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吴正人, 王琦峰, 陆世佳, 董帅, 刘梅. 倾斜壁面上液膜流中孤立波及其内部涡的演化特性研究. 力学学报, 2024, 54(8): 1-9. DOI: 10.6052/0459-1879-24-031
引用本文: 吴正人, 王琦峰, 陆世佳, 董帅, 刘梅. 倾斜壁面上液膜流中孤立波及其内部涡的演化特性研究. 力学学报, 2024, 54(8): 1-9. DOI: 10.6052/0459-1879-24-031
Wu Zhengren, Wang Qifeng, Lu Shijia, Dong Shuai, Liu Mei. Study on the evolution characteristics of solitary waves and internal vortices in liquid film flow on inclined walls. Chinese Journal of Theoretical and Applied Mechanics, 2024, 54(8): 1-9. DOI: 10.6052/0459-1879-24-031
Citation: Wu Zhengren, Wang Qifeng, Lu Shijia, Dong Shuai, Liu Mei. Study on the evolution characteristics of solitary waves and internal vortices in liquid film flow on inclined walls. Chinese Journal of Theoretical and Applied Mechanics, 2024, 54(8): 1-9. DOI: 10.6052/0459-1879-24-031

倾斜壁面上液膜流中孤立波及其内部涡的演化特性研究

STUDY ON THE EVOLUTION CHARACTERISTICS OF SOLITARY WAVES AND INTERNAL VORTICES IN LIQUID FILM FLOW ON INCLINED WALLS

  • 摘要: 研究了在重力作用下, 二维不可压黏性流体液膜沿倾斜壁面流动时, 其上孤立波及其内部涡的演化. 采用小参数摄动法与行波变换法, 首先推导出了非平整倾斜基底上液膜厚度的零阶和一阶的一般演化方程, 然后对该方程进行化简并采用Mathematica进行数值求解. 分析结果表明: 孤立波波形图中, 波前出现了一个毛细波, 而毛细波波谷处出现了完全开式涡; 通过对流量分析, 发现其与孤立波波形具有相同的变化趋势, 并且与波速呈正相关, 对于双峰与三峰孤立波, 前一波峰的流量比靠后的大; 随着波速增加到超过某一临界值时, 孤立波波峰内将出现涡流, 经过计算该临界波速与倾斜角呈正比关系, 对于双峰与三峰孤立波, 当波速继续增大, 靠后的波峰内也将出现涡流; 通过分析自由表面的速度分布得出: 该涡流的产生是自由表面的垂直速度在波前和波尾的速度梯度与大于波速的水平速度共同作用的结果, 波峰多更容易产生涡流; 通过分析在动坐标系下得到的迹线图, 发现该涡流面积也正比于波速且旋向为顺时针, 综合推断得出: 旋涡是在孤立波表面处开始形成的, 波峰内的流体沿壁面呈滚落状向下运动.

     

    Abstract: This paper investigates the evolution of solitary waves and internal vortices in a two-dimensional incompressible viscous liquid film flowing down an inclined wall under the influence of gravity. Using the method of small parameter perturbation and the traveling wave transformation, we first derive the general zeroth-order and first-order evolution equations for the film thickness on a non-smooth inclined substrate. These equations are then simplified and numerically solved using Mathematica. The analysis results show that in the waveform of the solitary wave, a capillary wave appears at the wavefront, and a fully open vortex forms at the trough of the capillary wave. Flow rate analysis indicates that it follows the same variation trend as the solitary wave profile and is positively correlated with the wave speed. For double-peak and triple-peak solitary waves, the flow rate of the preceding peak is greater than that of the subsequent peaks. When the wave speed increases beyond a certain critical value, vortices appear within the solitary wave peaks. Calculations show that this critical wave speed is directly proportional to the inclination angle. For double-peak and triple-peak solitary waves, further increase in wave speed results in vortices forming within the subsequent peaks as well. By analyzing the velocity distribution on the free surface, it is concluded that the generation of vortices is due to the combined effect of the velocity gradient of the vertical velocity at the wavefront and wave tail and the horizontal velocity exceeding the wave speed, with more wave peaks facilitating vortex formation. Analysis of the streaklines obtained in the moving coordinate system reveals that the vortex area is also proportional to the wave speed and rotates clockwise. Overall, it is inferred that the vortex starts to form at the surface of the solitary wave, with the fluid within the wave peaks rolling down along the wall.

     

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