Influence Of System Rotation On Stability Of Thermocapillary Convection In Annular Pools By Linear Stability Analysis

In order to understand the influence of system rotation on the stability ofthermocapillary convection, the thermocapillary flows in annular pools with innerradius of20mm, outer radius40mm and depths ranging from1mm to5mm wereinvestigated using linear stability analysis. The critical conditions for the onset ofoscillatory flow were determined under the pool rotation rates ranging from0to2.09rad/s, including in critical Marangoni number of Mac, critical azimuthal wave number ofmcand critical phase velocity of ωc. The dissipative structures for the oscillatory flowunder critical conditions were obtained numerically. The effects of pool rotation on thestability of thermocapillary convection and dissipative structure were analyzed. Thestability of thermocapillary flow in the pool heated from outer wall was compared withthat heated from inner wall. We found the following conclusions.(1) When the rotate rate is low, the Macnumber for the incipience of oscillatoryflow decreases with increasing rotation rate of pool, which means that the weak poolrotation destabilizes the axisymmetric steady thermocapillary convection. However,under higher rotation rate, the Macnumber for the incipience of oscillatory flowincreases with increase of pool rotation rate, i.e., the strong pool rotation stabilizes thesteady thermocapillary flow.(2) For layers heated at outer wall as well as heated at inner wall with depth of1mm, the critical wave number of mcincreases with increase of Ta numbers whenTa<2.0while mckeeps constant when Ta>2.0. For layers with depth of3mm and5mm,when the pool rotation rate is low the critical wave number of mcdecreases withincrease of pool rotation rate while the mcincreases with increasing the rotation ratewhen the rotation rate is high. In the pool heated from outer wall, the critical phasevelocity of ωcdecreases with increasing pool rotation rate. However, the ωcincreaseswith increase of rotation rate in the pool heated from inner wall. In the most cases, thewave patterns propagate azimuthally in the direction opposite to the pool rotationdirection.(3) Under the same pool rotation rate, the Macnumber for the incipience ofoscillatory flow decreases with increase of pool thickness from1mm to5mm. Thecritical wave number decreases with increase of pool thickness too.(4) The spiral wave patterns under critical conditions distributes uniformly in the pool along azimuthal direction. The wave pattern travels along radial direction andazimuthal direction. When the pool rotation rate is low, since the weak pool rotationdestabilizes the thermocapillary flow, the length of spiral wave pattern increases withincrease of pool rotation rate. Under higher pool rotation rate, the spiral wave patternbecomes shorter and shorter with increasing pool rotation rate because the stronger poolrotation stabilizes the thermocapillary flow.(5) The spiral wave patterns were bent at the outer wall when the pool heated fromouter wall while the bent occurs at the inner wall when the pool heated from inner wall.With increase of thickness, the size of bent wave becomes larger. The stronger poolrotation suppresses the bent waves in the pools heated from outer wall and from innerwall.