskonechnoy tsilindricheskoy trube [Gromeka-beltrami Flow in a Semiinfinite Cylindrical Pipe]. Mekhanika zhidkosti i gaza [Fluid and Gas Mechanics]. 1971, no. 2, pp. 117—120.
  6. Zuykov A.L. Funktsiya toka i zona retsirkulyatsii v laminarnom techenii s zakrutkoy [Current Function and Recirculation Zone of the Laminar Flow Having Vortex]. Vestnik MGSU [Proceedings of Moscow State University of Civil Engineering]. 2009, Special Issue no. 2, pp. 91—95.

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CREEPING COUNTER VORTEX FLOW

Vestnik MGSU 4/2013
  • Orekhov Genrikh Vasil’evich - Moscow State University of Civil Engineering (MGSU) Candidate of Technical Sciences, Associate Professor, Chair, Department of Hydroelectric Engineering and Use of Aquatic Resources; +7 (499) 182-99-58, Moscow State University of Civil Engineering (MGSU), 26 Yaroslavskoe shosse, Moscow, 129337, Russian Federation; This e-mail address is being protected from spambots. You need JavaScript enabled to view it .
  • Zuykov Andrey L’vovich - Moscow State University of Civil Engineering (MGSU) Doctor of Technical Sciences, Chair, Department of Hydraulics; +7(495)287-49-14, ext. 14-18, Moscow State University of Civil Engineering (MGSU), 26 Yaroslavskoe shosse, Moscow, 129337, Russian Federation; This e-mail address is being protected from spambots. You need JavaScript enabled to view it .
  • Volshanik Valeriy Valentinovich - Moscow State University of Civil Engineering (MGSU) Doctor of Technical Sciences, Professor, Professor, Department of Hydroelectric Engineering and Use of Aquatic Resource, Moscow State University of Civil Engineering (MGSU), 26 Yaroslavskoe shosse, Moscow, 129337, Russian Federation; This e-mail address is being protected from spambots. You need JavaScript enabled to view it .

Pages 172-180

The authors have performed an analytical research into one of the most complex types of heterogeneous 3D flows of fluids and gases, that is, a creeping counter vortex flow. The “creeping counter vortex flow” is the flow that is formed as a result of interaction between two or more slow concurrent co-axial circulatory longitudinal flows swirling in the opposite directions.Creeping flows are typical for numerous structural elements of machines, mechanisms, items of equipment and devices, if the flow velocity or cross dimensions of channels are small or, alternatively, if the viscosity of the fluid is high. This model designed by the coauthors, serves as the basis for the hydrodynamic theory of lubrication. If the flow velocity is small and the viscosity of the liquid media is substantial, inertial convective summands can be ignored for Navier — Stokes equations.The coauthors believe that the research into the phenomena of the creeping counter vortex flow as one of the types of heterogeneous 3D flows of fluids and gases has a strong potential in space technologies, and it may be elaborated in further research projects to be developed by the coauthors.

DOI: 10.22227/1997-0935.2013.4.172-180

References
  1. Korn G., Korn T. Spravochnik po matematike dlya nauchnykh rabotnikov i inzhenerov [Reference Book of Mathematics for Researchers and Engineers]. Moscow, Nauka Publ., 1970, 720 p.
  2. Zuykov A.L. Analiz izmeneniya profilya tangentsial’nykh skorostey v techenii za lokal’nym zavihritelem [Analysis of Changes in the Profile of Tangential Velocities of the Flow Shaped Up by the Local Swirler]. Vestnik MGSU [Proceedings of Moscow State University of Civil Engineering], 2012, no. 5, pð. 23—28.

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