### ANALYSIS OF CHANGES IN THE PROFILE OF TANGENTIAL VELOCITIES OF THE FLOW SHAPED UP BY THE LOCAL SWIRLER

Pages 23 - 28

The profile of tangential velocities of a longitudinal turbulent rotational flow (Fig. 1) at the inlet of a cylindrical tube with a local swirler is characterized by radial zoning. The fluid rotation pattern transforms from a forced vortex in the center of the flow alongside the tube axis into a free vortex at the periphery. The boundary between the zones of forced and free rotation represents the radius , where tangential velocity reaches its maximum value . Analysis of the profile approximation in Fig. 1 through the application of the Burgers-Batchelor (1) free and forced vortex methodology makes it possible to identify the following regularities. It is proven that the distribution of the tangential velocity and the change in the number of swirls are described by functions (8) and (9), where 0 and 0 stand for the tangential velocity and the number of swirls at the tube inlet immediately after the local swirler, where is the radius of the tube, is the radial coordinate, h is a constant value equal to 1.256. The author has identified that functions (8) and (9) represented in Fig. 2 depend on parameter2 2 8 = Re , where is the axial coordinate, Reis the turbulent analogue of the Reynolds number, calculated in accordance with formula (12). The author demonstrates that if > 0.0995 Rethe tangential velocity is not maximal, the fluid rotates as a rigid body, and its rotation pattern corresponds to the stage of rotation degeneration, in which the 0 ratio falls below 0.4306. The analysis demonstrates that the result of multiplying the maximal velocity at radius in any section of the tube remains constant and it is equal to 0.7152 0 .

DOI: 10.22227/1997-0935.2012.5.23 - 28

- Trinh C.M. Turbulence Modeling of Confined Swirling Flows. Roskilde, Riso National Laboratory, 1998, Riso-R-647(EN).
- Zuykov A.L. Approksimiruyushchie profili tsirkulyatsionnykh kharakteristik zakruchennogo techeniya [Approximating Profiles of Circulation Charactertistics of a Swirling Flow]. Vestnik MGSU [Proceedings of Moscow State University of Civil Engineering]. 2011, no. 5, pp. 185—190.
- Zuykov A.L. Kriterii dinamicheskogo podobiya tsirkulyatsionnykh techeniy [Criteria of Dynamic Similarity of Circulating Flows]. Vestnik MGSU [Proceedings of Moscow State University of Civil Engineering]. 2010, no. 3, pp. 106—112.
- Zuykov A.L. Radial’no-prodol’noe raspredelenie azimutal’nykh skorostey v techenii za lokal’nym zavikhritelem [Radial-Longitudinal Distribution of Azimuthal Velocity of the Flow behind the Local Swirler]. Vestnik MGSU [Proceedings of Moscow State University of Civil Engineering]. 2011, no. 2, pр. 119—123.
- Zuykov A.L., Volshanik V.V. Analiticheskoe issledovanie struktury potoka vyazkoy neszhimaemoy zhidkosti v tsilindricheskoy trube [Analytical Study of the Structure of the Flow of Viscous Incompressible Fluid in a Cylindrical Tube]. Moscow, Moscow State University of Civil Engineering, 2001.
- Spravochnik po gidravlicheskim raschetam [Handbook of Hydraulic Calculations]. Edited by Kiselyov P.G. Moscow, Energiya Publ., 1972.