A three-dimensional hybrid finite element volume tracking model for mould filling in casting processes
Metal casting is a complicated process in which flow momentum plays a crucial role in the mould filling process due to the high velocity of the liquid metal. Inertia and gravity effects may cause splashing, jetting or undesirable filling of the metal flow into the mould cavity. When considering complex parts, the accurate prediction of mould filling behaviour using empirical knowledge and intuition is nearly impossible. Therefore, numerical modelling and simulation are essential to predict such a complex physical problem and assist in part with mould design. A mould filling analysis can help the mould designer to determine the size and location of the gate as well as a proper runner system design for ensuring a complete and balanced filling of the part. Such an analysis can also be used to predict potential product defects, such as air entrapment, porosities, and help in correct positioning of overflows and venting systems. A three-dimensional finite element model combined with a volume tracking method has been developed in this work to simulate the cavity filling for casting processes. A mixed formulation based on a four node tetrahedral element with a bubble function at the centroid (P1(+)/P1) is employed to solve the flow equations. Such a finite element provides a small dimension of the element matrices and satisfies the Brezzi-Babuska condition to ensure a stable solution of the Navier-Stokes equations. A slip boundary condition combined with a friction model is implemented to better simulate the metal flow near the mould walls. An algebraic model is used to account for the turbulence effects during the mould filling. The flow fronts are tracked by a volume tracking method developed for the tetrahedral elements. This method can handle complicated flow front shapes and complex situations like merging and separation of flow fronts. The combination of a volume tracking technique with a FEM flow solver in three-dimensional unstructured meshes constitutes the major feature of this model. Examples of the filling simulations are presented to illustrate the capabilities of the numerical model. Copyright (C) 1999 John Wiley & Sons, Ltd.
finite element volume tracking mould filling mixed formulation three-dimensional flow front tracking