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Problems in electric melting of glass
400
Journal of Non-CrystallineSolids 123 (1990) 400-414 North-Holland
P R O B L E M S IN ELECTRIC M E L T I N G O F G L A S S Jaroslav S T A N E K Institute of Chemical Technology, Department of Sificates, Prague 6, Czechoslovakia
The resistivity-temperaturecharacteristics of different glasses were measured. From the relation, a criterion of stability of an electric furnace may be calculated. The release of energy around different electrodes as well as the power density distributions within the glass bath for different electrode-pairconfigurationsare shown. The optimal connectionsof electrodes from the point of view of minimum energy consumption is described. Theoretical as well as practical problems concerningthe corrosion of electrodes are described. Different ways of protecting electrodes against corrosion by glass melts are described. Furnaces for melting different types of glasses and new processesusing electricity for melting are mentioned.
1. Introduction Interest in the electric melting of glass has continued in spite of the fact that the price of electricity is higher than the price of fossil fuels. There are other reasons which make electricity attractive for the melting of glass. An electric melting furnace can achieve a very high efficiency, up to 80%, the specific melting energy being 0.85 to 1.1 k W h / k g glass. This efficiency cannot be achieved in a fuel-fired furnace. A cold top for an all-electric melting furnace has been introduced not only for economic or technical reasons. The conversion of borosilicate, lead, insulation fibre, tableware and other glass furnaces to cold top electric melting is also due to environmental considerations. It became clear very soon that not only had the environmental problems been reduced, but other benefits were also obtained to the considerable advantage of users. The stability of the cold top of an all-electric furnace, glass quality and conditions remain constant and consistent leading to an improved efficiency of electric melting.
2. Electrical transport properties of glass 2.1. Electrical conductivity
The most important properties for electric melthag are electrical conductivity (or resistivity) which is strongly temperature dependent. As the electri-
cal conductivity is of electrolytic character, it also depends on the chemical composition of the glass. The electrical conductivity is a function of the number of ions which take part in the current transport, of the magnitude of their charges and of their mobility. The mobility of the ions is dependent on the frictional resistance of cations which increases with their radii and furthermore on the attraction between the positive ions and the negatively charged SiO4 tetrahedra, in the case of silicate glasses. According to a general rule, alkali ions contribute most to the electrical conductivity. Borosilicate glasses usually conduct less well than silicate glasses; the oxides CaO, MgO, BaO and PbO likewise reduce conductivity because these cations with a larger charge are less mobile than alkali ions. The dependence of conductivity on the chemical composition of glass has been reported by several authors who tried to express it in terms of different, usually empirical, equations. Mazurin [1] has dedicated one volume of his extensive work dealing with the structure and properties of glasses to electrical properties. Sa~ek [2] has used the method of planned experiments to determine the direct effect of the individual oxides on the conductivity of glass liquids and glasses. He has proposed regression equations for computing the constants a and b from Rasch and Hinrichsen's relation log 2~ = a - ( b / T ) .
0022-3093/90/$03.50 © 1990 - ElsevierSciencePublishers B.V. (North-Holland)
(1)
J. Stan~k / Problems in electric melting of glass
401
20
where -/ is electrical conductivity, T is temperature and a and b are constants. From these equations the temperature dependence of the electric conductivity of glasses on their chemical composition for both high- and low-temperature regions can be determined with an accuracy better than _ 5% log ~/. It has been found on the basis of accurate analysis of the individual oxides that not only alkali but also certain other oxides have to be taken into account when calculating the conductivity of the glass. If only alkali oxides are assumed to be the sole variables in the equations, then the calculated values of the conductivity are lower than the measured ones. Other authors such as e.g. Yevstrop'ev and Toropov [3] and Konstanyan [4] have suggested similar equations:
Tlo i
1000 1100 1200 1300 1~00 1500
T[°C]
(2) (3) (4)
Fig. 1. Temperature dependence of the resistivity of various glasses: 1, television tube glass; 2, sheet glass; 3, white flint container glass; 4, water glass; OeJ, the resistivity of the glass melt; tg a = d o e l / d T is the slope of the characteristic p¢l-T.
where a, a', r , fl', a, b, n and TO are constants. Stevels [5] has derived and recommended the following formula
The resistivity-temperature characteristics are given in fig. 1. All the data have negative temperature coefficients. These negative coefficients indicate that, when glass is heated and melted, thermal instability can occur.
log "r = a -
( fl/T2),
log ~ = a' - ( f l ' / ( T log V = a -
(b/T"),
log "t = A - ( E / R T ) ,
To)),
(5)
in which A depends on the composition and temperature of the glass, R is the gas constant, and E is the activation energy for electrical conductivity. The value of E and the temperature dependence of electrical conductivity exhibit a discontinuity in the transformation range, but otherwise the relationship describes the temperature dependence of ~/ adequately over a wide temperature range. In the temperature range up to Tg, E has the values of 84-126 kJ mol-1; in the range of melting temperatures E decreases to 42-84 kJ mol- 1 By measuring the resistance of the liquid at different temperatures, we obtain the 'characteristic' of the glass liquid, i.e. the dependence of its resistivity on temperature. A suitable method for this purpose is the compensation method, which is based on the measurement of the voltage drop between two Pt electrodes immersed in the molten glass [6] for an alternating current (AC).
2.2. Thermal stability The power introduced into the furnace [7] may be expressed by
P~T) = UE/R~T),
(6)
where input P~T) as well as resistance R~T ) are both temperature dependent, and U = voltage. When the temperature T varies, then the variation of P~T) will be obtained by the differentiation of eq. (6) dP
U 2 dR R 2 d-T dT.
(7)
The resistance R~T ) between two parallel electrodes is proportional to the resistivity Pe~ of glass and to the layout and dimensions of electrodes Pel, 2b R¢T) = - ~ t n - d - ,
(8)
402
J. Stan~k / Problems in electric melting of glass
where l is length, b is distance and d is the diameter of the electrodes. By inserting this relation into eq. (7) we obtain U 2 1 dpel
dP =
R Pel d-TdT
(9)
and by introducing eq. (6) into eq. (9) we obtain 1 dP P dT
1 ape, Pel d T "
(10)
This equation shows that the change in power introduced into the furnace is inversely proportional to the change of resistivity of the glass. The expression 1 dpel Pei dT is the criterion of stability, in the range of the melting temperature of the furnace with regard to the temperature dependence of glass resistivity. This criterion contains the expression d p e l / d T = tan a,
(11)
which is the slope of the resistivity-temperature characteristic of the respective glass (see fig. 1). The dimension of the criterion of stability is (%o, ° C-1). Glasses having this criterion below 3 (%o, °C-1) may be electrically melted without any special measure being taken against the instability effect. It is preferable to use some type of automatic control for glasses having the criterion of stability higher than 3 (%o, ° C - I ) . The problem of stability at the melting temperature has also been studied by Trier [8], Hilbig [9] and Schumacher [10]. Trier has pointed out that for the thermal stability of an electric furnace not only the electrical but also the thermal properties of glass melt are of major importance. For the thermal stability, the absorption of energy and its transfer are important. The thermal instability of a particular volume element may be expressed by the instability factor D, dP/dT dq/dT
= D,
(12)
For D > 1, the particular volume element is thermally unstable; for D < 1 it is stable. The current density is given by i = 1/.4 (A cm-2),
(13)
where I is the electric current flowing through the surface area A of the volume element. The electric power p entering the unit volume of an element will be (14)
p = Pe,i 2
and its change with temperature will be dp dT
12 doel A2 d T "
(15)
The heat q given off by the volume element is given by TITS q= --((Xc+Xr)-F
A
+
a),
where: T is the temperature of the element, Ts is the ambient temperature, l is the linear extent of the element, Xc is the thermal conductivity of the m e l t , )k r is the infrared transmissivity, a is the heat transfer coefficient, V is the volume being considered, and A its surface. The change of the density of the volumetric heat flow may be expressed by dq = (X~ + )kr)(A//V) + dT l
(17)
Ot
Genzel's [11] formula may be used for the infrared transmissivity, (18)
)~r = ~ - ° n 2 T 3 F ,
where: F is the mean free path length of radiation quanta, n is the refractive index, and o is the radiation constant. F depends on the type of glass and temperature. It is high for clear glass, e.g. 5.71 cm for window glass, and low for green glass, 0.424 cm at 1300 o C. The instability factor D will then be as follows:
i2(dpe~/dT)l O = (X c + ~ _ o n Z T 3 F ) ( A / V )
where d P / d T is the change in power input with change in temperature G and d q / d T represents the change in heat transfer with temperature.
(16)
+ a"
(19)
In the molten glass in a furnace A~ is significantly smaller in comparison with Xr, and the part of
J. Stan~k / Problems in electric melting of glass
heat transfer by convection may be neglected. The instability factor, for a cube with edge length l ( A / V = 6 / l ) and with dominating radiation transfer, may be expressed by the following equation: i 2 ( d p e l / d T )12 Drad. =
32onZT3F
(20)
The thermal stability, 1/Drad., increases with increasing temperature and increasing free path of radiation (clear glass). It decreases with increasing current density i 2, increasing dPe~/dT, i.e. tan a, the slope of the resistivity-temperature characteristic and with increasing dimensions, l 2, of the element considered. When Xc prevails, as in the case of dark glasses and particularly for the domain of the surface layers of the refractory material, then
i2(dPel/dT) i 2 Otherm" =
6Xc
(21)
Hammerschmidt and Hausner [12] have compared the electrical conductivity of new and old refractory materials. Due to the diffusion of alkalis into the surface layers of refractory blocks, the conductivity of old blocks is higher than that of new ones. A local instability may occur if the conductivity of the surface layer of the refractories approaches the conductivity of the glass melt. Schumacher [10] has compared the heat transfer by radiation, convection and conduction in different glass liquids as well as in refractory materials and has found that the instability of the system may be brought about by (1) a great density of electric current flowing in the glass liquid parallel to the surface of the refractory blocks and penetrating partially into the sub-surface layers of the material; (2) high temperature gradients in the glass liquid; (3) high activation energy for conduction. Endress [13] has studied the dependence of the thermal stability of an electric melting furnace on changes of the electrical conductivity - or on the concentration of alkalis in the inside wall of the hole for an electrode holder in the refractory block. The heat transfer was simulated by means of a
403
thermo-electrical circuit which was used as a model. During furnace operation, the concentration of alkalis, consequently the conductivity, and also the rate of corrosion of the refractory material increase. The length of time in which these changes are realized and reach an undesirable level depends on the melting temperature of the glass and on the composition of the batch.
3. Release and distribution of the energy
The stability of electric melting may also be improved by the proper distribution of energy in the basin in the furnace. The amount of energy released at the individual points of the basin is directly proportional to the square of the voltage gradient, and inversely proportional to the resistivity Pei of the glass melt at the point concerned, W = (grad V) 2/0e,"
(22)
The release of energy around a rod electrode was derived by Gruenberg [14]. The power dissipated in a glass melt tends to be relatively close to the electrode. The electrode is surrounded by a cylinder of glass liquid having radius X - as shown in fig. 2. The distance in which the power Po will be
mill
~
"','!'tF"-; Fig. 2. Electrodes surrounded by a cylinder of glass melt. X is the radius of the cylinder in which the whole power virtually dissipates. Distances of second electrode b >> X.
404
J. Stan#k / Problems in electric melting of glass
liberated in the glass volume can be determined from In X -
PG2~rl Pel I 2
(23) '
where l is the length of the electrode, Pel is the resistivity of the glass melt and I is the total current of the electrode. The greater the value of X the more uniform is the power distribution between the electrodes. Hotter glass (i.e. lower P¢l), longer electrodes, and lower current between them yield better uniformity of the power distribution in the glass melt. The study published by Ganzala and Maddux [15] also deals with the distribution of energy between rod electrodes, especially from the point of view of their surface temperature. The power density measurements were carried out on a physical model. Three zone lengths, i.e. the distances between electrodes, were investigated (7, 13 and 25 cm). Figure 3 shows the distribution of a model power density for the shortest spacing. It was calculated for this zone that 89% of the total heat released was within three electrode diameters, i.e. only 11% was in the bulk. For the mid-length, i.e. 13 cm, zone and for the longest, i.e. 25 cm, zone, only 57% and 47%, respectively, of the total heat was released within the distance of three electrode diameters.
E
0115
I\ _ _ J /
~" 0,10
co
~.
0,05
P~ 0,00
t
0
I
2 cm ] r o m
t
4 electrode
5
I 8
centerLine
Fig. 3. Power density distribution as a function of the position between electrodes. Scale of the model 1 : 10.
100
50
0
"x.
qo
20 zone
30
40
Length ( c m )
Fig. 4. Power dissipated near electrodes as a function of zone length.
The ultimate objective was to reduce the service temperature of electrodes. Therefore, it is of interest to know the amount of heat liberated near the electrodes. The percentage of total power dissipated near the electrodes. The percentage of total power dissipated within three electrode diameters plotted against zone length is shown in fig. 4. The curve in fig. 4 may be described by a hyperbolic function Y= a + (b/X),
(24)
where Y is the percentage of power dissipated within three electrode diameters of both electrodes, X is the zone length, while a and b are the computed regression coefficients. The heat released near the electrodes in inversely proportional to the zone length which means that long zones, which would use more voltage and less current, will cause the electrodes to operate at lower temperatures by shifting more heat towards the centre of the zone. For electrode corrosion, the temperature of the electrode is decisive. The lower the temperature of the electrode surface, the smaller its corrosion. All the above-mentioned works declare that the energy released in the basis is far more uniformly distributed if the rod electrodes are longer and their spacing larger. The temperature of the electrode surface will be, in this case, lower too.
J. Stan~k / Problems in electric melting of glass
405
R
4. Resistances between variously grouped electrodes
4.1. Calculation A knowledge of the effective resistance between electrodes is important for the design of electric furnaces and their transformers. An exact determination in advance is difficult to obtain because of the many different electrode configurations and the influence of temperature on the conductivity of the glass. Many authors have tried to achieve accurate and reliable results [6,16-21]. All these calculations give results which can only be applied under certain conditions. To determine the resistances between electrodes, first of all the potential differences between them and the related currents must be determined. Assuming that the length of the electrodes is much greater than their diameter, then the equipotential surface can be considered as being cylindrical and the so-called coefficient of inherent potential is a , = (pe~/2vl) l n ( 2 / d )
(25)
and the coefficient of mutual potential, at uniform temperature, is
a,k = (&,/2~rl) ln(1/b,k ),
(26)
where &~ is the resistivity of the glass melt, l is the length, d the diameter of the electrodes, and b~k is the distance between the electrodes i and k. The effective resistance between two electrodes is a function of their inherent and mutual potentials and can be expressed as follows (see fig. 5):
R,k = ( &L/'~l ) ln( Zb,k/ d ).
(27)
The method of potential coefficients can also be used to determine the resistances between elec-
T
i-
Fig. 6. Arrangement of three electrodes for a three-phase supply with a network diagram. R, S, T, phases of a transformer; ~ = potential; U = voltage between phases; I = current; b = distance between electrodes.
trodes with a multiphase power supply. The simplest electrode configuration for a symmetrical three-phase system is given in fig. 6, which also shows the equivalent diagram. The resistance between the electrodes arranged in an equilateral triangle and connected to a three-phase power supply is as follows:
R = 3 (Pel/,Tr l ) ln(2b/d ).
b=
(28)
In this case the electrical resistance is 1.5 times that of two electrodes using a single phase alternating current if b = bik. In both the above calculated examples we ignored the tank boundaries which no doubt have a great influence on the result of the calculation. The influence of the upper surface on the field in a body such a glass tank can be taken into consideration by assuming equivalent, fictitious electrodes, of the same shape and dimensions as the real ones, positioned in the upper half space as mirror images reflected by the surface. The space around the fictitious electrodes is assumed to have the same physical properties as the lower half. The principle of superposition, or the method of potential coefficients, can then be applied to determine the resistances. The resistance of the arrangement shown in fig. 7 is given by R=(Pel/'ITl)
Fig. 5. Arrangement of two electrodes, d = diameter; distance between rod electrodes.
,
ln[(2b/d)~l
+ ( b 2 / n h , h 2 ) ].
(29)
Compared with the resistance of an infinitely extended bath of molten glass (see fig. 5 and eq.
406
J. Stan#k / Problems in electric melting of glass
/ J /
7
/// Fig. 7. Determination of the resistance between two electrodesby a single mirror image method: y = conductivityof the glass liquid (1/pel); h = distance between the electrode and glass level; b = distance between electrodes.
(27)), this gives an increase in resistance of In ¢1 + b 2 / 4 h l h 2 . Theoretically, the number of mirroring surfaces could be infinite; however, in actual practice, only one or two mirroring surfaces need be taken into consideration (usually the glass level and one wall). On the other hand, it is clear that even for relatively simple geometrical configurations of electrodes, the use of fairly intricate formulae is unavoidable in calculating the resistance, and with more electrodes in diverse positions the results may be unreliable. It is better then to model the configuration. 4.2. Modelling
By means of a model, not only the resistances between the electrodes but also the distribution of the electric field, the uniformity of the electrode loading, and the influence of the electrode length on the resistance and on the load can be observed and measured, and the results of the measurement can be applied to the actual furnace [6]. The electric current is fed into the model by means of electrodes, the positions of which are adjusted to attain the following: (1) optimum technological conditions i.e. favourable influence on the glass flow; (2) uniform loading of the electrodes; (3) uniform loading of the power supplies; (4) appropriate voltages between the electrodes.
The magnitude of the electric current in the glass melt is given by J = yE,
(30)
which is Ohm's law in vectorial form, where E is the vector of the intensity of the electric field, 3' is the conductivity of the glass liquid and J is the vector of the current density. An external magnetic field of induction, B, exerts a force on a conductor of volume V, through which a current of density J flows. This force is combined with the other forces acting on the liquid, namely gravity, pressure and the viscous forces. The amount of magnetic energy is very small, since the current density J in the liquid is relatively low: it is < 0.1 A cm-2. The conductivity of the glass -/is usually about 0.02 to 0.5 S cm -1 and the term y E x B which represents the force exerted by the magnetic field upon the current tube is small and can be neglected. It is necessary to establish the character of the alternating electric field when the electrodes are supplied by a current of comparatively low frequency (50 or 60 Hz). The wavelength X of an oscillation of frequency f in a medium of conductivity -/ and relative permeability/L can be calculated from )k = (109//fy/x) 1/2 (cm).
(31)
As # = 1, and y usually 0.02 to 0.05 - as stated above - the resulting wavelength is in the range X = 66-330 m. This is substantially greater than
J. Stan~k / Problems in electric melting of glass
the dimensions of a melting furnace. In such a case, the electric field in the glass liquid can be regarded as a potential eddy-free field of r o t e = 0, the intensity of which is a function of position and can be described by E = - grad ¢p.
407
b
!r
(32)
The distribution of the potential q0 is given by the partial differential equation a
a[
acp~
which is Laplace's equation for a current field, where the electric conductivity 3' = f ( T ) . A condition for the similarity of the current field in the model and that in a full scale furnace is that they can be described by differential equations of the same form. As the conductivity of the glass melt is a function of the temperature, 7 = f ( T ) or P~L= f ( T ) , the conductivity of the model liquid must be a similar function of temperature. The dependence of the resistivity on temperature is expressed by the slope of the 'p~ - T ' curve, the so-called 'characteristic', which may be described either by eq. (11) or by: (pelatmaxT) =(Pe'atmaxT) , P~l at rm=n T M Pel at rm=n T E
(34)
where Pe~ is the resistivity of the glass liquid (E) or of the model liquid (M) and T is the temperature in the corresponding temperature ranges. If other boundary conditions are also met, then it is possible to determine the electric values of the full-scale furnace from the values measured in the model. The geometrical boundary conditions are met when the model is an accurate scale model of the full-size furnace. A further condition is the similarity of the temperature fields in the model and the full-sized equipment, i.e.
T = f ( x , y, z).
(35)
The required temperature field can be achieved in the model by whatever technical means are needed if the distribution and gradients of temperatures in the full-size furnace are known. The model must be ac-powered to ensure that the measured voltages are not altered by the dc voltage created through electrode polarization.
Fig. 8. Diagram for the calculation of the resistance between electrodes from values measured in a model, b = distance between electrodes; F = vertical cross-section; Oel= resistivity of the model liquid. If those conditions are met, then the lines of force and the electric fields in the model and in the full-size equipment have similar shapes. This fact can be utilized to determine different electrical parameters, such as the resistance between the electrodes of a full-scale furnace from the resistance measured in the model. The values of resistances obtained in this way are, to date, probably the most reliable ones. Figure 8 shows an example with electrodes in a general position. The resistance between electrodes in the full-size equipment is given by the following expression: Pc, E(TE) RE = RM Pd M(TM) S,
(36)
where M as a subscript is the symbol for values referring to the model and E as a subscript is the symbol for values referring to the full-size equipment. Therefore, p~l E(TE) is the resistivity of the molten glass as a function of the corresponding temperature TE; P~l M(TM) is the resistivity of the model liquid as a function of the corresponding temperature TM; s is bM/b E is the scale of the model (it is the ratio of the characteristic dimensions of the model and of the equipment); and R M is the resistance between the electrodes in the model.
4.2.1. Modelling on conducting paper [22,23] Modelling on conducting paper is much simpler than the modelling by a physical model. This is due to the fact that a model made of conducting paper cannot simulate all the processes taking
408
J. Stan~k / Problems in electric melting of glass
place in the full-size equipment, such as convection. On the other hand the evaluation of potential fields tends to be much easier by means of conducting paper than by a physical model [22]. Provided the model is connected to a central measuring device and the measured data are evaluated by a computer, the results are then obtained very quickly and comparatively easily. The model of the furnace is cut from a part of the conducting paper strip. The electric current is introduced into the model by electrodes drawn, on the scale of the model, on the conducting paper by silver lacquer. When modelling an electric ~ass melting furnace, the electrodes in the model are connected with an alternating current source in the same manner as in the furnace. From the difference of voltages in a determined location, it is possible to identify not only the direction of current lines but also the current density in that location. From voltage differences, i.e. from grad V in different places of the model, the release power may also be determined in accordance with the equation P = ~,(grad V) z.
(37)
It is possible to simulate the phenomena occurring in two directions in a plane cut, the transfer of electric current in the glass liquid of constant properties surrounded by a refractory material having zero electric conductivity. By combining the mathematical modelling with modelling on conducting paper, the distribution of power in an electric glass melting furnace has been evaluated with differing locations of electrodes. Figure 9 shows an example - the distribution of power around six vertical electrodes. By means of this type of modelling it is also possible to find the optimal connections with a multiphase ac source, which tend to be very important from the point of view of conservation of energy [23].
5. The corrosion of electrodes
124,251
The corrosion of electrodes is another problem with which one must deal. The majority of electrodes being used today are made of molybdenum [6]. However, molybdenum is a costly material making it therefore necessary to keep its consumption and consequently its corrosion by glass melt
P,
J J J f j Z J J J J / J J J f f J J J f ~ J J J J J / / J J J J f J J J J J j f j j f J J J J J J J J J J J J J J f j j j J J J J J J J f f f J J J J / Fig. 9. Distribution of power around six vertical electrodes.
J. Stan~k / Problems in electric melting of glass
as low as possible. Besides, the products of corrosion affect the colour of glass. The reasons for metal corrosion by glass liquids in general are the successive and coupled electrode reactions, the course of which depends on several internal and external corrosion factors. The internal corrosion factors depend only on the metal itself, i.e. on its chemical purity, structure, character of its surface, presence of primary protective layers, mechanical stress, and deformation. From the point of view of the chemical purity of molybdenum it is essential to keep the carbon content as low as possible. Electrodes with carbon contents above 50 ppm cause bubble formation. The carbon content of 50 ppm is also critical from the point of view of corrosion, which increases rapidly in the range 60-70 ppm carbon [26]. Outer factors influencing the corrosion of electrodes are the chemical character of the corrosive environment, the kind of anions and cations, the character of the dissolved gases, temperature, contact with other metals, and electric current. Electric melting of lead glasses has so far been problematic because of considerable corrosion of the molybdenum electrodes, which increased the consumption of molybdenum and also impaired the quality of the glass. However, all-electric melting of such glasses is particularly desirable because it eliminates problems with emissions of harmful lead oxide. The electrode corrosion rate is decisively affected by the presence of corrosion depolarizers, such as lead oxide and some refining and colouring agents, as molybdenum undergoes electrolytical oxidation at the expense of these substances. The passage of alternating current through the heating electrodes is another significant corrosion factor. It has been proved that, in addition to the power load, a significant role is also played by loading the electrode with the electric current. A close relation exists between the amount of corroded molybdenum and that of precipitated lead [271. According to the theory of the corrosion of metals by the effect of alternating current, worked out by D6vay et al. [28], the high rate of corrosion is due to increased mean anodic, i.e., mean corrosion current, as shown in fig. 10 by dashed lines.
409
Mo~Mo~6e- , t ~ ~. S ~a~a] . / 1:_8
r, .
//
l
Fig. 10. Dependence of the rate of electrode processes on the polarizing potential: icor = anodic (corrosion) current; idep = corresponding cathodic (depolarizing) current; i~o, = increased corrosion current on molybdenum electrodes loaded by alternating current; i~ep ~ corresponding cathodic current.
The mean value of cathodic current, which is a measure of the depolarization reaction, e.g. precipitation of lead, increases simultaneously. All published experimental results, as well as technological experience, demonstrate that corrosion increases with increased loading by alternating current, and decreases with increasing frequency. However, these results apply to frequencies > 50 Hz. A detailed study of the frequency dependence of the corrosion of molybdenum electrodes in glass melts at frequencies around 50 Hz disclosed deviations toward lower values. More detailed investigation of these anomalies showed that in the low-frequency region, mostly below 50 Hz, the corrosion rate can actually decrease with decreasing frequency, jointly with the amount of precipitated depolarizer. Figure 11 shows the dependence of the decrease of electrode radius in a lead glass liquid on frequency at various current densities. The corresponding amounts of precipitated lead are plotted in fig. 12. Similar to the frequency dependence, the decrease of electrode radius and the amount of precipitated depolarizer also exhibit deviations from the assumed dependence on current density, if the interfering effect of increasing power load at the higher current densities is eliminated. The results obtained can be generalized so that the decrease of electrode radius and the amount of precipitated
410
:I/I
J. Stan~k / Problems in electric melting of glass
..i. o , , o
I
0
I
.
2Ac
I
100 frequency 200
I
300
I
f Hz
~0o
Fig. 11. Corrosion of the electrode represented as the decrease of electrode radius Ar for various current densities i.
depolarizer as a function of frequency in melted glass have a m a x i m u m and a minimum (also compare with fig. 13). For a given glass, the position of these extremes depends on current density and
0
temperature, shifting towards higher frequencies with increasing current density. In spite of m a n y patents concerning the protection of m o l y b d e n u m against corrosion, it is evi-
700 frequency 200
300
f Hz
bOO
Fig. ]2. The amount of precipitated lead in g for various current densities.
J. StanEk/ Problemsinelectricmeltingofglass ZOgo[
411
i=O. ~m
/ II
1,0
0
,,,,1
0,5
t
I
1 frequency 2
m-Ilpe
•
I
3
f Hz
I 4s,
z,
I
50
Fig. 13. Frequency dependence of the amount of lead deposited on a Mo electrode at two different current densities.
dent that the most important factor for the protection of the electrodes is low surface current load. It is therefore necessary to keep the load as low as possible.
6. Electric boosting Electrical energy for melting glass m a y be used in two ways, either as boosting energy for a conventional furnace or as the only energy source. The overall thermal efficiency of a furnace equipped with electric boosting is higher than that without boosting since the transfer of thermal energy from the electric current into the glass melts is very high. A major purpose of boosting is to strengthen the thermal barrier. The electrodes which are to strengthen the barrier should therefore be located either at the position of the flame thermal barrier or behind it in order to enlarge the melting area surface covered by the batch. Figure 14 shows a typical example of electric boosting in
Fig. 14. Electric boosting in a sheet glass furnace; E - vertical electrodes.
a sheet glass furnace where the electrodes strengthen the thermal barrier. If the output of the furnace is to be increased substantially, then a part of the energy (approximately ½) must also be released in the melting end of the furnace. An example of a layout of electrodes in the furnace is shown in fig. 15. This type of boosting m a y raise the output of the furnace by
I
I
y,
I
5'1 16 Z'
3'
)~'
21 Ir
Fig. 15. Diagram of electric boosting in a continuous tank. X, Y, Z - secondary windings of the transformer; X', Y', Z' voltage triangle between electrodes; 1, 2, 3, 4, 5, 6 - tappings from secondary transformer windings; 1', 2', 3', 4', 5', 6' electrodes.
J. StanFk / Problems in electric melting of glass
412 t2 t - ~ x x \ x x'¢.' x x x \ \ \ x x x x x x ~
gJ"l/////
-
/ /
b
glass in the melter and the batch blanket covering it [33]. This rate is only adjustable within limits and therefore it follows that electric furnaces cannot be operated with pull rates that vary as widely as those of flame-fired furnaces. 7.1. Design
.
.
.
.
.
.
.
.
.
.
.
JIV!II+
Fig. 16. A continuous furnace with boosting and deepening part of refining area: (a) side view; (b) top view, E - deepening part with electrodes.
some 130%. Another arrangement of electrodes is shown in fig. 16. The thermal, technological and economic advantages of using electric boosting are substantial, and electric boosting is, therefore, being regarded as the most efficient means of accelerating the melting process [29]. Another large technical as well as economical contribution is the electric heating of feeder channels. It enables not only more accurate temperature control but also a substantial decrease in the energy consumption in the feeder channel [30].
One of the first furnaces with a cold top was reported by Gell [34,35] - see fig. 17. Its melting rate has been substantially increased by deepening the melting part of the furnace and by adding another row of rod electrodes above the plates ones [31,36]. Another two-chamber electric melting furnace [6,42] can be built in various versions and sizes, either for manual production alone, or for both manual production and feeding for automatic production - see fig. 18. The batch is charged on to the surface, which is thus effectively insulated. The furnace is equipped with molybdenum rod electrodes, which are placed in an inclined position in the side walls on the furnace. The furnace proved satisfactory for melting glass with a low as well as high content of lead oxide. A typical representative of the shaft furnace principle is the electric furnace built by Sorg [3740], which has a polygonal cross-section with O
7. All-electric melting During the past ten years much valuable experience has been gained concerning the all-electric melting of glass. Thus, it was shown that electric melting of certain glasses is better than melting in flame-fired furnaces. The borosilicate and opal glasses melted electrically turn out to be of much higher quality than when melted by flame [31,32]. Electric furnaces differ from flame-fired furnaces in their mode of operation. In a flame-fired furnace the limit of the rate at which glass can be melted is governed by the refining rate. The limiting factor in an electric furnace is the batch melting rate, i.e. the heat transfer between the molten
b
Fig. 17. Gell furnace with plate electrodes: (a) side view; (b) top view.
J. Stan~k / Problems in electric melting of glass
413
6
II \ 2 Fig. 18. Furnace with horizontal rod electrodes: Side view; I, melting and refining end; 2, throat; 3, working end; 4, bridge wall; 5, charging end; 6, exhaust; 7, gathering holes; 8, feeder channel; 9-II, electrodes, 12 heating elements; 13, outlet.
molybdenum electrodes located in two or three horizontal planes - see fig. 19. Further development in all-electric shaft furnaces is the molybdenum-lined decagonal Summit furnace [41] developed by Coming Glass Works (see fig. 20). For glasses that are compatible with molybdenum this furnace can produce high quality glass without refractory defects at a low cost.
z
Large all-electric furnaces have been for melting packing glass. These furnaces were of melting capabilities up to 100 tons/24 h [6], 165 tons/24 h [43] and 250 tons/24 h [35]. The feeding sources for these furnaces consist usually of one-phase or three-phase transformers. Furnaces for the melting of lead crystal glass were constructed and have been described by a number of authors [44-49]. Some of these furnaces are equipped with stannic (SnO2) electrodes, others with molybdenum electrodes described in some of the above mentioned patents. Likewise, a furnace for melting colour [50] and opal glasses [32,51] has been built. Another use of electrical energy is the process of the immobilization of radioactive waste. This
4
V/AI
Fig. 19. Polygonal electric shaft furnace. 1, horizontal electrodes positioned in two or three rows; 2, batch rake; 3, auxiliary electrode in throat; 4, forehearth.
1 ~"
"
I t-'//A
t,
5
Fig. 20. Coming shaft furnace. 1, molybdenum electrodes; 2, Mo lining; 3, Mo pipe; 4, valve; 5, forehearth.
414
J. Stan~k / Problems in electric melting of glass
field is described in papers written by several authors [52-55]. The use of electric power for glass melting has entered the stage of technical and economical necessity. Evidence for these necessities is shown by the fact that nearly all glassworks have at least some electric boostings and all-electric melting furnaces. Further proof of the increasing interest in electric melting is the impressive number of publications dealing with this topic. The number of research and development departments dealing with this problem has grown considerably, too. No doubt, research and development have to tackle some more technical issues in order to make electric melting of common glasses cheaper and more economical.
References [1] O.V. Mazurin, Spravo~nik Tom I-IV, Izd. (Nauka, Leningrad, 1973). [2] L. ~agek and H. Meissnerovh, Scient. Papers of the Inst. of Chem. Technology, Prague, Sect. L5 (1974) 111. [3] K.S. Yevstrop'ev and N.A. Toropov, Chemistry of Silicon and Physical Chemistry of Silicates (Gosizdat, Moscow, 1956). [4] K.A. Konstanyan, Izv. Akad. Nauk Arm. SSR - Chem. Sci. 10 (1957) 237. [5] J.M. Stevels, The Physical Properties of Glass (Elsevier, Amsterdam, 1948). [6] J. Stan6"k, Electric Melting of Glass (Elsevier, Amsterdam, 1977). [7] A. Andrusieczko, Szklo i Ceramika 16 (1965) 209. [8] W. Trier, Glastechn. Ber. 53 (1980) 348. [9] G. Hilbig, Glasteclm. Ber. 54 (1981) 44. [10] R. Schnmacher, Glastechn. Bet. 55 (1985) 243. [11] L. Genzel, Glastechn. Bet. 26 (1953) 69. [12] R. Hammerschmidt and H. Hausner, Glastechn. Ber. 55 (1982) 30. [13] H. Endress, Elektrowgtrme Int. 44 (1986) B256. [14] N.R. Gruenberg, IEEE Trans. Ind. Appl. IA-8 (1972) 76. [15] G.W. Ganzala and J.F. Maddux, IEEE IAS 78, p. 966. [16] A. Andrusieczko, Glastechn. Bet. 42 (1969) 235. [17] J. Gailhbaud, Glastechn. Ber. 44 (1971) 314; 354. [18] J. Gailhbaud, Glastechn. Ber. 45 (1972) 56; 133. [19] T.K. Trunova, Steklo i Keram. (5) (1974) 14-15. [20] K.M. Tatevosyan, Stekio i Keram. (4) (1976) 5-8. [21] V.S. Golovin and V.G. Zsheltov, Steklo i Keram. (8) (1977) 12. [22] J. Bla~ek and J. Stanek, in: Prec. 5th Conf. on Electric Melting of Glass, 1980, l'lsti nad Labem, Czechoslovakia
(House of Technique) p. 91 (in Czech). [23] S. Kasa, A. Lis~,, M. Ngme~k and J. Stan~k, in: Prec. 13th Int. Cong. on Glass, Hamburg (DGG, 1983) p. 191. [24] J. Stan6"k and J. Matgj, J. Non-Cryst. Solids 84 (1986) 353. [25] J. Mat6j and J. Stane'tk, Glastechn. Ber. 61 (1988) 1. [26] J. Mat~j, Skiht~ a keramik 29 (1979) 259. [27] J. Matgj and V. Katihk, in: Prec. 5th Conf. on Electric Melting of Glass 1980, l]sti nad Labem, Czechoslovakia (House of Technique) p. 154. [28] J. D6vay and L. M6szS.ros, Acta Chim. Acad. Sci. Hung. 43 (1965) 25. [29] N.N. Teichmann, Glass 58 (12) (1981) 29. [30] S.L. Fitzgerald and B. Hamilton, Glass 57 (3) (1980) 6. [31] J. ~tverhk, V. Slhdek and L. Novhk, in: Proc. of 5th Conf. on Electric Melting of Glass 1980, l]sti nad Labem, Czechoslovakia (House of Technique) p. 6. [32] A.G. Lesnova et al., Steklo i Keram. (11) (1973) 10. [33] W.R. Steitz and C.W. Hibscher, Glass Industry 62 (2) (1981) 11. [34] P.A.M. Gell, Glass Industry 54 (3) (1973) 12; 54 (4) (1973) 14, 16. [35] P.A.M. Gell, Glass 58 (1981) 20. [36] Czechoslovak Patent no. 238229. [37] H. Pieper, Sprechsaal 105 (1972) 236. [38] H. Pieper, Glasteehn. Bet. 51 (1978) R1438. [39] E. Neukunft, Glastechn. Bet. 59 (1986) 6. [40] J. Goedicke, Giastechn. Ber. 59 (1986) 12. [41] R.W. Palmquist, in: Prec. 6th Conf. on Electric Melting of Glass, 1983 Usfi nad Labem, Czechoslovakia (House of Technique) p. 133. [42] W. Trier and K.L. Loewenstein (transl.), Glass Furnaces, Design Construction and Operation (SGT, Sheffield, 1987). [43] W. Hanot and W.A. Gillam, Ceram. Bull. 57 (1978) 728. [44] M.C. Reynolds, Glasteknisk Tidskrift 25 (1970) 115. [45] L.C. Bekker et al., Stekio i Keram. (2) (1976) 11-13. [46] K.A. Konstanyan et al., Steklo i Keram. (4) (1976) 6-8. [47] V. Siisser, Z. Habrman and J. l_&dr, Skl/d' a Keramik 27 (1977) 228. [48] A.R. Akopyan et al., Stekio i Keram. (2) (1978) 33, 34. [49] J. I.Adr, J. Vaeh and Z. Baloan in: Prec. 5th Conf. on Electric Melting of Glass, 1980, Usti had Labem, Czechoslovakia (House of. Technique) p. 1. [50] A. Piechurovski and S. Urbanek, Szklo i Ceram. 29 (1978) 185. [51] W. Kerner, Glass 58 (1981) 25. [52] M.S. Quigley and D.K. Kreid, in: Prec. ASME/AICHE Nat. Heat Transf. ConL, San Diego, 1979. [53] R.L. Hjelm and T.E. Donovan, in: Prec. ASME/AICHE Nat. Heat Transl. Conf., San Diego, 199. [54] J. Plodinec and P. Chrismar, in: Prec. of the IEEE IAS Ann. Meeting 1980, Cincinnati, OH. [55] C. Chapman, in: Prec. IEE IAS Ann. Meeting 1980, Cincinnati OH, Glass Industry 63 N(1) (1982) 10.
Journal of Non-CrystallineSolids 123 (1990) 400-414 North-Holland
P R O B L E M S IN ELECTRIC M E L T I N G O F G L A S S Jaroslav S T A N E K Institute of Chemical Technology, Department of Sificates, Prague 6, Czechoslovakia
The resistivity-temperaturecharacteristics of different glasses were measured. From the relation, a criterion of stability of an electric furnace may be calculated. The release of energy around different electrodes as well as the power density distributions within the glass bath for different electrode-pairconfigurationsare shown. The optimal connectionsof electrodes from the point of view of minimum energy consumption is described. Theoretical as well as practical problems concerningthe corrosion of electrodes are described. Different ways of protecting electrodes against corrosion by glass melts are described. Furnaces for melting different types of glasses and new processesusing electricity for melting are mentioned.
1. Introduction Interest in the electric melting of glass has continued in spite of the fact that the price of electricity is higher than the price of fossil fuels. There are other reasons which make electricity attractive for the melting of glass. An electric melting furnace can achieve a very high efficiency, up to 80%, the specific melting energy being 0.85 to 1.1 k W h / k g glass. This efficiency cannot be achieved in a fuel-fired furnace. A cold top for an all-electric melting furnace has been introduced not only for economic or technical reasons. The conversion of borosilicate, lead, insulation fibre, tableware and other glass furnaces to cold top electric melting is also due to environmental considerations. It became clear very soon that not only had the environmental problems been reduced, but other benefits were also obtained to the considerable advantage of users. The stability of the cold top of an all-electric furnace, glass quality and conditions remain constant and consistent leading to an improved efficiency of electric melting.
2. Electrical transport properties of glass 2.1. Electrical conductivity
The most important properties for electric melthag are electrical conductivity (or resistivity) which is strongly temperature dependent. As the electri-
cal conductivity is of electrolytic character, it also depends on the chemical composition of the glass. The electrical conductivity is a function of the number of ions which take part in the current transport, of the magnitude of their charges and of their mobility. The mobility of the ions is dependent on the frictional resistance of cations which increases with their radii and furthermore on the attraction between the positive ions and the negatively charged SiO4 tetrahedra, in the case of silicate glasses. According to a general rule, alkali ions contribute most to the electrical conductivity. Borosilicate glasses usually conduct less well than silicate glasses; the oxides CaO, MgO, BaO and PbO likewise reduce conductivity because these cations with a larger charge are less mobile than alkali ions. The dependence of conductivity on the chemical composition of glass has been reported by several authors who tried to express it in terms of different, usually empirical, equations. Mazurin [1] has dedicated one volume of his extensive work dealing with the structure and properties of glasses to electrical properties. Sa~ek [2] has used the method of planned experiments to determine the direct effect of the individual oxides on the conductivity of glass liquids and glasses. He has proposed regression equations for computing the constants a and b from Rasch and Hinrichsen's relation log 2~ = a - ( b / T ) .
0022-3093/90/$03.50 © 1990 - ElsevierSciencePublishers B.V. (North-Holland)
(1)
J. Stan~k / Problems in electric melting of glass
401
20
where -/ is electrical conductivity, T is temperature and a and b are constants. From these equations the temperature dependence of the electric conductivity of glasses on their chemical composition for both high- and low-temperature regions can be determined with an accuracy better than _ 5% log ~/. It has been found on the basis of accurate analysis of the individual oxides that not only alkali but also certain other oxides have to be taken into account when calculating the conductivity of the glass. If only alkali oxides are assumed to be the sole variables in the equations, then the calculated values of the conductivity are lower than the measured ones. Other authors such as e.g. Yevstrop'ev and Toropov [3] and Konstanyan [4] have suggested similar equations:
Tlo i
1000 1100 1200 1300 1~00 1500
T[°C]
(2) (3) (4)
Fig. 1. Temperature dependence of the resistivity of various glasses: 1, television tube glass; 2, sheet glass; 3, white flint container glass; 4, water glass; OeJ, the resistivity of the glass melt; tg a = d o e l / d T is the slope of the characteristic p¢l-T.
where a, a', r , fl', a, b, n and TO are constants. Stevels [5] has derived and recommended the following formula
The resistivity-temperature characteristics are given in fig. 1. All the data have negative temperature coefficients. These negative coefficients indicate that, when glass is heated and melted, thermal instability can occur.
log "r = a -
( fl/T2),
log ~ = a' - ( f l ' / ( T log V = a -
(b/T"),
log "t = A - ( E / R T ) ,
To)),
(5)
in which A depends on the composition and temperature of the glass, R is the gas constant, and E is the activation energy for electrical conductivity. The value of E and the temperature dependence of electrical conductivity exhibit a discontinuity in the transformation range, but otherwise the relationship describes the temperature dependence of ~/ adequately over a wide temperature range. In the temperature range up to Tg, E has the values of 84-126 kJ mol-1; in the range of melting temperatures E decreases to 42-84 kJ mol- 1 By measuring the resistance of the liquid at different temperatures, we obtain the 'characteristic' of the glass liquid, i.e. the dependence of its resistivity on temperature. A suitable method for this purpose is the compensation method, which is based on the measurement of the voltage drop between two Pt electrodes immersed in the molten glass [6] for an alternating current (AC).
2.2. Thermal stability The power introduced into the furnace [7] may be expressed by
P~T) = UE/R~T),
(6)
where input P~T) as well as resistance R~T ) are both temperature dependent, and U = voltage. When the temperature T varies, then the variation of P~T) will be obtained by the differentiation of eq. (6) dP
U 2 dR R 2 d-T dT.
(7)
The resistance R~T ) between two parallel electrodes is proportional to the resistivity Pe~ of glass and to the layout and dimensions of electrodes Pel, 2b R¢T) = - ~ t n - d - ,
(8)
402
J. Stan~k / Problems in electric melting of glass
where l is length, b is distance and d is the diameter of the electrodes. By inserting this relation into eq. (7) we obtain U 2 1 dpel
dP =
R Pel d-TdT
(9)
and by introducing eq. (6) into eq. (9) we obtain 1 dP P dT
1 ape, Pel d T "
(10)
This equation shows that the change in power introduced into the furnace is inversely proportional to the change of resistivity of the glass. The expression 1 dpel Pei dT is the criterion of stability, in the range of the melting temperature of the furnace with regard to the temperature dependence of glass resistivity. This criterion contains the expression d p e l / d T = tan a,
(11)
which is the slope of the resistivity-temperature characteristic of the respective glass (see fig. 1). The dimension of the criterion of stability is (%o, ° C-1). Glasses having this criterion below 3 (%o, °C-1) may be electrically melted without any special measure being taken against the instability effect. It is preferable to use some type of automatic control for glasses having the criterion of stability higher than 3 (%o, ° C - I ) . The problem of stability at the melting temperature has also been studied by Trier [8], Hilbig [9] and Schumacher [10]. Trier has pointed out that for the thermal stability of an electric furnace not only the electrical but also the thermal properties of glass melt are of major importance. For the thermal stability, the absorption of energy and its transfer are important. The thermal instability of a particular volume element may be expressed by the instability factor D, dP/dT dq/dT
= D,
(12)
For D > 1, the particular volume element is thermally unstable; for D < 1 it is stable. The current density is given by i = 1/.4 (A cm-2),
(13)
where I is the electric current flowing through the surface area A of the volume element. The electric power p entering the unit volume of an element will be (14)
p = Pe,i 2
and its change with temperature will be dp dT
12 doel A2 d T "
(15)
The heat q given off by the volume element is given by TITS q= --((Xc+Xr)-F
A
+
a),
where: T is the temperature of the element, Ts is the ambient temperature, l is the linear extent of the element, Xc is the thermal conductivity of the m e l t , )k r is the infrared transmissivity, a is the heat transfer coefficient, V is the volume being considered, and A its surface. The change of the density of the volumetric heat flow may be expressed by dq = (X~ + )kr)(A//V) + dT l
(17)
Ot
Genzel's [11] formula may be used for the infrared transmissivity, (18)
)~r = ~ - ° n 2 T 3 F ,
where: F is the mean free path length of radiation quanta, n is the refractive index, and o is the radiation constant. F depends on the type of glass and temperature. It is high for clear glass, e.g. 5.71 cm for window glass, and low for green glass, 0.424 cm at 1300 o C. The instability factor D will then be as follows:
i2(dpe~/dT)l O = (X c + ~ _ o n Z T 3 F ) ( A / V )
where d P / d T is the change in power input with change in temperature G and d q / d T represents the change in heat transfer with temperature.
(16)
+ a"
(19)
In the molten glass in a furnace A~ is significantly smaller in comparison with Xr, and the part of
J. Stan~k / Problems in electric melting of glass
heat transfer by convection may be neglected. The instability factor, for a cube with edge length l ( A / V = 6 / l ) and with dominating radiation transfer, may be expressed by the following equation: i 2 ( d p e l / d T )12 Drad. =
32onZT3F
(20)
The thermal stability, 1/Drad., increases with increasing temperature and increasing free path of radiation (clear glass). It decreases with increasing current density i 2, increasing dPe~/dT, i.e. tan a, the slope of the resistivity-temperature characteristic and with increasing dimensions, l 2, of the element considered. When Xc prevails, as in the case of dark glasses and particularly for the domain of the surface layers of the refractory material, then
i2(dPel/dT) i 2 Otherm" =
6Xc
(21)
Hammerschmidt and Hausner [12] have compared the electrical conductivity of new and old refractory materials. Due to the diffusion of alkalis into the surface layers of refractory blocks, the conductivity of old blocks is higher than that of new ones. A local instability may occur if the conductivity of the surface layer of the refractories approaches the conductivity of the glass melt. Schumacher [10] has compared the heat transfer by radiation, convection and conduction in different glass liquids as well as in refractory materials and has found that the instability of the system may be brought about by (1) a great density of electric current flowing in the glass liquid parallel to the surface of the refractory blocks and penetrating partially into the sub-surface layers of the material; (2) high temperature gradients in the glass liquid; (3) high activation energy for conduction. Endress [13] has studied the dependence of the thermal stability of an electric melting furnace on changes of the electrical conductivity - or on the concentration of alkalis in the inside wall of the hole for an electrode holder in the refractory block. The heat transfer was simulated by means of a
403
thermo-electrical circuit which was used as a model. During furnace operation, the concentration of alkalis, consequently the conductivity, and also the rate of corrosion of the refractory material increase. The length of time in which these changes are realized and reach an undesirable level depends on the melting temperature of the glass and on the composition of the batch.
3. Release and distribution of the energy
The stability of electric melting may also be improved by the proper distribution of energy in the basin in the furnace. The amount of energy released at the individual points of the basin is directly proportional to the square of the voltage gradient, and inversely proportional to the resistivity Pei of the glass melt at the point concerned, W = (grad V) 2/0e,"
(22)
The release of energy around a rod electrode was derived by Gruenberg [14]. The power dissipated in a glass melt tends to be relatively close to the electrode. The electrode is surrounded by a cylinder of glass liquid having radius X - as shown in fig. 2. The distance in which the power Po will be
mill
~
"','!'tF"-; Fig. 2. Electrodes surrounded by a cylinder of glass melt. X is the radius of the cylinder in which the whole power virtually dissipates. Distances of second electrode b >> X.
404
J. Stan#k / Problems in electric melting of glass
liberated in the glass volume can be determined from In X -
PG2~rl Pel I 2
(23) '
where l is the length of the electrode, Pel is the resistivity of the glass melt and I is the total current of the electrode. The greater the value of X the more uniform is the power distribution between the electrodes. Hotter glass (i.e. lower P¢l), longer electrodes, and lower current between them yield better uniformity of the power distribution in the glass melt. The study published by Ganzala and Maddux [15] also deals with the distribution of energy between rod electrodes, especially from the point of view of their surface temperature. The power density measurements were carried out on a physical model. Three zone lengths, i.e. the distances between electrodes, were investigated (7, 13 and 25 cm). Figure 3 shows the distribution of a model power density for the shortest spacing. It was calculated for this zone that 89% of the total heat released was within three electrode diameters, i.e. only 11% was in the bulk. For the mid-length, i.e. 13 cm, zone and for the longest, i.e. 25 cm, zone, only 57% and 47%, respectively, of the total heat was released within the distance of three electrode diameters.
E
0115
I\ _ _ J /
~" 0,10
co
~.
0,05
P~ 0,00
t
0
I
2 cm ] r o m
t
4 electrode
5
I 8
centerLine
Fig. 3. Power density distribution as a function of the position between electrodes. Scale of the model 1 : 10.
100
50
0
"x.
qo
20 zone
30
40
Length ( c m )
Fig. 4. Power dissipated near electrodes as a function of zone length.
The ultimate objective was to reduce the service temperature of electrodes. Therefore, it is of interest to know the amount of heat liberated near the electrodes. The percentage of total power dissipated near the electrodes. The percentage of total power dissipated within three electrode diameters plotted against zone length is shown in fig. 4. The curve in fig. 4 may be described by a hyperbolic function Y= a + (b/X),
(24)
where Y is the percentage of power dissipated within three electrode diameters of both electrodes, X is the zone length, while a and b are the computed regression coefficients. The heat released near the electrodes in inversely proportional to the zone length which means that long zones, which would use more voltage and less current, will cause the electrodes to operate at lower temperatures by shifting more heat towards the centre of the zone. For electrode corrosion, the temperature of the electrode is decisive. The lower the temperature of the electrode surface, the smaller its corrosion. All the above-mentioned works declare that the energy released in the basis is far more uniformly distributed if the rod electrodes are longer and their spacing larger. The temperature of the electrode surface will be, in this case, lower too.
J. Stan~k / Problems in electric melting of glass
405
R
4. Resistances between variously grouped electrodes
4.1. Calculation A knowledge of the effective resistance between electrodes is important for the design of electric furnaces and their transformers. An exact determination in advance is difficult to obtain because of the many different electrode configurations and the influence of temperature on the conductivity of the glass. Many authors have tried to achieve accurate and reliable results [6,16-21]. All these calculations give results which can only be applied under certain conditions. To determine the resistances between electrodes, first of all the potential differences between them and the related currents must be determined. Assuming that the length of the electrodes is much greater than their diameter, then the equipotential surface can be considered as being cylindrical and the so-called coefficient of inherent potential is a , = (pe~/2vl) l n ( 2 / d )
(25)
and the coefficient of mutual potential, at uniform temperature, is
a,k = (&,/2~rl) ln(1/b,k ),
(26)
where &~ is the resistivity of the glass melt, l is the length, d the diameter of the electrodes, and b~k is the distance between the electrodes i and k. The effective resistance between two electrodes is a function of their inherent and mutual potentials and can be expressed as follows (see fig. 5):
R,k = ( &L/'~l ) ln( Zb,k/ d ).
(27)
The method of potential coefficients can also be used to determine the resistances between elec-
T
i-
Fig. 6. Arrangement of three electrodes for a three-phase supply with a network diagram. R, S, T, phases of a transformer; ~ = potential; U = voltage between phases; I = current; b = distance between electrodes.
trodes with a multiphase power supply. The simplest electrode configuration for a symmetrical three-phase system is given in fig. 6, which also shows the equivalent diagram. The resistance between the electrodes arranged in an equilateral triangle and connected to a three-phase power supply is as follows:
R = 3 (Pel/,Tr l ) ln(2b/d ).
b=
(28)
In this case the electrical resistance is 1.5 times that of two electrodes using a single phase alternating current if b = bik. In both the above calculated examples we ignored the tank boundaries which no doubt have a great influence on the result of the calculation. The influence of the upper surface on the field in a body such a glass tank can be taken into consideration by assuming equivalent, fictitious electrodes, of the same shape and dimensions as the real ones, positioned in the upper half space as mirror images reflected by the surface. The space around the fictitious electrodes is assumed to have the same physical properties as the lower half. The principle of superposition, or the method of potential coefficients, can then be applied to determine the resistances. The resistance of the arrangement shown in fig. 7 is given by R=(Pel/'ITl)
Fig. 5. Arrangement of two electrodes, d = diameter; distance between rod electrodes.
,
ln[(2b/d)~l
+ ( b 2 / n h , h 2 ) ].
(29)
Compared with the resistance of an infinitely extended bath of molten glass (see fig. 5 and eq.
406
J. Stan#k / Problems in electric melting of glass
/ J /
7
/// Fig. 7. Determination of the resistance between two electrodesby a single mirror image method: y = conductivityof the glass liquid (1/pel); h = distance between the electrode and glass level; b = distance between electrodes.
(27)), this gives an increase in resistance of In ¢1 + b 2 / 4 h l h 2 . Theoretically, the number of mirroring surfaces could be infinite; however, in actual practice, only one or two mirroring surfaces need be taken into consideration (usually the glass level and one wall). On the other hand, it is clear that even for relatively simple geometrical configurations of electrodes, the use of fairly intricate formulae is unavoidable in calculating the resistance, and with more electrodes in diverse positions the results may be unreliable. It is better then to model the configuration. 4.2. Modelling
By means of a model, not only the resistances between the electrodes but also the distribution of the electric field, the uniformity of the electrode loading, and the influence of the electrode length on the resistance and on the load can be observed and measured, and the results of the measurement can be applied to the actual furnace [6]. The electric current is fed into the model by means of electrodes, the positions of which are adjusted to attain the following: (1) optimum technological conditions i.e. favourable influence on the glass flow; (2) uniform loading of the electrodes; (3) uniform loading of the power supplies; (4) appropriate voltages between the electrodes.
The magnitude of the electric current in the glass melt is given by J = yE,
(30)
which is Ohm's law in vectorial form, where E is the vector of the intensity of the electric field, 3' is the conductivity of the glass liquid and J is the vector of the current density. An external magnetic field of induction, B, exerts a force on a conductor of volume V, through which a current of density J flows. This force is combined with the other forces acting on the liquid, namely gravity, pressure and the viscous forces. The amount of magnetic energy is very small, since the current density J in the liquid is relatively low: it is < 0.1 A cm-2. The conductivity of the glass -/is usually about 0.02 to 0.5 S cm -1 and the term y E x B which represents the force exerted by the magnetic field upon the current tube is small and can be neglected. It is necessary to establish the character of the alternating electric field when the electrodes are supplied by a current of comparatively low frequency (50 or 60 Hz). The wavelength X of an oscillation of frequency f in a medium of conductivity -/ and relative permeability/L can be calculated from )k = (109//fy/x) 1/2 (cm).
(31)
As # = 1, and y usually 0.02 to 0.05 - as stated above - the resulting wavelength is in the range X = 66-330 m. This is substantially greater than
J. Stan~k / Problems in electric melting of glass
the dimensions of a melting furnace. In such a case, the electric field in the glass liquid can be regarded as a potential eddy-free field of r o t e = 0, the intensity of which is a function of position and can be described by E = - grad ¢p.
407
b
!r
(32)
The distribution of the potential q0 is given by the partial differential equation a
a[
acp~
which is Laplace's equation for a current field, where the electric conductivity 3' = f ( T ) . A condition for the similarity of the current field in the model and that in a full scale furnace is that they can be described by differential equations of the same form. As the conductivity of the glass melt is a function of the temperature, 7 = f ( T ) or P~L= f ( T ) , the conductivity of the model liquid must be a similar function of temperature. The dependence of the resistivity on temperature is expressed by the slope of the 'p~ - T ' curve, the so-called 'characteristic', which may be described either by eq. (11) or by: (pelatmaxT) =(Pe'atmaxT) , P~l at rm=n T M Pel at rm=n T E
(34)
where Pe~ is the resistivity of the glass liquid (E) or of the model liquid (M) and T is the temperature in the corresponding temperature ranges. If other boundary conditions are also met, then it is possible to determine the electric values of the full-scale furnace from the values measured in the model. The geometrical boundary conditions are met when the model is an accurate scale model of the full-size furnace. A further condition is the similarity of the temperature fields in the model and the full-sized equipment, i.e.
T = f ( x , y, z).
(35)
The required temperature field can be achieved in the model by whatever technical means are needed if the distribution and gradients of temperatures in the full-size furnace are known. The model must be ac-powered to ensure that the measured voltages are not altered by the dc voltage created through electrode polarization.
Fig. 8. Diagram for the calculation of the resistance between electrodes from values measured in a model, b = distance between electrodes; F = vertical cross-section; Oel= resistivity of the model liquid. If those conditions are met, then the lines of force and the electric fields in the model and in the full-size equipment have similar shapes. This fact can be utilized to determine different electrical parameters, such as the resistance between the electrodes of a full-scale furnace from the resistance measured in the model. The values of resistances obtained in this way are, to date, probably the most reliable ones. Figure 8 shows an example with electrodes in a general position. The resistance between electrodes in the full-size equipment is given by the following expression: Pc, E(TE) RE = RM Pd M(TM) S,
(36)
where M as a subscript is the symbol for values referring to the model and E as a subscript is the symbol for values referring to the full-size equipment. Therefore, p~l E(TE) is the resistivity of the molten glass as a function of the corresponding temperature TE; P~l M(TM) is the resistivity of the model liquid as a function of the corresponding temperature TM; s is bM/b E is the scale of the model (it is the ratio of the characteristic dimensions of the model and of the equipment); and R M is the resistance between the electrodes in the model.
4.2.1. Modelling on conducting paper [22,23] Modelling on conducting paper is much simpler than the modelling by a physical model. This is due to the fact that a model made of conducting paper cannot simulate all the processes taking
408
J. Stan~k / Problems in electric melting of glass
place in the full-size equipment, such as convection. On the other hand the evaluation of potential fields tends to be much easier by means of conducting paper than by a physical model [22]. Provided the model is connected to a central measuring device and the measured data are evaluated by a computer, the results are then obtained very quickly and comparatively easily. The model of the furnace is cut from a part of the conducting paper strip. The electric current is introduced into the model by electrodes drawn, on the scale of the model, on the conducting paper by silver lacquer. When modelling an electric ~ass melting furnace, the electrodes in the model are connected with an alternating current source in the same manner as in the furnace. From the difference of voltages in a determined location, it is possible to identify not only the direction of current lines but also the current density in that location. From voltage differences, i.e. from grad V in different places of the model, the release power may also be determined in accordance with the equation P = ~,(grad V) z.
(37)
It is possible to simulate the phenomena occurring in two directions in a plane cut, the transfer of electric current in the glass liquid of constant properties surrounded by a refractory material having zero electric conductivity. By combining the mathematical modelling with modelling on conducting paper, the distribution of power in an electric glass melting furnace has been evaluated with differing locations of electrodes. Figure 9 shows an example - the distribution of power around six vertical electrodes. By means of this type of modelling it is also possible to find the optimal connections with a multiphase ac source, which tend to be very important from the point of view of conservation of energy [23].
5. The corrosion of electrodes
124,251
The corrosion of electrodes is another problem with which one must deal. The majority of electrodes being used today are made of molybdenum [6]. However, molybdenum is a costly material making it therefore necessary to keep its consumption and consequently its corrosion by glass melt
P,
J J J f j Z J J J J / J J J f f J J J f ~ J J J J J / / J J J J f J J J J J j f j j f J J J J J J J J J J J J J J f j j j J J J J J J J f f f J J J J / Fig. 9. Distribution of power around six vertical electrodes.
J. Stan~k / Problems in electric melting of glass
as low as possible. Besides, the products of corrosion affect the colour of glass. The reasons for metal corrosion by glass liquids in general are the successive and coupled electrode reactions, the course of which depends on several internal and external corrosion factors. The internal corrosion factors depend only on the metal itself, i.e. on its chemical purity, structure, character of its surface, presence of primary protective layers, mechanical stress, and deformation. From the point of view of the chemical purity of molybdenum it is essential to keep the carbon content as low as possible. Electrodes with carbon contents above 50 ppm cause bubble formation. The carbon content of 50 ppm is also critical from the point of view of corrosion, which increases rapidly in the range 60-70 ppm carbon [26]. Outer factors influencing the corrosion of electrodes are the chemical character of the corrosive environment, the kind of anions and cations, the character of the dissolved gases, temperature, contact with other metals, and electric current. Electric melting of lead glasses has so far been problematic because of considerable corrosion of the molybdenum electrodes, which increased the consumption of molybdenum and also impaired the quality of the glass. However, all-electric melting of such glasses is particularly desirable because it eliminates problems with emissions of harmful lead oxide. The electrode corrosion rate is decisively affected by the presence of corrosion depolarizers, such as lead oxide and some refining and colouring agents, as molybdenum undergoes electrolytical oxidation at the expense of these substances. The passage of alternating current through the heating electrodes is another significant corrosion factor. It has been proved that, in addition to the power load, a significant role is also played by loading the electrode with the electric current. A close relation exists between the amount of corroded molybdenum and that of precipitated lead [271. According to the theory of the corrosion of metals by the effect of alternating current, worked out by D6vay et al. [28], the high rate of corrosion is due to increased mean anodic, i.e., mean corrosion current, as shown in fig. 10 by dashed lines.
409
Mo~Mo~6e- , t ~ ~. S ~a~a] . / 1:_8
r, .
//
l
Fig. 10. Dependence of the rate of electrode processes on the polarizing potential: icor = anodic (corrosion) current; idep = corresponding cathodic (depolarizing) current; i~o, = increased corrosion current on molybdenum electrodes loaded by alternating current; i~ep ~ corresponding cathodic current.
The mean value of cathodic current, which is a measure of the depolarization reaction, e.g. precipitation of lead, increases simultaneously. All published experimental results, as well as technological experience, demonstrate that corrosion increases with increased loading by alternating current, and decreases with increasing frequency. However, these results apply to frequencies > 50 Hz. A detailed study of the frequency dependence of the corrosion of molybdenum electrodes in glass melts at frequencies around 50 Hz disclosed deviations toward lower values. More detailed investigation of these anomalies showed that in the low-frequency region, mostly below 50 Hz, the corrosion rate can actually decrease with decreasing frequency, jointly with the amount of precipitated depolarizer. Figure 11 shows the dependence of the decrease of electrode radius in a lead glass liquid on frequency at various current densities. The corresponding amounts of precipitated lead are plotted in fig. 12. Similar to the frequency dependence, the decrease of electrode radius and the amount of precipitated depolarizer also exhibit deviations from the assumed dependence on current density, if the interfering effect of increasing power load at the higher current densities is eliminated. The results obtained can be generalized so that the decrease of electrode radius and the amount of precipitated
410
:I/I
J. Stan~k / Problems in electric melting of glass
..i. o , , o
I
0
I
.
2Ac
I
100 frequency 200
I
300
I
f Hz
~0o
Fig. 11. Corrosion of the electrode represented as the decrease of electrode radius Ar for various current densities i.
depolarizer as a function of frequency in melted glass have a m a x i m u m and a minimum (also compare with fig. 13). For a given glass, the position of these extremes depends on current density and
0
temperature, shifting towards higher frequencies with increasing current density. In spite of m a n y patents concerning the protection of m o l y b d e n u m against corrosion, it is evi-
700 frequency 200
300
f Hz
bOO
Fig. ]2. The amount of precipitated lead in g for various current densities.
J. StanEk/ Problemsinelectricmeltingofglass ZOgo[
411
i=O. ~m
/ II
1,0
0
,,,,1
0,5
t
I
1 frequency 2
m-Ilpe
•
I
3
f Hz
I 4s,
z,
I
50
Fig. 13. Frequency dependence of the amount of lead deposited on a Mo electrode at two different current densities.
dent that the most important factor for the protection of the electrodes is low surface current load. It is therefore necessary to keep the load as low as possible.
6. Electric boosting Electrical energy for melting glass m a y be used in two ways, either as boosting energy for a conventional furnace or as the only energy source. The overall thermal efficiency of a furnace equipped with electric boosting is higher than that without boosting since the transfer of thermal energy from the electric current into the glass melts is very high. A major purpose of boosting is to strengthen the thermal barrier. The electrodes which are to strengthen the barrier should therefore be located either at the position of the flame thermal barrier or behind it in order to enlarge the melting area surface covered by the batch. Figure 14 shows a typical example of electric boosting in
Fig. 14. Electric boosting in a sheet glass furnace; E - vertical electrodes.
a sheet glass furnace where the electrodes strengthen the thermal barrier. If the output of the furnace is to be increased substantially, then a part of the energy (approximately ½) must also be released in the melting end of the furnace. An example of a layout of electrodes in the furnace is shown in fig. 15. This type of boosting m a y raise the output of the furnace by
I
I
y,
I
5'1 16 Z'
3'
)~'
21 Ir
Fig. 15. Diagram of electric boosting in a continuous tank. X, Y, Z - secondary windings of the transformer; X', Y', Z' voltage triangle between electrodes; 1, 2, 3, 4, 5, 6 - tappings from secondary transformer windings; 1', 2', 3', 4', 5', 6' electrodes.
J. StanFk / Problems in electric melting of glass
412 t2 t - ~ x x \ x x'¢.' x x x \ \ \ x x x x x x ~
gJ"l/////
-
/ /
b
glass in the melter and the batch blanket covering it [33]. This rate is only adjustable within limits and therefore it follows that electric furnaces cannot be operated with pull rates that vary as widely as those of flame-fired furnaces. 7.1. Design
.
.
.
.
.
.
.
.
.
.
.
JIV!II+
Fig. 16. A continuous furnace with boosting and deepening part of refining area: (a) side view; (b) top view, E - deepening part with electrodes.
some 130%. Another arrangement of electrodes is shown in fig. 16. The thermal, technological and economic advantages of using electric boosting are substantial, and electric boosting is, therefore, being regarded as the most efficient means of accelerating the melting process [29]. Another large technical as well as economical contribution is the electric heating of feeder channels. It enables not only more accurate temperature control but also a substantial decrease in the energy consumption in the feeder channel [30].
One of the first furnaces with a cold top was reported by Gell [34,35] - see fig. 17. Its melting rate has been substantially increased by deepening the melting part of the furnace and by adding another row of rod electrodes above the plates ones [31,36]. Another two-chamber electric melting furnace [6,42] can be built in various versions and sizes, either for manual production alone, or for both manual production and feeding for automatic production - see fig. 18. The batch is charged on to the surface, which is thus effectively insulated. The furnace is equipped with molybdenum rod electrodes, which are placed in an inclined position in the side walls on the furnace. The furnace proved satisfactory for melting glass with a low as well as high content of lead oxide. A typical representative of the shaft furnace principle is the electric furnace built by Sorg [3740], which has a polygonal cross-section with O
7. All-electric melting During the past ten years much valuable experience has been gained concerning the all-electric melting of glass. Thus, it was shown that electric melting of certain glasses is better than melting in flame-fired furnaces. The borosilicate and opal glasses melted electrically turn out to be of much higher quality than when melted by flame [31,32]. Electric furnaces differ from flame-fired furnaces in their mode of operation. In a flame-fired furnace the limit of the rate at which glass can be melted is governed by the refining rate. The limiting factor in an electric furnace is the batch melting rate, i.e. the heat transfer between the molten
b
Fig. 17. Gell furnace with plate electrodes: (a) side view; (b) top view.
J. Stan~k / Problems in electric melting of glass
413
6
II \ 2 Fig. 18. Furnace with horizontal rod electrodes: Side view; I, melting and refining end; 2, throat; 3, working end; 4, bridge wall; 5, charging end; 6, exhaust; 7, gathering holes; 8, feeder channel; 9-II, electrodes, 12 heating elements; 13, outlet.
molybdenum electrodes located in two or three horizontal planes - see fig. 19. Further development in all-electric shaft furnaces is the molybdenum-lined decagonal Summit furnace [41] developed by Coming Glass Works (see fig. 20). For glasses that are compatible with molybdenum this furnace can produce high quality glass without refractory defects at a low cost.
z
Large all-electric furnaces have been for melting packing glass. These furnaces were of melting capabilities up to 100 tons/24 h [6], 165 tons/24 h [43] and 250 tons/24 h [35]. The feeding sources for these furnaces consist usually of one-phase or three-phase transformers. Furnaces for the melting of lead crystal glass were constructed and have been described by a number of authors [44-49]. Some of these furnaces are equipped with stannic (SnO2) electrodes, others with molybdenum electrodes described in some of the above mentioned patents. Likewise, a furnace for melting colour [50] and opal glasses [32,51] has been built. Another use of electrical energy is the process of the immobilization of radioactive waste. This
4
V/AI
Fig. 19. Polygonal electric shaft furnace. 1, horizontal electrodes positioned in two or three rows; 2, batch rake; 3, auxiliary electrode in throat; 4, forehearth.
1 ~"
"
I t-'//A
t,
5
Fig. 20. Coming shaft furnace. 1, molybdenum electrodes; 2, Mo lining; 3, Mo pipe; 4, valve; 5, forehearth.
414
J. Stan~k / Problems in electric melting of glass
field is described in papers written by several authors [52-55]. The use of electric power for glass melting has entered the stage of technical and economical necessity. Evidence for these necessities is shown by the fact that nearly all glassworks have at least some electric boostings and all-electric melting furnaces. Further proof of the increasing interest in electric melting is the impressive number of publications dealing with this topic. The number of research and development departments dealing with this problem has grown considerably, too. No doubt, research and development have to tackle some more technical issues in order to make electric melting of common glasses cheaper and more economical.
References [1] O.V. Mazurin, Spravo~nik Tom I-IV, Izd. (Nauka, Leningrad, 1973). [2] L. ~agek and H. Meissnerovh, Scient. Papers of the Inst. of Chem. Technology, Prague, Sect. L5 (1974) 111. [3] K.S. Yevstrop'ev and N.A. Toropov, Chemistry of Silicon and Physical Chemistry of Silicates (Gosizdat, Moscow, 1956). [4] K.A. Konstanyan, Izv. Akad. Nauk Arm. SSR - Chem. Sci. 10 (1957) 237. [5] J.M. Stevels, The Physical Properties of Glass (Elsevier, Amsterdam, 1948). [6] J. Stan6"k, Electric Melting of Glass (Elsevier, Amsterdam, 1977). [7] A. Andrusieczko, Szklo i Ceramika 16 (1965) 209. [8] W. Trier, Glastechn. Ber. 53 (1980) 348. [9] G. Hilbig, Glasteclm. Ber. 54 (1981) 44. [10] R. Schnmacher, Glastechn. Bet. 55 (1985) 243. [11] L. Genzel, Glastechn. Bet. 26 (1953) 69. [12] R. Hammerschmidt and H. Hausner, Glastechn. Ber. 55 (1982) 30. [13] H. Endress, Elektrowgtrme Int. 44 (1986) B256. [14] N.R. Gruenberg, IEEE Trans. Ind. Appl. IA-8 (1972) 76. [15] G.W. Ganzala and J.F. Maddux, IEEE IAS 78, p. 966. [16] A. Andrusieczko, Glastechn. Bet. 42 (1969) 235. [17] J. Gailhbaud, Glastechn. Ber. 44 (1971) 314; 354. [18] J. Gailhbaud, Glastechn. Ber. 45 (1972) 56; 133. [19] T.K. Trunova, Steklo i Keram. (5) (1974) 14-15. [20] K.M. Tatevosyan, Stekio i Keram. (4) (1976) 5-8. [21] V.S. Golovin and V.G. Zsheltov, Steklo i Keram. (8) (1977) 12. [22] J. Bla~ek and J. Stanek, in: Prec. 5th Conf. on Electric Melting of Glass, 1980, l'lsti nad Labem, Czechoslovakia
(House of Technique) p. 91 (in Czech). [23] S. Kasa, A. Lis~,, M. Ngme~k and J. Stan~k, in: Prec. 13th Int. Cong. on Glass, Hamburg (DGG, 1983) p. 191. [24] J. Stan6"k and J. Matgj, J. Non-Cryst. Solids 84 (1986) 353. [25] J. Mat6j and J. Stane'tk, Glastechn. Ber. 61 (1988) 1. [26] J. Mat~j, Skiht~ a keramik 29 (1979) 259. [27] J. Matgj and V. Katihk, in: Prec. 5th Conf. on Electric Melting of Glass 1980, l]sti nad Labem, Czechoslovakia (House of Technique) p. 154. [28] J. D6vay and L. M6szS.ros, Acta Chim. Acad. Sci. Hung. 43 (1965) 25. [29] N.N. Teichmann, Glass 58 (12) (1981) 29. [30] S.L. Fitzgerald and B. Hamilton, Glass 57 (3) (1980) 6. [31] J. ~tverhk, V. Slhdek and L. Novhk, in: Proc. of 5th Conf. on Electric Melting of Glass 1980, l]sti nad Labem, Czechoslovakia (House of Technique) p. 6. [32] A.G. Lesnova et al., Steklo i Keram. (11) (1973) 10. [33] W.R. Steitz and C.W. Hibscher, Glass Industry 62 (2) (1981) 11. [34] P.A.M. Gell, Glass Industry 54 (3) (1973) 12; 54 (4) (1973) 14, 16. [35] P.A.M. Gell, Glass 58 (1981) 20. [36] Czechoslovak Patent no. 238229. [37] H. Pieper, Sprechsaal 105 (1972) 236. [38] H. Pieper, Glasteehn. Bet. 51 (1978) R1438. [39] E. Neukunft, Glastechn. Bet. 59 (1986) 6. [40] J. Goedicke, Giastechn. Ber. 59 (1986) 12. [41] R.W. Palmquist, in: Prec. 6th Conf. on Electric Melting of Glass, 1983 Usfi nad Labem, Czechoslovakia (House of Technique) p. 133. [42] W. Trier and K.L. Loewenstein (transl.), Glass Furnaces, Design Construction and Operation (SGT, Sheffield, 1987). [43] W. Hanot and W.A. Gillam, Ceram. Bull. 57 (1978) 728. [44] M.C. Reynolds, Glasteknisk Tidskrift 25 (1970) 115. [45] L.C. Bekker et al., Stekio i Keram. (2) (1976) 11-13. [46] K.A. Konstanyan et al., Steklo i Keram. (4) (1976) 6-8. [47] V. Siisser, Z. Habrman and J. l_&dr, Skl/d' a Keramik 27 (1977) 228. [48] A.R. Akopyan et al., Stekio i Keram. (2) (1978) 33, 34. [49] J. I.Adr, J. Vaeh and Z. Baloan in: Prec. 5th Conf. on Electric Melting of Glass, 1980, Usti had Labem, Czechoslovakia (House of. Technique) p. 1. [50] A. Piechurovski and S. Urbanek, Szklo i Ceram. 29 (1978) 185. [51] W. Kerner, Glass 58 (1981) 25. [52] M.S. Quigley and D.K. Kreid, in: Prec. ASME/AICHE Nat. Heat Transf. ConL, San Diego, 1979. [53] R.L. Hjelm and T.E. Donovan, in: Prec. ASME/AICHE Nat. Heat Transl. Conf., San Diego, 199. [54] J. Plodinec and P. Chrismar, in: Prec. of the IEEE IAS Ann. Meeting 1980, Cincinnati, OH. [55] C. Chapman, in: Prec. IEE IAS Ann. Meeting 1980, Cincinnati OH, Glass Industry 63 N(1) (1982) 10.