Math. Model. Nat. Phenom.
Volume 17, 2022
|Number of page(s)||13|
|Published online||18 August 2022|
Structural changes of a radially symmetric thermocapillary flow in the shallow cavity partially covered by a solid film*
Department of Theoretical Physics, Perm State University, Perm, Russia
** Corresponding author: demin.psu.ru
Accepted: 16 May 2022
This paper presents a numerical study of spatial transformations of a radially symmetric flow in a shallow fluid-filled cylindrical cavity partially covered by a solid non-deformable film. The upper central part of the liquid has a free surface where an intense light beam is focused to produce a hot spot on the symmetry axis. The heating generates a divergent thermocapillary motion on the free surface, which causes the fluid to flow under the immovable solid film. The edge of this film induces thermal perturbations, which, at specific heat generation values, begin to increase and give rise to a gradual radial flow symmetry breakdown that visually demonstrates the onset of vorticity in the azimuthal plane. Three-dimensional calculations have been carried out based on the interfacial hydrodynamics equations using Comsol Multiphysics software. The results of numerical calculations confirm that the instability occurs in the area corresponding to the boundary between the free surface and the solid film. The motion in the azimuthal direction becomes more evident with the growth of heating intensity. The vorticity in the azimuthal plane makes the flow structure significantly more complex compared to the axisymmetric radial flow. Thus, there is a predominantly radial flow in the area of free surface and, at the same time, the vortices with the azimuthal velocity component are observed under the film. As in the experiment, the number of vortices is determined by the ratio of the area of free surface to the covered area. It is shown that the appearance of motion in the azimuthal direction depends on the joint action of several physical mechanisms, which have been initialized in the theoretical model by means of various piecewise thermal and mechanical conditions at the upper boundary.
Mathematics Subject Classification: 76D05 / 76E30 / 80A19
Key words: Thermocapillary flow / solid film / three dimensional flow / numerical simulation
© The authors. Published by EDP Sciences, 2022
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