Numerical Study On The Influence Of Wall Topography On Evolution Of Solitary Wave On A Liquid Film

Liquid film flow has important industrial application and academic value. On the one hand, it is widely used in energy, chemical industry and other fields because of its strong ability of heat and mass transfer; On the other hand, it also involves nonlinearity, solitary wave, chaos and many other hot subjects. As a result, it has attracted many scholars to do extensive research since more than ten years ago. At the same time, insight into the hydrodynamic characteristics of the flowing liquid film and study on the influence of wall topography on evolution of surface wave on a liquid film have become a challenging research topic.In this paper, the incompressible viscous fluid with surface tension flowing along the uneven inclined wall is studied, mainly including the following contents:(1) By means of setting up physical model, assuming that liquid film parameter and wall topography parameter are of the same order, nondimensionalizing governing equation and boundary conditions, solving with perturbation method, the equation of the thickness of the flowing liquid film down the uneven inclined wall is obtained.(2) The equation of the thickness of the liquid film down the uneven inclined wall is simplified, the nonlinear ordinary differential equation with boundary value conditions is transformed into the eigenvalue problem of solitary wave using traveling wave transformation and numerical integration, and the figures of wave profiles, streamlines, instantaneous flow rate, velocity distribution at the free surface and streaklines for solitary wave on the flowing liquid film are drawn.(3) A new method is used to study evolution of surface wave on the flowing liquid film down the vertical corrugated wall, firstly wall function item is equated to constant value, secondly the nonlinear ordinary differential equation is transformed into nonlinear algebraic equations using traveling wave transformation and Fourier series expansion, finally the figures of evolution of surface wave are obtained using Mathematica numerical solution. The results show that surface wave divides constantly with the passing of time, and finally it evolves into the static envelope wave.