A Streamline‐Upwind Model for Filling Front Advection in Powder Injection Moulding

The filling process of powder injection molding is modeled by the flows of two variably adjacent domains in the mold cavity. The feedstock is filled into the cavity while the air is expelled out by the injected feedstock [1]. Eulerian description is adopted. The filling patterns are determined by the solution of an advection equation, governed by the velocity field in both the feedstock flow and air flow [2]. In the real physics, the advance of filling front depends mainly on the flow of feedstock that locates behind the front. The flow of air in front of the injected material plays in fact no meaningful effect. However, the actual algorithm for solution of the advection equation takes equally the importance for both the flow of viscous feedstock and that of the slight air. Under such a condition, the injection flow of feedstock in simulation may be misdirected unrealistically by the velocity field in the air portion of the mold cavity. To correct this defect, an upwind scheme is proposed to reinforce the effect of upwind flow and reduce the effect of downstream flow. The present paper involves the investigation of an upwind algorithm for simulation of the filling state during powder injection molding. A Petrov‐Galerkin upwind based method (SUPG) is adopted for numerical simulation of the transport equation instead of the Taylor‐Galerkin method in previous work. In the proposed implementation of the Streamline‐Upwind/Petrov‐Galerkin (SUPG) approach. A stabilization method is used to prevent oscillations in the convection‐dominated problems. It consists in the introduction of an artificial diffusion in streamline direction. Suitable modification of the test function is the important issue. It ensures the stable simulation of filling process and results in the more realistic prediction of filling patterns. The implementation of upwind scheme in mould filling state simulation, based on an advection equation and the whole velocity field of feedstock and air flow, makes the prediction of filling evolution mostly dependent on the flow effect of injected material. This new procedure reveals its effectiveness for complicated filling flows with front joining. It can be furthermore adapted to the prediction of powder segregation effect in injection process. It involves the solution of two coupled advection equations for evolution of the powder and binder volume fractions that should be dominated only by the upwind flows of each phase. The numerical results obtained by the proposed approach are compared with experimental ones. The efficiency of the proposed approach is approved.