Dendritic solidification of binary alloys with free and forced convection

P. Zhao, J. C. Heinrich, David R Poirier

Research output: Contribution to journalArticle

29 Citations (Scopus)

Abstract

Dendritic solidification with forced convection and free convection driven by contraction and thermosolutal buoyancy is simulated in two-dimensional space using a sharp-interface model. Both pure substances and alloys are considered. The model is formulated using the finite element method and works directly with primitive variables. The coupled energy- and solutal concentration-equations, along with the Navier-Stokes equations for incompressible flow, are solved using different meshes. Temperature is solved in a fixed mesh that covers the whole domain (solid + liquid) where the solid-liquid interface is explicitly tracked using marker points. The concentration and momentum equations are solved in the liquid region using an adaptive mesh of triangular elements that conforms to the interface. The velocity boundary conditions are applied directly on the interface. The model is validated using a series of problems that have analytical, experimental and numerical results. Four simulations are presented: (1) crystal growth of succinonitrile with thermal convection under two small undercoolings; (2) dendritic growth into an undercooled pure melt with a uniform forced flow; (3) equiaxial dendritic growth of a pure substance and an alloy with contraction-induced convection; and (4) directional solidification of Pb-0.2 wt% Sb alloy with convection driven by the combined action of contraction, thermal and solutal buoyancy. Some of the simulation results are compared to those reported using other methods including the phase-field method; others are new. In each case, the effects of convection on dendritic solidification are analysed.

Original languageEnglish (US)
Pages (from-to)233-266
Number of pages34
JournalInternational Journal for Numerical Methods in Fluids
Volume49
Issue number3
DOIs
StatePublished - Sep 30 2005

Fingerprint

Binary Alloys
Forced Convection
Free Convection
forced convection
Binary alloys
Forced convection
Solidification
binary alloys
Natural convection
free convection
solidification
convection
Dendritic Growth
contraction
Convection
mesh
Contraction
Buoyancy
Liquid
buoyancy

Keywords

  • Adaptive meshing
  • Convection
  • Dendritic solidification
  • Finite element
  • Interface tracking
  • Moving boundary

ASJC Scopus subject areas

  • Condensed Matter Physics
  • Safety, Risk, Reliability and Quality
  • Applied Mathematics
  • Computational Theory and Mathematics
  • Computer Science Applications
  • Computational Mechanics
  • Mechanics of Materials

Cite this

Dendritic solidification of binary alloys with free and forced convection. / Zhao, P.; Heinrich, J. C.; Poirier, David R.

In: International Journal for Numerical Methods in Fluids, Vol. 49, No. 3, 30.09.2005, p. 233-266.

Research output: Contribution to journalArticle

@article{ac636f418f7d4669ae38db1738fc3d5b,
title = "Dendritic solidification of binary alloys with free and forced convection",
abstract = "Dendritic solidification with forced convection and free convection driven by contraction and thermosolutal buoyancy is simulated in two-dimensional space using a sharp-interface model. Both pure substances and alloys are considered. The model is formulated using the finite element method and works directly with primitive variables. The coupled energy- and solutal concentration-equations, along with the Navier-Stokes equations for incompressible flow, are solved using different meshes. Temperature is solved in a fixed mesh that covers the whole domain (solid + liquid) where the solid-liquid interface is explicitly tracked using marker points. The concentration and momentum equations are solved in the liquid region using an adaptive mesh of triangular elements that conforms to the interface. The velocity boundary conditions are applied directly on the interface. The model is validated using a series of problems that have analytical, experimental and numerical results. Four simulations are presented: (1) crystal growth of succinonitrile with thermal convection under two small undercoolings; (2) dendritic growth into an undercooled pure melt with a uniform forced flow; (3) equiaxial dendritic growth of a pure substance and an alloy with contraction-induced convection; and (4) directional solidification of Pb-0.2 wt{\%} Sb alloy with convection driven by the combined action of contraction, thermal and solutal buoyancy. Some of the simulation results are compared to those reported using other methods including the phase-field method; others are new. In each case, the effects of convection on dendritic solidification are analysed.",
keywords = "Adaptive meshing, Convection, Dendritic solidification, Finite element, Interface tracking, Moving boundary",
author = "P. Zhao and Heinrich, {J. C.} and Poirier, {David R}",
year = "2005",
month = "9",
day = "30",
doi = "10.1002/fld.988",
language = "English (US)",
volume = "49",
pages = "233--266",
journal = "International Journal for Numerical Methods in Fluids",
issn = "0271-2091",
publisher = "John Wiley and Sons Ltd",
number = "3",

}

TY - JOUR

T1 - Dendritic solidification of binary alloys with free and forced convection

AU - Zhao, P.

AU - Heinrich, J. C.

AU - Poirier, David R

PY - 2005/9/30

Y1 - 2005/9/30

N2 - Dendritic solidification with forced convection and free convection driven by contraction and thermosolutal buoyancy is simulated in two-dimensional space using a sharp-interface model. Both pure substances and alloys are considered. The model is formulated using the finite element method and works directly with primitive variables. The coupled energy- and solutal concentration-equations, along with the Navier-Stokes equations for incompressible flow, are solved using different meshes. Temperature is solved in a fixed mesh that covers the whole domain (solid + liquid) where the solid-liquid interface is explicitly tracked using marker points. The concentration and momentum equations are solved in the liquid region using an adaptive mesh of triangular elements that conforms to the interface. The velocity boundary conditions are applied directly on the interface. The model is validated using a series of problems that have analytical, experimental and numerical results. Four simulations are presented: (1) crystal growth of succinonitrile with thermal convection under two small undercoolings; (2) dendritic growth into an undercooled pure melt with a uniform forced flow; (3) equiaxial dendritic growth of a pure substance and an alloy with contraction-induced convection; and (4) directional solidification of Pb-0.2 wt% Sb alloy with convection driven by the combined action of contraction, thermal and solutal buoyancy. Some of the simulation results are compared to those reported using other methods including the phase-field method; others are new. In each case, the effects of convection on dendritic solidification are analysed.

AB - Dendritic solidification with forced convection and free convection driven by contraction and thermosolutal buoyancy is simulated in two-dimensional space using a sharp-interface model. Both pure substances and alloys are considered. The model is formulated using the finite element method and works directly with primitive variables. The coupled energy- and solutal concentration-equations, along with the Navier-Stokes equations for incompressible flow, are solved using different meshes. Temperature is solved in a fixed mesh that covers the whole domain (solid + liquid) where the solid-liquid interface is explicitly tracked using marker points. The concentration and momentum equations are solved in the liquid region using an adaptive mesh of triangular elements that conforms to the interface. The velocity boundary conditions are applied directly on the interface. The model is validated using a series of problems that have analytical, experimental and numerical results. Four simulations are presented: (1) crystal growth of succinonitrile with thermal convection under two small undercoolings; (2) dendritic growth into an undercooled pure melt with a uniform forced flow; (3) equiaxial dendritic growth of a pure substance and an alloy with contraction-induced convection; and (4) directional solidification of Pb-0.2 wt% Sb alloy with convection driven by the combined action of contraction, thermal and solutal buoyancy. Some of the simulation results are compared to those reported using other methods including the phase-field method; others are new. In each case, the effects of convection on dendritic solidification are analysed.

KW - Adaptive meshing

KW - Convection

KW - Dendritic solidification

KW - Finite element

KW - Interface tracking

KW - Moving boundary

UR - http://www.scopus.com/inward/record.url?scp=24944498387&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=24944498387&partnerID=8YFLogxK

U2 - 10.1002/fld.988

DO - 10.1002/fld.988

M3 - Article

AN - SCOPUS:24944498387

VL - 49

SP - 233

EP - 266

JO - International Journal for Numerical Methods in Fluids

JF - International Journal for Numerical Methods in Fluids

SN - 0271-2091

IS - 3

ER -