Steady flow instability in an annulus with deflectors at rotational vibration

Abstract

Experimental study and direct numerical simulation of dynamics of an isothermal low-viscosity fluid are done in a coaxial gap of a cylindrical container making rotational vibrations relative to its axis. On the inner surface of the outer wall of the container, semicircular deflectors are placed regularly, playing the role of flow activators. As a result of vibrations, the activators oscillate tangentially. In the simulation a two-dimensional configuration is considered, excluding the end-wall effects. In the experiment a container with large aspect ratio is used. Steady streaming is generated in the viscous boundary layers on the activators. On each of the latter, beyond the viscous domain, a symmetric vortices pair is formed. The steady streaming in the annulus has an azimuthal periodicity. With an increase in the vibration intensity, a competition between the vortices occurs, as a result of which one of the vortices (let us call it even) approaches the activator and the other one (odd) rolls away and couples with the vortices from the neighbouring pairs. Streamlines of the odd vortices close on each other, forming a flow of a cogwheel shape that encircles the inner wall. Comparison of the experiment and the simulation reveals an agreement at moderate vibration intensity.

Steady flow in an annulus with a varying number of deflectors at rotational vibration

“…The present work is a numerical study of steady flows in an annulus at rotational vibrations. This work continues the research started by Kozlov et al (2016) and discovers the role of geometrical parameters. The study is carried out following the principle of the vibrational mechanics: equations are averaged over an oscillation period and the oscillating variables vanish, then the average variables are used for the analysis of the studied systemʼs behaviour.…”

“…In the supercritical domain the discrepancy increases with Re p . This is attributed to the appearance of three-dimensional flow features, which were observed in experiments (Kozlov et al 2016). Hence, the 2D numerical model is valid only at relatively low vibration amplitudes.…”

“…The chosen parameter values correspond to the conditions of previously published experiments (Kozlov et al 2016): R 1 =30.0 mm, R 2 =50.0 mm, R a =8.0 mm, Ω=62.8 s −1 . As follows from the cited work, at ω∼4000 the studied systemʼs dynamics asymptotically approach the high-frequency limit.…”

“…Numerical results were compared to experiments for the case of the annulus with six activators (Kozlov et al 2016). In experiments, a transparent container with annulus was made of two coaxial acrylic cylinders.…”

“…Previously, Kozlov et al (2016) studied experimentally and numerically steady flows in an annulus with six deflectors. The annulus performed rotational vibrations, and each deflector acted as flow activator.…”