### Hydraulic modeling of the flows with counter-rotating coaxial layers

Pages 114-125

The article is devoted to hydraulic modeling of flows with counter-rotating coaxial layers. Dynamic similarity criteria of such flows were found by the inspection analysis of the Reynolds equations. It was found that the hydrodynamic similarity criteria for physical modeling of unsteady turbulent circular-longitudinal flows with counter-rotating coaxial layers of viscous incompressible fluid are: Strouhal number - the ratio of forces of local and convective inertia, Rossby number characterizes the ratio of the azimuthal and axial velocity, Froude number - the ratio of forces of convective inertia to the forces of gravity, Euler number - the ratio of pressure forces to the convective forces of inertia, Weber number - the ratio of the convective inertia forces to surface tension forces, Reynolds number - the ratio of the convective inertia forces to the forces of molecular viscosity, Karman number - the ratio of dispersion velocity vector of fluid particles to the flow velocity. The limit value of the Reynolds number was found at the lower boundary conditions of automodel zone of such flow. It is shown that Weber and Rossby criteria for physical modeling of such flows are not determinative. It was found out that turbulent circular-longitudinal flow with counter-rotating coaxial layers are not modeled using Karman criterion. In this connection, there is a need to conduct experimental methodological research of turbulent flows with counter-rotating coaxial layers on stands equipped means of three-dimensional laser Doppler anemometry. Integral criteria of dynamic similarity of circular-longitudinal flows was considered - Heeger-Baer number (swirl number) and Abramovich number, characterizing the ratio of the angular momentum and momentum of such flows. In comparison with the swirl number, Heeger-Baer number is more preferable. Abramovich number is equal to the geometric characteristics of the local swirler as similarity criterion of circular-longitudinal incompressible fluid flows, including counter-rotating coaxial layers. Basing on summation of the angular momenta of coaxial counter-rotating layers, integral criterion of dynamic similarity of these flows was obtained. A common system of basic hydrodynamic similarity criteria was defined for physical modeling of unsteady turbulent circular-longitudinal viscous liquid flows with counter-rotating coaxial layers. For this kind of flow criterial equation was compiled.

DOI: 10.22227/1997-0935.2014.6.114-125

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