FRECKLE SUPPRESSION IN DIRECTIONAL SOLIDIFICATION OF BINARY AND MULTICOMPONENT ALLOYS USING MAGNETIC FIELDS

1
FRECKLE SUPPRESSION IN DIRECTIONAL
SOLIDIFICATION OF BINARY AND MULTICOMPONENT
ALLOYS USING MAGNETIC FIELDS
Deep Samanta and Nicholas Zabaras Materials
Process Design and Control Laboratory Sibley
School of Mechanical and Aerospace
Engineering188 Frank H. T. Rhodes Hall Cornell
University Ithaca, NY 14853-3801 Email
zabaras_at_cornell.edu URL http//mpdc.mae.cornell.e
du/
2
RESEARCH SPONSORS
NATIONAL AERONAUTICS AND SPACE ADMINISTRATION
(NASA)
NASA Microgravity Materials Science program
DEPARTMENT OF ENERGY (DOE) Industry
partnerships for aluminum industry of the future
- Office of Industrial Technologies
CORNELL THEORY CENTER
3
OUTLINE OF THE PRESENTATION

• Introduction and motivation for the current study
• Effect of magnetic fields and gradients on
  convection
• Numerical model of alloy solidification under the
  influence of magnetic fields and gradients
• Computational strategies for solving the coupled
  numerical system
• Numerical Examples
• damping convection and reducing
  macrosegregation during horizontal
• alloy solidification with magnetic
  fields and gradients
• freckle suppression during directional
  solidification of alloys using
• magnetic fields
• Conclusions
• Current and Future Research

4
Introduction and motivation for the current study
5
INTRODUCTION

• Solidification is a commonly used method for
  obtaining near net shape objects in industry.
• Different casting processes place different
  restrictions on the solidification process.
• Homogenous material distribution is one of the
  key objectives.
• Solidification of alloys often accompanied by
  large scale solute variations.
• Macrosegregation results in non uniform
  properties in the final cast alloy.
• Leads to significant material loss to remove
  these defects.
• Need to develop methods to remove these defects
  for better quality castings.

Close view of a freckle in a Nickel based
super-alloy blade
Freckles in a single crystal Nickel based
superalloy blade
Freckles in a cast ingot (Ref. Beckermann C.)
(Ref Beckermann C., 2000)
6
DEFECTS IN CASTINGS
(a) Macro-segregation patterns in a steel
ingots (b) Centerline segregation in
continuously cast steel (Ref Beckermann C.,
2000) (c) Freckle defects in directionally
solidified blades (Ref Tin and Pollock,
2004) (d) Freckle chain on the surface of a
single crystal superalloy casting (Ref. Spowart
and Mullens, 2003)
(b)
(a)
(c)
(d)
7
MACROSEGREGATION CAUSES AND METHODS OF CONTROL
Non uniform properties on macro scale
Large scale distribution of solute
Macrosegregation
Thermosolutal convection
Control of macro segregation
Macrosegregation
Thermal and solutal buoyancy in the liquid and
mushy zones

• Electromagnetic fields
• Constant magnetic fields
• Rotating magnetic fields
• Combination of magnetic field and field
  gradients

Control or suppression of convection
Macrosegregation

• MEANS OF SUPPRESSING CONVECTION
• Control the boundary heat flux
• Multiple-zone controllable furnace design
• Rotation of the furnace
• Micro-gravity growth
• Electromagnetic fields

8
Convection damping through magnetic fields and
gradients
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BRIEF REVIEW OF MAGNETO-HYDRODYNAMICS
Maxwells equations for EM
1) Quasi magnetostatic assumption 2) Non
relativistic assumption
0
Equations of Motion Energy
0
JxB Lorentz force term
Kelvin force
Joule heating Thermo-magnetic cross-effects
cross effects
10
BRIEF REVIEW OF MAGNETO-HYDRODYNAMICS
Behavior of a material in a magnetic field

• Paramagnetic Weakly attracted towards the
  field. Examples include N2, O2 gas.
• Diamagnetic Weakly repelled by the field.
  Examples include Water, Germanium, Bismuth,
  Copper.
• Ferromagnetic Strongly attracted towards the
  field. Examples include Iron, Nickel and Cobalt.
  Nature of the material corresponds to its
  magnetic susceptibility, ?.
• Diamagnetic ? -1e-8, Paramagnetic ? 1e-7,
  Ferromagnetic ? 10.
• ? depends on temperature for paramagnetic
  materials.
• Curies law for paramagnetic materials ? ? 1/T.
  In the presence of a thermal gradient, a
  paramagnetic material experiences a body force in
  a magnetic field.
• An electrically conducting moving body
  experiences Lorentz damping force due to the
  magnetic field.
• Diamagnetic materials ? ??m 1/T (?m mass
  magnetic susceptibility ? constant).
• A magnetic field provides a means of control
  with or without a magnetic gradient.

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CONVECTION DAMPING USING MAGNETIC FIELDS
Application of magnetic field on a
moving fluid
Non - conducting fluid
Conducting fluid
Produces both Lorentz Kelvin forces
Produces Kelvin force
Kelvin force proportional to 1) mass magnetic
susceptibility 2) Magnitude of Magnetic field
superimposed with gradient
Lorentz force proportional to 1) electrical
conductivity 2) Magnitude of magnetic field
Both damp convection
12
MAGNETIC GRADIENTS IN FLOW CONTROL

• Suppression/reversal of natural convection by
  exploiting the temperature/composition dependence
  of magnetic susceptibility J.W. Evans et.al.,
  J. Appl. Phys (2000)
• Applied to reversal of flow of aqueous salt
  solution

System specifications Natural convection in a
square cavity Cavity filled with water Left wall
at 30 C. Right wall at 10 C Magnetic gradient
corresponding to ? 2
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MAGNETIC GRADIENTS IN FLOW CONTROL

• Suppression/reversal of natural convection by
  exploiting the temperature/composition dependence
  of magnetic susceptibility J.W.Evans et.al., J.
  Appl. Phys (2000)
• Applied to reversal of flow of aqueous salt
  solution

System specifications Natural convection in a
square cavity Cavity filled with water Left wall
at 30 C. Right wall at 10 C Magnetic gradient
corresponding to ? 2
14
MAGNETIC GRADIENTS IN FLOW CONTROL

• Suppression/reversal of natural convection by
  exploiting the temperature/composition dependence
  of magnetic susceptibility J.W.Evans et.al., J.
  Appl. Phys (2000)
• Applied to reversal of flow of aqueous salt
  solution

System specifications Natural convection in a
square cavity Cavity filled with water Left wall
at 30 C. Right wall at 10 C Magnetic gradient
corresponding to ? 2
15
PREVIOUS WORK

• Effect of magnetic field on transport phenomena
  in Bridgeman crystal growth Oreper et al.
  (1984) and Motakef (1990).
• Numerical study of convection in the horizontal
  Bridgeman configuration under the influence of
  constant magnetic fields Ben Hadid et al.
  (1997).
• Simulation of freckles during directional
  solidification of binary and multicomponent
  alloys Poirier, Fellicili and Heinrich
  (1997-04).
• Effects of low magnetic fields on the
  solidification of a Pb-Sn alloy in terrestrial
  gravity conditions Prescott and Incropera
  (1993).
• Effect of magnetic gradient fields on Rayleigh
  Benard convection in water and oxygen Tagawa et
  al.(2002-04). Suppression of thermosolutal
  convection by exploiting the temperature/compositi
  on dependence of magnetic susceptibility Evans
  (2000).
• Solidification of metals and alloys with
  negligible mushy zone under the influence of
  magnetic fields and gradients Control of
  solidification of conducting and non conducting
  materials using tailored magnetic fields
  B.Ganapathysubramanian and Zabaras (2004-05)

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EFFECTS OF CONVECTION ON SOLIDIFICATION

• Buoyancy driven thermal and solutal convection
  predominantly influence macrosegregation.
• Large scale freckling and distribution of solute
  severely degrades quality of the casting
• Control of thermosolutal convection is a key
  objective in controlling segregation in alloys
• Need to explore methods to damp convection
  during solidification

• Application of magnetic fields and magnetic
  field gradients during
• solidification of alloys.
• Production of both Lorentz and Kelvin damping
  forces
• Suitable for both non metallic and metallic
  alloy solidification
• Successfully applied for the growth of metals
  and crystal growth

17
Numerical model of alloy solidification underthe
influence of magnetic fields and gradients
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PROBLEM DEFINITION
B(t)
g
SOLID
qs
MELT
Mushy zone

• Application of magnetic field on an electrically
  conducting fluid produces
• additional body force Lorentz force.
• This force is used for damping flow during
  solidification of electrically
• conducting metals and alloys.
• Application of a constant magnetic gradient also
  produces Kelvin force
• that acts directly on the thermosolutal buoyancy
  force.
• Combination of magnetic field and magnetic field
  gradients is suitable for
• all kinds of alloys.

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NUMERICAL MODEL
SALIENT FEATURES
Microscopic transport equations

• Single domain model based on volume averaging is
  used.
• Single set of transport equations for mass,
  momentum, energy
• and species transport.
• Individual phase boundaries are not explicitly
  tracked.
• Complex geometrical modeling of interfaces
  avoided.
• Single grid used with a single set of boundary
  conditions.
• Solidification microstructures are not modeled
  here and empirical relationships used for drag
  force due to permeability.

wk
Volume- averaging process
dAk
(Ref Gray et al., 1977)
Macroscopic governing equations
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IMPORTANT ASSUMPTIONS AND SIMPLIFICATIONS
TRANSPORT EQUATIONS FOR SOLIDIFICATION

• Only two phases present solid and liquid with
  the solid phase assumed to be stationary.
• The densities of both phases are assumed to be
  equal and constant except in the Boussinesq
  approximation term for thermosolutal buoyancy.
• Interfacial drag in the mushy zone modeled using
  Darcys law.
• The mushy zone permeability is assumed to vary
  only with the liquid volume
• fraction and is either isotropic or anisotropic.
• The solid is assumed to be stress free and pore
  formation is neglected.
• Material properties uniform (µ, k etc.) in an
  averaging volume dVk but can globally vary
• Darcy drag force is assumed to be linear in
  velocity and quadratic drag term
• is neglected

21
IMPORTANT ASSUMPTIONS AND SIMPLIFICATIONS
MAGNETO-HYDRODYNAMIC (MHD) EQUATIONS

• Phenomenological cross effects galvomagnetic,
  thermoelectric and thermomagnetic are neglected
• The induced magnetic field is negligible,
  the applied field
• Magnetic field assumed to be quasistatic
• The current density is solenoidal,
• The external magnetic field and gradient are
  applied only in a single direction
• Spatial variations in the magnetic field
  negligible due to small size of problem domains
• Charge density is negligible,

Electromagnetic force per unit volume on fluid
Current density
22
IMPORTANT ASSUMPTIONS AND SIMPLIFICATIONS
Volume averaged current density equation
Assumption of interfacial fluxes
Volume- averaging process
Boussinesq approximation for the body force terms

Diamagnetic materials
Paramagnetic materials
(Ref Toshio and Tagawa 2000, Evans C.G., 2000)
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GOVERNING EQUATIONS
where
(Ref Toshio and Tagawa (2002-04), Evans et al.
(2000), Zabaras and Ganapathysubramanian B.,
2004-05)
24
PERMEABILITY EXPRESSIONS IN ALLOY
SOLIDIFICATION
Isotropic permeability (empirical relation based
on Kozeny Carman relationship)
d dendrite arm spacing important
microstructural parameter.
Anisotropic permeability (obtained experimentally
and from regression analysis for directional
solidification of binary alloys, Heinrich et al.,
1997)
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CLOSURE RELATIONSHIPS

• Segregation models needed for closure of the
  numerical model
• Relationships between auxiliary field variables
  derived from thermodynamic relations
• Linear phase diagram with constant slopes of
  solidus and liquidus lines used

(Infinite back diffusion)
Lever rule
(Ref Flemings, 1970)
Scheil rule
(No back diffusion)
Finite Back Diffusion
(Ref Kurz and Fisher, 1989)
Back diffusion parameter

• Lever and Scheil rule form the lower and upper
  limits of liquid mass fractions
• Other models take into account back diffusion or
  solidification histories (paths)
• History based solidification eliminates
  equilibrium assumptions

26
CLOSURE RELATIONSHIPS
HISTORY BASED SEGREGATION MODEL (RefHeinrich et
al.1997 - 99, 2004)
(re melting)
(solidification)
H(f) is a function that gives I for old values of
f
(solidification)
(re melting)

• Solidification histories explicitly taken into
  account
• Equilibrium assumption is not invoked
• Microsegregation in solid phase modeled

27
Computational strategies to solve the coupled
numerical system
28
COMPUTATIONAL STRATEGY AND NUMERICAL TECHNIQUES

• SUPG based finite element discretization
  technique used for thermal and solutal problems
  ?to stabilize advective effects.
• A modified form of SUPG-PSPG technique used for
  fluid flow incorporating effects of the Darcy
  drag force in the stabilizing parameters.
• Stabilizing parameters take into account the
  underlying regime ? advective / diffusive /Darcy
  dominated.

Fluid flow problem
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COMPUTATIONAL STRATEGY AND NUMERICAL TECHNIQUES

• Stabilizing techniques needed to accommodate
  equal-order velocity-pressure interpolations
• Absolutely necessary for convection dominated
  problems
• Stabilizing terms derived by minimizing the
  momentum equation residual or a subgrid scale
  approach

Stabilized FE formulation for the momentum
equation (RefZabaras and Samanta, 2004)
Pressure stabilizing term
Darcy drag stabilizing term
Advection stabilizing term
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COMPUTATIONAL STRATEGY AND NUMERICAL TECHNIQUES
Convection stabilizing parameter
Pressure stabilizing parameter
Darcy stabilizing parameter
(RefZabaras and Samanta, 2004)

• Stabilizing parameters are time constants
  representing the dominant underlying phenomenon
• Smooth transition between advective, diffusive
  or Darcy dominated flow regimes
• The Darcy stabilizing term is chosen to provide
  a linear additional term (1 e)wh
• The combined shape function is

(Ref Tezduyar T.E., 1992)
31
COMPUTATIONAL STRATEGY AND NUMERICAL TECHNIQUES
Modified energy equation
(Ref Heinrich, Poirier and Felicilli et al.)
Stabilized finite element formulation for energy
equation
Implicit factor (Scheil rule / History)
32
COMPUTATIONAL STRATEGY AND NUMERICAL TECHNIQUES
(Ref Incropera, 1987 Heinrich, 1991)
Stabilized finite element formulation of the
solute equation

• Multistep Predictor Corrector method used for
  thermal and solute problems.
• Backward Euler fully implicit method for time
  discretization and Newton-Raphson method for
  solving heat transfer, fluid flow and deformation
  problems.
• Thermal and solutal transport problems along
  with the thermodynamic update scheme solved
  repeatedly in a inner loop in each time step.
• Fluid flow and electric potential problems
  decoupled from this iterative loop and solved
  only once in each time step.

33
COMPUTATIONAL STRATEGY AND NUMERICAL TECHNIQUES
SOLUTION ALGORITHM AT EACH TIME STEP
All fields known at time tn
n n 1
Solve for the induced electric potential
Advance the time to tn1
Decoupled momentum solution only once in each
time step
Check if convergence satisfied
Solve for the temperature field
(energy equation)
Solve for velocity and pressure fields (momentum
equation)
(Ref Heinrich, et al.)
Inner iteration loop
Solve for the concentration field
(solute equation)
Yes
Is the error in
liquid concentration and liquid mass
fraction less than tolerance
Solve for liquid concentration, mass
fraction and density (Thermodynamic relations)
Segregation model (Scheil rule)
No
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Numerical Examples
35
DAMPING CONVECTION IN HORIZONTAL ALLOY
SOLIDIFICATION
g
SOLID
H 0.02 m
MELT
qs h(T Tamb)
Mushy zone
L 0.08 m

• Solidification of Pb Sn alloy studied under
  the influence of magnetic fields and field
  gradients
• Lorentz force dominates and Kelvin force is
  negligible
• A magnetic field of 5 T combined with a gradient
  of 20 T/m
• Effect of Lorentz force on macrosegregation to
  be studied
• Diamagnetic susceptibility, ? -1.36 x 10-9
  m3/kg

36
HORIZONTAL SOLIDIFICATION OF A METAL ALLOY (Pb
Sn)
Important properties and initial conditions for
this example
(Ref C. Beckermann, 2002 )
37
HORIZONTAL SOLIDIFICATION OF A METAL ALLOY (Pb
Sn)
(i)
(ii)
(iii)
(iv)
(b) A magnetic field of 5 T combined with a
gradient of 20 T/m
(a) No magnetic field or gradients
(i) Isotherms (ii) velocity vectors and
liquid mass fractions (iii) isochors
(iv) liquid solute concentration
38
HORIZONTAL SOLIDIFICATION OF A METAL ALLOY (Pb
Sn)

• Significant damping in thermosolutal convection
  in the whole cavity
• Freckle formation is largely inhibited
• Substantial reduction in macrosegregation and
  solute concentration variations
• Horizontal velocity damped out small vertical
  velocities are induced causing small cyclic
  perturbations in concentration

• Maximum solute concentration differences
• 1. in the presence of magnetic field and
  gradients
• ?C 0.43 wt. Sn at t 40 sec
  ?C 1.79 wt. Sn at t 160 sec
• 2. absence of magnetic field and gradients
• ?C 9.81 wt. Sn at t 40 sec
  ?C 14.86 wt. Sn at t 160 sec
• Maximum velocity magnitudes
• 1. in the presence of magnetic field and
  gradients
• Vmax 1.32 mm/s at t 40 sec
  Vmax 4.98 mm/s at t 160 sec
• 2. absence of magnetic field and gradients
• Vmax 74.4 mm/s at t 40 sec
  Vmax 149.2 mm/s at t 160 sec

39
HORIZONTAL SOLIDIFICATION OF A METAL ALLOY (Al
Cu)
Important properties and initial conditions for
this example
(Ref C. Beckermann 1995, Tsai 1993 )
40
HORIZONTAL SOLIDIFICATION OF A METAL ALLOY (Al
Cu)
(i)
(ii)
(iii)
(iv)
(b) A magnetic field of 5 T combined with a
gradient of 20 T/m
(a) No magnetic field or gradients
(i) Isotherms (ii) velocity vectors and
liquid mass fractions (iii) isochors (iv)
liquid solute concentration (t 60 sec)
(a) ?C 0.855 wt Cu
(b) ?C 0.006 wt Cu
41
HORIZONTAL SOLIDIFICATION OF A METAL ALLOY (Al
Cu)
(i)
(ii)
(iii)
(iv)
(b) A magnetic field of 5 T combined with a
gradient of 20 T/m
(a) No magnetic field or gradients
(i) Isotherms (ii) velocity vectors and
liquid mass fractions (iii) isochors (iv)
liquid solute concentration (t 144 sec)
(a) ?C 1.16 wt Cu
(b) ?C 0.006 wt Cu
42
FRECKLE SUPPRESSION IN 2D DIRECTIONAL
SOLIDIFICATION (BINARY ALLOY)
?T/?z G
Important parameters
ux uz 0
L x B 0.04m x 0.007m C0 10 by weight Tin (Sn)
ux uz 0
ux uz 0
T(x,z,0) T0 Gz C(x,z,0) C0
?T/?x 0
g
?T/?x 0
Insulated boundaries on the rest of faces
Direction of solidification
?C/?x 0
?C/?x 0
ux uz 0
?T/?t r

• Mushy zone permeability assumed to be
  anisotropic
• Formation of freckles and channels due to
• thermosolutal convection
• Only Lorentz force present and Kelvin force
  negligible

magnetic field of 2T combined with a gradient of
10 T/m in x dir
43
FRECKLE SUPPRESSION IN 2D DIRECTIONAL
SOLIDIFICATION (BINARY ALLOY)
(b)
(a)
(i) CSn
(ii) fl
(i) CSn
(ii) fl

• (a) No magnetic field/gradient
  (b) Combined magnetic field/gradient (2T with 10
  T/m)
• Significant damping of convection throughout the
  cavity
• Freckle formation is totally suppressed ?
  homogeneous solute distribution
• (a) ?C Cmax Cmin 2.63 wt Sn (t 790 s)
  (b) ?C Cmax Cmin 1.3 wt Sn (t 790 s)

44
FRECKLE SUPPRESSION IN 3D DIRECTIONAL
SOLIDIFICATION (BINARY ALLOY)
z
Important parameters
L x B x H 0.01m x 0.01m x 0.02m C0 10 by
weight Tin
?T/?z G
vx vy 0 on all surfaces A combined magnetic
field and gradient applied in x
Direction of solidification
g
Insulated boundaries on the rest of faces
x
y
?T/?t r
No of unknowns in fluid flow solver 110864 No
of unknowns in thermal solver 27716 No of
unknowns in solutal solver 27716

• Mushy zone permeability assumed to be
  anisotropic
• Formation of freckles and channels due to
  thermal solutal convection
• Only Lorentz force present and no Kelvin force

45
FRECKLE SUPPRESSION IN 3D DIRECTIONAL
SOLIDIFICATION (BINARY ALLOY)
(a)
(b)

• Liquid mass
  fraction at t 1800 s
• (a) (NO magnetic field) (b) magnetic field
  of 5T combined with a gradient of 20 T/m in x
  dir
• Freckles present in (a) but absent in (b)
• Suppression of thermosolutal convection by
  magnetic field.

46
FRECKLE SUPPRESSION IN 3D DIRECTIONAL
SOLIDIFICATION (BINARY ALLOY)
(a)
(b)

• Solute
  concentration at t 1800 s
• (a) (NO magnetic field) (b) magnetic field
  of 5T combined with a gradient of 20 T/m in x
  dir
• Freckles present in (a) but absent in (b)
• (a) ?C 10.5 wt Sn (b) ?C 1.97 wt
  Sn ? drastic reduction in concentration
  variations.

47
FRECKLE SUPPRESSION IN A MULTICOMPONENT ALLOY
(Ni-Al-Ta ALLOY)
?T/?z G
L x B 0.02m x 0.007m C10 5.8 by wt. Al C20
15.2 by wt. Ta
ux uz 0
ux uz 0
ux uz 0
T(x,z,0) T0 Gz C(x,z,0) C0
Insulated boundaries on the rest of faces
?T/?x 0
g
?T/?x 0
Direction of solidification
?C/?x 0
?C/?x 0
Boussinesq approximation for a multicomponent
alloy (Ref. Heinrich et al. (1997-98)
ux uz 0
?T/?t r
Segregation rules defined for each species
48
FRECKLE SUPPRESSION IN A MULTICOMPONENT ALLOY
(Ni-Al-Ta ALLOY)
(re melting)
(solidification)
H(f) is a function that gives Ij for old values
of f
(solidification)
(re melting)
Some important properties Thermal expansion
coefficient, ßT 1.15 x 10-4 K-1
Solute partition coefficients
0.54 (Al), 0.48 (Ta) Solutal expansion
coefficients, ßc1 ßc2 2.26 (Al) , -0.382 (Ta)
Eutectic temperature 1560 K Liquidus surface
slopes, mliq1, mliq2 -517.0 (Al), -255.0 (Ta)
Thermal conductivity 0.08 kWm-1K-1 (both s
and l) Heat capacity 0.66
kWm-1K-1 (both s and l) Electrical conductivity
of the alloy 2.1217 x106 ohm.m
Latent heat 290.0 kJ Curie temperature 633.0
K
(Ref Heinrich et al, 1997-98)
49
FRECKLE SUPPRESSION IN A MULTICOMPONENT ALLOY
(Ni-Al-Ta ALLOY)
where
50
FRECKLE SUPPRESSION IN A MULTICOMPONENT ALLOY
(Ni-Al-Ta ALLOY)
(b)
(a)
(ii) CTa
(i) CAl
(iii) fl
(ii) CTa
(i) CAl
(iii) fl

• (a) No magnetic field/gradient
  (b) Combined magnetic field/gradient (2T with 10
  T/m)
• Significant damping of convection throughout the
  cavity
• Freckle formation is suppressed ? homogeneous
  solute distribution for both species
• (a) ?C Cmax Cmin 0.4 wt Al (t 35 s)
  (b) ?C Cmax Cmin 0.005 Al (t 35 s)

51
CONCLUSIONS

• Magnetic fields successfully used to damp
  convection during solidification of alloys.
• Near homogenous solute element distributions
  obtained.
• Suppression of freckle defects during
  directional solidification of alloys possible.
• Minimization of solute concentration variations
  leads to uniform properties in the final cast
  product.
• Demostration of successful elimination of some
  casting defects using magnetic fields in
  terrestrial gravity conditions

52
CURRENT AND FUTURE RESEARCH

• Computational design of crystal growth processes
• Optimize crystal growth with improved growing
  speeds
• Coupling of models to predict stresses in the
  cooling crystal with growth simulator
• Design for improved quality and defect control
• Computational design of binary alloy
  solidification processes
• Melt flow control
• Control of thermal, flow and segregation
  conditions within the mushy zone
• Control of segregation patterns and defects in
  the product
• Multi-length scale design of solidification
  processes
• Effect of magnetic fields and gradients on
  underlying microstructure
• Controlling magnetic fields to obtain a desired
  microstructure that yields uniform
• properties

Cast components with desired properties and
microstructure
53
RELEVANT PUBLICATIONS

• D. Samanta and N. Zabaras, Modeling melt
  convection during solidification of alloys using
  stabilized techniques, in press in International
  Journal for Numerical Methods in Engineering.
• B. Ganapathysubramanian and N. Zabaras, Using
  magnetic field gradients to control the
  directional solidification of alloys and the
  growth of single crystals, Journal of Crystal
  growth, Vol. 270/1-2, 255-272, 2004.
• B. Ganapathysubramanian and N. Zabaras, Control
  of solidification of non-conducting materials
  using tailored magnetic fields, Journal of
  Crystal growth, Vol. 276/1-2, 299-316, 2005.
• B. Ganapathysubramanian and N. Zabaras, On the
  control of solidification of conducting materials
  using magnetic fields and magnetic field
  gradients, International Journal of Heat and
  Mass Transfer, in press.

CONTACT INFORMATION http//mpdc.mae.cornell.edu/