Effect Of Surface Heat Dissipation On Thermocapillary Convection In Annular Pool

Thermocapillary convection widely exists in industrial production and natural phenomena,such as crystal growth,film coating,droplet and liquid layer evaporation.An annular liquid pool is a theoretical model abstracted from Czochralski crystal growth technology.Therefore,in order to improve the quality of crystal growth,it is nessary to understand and control the flow of melt.Up to now,researchers have done a lot of researches on thermocapillary convection in an annular liquid pool,and achieved fruitful results.However,in previous studies,it is always assumed that the free surface is adiabatic.In fact,due to the non-equilibrium thermodynamic effect on the free surface,the heat dissipation of the liquid layer is inevitable,that is,surface heat dissipation effect and thermocapillary convection are often coupled together and influence each other,which makes the thermocapillary flow with surface heat dissipation in an annular liquid pool more complicated.In this thesis,the influence of surface heat dissipation on the flow structure and the stability of thermocapillary convection in an annular liquid pool is simulated numerically,and the effects of Prandtl(Pr)number,aspect ratio ? and Biot(Bi)number on the stability of thermocapillary convection are analyzed.The critical conditions for the flow destabilization with different Prandtl numbers and their variations with heat dissipation Biot number are determined.After flow destabilization,the evolution of flow pattern with Marangoni number is discussed under different conditions.The variations of wave number,amplitude and frequency of oscillating flow under various conditions are obtained,and the coupling mechanism between surface heat dissipation and thermocapillary convection is further revealed.The main research contents and results are as follows:Firstly,a theoretical model of thermocapillary convection considering surface heat dissipation in an annular liquid pool is established,and thermocapillary convection of silicon melt with Pr=0.011 in an annular liquid pool is numerically simulated systematically.The critical conditions of flow destabilization and the evolution process of flow pattern under different heat dissipation Biot numbers are determined.The results showed that:(1)With the increase of heat dissipation Biot number,the thermocapillary convection cell moves outward gradually,the radial temperature gradient on the free surface near the inner wall decreases and near the outer wall increases;the flow intensity increases first and then decreases slightly.(2)Under different aspect ratios and surface heat dissipation Biot numbers in an annular shallow pool,with the increase of Marangoni number,axisymmetric steady flow may be transited directly into three-dimensional unsteady flow,or first into three-dimensional steady flow,and then into three-dimensional unsteady flow,but the range of Marangoni numbers for three-dimensional steady flow is narrow.(3)When the flow is unstable,the amplitude of surface temperature fluctuation increases monotonously with the increase of Marangoni number,but wave number and frequency depend mainly on the flow pattern.When the flow pattern changes,wave number will have a mutation.(4)With the increase of Marangoni number,there are two flow regime transitions in thermocapillary convection under all heat dissipating Biot numbers in a deep pool with an aspect ratio of 1.0.The first is from axisymmetric steady-state flow to three-dimensional steady-state flow,and the second is to three-dimensional oscillatory flow.The critical Marangoni numbers of flow pattern transition decreases slightly with the increase of Biot number.The physical mechanism of flow destabilization is the sudden change of flow direction near the upper part of the inner wall and the lower part of the outer wall.Therefore,the maximum temperature and velocity fluctuations occur near the lower part of the outer wall.(5)In a deep annular pool,with the increase of Biot number,the azimuthal temperature fluctuation on the free surface gradually shrinks to the inner wall,and the fluctuation area of temperature decreases,while it remains unchanged basically at the bottom,but the fluctuation amplitude increases.Then,thermocapillary convection of 0.65 cSt silicone oil with Pr=6.7 in an annular liquid pool with surface heat dissipation is simulated numerically.The critical condition of flow destabilization and the evolution process of flow pattern are determined and compared with the results of the silicon melt.The results show that:(1)In the shallow pool with ?=0.05,when Bi<10,the critical Marangoni number of flow destabilization is almost unchanged;when Bi?10,the critical Marangoni number increases with Biot number.In the shallow pool with ?=0.1,the critical Marangoni number of flow destabilization first decreases and then increases with the increase of surface heat dissipation Biot number.(2)In a shallow pool,when Biot number is small,the flow pattern after destabilization is dominated by HTWs;with the increase of Biot number,the radial rollers near the outer wall gradually expand to the inner wall and eventually occupy the whole pool,so the radial rolls dominate the flow pattern after destabilization.(3)With the increase of Marangoni number,the evolution process of flow pattern under small Biot numbers in a shallow pool is similar to that under surface adiabatic condition,and the main frequency of fluctuation increases gradually.When Biot number is large,the flow pattern after flow destabilization is a radial roll cell with azimuthal alternating transformation,its fluctuation frequency is large;then it gradually evolves into azimuthal wave,and its fluctuation frequency will be slightly reduced.(4)In a deep pool with aspect ratio of ?=1.0,with the increase of Biot number,the critical Marangoni number of flow destabilization increases gradually,the flow is enhanced and the critical wave number increases.(5)When 0<Bi<10,the flow pattern after flow destabilization first transforms into a radial rolling with azimuthal reciprocating oscillation,and the destabilization mechanism should be belonged to Marangoni-Bénard instability.When Marangoni number continues to increase,the flow will evolve azimuthal waves.When Bi?10,the flow pattern after flow instability becomes directly azimuthal waves.With the increase of Biot number,the fluctuation frequency of three-dimensional oscillatory flow increases and wave number increases.Finally,the calculation method of vapor-liquid interfacial evaporation mass flux in pure steam environment and its influencing factors are analyzed.Then the thermocapillary convection process of water with surface evaporation in an annular liquid pool is simulated by using the determined evaporation mass flux formula,and the coupling effect between surface evaporation and thermocapillary convection is revealed.The results showed that:(1)The vapor-liquid interface evaporation rate increases with the increase of evaporation temperature difference and interface temperature.The results of staticstical rate theory are basically the same as those predicted by Hertz-Knudsen equation,but the deviation increases with the increase of temperature difference.(2)Due to the endothermic effect of surface evaporation,the free surface temperature decreases,the temperature gradient near the wall increases,the thermal capillary force increases,the flow is enhanced,and the isotherms shrink to the wall.There is a large isothermal region in the middle of the liquid pool.(3)With the increase of Marangoni number,the flow ie enhanced,and the flow cells near the wall gradually expand to the middle of the liquid pool;the enhanced thermocapillary convection will carry more hot fluid along the free surface to the inner wall,making the evaporation area expand,and the evaporation rate increases.(4)With the increase of enviromental temperature,the condensation rate near the inner wall increases,the radial temperature gradient increases,thermocapillary convection strengthens;near the outer wall the temperature gradient decreases,and thermocapillary convection gradually weakens.With the increase of ambient vapor pressure ratio,the evaporation rate gradually slows down,and the condensation process may occur near the inner wall.Therefore,the radial temperature gradient increases and the flow is enhanced,while the flow near the outer wall decreases.