Mathematical modeling of the filling process of a slender mould cavity

In this paper, three mathematical models of the solidification of a thin-walled casting, which take into account the filling process of the mould cavity with molten metal, have been proposed. In the general model, velocity and pressure fields were obtained by solving the momentum equations and the continuity equation, while the thermal fields were obtained by solving the heat conduction equation containing the convection term. In the simplified models, making assumptions relating to both the material and the geometry of the region, the general equations for momentum and continuity have been reduced to single an equation for pressure. This approach leads to the essential acceleration of fluid flow computations. In this model, coupling of the thermal and fluid flow phenomena by changes in the fluidity function and thermophysical parameters of alloy with respect to temperature has been taken into consideration. The problem has been solved by the finite element method.