Experimental and numerical investigations of rotating flows with deformable free surface

Overview & Synopsis

This work is a contribution to the understanding of instabilities in rotating flows with deformable free surface. The configuration under study is a cylindrical container partially filled with water or water-glycerin mixture and the rotation is driven by a disk located at the bottom. In such flow, several families of instability patterns can be triggered depending on the flow parameters (Froude and Reynolds numbers and aspect ratio). As a mean of investigation, steady and unsteady simulations are conducted using the two in-house codes ROSE and Sunfluidh, in conjunction with experiments. The novelty lies in two-phase numerical simulations with strongly deformed interface and large density ratio between the phases, in accurate surface height and Laser-Doppler Velocimetry measurements, and in cross validations between numerical and experimental techniques. The base flow is first carefully described. Axisymmetric steady solutions show the structure of the rotating flow: a central solid body rotation and a toroidal flow cell located at the periphery, the intensity and geometry of which are characterized. Focusing on Reynolds numbers large enough so that boundary layers form at solid walls, two additional layers are described: an internal layer at the edge of the central region and a layer under the free surface never reported before. This flow structure is shown to be robust as Froude number is varied. Three-dimensional unsteady simulations reveal that the time and space averaged flow shows many similarities with steady axisymmetric solutions and that the surface remains almost flat even though three-dimensional large structure instabilities have developed in the bulk. Through this full numerical approach corroborated by velocity measurements, the flow structure is thus clarified and compared to the simplified models used in the literature. The transient spin-up dynamics of a fluid from rest are also investigated for two configurations, namely Newton's bucket and the bottom-driven flow. Experimental surface height and velocity evolution are found in very good agreement with axisymmetric unsteady simulations. These results are meant to serve as a benchmark for unsteady rotating two-phase flow simulations. Large amplitude three-dimensional surface deformation waves known as rotating polygons are eventually studied experimentally. These patterns are usually observed at very large Reynolds number. Conducting investigations in more viscous flow regimes, the link between bulk and surface polygon instabilities is tentatively elucidated. Through a spectral analysis of surface deformation and velocity measurements, the phase-velocity to disk speed ratio is found to be close to 1/3 for rotating polygons whereas it is 2/3 for the bulk instability.