Hydrodynamic structure of laminar flows with oppositely-swirled coaxial layers

Abstract

The article is devoted to the theoretical study of hydrodynamics of laminar flows with coaxial layers swirled in opposite directions and moving along the pipe. Such flows in a turbulent range have a wide practical application potential in technologies of dissipation of mechanical energy and mixing multiphase and heterogeneous media in microbiology, chemistry, ecology, heat engineering, power engineering, engine and rocket engineering. The article describes the tensor of viscous tangents (τii) and normal (σii) stresses. The questions of stability of flow according to the Rayleigh (Ra) and Richardson (Ri) criteria are considered. Calculation formulas and graphs of radial-axial distributions of viscous stress components, local stability zones are given, the point of “crisis and decay of the flow” or “vortex breakdown” is indicated. The solutions are obtained in the form of Fourier-Bessel series. The analysis of the hydrodynamic structure of the flow is made.