Modeling of dendritic solidification systems: Reassessment of the continuum momentum equation and application to solidification of a lead-tin alloy

Technical Report · Fri Feb 01 04:00:00 EST 1991

OSTI ID:6198347

Prescott, P J; Incropera, F P

In recent years there has been renewed interest in modeling transport phenomena associated with the dendritic solidification of binary mixtures. Solidification occurs in a two-phase (mushy) region characterized by complex, solid-liquid interfacial geometries, and development of a model which is amenable to solution dictates the use of continuum (mixture theory) assumption and/or volume-averaging procedures. A review of the recent literature would suggest that solidification models developed from mixture theory assumptions are less valid and less general than similar models based on volume-averaging, particularly with regard to the respective momentum equations which describe interdendritic fluid flow. In this report, these different approaches are shown to yield identical macroscopic conservation equations, and the continuum momentum equation is reconsidered in an effort to reconcile matters which have lead to confusion about the validity of the continuum model. Consistency between recently presented momentum equations is demonstrated. Using a continuum model for conservation of total mass, momentum, energy and species, numerical simulations of a binary metal alloy (Pb-Sn) undergoing solidification phase-change are performed. The system is contained in an axisymmetric, annular mold, which is cooled along its outer vertical wall. Results show that thermosolutal convection in the melt and mush zones is strongly coupled land that macrosegregation is reduced with increased cooling rate. For low cooling rates, solutally induced convection in the mushy zone favors the development of channels, which subsequently spawn macrosegregation in the form of A-segregates. With increasing solidification rate, however, thermosolutal interactions in the melt contribute to reducing the formation of channels and A-segregates. 61 refs., 14 figs., 1 tab.

• Research Organization: Purdue Univ., Lafayette, IN (USA). Heat Transfer Lab.
• Sponsoring Organization: DOE/ER
• DOE Contract Number: FG02-87ER13759
• OSTI ID: 6198347
• Report Number(s): DOE/ER/13759-4; ON: DE91008228
• Country of Publication: United States
• Language: English

Related Subjects

36 MATERIALS SCIENCE
360102* -- Metals & Alloys-- Structure & Phase Studies
ALLOY SYSTEMS
ALLOYS
BINARY ALLOY SYSTEMS
CONVECTION
CRYSTALS
DENDRITES
DOCUMENT TYPES
ENERGY TRANSFER
HEAT TRANSFER
LEAD ALLOYS
MASS TRANSFER
MATHEMATICAL MODELS
PHASE TRANSFORMATIONS
PHYSICAL PROPERTIES
PROGRESS REPORT
SEGREGATION
SOLIDIFICATION
TIN ALLOYS