A computer simulation of solidification taking into account the movement of the liquid phase

Abstract

In the paper, we present the results of solidification simulation taking into account the movement of the liquid phase. The results are obtained from an author software which is implemented on the base of a stabilized finite elements method (Petrov-Galerkin formulation). Using that formulation the Navier-Stokes equation is solved together with the convection term (Boussinesq approximation). The Finite Element Method (FEM) formulation is responsible for solidification, approximating the solution of the heat conduction equation (with the internal heat source term responsible for the heat released during the phase transition). The movement of the liquid phase in a solidifying cast that is caused by convection can significantly affect the process of heat transfer from the casting to the mold, which in turn has an influence on the temperature distribution in the cast and may cause a change in the location of the defects. The presented results allow to assess under what conditions the effect of convection on the solidification process is significant.

Computer evaluation of the influence of liquid metal movements on defects formation in the casting

“…It was assumed that the solidification front is mushy. The mathematical model is based on solving the following system of equations in a cylindrical axisymmetric coordinate system [2,[4][5][6][7][8][9][10]: -the Navier-Stokes equations:…”

“…The boundary conditions, on the indicated surfaces ( Fig. 1), specified in the considered problem were as follows: -for velocity [2,5,[7][8][9]:…”

“…where: Ta In the applied model of solid phase growth, the internal heat sources are not come evident in the equation of heat conductivity (3), because they are in the effective specific heat of the mushy zone [2,[7][8][9][10]. The above equations were solved by the finite element method in the weighted residuals formulation [2,5,[7][8][9][10]. In the numerical simulations, coupling of the thermal and flow phenomena by change in the thermophysical parameters of metals alloy depending on the temperature, has been taken into consideration.…”

“…The work analysed the formation of a casting by gravitational pouring of molten metal into a metal mould, but the development of other casting methods has recently been devoted a lot of attention, mainly continuous casting [1,2] or the lost-wax casting technology [3]. Direct examining of the phenomena occurring during the casting process is difficult due to the lack of optical access and high temperature, which is why computer simulation seems to be a good solution to this problem [1,2,[4][5][6][7][8][9][10][11][12]. In order to obtain an effective numerical solution to the problem under investigation, the number of analysed phenomena should be limited to the most important ones which have a direct impact on the quality of the casting.…”

“…This requires the formulation of adequate mathematical model that takes into account the mutual influence of thermal and flow phenomena in the process of filling the cavity of the casting mold and after its completion [2,[4][5][6][7]. Some researchers neglect in the numerical analysis of the casting process the period of filling the mold cavity with liquid metal, assuming as the initial condition for the numerical calculation that the mould cavity is fully filled [8][9][10][11]. Other researchers in turn, focus in their research on the analysis of the formation and evolution of a shrinkage cavity or other defects of the casting process [3,[10][11][12].…”