Numerical Simulations On Thermocapillary Convection In The Annular Pool Heated From Inner Cylinder With Surface Heat Dissipation

When a tangential temperature difference is applied on the free surface,the surface tension gradient induced by temperature gradient will drive fluid flow,which is called thermocapillary convection.Thermocapillary convection has strong relationships with the industrial processes and common phenomena,such as the coffee-ring effect,the manipulation of microfluidic chip and the progress of crystal growth and film coating.Due to the existence of heat exchange between free surface and the ambient,the coupling of heat dissipation and thermocapillary convection was inevitable.In this thesis,the numerical simulations were performed to explore the thermocapillary convection in annular pools heated from inner cylinder with heat dissipation on the free surface.The effect of heat dissipation on the basic flow,critical conditions and flow pattern after flow destabilization was analyzed.The numerical results are summarized as follows:For 0.65 c St silicone oil with Pr=6.7,it is found that the center location of main roll cell gradually moves to the outer cylinder and the temperature gradient near the inner cylinder increases with the increase of Biot number.When the free surface is adiabatic,the temperature drop near hot cylinder is larger and the flow intensity is stronger in the annular pool with the heated inner cylinder than that with the heated outer cylinder.The critical Marangoni number of flow destabilization decreases first and then increases with the increase of Biot number.The temperature fluctuation pattern depends on the coupling effect of heat dissipation and thermocapillary convection in the annular pool.The temperature fluctuation presents the multicellular wave when the surface is adiabatic,and exhibits the hydrothermal waves when the heat dissipation is considered.At a fixed Biot number,with the increase of Marangoni number,the wave number increases first and then decreases,but the dimensionless oscillatory frequency increases monotonically.When the Marangoni number is small,the sequence of temperature fluctuation with Biot number is the multicellular wave → several groups of the HTWs→ a single group of the HTWs.However,at a large Marangoni number,the patterns transition of temperature fluctuation with Biot number is the multicellular wave →several groups of the HTWs → the radial moving waves.For the silicone melt with Pr=0.011,with the increase of Biot number,the isotherms of basic flow are seriously compressed near the hot inner cylinder,the critical Marangoni number of flow destabilization increases monotonically and the critical wave number almost keeps constant.With the increase of Marangoni number,thermocapillary convection will first evolves from the basic flow to three-dimensional stationary flow with longitudinal stationary stripes on the free surface,and then to three-dimensional oscillatory flow featured with the combination of stationary stripes and azimuthal waves.The secondary transition is maintained by the mutual effect of radial convection,azimuthal local flow and heat dissipation.For the pool with adiabatic free surface,after thermocapillary convection destabilizes,the amplitude of temperature fluctuation increases and the wave number decreases with the increase of Marangoni number.The heat dissipation influences the temperature fluctuation pattern on the free surface.With the increase of Biot number,the destabilization of thermocapillary flow will be impaired and the wave number almost keeps constant when Marangoni number is small,but the wave number increases significantly and the temperature fluctuation becomes more complicated at a large Marangoni number.With the increase of aspect ratio,the evolution of temperature fluctuation on the free surface is the spokes pattern→ the coupling of radial waves and the HTWs → the spoke pattern.