基于水平集方法的毛管上升特征研究

Study of characteristic of capillary rise using level set method

毛管上升现象与许多行业密切相关,系统地对此现象进行研究具有重大意义。与传统理论研究方法不同,本文使用N-S方程耦合水平集方法模拟毛管气液上升行为。通过与简化条件的解析解对比,验证了模拟方法的可靠性。此外,详细地研究了毛管振荡现象,并分析了影响毛管振荡行为的主要因素。结果表明,水平集方法能够精确地表征毛管振荡现象,与数值解相比具有更高的精度。毛管长度的增加能够减弱液柱振荡,主要归结于非湿相气体的粘滞力作用;湿相密度和湿相粘度同样对毛管振荡现象影响显著。湿相密度越大,惯性力越大,促进了毛管振荡;而湿相粘度变大,会增大粘滞力作用,因此减弱了毛管振荡现象。毛管振荡是由多种影响因素共同控制的,流体的惯性力是造成毛管振荡的主要原因,而粘滞力是减弱毛管振荡行为的主要因素,使液柱振荡逐渐衰减,并稳定至平衡高度。

The study of dynamic capillary rise is crucial for many industries and applications.Unlike the traditional theoretical work on the penetration of liquids into circular cylindrical capillaries,capillary force,gravity,inertial force,viscous force,etc.,are not taken into account entirely.This paper used time-dependent N-S equation coupling level set method for simulating the liquid rise in capillary tubes under different conditions.To begin with,we validated the model by comparing the simulation results with the simplified analytical solutions.Then,we investigated capillary oscillation phenomena in detail and the main impacts on oscillation behaviors in capillary tubes were discussed.The results show that this coupling method can accurately capture characteristics of rebounds of liquids in cylindrical tubes.With the increase of the capillary tube’s length,the magnitude of capillary oscillation seems to be weakened which is attributed to the resistance of air theoretically,the capillary oscillation will vanish if the length of tube is indefinite.In addition,the liquid viscosities also produce a remarkable effect on the oscillating behavior in capillary tubes,increasing the viscosity of liquid results in a greater viscous resistance of the wetting liquid,thus the oscillation is reduced and even disappears.Moreover,the liquid density has a positive correlation with the inertial force.Therefore,a more drastic oscillation behavior will emerge when using a higher density of liquid for simulation.In conclusion,the capillary oscillation is controlled by a variety of factors.The inertial force of the liquid is the principal reason that may give rise to the oscillation of liquid column.