Thermosolutal convection during dendritic solidification of alloys

Part i. Linear stability analysis

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

Research output: Contribution to journalArticle

50 Citations (Scopus)

Abstract

This paper describes the simulation of thermosolutal convection in directionally solidified (DS) alloys. A linear stability analysis is used to predict marginal stability curves for a system that comprises a mushy zone underlying an all-liquid zone. In the unperturbed and nonconvecting state . e.}, the basic state), isotherms and isoconcentrates are planar and horizontal. The mushy zone is realistically treated as a medium with a variable volume fraction of liquid that is con-sistent with the energy and solute conservation equations. The perturbed variables include tem-perature, concentration of solute, and both components of velocity in a two-dimensional system. As a model system, an alloy of Pb-20 wt pct Sn, solidifying at a velocity of 2 X 10-3 cm s-1 was selected. Dimensional numerical calculations were done to define the marginal stability curves in terms of the thermal gradient at the dendrite tips, G L, vs the horizontal wave number of the perturbed quantities. For a gravitational constant of 1 g, 0.5 g, 0.1 g, and 0.01 g, the marginal stability curves show no minima; thus, the system is never unconditionally stable. Nevertheless, such calculations quantify the effect of reducing the gravitational constant on reducing convection and suggest lateral dimensions of the mold for the purpose of suppressing convection. Finally, for a gravitational constant of 10-4 g, calculations show that the system is stable for the thermal gradients investigated (2.5 ≤G L ≤ 100 K-cm-1).

Original languageEnglish (US)
Pages (from-to)711-721
Number of pages11
JournalMetallurgical Transactions B
Volume20
Issue number5
DOIs
StatePublished - Oct 1989
Externally publishedYes

Fingerprint

Linear stability analysis
gravitational constant
solidification
Solidification
convection
mushy zones
Thermal gradients
solutes
curves
Liquids
gradients
Isotherms
conservation equations
Volume fraction
Conservation
energy conservation
dendrites
liquids
isotherms
Convection

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 i. Linear stability analysis. / Nandapurkar, P.; Poirier, David R; Heinrich, J. C.; Felicelli, S.

In: Metallurgical Transactions B, Vol. 20, No. 5, 10.1989, p. 711-721.

Research output: Contribution to journalArticle

@article{895b3695323b48aea69b843dab6db586,
title = "Thermosolutal convection during dendritic solidification of alloys: Part i. Linear stability analysis",
abstract = "This paper describes the simulation of thermosolutal convection in directionally solidified (DS) alloys. A linear stability analysis is used to predict marginal stability curves for a system that comprises a mushy zone underlying an all-liquid zone. In the unperturbed and nonconvecting state . e.}, the basic state), isotherms and isoconcentrates are planar and horizontal. The mushy zone is realistically treated as a medium with a variable volume fraction of liquid that is con-sistent with the energy and solute conservation equations. The perturbed variables include tem-perature, concentration of solute, and both components of velocity in a two-dimensional system. As a model system, an alloy of Pb-20 wt pct Sn, solidifying at a velocity of 2 X 10-3 cm s-1 was selected. Dimensional numerical calculations were done to define the marginal stability curves in terms of the thermal gradient at the dendrite tips, G L, vs the horizontal wave number of the perturbed quantities. For a gravitational constant of 1 g, 0.5 g, 0.1 g, and 0.01 g, the marginal stability curves show no minima; thus, the system is never unconditionally stable. Nevertheless, such calculations quantify the effect of reducing the gravitational constant on reducing convection and suggest lateral dimensions of the mold for the purpose of suppressing convection. Finally, for a gravitational constant of 10-4 g, calculations show that the system is stable for the thermal gradients investigated (2.5 ≤G L ≤ 100 K-cm-1).",
author = "P. Nandapurkar and Poirier, {David R} and Heinrich, {J. C.} and S. Felicelli",
year = "1989",
month = "10",
doi = "10.1007/BF02655929",
language = "English (US)",
volume = "20",
pages = "711--721",
journal = "Metallurgical and Materials Transactions B",
issn = "1073-5615",
publisher = "Springer International Publishing AG",
number = "5",

}

TY - JOUR

T1 - Thermosolutal convection during dendritic solidification of alloys

T2 - Part i. Linear stability analysis

AU - Nandapurkar, P.

AU - Poirier, David R

AU - Heinrich, J. C.

AU - Felicelli, S.

PY - 1989/10

Y1 - 1989/10

N2 - This paper describes the simulation of thermosolutal convection in directionally solidified (DS) alloys. A linear stability analysis is used to predict marginal stability curves for a system that comprises a mushy zone underlying an all-liquid zone. In the unperturbed and nonconvecting state . e.}, the basic state), isotherms and isoconcentrates are planar and horizontal. The mushy zone is realistically treated as a medium with a variable volume fraction of liquid that is con-sistent with the energy and solute conservation equations. The perturbed variables include tem-perature, concentration of solute, and both components of velocity in a two-dimensional system. As a model system, an alloy of Pb-20 wt pct Sn, solidifying at a velocity of 2 X 10-3 cm s-1 was selected. Dimensional numerical calculations were done to define the marginal stability curves in terms of the thermal gradient at the dendrite tips, G L, vs the horizontal wave number of the perturbed quantities. For a gravitational constant of 1 g, 0.5 g, 0.1 g, and 0.01 g, the marginal stability curves show no minima; thus, the system is never unconditionally stable. Nevertheless, such calculations quantify the effect of reducing the gravitational constant on reducing convection and suggest lateral dimensions of the mold for the purpose of suppressing convection. Finally, for a gravitational constant of 10-4 g, calculations show that the system is stable for the thermal gradients investigated (2.5 ≤G L ≤ 100 K-cm-1).

AB - This paper describes the simulation of thermosolutal convection in directionally solidified (DS) alloys. A linear stability analysis is used to predict marginal stability curves for a system that comprises a mushy zone underlying an all-liquid zone. In the unperturbed and nonconvecting state . e.}, the basic state), isotherms and isoconcentrates are planar and horizontal. The mushy zone is realistically treated as a medium with a variable volume fraction of liquid that is con-sistent with the energy and solute conservation equations. The perturbed variables include tem-perature, concentration of solute, and both components of velocity in a two-dimensional system. As a model system, an alloy of Pb-20 wt pct Sn, solidifying at a velocity of 2 X 10-3 cm s-1 was selected. Dimensional numerical calculations were done to define the marginal stability curves in terms of the thermal gradient at the dendrite tips, G L, vs the horizontal wave number of the perturbed quantities. For a gravitational constant of 1 g, 0.5 g, 0.1 g, and 0.01 g, the marginal stability curves show no minima; thus, the system is never unconditionally stable. Nevertheless, such calculations quantify the effect of reducing the gravitational constant on reducing convection and suggest lateral dimensions of the mold for the purpose of suppressing convection. Finally, for a gravitational constant of 10-4 g, calculations show that the system is stable for the thermal gradients investigated (2.5 ≤G L ≤ 100 K-cm-1).

UR - http://www.scopus.com/inward/record.url?scp=0024749227&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=0024749227&partnerID=8YFLogxK

U2 - 10.1007/BF02655929

DO - 10.1007/BF02655929

M3 - Article

VL - 20

SP - 711

EP - 721

JO - Metallurgical and Materials Transactions B

JF - Metallurgical and Materials Transactions B

SN - 1073-5615

IS - 5

ER -