Abstract
We numerically model the instability of viscous incompressible fluid flows caused by torsional oscillations of the inner sphere in a thin spherical layer with respect to the state of rest. We show that an increase in the frequency of torsional oscillations leads to a change in the mode of the instability, with a transition from secondary flows in the form of Taylor vortices to the structures, which were not previously observed. The revealed instability is found in the frequency range from 0.61 to 2.45 Hz or, if the wavelengths are taken relative to the layer thickness, from 0.67 to 1.33.
Highlights
Flows caused by torsional oscillations can be used to determine rheological properties of fluids [1] and for intensifying filtration [2]
We show that an increase in the frequency of torsional oscillations leads to a change in the mode of the instability, with a transition from secondary flows in the form of Taylor vortices to the structures, which were not previously observed
The stability limit was determined by decreasing Re at f = const according to the form of the flow structure, magnitude of Mout, and ratio Eψ/Eφ (where E u 2 and E are the azimuthal and meridional components of the kinetic energy of the flow determined by integration over the whole volume of the spherical layer)
Summary
Flows caused by torsional oscillations can be used to determine rheological properties of fluids [1] and for intensifying filtration [2]. A possible dependence of the secondary flow structures and the types of instability of the oscillation frequency is of special interest. Such dependence was revealed based on the measurements of velocity fields in a cylindrical thin layer β = (r2 – r1)/r1 = 0.087, where r1 and r2 are the inner and outer radii [1, 5]. In a spherical layer with β = 4.3 [6] at torsional oscillations of the inner sphere the structure of secondary flows in two-dimensional calculations remains constant over a wide range of frequency variations. At other values of β, the dependence of the instability type on the frequency in spherical layers has not been previously studied
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