STABILITY CONDITIONS IN
INDUCTIVE MELTING OF OXIDES IN INDUCTOR CRUCIBLE FURNACE
NACKE
Bernard
Institute of
Electrothermal Processes,
Wilhelm-Busch-Str. 4,D-30167
nacke@ewh.uni-hannover.de
FRISHFELDS
Vilnis, JAKOVICS Andris
Department of Physics,
ajakov@latnet.lv
Abstract: Modeling of high frequency inductive heating
of oxides with high melting temperatures in crucible furnace is considered in
order to find the most appropriate regime of exploitation of the furnace. The
necessary initial heating of the load for such kind of oxides is performed by
insertion of Mo ring which burns out at high temperatures. The initial heating
of the Mo ring is experimentally tested in small laboratory furnace. Different
regimes of voltage and current during a set stages of
induction process are studied. The influence of the properties of the initial
material in stationary case of inductive melting is discussed.
1.
Introduction
High frequency
inductive melting in inductor crucible furnace (ICF), where the melt is placed
directly in the water cooled inductor, is well suited for treatment of ceramic
materials with low heat and electrical conductivities at low temperatures such
as zircon. This method of inductive melting has significant advantages such as
-
possibility to melt materials
with high melting temperature about 3000 °C (glass, ceramics, oxides) without refractory crucible,
-
high purity of the melt and
final product,
-
homogeneous material and crystal
structure,
-
different gaseous atmospheres
and vacuum can be used,
-
semi-continuous process.
However,
there are some essential difficulties appearing in this method of melting:
-
energy transfer to melt at low
temperatures,
-
control of supplied power during
start-up and melting,
-
ensuring of process stability.
The
melted material in this method is separated from the inductor only by a thin
layer of cold porous oxide material (skull). The stability and power
requirements depend significantly on the properties of this layer. In order to
describe the melting process and the variation of the thickness and properties
of the skull, electromagnetic calculations of vector potential are performed
together with heat balance equations in the system. The modeling allows
minimizing of the necessary input energy by appropriate choice of the regime of
inductive heating.
There
are several possibilities to heat up the load till the temperature is high
enough for inductive heating of oxide material:
-
insertion of start-up metallic
chips burning out at certain temperature,
-
insertion of start-up metallic
(e.g. Mo) ring burning out at certain temperature,
-
plasma heating of the top surface of load.
The
second possibility of initial heating is chosen to build an appropriate
industrial furnace due to the simplicity of this kind of initial heating.
The
characteristic shape of the furnace for melting of zirconium oxide (ZrO2)
and zircon (ZrO2-SiO2) is shown in fig. 1. The melting
furnace additionally includes a unit of compensating capacity. The inductor and
bottom are made from water cooled Cu material.
Figure 1. Axial cross-section of experimental
furnace (a) and top-view of the furnace (b)
The
corresponding 2D program is elaborated to investigate the stability conditions
of such a furnace. The results of simulations are tested with commercial
software packet ANSYS up to the melting point.
2.
Harmonic axial symmetric magnetic field
In order
to find the Joule heat sources inside the load, we must calculate the
distribution of electromagnetic field. The common way in axial symmetric case
is to use vector potential 
with only one vector
component instead of magnetic induction with two components. The
electromagnetic radiation can be surely neglected for the characteristic range
of frequencies 80 kHz – 400 kHz and size of inductor. Then, the equation for
vector potential in the case of axial symmetry in non-magnetic material is
,
where 
is azimuthal component
of vector potential 
; and quantities vary in harmonic way
; 
; 
,
where j – density of current; U is the scalar potential the gradient
of which differs from zero only in the inductor. Both the amplitude of total
current
or
amplitude of voltage can be given to characterize the source of harmonic
magnetic field. As the inductor is made from one massive coil the distribution
of current density in the inductor must be calculated additionally using the
independence of scalar potential in the cross-section of the inductor. The
conductivity of the oxide material rapidly increases with temperature.
Therefore, the electromagnetic field should be recalculated time after time
during the electromagnetic heating coupling the electromagnetic and
thermodynamic parts of the problem. The conductivity (in 1/(W×m)), e.g. of ZrO2,
according to experimental data [1] can be approximated by following
semiconductor like equation up the temperature 2000 °C
.
At T>2000 °C, the conductivity is only slightly
dependent of temperature as the metallization takes place. Such behavior is characteristic
for dominant part of oxides despite of the fact, that the charge carriers are
usually the anions rather than electrons and holes. However, the conductivity
depends very much on the impurities and microscopic modifications of the oxide
material. Thus, the problem of inductive heating of oxide materials can be
considered only qualitatively.
3.
Temperature distribution in the load
The
electromagnetic induction appears as Joule heat in the thermodynamic equations
.
Heat capacity is dependent
from the temperature, e.g. for ZrO2 see fig. 2. The boundary
conditions are given by constant temperature 400 K at water-cooled inductor and
bottom of the furnace (see fig. 1). Zero heat flux is assumed in the gap
between the bottom and the inductor. The boundary conditions at the top of the
load depend on the fact whether the load is coated with some radiation
preventing material or not. We will consider the last case where the load
material is just put in the air atmosphere. The radiation heat losses in this
case are dominant and following boundary condition should be set
,
where Tout is temperature of the
atmosphere (»300 K), sSB – Stephan-Boltzmann constant and e – radiation constant of surface
material.
The
initial material is usually like a powder consisting of small grains.
Therefore, the initial material is porous with some porosity coefficient 
given by volume
fraction of void. The porosity decreases both electric and heat conductivity, allowing
the skin layer smaller to become. Let us make a linear approximation:
,
where 
is some critical porosity. For dense packing of equal sized
grains the porosity is 
. The porosity decreases at the vicinity of melting point or
at solidus line in binary mixture. The irreversible decrease of porosity is
chosen in correspondence of geometric factors, that do
not include melt filtration. The porosity influences strongly the properties of
the skull layer. For example, the relationship between porosity, total power,
thickness of the skull and radiation losses in stationary regime with constant
amplitude of current can be expressed by the following nomogram in fig. 3 for
small experimental furnace (rind=0.035 m, f=400 kHz).
Despite
the fact, that average porosity of the load decreases the total volume of the
melt is approximated to remain constant. Moreover, the effective value of heat
conductivity (leff>> lOxide) is used in the melt to approximate the
intensive convective heat exchange to characterize the process qualitatively.
For one-component system, we
will include the phase transition associated with the melting because of higher
latent heat neglecting various allotropic transformations, e.g. for ZrO2.
The most important binary system, we consider, is zircon ZrO2-SiO2.
Its phase diagram is given in [2]. We are approximating the phase diagram of
such system by binary phase diagram with eutectics. Then, the melting occurs
continuously with temperature along solidus and liquidus curves. That improves
the numerical stability of the simulations, as the dependence of enthalpy is
less sharp. The spatial redistribution of components ZrO2, SiO2
is neglected in the elaborated program despite the difference of their melting
temperatures.
4.
Simulations of power control during the inductive
heating of oxides
The
exploitation of the induction crucible for heating of oxides demands a lot of
energy. Let us test the most important stages of the inductive heating process.
As said before the initial heating of the load is performed by insertion of Mo
ring in the load burning out at some temperature. If we start from the cold
load, then the inductive heating produces following sharp temperature
distribution shown in fig. 4a. The Mo ring is heated in this figure by
amplitude of voltage - 1450 V and the time of heating is 7 minutes. A more
intense heating of Mo would produce much sharper distribution of temperature.
As shown in the diagram (fig. 4b) much higher voltage is necessary afterwards
to ensure that melt temperature will increase rather than cools down. However,
the maximal voltage of the inductor is usually limited. Consequently, the
moderate heating of the Mo ring is necessary followed by exploitation of the
furnace in the maximal regime after burnout of the Mo. Afterwards, the average
temperature is high enough with sufficiently high conductivity of the oxide
material. In this stage the applied voltage should be reduced to ensure the
appropriate conditions for the material processing.
Figure 4. The distribution of temperature in zircon load
before burnout of Mo ring (a) and the diagram expressing the relationship
between the voltage before and after burnout of Mo ring (b).
Figure 5. Behavior of power parameters and temperatures
during inductive heating of zircon in experimental furnace (fig. 1) by f=300
kHz
The
example of inductive heating of zircon in industrial furnace of fig. 1 is shown
in fig. 5. The amplitude of voltage is chosen 1450 V, 2350 V, and 1350 V before
and after burnout of Mo ring, and after reaching of melting temperature of
zircon, respectively. The frequency is set to be 300 kHz. Lower frequencies are
less effective for heating of oxide materials, since inductive heating occurs
mainly in metallic parts rather than in load [3]. The initial material contains
a mixture of ZrO2 and SiO2 grains. For simplicity, the
components are set as insoluble in each other. Thus the figure shows a plateau
at the temperature of Mo ring close to melting temperature of SiO2.
The figure shows the behavior of maximal temperature in the load, temperature
in the center of the ring, and temperature in center of the furnace. The small
difference between first two temperatures in initial stage suggests that
temperature distribution in Mo ring is almost homogeneous due to much higher
thermal conductivity. The major power losses occur through the heat transfer to
the inductor. The radiation heat losses (e=0,68)
exceed heat transfer to the bottom because the Cu bottom changes the
distribution of electromagnetic field.
Example
of the stationary distribution of temperature is shown in fig. 6a. The figure
shows that small layer of non-melted material is present at the top of the melt
due to significant radiation losses. The analysis of the turbulent behavior of
the melt of course would influence the properties of this layer. A very sharp
temperature distribution is present in the skull layer at the inductor. The
photo in fig. 6b shows the characteristic cross-section of such a skull.
Figure 6. Stationary distribution of
temperature in zircon melt (a) and the photo of the oxide material with skull
layer (bottom) (b).
5. Conclusion
The
moderate values of current and voltage should be used in presence of Mo ring to
heat up the load. Afterwards, the maximal regime must be set for the furnace to
escape from the cooling of the load. Finally, reduced voltage and current are
needed to keep the melt in stationary regime.
The
frequency of the current should not be lower than 200 kHz to ensure effective
melting. The predominant heat losses occur through the heat transfer to the
water-cooled inductor.
6.
References
1. Campbell, E.: High-temperature
technology.
2. Parfenekov, V.N., Grebenshcikov, R.G., Toropov, N.A.:
Dokl. Akad. Nauk SSSR, 185 (1969) 840.
3. Fasholz, J., Decker, E., Röttgen, H.:
Induktive Erwärmung.