Papers by Keyword: Casting Solidification

Abstract: The system casting-mould is considered. The thermal processes proceeding in a casting sub-domain are described using the one domain approach. The model of solidification process is supplemented by the energy equation concerning the mould sub-domain, the continuity conditions given on the contact surface between casting and mould, boundary conditions on the outer surface of the system and the initial ones. To solve the problem the generalized variant of finite difference method (GFDM) is used. Temporary and local values of temperature can be found at the optional set of collocation points from the domain considered. This essential advantage of GFDM allows to locate and thicken nodes at the regions for which the temperature gradients and cooling (heating) rates are considerable. In the final part of the paper, the example of numerical simulation is shown.

Abstract: The paper deals with the inverse problems appearing in the thermal theory of foundry processes. In particular, the problems connected with identification of casting and mould thermophysical parameters can be considered. To estimate the parameters determining heat transfer processes in the system casting-mould, the additional information concerning the changes of temperature at the points selected from the domain considered is necessary. The localization of sensors should assure the best conditions of identification process. Generally speaking, the sensor should be located at the point for which the sensitivity of temperature field with respect to parameter estimated achieves maximum. In the case of simultaneous identification of several parameters, the proper choice of sensors localization is more complicated. The main goal of the paper is to discuss a theoretical base connected with the problem formulated, to present the possibilities of numerical methods application, to solve the problem, and finally to show the examples of inverse problems solutions (in particular, the latent heat of binary alloy will be estimated).

Abstract: The heat transfer during the casting solidification process includes: the heat radiation of the high temperature casting and the mold, the heat convection between the casting and the mold, and the heat conduction in the casting and the casting to the mold. In this paper, a formula of time step in simulation of solidification is derived, considering the heat radiation, convection and conduction based on the conservation of energy. The different heat transfer condition between the ordinary sand casting and the permanent mold casting is taken into account in this formula. The characteristic of heat transfer in the interior and surface of the casting is also considered. The numerical experiments show that this formula can avoid radiation of the computation, and can improve the computational efficiency about 20% in the simulation of solidification process.

Abstract: 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.

Abstract: The methods of sensitivity analysis allow to estimate the influence of parameters determining the geometrical, physical, boundary and initial conditions on the course of thermal processes in the system considered. In this paper the possibilities of shape sensitivity analysis application (SSA) in the thermal theory of foundry processes are discussed. In particular, the direct approach is presented because it seems that for practical applications this variant of sensitivity analysis is more effective. The theoretical base of SSA is presented in chapters 1 and 2, next the practical aspects of the method are discussed. In the final part of the paper the examples of computations can be found.

Abstract: In the paper the problem of casting and mould thermophysical parameters identification is discussed. So, it is assumed that in the mathematical model describing the thermal processes in the system considered the selected parameter (or parameters) is unknown. On the basis of additional information concerning the cooling (heating) curves at the selected set of points the unknown parameter can be found. The inverse problem is solved using the least squares criterion in which the sensitivity coefficients are applied. On the stage of numerical simulation the boundary element method is used. In the final part of the paper the examples of computations are shown.