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

Abstract

In this paper, we aim at characterizing the spin-up process and the permanent regime of a rotating flow with free surface. The motion is created by the quasi-impulsive rotation of a disk located at the bottom of a cylindrical tank partially filled with a Newtonian water-glycerol mixture at a fixed initial aspect ratio (height to radius) of 0.25. Two experimental setups with different radius sizes and two numerical codes with distinct formulations are used, allowing for numerous comparisons and cross validations. Time-dependent surface height profiles and azimuthal velocity profiles are accurately measured with a laser line sensor and Laser Doppler Velocimetry respectively. These measurements are compared to numerical results showing an overall excellent agreement and whenever a discrepancy exists, explanations are given. The spin-up and permanent regime for two typical flow cases are detailed: (i) one for which the angular speed moderately deforms the free surface and (ii) one at higher angular speed for which the disk becomes partially dewetted. The shape of the free surface in the permanent regime for intermediate rotation speeds is also reported. The flow parameters are chosen in such a way that large deformations of the free surface are achieved, yet remaining under the threshold of appearance of rotating polygonal patterns. This enables us to characterize realistic base flows on which this instability may develop.

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

“…While this is technically much more involved, especially on the numerical side (see e.g. Yang et al 2020), one can wonder whether pollution effects can also affect the thresholds in the large deformation regime investigated by many others (Vatistas, Abderrahmane & Siddiqui 2008; Tophøj et al 2013) also in the presence of additional surfactants (Jansson et al 2006). These regimes involve not only finite deformations of the fluid interface but also partial dewetting, which makes the dynamics of the concentration field more complex by involving moving triple contact lines.…”

“…A second-order backward Euler differentiation is used for time discretisation. Details can be found in Yang et al (2020). The interface condition is as in (2.3) and (2.4).…”

“…A numerical estimation of the height as a function of the rotation speed is possible for the steady base flow. This is achieved using the variation of the numerical code ROSE with coordinate transformations used in Yang et al (2020). Two sets of parameters typical of the present range of interest have been considered.…”

On the role of roughness valleys in turbulent Rayleigh–Bénard convection

“…As a consequence, Dirichlet boundary conditions are applied to all walls for velocity and to the top smooth and bottom rough plates for temperature, whereas homogeneous Neumann boundary conditions are applied to all walls for the pressure and to the vertical walls for temperature. SUNFLUIDH code is a general purpose solver for modelling quasi-incompressible fluid flows, such as rotating flows with a free interface (Yang et al 2020), turbulent flows (Derebail Muralidhar et al 2019) or multi-physics studies (Hireche et al 2020).…”

“…SUNFLUIDH code is a general purpose solver for modelling quasi-incompressible fluid flows, such as rotating flows with a free interface (Yang et al. 2020), turbulent flows (Derebail Muralidhar et al. 2019) or multi-physics studies (Hireche et al.…”