A simple two-dimensional model for the solidification of a “warm” solid seed placed in an under cooled liquid melt is presented. Under the physically restrictive assumptions of no surface anisotropy or curvature and kinetic under-cooling a closed form similarity solution can be constructed for this problem. A fixed grid enthalpy “like” solution can also be constructed. When this enthalpy solution is implemented in a one-dimensional cylindrical geometry it produces excellent agreement with the analytical solution. When implemented in a two-dimensional geometry, however, due to the lack of front stability provided by the surface under-cooling, dendritic crystals are predicted. Theses crystals are referred to as “numerical crystals” to highlight the fact that they are a pure artefact of the anisotropies introduced by the grid, and the initialization and operation of the proposed numerical method. The paper closes by suggesting that the proposed analytical solution, although not physically complete, is a rigorous and hard test for the quality of a given crystal growth algorithm, since an “ideal” two-dimensional numerical method should be able to recover the cylindrical growth of the seed without forming dendrites.
|Original language||English (US)|
|Number of pages||4|
|Journal||International Conference on Computational Methods for Thermal Problems|
|State||Published - 2009|
|Event||1st International Conference on Computational Methods for Thermal Problems, THERMACOMP 2009 - Naples, Italy|
Duration: Sep 8 2009 → Sep 10 2009
Bibliographical noteFunding Information:
The objective of this paper is to highlight recent advances in modeling and understanding geological systems through the adoption and development of key concepts from the field of numerical heat transfer. The work reported was carried out in close collaboration with my student Jorge Lorenzo-Trueba and colleagues Chris Paola, Department of Geology and Geophysics, University of Minnesota and John Swenson, Department of Geology, University of Minnesota-Duluth. This work was supported by the STC program of the National Science Foundation via the National Center for Earth-surface Dynamics under the agreement Number EAR-0120914.
Acknowledgement: The authors would like to express their gratitude to Slovenian Technology Agency (RV) and Slovenian Research Agency (BŠ) for funding of the represented research.
The authors acknowledge the financial support by DFG through a joint research project on fundamentals of boiling heat transfer and SFB 540. We would like thank Hein Auracher and co-workers for giving access to experimental data .
This work is been carried included in the research project called CRISÁLIDA with the support of Grupo Ormazabal. CRISÁLIDA is funded by Ministerio de Industria, Turismo y Comercio through the program CENIT (Consorcios Estratégicos Nacionales en Investigación Técnica). The financial support of Cátedra Fundación Antonio Aranzábal–Universidad de Navarra is gratefully acknowledged.
© 2009 by the authors of the abstracts.
- Crystal growth
- Enthalpy method
- Similarity solution