Numerical Simulation of Grain Growth During SolidificationStephanie M. Janicek - Purdue Graduate Student
Ms. Janicek's Summary:
The effects of buoyancy driven fluid flow and compositional changes on grain growth were analyzed with a two dimensional cellular automaton-finite volume model. The cellular automaton predicts texture, grain size distribution, and columnar-to-equiaxed grain transitions; however, it is dependent on nucleation parameters that must be determined experimentally. Experimental castings of aluminum alloys with primarily unidirectional solidification both parallel and perpendicular to gravity were performed to analyze any buoyancy driven fluid flow effects. Once the model was validated against the laboratory scale experimental results, grain structure predictions were made for the electroslag remelting of superalloys.
[This presentation was at a technical level far above this webmaster's understanding - so below is summarized the more non-technical aspects of the presentation]
The approach to this modeling is to use a "Cellular Automation" model on a microscale to represent nucleation and dendritic cell growth. Nucleation is assigned a Gaussian distribution. A KGT model is used to represent growth. A fraction of solid / liquid is also derived at the cellular automation level.
At the macro scale the Finite Volume method is applied to represent the dynamics of composition, temperature, and velocity as a grid containing the "cellular automation" cells.
These two models are coupled by assigning the Finite Volume velocity parameters to all contained Cellular Automation (CA) cells, and the average values from the "CA" cells model are passed back to the Finite Volume boundary conditions.
Using a desktop computer, the calculations for one solidification take 1 to 6 days to complete. When compared to actual solidification of ingots with either a bottom or side chill plate, the basic characteristics of the solidified grains are shown by the model, however, at the present time equiaxed regions of the experimental solidifications are not captured by the models.
It is felt the model approach can be improved by:
1) incorporating multi-component dendrite growth
2) allowing for "free-floating" equiaxed grain development
3) allowing fragmentation of dendrites to create the "free-floating" grains
Ultimately the goal of this model is to simulate the Electroslag Remelting Process to a point where structural prediction is accurate. While progress has been made, there is still a considerable way to go.