Numerical simulation of mold filling processes

A finite element based, explicit, time-marching scheme is developed for the analysis of three-dimensional, coupled, incompressible fluid flow and heat transfer problems with moving boundaries. The fractional Volume of Fluid (VOF) method is utilized to track the moving free surface. A fractional step method is used to solve the continuity and momentum equations. In this two-step scheme, the velocity field is obtained via explicit (forward difference) time integration of the momentum equations. Then, the pressure field is obtained via solution of an elliptic Poisson equation which results from the fractional step formulation. A conjugate gradient (CG) iterative solution algorithm which utilizes an element-by-element (EBE) data structure which is compatible with the finite element discretization is used to obtain the solution of the large system of algebraic equations that results from the Poisson equation. This algorithm has the important feature that solution time is dependent only on the number of elements in the model, not the element/node ordering or regularity of the grid. A modified formulation of the Poisson equation is developed which is considerably more efficient over the standard fractional step implementation. Regions of the domain which solidify are removed from all fluid transport equations in order to make the solution more efficient. The numerical algorithm is used to analyze the mold filling portion of the manufacturing process of sand casting. Different physical aspects of the phenomena such as moving wave front, gravity forced flow, latent heat release and flow with solidification are studied. In each case, the numerical schemes are tested and verified with two-dimensional test cases which are then extended to three-dimensional models. The filling of a three-dimensional casting is analyzed and compared with experimental results for filling time and temperature distribution during the filling process