NACKE Bernard

Institute of Electrothermal Processes, University of Hannover,

Wilhelm-Busch-Str. 4,D-30167 Hannover, GERMANY


Department of Physics, University of Latvia, Zellu 8, LV-1002, Riga, LATVIA


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


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Figure 2. Heat capacity and enthalpy of ZrO2
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.

Text Box:  
Figure 3.Nomogram between initial porosity, total power, radiation losses and thickness of skull layer at   in final stationary case for small experimental furnace.
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.

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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. New York: John Wiley & Sons, Inc. 1956.

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. Heidelberg: Energie-Verlag GmbH 1978.