Numerische Behandlung der Nichtlinearitäten bei Phasenübergängen in Gießprozessen
Final Report Abstract
In this project a binary fluid solidification model was implemented in framework of the Star-CD flow solver and was coupled with the flow model for multiphase systems, based on the mixture theory. Additionally an attempt to the effective viscosity model (developed using experimental data) validation in the finite volume Navier-Stokes equation solver was performed. Moreover, the first results of the aluminum-silicon alloy solidification in the three dimensional domains were presented along with some preliminary results obtained on polyhedral meshes. The verification of the binary fluid model implementation was carried out with an aid of the new proposition of the semi-solution to the heat diffusion equation that accounts for heat conduction dominated solidification of a binary fluid and variation of the heat conductivity in the mushy zone region. The convergence of the results obtained with the implemented model was shown in the case of aluminum-silicon Al-4.1%Si alloy solidification in a 2D rectangular cavity. The convergence study was performed regarding to the coupling of the new solidification model and the flow governing equations and, moreover, the results obtained on three gradually refined meshes. In comparison to the results reported in the literature the initial solidification rates of the selected alloy were predicted to be larger. However, final positions of the solidification fronts are similar to data reported in literature. The developed numerical model based on the mixture theory model predicts more pronounced macrosegregation in comparison to model based solely on volume averaging (Darcy-Brinkman or two-fluid model). The reason for this difference is connected to mathematically different formulations of the momentum equations in both modeling approaches. In the mixture model vanishing liquid volume fraction in the mushy zone does not have the influence on the magnitude of the source terms in the Navier-Stokes equations that govern the solutal and the thermal buoyancies. The model developed in the framework of the present project will be used as a template in implementation of the binary fluid solidification model in the Star-CCM+ solver developed by a company. The authors plan further investigation of a binary fluid solidification in cavity under rotation. Moreover, the experiences gathered during this project should be used in implementation of the double diffusive solidification model in the in-house code FASTEST and its coupling with the interface capturing volume of fluid method.
Publications
- “Modelling of solidification of binary liquids with nonlinear viscosity models”, Fifth International Conference on Computational Method in Multiphase Flow V, New Forest, (United Kingdom) 2009
Waclawczyk T., Sternel D., Schaefer M.
- “Verification of a binary fluid solidification model”, International Conference on Numerical Analysis and Applied Mathematics, ICNAAM 2011, Halkidiki (Greece)
Waclawczyk T., Sternel D., Schaefer M.
