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Cold Crucible Melting of Reactive Metals

Using Combined DC and AC Magnetic Fields

V. Bojarevics

1

, K. Pericleous

1

, R.A. Harding

2

and M.Wickins

2

1

University of Greenwich, School of Computing and Mathematics, London, SE10 9LS, UK

2

The University of Birmingham, IRC in Materials Processing, Birmingham B15 2TT, UK

Abstract

Cold crucible furnace is widely used for melting reactive metals for high quality castings. Although the water cooled

copper crucible avoids contamination, it produces a low superheat of the melt. Experimental and theoretical

investigations of the process showed that the increase of the supplied power to the furnace leads to a saturation in the

temperature rise of the melt, and no significant increase of the melt superheat can be obtained. The computer model of

the process has been developed to simulate the time dependent turbulent flow, heat transfer with phase change, and AC

and DC magnetohydrodynamics in a time varying liquid metal envelope. The model predicts that the superimposition of

a strong DC field on top of the normal AC field reduces the level of turbulence and stirring in the liquid metal, thereby

reducing the heat loss through the base of the crucible and increasing the superheat. The direct measurements of the

temperature in the commercial size cold crucible has confirmed the computer predictions and showed that the addition

of a DC field increased the superheat in molten TiAl from ~45˚C (AC field only) to ~81˚C (DC + AC fields). The

present paper reports further predictions of the effect of a DC field on top of the AC field and compares these with

experimental data.

Keywords: cold crucible, liquid metal, AC electromagnetic field, turbulent flow, free surface dynamics, turbulent

thermal losses, numerical modelling

Acknowledgments

The authors

1, 2

acknowledge the financial assistance of the EU IP project IMPRESS (NMP3-CT-2004-500635) and the

EPSRC (GR/N14316 & GR/N14064) for parts of this research.

Introduction

The main problem with the induction furnace design stems from the fact that liquid stirring causes crucible erosion

and contamination of the melt. This is especially serious where reactive melts are concerned, such as those involving

titanium or zirconium alloys. With the drive for lightweight high strength alloys (e.g. TiAl) in the aerospace industry as

a replacement for heavier Nickel superalloys this has led to an increased research effort in this area [1,2]. Although

melting crucibles can be made from refractories such as yttria and calcia, some reaction is nevertheless inevitable. For

this reason, it is now usual to melt these alloys in a water-cooled segmented copper crucible. Then, the first metal to

melt re-solidifies on the crucible base and walls to form a protective ‘skull’ which itself acts as a crucible (hence the

alternative name for the cold crucible melting is Induction Skull Melting (ISM)). The downside is the severe heat loss to

the water-cooling circuit. Contact with the water-cooled surfaces needs to be minimized to achieve the superheat needed

to cast thin-section components (i.e. turbine blades). To reduce wall-contact area, the induced magnetic field is used to

“squeeze” the melt away from the walls, so that ideally only the base remains in contact [3]. The metal can then be

poured into the mould by rotation, or alternatively it can be sucked into the mould through a refractory snorkel using

counter-gravity filling. The factors affecting the maximum superheat attainable in the cold crucible process for a given

power input are many: (a) electromagnetic coupling efficiency, (b) coil frequency, (c) heat loss by convection, (d) heat

loss by radiation, (e) coil design and position, etc. A comprehensive computer model of the process was developed at

Greenwich [3,4]. This model simulates the coupled influences of turbulent flow, heat transfer with phase change, and

magneto-hydrodynamics in a time-varying liquid metal envelope. It has been used to study systematically all the

influential parameters listed, for a range of melt materials and it was validated against experiments performed at

Birmingham University [3]. One very interesting outcome of this investigation concerns the role of turbulence in the

thermal efficiency of the process. The model predicted that the superimposition of a strong DC field on top of the

normal AC field would reduce the turbulent stirring in the liquid metal which would, in turn, reduce the heat loss

through the base of the crucible and wall finger segments and so increase superheat [4]. This prediction was later

confirmed in experiments performed by Consarc Corp. in Birmingham [5,6]. It can be noted that Mortimer [7] has

described the use of a DC field to stabilize the melt in a containerless (semi-levitation) melting process although no

effect on superheat was reported.

In this paper, the mathematical model for the turbulent flow in the cold crucible melting process will be described

briefly and the effect of the DC field on the attainable superheat discussed.

Mathematical Model Description

A spectral collocation method has been used in Greenwich to develop a mathematical model of the process. This

model has been described in detail in [3], with the exception of a new magneto-hydrodynamic turbulence damping

terms included in this study. The model is axisymmetric and it solves the time-dependent Navier-Stokes and continuity

equations for an incompressible fluid, and the thermal energy conservation equations for the fluid and solid zones of the

metal charge. An effective viscosity

e

(R, t) is used to represent turbulence, which varies in time and position. The

local (AC cycle-averaged) electromagnetic force F(R, t) is recomputed during the time evolution of the melting front

and of the free surface of the liquid metal, which is confined by the magnetic force.

In cases where a combination of high frequency AC and DC magnetic fields has been used, we need further to obtain

the time average of the force over the field oscillation period, which is of a very small time scale 10

-3

- 10

-4

s. The

electric current in the axisymmetric case is given by Ohm's law for a moving medium:

v

)( JJBvAJ +=×+−∂=

ACt

σ

, (1)

where is the electrical conductivity, A – the vector potential related to the magnetic field B = rot A. The part of the

current J

AC

is induced in the conducting medium in the assumption of the absence of velocity. It is computed

according to the mutual inductance algorithm with elliptic integrals described in detail previously [3] and tested against

analytical solutions and experimental measurements. The same elliptic integral representation can be used to represent

the DC magnetic field created by an additional external coil. The solution in the liquid volume depends on its free

surface shape and needs to be recomputed when the shape changes. The resulting electromagnetic force f, time-

averaged over the AC period, similarly to (1) can be decomposed in two parts:

vAC

fff +=

, (2)

where the second, fluid velocity dependent part of the force f

v

in the axisymmetric and low magnetic Reynolds number

case has the following components in spherical co-ordinates (R, , ):

, )v(

)v(

2

v

2

vR

〉〈−〉〈=

〉〈−〉〈−=

RR

R

BBBuf

BBBuf

θθ

θθ

σ

σ

(3)

where the notation

〈⋅〉

denotes time averaging over the AC period. The magnetic field components in the expressions

(3) include AC and DC parts, both of which have a time average contribution to the force. It is of interest to note that,

even if there is only an AC field, there is, in principle, an average f

v

contributing to the interaction with the velocity

field.

The details of dynamic numerical simulation technique are described in publications [3,4]. The shape and position of

the liquid metal depend on the instantaneous balance of forces acting upon it. Hence, the electromagnetic field and the

associated force field are strongly coupled to the free surface dynamics of the liquid metal, the turbulent fluid flow

within it, and the heat transfer and radiation losses. This dynamic coupling of fields has been addressed here using a

unique spectral-collocation approach. The present modelling approach is based on the turbulent momentum and heat

transfer equations for an incompressible fluid:

, ))(()(

11

gfvvvvv ++∇+∇⋅∇+∇−=∇⋅+

−−

ρνρ∂

T

et

p

(4)

, 0

=

⋅

∇

v

(5)

1 2

( ) ( ) | | / ,

p t p e

C T T C T

∂ α ρ σ

−

+ ⋅∇ = ∇ ⋅ ∇ +v J

(6)

where v is the velocity vector, p - the pressure,

ρ

- the density,

e

ν

(sum of turbulent and laminar viscosity) is the

effective viscosity which is variable in time and position [8], f is the electromagnetic force, g - the gravity vector, T - the

temperature,

e

α

is the effective thermal diffusivity, C

p

- the specific heat, and

σ

/||

2

J

is the Joule heat.

The effective thermal diffusivity,

e

(R, t), is assumed to be proportional to the turbulent effective viscosity. The

temperature boundary conditions depend on

e

at the wall and the free surface. Therefore the turbulence model is

important, as it has a direct influence on the thermal fluxes at the walls. Turbulence is represented by the two-equation

k- model [8], which resolves the low Reynolds number flow from laminar to developed turbulent states. This model

with an appropriate modification can be considered suitable for the flow within the slowly moving mushy zones during

the phase change steps and, at the same time, for the bulk of the fully molten metal at the final mixing stages. The

variable is related to the reciprocal turbulent time scale (frequency of vorticity fluctuations) and the k variable is the

turbulence kinetic energy per unit mass. In the presence of a strong DC magnetic field, an additional modification to the

turbulence model has been added, based on an adapted version of Widlund’s model [9,10]. The k- equations with the

magnetic damping terms are:

*

2

2

[( ) ]

/( )

m

t k T

k

k k k G k

B

α

ν σ ν β ω

ρ σ

∂ + ⋅∇ = ∇ ⋅ + ∇ + − −v

(7)

2

2

[( ) ] -

/( )

m

t T

G

k B

ω

α ω

ω

ω ω ν σ ν ω α β ω

ρ σ

∂ + ⋅∇ = ∇ ⋅ + ∇ + −v

(8)

where G is the turbulent kinetic energy generation term and it is a function of the mean velocity strain rate . The

‘anisotropy function’

m

is the subject of a third evolution equation in [9,10]. However, here it was set equal to 1/3, a

value that corresponds to isotropic turbulence. The magnetic field is represented by its local magnitude B. Different

model constants and ‘wall damping’ functions are defined as:

* *

1

2

1 1

2 2

* *

2 ( : ) ( )

, , , - functions depending on

T T

k

T

k

G

k

R

ω

ν α ν

ω

σ σ

α α β β

ω ν

= = ∆ ∆ ∆ = ∇ + ∇

= =

=

⋅

v v

(9)

The full expressions for the functions can be found elsewhere [8]. The solution is sought with the time dependent

boundary conditions where the fluid contacts the solid wall:

2

0

0, 6 (0.1 ) / ,

k R

ω ν β

−

= =

and at the free surface:

.0 ,0

nn

=

∂

=

∂

ω

k

R

0

is a typical scale of the problem, equal to the crucible radius. Using the pseudo-spectral representation, the

computation follows in detail the time development of the melting front, free surface evolution, and turbulent flow

characteristics determined by the coupled non-linear transport equations, accounting for a continuous generation and

destruction of the turbulent energy.

Numerical results for magnetically damped melting process

The AC and DC magnetic field was computed at each time step during the melting cycle for the coil configuration

shown in Figure 1, showing also the computed AC and DC magnetic fields in the liquid metal region at the final stage

of the melting process. The AC coil current was gradually increased in steps until a time of 585 s, then kept constant in

the modeling run until a time of 940 s. The corresponding part of the total power, which is released in the liquid metal,

is recorded in Figure 2. As shown in the figure, during the interval 585-645 s, the melt was held at a constant power

supply, and a stable maximum temperature of about 1585

o

C is established. The DC coil current was switched on at 645

s and increased in steps corresponding to the respective values: 1200, 2400, 3600 and 4800 A. The computed maximum

magnetic field values are located at the bottom part of the metal and these are respectively: 0.2, 0.4, 0.6 and 0.8 T. It

should be noted that the ferromagnetic core was not modeled in this simulation because of the unknown magnetic

properties for the core material (most probably close to the magnetic saturation limit). This would account for higher

DC current magnitudes in the model to achieve the same field strengths as used in the experimental work.

Figure 1. The AC and DC magnetic fields, and the induced electric current distribution in a section of the liquid TiAl

metal load with the crucible and coil setup

Figure 2. The computed temperature response in the liquid metal (5 kg TiAl) on the applied AC power and the DC

magnetic field

Figure 3. The computed liquid metal shapes, fluid flow and the temperature distribution in the 5 kg TiAl metal load

with the crucible and coil setup

The time-averaged melt shapes were found to be quite similar with and without the DC magnetic field, however the

metal interface was considerably more stable in the presence of the DC field, as can be seen from the comparison of two

pictures on the Figure 3. The recorded temperature curve in Figure 2 also exhibits some oscillations in the thermal field

as the result of the time dependent local perturbations of the turbulent velocity field and the free surface dynamics.

Typically an abrupt increase in the DC field magnitude led to an increase in the temperature, followed by a small

gradual decrease. Nevertheless, the final temperature was always higher for the larger DC field. Comparison of the two

sides in Figure 3 shows an increase in the re-solidified skull in the middle of the crucible base for the high DC field

case, which can be explained by the considerable flow damping in this region. The detailed structure of the turbulent

kinetic energy distribution in the molten metal with the DC magnetic field and without are represented in Figure 4. The

turbulence energy is particularly suppressed in the bottom part of the flow. This is of importance for the turbulent

thermal loss decrease for the whole melt volume, because this part is directly contacting to the water cooled copper

bottom. The side surface and the top are in contact with the argon atmosphere only because of the magnetic

confinement.

The DC field is shown to increase the superheat. This follows the trend predicted in earlier, theoretical simulations

[4] and it is also shown here in Figure 5 together with the experimental measurements [5]. The correspondence is

qualitatively right, and the better accuracy is not possible because of the presence in the experiment of the

ferromagnetic core for which the magnetic saturation properties are unknown. The numerical model predicts that the

increase in superheat accelerates, particularly once the DC current exceeds 2400 A (equivalent to a field of 0.4 T).

Figure 4. The computed flow and the turbulent kinetic energy in the liquid TiAl metal

Figure 5. The dependence on the applied DC coil current of the measured and the computed relative superheat above

the conventional AC only melting of the TiAl in the cold crucible

Figure 6. The computed temperature drop after the liquid metal collapse in the cold crucible when the AC power is

abruptly switched off

Figure 7. The instantaneous views of the computed liquid metal collapse in the cold crucible with and without the DC

magnetic field after the AC power is abruptly switched off

An additional interesting physical effect is observed when the AC power in the induction coil is switched off. Then

the magnetic confinement ceases and the metal collapses under the action of gravity. Without the DC magnetic field

(switched off simultaneously with the AC) the liquid collapses very fast, generating additional turbulence. The high

thermal losses at this stage are crucial for the retention of the acquired superheat before the metal fills into the casting

mould. However, if the DC magnetic field is left on during the collapse stage, then the magnetic damping considerably

slows down the downward motion as demonstrated in Figure 7. Because the damping acts directly on the velocity

component normal to the magnetic field direction, the most active interaction occurs at the bottom part of the flow

where the radial velocity is dominating. This leads to a considerable damping of the turbulence in the bottom part as

well. The overall result is manifested in the cooling curves shown in Figure 6. Finally the thermal losses balance out,

but with a considerable delay of about 5-6 seconds.

Conclusions

• The presence of the strong magnetic field (both DC and AC) leads to a considerable damping of the large scale

velocity field and the free surface stabilization in the magnetically suspended liquid metal in the cold crucible.

• The microscopic turbulent vortices are affected

1) by the magnetic damping directly at these scales, and

2) by the reduction of the turbulence generating terms depending on the macroscopic motion.

• The turbulent effective thermal diffusion is proportionally reduced in the presence of the strong magnetic field.

This affects the rate of the thermal losses at the water cooled boundaries in the cold crucible.

• The overall increase of the molten metal superheat is predicted by the numerical model and confirmed by the

direct temperature measurements.

References

[1] D. Jarvis, O. Minster, IMPRESS New industrial materials with the help of space research,

www.esa.int/esapub/onstation17/os17_chapter7.pdf

[2] T. Noda, Application of cast gamma TiAl for automobiles, Intermetallics, 6, 709-713 (1998).

[3] V.Bojarevics, R.A.Harding, K.Pericleous, and M.Wickins. The Development and Validation of a Numerical Model

of an Induction Skull Melting Furnace. Metall. Materials Tran. B, 2004, 35, 785-803.

[4] V. Bojarevics and K. Pericleous, Modelling Induction Skull Melting Design Modifications, Proc. 2003 Int. Symp.

On Liquid Metal Processing and Casting. Eds. P. Lee, A. Mitchell, J-P. Bellot and A. Jardy, Nancy (France),

American Vacuum Society, 183-192 (2003).

[5] R. A. Harding, M.Wickins, G. Keough, K. Pericleous and V. Bojarevics, The Use of Combined DC and AC Fields

to Increase Superheat in an Induction Skull Melting Furnace, Int. Symp. Liquid Metal Processing and Casting,

Santa Fe, New Mexico, Sept 2005

[6] R. J. Roberts, G.A. Keough, U.S. Patent 20050175063.

[7] J.H. Mortimer, U.S. Patent 5,003,551.

[8] D.C. Wilcox, Turbulence Modeling for CFD, 2

nd

ed., DCW Industries, California (1998).

[9] O. Widlund. Modelling of magnetohydrodynamic turbulence. Ph.D. Thesis, Royal Institute of Technology,

Stockholm, Sweden, ISSN 0348-467X (2000).

[10] O. Widlund. Draft of K- - closure for modeling of MHD turbulence (unpublished manuscript, 2002).