电场作用下导电射流稳定性的理论与实验研究

Theoretical and Experimental Investigation on Instability of a Conducting Liquid Jet under a Radial Electric Field

建立导电射流在径向电场作用下的线性稳定性粘性模型,通过正则模方法,推导了轴对称和非轴对称模态下的色散关系,通过计算求得增长率随波数及电欧拉数的变化,并在理论上预测了最有可能波长。选用酒精和酒精甘油混合物作实验液体,观察了径向电场对射流不稳定性行为的影响规律,并测量射流表面波的波长。实验结果和理论结果在定性方面取得了较好的一致。但通过与实验比较,理论预测的最有可能波长在非轴对称模态出现较大偏差,普遍比实验结果小。而且,实验表明,最大增长率并不是判断主导模态的好标准,因为在非轴对称的最大增长率小于轴对称的最大增长率情况下,实验显示非轴对称模态要比轴对称模态明显了。因此,对于非轴对称的不稳定机理,需要进一步研究。对轴对称模态,理论给出了较好的预测。

A model of a conducting viscous liquid jet under a radial electric field was established, in order to study the linear instability behaviors of it. In terms of the normal mode method, the dispersion relations for both the axisymmetric case and the non-axisymmetric case were derived analytically. The growth rate for different wave number and electrical Euler number were calculated, and the most possible wave length was predicted theoretically. In experiments, ethanol and a mixture of ethanol and glycerol were chosen as experimental liquids. The behavior of a jet under the radial electric field was observed, and the length of surface wave was measured. The experimental result agrees well with the theoretical result quantitatively. However, the theory predicts much smaller wave length than that observed in experiment for non-axisymmetric case. Moreover, the experiment shows that the predominant mode cannot be predicted according to the maximum growth rate, because the non-axisymmetric mode becomes predominant when its growth rate is smaller than that of axisymmetric mode. Hence, the mechanism of non-axisymmetric instability of jet needs to be studied further. For the axisymmetric mode, the theory shows good prediction.