气流速度振荡场中幂律液膜不稳定性分析

采用线性稳定性分析研究了处于气流速度振荡场中幂律液膜时间模式的不稳定性。振荡的气流速度导致动量方程为含有时间周期系数的希尔方程，采用Floquet理论进行求解。详细研究了不同振荡幅值和振荡频率下表观雷诺数、幂律指数及无量纲速度因子对各不稳定区间的影响。结果表明：振荡幅值的增加或振荡频率的减小会使液膜不稳定区域的个数增加，且Kelvin-Helmholtz（K-H）不稳定区域的最大增长率、主导波数和截止波数随振荡幅值和振荡频率的增加而增加；表观雷诺数、幂律指数和无量纲速度因子的增加增强了K-H不稳定区域内的不稳定性，使参数不稳定区域内的增长率先减小后增加；振荡幅值的变化不改变最大增长率发生转折时对应的流变参数，而当振荡频率较小时，幂律指数和无量纲速度因子的增加却使最大增长率单调增加。

Instability of power-law liquid sheets in presence of gas velocity oscillations

Temporal instability analysis of a power-law sheet in a gas velocity oscillation field was performed with linear stability analysis. The oscillation of gas velocity induced the momentum equation to be a Hill equation with a time period coefficient, which was solved using Floquet theory. For different oscillation amplitudes and frequencies, the effects of the generalized Reynolds number, power-law index and dimensionless velocity factor on various unstable regions were studied. Results show that the increase of the oscillation amplitude or the decrease of the oscillation frequency will increase the number of unstable regions of the sheet, and the maximum growth rate, dominant wave number and cut-off wave number of the Kelvin-Helmholtz (K-H) unstable region increase with the increase of the oscillation amplitude and frequency. The increase in generalized Reynolds number, power-law index and dimensionless velocity factor enhances the instability of the K-H unstable region, causing the growth rate in the parametric instability region to decrease first and then increase. The variations of the oscillation amplitude do not change the rheological parameters corresponding to the transition of the maximum growth rate. When the oscillation frequency is small, the increase of power-law index or dimensionless velocity factor leads to monotonous increase of the maximum growth rate in the parametric instability region.