Romuald Szopa

Analysis of thermal processes in solidifying casting using the combined variant of the BEM

Abstract In the paper the numerical model of heat transfer processes proceeding in the heterogeneous system casting-mould-core is presented. The problem is treated as a 2D boundary-initial task. Non-steady temperature field is found on the basis of the boundary element method. In particular, the variant called the BEM using discretization in time is applied [Curran et al., Appl. Math. Modelling 4 (1980) 398; W. Sichert, Berechnung von Instationaren thermishen Problemen mittels der Rangelementmethode (1989)]. The method is adapted for non-homogeneous system, at the same time the solidification process is taken into account by the approach called the one domain method [V.R. Voller, Comput. Modelling Free Moving Problems, 1991, p. 3], while the numerical model of this phenomena bases on the temperature field correction method [E. Majchrzak, B. Mochnacki, Comput. Assisted Mech. Eng. Sci. 3 (4) (1996) 327; E. Majchrzak, B. Mochnacki, Eng. Anal. Boundary Elements 16 (1995) 99]. In the final part of the paper the computations of complex casting solidification are shown.

Application of the boundary element method for the numerical modelling of the solidification of cylindrical and spherical castings

Abstract From the mathematical point of view the solidification process proceeding in the domain casting–mould is described by the system of partial differential equations and boundary/initial conditions. It should be pointed out that taking into account the complex form of the governing equations and the physical, geometrical, boundary and initial conditions an effective solution can be obtained only using numerical methods. In this paper the combined variant of the boundary element method called the BEM using discretization in time is applied. In particular the well-known numerical algorithm for domains oriented in the cartesian co-ordinate system is considered. In order to adapt the method for numerical simulation of the heat-transfer processes proceeding in domains oriented in other co-ordinate systems a certain algorithm consisting in the introduction of an artificial source is used.

Macro and Macro/Micro Models of Solidification - Numerical Aspects of Process Simulation

The solidification models basing on the Fourier equation with the additional term controlling the kinetics of phase transition are discussed. The different approaches to this term definition lead to the different solidification models, in particular the macro and the macro/micro ones can be taken into account. In the case of macro description the equation in which the parameter called a substitute thermal capacity is considered, while in the case of macro/micro approach the linear or exponential models of crystallization can be introduced. The solution of the problem can be found using the numerical methods. In this paper the boundary element method using discretization in time is applied, the examples of numerical simulations are also shown.

Numerical Modeling of Solidification Substitute – Thermal Capacity of Binary Alloy

Mathematical description of alloys solidification on the macro scale can be formulated using the one domain method (fixed domain approach). The energy equation corresponding to this model contains the parameter called the substitute thermal capacity (STC). The analytical form of STC results from the assumption concerning the course of the function fS = fS (T) describing the changes of solid state volumetric fraction and the temperature at the point considered. Between border temperatures TS , TL the function fS changes from 1 to 0. In this paper the volumetric fraction fS (more precisely fL = 1- fS ) is found using the simple models of macrosegregation (the lever arm rule, the Scheil model). In this way one obtains the formulas determining the course of STC resulting from the certain physical considerations and this approach seems to be closer to the real course of thermal processes proceeding in domain of solidifying alloy.