Axisymmetric rotating flow with free surface in a cylindrical tank

Abstract

The flow induced by a disk rotating at the bottom of a cylindrical tank is characterised using numerical techniques – computation of steady solutions or time-averaged two-dimensional and three-dimensional direct simulations – as well as laser-Doppler velocimetry measurements. Axisymmetric steady solutions reveal the structure of the toroidal flow located at the periphery of the central solid body rotation region. When viewed in a meridional plane, this flow cell is found to be bordered by four layers, two at the solid boundaries, one at the free surface and one located at the edge of the central region, which possesses a sinuous shape. The cell intensity and geometry are determined for several fluid-layer aspect ratios; the flow is shown to depend very weakly on Froude number (associated with surface deformation) or on Reynolds number if sufficiently large. The paper then focuses on the high Reynolds number regime for which the flow has become unsteady and three-dimensional while the surface is still almost flat. Direct numerical simulations show that the averaged flow shares many similarities with the above steady axisymmetric solutions. Experimental measurements corroborate most of the numerical results and also allow for the spatio-temporal characterisation of the fluctuations, in particular the azimuthal structure and frequency spectrum. Mean azimuthal velocity profiles obtained in this transitional regime are eventually compared to existing theoretical models.

Large axisymmetric surface deformation and dewetting in the flow above a rotating disk in a cylindrical tank: Spin-up and permanent regimes

“…The contact angle of the liquid at the side wall is imposed to be 90 • . More details on this code can be found in [23,24]. The second one called Sunfluidh is a more general purpose time-stepper code for two-fluid flows, used here in the axisymmetric framework.…”

“…The characteristics of both setups are listed in table I. The large tank with a radius of 140 mm is exactly the one used in [24] while the small one with a radius of 70 mm is designed to explore a larger range of parameter values. Both large and small setups can be mounted on the experiment to obtain a diffusive reflection without significantly changing the fluid properties [37].…”

“…The evolution of the azimuthal velocity component V θ (t) at a given probe (r 0 , z 0 ) is measured by Laser Doppler Velocimeter (LDV) using the same Dantec BSA system as in [24]. With the help of a horizontal displacement platform and a vertical one, any position in the fluid can be reached.…”

“…In a previous paper [24], we numerically described the mean base flow at large Reynolds numbers, yet focusing mainly on the flat surface case to circumvent the difficulty of 3D twophase flow numerical simulations. In the present paper, we investigate another parameter range where surface deformations are large and Reynolds numbers are kept moderate.…”

Influence of interface pollution on the linear stability of a rotating flow

“…Flow set-up and related investigation techniques 2.1. Base flow description We briefly recall the main features of the base flow as described by Iwatsu (2004) and Yang et al (2019). It is axisymmetric with three non-zero velocity components.…”