**2.3 Temperature of the levitated melt**

Along with the retained metal melt, the production and regulation of its temperature are of great importance. For two-coil inductors, the theoretical foundations and technological designs that provide the necessary heating of the samples were considered in [6, 7]. The validity of the functional dependence (4), which relates the electromagnetic lifting force to the power absorbed by the metal, has been proved experimentally. In the steady state in vacuum, the power transmitted to the metal is equal to the radiated power. For most metals, the temperature dependence of the power *P*s radiated from a unit surface is well known (**Figure 4**). This power is usually determined by the reverse calculation. It is known that ensuring the transmission of a given power *P*s depends on a number of factors: the mass of the melt, the surface of the sample, the frequency of the field and coefficient A. The mass of the melt during levitation in a multi-coil inductor can be determined by knowing the minimum frequency of the electromagnetic field that implements the levitation of a metal melt with a given height and physical properties.

Obtaining high temperatures during the levitation of metal melts has no fundamental obstacles. In practice, this is accomplished by choosing, for example, a multi-coil inductor, the conical part of which is open at a small angle and whose field has a small tension gradient. To obtain the necessary lifting force, a sufficiently large current is needed, due to which the metal is heated. Due to the fact that the power increases proportionally with frequency, and the lifting force is much less dependent on it, the field frequency is increased to obtain a higher temperature. In each case, the field frequency must be chosen so that the value *X* = *R*/Δ (here *R* is the radius of the sphere and Δ is the thickness of the skin layer) is more than 10 and the value of *F* does not depend on the change in ρ. Otherwise, during heating, the

#### **Figure 4.**

*Dependence of the specific radiation power on the temperature of refractory metals. ABB—the absolutely black body.*

value of *X* may become less than 10, and the value of *F* at *I* = Const. will decrease, which will lead to the discharge of the molten drop. Low temperatures of the melt can be obtained at such a frequency and diameter of the spherical sample, when the value of *X* is more than 10. In this regard, *F* should be about 50% less than its full value (when *X* is more than 10). As mentioned above, the current in this case is regulated within certain limits, and the shape of the inductor must be such that the intensity gradient is maximum. In this case, the stabilizing forces become very small.

Temperature control can be done in two ways. The first is the selection of such an inductor shape in which there is a strong dependence of the *P*/*F* and *F* ratios on the position of the sample inside the inductor. An inductor is suitable for this, in which there exists a possibly large linear decrease in field strength along the axis of the inductor. In this case, *P* also depends linearly on the position of the sample. If the current is increased, the sample rises to the upper part of the inductor and its temperature decreases. The second method consists in the separate action of two inductors fed by currents of two frequencies: the lower one-for levitation of the metal at the lowest temperature-and the upper one-only for heating and melting the sample with regulation of current and frequency. In EML, samples simultaneously participate in heating and soaring, so that the power of EML unambiguously indicates a high temperature distributed around the soaring sample. This explains the interest in studying factors regarding the influence on the temperature characteristics of EML with the final goal of gaining additional knowledge in order to not only fully realize the levitation and melting of samples with low conductivity and high density at relatively low temperatures, but also fully use the primary role of inductors on the temperature characteristics of the electromagnetic field. So, in [6, 39] for the first time, using the finite element analysis, the influence of the design of inductors and the mass of samples on the temperature characteristics of levitation were studied. The modeling capabilities are confirmed experimentally as a result of a detailed analysis of the effect of the inductor on the temperature characteristics of levitation when choosing the optimal inductor in various applications. The shape of the metal

**171**

to 14,000°C.

*Electromagnetic Levitation of Metal Melts DOI: http://dx.doi.org/10.5772/intechopen.92230*

two-coil inductor [6].

(~7.5 cm2

(2.5 kW).

melt depends on the degree of compression of the melt by an electromagnetic field, which is largely determined by the configuration of the inductor. In a multi-coil inductor, the limiting melt height can be approximately two times smaller than in a

To obtain a given stable steady-state temperature, not only two-frequency levitation, cooling gas mixtures, but also other heating sources (electron beam, light beam, electromagnetic beam with a frequency corresponding to the centimeter and millimeter wavelength ranges) can be used. Refractory metals are known (Group 3), which, under experimental conditions, levitated in an inductor, but were not melted. Therefore, for their additional heating, a source of thermal energy-an electron beam-was used [6, 7]. Indirect heating is also used due to the relatively low efficiency of induction heating, which is mainly due to the presence of a large gap between the inductor and the metal sample and, in fact, depends on the design of the inductor. The use of additional heating is shown by the example of tungsten, which should melt at a frequency of 440 kHz, a power of 160 kW and a mass of 28 g. **Figure 5** shows experimentally determined temperatures depending on their mass and voltage at the inductor (40–90 V). Obviously, an increase in the mass of the sample cannot lead to a significant increase in the temperature of the metal (~3000°C). At this temperature, the power emitted by the melt surface

, the shape of the melt is a spinning top) is 1.7 kW, which corresponds

to 1.7% of the power consumed by the generator. This complicates the cooling of the inductor with water and significantly increases the voltage (up to 300 V). The arrow in **Figure 5** shows the temperature rise of a metal after being heated by an electron beam (~3700°C). Radiated power increases to 3.4 kW, that is, 1.7 kW is additionally transmitted, which is 68% of the total power of the electron beam unit

Similar results were obtained with EML of a 30 g Nb sample in a multi-coil inductor at a voltage of 30 V, a generator power of 25 kW and a frequency of 80 kHz. The metal temperature was 2100°С, which in terms of absorbed power is 0.5 kW or 2% of the power consumed by the generator. The metal was heated by an electron beam to a melting point of ~2415°С, and the power was 1.2 kW. The melt surface emitted ~1 kW. This means that the electron beam additionally transmitted at least 0.5 kW or 40% of the power consumed by the electron beam setup. By the way, electromagnetic levitation of the Nb melt without additional heating can be carried out in the same type of inductor using a more powerful generator (60 kW)

Additional heating may also be necessary in specific cases, for example, with silicon levitation. Pure silicon is known to have an extremely high electrical resistance; therefore, at ordinary frequencies (of the order of hundreds of kilohertz) and power (tens of kilowatts), silicon cannot be levitated. With increasing temperature, the electrical resistance of silicon decreases, especially sharply at the melting temperature; therefore, for silicon levitation, it is necessary to pre-heat it with an electron beam. If the field frequency during silicon levitation is about 200 kHz, then the sample should be heated to 10,000°C, and at frequencies of 70–80 kHz, up

Two-frequency heating has been studied in less detail. The experiments with aluminum were carried out in air. An inductor for EML was connected to a machine generator with a frequency of 8 kHz, and an inductor for heating, from a generator with a frequency of 440 kHz. Five different two-coil inductors were tested, producing a two-frequency field. The most rational were (1) an inductor with a single coil for holding the sample, placed above the main heating coil; (2) an inductor with a single holding coil placed between two main heating coils; and (3) an inductor with

with a frequency of 440 kHz and a voltage of 160 V.

a single holding coil placed above the main heating coil.

#### *Electromagnetic Levitation of Metal Melts DOI: http://dx.doi.org/10.5772/intechopen.92230*

*Magnetic Materials and Magnetic Levitation*

value of *X* may become less than 10, and the value of *F* at *I* = Const. will decrease, which will lead to the discharge of the molten drop. Low temperatures of the melt can be obtained at such a frequency and diameter of the spherical sample, when the value of *X* is more than 10. In this regard, *F* should be about 50% less than its full value (when *X* is more than 10). As mentioned above, the current in this case is regulated within certain limits, and the shape of the inductor must be such that the intensity gradient is maximum. In this case, the stabilizing forces become

*Dependence of the specific radiation power on the temperature of refractory metals. ABB—the absolutely* 

Temperature control can be done in two ways. The first is the selection of such an inductor shape in which there is a strong dependence of the *P*/*F* and *F* ratios on the position of the sample inside the inductor. An inductor is suitable for this, in which there exists a possibly large linear decrease in field strength along the axis of the inductor. In this case, *P* also depends linearly on the position of the sample. If the current is increased, the sample rises to the upper part of the inductor and its temperature decreases. The second method consists in the separate action of two inductors fed by currents of two frequencies: the lower one-for levitation of the metal at the lowest temperature-and the upper one-only for heating and melting the sample with regulation of current and frequency. In EML, samples simultaneously participate in heating and soaring, so that the power of EML unambiguously indicates a high temperature distributed around the soaring sample. This explains the interest in studying factors regarding the influence on the temperature characteristics of EML with the final goal of gaining additional knowledge in order to not only fully realize the levitation and melting of samples with low conductivity and high density at relatively low temperatures, but also fully use the primary role of inductors on the temperature characteristics of the electromagnetic field. So, in [6, 39] for the first time, using the finite element analysis, the influence of the design of inductors and the mass of samples on the temperature characteristics of levitation were studied. The modeling capabilities are confirmed experimentally as a result of a detailed analysis of the effect of the inductor on the temperature characteristics of levitation when choosing the optimal inductor in various applications. The shape of the metal

**170**

very small.

**Figure 4.**

*black body.*

melt depends on the degree of compression of the melt by an electromagnetic field, which is largely determined by the configuration of the inductor. In a multi-coil inductor, the limiting melt height can be approximately two times smaller than in a two-coil inductor [6].

To obtain a given stable steady-state temperature, not only two-frequency levitation, cooling gas mixtures, but also other heating sources (electron beam, light beam, electromagnetic beam with a frequency corresponding to the centimeter and millimeter wavelength ranges) can be used. Refractory metals are known (Group 3), which, under experimental conditions, levitated in an inductor, but were not melted. Therefore, for their additional heating, a source of thermal energy-an electron beam-was used [6, 7]. Indirect heating is also used due to the relatively low efficiency of induction heating, which is mainly due to the presence of a large gap between the inductor and the metal sample and, in fact, depends on the design of the inductor. The use of additional heating is shown by the example of tungsten, which should melt at a frequency of 440 kHz, a power of 160 kW and a mass of 28 g. **Figure 5** shows experimentally determined temperatures depending on their mass and voltage at the inductor (40–90 V). Obviously, an increase in the mass of the sample cannot lead to a significant increase in the temperature of the metal (~3000°C). At this temperature, the power emitted by the melt surface (~7.5 cm2 , the shape of the melt is a spinning top) is 1.7 kW, which corresponds to 1.7% of the power consumed by the generator. This complicates the cooling of the inductor with water and significantly increases the voltage (up to 300 V). The arrow in **Figure 5** shows the temperature rise of a metal after being heated by an electron beam (~3700°C). Radiated power increases to 3.4 kW, that is, 1.7 kW is additionally transmitted, which is 68% of the total power of the electron beam unit (2.5 kW).

Similar results were obtained with EML of a 30 g Nb sample in a multi-coil inductor at a voltage of 30 V, a generator power of 25 kW and a frequency of 80 kHz. The metal temperature was 2100°С, which in terms of absorbed power is 0.5 kW or 2% of the power consumed by the generator. The metal was heated by an electron beam to a melting point of ~2415°С, and the power was 1.2 kW. The melt surface emitted ~1 kW. This means that the electron beam additionally transmitted at least 0.5 kW or 40% of the power consumed by the electron beam setup. By the way, electromagnetic levitation of the Nb melt without additional heating can be carried out in the same type of inductor using a more powerful generator (60 kW) with a frequency of 440 kHz and a voltage of 160 V.

Additional heating may also be necessary in specific cases, for example, with silicon levitation. Pure silicon is known to have an extremely high electrical resistance; therefore, at ordinary frequencies (of the order of hundreds of kilohertz) and power (tens of kilowatts), silicon cannot be levitated. With increasing temperature, the electrical resistance of silicon decreases, especially sharply at the melting temperature; therefore, for silicon levitation, it is necessary to pre-heat it with an electron beam. If the field frequency during silicon levitation is about 200 kHz, then the sample should be heated to 10,000°C, and at frequencies of 70–80 kHz, up to 14,000°C.

Two-frequency heating has been studied in less detail. The experiments with aluminum were carried out in air. An inductor for EML was connected to a machine generator with a frequency of 8 kHz, and an inductor for heating, from a generator with a frequency of 440 kHz. Five different two-coil inductors were tested, producing a two-frequency field. The most rational were (1) an inductor with a single coil for holding the sample, placed above the main heating coil; (2) an inductor with a single holding coil placed between two main heating coils; and (3) an inductor with a single holding coil placed above the main heating coil.

#### **Figure 5.**

*The dependence of the power of the generator and the temperature of tungsten of various masses on the voltage at the inductor; the arrow shows the temperature of the metal after additional heating by an electron beam: 1—*P, *kW; 2–28.5 g; 3–20 g; 4–10 g.*

In axisymmetric EML, the Lorentz force vanishes on the axis of symmetry. At the lowest point on the axis of the levitated sample, only the surface tension of the melt prevents the flow of the melt, which affected the limitation of the mass of the melt-not more than 50–100 g. With electromagnetic two-frequency levitation, lifting forces also arise along the axis of the levitated sample. Digital models developed to optimize EML were implemented in [13–18]. At the same time, data were obtained on the electromagnetic flux and the dynamics of the free surface, for which calculations of the electromagnetic force, as well as modeling of the melt volume and restoration of the shape of the free surface, were made.

#### **2.4 Setups for EML of melts**

Depending on the voltage at the inductor, its design and the conditions of the technology and experiment, all setups for EML are divided into two groups: with an internal inductor and an external inductor relative to the reaction vessel. The first group includes setups powered by quenching circuit generators and equipped with two-coil or multi-coil inductors of all known types when operating in a vacuum or inert gas environment. The second group includes setups with multi-coil inductors, powered by generators without a quenching circuit for operation at atmospheric pressure or low discharge. The setup with a two-coil inductor, designed to obtain samples used in metal research, appeared in the middle of the last century [6, 39]. The metal vessel housed an inductor for levitation, a rotary table with copper molds, a table for initial samples and a manipulator. Later, the same authors [6, 39] developed a 27-position setup for levitation, consisting of a high-frequency generator, a reaction vessel and a vacuum unit. Another reaction vessel is shown in **Figure 6b**. A sample with a manipulator was placed in a double-coil inductor, where levitation and melting of the metal took place. A transparent shutter 6 protected the sight glass 8 from condensation of metal vapors on it. After a given exposure, the melt was poured into the mold 2, located coaxially with the inductor 4. A characteristic feature of such setups was the presence of a rotating table with molds and a manipulator.

**173**

**Figure 6.**

*Electromagnetic Levitation of Metal Melts DOI: http://dx.doi.org/10.5772/intechopen.92230*

coil, which provided finer regulation.

using the hammer-anvil device.

Another feature of such setups was devices for various physicochemical studies, for example, the interaction of elements in the melt-slag-gas system. The reaction vessel shown in **Figure 6** is made of copper, and the flanges of the vessel are closed with plexiglass covers. Water cools the inductor and the stabilizer ring, located directly above the conical multi-coil inductor. A copper pin crystallizer cooled by liquid nitrogen is intended for crystallization of the drop with a liquid slag (in the lower part of the drop). The mold could be moved in vertical and horizontal planes without violating the tightness of the reaction vessel. The setup was powered by a 10 kW generator with power regulation at the inductor by lowering the primary

Typical for setups of the second group with an external inductor relative to the reaction vessel is the use of multi-coil inductors, quartz glass for the reaction vessel and various means for instant crystallization of metal melts (**Figure 7a**,**b**). This is explained by the fact that such plants were used for high-temperature studies of the solubility of gases in melts, in particular, nitrogen in iron-carbon melts and the pressure of saturated iron vapor. The body of the reaction vessel is made of quartz glass with polished joints of individual elements. The location of the reaction vessel in the inductor is characteristic-its configuration repeats the internal shape of the inductor, which led to a slight increase in the diameters of the upper and lower coils of the inductor and, as a result, to a decrease in the efficiency of the inductor and an increase in the used power of the generator. At the bottom of the reaction vessel was a turntable with molds for melt crystallization. The turntable was rotated in such a way that there was a free socket on the same axis as the reaction vessel, which made it possible to measure the temperature of the melt using an optical pyrometer. Depending on the purpose of the experiment, some elements were changed in the setups of the second group and additional devices were introduced, for example, to crystallize the melt when oxygen was falling in the atmosphere or to crystallize at an increased velocity

*a—Multi-position setup for levitation and studies in systems "melt-gas"; b—Levitation setup for* 

*physicochemical studies in "melt-gas" and "melt-slag-gas" systems.*

### *Electromagnetic Levitation of Metal Melts DOI: http://dx.doi.org/10.5772/intechopen.92230*

*Magnetic Materials and Magnetic Levitation*

In axisymmetric EML, the Lorentz force vanishes on the axis of symmetry. At the lowest point on the axis of the levitated sample, only the surface tension of the melt prevents the flow of the melt, which affected the limitation of the mass of the melt-not more than 50–100 g. With electromagnetic two-frequency levitation, lifting forces also arise along the axis of the levitated sample. Digital models developed to optimize EML were implemented in [13–18]. At the same time, data were obtained on the electromagnetic flux and the dynamics of the free surface, for which calculations of the electromagnetic force, as well as modeling of the melt

*The dependence of the power of the generator and the temperature of tungsten of various masses on the voltage at the inductor; the arrow shows the temperature of the metal after additional heating by an electron beam:* 

Depending on the voltage at the inductor, its design and the conditions of the technology and experiment, all setups for EML are divided into two groups: with an internal inductor and an external inductor relative to the reaction vessel. The first group includes setups powered by quenching circuit generators and equipped with two-coil or multi-coil inductors of all known types when operating in a vacuum or inert gas environment. The second group includes setups with multi-coil inductors, powered by generators without a quenching circuit for operation at atmospheric pressure or low discharge. The setup with a two-coil inductor, designed to obtain samples used in metal research, appeared in the middle of the last century [6, 39]. The metal vessel housed an inductor for levitation, a rotary table with copper molds, a table for initial samples and a manipulator. Later, the same authors [6, 39] developed a 27-position setup for levitation, consisting of a high-frequency generator, a reaction vessel and a vacuum unit. Another reaction vessel is shown in **Figure 6b**. A sample with a manipulator was placed in a double-coil inductor, where levitation and melting of the metal took place. A transparent shutter 6 protected the sight glass 8 from condensation of metal vapors on it. After a given exposure, the melt was poured into the mold 2, located coaxially with the inductor 4. A characteristic feature of such setups was the presence of a rotating table with molds and a manipulator.

volume and restoration of the shape of the free surface, were made.

**2.4 Setups for EML of melts**

*1—*P, *kW; 2–28.5 g; 3–20 g; 4–10 g.*

**Figure 5.**

**172**

Another feature of such setups was devices for various physicochemical studies, for example, the interaction of elements in the melt-slag-gas system. The reaction vessel shown in **Figure 6** is made of copper, and the flanges of the vessel are closed with plexiglass covers. Water cools the inductor and the stabilizer ring, located directly above the conical multi-coil inductor. A copper pin crystallizer cooled by liquid nitrogen is intended for crystallization of the drop with a liquid slag (in the lower part of the drop). The mold could be moved in vertical and horizontal planes without violating the tightness of the reaction vessel. The setup was powered by a 10 kW generator with power regulation at the inductor by lowering the primary coil, which provided finer regulation.

Typical for setups of the second group with an external inductor relative to the reaction vessel is the use of multi-coil inductors, quartz glass for the reaction vessel and various means for instant crystallization of metal melts (**Figure 7a**,**b**). This is explained by the fact that such plants were used for high-temperature studies of the solubility of gases in melts, in particular, nitrogen in iron-carbon melts and the pressure of saturated iron vapor. The body of the reaction vessel is made of quartz glass with polished joints of individual elements. The location of the reaction vessel in the inductor is characteristic-its configuration repeats the internal shape of the inductor, which led to a slight increase in the diameters of the upper and lower coils of the inductor and, as a result, to a decrease in the efficiency of the inductor and an increase in the used power of the generator. At the bottom of the reaction vessel was a turntable with molds for melt crystallization. The turntable was rotated in such a way that there was a free socket on the same axis as the reaction vessel, which made it possible to measure the temperature of the melt using an optical pyrometer. Depending on the purpose of the experiment, some elements were changed in the setups of the second group and additional devices were introduced, for example, to crystallize the melt when oxygen was falling in the atmosphere or to crystallize at an increased velocity using the hammer-anvil device.

#### **Figure 6.**

*a—Multi-position setup for levitation and studies in systems "melt-gas"; b—Levitation setup for physicochemical studies in "melt-gas" and "melt-slag-gas" systems.*

**Figure 7.**

*Schemes of levitation quartz setups for studying the solubility of gases in liquid metals with fixation of dissolved gas using: a—Crystallization in molds; b—crystallization with a hammer and anvil.*

#### **2.5 Inductor designs**

The inductor and the heated metal sample form a single electromagnetic system, similar to a transformer in short circuit mode. However, the functions of its parts are clearly separated in the transformer: electric current passes through the windings, magnetic flux through the magnetic circuit. In contrast, the surface layer of the heated sample is simultaneously a secondary electrical winding and part of the magnetic circuit. Therefore, in the general case, when calculating the parameters of the inductor, it is necessary to take into account not only the magnetic flux passing in the gap, but also the flux in the metal. In addition, the consideration is also complicated by the fact that the values of ρ and μ at different points of the cross section of the heated metal are different and change over time. The heating process (cold, intermediate and hot modes) during electromagnetic levitation and the assumptions made to simplify the relationship between *ρ* and *μ* for subsequent calculations (*ρ* × *μ* = Const.) are studied in detail and are available in the reference literature. The values of μ are determined as a function of the magnetic field strength at the interface, using the magnetization curve. Due to the fact that the magnetization of the magnetic field depends on the specific power in the heated sample, the magnetic permeability is its function. Examples of the general calculation of the inductor are quite possible, and the necessary relations can be obtained from solving the electromagnetic field equation as applied to the propagation of electromagnetic energy inside a flat conductor of infinite thickness. Examples of calculating a single-coil quenching cylindrical inductor, with which the diameter of the inductor and its width, voltage and current, the efficiency of the inductor and the power supplied to it could be determined. However, it is impossible to use this calculation to determine the parameters of inductors for EML, since it does not take into account the main difference between EML and known heating methods-the existence of a force supporting a metal sample in solid and liquid states.

In this regard, the most important and necessary feature of EML is the use of special inductors, the electromagnetic field of which holds and heats the metal

**175**

**Figure 8.**

*the field frequency is 200 kH.*

*Electromagnetic Levitation of Metal Melts DOI: http://dx.doi.org/10.5772/intechopen.92230*

the first inductor.

sample. As noted above, the great merit of Alex Vogel [6] and his lab consists in the development of two-coil inductors, consisting of two parallel coils connected in parallel. The inductor design is shown in **Figure 8**. The vertical bends of the profiled copper tube are made for stable melt levitation. One of the important operating parameters of two-coil inductors is the relationship between the power referred to the mass of the metal and the square of the amplitude of the magnetic field.

In addition, a feature of this inductor is the presence of two critical voltages: the first and second, indicating a limitation of stability in the lower and upper positions. It also has some disadvantages: manufacturing difficulties (profiled copper tube); the maximum achievable temperature of the melt is always lower than in the inductors of two other designs; the need to place an inductor inside the reaction vessel. However, this inductor has several advantages: its dimensions are relatively small; the field is symmetrical; potential difference is minimal; the bottom of the inductor is at the same potential; and the mass of the sample is greatest. Two-coil inductors of two other types differ significantly in their characteristics from the inductor described above. Their designs are presented in **Figures 9** and **10**. In both cases, the *P*/*G* values monotonically increase with increasing power supplied to the inductor. A higher temperature of the metal melt is achieved as a result of a larger compression of the melt by the field. However, this leads to an increase in hydrostatic pressure in the melt and levitation of a smaller volume of metal compared to

The inductor of the second type has the following characteristic features: (1) the maximum potential difference between the inputs is lower than in the third inductor; (2) the bottom of the inductor is not equipotential, although the low voltage at the lower coil and the large contact resistance between the inductor and the sample exclude melt welding; (3) higher losses in current leads than in the third inductor; and (4) the limiting temperature of melt during levitation is always less than in the third inductor. For the inductor of the third type, the characteristic of the inductor of the second type is valid with the difference that: (1) the potential difference between the inputs of the inductor is maximum; (2) losses in current leads are minimal; (3) the highest sample temperature; (4) the smallest sample mass [7]. Multi-coil inductors having a reverse coil or a stabilizing ring are most widely used in the practice of electromagnetic levitation. **Figure 11** shows the multi-coil inductor with a stabilizer ring, which was used for several physical studies with Nb, Mo, Fe, Co and Ni [7]. The main advantages of these inductors are as follows: (1) the possibility of using generators of low (8–15 kW) and medium (30–60 kW) power; (2) obtaining an electromagnetic field of almost any configuration; (3) a small

*Type 1 (a) inductor and the dependence of the power transmitted to the sample on the voltage across the inductor (b);* h *is the distance from the center of the sample to the upper plane of the lower part of the coil, and* 

#### *Electromagnetic Levitation of Metal Melts DOI: http://dx.doi.org/10.5772/intechopen.92230*

*Magnetic Materials and Magnetic Levitation*

**2.5 Inductor designs**

**Figure 7.**

The inductor and the heated metal sample form a single electromagnetic system, similar to a transformer in short circuit mode. However, the functions of its parts are clearly separated in the transformer: electric current passes through the windings, magnetic flux through the magnetic circuit. In contrast, the surface layer of the heated sample is simultaneously a secondary electrical winding and part of the magnetic circuit. Therefore, in the general case, when calculating the parameters of the inductor, it is necessary to take into account not only the magnetic flux passing in the gap, but also the flux in the metal. In addition, the consideration is also complicated by the fact that the values of ρ and μ at different points of the cross section of the heated metal are different and change over time. The heating process (cold, intermediate and hot modes) during electromagnetic levitation and the assumptions made to simplify the relationship between *ρ* and *μ* for subsequent calculations (*ρ* × *μ* = Const.) are studied in detail and are available in the reference literature. The values of μ are determined as a function of the magnetic field strength at the interface, using the magnetization curve. Due to the fact that the magnetization of the magnetic field depends on the specific power in the heated sample, the magnetic permeability is its function. Examples of the general calculation of the inductor are quite possible, and the necessary relations can be obtained from solving the electromagnetic field equation as applied to the propagation of electromagnetic energy inside a flat conductor of infinite thickness. Examples of calculating a single-coil quenching cylindrical inductor, with which the diameter of the inductor and its width, voltage and current, the efficiency of the inductor and the power supplied to it could be determined. However, it is impossible to use this calculation to determine the parameters of inductors for EML, since it does not take into account the main difference between EML and known heating methods-the existence of a force sup-

*Schemes of levitation quartz setups for studying the solubility of gases in liquid metals with fixation of dissolved* 

*gas using: a—Crystallization in molds; b—crystallization with a hammer and anvil.*

In this regard, the most important and necessary feature of EML is the use of special inductors, the electromagnetic field of which holds and heats the metal

**174**

porting a metal sample in solid and liquid states.

sample. As noted above, the great merit of Alex Vogel [6] and his lab consists in the development of two-coil inductors, consisting of two parallel coils connected in parallel. The inductor design is shown in **Figure 8**. The vertical bends of the profiled copper tube are made for stable melt levitation. One of the important operating parameters of two-coil inductors is the relationship between the power referred to the mass of the metal and the square of the amplitude of the magnetic field.

In addition, a feature of this inductor is the presence of two critical voltages: the first and second, indicating a limitation of stability in the lower and upper positions. It also has some disadvantages: manufacturing difficulties (profiled copper tube); the maximum achievable temperature of the melt is always lower than in the inductors of two other designs; the need to place an inductor inside the reaction vessel. However, this inductor has several advantages: its dimensions are relatively small; the field is symmetrical; potential difference is minimal; the bottom of the inductor is at the same potential; and the mass of the sample is greatest. Two-coil inductors of two other types differ significantly in their characteristics from the inductor described above. Their designs are presented in **Figures 9** and **10**. In both cases, the *P*/*G* values monotonically increase with increasing power supplied to the inductor. A higher temperature of the metal melt is achieved as a result of a larger compression of the melt by the field. However, this leads to an increase in hydrostatic pressure in the melt and levitation of a smaller volume of metal compared to the first inductor.

The inductor of the second type has the following characteristic features: (1) the maximum potential difference between the inputs is lower than in the third inductor; (2) the bottom of the inductor is not equipotential, although the low voltage at the lower coil and the large contact resistance between the inductor and the sample exclude melt welding; (3) higher losses in current leads than in the third inductor; and (4) the limiting temperature of melt during levitation is always less than in the third inductor. For the inductor of the third type, the characteristic of the inductor of the second type is valid with the difference that: (1) the potential difference between the inputs of the inductor is maximum; (2) losses in current leads are minimal; (3) the highest sample temperature; (4) the smallest sample mass [7].

Multi-coil inductors having a reverse coil or a stabilizing ring are most widely used in the practice of electromagnetic levitation. **Figure 11** shows the multi-coil inductor with a stabilizer ring, which was used for several physical studies with Nb, Mo, Fe, Co and Ni [7]. The main advantages of these inductors are as follows: (1) the possibility of using generators of low (8–15 kW) and medium (30–60 kW) power; (2) obtaining an electromagnetic field of almost any configuration; (3) a small

#### **Figure 8.**

*Type 1 (a) inductor and the dependence of the power transmitted to the sample on the voltage across the inductor (b);* h *is the distance from the center of the sample to the upper plane of the lower part of the coil, and the field frequency is 200 kH.*

#### **Figure 9.**

*Type 2 (a) inductor and the dependence of the power transmitted to the sample on the voltage across the inductor (b); the distance from the center of the sample to the plane of the lower coil of the inductor is constant, and the frequency is 200 kHz.*

#### **Figure 10.**

*Type 3 (a) inductor and the dependence of the power transmitted to the sample on the voltage across the inductor (b); the distance from the center of the sample to the plane of the lower coil of the inductor is constant, and the frequency is 200 kHz.*

#### **Figure 11.**

*Multi-coil inductor with stabilizing water-cooled ring. 1—Inductor, 2—stabilizing ring, 3—coaxial water cooling.*

potential difference at the inductor when using generators with a quenching circuit; (4) the accuracy with which inductors are made is not limited; (5) relative ease of manufacture, no shaped tubes, special welding; and (6) ease of operation. The

**177**

*Electromagnetic Levitation of Metal Melts DOI: http://dx.doi.org/10.5772/intechopen.92230*

affects the lifting force during levitation.

and the refractory material of the crucible.

**3.1 Physical properties and chemical reactions studied by EML**

The study of heterogeneous systems with the help of EML encounters a number

of difficulties with which it was not necessary to deal with the study of liquid

**3. EML in physical research**

disadvantages are also simple: (1) low mass of the sample; (2) limited temperature

Previously, the behavior of the melt during levitation in a multi-coil inductor (the number of coils of the conical part, the angle of inclination and the number of reverse coils) and the parameters of the levitated sample (levitation and melt temperature) were examined in detail. A rigorous calculation of a multi-coil inductor for levitation of a melt is still impossible. In this regard, the selection and manufacture of such inductors are carried out empirically, taking into account general ideas about their work. The literature describes more than two dozen designs of multi-coil inductors used for various physical studies. It is almost impossible to classify them according to any criteria, since the tasks solved by their creators were always different. The technique for selecting multi-coil inductors is as follows [7]: the selection criteria are stable levitation (determining the location of the sample in the potential well of the electromagnetic field) and the maximum possible regulation of the temperature of the metal (e.g., solid copper and liquid iron). A generator with a power of 30 kW and a frequency of 230 kHz was used. Inductors were prepared from a copper tube with an outer diameter of 4 and 6 mm. The initial shape, the number of coils of the conical part and the cone angle (~60°) were selected in accordance with the data of [7]. The internal diameters of the lower coil of the conical inductor and the upper return coil (*d*1 = 15.5 mm; *d*2 = 22 mm) were the same for all multi-coil inductors and were selected in connection with the required metal mass (average weight 3.5 g) and dimensions of the reaction vessel. Stable levitation of the melt was determined visually: the time from the moment of melting to the outflow of the metal from the inductor was noted (the latter phenomenon is associated with the saturation of liquid copper with oxygen, which reduces the surface tension of the copper melt during levitation in air). It turned out that along with the size *d*1, the number of spiral coils

The emergence of new metallurgical processes, such as electroslag melting, electron beam melting, arc melting, induction vacuum melting and plasma melting, revealed the limitations of the available thermodynamic and kinetic data necessary for the correct refining of liquid metal. A characteristic feature of these methods are higher temperatures in comparison with the temperatures at which traditional methods of melting steel and alloys are carried out. The melting temperature of high alloyed steels can reach 1700–1750°C, and temperatures up to 2000–2500°C develop in the reaction zone when the steel is purged with oxygen or air. When melting refractory metals in the arc and electron beam setups, local overheating of the metal is possible at 1000°C above the melting temperature. There are almost no experimental data on the behavior of liquid metals at such high temperatures, which is explained by the limited capabilities of experimental methods. Electromagnetic levitation significantly extends the temperature range of studies related to the solubility of gases in liquid metals, the processes of interaction of metal and slag melts with the participation of the gas phase, etc. It is known that such studies are impossible due to chemical reactions developing between the melt

control; and (3) the possibility of burning the inductor with the melt.

#### *Electromagnetic Levitation of Metal Melts DOI: http://dx.doi.org/10.5772/intechopen.92230*

*Magnetic Materials and Magnetic Levitation*

**176**

**Figure 11.**

*cooling.*

**Figure 10.**

**Figure 9.**

*and the frequency is 200 kHz.*

*and the frequency is 200 kHz.*

*Type 3 (a) inductor and the dependence of the power transmitted to the sample on the voltage across the inductor (b); the distance from the center of the sample to the plane of the lower coil of the inductor is constant,* 

*Type 2 (a) inductor and the dependence of the power transmitted to the sample on the voltage across the inductor (b); the distance from the center of the sample to the plane of the lower coil of the inductor is constant,* 

*Multi-coil inductor with stabilizing water-cooled ring. 1—Inductor, 2—stabilizing ring, 3—coaxial water* 

potential difference at the inductor when using generators with a quenching circuit; (4) the accuracy with which inductors are made is not limited; (5) relative ease of manufacture, no shaped tubes, special welding; and (6) ease of operation. The

disadvantages are also simple: (1) low mass of the sample; (2) limited temperature control; and (3) the possibility of burning the inductor with the melt.

Previously, the behavior of the melt during levitation in a multi-coil inductor (the number of coils of the conical part, the angle of inclination and the number of reverse coils) and the parameters of the levitated sample (levitation and melt temperature) were examined in detail. A rigorous calculation of a multi-coil inductor for levitation of a melt is still impossible. In this regard, the selection and manufacture of such inductors are carried out empirically, taking into account general ideas about their work. The literature describes more than two dozen designs of multi-coil inductors used for various physical studies. It is almost impossible to classify them according to any criteria, since the tasks solved by their creators were always different. The technique for selecting multi-coil inductors is as follows [7]: the selection criteria are stable levitation (determining the location of the sample in the potential well of the electromagnetic field) and the maximum possible regulation of the temperature of the metal (e.g., solid copper and liquid iron). A generator with a power of 30 kW and a frequency of 230 kHz was used. Inductors were prepared from a copper tube with an outer diameter of 4 and 6 mm. The initial shape, the number of coils of the conical part and the cone angle (~60°) were selected in accordance with the data of [7]. The internal diameters of the lower coil of the conical inductor and the upper return coil (*d*1 = 15.5 mm; *d*2 = 22 mm) were the same for all multi-coil inductors and were selected in connection with the required metal mass (average weight 3.5 g) and dimensions of the reaction vessel. Stable levitation of the melt was determined visually: the time from the moment of melting to the outflow of the metal from the inductor was noted (the latter phenomenon is associated with the saturation of liquid copper with oxygen, which reduces the surface tension of the copper melt during levitation in air). It turned out that along with the size *d*1, the number of spiral coils affects the lifting force during levitation.
