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Multiparticle interfacial drag in equiaxed solidification

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Abstract

A physical model is proposed for the solid/liquid interfacial drag in both globular and dendritic equiaxed solidification. By accounting for the presence of multiple particles and the nonsphericity and porosity of the individual equiaxed crystals, a drag correlation is developed, which is valid over the full range of solid volume fractions. It is shown that neither the solid liquid interfacial area concentration nor the grain size alone is adequate to characterize the interfacial drag for equiaxed dendritic crystals in both the free particle and packed bed regimes; thus, the present model is based on a multiple length scale approach. The model predictions are compared to previous analytical and numerical results as well as to experimental data available in the literature, and favorable agreement is achieved.

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Abbreviations

A :

interfacial area, m2

Ce :

settling ratio

Cp :

shape factor function

d :

diameter, m

K :

permeability, m2

Md :

solid/liquid interfacial drag per unit volume, N/m3

n :

index in Eq. [10]

S :

interfacial area concentration, A/V0, m−1

V0 :

volume of the control element, m3

<vk>k :

volume-averaged intrinsic velocity of phase it, m/s

β dimensionless diameter, Eq. [11]:

εk volume fraction of phasek

εsi :

internal solid fraction, εs/(εs + εd a)

kv :

flow partition coefficient for the interdendritic region, Eq. [13]

ρ:

density, kg/m3

μ :

viscosity, N-s/m2

ϕe :

shape factor or sphericity of the dendrite envelope

d :

dinterdendritic liquid

e :

dendrite envelope

k :

a phase,k = s, d, orll extradendritic liquid

e :

dendrite envelope

f:

total liquid(d +l)

s :

solid

m :

multiple particles

s :

single particle

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Authors and Affiliations

  1. Department of Mechanical Engineering, University of Iowa, 52242-1527, Iowa City, IA

    C. Y. Wang (Research Assistant) & C. Beckermann (Associate Professor)

  2. Software Development Engineer, Engineering Mechanics Research Corporation, 48098, Troy, MI

    S. Ahuja

  3. NASA Lewis Research Center, 44135, Cleveland, OH

    H. C. de Groh (Materials Research Engineer)

Authors
  1. C. Y. Wang
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  2. S. Ahuja
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  3. C. Beckermann
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  4. H. C. de Groh
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Formerly Graduate Research Assistant, Department of Mechanical Engineering, University of Iowa

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Wang, C.Y., Ahuja, S., Beckermann, C. et al. Multiparticle interfacial drag in equiaxed solidification. Metall Mater Trans B 26, 111–119 (1995). https://doi.org/10.1007/BF02648984

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