Numerical Study On The Influence Of Waving Wall On Liquid Surface Waves

In the study of surface waves of liquid film, different wall structures will largely influence the evolution of the surface waves, Along with the change of wall structure, the flow structure and state of liquid will change, leading to a series of complex surface waves arise at interface, Its evolution has important applications in industrial equipment, such as the heat exchanger, condenser, microfluidics and nuclear power plant cooling system, etc. So it is of great significance to study on the evolution theory and numerical research of surface waves under different wall structures.In this paper, the evolution rule of surface waves flow on the waving wall is studied, according to different research objects, two cases of vertical waving wall and inclined waving wall were studied. The small parameter perturbation method is used to solve control equations and boundary conditions, then the zeroth and first order equations are derived. Then the steady flow solutions and perturbation equation are obtained, the perturbation equation is solved using the derivative expansion method. Then the software of matlab is used to simulate the surface waveform. We can obtain the conclusion as follows:1) The research of surface waves on vertical waving wall: As the wall structure is simple harmonic, when the frequency of wall is small, the wavelength of static waves and traveling waves is close, promoting the merger between surface waves, and surface wave amplitude is obviously increased when wall frequency, wall depth or Re increases; As the wall structure is the single-wave packet, the increase of wall amplitude and the decrease of the wall width both can lead to the distortion more violent and the amplitude increases obviously. While the increase of Re can cause the perturbation more seriously and the waveform distorted, and the amplitude of the surface wave increases in the whole flow field.2) The research of surface waves on inclined waving wall. By solving the control equations and boundary conditions for the zeroth order and first order equation of surface waves, Considering the wall shape is simple harmonic, under different angles, the evolution of the disturbance waveform over time and the changes of waveform when flow on different wall shapes are researched, and the influence of parameters such as Re, wall disturbance waveform amplitude and angle on the evolution and stability analysis are studied as well.