Thermosolutal convection during dendritic solidification of alloys: Part II. Nonlinear convection

J. C. Heinrich, S. Felicelli, P. Nandapurkar, David R Poirier

Research output: Contribution to journalArticle

48 Citations (Scopus)

Abstract

A mathematical model of thermosolutal convection in directionally solidified dendritic alloys has been developed that includes a mushy zone underlying an all-liquid region. The model assumes a nonconvective initial state with planar and horizontal isotherms and isoconcentrates that move upward at a constant solidification velocity. The initial state is perturbed, nonlinear calculations are performed to model convection of the liquid when the system is unstable, and the results are compared with the predictions of a linear stability analysis. The mushy zone is modeled as a porous medium of variable porosity consistent with the volume fraction of, interdendritic liquid that satisfies the conservation equations for energy and solute concentrations. Results are presented for systems involving lead-tin alloys (Pb-10 wt pct Sn and Pb-20 wt pct Sn) and show significant differences with results of plane-front solidification. The calculations show that convection in the mushy zone is mainly driven by convection in the all-liquid region, and convection of the interdendritic liquid is only significant in the upper 20 pct of the mushy zone if it is significant at all. The calculated results also show that the systems are stable at reduced gravity levels of the order of 10-4 g 0 (g 0=980 cm·s-1) or when the lateral dimensions of the container are small enough, for stable temperature gradients between 2.5≤G l≤100 K·cm-1 at solidification velocities of 2 to 8 cm·h-1.

Original languageEnglish (US)
Pages (from-to)883-891
Number of pages9
JournalMetallurgical Transactions B
Volume20
Issue number6
DOIs
StatePublished - Dec 1989

Fingerprint

mushy zones
solidification
Solidification
convection
Liquids
liquids
tin alloys
Tin alloys
lead alloys
Lead alloys
Linear stability analysis
conservation equations
microgravity
containers
Thermal gradients
Containers
Isotherms
Porous materials
Volume fraction
Conservation

ASJC Scopus subject areas

  • Condensed Matter Physics
  • Metals and Alloys
  • Materials Chemistry
  • Mechanics of Materials
  • Engineering(all)

Cite this

Thermosolutal convection during dendritic solidification of alloys : Part II. Nonlinear convection. / Heinrich, J. C.; Felicelli, S.; Nandapurkar, P.; Poirier, David R.

In: Metallurgical Transactions B, Vol. 20, No. 6, 12.1989, p. 883-891.

Research output: Contribution to journalArticle

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