| A numerical formulation is presented for simulating the injection-molding filling of thin cavities, together with the delivery system, in three dimensions. The modelling is based on generalized Hele-Shaw flow for an inelastic, non-Newtonian fluid under non-isothermal conditions, which has been previously shown to be satisfactory for simulating the polymer melt flow in the cavities. A hybrid numerical scheme is employed in which the injection-molded part is described by two-dimensional triangular elements, provided that the cavity thickness is relatively thin, and the gapwise and time derivatives are expressed in terms of finite differences. The elements are flat, but can have any orientation in 3-D space to approximate the surfaces of the molded part.; A triangular element is further divided into three sub-areas by joining the centroid of the element to the mid-point of its three edges. The control volume associated with any vertex node is then defined as the sum of all such sub-areas containing that node multiplied by each respective thickness. The numerical calculation of the flow field (or the pressure field) is based on the conservation of mass in each control volume which, at any given instant, can be either empty, partially filled, or totally filled with polymer melt. The melt-front location is defined by the partially filled control volumes which are allowed to advance in the calculation such that one partially filled control volume gets filled during each properly chosen time step with all of its adjacent empty control volumes then becoming new melt-front control volumes. The pressure and temperature are calculated at each time step, with the resulting pressure field determining the flow direction which, in turn, determines which partially-filled control volume should get filled during the following time step.; One-dimensional flow segments, such as circular or non-circular tubes, can also be employed to represent the delivery system. This one-dimensional flow is coupled with the cavity filling in order to form a complete simulation of the mold filling. Comparisons with experiment have been made for various mold geometries. The results show good agreement in terms of pressure traces, melt-front advancements, and weldline locations. |
