Numerical Simulation On Oscillatory Coupled Thermo-solutocapillary Convection

The floating half-zone method of liquid bridge is a simplified geometric model to simulate the growing crystal process of float-zone method.Its free surface is maintained by the surface tension of the liquid.When temperature difference or concentration difference is applied to both ends of the liquid bridge,it will form temperature gradient or concentration gradient on the free surface,which will result in the uneven distribution of surface tension and drive the flow of liquid bridge as well as the capillary convection.In the present paper,a physical and mathematical model of liquid bridge has been built based on the Fortran language.The continuity equation,Navier-Stokes equation,energy equation,mass transfer equation,and Level set function have also been adopted as the control equation to study the thermo-capillary convection,solute capillary convection and thermo-solute capillary convection in liquid bridge The flow characteristics in liquid bridge and the distribution of the concentration,temperature and velocity on the free surface of the liquid bridge arc also discussed and analyzed.The staggered grids are adopted in the computation process and the projection method is used to solve the Navier-Stokes equation to ensure the satisfaction of continuum equation.The Quick schemes and standard central difference schemes are adopted in the convective and diffusion term of energy equation and concentration transport equation respectively while the second-order essentially nonoscillatory(ENO)schemes is adopted in the convective term of Level set function.To ensure that the Level set function is a distance function in the whole computation process,the re-initialization function is added.Similarly,in order to avoid the dissipation of the fluid medium,the area-preserving procedure is inserted into the main procedure.The research features of this paper is to study thermocapillary convection,solute capillary convection and thermos-solute capillary convection under different conditions on the premise of considering the dynamic deformation of free surface.On the base of validation of the computation code,this paper focuses on the research and analysis from the following questions:(1)The flow fielddistribution of thermocapillary convection,solute capillary convection with non-gravity conditions in liquid bridge.The relationship between free surface deformation and concentration,temperature and velocity distribution on liquid bridge surface.The thermos-capillary convection and the solute capillary convection oscillating flow are investigated as well.(2)The thermocapillary convection and the solute capillary convection are coupled into the liquid bridge.The study was carried out separately about the thermo-solutecapillary convection dominated by thermocapillary force,the thermos-solute capillary convection dominated by capillary force and thermos-solute capillary convection that thermocapillary force and capillary force are equal.The results are compared with pure thermocapillary convection and pure solute capillary convection,and how they affect each other when they are coupled.According to the experimental results of this article,we have the following conclusions(1)In thermocapillary convection,the solution in the liquid bridge flows from the hot side toward cold side along the free surface of the liquid bridge,while it flow from the cold side toward hot side in the center of the liquid bridge.This leads to the isotherm bend downward near the free surface.The free surface deformation shows an inward depression on the upper part of the liquid bridge,however it shows the opposite phenomenon.The deformation,axial velocity and radial velocity increase with the temperature difference rising.(2)In solute capillary convection,the solution in the liquid bridge flows from the low concentration side toward high concentration side along the free surface of the liquid bridge,while it flow from the high concentration side toward low concentration side in the center of the liquid bridge.The results of these flow is that concentration contour bend upwards near to the free surface of liquid bridge.Different from the thermocapillary convection,the deformation of free surface in solute capillary convection is disorderly.The axial velocity and radial velocity decresse with the concentration difference rising.(3)The oscillation of thermocapillary convection or solute capillary convection is more intense with the increase of temperature difference of concentration difference.When oscillation occur,the closer to the hot side,the stronger the oscillation in thermocapillary convection.However in solute capillary convection,both two ends of liquid bridge intensely oscillate.The oscillation starts at the middle of surface in thermocapillary convection while the upper end of surface in solute capillary convection.(4)When one of the capillary force is in dominant position in thermo-solute capillaryconvection,the flow field in liquid bridge is similar to the same capillary convection.If the thermocapillary force is equal to the solute capillary force,the flow field will not disappear but maintain like one of the capillary convection.(5)When temperature difference and concentration difference are both small,the thermocapillary force and the solute capillary force influent each others.In this positon,two of them restrain the posibility of oscillation.With the increase of temperature difference and concentration difference,the thermocapillary force and the solute capillary force make the oscillation more intensively toghter.In the situation that one of them is big and another is so small,the smaller one weaken the bigger one,but during the temperature and concentration spread,there is still oscillation.