沿倾斜壁面下降的蒸发/冷凝降膜二维表面波的线性稳定性

Linear Stability of the Two-Dimensional Waves of Evaporating/Condensing Film Draining down an Inclined Plate

基于边界层理论和完整的边界条件 ,采用Collocation方法 ,推导出了沿倾斜璧面下降的在蒸发、等温和冷凝状态下普遍适用的二维降膜表面波扰动时域演化方程 ,并分析了不同因素的影响 .结果表明 :蒸发不利于稳定 ,冷凝有利于稳定 ,在蒸发状态下 ,热毛细力导致其失稳 ,在冷凝状态下 ,则促进其稳定 ;表面张力有促进流动稳定的作用 ,液膜的稳定性随倾角和雷诺数的增大逐渐减小 ,随Ka数的增大逐渐加强 ;在小雷诺数下 ,液膜的稳定性主要取决于蒸汽压力和热毛细力的变化 ,在高雷诺数下 ,则取决于惯性力 ;流体物性和壁面倾角在整个雷诺数范围内对液膜的稳定性起着非常重要的作用 .

The time evolution formulation of the two-dimensional waves of the evaporating or isothermal or condensing liquid films falling down an inclined wall is established with the collocation method based on the boundary layer theory and complete boundary conditions. Calculations show that the evaporation process destabilizes the film flow but the condensation process stabilizes the film flow, while the thermo-capillary takes a stabilizing effect if under evaporation conditions but an adverse effect if under condensation conditions. For lower Reynolds number, the vapor recoil and thermo-capillary take dominant effects comparing to the inertia force on flow stability. For higher Reynolds number, the stability is controlled by the inertia force. Present study indicates that the disturbance increases with the increase of Reynolds number and inclination angle, but decreases with the increase of Ka numbers. Furthermore, the effects of liquid properties and inclination angle are always significant.