Filling Process in an Open Tank

A numerical simulation for a filling process in an open tank is performed in this paper. A single set of governing equations is employed for the entire physical domain covering both water and air regions. The great density jump and the surface tension existing at the free surface are properly handled with the extended weighting function scheme and the NAPPLE algorithm. There is no need to smear the free surface. Through the use of a properly defined boundary condition, the method of “extrapolated velocity” is seen to provide accurate migrating velocity for the free surface, especially when the water front hits a corner or a vertical wall. In the present numerical procedure, the unsteady term of the momentum equation is discretized with an implicit scheme. Large time-steps thus are allowed. The numerical results show that when the water impinges upon a corner, a strong pressure gradient forms in the vicinity of the stagnation point. This forces the water to move upward along the vertical wall. The water eventually falls down and generates a gravity wave. The resulting free surface evolution is seen to agree well with existing experimental data. Due to its accuracy and simplicity, the present numerical method is believed to have applicability for viscous free-surface flows in industrial and environmental problems such as die-casting, cutting with water jet, gravity wave on sea surface, and many others.