Abstract
The article is devoted to the theoretical study of laminar flows with the coaxial layers rotating in opposite directions moving along the pipe. These flows have a wide practical application potential in technologies of mixing multiphase and heterogeneous media in microbiology, chemistry, ecology, heat engineering, power engineering, civil engineering and engine and rocket science. Such flows have a complicated three-dimensional structure. The theoretical model of the test flow is based on the Navier – Stokes's equations and Fourier – Bessel's method of expansion of differential equations. The article presents the formulas and graphs showing the radial-axial distributions of tangential, axial and radial flow velocities, stream functions and viscous vortex components. The authors made the theoretical analysis of the kinematic structure of such flows.
Highlights
Fluid flows with oppositely–rotation coaxsial layers have a complicated three-dimensional structure (Fig. 1)
Assuming that the radial velocity is much smaller than the azimuthal and axial ones and taking classical Ozeen approximation [17] equations (1) are scaled to normalized by pipe radius R and average flow velocity V = Q/ R2 closed system of two linear differential equations of parabolic type with two unknowns normalized velocities u and ux [13]
Liquids flows in pipes with cocurrent counter–rotation coaxsial layers have a complicated three-dimensional structure
Summary
Fluid flows with oppositely–rotation coaxsial layers have a complicated three-dimensional structure (Fig. 1) Such currents arise in cyclones and behind Francis turbines [1,2,3,4,5]. The range of application of such flows expanded [7], since the opposite rotation of interacting layers in the turbulent range allows one to obtain a number of effects, among which one should note the intensive mixing of the medium. This effect has a wide practical application in technologies including mixing of multiphase and heterogeneous media in microbiology, chemistry, ecology, heat, power and civil engineering, engine and rocket engineering. The purpose of our research is improvement and analysis of the theoretical model of laminar flow with oppositely-rotation coaxial layers
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