A Lagrangian boundary element approach to transient three‐dimensional free surface flow in thin cavities

Abstract

AbstractThe lubrication theory is extended for transient free‐surface flow of a viscous fluid inside a three‐dimensional thin cavity. The problem is closely related to the filling stage during the injection molding process. The pressure, which in this case is governed by the Laplace's equation, is determined using the boundary element method. A fully Lagrangian approach is implemented for the tracking of the evolving free surface. The domain of computation is the projection of the physical domain onto the (x, y) plane. This approach is valid for simple and complex cavities as illustrated for the cases of a flat plate and a curved plate. It is found that the flow behavior is strongly influenced by the shape of the initial fluid domain, the shape of the cavity, and inlet flow pressure. Copyright © 2001 John Wiley & Sons, Ltd.