Numerical Simulation Of 2D Filling Of The Mold

Filling of a mold is an essential part of the permanent mold casting process and affects significantly the heat transfer and solidification of the melt. For this reason, the simulation of filling has been performed in this paper. And for the sake of simple, we considered a 2D model without gravity.A finite element method is presented for the numerical simulation of time-dependent incompressible viscous flows. Governing equations are the unsteady Navier-Stokes equation and the continuity equation:The numerical method is based on a fraction step approach to the time integration of the Navier-Stokes equations in which only the incompressibility condition is treated implicitly. This leads to a computational scheme of extremely simple algorithmic structure that is particularly attractive for cost-effective solutions of large -scale problems.In the filling of mold, we have the free face of the flow, for this reason, a volume of fluid (VOF) - based algorithm utilizing a fixed grid system has been investigation. In order to reduce numerical smearing at the free surface represented on a fixed grid system, a new free surface-tracking algorithm based on the donor-acceptor scheme has been proposed. Novel features of the proposed algorithm are characterized by two numerical tools: the orientation vector to represent the free surface orientation in each cell and the mesh integral algorithm to determine the fluid volume flux at each cell boundary. Whit the mesh integral algorithm, the position parameter of free surface can be easily obtained. The proposed algorithm can be easily implemented in regular grid systems usually encountered in the finite element method (FEM). Moreover, the proposed algorithm can be extended and applied to the 3D free surface flow problems with little modification.Combination of the explicit fractional step formulation and the proposed free surface-tracking scheme resulted in an efficient solution algorithm. At last, validity of the present...