Rotating and thermocapillary-buoyancy-driven flow in a cylindrical enclosure with a partly free surface

Abstract

In order to understand the characteristics of the complex flow driven by the combined thermocapillary-buoyancy effect and differential rotation of a cylindrical pool and a disk on the free surface, a series of unsteady three-dimensional numerical simulations were performed. Results indicate that the flow is axisymmetric and steady at a small temperature difference and low rotation rates. The basic meridional flow structures are composed of toroidal circulations. With an increase of the rotation rate and/or temperature difference, the basic flow transits to a three-dimensional oscillatory flow. Without rotation, the unstable thermocapillary-buoyancy flow is characterized by pulsating spoke patterns with the periodic growth and decay of temperature and velocity oscillations. When the disk and/or cylinder rotate, the oscillatory flow behaves as temperature and velocity fluctuation waves traveling in the azimuthal direction. The wave propagation velocity and direction, fluctuation amplitude, and wave number depend on the interaction of the thermocapillary, buoyancy, centrifugal and Coriolis forces. The critical conditions for the flow transition are determined. It is found that the critical thermocapillary Reynolds number initially increases before decreasing with the increase of the disk rotation rate, but the rotation of cylinder always retards the flow instability. In addition, the mechanisms of the flow instabilities are discussed and briefly summarized.

Atomic-scale thermocapillary flow in focused ion beam milling

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Flow Instabilities of Coupled Rotation and Thermal-Solutal Capillary Convection of Binary Mixture in Czochralski Configuration

“…With the influence of rotation, the oscillatory flow behaves as travelling waves, the oscillation amplitude and wave numbers vary with the rotation rate [30]. In our previous work [31][32][33], a series of numerical simulations on the convections of silicon melt in a Cz configuration have been conducted. The critical conditions for flow transitions have been determined and the stability diagrams have been mapped and several mechanisms for flow instabilities have been identified, such as Rayleigh-Marangoni-Benard instability, baroclinic instability, hydrothermal wave, as well as the elliptic and shear instabilities.…”

Numerical Simulation on Effect of Rotation on Thermal Convection in a Shallow Model Czochralski Configuration with a Heated Bottom

“…The rotations of the crystal and crucible have an important influence on thermocapillary convection in the Cz configuration. For the silicon melt with the low Prandtl ( Pr ) number, the crystal rotation can destabilize the flow in the deep melt pool, but it increases the stability of the flow in the shallow melt pool . Furthermore, a weak rotation of the crucible can suppress the instability of thermocapillary convection .…”

“…For the silicon melt with the low Prandtl ( Pr ) number, the crystal rotation can destabilize the flow in the deep melt pool, but it increases the stability of the flow in the shallow melt pool . Furthermore, a weak rotation of the crucible can suppress the instability of thermocapillary convection . When the driven forces, including centrifugal and Coriolis forces and/or thermocapillary force, exceed the threshold values, the moving spoke pattern can be observed on the free surface.…”