Numerical simulation of wavy liquid film flowing down on a vertical wall and an inclined wall

Interfacial wave behavior and flow characteristics of falling liquid films on a vertical wall and an inclined wall have been studied by means of a numerical simulation, in which the algorithm is based on MAC method. Basic equations are discretized on a staggered grid fixed on a physical space. Interfacial boundary conditions are treated with a newly proposed method and the wave behavior can be calculated accurately. Simulation results agree well with experimental observations. For both the simulation and the experiment of the vertical wall, a low-frequency disturbance develops to a solitary wave, which is a big-amplitude wave accompanied by small-amplitude short capillary waves. In the big wave, a circulation flow generates and grows downstream, in which the scale of the circulation flow is comparable to the wave amplitude, while there is no circulation in the capillary waves. Although waves on the slightly inclined wall develop to the solitary wave, no circulation flow appears in the big wave because of the gravitational effect. Increasing the frequency, the wave amplitude becomes small and accompanied capillary waves disappear. In a certain frequency, the circulation flow repeats generation and collapse due to the wave interaction. (C) 2000 Editions scientifiques et medicales Elsevier SAS.