Linear Stability Analysis Of Thermocapillary Flow In An Annular Two-layer System

As a new field of engineering thermophysics, the research on the hydrodynamicand thermodynamic features of thermocapillary convection is developed in recent years.In the crystal growth process, stability of the flow concerns directly with the quality ofthe crystal growth. The liquid encapsulation Czocharalski (LEC) technology caneffectively suppress thermocapillary convection in the melt. However, there is a lack ofthe understanding on the basic characteristics, critical condition for the incipience of theflow instability, influence of physical parameters and geometry parameters on the flowstability, and the mode of flow pattern after the flow losing stability in an annulartwo-layer system basing on the liquid encapsulation Czocharalski technology.Aiming at the thermocapillary convection in an annular two-layer system underhorizontal temperature gradient, both linear stability analysis and experimentalobservation are performed to obtain a series of neutral curves and show the variation ofcritical Marangoni number, critical wave number and critical phase velocity withdifferent aspect ratio, different radius ration between the cold inner wall and the hotouter wall, and different liquid layer depth, which are significant to engineeringapplications. The results with rigid upper wall and those with free upper surface arecompared. The influence of the gravity on the critical condition of the flow patterntransition is discussed, and the physical mechanism of the thermal convention transitionis revealed. The following conclusions could be made:①For the annular two-layer system with upper rigid wall, under the microgravitycondition, there exists the minimum critical Marangoni number at the ratio of the lowerliquid thickness to the total depth=0.375, then it increases with the decrease of thedepth of the upper liquid. Under the gravity condition, the most stable region is around=0.75.②For the annular two-layer system with upper free surface, under the microgravitycondition, the maximum critical Marangoni number appears at=0.5-0.833. And thevalue correspomding to the maximum critical Marangoni number would decreasewith increase of the aspect ratio of the cavity. For the annular two-layer system underthe normal gravity condition, there exists the maximum critical Marangoni number at≈0.625-0.833. The variation tendency of the critical Marangoni number with is thesame as one under the microgravity condition. ③Critical Marangoni number decreases with the increase of the aspect ratio of thecavity and radius ration between the cold inner wall and the hot outer wall.④The mode of flow pattern transition of thermal convection is predicted inannular two-layer system, which depends mainly on the ratio of the lower liquidthickness to the total depth. Three transition modes have been found, they are the firsttype of hydrothermal wave, the second type of hydrothermal wave andthree-dimentional stationary flow.⑤The upper surface condition and the gravity level have great effects on thestability of the thermal convection in two-layer system. The critical Marangoni numberwith rigid upper wall at the same ε is much larger than one with upper free surface.However, the influence of gravity is more complex. At the condition of rigid upper wall,the critical Marangoni number at the microgravity is larger than that at the normalgravity, which means that buoyance can reduce the stability of the flow. On the contrary,at the condition of upper free surface, the critical Marangoni number at the microgravityis smaller than that at the normal gravity.Experimental observation is performed by the schlieren technique for the systemscomposed of0.65silicone oil and water, and1.0silicone oil and water. The criticalMarangoni number and the temperature disturbance pattern are compared. It can befound that a good agreement is obtained between linear stability analysis andexperimental observation.