Investigation On Intabilities And The Mechanisms Of Thermocapillary Convection In Rotating Annular Pools

The Czochralski technology is one of the most frequently-employed methods for producing single crystal in the industry,in which the flow of the melt is quite complex since the coupled influence of the thermocapillary force induced by the tangential temperature gradient,the buoyance force in the terrestrial environment and the inertial force induced by system rotation.A comprehensive study on the complex melt flow,including the basic flow structure,stability parameters space and instability mechanism may help improving the controlling technology in the crystal growth process.Moreover,the investigation on complex thermocapillary flow does not only extend the fields of hydrodynamic stability,but also improve the development of non-equilibrium thermodynamic including bifurcation theory and dissipative structure theory.In the present work,we conduct a series of linear stability analysis(LSA),direct numerical simulation(DNS)and experiments to investigate the complex thermocapillary flow in the rotating annular pools.The basic flow,flow instability and instability mechanism are revealed in detail.Firstly,the thermocapillary flow of three representative liquids with different Prandtl number in a rotating annular pool is investigated by linear stability analysis.In the absence of gravity,the instability mechanism of liquid with medium Prandtl number and high Prandtl number are much similar.The energy necessary to create and sustain the disturbances is come from the interaction between the basic temperature profile and the perturbation flow,which is mainly driven by the thermocapillary force acting on the free surface.The pool rotation affects the instability by changing the basic flow and leads to some new critical modes for which the disturbances can receive energy more efficiently.While in the small Prandtl number liquid pool,the thermocapillary force just acts here to drive a basic flow.The perturbation flow which triggers an unstable flow is mainly supplied by centrifugal instability mechanism and some inertial forces.The kinetic energy transport process associated with the pool rotation only plays significant role when the rotation rate is large.The gravity has two effects on the thermocapillary instability.On one hand,buoyance force in the gravity environment enhances the basic thermocapillary flow and changes the basic flow structure.The perturbation flow interacts with the basic flow in an alternative way accordingly.On the other hand,the buoyance force induced by the interior perturbation temperature also creates perturbation flow directly.The combination of these two effects leads to some more complex thermocapillary instabilities.In the non-rotating pool,the axisymmetric basic flows of medium Prandtl number liquid and high Prandtl number liquid lose their stability to a three-dimensional stationary flow.The perturbation flow in the medium Prandtl number liquid pool is mainly created by the inertial force while that for large Prandtl number liquid is driven by thermocapillary force.Then the interior perturbation temperature receives energy from the regions called "cold finger" and "hot finger" by these perturbation flows and activates stationary flow under the advection transport of basic flow.When the pool rotates,the basic flow becomes to oscillatory flow under the mechanism of hydrothermal wave instability of high Prandtl number liquid.For the small Prandtl number liquid,the buoyance force just enhances the basic flow slightly.It does not affect the perturbation fields since its strong thermal diffusion.The enhancement of the buoyance to the basic flow reduces the flow stability because the perturbation flow can receive kinetic energy from the strong basic flow more efficiently.The thermocapillary flow in a bilayer annular pool with and without rotation are investigated by a series of direct numerical simulations.The numerical results indicate that the basic flow is steady two-dimensional when the Reynolds number is small.The thermocapillary force acts on both the free surface and liquid-liquid interface to drive a pair of counter-rotating circulations in the upper layer.When the pool rotates,the flow in the azimuthal direction is induced by the Coriolis force and the radial flow in the lower part of the lower layer is suppressed.When the Reynolds number exceeds a threshold value,the flows in both layers change to three-dimensional oscillatory flow simultaneously.The weak rotation destabilizes the axisymmetric basic flow,while the strong rotation exerts a stabilizing effect on it.The unstable flow is basically triggered by hydrothermal wave instability mechanism in which the vertical perturbation flows absorb thermal energy from the parabolic-like temperature profiles and create two groups of opposite interior temperature disturbances in the upper layer.They conduct the surface and interface respectively and activate unstable flow.By experiment,the hydrothermal wave is observed in the rotating shallow annular single layer.The critical Reynolds number for the incipience of hydrothermal wave decreases slightly with increasing rotation rate.The wave pattern in the deep layer is characterized by stationary waves,which is composed by straight waves and cone-shape waves near the outer wall.When the system rotates,the waves are pulled towards the counterclockwise direction,but they remain stationary.Contrary to trend in the shallow pool,the increase of rotation rate stabilizes the flow in the deep layer.For bilayer annular pool,the wave pattern in the non-rotating pool is characterized by two groups of hydrothermal waves propagating in opposite azimuthal directions to each other.The increase in the thickness of lower layer reduces the flow stability.When the system rotates in the counterclockwise direction,there is only one group of waves propagating in the clockwise direction.The system rotation destabilizes the thermocapillary flow in the bilayer annular pool.