环形池内反常热毛细对流及稳定性线性稳定性分析

Linear Stability Analysis of Anomalous Thermocapillary Convection and Stability in Annular Pools

线性稳定性分析研究了环形池内反常热毛细对流及其稳定性,分析了液层深度对它们的影响。结果表明;当Ma较小时,反常热毛细对流为稳定的轴对称流动;当Ma超过临界值后,反常热毛细对流失稳,形成三维稳态波纹,波纹的形态与液层厚度有关。当液层深度H(H=d/ΔR,d为环形池深度,△R为内外径宽)小于0.0833时,失稳波纹为波数较多、位于环形池外环边沿、短小细密的"边沿波";当H大于0.0833时,为波数较少、波纹较宽、几乎占据整个液层、呈轮辐状的"轮形波";H等于0.0833时,同时存在这两种波纹的可能性。随着液层深度的增加,对流失稳的临界Ma数逐渐减小。能量收支分析讨论了它们的失稳机理。

Anomalous thermocapillary convection and its stability are investigated in annular pools by linear stability analysis, and the influence of liquid layer depths （H = d/△R=O.05-0.5） is investigated. The results reveal that when Ma is small, anomalous thermocapillary convection is a two-dimensional steady axisymmetric flow. When Ma exceeds a certain threshold value it is destabilized to be steady three-dimensional flow. As to the different liquid layer depths, two kinds of instability patterns can occur. In shallow pools （H〈0.0833）, the instability patterns are short and thin ＂marginal patterns＂ with more wave numbers, located near the outer wall of the annular pools. In deep pools （H〉0.0833）, the basic flow destabilizes into a wide spoke-like perturbation patterns with less wave number, occupying the whole liquid layer, called as ＂spoke patterns＂. When H=0.0833, two kinds of wave patterns are possible with equal probability. With increasing the liquid layer depth, the critical Marangoni number decreases. Their instability mechanisms are explained by energy budgets analysis.