A fast simulation of transient metal flow and solidification in a narrow channel. Part I: Model development using lubrication approximation

A fast numerical algorithm for modelling transient flow and solidification of liquid metal in a narrow gap is presented. The problem is closely related to the die-cast process, and, in particular, to metal flow in thin ventilation channels. After integrating over the channel thickness and employing the lubrication approximation, the Navier-Stokes equations are reduced to 2-D equations for modelling the in-plane flow. The flow model is solved along with a heat balance equation after including the effects of solidification in a control volume. The flow variables and temperature distribution are solved in three stages. In step one, commercial software FLOW3D® is used to solve 3-D Navier-Stokes equations coupled with the heat balance equation for flow and solidification in the main cavity. In step two, the flow and heat transfer variables from the main model are transferred as the entrance boundary condition for the proposed numerical simulation. Finally, in step three, the metal flow and solidification in a thin channel is modelled using the 2-D equations coupled with the 1-D heat balance equation. Since the solid-liquid interface introduces non-linearity in the flow, the 2-D flow equations are solved iteratively while a staggered grid arrangement as required by the SIMPLE algorithm is used for discretization. Later in part II, the proposed simulation is applied to predict parts produced by the high pressure die cast process (HPDC). The model is validated by comparing its results with those obtained from the commercial flow-and-solidification software Flow3D® as well as with the experimentally measured Secondary Dendrite Arm Spacing (SDAS).