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Equiaxed dendritic solidification with convection: Part II. Numerical simulations for an Al-4 Wt pct Cu alloy

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Abstract

The multiphase model developed in part I for equiaxed dendritic solidification with melt convection and solid-phase transport is applied to numerically predict structural and compositional development in an Al-4 wt pct Cu alloy solidifying in a rectangular cavity. A numerical technique combining a fully implicit control-volume-based finite difference method with a multiple time-step scheme is developed for accurate and efficient simulations of both micro- and macroscale phenomena. Quantitative results for the dendritic microstructure evolution in the presence of melt convection and solid movement are obtained. The remarkable effects of the solid-liquid multiphase flow pattern on macrosegregation as well as the grain size distribution are illustrated.

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Abbreviations

C :

concentration of a chemical species, wt pct

c :

specific heat, J/kg K

C ∃ :

settling ratio

d e :

mean characteristic diameter of the dendrite envelope, m

D :

mass diffusion coefficient, m2/s

h :

chill heat-transfer coefficient (W/m2 K) or enthalpy (J/kg)

Iv:

Ivantsov function

k :

thermal conductivity, W/m K

l :

species diffusion length, m

m l :

liquidus line slope, K/wt pct

Ms d :

solid/liquid interfacial drag, N/m s

n :

equiaxed nuclei density, m-3

n :

outwardly directed unit normal vector

Pe∃ :

multiphase Pelcet number, ⃛l|vl -v s|de/Dl

Pet :

solutal Peclet number at the dendrite tip,-V tRt/2Dl

Pe∞:

ambient Pelcet number for dendrite tips, |vl -

R t :

tip radius, m

S :

interfacial area concentration, m-1

t :

time, s

T :

temperature, K

T :

cooling rate,∂T/∂t (K/s)

v:

velocity vector, m/s

w :

interface velocity, m/s

β :

dimensionless parameter

γ :

momentum dispersion coefficient

γ:

interfacial phase change rate (kg/m3 s) or Gibbs-Thomson coefficient (m K)

δh :

latent heat of phase change, J/kg

⃛:

volume fraction

⃛ si :

internal solid fraction, ⃛s/(⃛ s + ⃛d)

k :

partition coefficient, wt pct/wt pct

k v :

flow partition coefficient

λ 2 :

secondary dendrite arm spacing, m

λ p :

slip coefficient for solid, m

p :

density, kg/m3

Μ :

viscosity, Pa s

Σ* :

stability constant

ψ :

a field property

Ω :

solutal supersaturation,(C e- Cl)/[Ce(l-k)]

d :

interdendritic liquid

e :

dendrite envelope

E :

eutectic point

eff:

effective

f :

total liquid phase(d + l)

g :

grain

k :

phasek

I :

extradendritic liquid

L :

liquidus

Id :

extradendritic-interdendritic liquid interface

m :

melting point of pure metals

n :

normal direction

N :

nucleation

0:

initial state

s :

solid

sd :

solid-interdendritic liquid interface

t :

dendrite tip or tangential

w :

wall

c :

critical

-:

interfacial area-averaged

*:

effective

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Authors and Affiliations

  1. Department of Mechanical Engineering, University of Hawaii at Manoa, 96822, Honolulu, HI

    C. Y. Wang (Assistant Professor)

  2. Department of Mechanical Engineering, The University of Iowa, 52242, Iowa City, IA

    C. Beckermann (Associate Professor)

Authors
  1. C. Y. Wang
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  2. C. Beckermann
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Wang, C.Y., Beckermann, C. Equiaxed dendritic solidification with convection: Part II. Numerical simulations for an Al-4 Wt pct Cu alloy. Metall Mater Trans A 27, 2765–2783 (1996). https://doi.org/10.1007/BF02652370

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