Influence of the inclined waving wall on the surface wave evolution of liquid film

Abstract

In this paper, the evolution of the fluid surface wave on an inclined waving wall is investigated. The waving wall is assumed to have a sinusoidal fluctuating surface, and the linear stability of the liquid film flow is analyzed. In addition, the evolutions of the disturbance wave under different tilt angles, and the variations in this wave when passing through different wall shapes are studied. It can be observed that the time evolution of the disturbance wave appears to be a near periodic variation of a larger wavelength. Further, by comparing its flow structure with that for the flat plate wall, it is found that the wave conditions are more complex. When the fluid flows through the waving wall, the disturbance wave no longer displays a regular change in space, and its amplitude increases with the tilt angle of the wall increasing. For the same tilt angle, the amplitude of the disturbance wave in the waving wall is greater than that for the flat plate wall, and the distortions in waveform are more obvious. As Re increases, the amplitude of the disturbance wave increases gradually, and the distortion of the corresponding wave increases as well. Further, with the increase of wall surface amplitude, the amplitudes of the static and disturbance waves increase, whereas the corresponding traveling-wave period remains unchanged. Finally, the influence of the wall tilt angle on flow stability is analyzed.