Abstract
Two-dimensional fountain flow in the filling process inside a small channel is studied in this thesis. In addition, variation of a group of dimensionless parameters which dominate the free surface meniscus and flow field in the filling process are discussed respectively as well, including Reynold number, Capillary number, and the Contact angle. For a fountain flow problem, the surface tension term in force balance equation is highly related to the free surface curvature on liquid-air interface, however, there isn’t a simple and effective method for the curvature calculation on free surface in the past. For a fountain flow inside a channel, free surface shape can be approximately regarded as a circle, thus, a least square method is proposed in this thesis to handle the curvature calculation on free surface. By this numerical method, a best fitting circle is calculated according to the present free surface shape in filling process at every time step. After that, it provides a curvature to surface tension term in force balance equation, and then we get the two-phase pressure difference between liquid-air interface. Lastly, a uniform free surface pressure is properly estimated through this numerical method.