V. Alexiades - UTK and ORNL

Binary Alloy Solidification

Solidification processing is an area of great technological importance in materials science (crystal growth, ceramics, polymers, welding), in geology (volcanic systems, crustal magmas, ore deposits), as well as in energy and environmental sciences (Latent Heat Thermal Energy Storage, In Situ Vitrification).

We are developing a comprehensive mathematical and computational tool capable of modeling melting and solidification of multicomponent systems, such as metallic alloys, polymer blends, and geologic magmas. The fully-coupled and robust model will integrate thermochemistry with heat and mass transfer in 3-dimensions.

Such a tool can be used to simulate difficult or expensive or hazardous or even technically or financially infeasible experiments, including ones involving high temperature materials, contaminated materials, or a microgravity environment.

In addition to enabling direct simulation of such processes, an efficient direct-process simulator is prerequisite tool in parameter identification (inverse) problems, as well as in determining sensitivities to various parameters involved in the processes. <

The general framework for the model is the weak formulation of the pertinent conservation laws of heat and mass transfer, complemented by constitutive laws for fluxes, and by thermal Equations of State for each phase, relating the energy to the variables (composition, temperature, pressure) characterizing the local thermodynamic state. <

The heart of our model, and a unique feature of our approach, is precisely the development and effective use of such a general expression for the energy. The expression is directly derived from, and thus fully consistent with, thermodynamics, encoding the thermochemistry of the system and its phase transitions, and thus enabling a thermodynamically consistent treatment of constitutional supercooling and segregation effects. With such formulations, (akin to shock-capturing in gas dynamics) it becomes possible to numerically simulate the entire process effectively.

The current version of the model takes into account conductive heat transfer, coupled with diffusive mass transfer, for a binary system, with thermodynamically consistent treatment of constitutional supercooling effects, and thermophysical properties depending on composition and temperature. A 2-dimensional implementation has been parallelized via domain decomposition and message passing. It has been applied successfully to
  • infrared detector alloy Mercury-Cadmium-Telluride ,
  • Diopside-Anorthite, and
  • Feldspar-Pyroxene magmas. Incorporation of convection in the melt is under development.
  • Translation into Czech by Barbora LebedovĂ¡ (Feb. 2017)   in her Science Blog.
  • Translation into Swedish by Weronika Pawlak (May 2017)
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