Research On The Dynamics Of Liquid Film Flowing Down A Corrugated Wall

Gravity driven films flowing along an inclined smooth or corrugated wall are studied numerically by using direct numerical method, including its interaction between surface waves, influences of wall topology on its steady and unsteady flow characteristics, as well as the evolution of three dimensional flows. The stability of two dimensional film flows along an inclined wavy wall in the presence of a normal electric field is investigated theoretically, as well as the characteristics of steady flows.For film flowing over an inclined plate, the evolution characteristics of noise driven flow with different Reynolds and inclination angles are studied numerically. Results indicate that the interaction between solitary waves might result in coalescence. The height of the large solitary wave drops down during the coalescence while the height of the medium solitary wave changes contrarily. The phase velocity of the solitary wave is found to be linearly related with its height during this dynamic process. As for the interaction between two solitary waves with same size, the front solitary wave, which initially divides into two small harmonic waves, then develops to relatively larger ones. During of merging process between solitary waves,two dimensional solitary wave might breakup due to transverse instability, resulting in transition from two dimensional to three dimensional flow, with the occurrence of three dimensional solitary waves.Two dimensional steady film flows along a substrate with rectangular corrugations are studied numerically by using direct numerical method. Results indicate that the phase shift between the surface wave and the wall corrugation increases as the Reynolds number. The parametric studies on the interesting resonant phenomenon indicate that the peak Reynolds numbers increase as the raise of the wall depth or the decline of the inclination angle. The dependence of the flow fields is analyzed on the Reynolds numbers and wall depth in details. It is found that the vortical structures in the steady flows, either produced by the interaction between capillary wrinkling and inertia, or by the rectangular geometry, are closely related to the remarkable deformation of the free surfaces. This conclusion is also confirmed by the transient flow development of two typical simulations, i.e., flows in capillary-inertial regime and in inertial regime.Unsteady falling film flows, with periodic or random perturbations at inlet, along a substrate with rectangular corrugations are studied numerically by using direct numerical method.Results indicate that the imposed periodic perturbations with different frequencies induce traveling surface waves with different wavelengths. When the wavelength of structured wall is relatively short, it is found that the static deformed waves due to corrugations ride on the progressive wave resulted from the imposed external perturbations. If these two wavelengths become closer to each other, the nonlinear effect promotes the coalescence between neighboring surface waves. At the dimensionless film height is chosen to be 0.26, the wavelength of wall equals to that of progressive wave when the perturbed frequency f=7Hz, resonant phenomenon can be observed in the film flow. Additionally, the present paper discusses the effect of corrugations on the structure of film flow field, and finds that the phase velocity decreases as the trough depth of the wall increasing.Results for the random perturbations indicate that the nonlinear effect due to wall topography promotes the coalescence between neighboring surface waves, therefore the front solitary wave is of capability to capture the wave in the rear. The Hilbert-Huang transformation is applied to obtain the wave modes with different scales, to reveal the spacial distribution of wavenumber and energy. The waves with relatively large scale represent the solitary waves, whiles the waves with smaller scales stand for static deformed waves. When wall depth increases, the velocity of progressive waves becomes decreasing, because static surface waves adsorbs more fraction of wave energy in flow whereas the kinetic energy of solitary waves reduces. The amplitude change of dominant wave with Reynolds number exhibits a resonant characteristic. It is due to the resonant effect of static surface waves riding on progressive waves in unsteady flows. For the three dimensional flow, it is found that transverse depressions and elevations appear in flow, which rid on solitary waves. Its amplitude increases with downstream distance and its maximum is in order of average film thickness approximately. In addition, the spatial pattern of 3D film flow and its temporal evolution is discussed in detail.Finally,the stability of two dimensional film flows along an inclined wavy wall in the presence of a normal electric field is investigated theoretically, as well as the characteristics of steady flows. To analyze the influences of the electric field and the wavy structures, a set of evolution equations describing the effect of electrical field on the liquid film is derived based on the WRIBL approach. In the case of small amplitude of wall, the capillary is helpful for stabilizing the film flows, whereas the electric field promotes the development of the linear perturbations. An equilibrium condition for the two competing effects is proposed, and results indicate that the wall structure will enhance these effects. The investigations on the steady flows show the dependence of the relative amplitude and the phase difference on the physical parameters, and indicate that the electric field is benefit for suppressing the resonant phenomenon in film down a structured wall.