随时间变化的非平整壁面对液膜表面波演化特性的影响

Influence of uneven wall changing over time on the characteristics of liquid surface wave evolution

本文对非平整壁面上的液膜表面波演化过程进行了研究.针对非平整壁面随时间变化的特性,采用小参数摄动法对控制方程和边界条件进行求解,推导出波动壁面上液膜表面波的扰动方程,采用导数展开法对其进行求解,并选取简谐波形状的壁面进行数值研究.对波动壁面下不同参数的影响规律研究可得,当壁面频率较小时,静态波与行进波的波长比较相近,促进表面波之间的合并,且壁面频率、壁面振幅及Re数的增加,均会使表面波的振幅明显增大;对比波动壁面与非平整壁面可得,在相同位置处,随着时间的演化,非平整壁面上表面波呈周期变化,而波动壁面上表面波呈波长更大的近周期变化;壁面振幅和壁面频率的降低,均会使两种壁面结构下的表面波振幅减小,但所形成的表面波形有所不同,即波动壁面引起的表面波可看作波动壁面结构与非平整壁面引起的表面波叠加而成.

This paper mainly studied the evolution of liquid surface waves along an uneven wall. Considering the characteristic of the uneven wall changing over time, the perturbation equation for the surface waves is derived by using the small parameter perturbation method to solve the control equations under the given boundary conditions. The method of derivative expansion is used to find the solution to the equation and numerical research is then carried out for the wall shape of a simple harmonic. By studying the influence of different parameters on the wavy wall, it can be found that when the frequency of the wall is small, the wavelengths of static waves and traveling waves are close to each other, promoting the merger between the surface waves, and the surface wave amplitude is obviously increased when the wall frequency and wall depth or Re increase. By contrast of the two cases of wavy wall and uneven wall, the surface wave on uneven wall has a periodical change at the same location with the increase of time, while the surface wave on wavy wall has an almost periodic change with a longer wavelength. Although the decrease of the wall amplitude and the wall frequency both can cause surface wave amplitudes reduced, the surface waveforms are different, for the surface wave on the wavy wall can be regarded as the superposition of wavy wall waveform and surface waveform caused by uneven wall.