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Metallurgical and Materials Transactions A

, Volume 35, Issue 2, pp 623–629 | Cite as

Liquid convection effects on the pushing-engulfment transition of insoluble particles by a solidifying interface: Part II. Numerical calculation of drag and lift forces on a particle in parabolic shear flow

  • S. Mukherjee
  • M. A. R. Sharif
  • D. M. Stefanescu
Article

Abstract

In this work, lift and drag forces acting on a particle in the close vicinity of a wall are calculated by numerically solving the incompressible two-dimensional Navier-Stokes equations. The flow field computations are done using the well-known Marker and Cell (MAC) method on a staggered grid. A parabolic shear flow at the inlet is assumed. The particle is assumed to be nonrotating and Magnus forces are not considered. The numerical results are compared to those obtained from analytical/empirical expressions for drag and lift forces from different theoretical models. Reasonably good agreement has been found between the two approaches.

Keywords

Material Transaction Drag Force Drag Coefficient Lift Force Lift Coefficient 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

List of Symbols

AP

surface area of the spherical particle

CL

lift coefficient

CD

drag coefficient

D

dilatation

FD

drag force

FS

Saffman force

Fxp, Fyp

force due to pressure effect

{ie628-1}

force due to viscous effect

RI

radius of curvature of the interface

Rp

radius of the particle

Re

flow Reynolds number

Rep

particle Reynolds number

Vo

maximum convection velocity

Vrel

velocity of the particle relative to the liquid

VLx

liquid velocity in the x direction

VP

particle velocity

d

distance between the particle and the solid/liquid interface

i,j

location of grid points

ka

function of thermal conductivities

P

pressure

t

time

u, v

fluid velocity along the x and y directions respectively

Δx, Δy

grid sizes in x and y directions (Cartesian coordinate system)

Δr, Δz

grid sizes in r and z directions (cylindrical coordinate system)

Δt

time-step

α

interface curvature in BC model

δ

boundary layer width

η

dynamic viscosity of the melt

v

kinematic viscosity of the melt

ρ

density

τ

shear stress

Δρ

density difference

Subscripts

I

interface

L

liquid

P

particle/phase field

S

solid

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Copyright information

© ASM International & TMS-The Minerals, Metals and Materials Society 2004

Authors and Affiliations

  • S. Mukherjee
    • 1
  • M. A. R. Sharif
    • 2
  • D. M. Stefanescu
    • 1
    • 3
  1. 1.Metallurgical and Materials EngineeringThe University of AlabamaTuscaloosa
  2. 2.Aerospace Engineering and MechanicsThe University of AlabamaTuscaloosa
  3. 3.Solidification LaboratoryThe University of AlabamaTuscaloosa

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