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
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
Incorporation of convection in the melt is under development.
Translation into Czech by Barbora Lebedová (Feb. 2017)
Translation into Swedish by Weronika Pawlak (May 2017)
Translation into Ukrainian by Sandi Wolfe (Aug. 2019)
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