Stability of Rimming Flow under Vibration

Abstract

The structure of rimming flow in a horizontal rotating cylinder subjected to vibration is experimentally investigated. Under vibration liquid performs oscillations. In the resonant domain oscillations have a form of progressive two-dimensional azimuth wave which generates averaged flow in the direction of its propagation. It is found that the plane motion is unstable to the spatially periodic vortical flow appearance. The transition to the vortical flow is determined by the oscillatory liquid flow instability in viscous Stokes layer near cylindrical wall. The threshold of 2D flow instability and the structure of overcritical flows in a wide range of dimensionless parameters are investigated.

Flow patterns in a rotating horizontal cylinder partially filled with liquid

“…It is worth mentioning that the quasisteady assumption should be valid for both forced and wavy disturbances of fluid motion. Then we can compare our results with the experimental findings of Kozlov and Polezhaev [30]. The individual particles of a perfect liquid in a progressive wave do not exactly describe closed paths; in addition to their orbital motion, they also possess a mean flow in the direction of wave propagation.…”

“…Kozlov and Polezhaev [30] stated that, in the limit of the thin Stokes boundary layer (δ h), the experimental data on the spatial period of vortices are in good agreement (Fig. 10).…”

“…This proves that the onset of spatially periodic flow is caused by the instability of the viscous boundary layer and, in the limit of the high dimensionless velocity, the spatial period λ depends only on the thickness δ. The experimentally observed wave [30], circle corresponds to k δ = 0.67, obtained in the limit ω > 500 (Fig. 9).…”

Oscillatory and Steady Flows in the Annular Fluid Layer inside a Rotating Cylinder

“…Furthermore, oscillatory fluid motion is centrifugally unstable to the onset of spatially periodic flow similar to Taylor-Gortler vortices [5]. The dynamics of an annular fluid layer inside a rotating cylinder in the field of gravity is qualitatively similar to libration-driven flows.…”

“…This result gives the opportunity to determine the stability parameters of the centrifugal instability in the viscous boundary layer [5] and the onset of a quasistationary relief at the interface between the granular medium and the fluid inside a rotating cylinder [4]. The specific feature of these problems is the inability to experimentally measure the velocity of the oscillatory fluid motion near the Stokes boundary layer.…”