A Combined Experimental and Computational Approach for the Design of Mold Topography that Leads to Desired Ingot Surface and Microstructure in Aluminum Casting.
Solidification of dendritic alloys is modeled using stabilized finite element techniques to study convection and macrosegregation driven by buoyancy and shrinkage. The adopted governing macroscopic conservation equations of momentum, energy and species transport are derived from their microscopic counterparts using the volume-averaging method. A single domain model is considered with a fixed numerical grid and without boundary conditions applied explicitly on the freezing front. The mushy zone is modeled here as a porous medium with either an isotropic or an anisotropic permeability. The stabilized finite-element scheme, previously developed by authors for modeling flows with phase change, is extended here to include effects of shrinkage, density changes and anisotropic permeability during solidification. The fluid flow scheme developed includes streamline-upwind/Petrov-Galerkin (SUPG), pressure stabilizing/Petrov-Galerkin, Darcy stabilizing/Petrov-Galerkin and other stabilizing terms arising from changes in density in the mushy zone. For the energy and species equations a classical SUPG-based finite element method is employed with minor modifications. The developed algorithms are first tested for a reference problem involving solidification of lead-tin alloy where the mushy zone is characterized by an isotropic permeability. Convergence studies are performed to validate the simulation results. Solidification of the same alloy in the absence of shrinkage is studied to observe differences in macrosegregation. Vertical solidification of a lead-tin alloy, where the mushy zone is characterized by an anisotropic permeability, is then simulated. The main aim here is to study convection and demonstrate formation of freckles and channels due to macrosegregation. The ability of stabilized finite element methods to model a wide variety of solidification problems with varying underlying phenomena in two and three dimensions is demonstrated through these examples.
- Research Organization:
- Cornell Univ., Ithaca, NY (United States)
- Sponsoring Organization:
- USDOE Office of Industrial Technologies (OIT) - (EE-20)
- DOE Contract Number:
- FC36-02ID14396
- OSTI ID:
- 850516
- Report Number(s):
- DOE/ID/14396; IJNMBH; Report 3 of 7; TRN: US200707%%272
- Journal Information:
- International Journal for Numerical Methods in Engineering, Journal Name: International Journal for Numerical Methods in Engineering; ISSN 0029-5981
- Country of Publication:
- United States
- Language:
- English
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Related Subjects
42 ENGINEERING
ALGORITHMS
ALLOYS
ALUMINIUM
BOUNDARY CONDITIONS
CASTING
CONVECTION
CONVERGENCE
DESIGN
FINITE ELEMENT METHOD
FLUID FLOW
FREEZING
MICROSTRUCTURE
PERMEABILITY
SHRINKAGE
SOLIDIFICATION
TOPOGRAPHY
TRANSPORT
solidification
stabilized finite element method
convection
shrinkage
density change
anisotropic permeability