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Bubble removal and sand dissolution in an electrically heated glass melting channel with defined melt flow examined by mathematical modelling
Journal of Non-Crystalline Solids 456 (2017) 101–113
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Bubble removal and sand dissolution in an electrically heated glass melting channel with defined melt flow examined by mathematical modelling Lukáš Hrbek ⁎, Petra Kocourková, Marcela Jebavá, Petra Cincibusova, Lubomír Němec Laboratory of Inorganic Materials, Joint Workplace of the University of Chemistry and Technology Prague, Technická 5, 166 28 Prague 6, Czech Republic The Institute of Rock Structure and Mechanics of the ASCR, v.v.i., V Holešovičkách 41, 182 09 Prague 8, Czech Republic
a r t i c l e
i n f o
Article history: Received 16 March 2016 Received in revised form 31 October 2016 Accepted 11 November 2016 Available online 16 November 2016 Keywords: Glass melt flow Mathematical modelling Energy distribution Space utilization Melting performance
a b s t r a c t The electrically heated glass melting channel as a part of the segmented melting furnace was examined by mathematical modelling. Different melt flow characters were set up by proper configurations of the heating electrodes in the channel with either level or close-to-bottom melt input. The sand particle dissolution and bubble removal of defined sizes were followed up to the achievement of the critical state. This was characterized by the termination of the less effective melting phenomenon just before the output from the channel. The utilization of the melting space, the melting performance, and the specific heat losses in the critical state were evaluated. The effect of the melt input character and melt input temperature, electrode length, and energy distribution were investigated. The results have shown that the best results were attained when the energy distribution in the channel was balanced or when it was near the balanced state. Hence, no or only weak longitudinal circulations of the melt arose in the space and the helical-like melt flow could be set. This state was achieved when the melt input temperature was equivalent or not far from the average temperature of the melt in the space. Such as state can be set up by an energy shift to the regions with lower temperature and by enhancement of the transversal melt circulations. © 2016 Elsevier B.V. All rights reserved.
1. Introduction The melt flow character plays a significant role in the continual glass melting process owing to its considerable impact on the history of the homogenization phenomena accomplished in the melt – quartz dissolution, bubble removal, and chemical homogenization. In the industrial melting process, the batch conversion in the batch blanket and phenomena in the melt are practically serially ordered. Besides the batch conversion rate, the slow homogenization of the melt may also limit the melting performance of the entire melting process. The naturally set melt flow in the horizontal glass melting spaces is characterized by powerful longitudinal circulations which are indicated by the broad residence time distribution function of the melt, and consequently by the short critical trajectories along which the homogenization phenomena occur. Due to this effect, glass producers are forced to build large glass melting furnaces with low specific performance and with high specific heat losses. The way to ensure better cooperation of the melt flow with the melting process leads to either uniform melt flow or to efficient transversal melt circulations resulting in a helical-like flow, both ⁎ Corresponding author. E-mail address: [email protected] (L. Hrbek).
http://dx.doi.org/10.1016/j.jnoncrysol.2016.11.013 0022-3093/© 2016 Elsevier B.V. All rights reserved.
characterized by lower dead spaces and a narrower residence time distribution function. The strengthening of the transversal circulation appears easier to implement under industrial melting conditions; several patents describe the use of different mechanical or heating means to fulfil the task to set the helical-like melt flow [1–5]. In fact, the superposition of the evoked transversal circulations on the already existing longitudinal ones leads to the desired helical-like flow only when the ratio between the transversal and longitudinal velocity component of the melt is sufficiently high. The character of the helical-like melt flow and its relation to the running homogenization phenomena was studied in [6–10]. The relative quantity called utilization of the space has been introduced. The quantity indicates which part of the melting space is used for either the dissolution of quartz relicts or bubble removal under a given character of the melt flow. Applying space utilization, the temperature conditions of efficient helical-like flow were determined in the model channel by mathematical modelling. The results have shown that melt flow structures were attained – advantageous simultaneously for both phenomena – at relatively high ratios between the transversal and longitudinal temperature gradients. The ratios of temperature gradients corresponding to highest utilization values of 0.6–0.8 move mostly between 5 and 10 [6,8–10]. However, it would be difficult to realize the corresponding melt velocity ratios in the classic
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melting space with the batch blanket owing to the existing strong longitudinal melt circulations; therefore, the published patented solutions appear less probable. The results of mathematical modelling may nevertheless assist in the construction of special melting spaces without a batch blanket if the previous batch conversion to glass was ensured in a separated space or region. Several ways of rapid batch conversion have been published in the literature: the examples include submerged combustion [11–12], mechanical stirring of the converting batch [13–14], or in flight melting [15–16]. In the subsequent melting module, the desired helical flow may be set up relatively easily with the currently used heating elements such as the application of Joule heat and electrodes. Such a module manifests a very high homogenization ability up to 10 tons/(m3 day) and correspondingly low heat losses [17]. However, the detailed conditions of the module application are not known yet whereas the following are: convenient average temperature in the module, the acceptable difference between the input and average temperature of the melt, and the efficient energy distribution inside the module. The detailed investigation of the mentioned factors in the glass melting module heated by electrodes is the subject of this work. 2. Theoretical The quantity “utilization of the melting space u” has been used for the evaluation of the character of the melt flow with respect to sand dissolution and bubble removal [6–10]. The utilization of the continual space for bubble removal (fining) uF expresses the relation between the reference fining time in a quiescent melt τFref and the theoretical mean residence time of the melt in the space under critical conditions τG. Similarly, the utilization for sand dissolution uD expresses the relation between the average sand dissolution time in the space, τDave and τG [6]. The critical state then describes the situation when the bubble of the initially minimal radius attains the melt level just at the output from the space, or the initially maximal sand particle dissolves right there. u F;D ¼
τHref V ; τG ¼ ; u∈h0; 1i τG V_
ð1Þ
where τHref is either τFref or τDave, V is the volume of the space (m3), and V_ is the volume flow rate (melting performance or pull rate) (m3/s). For the plug flow, τHref = τG is valid, so uF,D = 1 [8]. Both values of the space utilization may be involved in the expressions for the heat losses of the process and for the melting performance. In the critical state, the values of the melting performance and specific heat losses represent the maximum and minimum values, respectively. If both homogenization phenomena are considered as parallel, then the less efficient phenomenon is the controlling one. The specific heat losses of the space through boundaries decrease, and the performance of the melting process increases with space utilization according to: L
H LM
H_ τDave 1 ¼ or H LM ρV uD
VuD Vu F or V_ ¼ V_ ¼ τDave τ Fref
L H_ τ Fref 1 ¼ ρV u F
The space utilization for the sand dissolution uD may be expressed with the assistance of two fractions of dead spaces – the fraction of dead space for the melt flow mG and the fraction of space of the sand dissolution as the overprocessing mD. Similarly, the space utilization for the bubble removal uF can be expressed through the fraction of virtual dead space for bubble removal mvirt and virtual bubble rising distance hvirt [9]. The mentioned quantities provide a more detailed view of the character of the melt flow. Only the values of the space utilization as a final quantity will be applied in this work. If bubble nucleation on the sand particles does not occur, both phenomena run simultaneously, so the less efficient phenomenon becomes the controlling one. When the melting conditions are varied and sand dissolution is the controlling phenomenon, the effect of melt flow changes – described by the utilization value uD may be separated from the effect of different time-temperature histories described by the value of τDave. If bubble removal controls the melting, both effects are separable only when the average temperature in the space varies – at a constant average temperature, the value of τFref is constant. The quantities defined by Eqs. (1)–(3a, b) may be acquired by modelling the critical state of bubble removal (in the critical state, the initial minimal bubble is removed just at the space exit) or the critical state of sand dissolution (the maximal particle is dissolved just at the output) in the melting space with adjusted flow patterns. Here, the demanded flow patterns have been set by proper energy distribution in the model melting space. The set up of the controlled flow in glass melting spaces substantially depends on the distribution of energy delivered to the melting space in the case when no other tool is used to affect the melt flow. The specific energy consumption of a melting space with electric or other inner heating is given by: H 0M ¼ H TM þ H LM
ð4Þ
where HTM is the theoretical energy to convert the inputting batch and to heat the arising melt to the space exit temperature. The crucial condition of the control of the favorable melt flow is the balanced distribution of delivered energy between the input (batch) region and subsequent region where the melting phenomena are completed. If the distribution is balanced, the necessary energetic condition for the uniform or efficient helical flow [19] is fulfilled; otherwise, clockwise longitudinal circulations occur with energy being in excess in the input region, and counterclockwise when the energy supplied here is lower than a balanced one. Most of energy should regularly be delivered to the input region in order to convert the batch, to heat the arising melt, and to cover the heat losses of the region while the needed energy in the subsequent part of the space includes only the heat losses. If the fraction of the input region is designated by ξ, Eq. (4) can be written as [19]: H 0M ¼ H TM þ ξH LM þ ð1−ξÞH LM
ð5Þ
ð2a; bÞ
ð3a; bÞ
where HLM are the specific heat losses (J/kg), H_ L is the total heat flux across the space boundaries (J/s) and ρ is the glass density (kg/m3). The quantity τFref is the fining time which the critical bubble needs to ascend the distance h0 in a quiescent liquid at average temperature in the space; the details of τFref calculation are given in [7]. The former expressions in Eqs. (2a, ba, b) and (3a, ba, b) are valid for the case of sand dissolution as the controlling phenomenon, and the latter ones for the controlling phenomenon being bubble removal.
The energetic equilibrium in the melting space is attained if the specific energy given by the term HTM + ξHLM is delivered to the input region Hglass1, and the energy provided for the subsequent region Hglass2 is equivalent to (1 − ξ)HLM. Usually, the inequality Hglass1 b HTM + ξHLM is valid in horizontal industrial melting furnaces, so intensive counterclockwise longitudinal circulations set up and restrict the melt flow control. In addition, the vertical and other detailed distribution of energy in each region play the role, and local convection currents can be expected even though an energetic balance exists. This work tries to reveal the best conditions to achieve high space utilization in the common modulus for sand dissolution and fining when the type of the melt input is varied, as well as the average and input temperatures, and the energy distribution inside the modulus.
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3. Calculation procedure and conditions The model melting space was chosen for calculations corresponding to the small horizontal melting furnace, as is obvious form the side view in Fig. 1. A Glass Furnace Model was used for mathematical modelling [18]. The model describes the calculation of the temperature, velocity and electric power fields, obtained from the solution of the relevant conservation equations. Their solution is coupled with submodels of sand dissolution and bubble removal, prepared in cooperation with authors´ workplace. The melt, sand particle and bubble trajectories are obtained along with the kinetics of particles along their pathways. The transversal barrier from the refractory material on the right side of the space served as the reference mark where the sand dissolution or bubble removal should be terminated – the achievement of the critical state. The either close-to-bottom or level input of the raw melt was assumed in the segmented melter, so both ways were tested in this work. The close-to-bottom input of the glass melt in Fig. 1 was located in the centre of the input front wall and had a width of 1 m and height of 0.25 m. The other case with the level input involved a strip of glass level close to the front wall with the width of 1 m and the length of 0.2 m. 16 vertical bottom electrodes were located regularly in the longitudinal axis of the space. The regular height of electrodes in the case with the bottom input was 0.8 m, and was 0.6 and 0.3 m in the case with the level input. Two transversal rows, each having six electrodes, were also applied at distances of 1.06 m and 5.2 m from the inner side of the front wall to simulate roughly the melt flow arrangement in an industrial furnace. Two layers of refractory materials formed the walls and bottom of the space. The free level of glass was insulated in the case of the level input owing to the necessary boundary condition. The input and output melt velocities had a full-parabolic profile for the close-to-bottom input. A half parabolic profile in the X-direction and the full parabolic profile in the Y-direction were set for the level input. Non-slip conditions, i.e. zero melt velocities were assumed on the solid boundaries, and the free level condition on the boundary between the atmosphere and glass melt. The type of float glass was chosen as the model glass. The temperature dependence of the glass density and kinematic viscosity in the temperature interval 900–1800 °C are presented in [19]. The raw melt containing sand particles and bubbles entered the melting modulus. The average sand dissolution rate and average bubble growth rates obtained by laboratory experiments were used to follow the history of the phenomena in the melting modulus. The temperature dependences of both quantities are presented in [19], as well. The semiempirical model of bubble behaviour was applied; the model takes into account the changes of the bubble size as well as the bubble composition at varying temperature [20]. The bubbles with an initial radius of 5 × 10−5 m as the smallest ones (experience from laboratory melts) and the sand particles of 5 × 10−4 m
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Table 1 The energy distribution set-up to the single pairs of electrodes in the case with the longitudinal row of electrodes. No. of electrode pairs
1
2
3
4
5
6
7
8
Power supply in %
15
15
15
15
12
10
10
8
as the maximal ones (coming from the sieve analysis) were chosen for tracing. The history of around 104 bubbles and sand particles with regularly located starting points at the given input were tracked using the average rates of sand dissolution and bubble growth applied in the semiempirical model of bubble behaviour. Bubble nucleation inside the space was not considered. The sand trajectories were calculated in accord with the velocity components of the melt flow whereas the bubble trajectories were obtained as a result of the vx and vy components of the melt velocity and the sum of the vz component with the instant bubble rising velocity according to the Stokes' law. The trajectories and sand radii were calculated with the time step mostly at 1 s and the time step for bubble radii calculation at 0.1 s. A calculation grid was used with a distance of 2.5 cm between grid points. The controlling phenomenon was characterized by the fact that the critical particle (sand or bubble) reached the location above the transversal refractory barrier in front of the output, i.e. the critical particle had the highest x-coordinate. The given controlling phe_ nomenon then determined the critical mass melting performance M, the mean residence time of the melt in the space τG, and the average sand dissolution time τDave. The value of τFref was obtained from Eq. (3b) in [7] and the values of both space utilizations from Eq. (1). The specific energy consumption was calculated according Eq. (2a, b). The input temperature in individual calculations was varied between 1320 and 1445 °C at a constant average temperature of 1420 °C in the space. The level melt input and the close-to-bottom input were applied. In another set of calculations, the equivalent bottom input temperatures and average melt temperatures were applied between 1320 and 1420 °C. Finally, the amount of energy supplied to the first six electrodes was increased from 45% to 60, 70, 85 and 100% at a melt input temperature of 1320 °C. The modified configurations of the transversal rows of electrodes and the partial stripping of the insulation of the side walls were also examined when the level input of the melt was applied. Table 1 shows the energy distribution in single pairs of electrodes in the case with the longitudinal row of electrodes.
4. Results of calculations In the first run of calculations, the space with the close-to-bottom input was investigated. The input temperature varied between 1320 and 1445 °C with the constant average temperature inside the space
Fig. 1. The view of the central longitudinal section through the melting modulus with the close-to-bottom input of the glass melt. The inner length is 6.77 m (6.225 m to the transversal barrier made from the refractory material), the width is 2 m, and the height of the glass layer is 1 m.
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Table 2 The values of the quantities characterizing the space utilization, melting performance, specific energy consumption, and specific heat losses in the space with the close-to-bottom input of glass melt. The length of the electrodes was 0.8 m. Case no.
t (°C)
u (controlling)
τDave, τFref (s)
τG (s)
_ (kg/s) (t/day) M
HLM (kJ/kg)
1 2 3 4 5 6 7 8 9 10
1320 1345 1370 1395 1420 1445 1320–1320 1345–1345 1370–1370 1395–1395
uD = 0.27 uD = 0.31 uD = 0.37 uD = 0.46 uD = 0.54 uF = 0.25 uF = 0.54 uF = 0.61 uF = 0.65 uF = 0.68
τDave = 2537 τDave = 2291 τDave = 2128 τDave = 1969 τDave = 1855 τFref = 1878 τFref = 11.594 τFref = 7529 τFref = 4808 τFref = 3024
9387 7314 5741 4400 3426 7611 21,461 12,298 7433 4477
3.00259.2 3.85332.6 4.90423.4 6.40553.0 8.22710.0 3.70319.7 1.32112.3 2.30198.7 3.80328.3 6.30544.3
155.4 121.4 95.5 73.2 56.7 126.7 365.2 209.6 126.8 76.5
of 1420 °C. Subsequently, the input and average temperature were equivalent but varied between 1320 and 1420 °C. The relevant calculated values are assembled in Table 2. Only the values of the controlling phenomenon are listed. The established character of the melt flow in the critical state provides additional useful information to the quantities in Table 2. In the following color Fig. 2 with the streamlines of the melt, the left picture presents the longitudinal vertical section through the space situated in the longitudinal axis of the space in the case simulating the melt flow character in the industrial space and similar Figs. 4, 6, 7, 9, 11, 13, and 14 present the sections in ¼ or ¾ of the space width when the row of electrodes situated in the central longitudinal axis was applied. The right pictures show the flow patterns in the transversal section through the space at X = 4.6 m where X is the longitudinal distance from the inner side of the front wall. The distance X in Fig. 2 was 4 m. Fig. 2 shows the flow patterns marked by streamlines of the melt which represent the case simulating the melt flow in an industrial space (case 1 in Table 4) with level input at 1320 °C and 45% of energy supplied to the first transversal row of electrodes. The projections of the critical trajectories of the controlling phenomenon into planes XY and XZ are in the following Fig. 3. Case 1 from Table 4, illustrated by Figs. 2 and 3, serves as standard of the melt flow character in the industrial melting space. The varying character of the input and the electrode length has only a minor effect on the overall picture of the melt flow. The continuous backflow along the level and spring point located near the output are obvious in Fig. 2, corresponding to the character of the melt flow in industrial melting spaces. The critical sand trajectories (sand dissolution is the controlling phenomenon) in Fig. 3 run near the bottom and elevate to the spring point. The space utilization 0.1 is low and corresponds to values obtained by a simulation of an industrial space [21]. Fig. 4 provides the picture of the longitudinal and transversal flow patterns of the melt when the heating by the central longitudinal row
of electrodes is applied (case 1, Table 2). Compared with the previous case, the value of the space utilization of 0.27 is much higher although the horizontal distribution of energy in the space is very similar. The more apparent helical flow, noticeable in the right picture, appears responsible for the increase. The established flow structure in the longitudinal section is characterized by two forward flows along the level and bottom and by the less noticeable spring point near the input. The presence of hot glass near the level supports the forward flow along the level but the strong stream of cold input melt creates the second forward flow along the bottom. The backflow then occurs between both forward flows. The case corresponds to the melt flow in the space with the simulated glass batch when most of energy is supplied in the input region near the level [19]. The critical trajectory also runs near the bottom; nevertheless, a slight tendency to the helical movement is apparent, as Fig. 5 shows. The character of the middle backflow fades with the increasing melt input temperature, and an approximately uniform flow sets when input melt temperature reaches 1395 °C. The space utilization increases with growing melt input temperature (see Table 2). When the level input of the melt is applied, the helical flow in the transversal section and in the character of critical trajectories is apparent, as well. The former statement is obvious from Fig. 6 (case 1, Table 3). The value of the space utilization of 0.26 is also higher compared with the case with the transversal rows of electrodes. In the longitudinal section, the colder inputting melt sinks to the bottom and the longitudinal circulation occurs with the forward flow near the bottom and backward flow along the level. The spring point occurs near the output and shifts to the input with increasing input temperature of the melt. The critical trajectories run also near the bottom with a tendency to the helical form. The space utilization grows again with increasing temperature. If the temperatures of the inputting melt and the melt average temperature in the space were equivalent, the almost uniform melt flow set in the space at both kinds of inputs. Fig. 7 represents the character of the melt flow for the case of the input close-to-bottom. The almost uniform flow pattern is obvious which can be more easily transformed to the
Fig. 2. The character of the longitudinal and transversal melt flow patterns marked by the streamlines of the melt when the melt is heated by two transversal rows of electrodes, 1.06 and 5.2 m distant from the inner side of the front wall. The central longitudinal section through the space (XZ plane) and the transversal section at the distance of 4.0 m from the inner side of the front wall (YZ plane). The arrows → and ← highlight the main directions of the melt flow, the arrow ↓ points at the input and the spring point position. The level input of the melt is applied with a melt input temperature of 1320 °C (case 1, Table 4).
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Fig. 3. The critical trajectories of sand are projected into planes XY and XZ when sand dissolution is the controlling phenomenon. The heating by two transversal rows of electrodes is applied; the melt input temperature is 1320 °C with the level melt input (case 1, Table 4).
helical-like flow, as the right picture of Fig. 7 shows (case 5, Table 2). The high values of space utilization can be then read from both Tables 2 and 3 achieving and exceeding the values corresponding with the pure uniform flow [8]. The critical trajectories run approximately in the region of the centre of transversal circulations, and are thus almost independent from the circulation intensity (see Fig. 8). The case of a melt input temperature higher than the average one provides a completely different flow picture. As Fig. 9 shows, the hotter input glass is elevated to the level just behind the close-to-bottom input, and continues as the rapid level stream to the output. The character of the longitudinal flow is completed by a slow backflow near the bottom. The arising reverse longitudinal circulations are caused by the slightly unbalanced energy distribution due to inputting hot glass. The transversal circulations are restricted to the upper part of the space only. The same character is evident in the case of the level input where the input hot melt forms a strong straight forward flow along the level. Similarly, the critical trajectories run along the level, as Fig. 10 shows in the case of the close-to-bottom input. Both cases correspond to the case of unbalanced energy distribution with a higher amount of energy near the input. Consequently, the utilization of the space appreciably decreases because of the arising longitudinal circulations, as can be seen from both Tables 2 and 3 (both cases 6).
If both the input and average temperatures of the melt in the space are equivalent, the uniform character of the flow remains in essence preserved at all temperatures. This effect is caused by the approximately balanced energy distribution in the space. The space utilization maintains the high value even at low temperatures, and the observed decrease of the mass performance and the increase of the specific heat losses in Table 2 are caused by slowing of the bubble removal kinetics at decreasing temperature (bubble removal is the controlling phenomenon, because the temperature dependence of its kinetics is steep). In case 2 in Table 4 the central longitudinal row of electrodes shortened to 0.3 m was used. Higher values of space utilization were achieved than both relevant cases with longer electrodes 0.8 and 0.6 m showed, presented as cases 1 in Tables 2 and 3. The reason can most probably be found in the effective heating of the viscous glass melt near the bottom which leads to more intensive transversal circulations. The value of the space utilization of 0.34 is also much higher than the value of 0.1 attained in the space with transversal rows of electrodes, presented as case 1 in Table 4 and depicted in Figs. 2 and 3. Accordingly, the simulation of the melt flow character in the industrial melting spaces did not provide conditions for efficient space utilization. Different installations of the longitudinal row of electrodes were also tested in order to find the optimal configuration. For instance, the
Fig. 4. The character of the longitudinal and transversal melt flow patterns marked by the streamlines of the melt when the melt is heated along the central longitudinal axis of the space. The longitudinal section through the space corresponding ¼ or ¾ of the space width (XZ plane) and the transversal section at the distance of 4.6 m from the inner side of the front wall (YZ plane). The arrows → and ← highlight the main directions of the melt flow, the arrow ↓ points at the spring point position. The close-to-bottom input of melt is applied with a melt input temperature of 1320 °C (case 1, Table 2).
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Fig. 5. The critical trajectories of sand are projected into planes XY and XZ when sand dissolution is the controlling phenomenon. The close-to-bottom input of the melt with a temperature of 1320 °C is applied (case 1, Table 2).
installation of heating electrodes near one of the sidewalls resulted in a decrease of the space utilization at both temperatures 1320 °C and 1420 °C (compare cases 3 and 4 in Table 4 with cases 1 and 5 in Table 3). The reason for that most probably lies in two facts: the intensity of the transversal circulations is lower when only one transversal circulation circle is established instead of two, and the critical trajectory of a particle runs near the longitudinal axis of the space where the longitudinal component of the melt velocity reaches its highest values. The following reciprocal arrangement of electrodes, six to the left side and six to the right side, was chosen to disturb the pathway of the critical trajectory by a reversal of the transversal circulations. Nevertheless, the space utilization values again show a decrease compared to the cases with the central row of electrodes (cases 5 and 6 in Table 4 as compared with cases 1 and 5 in Table 3) and are similar to values attained in the case with all the electrodes close to one sidewall (cases 3 and 4 in Table 4). The critical trajectory running in the central region of transversal rotation showed to be practically unaffected. Consequently, the original installation of the central longitudinal row of electrodes appeared most effective. The transversal circulation may be supported and the balanced state of energy may be improved by stripping off a part of the outside
insulation of the sidewalls. The comparison of results from Table 4 with standard cases in Table 3 proves a beneficial effect of stripping at the lowest temperature of 1320 °C where the space utilization increased from 0.26 to 0.31 (case 1 in Table 3 and case 7 in Table 4). The heat losses increased from 81.8 kJ/kg to 87.6 kJ/kg only, so the reduction of insulation at lower temperatures seems to be promising. As was already described, the system shifts to the balanced state and the space utilization increases if the transfer of the substantial part of energy to the input part of the space is realized. This fact was already apparent from the effect of increasing the melt input temperature presented in Tables 2 and 3. So, the temperature of the inputting melt may be managed by conditions in the anterior space (module), and the proper distribution of energy in the present module is then relevant. Therefore, the part of energy supplied to the first six electrodes was gradually increased from the original 45% up to 100% of the entire energy when a constant melt input temperature of 1320 °C and level input were applied. Electrodes of both 0.6 and 0.3 m length were used. The space utilization increased gradually from the value of 0.26 to 0.32 in cases with electrodes of 0.6 m long (case 1 in Table 3 and cases 10, 12 in Table 4), and from the value of 0.34 to 0.47 in cases with electrodes of 0.3 m long (cases 9, 11, 13, 14 in Table 4) at 80% of energy supplied to the
Fig. 6. The character of the longitudinal and transversal melt flow patterns marked by the streamlines of the melt when the melt is heated along the central longitudinal axis of the melting space. The longitudinal section through the space corresponding ¼ or ¾ of the space width (XZ plane) and the transversal section at the distance of 4.6 m from the inner side of the front wall (YZ plane). The arrows → and ← highlight the main directions of the melt flow, the arrow ↓ points at the spring point position. The level input of melt is applied with a melt input temperature of 1320 °C (case 1, Table 3).
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107
Table 3 The temperature dependences of quantities characterizing the space utilization, melting performance, specific energy consumption, and specific heat losses in the space with the level input of the glass melt. The regular lengths of the electrodes were 0.6 m. Case no.
t (°C)
u (controlling)
τDave, τFref (s)
τG (s)
_ (kg/s) (t/day) M
HLM (kJ/kg)
1 2 3 4 5 6
1320 1345 1370 1395 1420 1445
uF = 0.26 uF = 0.30 uF = 0.37 uF = 0.48 uD = 0.53 uD = 0.16
τFref = 1877 τFref = 1878 τFref = 1878 τFref = 1878 τDave = 1928 τDave = 1892
7223 6281 5069 3904 3634 11,557
4.00345.6 4.60397.4 5.70492.5 7.40639.4 8.00691.2 2.50216.0
81.8 71.3 57.7 44.5 41.5 132.1
first six electrodes. The critical trajectories remained near the space bottom. Substantial changes of the melt flow structure were noticed above this energy value. Fig. 11 presents the picture of the melt flow when 85% of the entire energy was supplied to the first six electrodes. The spring point shifted more closely to the input and almost uniform longitudinal flow developed behind the spring point. This effect was more distinct in the case with shorter electrodes. The critical trajectories replaced to the level, as Fig. 12 shows, and the space utilization still kept at high value. When 90% of energy was supplied to the first six electrodes, the forward working flow with critical trajectories near the level accelerated, and the overall view showed longitudinal circulations with a weak back flow near the bottom. The picture of the flow
patterns is clear from Fig. 13. The new development of longitudinal circulations (new unbalanced state) leads to a decrease of the space utilization in the cases with both electrode lengths to the values of 0.26 and 0.27, respectively (compare cases 17 with 15 and 18 with 16 in Table 4). If the entire energy was supplied to the first six electrodes, more apparent longitudinal circulations developed but the space utilization slightly increased with respect to the previous case characterized by 90% of the energy supplied to the first six electrodes (cases 19 and 20 in Table 4). However, the upper forward flow appeared more massive owing to the higher flow rate of the melt. The character of the melt flow is depicted in Fig. 14.
Fig. 7. The character of the longitudinal and transversal melt flow patterns marked by the streamlines of the melt when the melt is heated along the central longitudinal axis of the melting space. The longitudinal section through the space corresponding ¼ or ¾ of the space width (XZ plane) and the transversal section at the distance of 4.6 m from the inner side of the front wall (YZ plane). The arrows → and ← highlight the main directions of the melt flow, the arrow ↓ points at the spring point position. The close-to-bottom input of melt is applied with a melt input temperature of 1420 °C (case 5, Table 2).
Fig. 8. The critical trajectories of sand are projected into planes XY and XZ when sand dissolution is the controlling phenomenon. The close-to-bottom input of melt with the temperature of 1420 °C is applied (case 5, Table 2).
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Fig. 9. The character of the longitudinal and transversal melt flow patterns marked by the streamlines of the melt when the melt is heated along the central longitudinal axis of the melting space. The longitudinal section through the space corresponding ¼ or ¾ of the space width (XZ plane) and the transversal section at the distance of 4.6 m from the inner side of the front wall (YZ plane). The arrows → and ← highlight the main directions of the melt flow. The close-to-bottom input of melt is applied with a melt input temperature of 1445 °C (case 6, Table 2).
5. Discussion of results The input temperature of melt appears a sensitive factor of the melting efficiency because its values, either lower or higher with respect to the average temperature in the space, indicate an unbalanced energetic state [19]. This state leads to the formation of different kinds of longitudinal circulations, shown by Figs. 4, 6, and 9. At lower input temperatures of melt, the forward flow and critical trajectories move along the bottom maintaining a relatively low temperature. The higher glass viscosity slows down the transversal drift of the critical trajectory to the longitudinal axis (see Fig. 5 with the close-to-bottom input), and restricts the effect of the helical-like flow. At the highest input temperature, the critical trajectory then runs in the hot forward flow along the melt level, as Fig. 9 demonstrates. The overall effect of the melt input temperature is quantitatively summarized in Tables 2 and 3, and demonstrated by Figs. 15 and 16. The values of the space utilization related to the relevant controlling phenomenon, mass melting performance (pull rate), and specific heat losses are plotted as functions of the melt input temperature for both types of melt input. When the higher melt input temperatures are gradually set, the increase of the specific melting performance and decrease of the specific heat losses is apparent up to the input temperature of 1420 °C, as well as the rapid worsening of both values at 1445 °C. The presented values of the specific heat losses are nevertheless relatively low owing to the melt level insulation as a necessary boundary condition at modelling.
Naturally, the values should be higher and the decrease should be more significant in a real case. The increasing or decreasing characters of the curves correspond to the above-mentioned longitudinal energy balance in the space. At an input temperature of 1420 °C, the energy in the space is almost balanced and the either uniform or helical flow can be set in the space; both types of flows are characterized by high values of the space utilization and mass melting performance, and by low values of the specific heat losses. At input temperatures lower or higher than the average temperature in the space, the developed longitudinal circulations disturb the above-mentioned beneficial melt flow types. In this work, the helical melt flow was preferred as the more convenient, because it works also under the presence of weak longitudinal circulations. In addition, the establishment of the only uniform flow appears to be very sensible to the character of heating. The almost parallel course of curves of the space utilization and the mass melting performance in both figures shows that the change of the flow character is the principal factor of the increase of the melting performance. This finding is confirmed by the following Fig. 17 where the percentage contributions of the u increase and τDave decrease to the growth of the mass melting performance are depicted for the close-to-bottom input (related to the values at 1320 °C). The steepness of the curve of uD is considerably higher than shows the curve of τD, consequently, the percentage contributions of the melt flow character are always more significant than the relevant contributions of the time-temperature history. Similar results were obtained for the case with a level input.
Fig. 10. The critical trajectories of bubbles are projected into planes XY and XZ when bubble removal is the controlling phenomenon. The close-to-bottom input of melt with the temperature of 1445 °C is applied (case 6, Table 2).
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Table 4 The values of quantities as the space utilization, the melting performance, the specific energy consumption, and other factors are in the space with the level input of melt. The location of the rows of electrodes and the energy distribution are varied. Case no.
t (°C)
Arrangement
u (controlling)
τDave, τFref (s)
τG (s)
_ (kg/s) (t/day) M
HLM (kJ/kg)
1
1320
uD = 0.10
τDave = 2271
22,239
1.3179.7
251.3
2 3 4 5
1320 1320 1420 1320
uF = 0.34 uF = 0.21 uD = 0.39 uF = 0.20
τFref = 1878 τFref = 1879 τDave = 1917 τFref = 1878
5560 9029 4897 9326
5.2449.3 3.2276.5 5.9509.8 3.1267.8
62.9 102.3 56.0 102.3
6
1420
uF = 0.43
τFref = 1878
4380
6.6570.2
56.0
7 8 9
1320 1420 1320
uF = 0.31 uF = 0.52 uF = 0.34
τFref = 1877 τFref = 1878 τFref = 1878
6023 3614 5560
4.8414.7 8.0691.2 5.2449.3
87.6 52.7 62.9
10
1320
uF = 0.29
τFref = 1877
6566
4.4380.2
74.3
11
1320
uF = 0.38
τFref = 1877
4985
5.8501.1
56.4
12
1320
uF = 0.32
τFref = 1879
5896
4.9423.4
66.8
13
1320
uF = 0.42
τFref = 1879
4448
6.5561.6
50.3
14
1320
uF = 0.47
τFref = 1878
3988
7.25626.4
45.9
15
1320
uD = 0.30
τDave = 2085
6962
4.2362.9
78.8
16
1320
uD = 0.40
τDave = 2059
5163
5.6483.4
58.3
17
1320
uD = 0.26
τDave = 2046
7809
3.7319.7
88.4
18
1320
uD = 0.27
τDave = 2078
7608
3.8328.3
85.9
19
1320
uD = 0.29
τDave = 1938
6719
4.3371.5
76.2
20
1320
2 trans. rows of el. (0.3 m), 45% of energy to the first row Electrodes 0.3 m long Electrodes near one sidewall Electrodes near one sidewall 6 el. left side 6el. right side 6 el. left side 6 el. right side Stripping of insulation (0.5h0) Stripping of insulation (0.5h0) 45% of energy to the first 6 el.(0.3 m) 60% of energy to the first 6 el.(0.6 m) 60% of energy to the first 6 el.(0.3 m) 70% of energy to the first 6 el.(0.6 m) 70% of energy to the first 6 el.(0.3 m) 80% of energy to the first 6 el.(0.3 m) 85% of energy to the first 6 el.(0.6 m) 85% of energy to the first 6 el.(0.3 m) 90% of energy to the first 6 el.(0.6 m) 90% of energy to the first 6 el.(0.3 m) 100% of energy to the First 6 el. (0.6 m) 100% of energy to the First 6 el. (0.3 m)
uD = 0.41
τDave = 1903
4663
6.2535.7
52.9
The following Fig. 18 indicates that the helical character of flow intensifies when the melt input temperature increases although the amount of energy for establishment of the helical melt circulations decreased. The average values of the circulation and longitudinal velocities of the melt were read at the distance of 4.6 m from the inner side of the front wall, and their ratio provided a cursory but instructive view on the melt flow character. The increasing ratio vcirc/vlong indicating the melt transversal circularity is apparent in Fig. 18 and was found also for the space with close-to-bottom input. This fact is caused by the slowing down the longitudinal melt circulations when the system approaches the energy balanced state. Thus, both the approach to the uniform
flow and the more distinct helical flow contribute to the higher space utilization when the melt input temperature increases. If the temperatures of the inputting glass and the average temperature in the space are identical, the space utilization keeps high value at all the temperatures, as results from Table 2. The controlling phenomenon fixes at the bubble removal below 1420 °C, because the fining steeply slows with decreasing temperature. The principal effect of temperature on the mass melting performance and specific heat losses may thus be ascribed to the decrease of the reference fining time τFref. This effect is obvious from Fig. 19 where the curve of the relative reference fining time essentially copies the dependence of the relative mass
Fig. 11. The character of the longitudinal and transversal melt flow patterns marked by the streamlines of the melt when the melt is heated along the central longitudinal axis of the melting space. The longitudinal section through the space corresponding ¼ or ¾ of the space width (XZ plane) and the transversal section at the distance of 4.6 m from the inner side of the input front wall (YZ plane). The arrows → and ← highlight the main directions of the melt flow, the arrow ↓ points at the spring point position. The level input of melt with a melt input temperature of 1320 °C. The length of electrodes is 0.3 m; 85% of energy is supplied to the first six electrodes (case 16, Table 4).
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Fig. 12. The critical trajectories of sand are projected into planes XY and XZ when sand dissolution is the controlling phenomenon. The level input of melt with the temperature of 1320 °C is applied. The length of electrodes is 0.3 m; 85% of energy is supplied to the first six electrodes (case 16, Table 4).
performance while the relative space utilization retains an almost constant value. As is obvious from the figures and numerical results, the transversal circulations needed for the achievement of the helical flow are mostly weak with respect to the existing longitudinal flow, and all the factors how to strengthen them should be the centre of interest. In agreement with [19], the horizontal and vertical balancing of energy distribution was examined to slow the existing longitudinal circulations and to promote the transversal ones and, consequently, to achieve higher space utilization. That is why both the 0.6 and 0.3 m long electrodes were applied when the part of Joulean energy supplied to the first electrodes grew from 45% to 90% in this work. The results of these experiments are amassed in cases 2 and 9–19 in Table 4 and the following Fig. 20 represents the modelling experiments with an electrode length of 0.3 m. The shortening of the electrodes to 0.3 m in case 2 brought the maximal developed energy closer to the bottom, caused the increase of the bottom temperature by about 6 °C, and supported the central ascending stream of the melt. This effect led to the apparent increase of the space utilization. Similar growth is indicated by Table 4 when increasing the amount of energy supplied to the first six electrodes. The further explanation of curves in Fig. 20 and in Table 4 corresponds to considerations about a balanced energetic state and relevant flow character. Bubble removal was the controlling phenomenon
at 45–80% of energy supply to the first six electrodes, because the forward flow moved near the bottom. The shift of the amount of energy to the input from 45% to 80% reduced the intensity of the longitudinal circulations which was indicated by the decrease of melt velocities on the level and also near the bottom – the average maximal melt velocity of the forward flow near the bottom decreased by 15.8% and by 19.9% for the electrode lengths 0.3 and 0.6, respectively. The almost uniform flow, obvious from Fig. 11, was observed already at 70% of energy inputted to the first six electrodes. Simultaneously, the already described circularity of the melt increased from 0.754 to 1.03. Consequently, the tendency to both the uniform and the helical flow led to the increase of the space utilization. The contribution of the helical flow to the increase of the space utilization at low amounts of energy at the input can be assessed from the comparison of cases with and without the evoked transversal circulations. The relatively high value of the space utilization of 0.34 resulted in the case with the central longitudinal row of electrodes and 45% of energy localized to the input (helical flow, case 9, Table 4), whereas the relevant case with two transversal rows of electrodes (without helical flow, case 1, Table 4) provided a space utilization value of only 0.1. When the amount of Joulean energy in the input region rises above 80%, the forward melt flow and critical trajectories of particles shifted to the melt level, and the sand dissolution became the controlling phenomenon, as is clear from Fig. 12. The
Fig. 13. The character of the longitudinal and transversal melt flow patterns marked by the streamlines of the melt when the melt is heated along the central longitudinal axis of the melting space. The longitudinal section through the space corresponding ¼ or ¾ of the space width (XZ plane) and the transversal section at the distance of 4.6 m from the inner side of the front wall (YZ plane). The arrows → and ← highlight the main directions of the melt flow, the arrow ↓ points at the spring point position. The level input of melt with a melt input temperature of 1320 °C. The length of electrodes is 0.3 m; 90% of energy is supplied to the first six electrodes (case 18, Table 4).
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Fig. 14. The character of the longitudinal and transversal melt flow patterns marked by the streamlines of the melt when the melt is heated along the central longitudinal axis of the melting space. The longitudinal section through the space corresponding ¼ or ¾ of the space width (XZ plane) and the transversal section at the distance of 4.6 m from the inner side of the front wall (YZ plane). The arrows → and ← highlight the main directions of the melt flow, the arrow ↓ points at the spring point position. The level input of melt with a melt input temperature of 1320 °C. The length of electrodes is 0.3 m; 100% of energy is supplied to the first six electrodes (case 20, Table 4).
transversal circularity of melt decreased by about 10% between 70 and 90% of energy supplied to the input, and the average velocity of the forward melt flow on the level grew by 33% between 85% and 90% of supplied energy. Both were responsible for the decrease of the space utilization. At 90% of energy supply to the input, the overall character of the longitudinal melt flow clearly showed the transition to the flow type with the relatively fast forward flow along the level and development of a backflow near the bottom, as Fig. 13 shows. Consequently, this flow type with developing longitudinal circulations shows lower space utilization. The results are in agreement with the achieved character of the melt flow in a space with a simulated batch blanket [19]. The sudden increase of the space utilization and the relevant growth of the melting performance between 90 and 100% of the transferred Joulean energy appears surprising, as well as the decrease of the specific heat losses. This fact is also obvious from Fig. 20 and from Table 4 (cases 19 and 20). The utilization decrease should rather be expected with further development of the longitudinal circulations. Nevertheless, Fig. 21 helps to explain the opposite behaviour. The curve of the relative space utilization copies the development of the relative mass melting performance well and thus shows the dominating affect of the melt flow character up to 90% of the transferred energy. At 100% of the transferred energy, however, the space utilization and the melting kinetics – represented by the average sand dissolution time – play the almost equivalent role. The reduced values of the average sand dissolution times between 90 and 100% of energy raise the melting performance. As a result, the effect of the developed longitudinal circulations is
weakened and the space utilization then increases. This leads to further increase of the melting performance. The strengthening of the helical flow and its significance for the space utilization at a slightly unbalanced energy distribution was also modelled by stripping a part of the sidewall insulation (cases 7 and 8 in Table 4). As the higher heat losses only very slightly raised the specific heat losses, this step aspires as a usable factor of melt flow control. On the other hand, the electrode arrangements other than the central longitudinal row (cases 3–6 in Table 4) did not prove their efficiency. 6. Conclusion The character of the melt flow can become a valuable factor the significance of which for glass melting may be comparable with the time temperature conditions of the process. This fact is indicated by the theoretical considerations and proved by the results of the mathematical modelling. In agreement with the results achieved by modelling involving simulated batch loading [19], a considerable increase of the melting performance and, consequently, a decrease of the specific heat losses can be achieved under conditions of controlled melt flow. The applied quantity space utilization provides a quantitative evaluation of the melt flow quality with respect to the melting phenomena. The longitudinal distribution of energy supplied to the melting space appears to be the main factor of the flow control. Another important factor sharing in the formation of the melt flow character is the melt flow rate; however, its values are restricted to the accomplishment of all the melting phenomena inside the space. Two final beneficial melt flow characters
Fig. 15. The values of the space utilization of the controlling phenomenon u, mass melting _ and specific heat losses HLM as a function of the melt input temperature performance M, tinput. The space with the close-to-bottom input of melt. The lines serve only as a guide for the eyes.
Fig. 16. The values of the space utilization of the controlling phenomenon u, mass melting _ and specific heat losses HLM as a function of the melt input temperature performance M, tinput. The space with the level input of melt.
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Fig. 17. The percentage contributions of the uD increase and τDave decrease (related to the _ The close-to-bottom values at 1320 °C) to the increase of the mass melting performance M. input of melt.
may be selected: the uniform flow and the helical flow evoked by proper transversal energy distribution. Whereas the uniform flow does not almost tolerate the simultaneous presence of the longitudinal circulation components, the helical flow admits longitudinal circulations of low intensity. That is why the application of the helical flow was the subject of this work aiming at modelling the melting (homogenization) modulus of a segment furnace. The simplest corresponding heating arrangement was realized by the central longitudinal row of electrodes. Both the decreasing difference between the melt input and the average temperature and the substantial supply of energy to the melt input led to balanced horizontal energy distribution, and resulted in an increase of the space utilization as an indicator of melting performance and specific heat losses. The calculated values of the space utilization were considerably higher as compared with the values achieved by simulation of the melt flow in an industrial melting space, which is usually characterized by intensive longitudinal melt circulations. Although the achieved intensity of the transversal circulations was relatively low, the significance of the simulated helical flow was high and was thus proven, as in [19]. The fact that transversal circulations of only a low intensity can be achieved poses a requirement to maintain the horizontal energy distribution near the balanced state. When the melt input
Fig. 18. The space utilization and the ratio of the average value of the transversal circulation melt velocity vcirc to the longitudinal melt velocity vlong as a function of the melt input temperature at the distance of 4.6 m from the inner side of the input front wall. Each velocity was measured in four points of the transversal section through the space. The space with the level input of melt.
Fig. 19. The dependences of the relative values of the space utilization uF/uF0, the mass _ M _ 0 , and the reference bubble removal time τFref0/τFref (its melting performance M= reciprocal value) on the melt input temperature tinput. The values of the quantities were related to the values at 1320 °C. The close-to-bottom input of melt.
temperature was 100 °C lower than the average temperature in the space, the supply of about 70–80% of Joulean energy to the input region of the space corresponded to the approximately balanced state here. The setting up of a helical flow of the described intensity in the modulus can thus facilitate the way to glass melting in a relatively small and efficient two-space melter. When the melt input temperature increases or the relevant energy to the melt input region is supplied to approach the balanced state of energy, the uniform flow gradually takes the beneficial glass melting role. The question of the application of a pure uniform flow therefore remains relevant. The attempts to arrange the energy sources to set the uniform flow by planar heating in [19] led, however, to arising Bernard's circulation flows and to very low values of space utilization. Despite these results, the application of the uniform flow under conditions of very high flow rates and a high portion of energy supplied to the input region of the space seems to be promising. This will also be a subject of subsequent modelling experiments.
_ and specific heat losses HLM as Fig. 20. The space utilization u, mass melting performance M, a function of the part of energy brought to the first six electrodes. The level input of melt, electrodes 0.3 m long.
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References [1] [2] [3] [4] [5] [6] [7] [8] [9] [10] [11]
[12] [13] [14] [15] [16] [17] Fig. 21. The dependences of the relative values of the space utilization uD/uD0, the mass _ M _ 0 , and the average sand dissolution time τDave0/τDave (its melting performance M= reciprocal value) on the amount of energy brought to the first six electrodes. The values of quantities indexed by 0 were related to the values calculated at 1320 °C. A level input of melt.
Acknowledgement This work was financially supported from specific university research (MSMT No. 20-SVV/2016).
[18] [19] [20] [21]
V. Mulholland, US Patent No. 2 068 925 (1937). H.L. Penberthy, US Patent No. 3 268 320 (1966). F.V. Atkeson, US Patent No. 3 305 340 (1967). Y. Takashi, Japan Patent No. S55 116 632 (1980). S. Heurtey, French Patent No. 2 787 784 A1 (2000). M. Polák, L. Němec, J. Non-Cryst. Solids 357 (2011) 3108. P. Cincibusová, L. Němec, Glass Technol.: Eur. J. Glass Sci. Technol. A 53 (2012) 150. L. Němec, P. Cincibusová, Glass Technol.: Eur. J. Glass Sci. Technol. A 53 (2012) 279. M. Polák, L. Němec, J. Non-Cryst. Solids 358 (2012) 1210. P. Cincibusová, L. Němec, Glass Technol.: Eur. J. Glass Sci. Technol. A 56 (2015) 52. G. Aronchik, B.A. Purnode, D. Rue, Proceedings of the 9th International Seminar on Mathematical Modelling of Furnace Design and Operation, Velké Karlovice (CZ), 2007 23–32. G. Villeroy de Galhau, Y. Lefrere, M. Rayer, Demande Internationale de PCT brevet, Numero de Publication International WO (2013/132 184 A1). J.L. Barton, Boletin de la espaňola de ceramica y vidrio, Madrid, 1992 165–184. C.P. Ross, Am. Ceram. Soc. Bull. 83 (2004) 18. D.J. Bender, J.G. Hnat, A.F. Litka, L.W. Donaldson Jr., G.K. Ridderbusch, D.J. Tessari, J.R. Sacks, Glass Ind. 3 (1991) 10. O. Sakamoto, Res. Reports, 59, Asahi Glass Co. Ltd, 2009 55060. L. Němec, M. Polák, P. Cincibusová, M. Jebavá, J. Brada, M. Trochta, J. Kloužek, PCT Application No. PCT/CZ2013/000102. Glass Furnace Model 4.17, Glass Service, Inc., Vsetín, Czech Republic, 2015. M. Jebavá, P. Dyrčíková, L. Němec, J. Non-Cryst. Solids 430 (2015) 52. L. Němec, M. Vernerová, P. Cincibusová, M. Jebavá, J. Kloužek, Ceramics-Silikáty 56 (2012) 367. M. Jebavá, L. Němec, J. Brada, (prepared for publication).
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Journal of Non-Crystalline Solids journal homepage: www.elsevier.com/locate/jnoncrysol
Bubble removal and sand dissolution in an electrically heated glass melting channel with defined melt flow examined by mathematical modelling Lukáš Hrbek ⁎, Petra Kocourková, Marcela Jebavá, Petra Cincibusova, Lubomír Němec Laboratory of Inorganic Materials, Joint Workplace of the University of Chemistry and Technology Prague, Technická 5, 166 28 Prague 6, Czech Republic The Institute of Rock Structure and Mechanics of the ASCR, v.v.i., V Holešovičkách 41, 182 09 Prague 8, Czech Republic
a r t i c l e
i n f o
Article history: Received 16 March 2016 Received in revised form 31 October 2016 Accepted 11 November 2016 Available online 16 November 2016 Keywords: Glass melt flow Mathematical modelling Energy distribution Space utilization Melting performance
a b s t r a c t The electrically heated glass melting channel as a part of the segmented melting furnace was examined by mathematical modelling. Different melt flow characters were set up by proper configurations of the heating electrodes in the channel with either level or close-to-bottom melt input. The sand particle dissolution and bubble removal of defined sizes were followed up to the achievement of the critical state. This was characterized by the termination of the less effective melting phenomenon just before the output from the channel. The utilization of the melting space, the melting performance, and the specific heat losses in the critical state were evaluated. The effect of the melt input character and melt input temperature, electrode length, and energy distribution were investigated. The results have shown that the best results were attained when the energy distribution in the channel was balanced or when it was near the balanced state. Hence, no or only weak longitudinal circulations of the melt arose in the space and the helical-like melt flow could be set. This state was achieved when the melt input temperature was equivalent or not far from the average temperature of the melt in the space. Such as state can be set up by an energy shift to the regions with lower temperature and by enhancement of the transversal melt circulations. © 2016 Elsevier B.V. All rights reserved.
1. Introduction The melt flow character plays a significant role in the continual glass melting process owing to its considerable impact on the history of the homogenization phenomena accomplished in the melt – quartz dissolution, bubble removal, and chemical homogenization. In the industrial melting process, the batch conversion in the batch blanket and phenomena in the melt are practically serially ordered. Besides the batch conversion rate, the slow homogenization of the melt may also limit the melting performance of the entire melting process. The naturally set melt flow in the horizontal glass melting spaces is characterized by powerful longitudinal circulations which are indicated by the broad residence time distribution function of the melt, and consequently by the short critical trajectories along which the homogenization phenomena occur. Due to this effect, glass producers are forced to build large glass melting furnaces with low specific performance and with high specific heat losses. The way to ensure better cooperation of the melt flow with the melting process leads to either uniform melt flow or to efficient transversal melt circulations resulting in a helical-like flow, both ⁎ Corresponding author. E-mail address: [email protected] (L. Hrbek).
http://dx.doi.org/10.1016/j.jnoncrysol.2016.11.013 0022-3093/© 2016 Elsevier B.V. All rights reserved.
characterized by lower dead spaces and a narrower residence time distribution function. The strengthening of the transversal circulation appears easier to implement under industrial melting conditions; several patents describe the use of different mechanical or heating means to fulfil the task to set the helical-like melt flow [1–5]. In fact, the superposition of the evoked transversal circulations on the already existing longitudinal ones leads to the desired helical-like flow only when the ratio between the transversal and longitudinal velocity component of the melt is sufficiently high. The character of the helical-like melt flow and its relation to the running homogenization phenomena was studied in [6–10]. The relative quantity called utilization of the space has been introduced. The quantity indicates which part of the melting space is used for either the dissolution of quartz relicts or bubble removal under a given character of the melt flow. Applying space utilization, the temperature conditions of efficient helical-like flow were determined in the model channel by mathematical modelling. The results have shown that melt flow structures were attained – advantageous simultaneously for both phenomena – at relatively high ratios between the transversal and longitudinal temperature gradients. The ratios of temperature gradients corresponding to highest utilization values of 0.6–0.8 move mostly between 5 and 10 [6,8–10]. However, it would be difficult to realize the corresponding melt velocity ratios in the classic
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melting space with the batch blanket owing to the existing strong longitudinal melt circulations; therefore, the published patented solutions appear less probable. The results of mathematical modelling may nevertheless assist in the construction of special melting spaces without a batch blanket if the previous batch conversion to glass was ensured in a separated space or region. Several ways of rapid batch conversion have been published in the literature: the examples include submerged combustion [11–12], mechanical stirring of the converting batch [13–14], or in flight melting [15–16]. In the subsequent melting module, the desired helical flow may be set up relatively easily with the currently used heating elements such as the application of Joule heat and electrodes. Such a module manifests a very high homogenization ability up to 10 tons/(m3 day) and correspondingly low heat losses [17]. However, the detailed conditions of the module application are not known yet whereas the following are: convenient average temperature in the module, the acceptable difference between the input and average temperature of the melt, and the efficient energy distribution inside the module. The detailed investigation of the mentioned factors in the glass melting module heated by electrodes is the subject of this work. 2. Theoretical The quantity “utilization of the melting space u” has been used for the evaluation of the character of the melt flow with respect to sand dissolution and bubble removal [6–10]. The utilization of the continual space for bubble removal (fining) uF expresses the relation between the reference fining time in a quiescent melt τFref and the theoretical mean residence time of the melt in the space under critical conditions τG. Similarly, the utilization for sand dissolution uD expresses the relation between the average sand dissolution time in the space, τDave and τG [6]. The critical state then describes the situation when the bubble of the initially minimal radius attains the melt level just at the output from the space, or the initially maximal sand particle dissolves right there. u F;D ¼
τHref V ; τG ¼ ; u∈h0; 1i τG V_
ð1Þ
where τHref is either τFref or τDave, V is the volume of the space (m3), and V_ is the volume flow rate (melting performance or pull rate) (m3/s). For the plug flow, τHref = τG is valid, so uF,D = 1 [8]. Both values of the space utilization may be involved in the expressions for the heat losses of the process and for the melting performance. In the critical state, the values of the melting performance and specific heat losses represent the maximum and minimum values, respectively. If both homogenization phenomena are considered as parallel, then the less efficient phenomenon is the controlling one. The specific heat losses of the space through boundaries decrease, and the performance of the melting process increases with space utilization according to: L
H LM
H_ τDave 1 ¼ or H LM ρV uD
VuD Vu F or V_ ¼ V_ ¼ τDave τ Fref
L H_ τ Fref 1 ¼ ρV u F
The space utilization for the sand dissolution uD may be expressed with the assistance of two fractions of dead spaces – the fraction of dead space for the melt flow mG and the fraction of space of the sand dissolution as the overprocessing mD. Similarly, the space utilization for the bubble removal uF can be expressed through the fraction of virtual dead space for bubble removal mvirt and virtual bubble rising distance hvirt [9]. The mentioned quantities provide a more detailed view of the character of the melt flow. Only the values of the space utilization as a final quantity will be applied in this work. If bubble nucleation on the sand particles does not occur, both phenomena run simultaneously, so the less efficient phenomenon becomes the controlling one. When the melting conditions are varied and sand dissolution is the controlling phenomenon, the effect of melt flow changes – described by the utilization value uD may be separated from the effect of different time-temperature histories described by the value of τDave. If bubble removal controls the melting, both effects are separable only when the average temperature in the space varies – at a constant average temperature, the value of τFref is constant. The quantities defined by Eqs. (1)–(3a, b) may be acquired by modelling the critical state of bubble removal (in the critical state, the initial minimal bubble is removed just at the space exit) or the critical state of sand dissolution (the maximal particle is dissolved just at the output) in the melting space with adjusted flow patterns. Here, the demanded flow patterns have been set by proper energy distribution in the model melting space. The set up of the controlled flow in glass melting spaces substantially depends on the distribution of energy delivered to the melting space in the case when no other tool is used to affect the melt flow. The specific energy consumption of a melting space with electric or other inner heating is given by: H 0M ¼ H TM þ H LM
ð4Þ
where HTM is the theoretical energy to convert the inputting batch and to heat the arising melt to the space exit temperature. The crucial condition of the control of the favorable melt flow is the balanced distribution of delivered energy between the input (batch) region and subsequent region where the melting phenomena are completed. If the distribution is balanced, the necessary energetic condition for the uniform or efficient helical flow [19] is fulfilled; otherwise, clockwise longitudinal circulations occur with energy being in excess in the input region, and counterclockwise when the energy supplied here is lower than a balanced one. Most of energy should regularly be delivered to the input region in order to convert the batch, to heat the arising melt, and to cover the heat losses of the region while the needed energy in the subsequent part of the space includes only the heat losses. If the fraction of the input region is designated by ξ, Eq. (4) can be written as [19]: H 0M ¼ H TM þ ξH LM þ ð1−ξÞH LM
ð5Þ
ð2a; bÞ
ð3a; bÞ
where HLM are the specific heat losses (J/kg), H_ L is the total heat flux across the space boundaries (J/s) and ρ is the glass density (kg/m3). The quantity τFref is the fining time which the critical bubble needs to ascend the distance h0 in a quiescent liquid at average temperature in the space; the details of τFref calculation are given in [7]. The former expressions in Eqs. (2a, ba, b) and (3a, ba, b) are valid for the case of sand dissolution as the controlling phenomenon, and the latter ones for the controlling phenomenon being bubble removal.
The energetic equilibrium in the melting space is attained if the specific energy given by the term HTM + ξHLM is delivered to the input region Hglass1, and the energy provided for the subsequent region Hglass2 is equivalent to (1 − ξ)HLM. Usually, the inequality Hglass1 b HTM + ξHLM is valid in horizontal industrial melting furnaces, so intensive counterclockwise longitudinal circulations set up and restrict the melt flow control. In addition, the vertical and other detailed distribution of energy in each region play the role, and local convection currents can be expected even though an energetic balance exists. This work tries to reveal the best conditions to achieve high space utilization in the common modulus for sand dissolution and fining when the type of the melt input is varied, as well as the average and input temperatures, and the energy distribution inside the modulus.
L. Hrbek et al. / Journal of Non-Crystalline Solids 456 (2017) 101–113
3. Calculation procedure and conditions The model melting space was chosen for calculations corresponding to the small horizontal melting furnace, as is obvious form the side view in Fig. 1. A Glass Furnace Model was used for mathematical modelling [18]. The model describes the calculation of the temperature, velocity and electric power fields, obtained from the solution of the relevant conservation equations. Their solution is coupled with submodels of sand dissolution and bubble removal, prepared in cooperation with authors´ workplace. The melt, sand particle and bubble trajectories are obtained along with the kinetics of particles along their pathways. The transversal barrier from the refractory material on the right side of the space served as the reference mark where the sand dissolution or bubble removal should be terminated – the achievement of the critical state. The either close-to-bottom or level input of the raw melt was assumed in the segmented melter, so both ways were tested in this work. The close-to-bottom input of the glass melt in Fig. 1 was located in the centre of the input front wall and had a width of 1 m and height of 0.25 m. The other case with the level input involved a strip of glass level close to the front wall with the width of 1 m and the length of 0.2 m. 16 vertical bottom electrodes were located regularly in the longitudinal axis of the space. The regular height of electrodes in the case with the bottom input was 0.8 m, and was 0.6 and 0.3 m in the case with the level input. Two transversal rows, each having six electrodes, were also applied at distances of 1.06 m and 5.2 m from the inner side of the front wall to simulate roughly the melt flow arrangement in an industrial furnace. Two layers of refractory materials formed the walls and bottom of the space. The free level of glass was insulated in the case of the level input owing to the necessary boundary condition. The input and output melt velocities had a full-parabolic profile for the close-to-bottom input. A half parabolic profile in the X-direction and the full parabolic profile in the Y-direction were set for the level input. Non-slip conditions, i.e. zero melt velocities were assumed on the solid boundaries, and the free level condition on the boundary between the atmosphere and glass melt. The type of float glass was chosen as the model glass. The temperature dependence of the glass density and kinematic viscosity in the temperature interval 900–1800 °C are presented in [19]. The raw melt containing sand particles and bubbles entered the melting modulus. The average sand dissolution rate and average bubble growth rates obtained by laboratory experiments were used to follow the history of the phenomena in the melting modulus. The temperature dependences of both quantities are presented in [19], as well. The semiempirical model of bubble behaviour was applied; the model takes into account the changes of the bubble size as well as the bubble composition at varying temperature [20]. The bubbles with an initial radius of 5 × 10−5 m as the smallest ones (experience from laboratory melts) and the sand particles of 5 × 10−4 m
103
Table 1 The energy distribution set-up to the single pairs of electrodes in the case with the longitudinal row of electrodes. No. of electrode pairs
1
2
3
4
5
6
7
8
Power supply in %
15
15
15
15
12
10
10
8
as the maximal ones (coming from the sieve analysis) were chosen for tracing. The history of around 104 bubbles and sand particles with regularly located starting points at the given input were tracked using the average rates of sand dissolution and bubble growth applied in the semiempirical model of bubble behaviour. Bubble nucleation inside the space was not considered. The sand trajectories were calculated in accord with the velocity components of the melt flow whereas the bubble trajectories were obtained as a result of the vx and vy components of the melt velocity and the sum of the vz component with the instant bubble rising velocity according to the Stokes' law. The trajectories and sand radii were calculated with the time step mostly at 1 s and the time step for bubble radii calculation at 0.1 s. A calculation grid was used with a distance of 2.5 cm between grid points. The controlling phenomenon was characterized by the fact that the critical particle (sand or bubble) reached the location above the transversal refractory barrier in front of the output, i.e. the critical particle had the highest x-coordinate. The given controlling phe_ nomenon then determined the critical mass melting performance M, the mean residence time of the melt in the space τG, and the average sand dissolution time τDave. The value of τFref was obtained from Eq. (3b) in [7] and the values of both space utilizations from Eq. (1). The specific energy consumption was calculated according Eq. (2a, b). The input temperature in individual calculations was varied between 1320 and 1445 °C at a constant average temperature of 1420 °C in the space. The level melt input and the close-to-bottom input were applied. In another set of calculations, the equivalent bottom input temperatures and average melt temperatures were applied between 1320 and 1420 °C. Finally, the amount of energy supplied to the first six electrodes was increased from 45% to 60, 70, 85 and 100% at a melt input temperature of 1320 °C. The modified configurations of the transversal rows of electrodes and the partial stripping of the insulation of the side walls were also examined when the level input of the melt was applied. Table 1 shows the energy distribution in single pairs of electrodes in the case with the longitudinal row of electrodes.
4. Results of calculations In the first run of calculations, the space with the close-to-bottom input was investigated. The input temperature varied between 1320 and 1445 °C with the constant average temperature inside the space
Fig. 1. The view of the central longitudinal section through the melting modulus with the close-to-bottom input of the glass melt. The inner length is 6.77 m (6.225 m to the transversal barrier made from the refractory material), the width is 2 m, and the height of the glass layer is 1 m.
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Table 2 The values of the quantities characterizing the space utilization, melting performance, specific energy consumption, and specific heat losses in the space with the close-to-bottom input of glass melt. The length of the electrodes was 0.8 m. Case no.
t (°C)
u (controlling)
τDave, τFref (s)
τG (s)
_ (kg/s) (t/day) M
HLM (kJ/kg)
1 2 3 4 5 6 7 8 9 10
1320 1345 1370 1395 1420 1445 1320–1320 1345–1345 1370–1370 1395–1395
uD = 0.27 uD = 0.31 uD = 0.37 uD = 0.46 uD = 0.54 uF = 0.25 uF = 0.54 uF = 0.61 uF = 0.65 uF = 0.68
τDave = 2537 τDave = 2291 τDave = 2128 τDave = 1969 τDave = 1855 τFref = 1878 τFref = 11.594 τFref = 7529 τFref = 4808 τFref = 3024
9387 7314 5741 4400 3426 7611 21,461 12,298 7433 4477
3.00259.2 3.85332.6 4.90423.4 6.40553.0 8.22710.0 3.70319.7 1.32112.3 2.30198.7 3.80328.3 6.30544.3
155.4 121.4 95.5 73.2 56.7 126.7 365.2 209.6 126.8 76.5
of 1420 °C. Subsequently, the input and average temperature were equivalent but varied between 1320 and 1420 °C. The relevant calculated values are assembled in Table 2. Only the values of the controlling phenomenon are listed. The established character of the melt flow in the critical state provides additional useful information to the quantities in Table 2. In the following color Fig. 2 with the streamlines of the melt, the left picture presents the longitudinal vertical section through the space situated in the longitudinal axis of the space in the case simulating the melt flow character in the industrial space and similar Figs. 4, 6, 7, 9, 11, 13, and 14 present the sections in ¼ or ¾ of the space width when the row of electrodes situated in the central longitudinal axis was applied. The right pictures show the flow patterns in the transversal section through the space at X = 4.6 m where X is the longitudinal distance from the inner side of the front wall. The distance X in Fig. 2 was 4 m. Fig. 2 shows the flow patterns marked by streamlines of the melt which represent the case simulating the melt flow in an industrial space (case 1 in Table 4) with level input at 1320 °C and 45% of energy supplied to the first transversal row of electrodes. The projections of the critical trajectories of the controlling phenomenon into planes XY and XZ are in the following Fig. 3. Case 1 from Table 4, illustrated by Figs. 2 and 3, serves as standard of the melt flow character in the industrial melting space. The varying character of the input and the electrode length has only a minor effect on the overall picture of the melt flow. The continuous backflow along the level and spring point located near the output are obvious in Fig. 2, corresponding to the character of the melt flow in industrial melting spaces. The critical sand trajectories (sand dissolution is the controlling phenomenon) in Fig. 3 run near the bottom and elevate to the spring point. The space utilization 0.1 is low and corresponds to values obtained by a simulation of an industrial space [21]. Fig. 4 provides the picture of the longitudinal and transversal flow patterns of the melt when the heating by the central longitudinal row
of electrodes is applied (case 1, Table 2). Compared with the previous case, the value of the space utilization of 0.27 is much higher although the horizontal distribution of energy in the space is very similar. The more apparent helical flow, noticeable in the right picture, appears responsible for the increase. The established flow structure in the longitudinal section is characterized by two forward flows along the level and bottom and by the less noticeable spring point near the input. The presence of hot glass near the level supports the forward flow along the level but the strong stream of cold input melt creates the second forward flow along the bottom. The backflow then occurs between both forward flows. The case corresponds to the melt flow in the space with the simulated glass batch when most of energy is supplied in the input region near the level [19]. The critical trajectory also runs near the bottom; nevertheless, a slight tendency to the helical movement is apparent, as Fig. 5 shows. The character of the middle backflow fades with the increasing melt input temperature, and an approximately uniform flow sets when input melt temperature reaches 1395 °C. The space utilization increases with growing melt input temperature (see Table 2). When the level input of the melt is applied, the helical flow in the transversal section and in the character of critical trajectories is apparent, as well. The former statement is obvious from Fig. 6 (case 1, Table 3). The value of the space utilization of 0.26 is also higher compared with the case with the transversal rows of electrodes. In the longitudinal section, the colder inputting melt sinks to the bottom and the longitudinal circulation occurs with the forward flow near the bottom and backward flow along the level. The spring point occurs near the output and shifts to the input with increasing input temperature of the melt. The critical trajectories run also near the bottom with a tendency to the helical form. The space utilization grows again with increasing temperature. If the temperatures of the inputting melt and the melt average temperature in the space were equivalent, the almost uniform melt flow set in the space at both kinds of inputs. Fig. 7 represents the character of the melt flow for the case of the input close-to-bottom. The almost uniform flow pattern is obvious which can be more easily transformed to the
Fig. 2. The character of the longitudinal and transversal melt flow patterns marked by the streamlines of the melt when the melt is heated by two transversal rows of electrodes, 1.06 and 5.2 m distant from the inner side of the front wall. The central longitudinal section through the space (XZ plane) and the transversal section at the distance of 4.0 m from the inner side of the front wall (YZ plane). The arrows → and ← highlight the main directions of the melt flow, the arrow ↓ points at the input and the spring point position. The level input of the melt is applied with a melt input temperature of 1320 °C (case 1, Table 4).
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105
Fig. 3. The critical trajectories of sand are projected into planes XY and XZ when sand dissolution is the controlling phenomenon. The heating by two transversal rows of electrodes is applied; the melt input temperature is 1320 °C with the level melt input (case 1, Table 4).
helical-like flow, as the right picture of Fig. 7 shows (case 5, Table 2). The high values of space utilization can be then read from both Tables 2 and 3 achieving and exceeding the values corresponding with the pure uniform flow [8]. The critical trajectories run approximately in the region of the centre of transversal circulations, and are thus almost independent from the circulation intensity (see Fig. 8). The case of a melt input temperature higher than the average one provides a completely different flow picture. As Fig. 9 shows, the hotter input glass is elevated to the level just behind the close-to-bottom input, and continues as the rapid level stream to the output. The character of the longitudinal flow is completed by a slow backflow near the bottom. The arising reverse longitudinal circulations are caused by the slightly unbalanced energy distribution due to inputting hot glass. The transversal circulations are restricted to the upper part of the space only. The same character is evident in the case of the level input where the input hot melt forms a strong straight forward flow along the level. Similarly, the critical trajectories run along the level, as Fig. 10 shows in the case of the close-to-bottom input. Both cases correspond to the case of unbalanced energy distribution with a higher amount of energy near the input. Consequently, the utilization of the space appreciably decreases because of the arising longitudinal circulations, as can be seen from both Tables 2 and 3 (both cases 6).
If both the input and average temperatures of the melt in the space are equivalent, the uniform character of the flow remains in essence preserved at all temperatures. This effect is caused by the approximately balanced energy distribution in the space. The space utilization maintains the high value even at low temperatures, and the observed decrease of the mass performance and the increase of the specific heat losses in Table 2 are caused by slowing of the bubble removal kinetics at decreasing temperature (bubble removal is the controlling phenomenon, because the temperature dependence of its kinetics is steep). In case 2 in Table 4 the central longitudinal row of electrodes shortened to 0.3 m was used. Higher values of space utilization were achieved than both relevant cases with longer electrodes 0.8 and 0.6 m showed, presented as cases 1 in Tables 2 and 3. The reason can most probably be found in the effective heating of the viscous glass melt near the bottom which leads to more intensive transversal circulations. The value of the space utilization of 0.34 is also much higher than the value of 0.1 attained in the space with transversal rows of electrodes, presented as case 1 in Table 4 and depicted in Figs. 2 and 3. Accordingly, the simulation of the melt flow character in the industrial melting spaces did not provide conditions for efficient space utilization. Different installations of the longitudinal row of electrodes were also tested in order to find the optimal configuration. For instance, the
Fig. 4. The character of the longitudinal and transversal melt flow patterns marked by the streamlines of the melt when the melt is heated along the central longitudinal axis of the space. The longitudinal section through the space corresponding ¼ or ¾ of the space width (XZ plane) and the transversal section at the distance of 4.6 m from the inner side of the front wall (YZ plane). The arrows → and ← highlight the main directions of the melt flow, the arrow ↓ points at the spring point position. The close-to-bottom input of melt is applied with a melt input temperature of 1320 °C (case 1, Table 2).
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Fig. 5. The critical trajectories of sand are projected into planes XY and XZ when sand dissolution is the controlling phenomenon. The close-to-bottom input of the melt with a temperature of 1320 °C is applied (case 1, Table 2).
installation of heating electrodes near one of the sidewalls resulted in a decrease of the space utilization at both temperatures 1320 °C and 1420 °C (compare cases 3 and 4 in Table 4 with cases 1 and 5 in Table 3). The reason for that most probably lies in two facts: the intensity of the transversal circulations is lower when only one transversal circulation circle is established instead of two, and the critical trajectory of a particle runs near the longitudinal axis of the space where the longitudinal component of the melt velocity reaches its highest values. The following reciprocal arrangement of electrodes, six to the left side and six to the right side, was chosen to disturb the pathway of the critical trajectory by a reversal of the transversal circulations. Nevertheless, the space utilization values again show a decrease compared to the cases with the central row of electrodes (cases 5 and 6 in Table 4 as compared with cases 1 and 5 in Table 3) and are similar to values attained in the case with all the electrodes close to one sidewall (cases 3 and 4 in Table 4). The critical trajectory running in the central region of transversal rotation showed to be practically unaffected. Consequently, the original installation of the central longitudinal row of electrodes appeared most effective. The transversal circulation may be supported and the balanced state of energy may be improved by stripping off a part of the outside
insulation of the sidewalls. The comparison of results from Table 4 with standard cases in Table 3 proves a beneficial effect of stripping at the lowest temperature of 1320 °C where the space utilization increased from 0.26 to 0.31 (case 1 in Table 3 and case 7 in Table 4). The heat losses increased from 81.8 kJ/kg to 87.6 kJ/kg only, so the reduction of insulation at lower temperatures seems to be promising. As was already described, the system shifts to the balanced state and the space utilization increases if the transfer of the substantial part of energy to the input part of the space is realized. This fact was already apparent from the effect of increasing the melt input temperature presented in Tables 2 and 3. So, the temperature of the inputting melt may be managed by conditions in the anterior space (module), and the proper distribution of energy in the present module is then relevant. Therefore, the part of energy supplied to the first six electrodes was gradually increased from the original 45% up to 100% of the entire energy when a constant melt input temperature of 1320 °C and level input were applied. Electrodes of both 0.6 and 0.3 m length were used. The space utilization increased gradually from the value of 0.26 to 0.32 in cases with electrodes of 0.6 m long (case 1 in Table 3 and cases 10, 12 in Table 4), and from the value of 0.34 to 0.47 in cases with electrodes of 0.3 m long (cases 9, 11, 13, 14 in Table 4) at 80% of energy supplied to the
Fig. 6. The character of the longitudinal and transversal melt flow patterns marked by the streamlines of the melt when the melt is heated along the central longitudinal axis of the melting space. The longitudinal section through the space corresponding ¼ or ¾ of the space width (XZ plane) and the transversal section at the distance of 4.6 m from the inner side of the front wall (YZ plane). The arrows → and ← highlight the main directions of the melt flow, the arrow ↓ points at the spring point position. The level input of melt is applied with a melt input temperature of 1320 °C (case 1, Table 3).
L. Hrbek et al. / Journal of Non-Crystalline Solids 456 (2017) 101–113
107
Table 3 The temperature dependences of quantities characterizing the space utilization, melting performance, specific energy consumption, and specific heat losses in the space with the level input of the glass melt. The regular lengths of the electrodes were 0.6 m. Case no.
t (°C)
u (controlling)
τDave, τFref (s)
τG (s)
_ (kg/s) (t/day) M
HLM (kJ/kg)
1 2 3 4 5 6
1320 1345 1370 1395 1420 1445
uF = 0.26 uF = 0.30 uF = 0.37 uF = 0.48 uD = 0.53 uD = 0.16
τFref = 1877 τFref = 1878 τFref = 1878 τFref = 1878 τDave = 1928 τDave = 1892
7223 6281 5069 3904 3634 11,557
4.00345.6 4.60397.4 5.70492.5 7.40639.4 8.00691.2 2.50216.0
81.8 71.3 57.7 44.5 41.5 132.1
first six electrodes. The critical trajectories remained near the space bottom. Substantial changes of the melt flow structure were noticed above this energy value. Fig. 11 presents the picture of the melt flow when 85% of the entire energy was supplied to the first six electrodes. The spring point shifted more closely to the input and almost uniform longitudinal flow developed behind the spring point. This effect was more distinct in the case with shorter electrodes. The critical trajectories replaced to the level, as Fig. 12 shows, and the space utilization still kept at high value. When 90% of energy was supplied to the first six electrodes, the forward working flow with critical trajectories near the level accelerated, and the overall view showed longitudinal circulations with a weak back flow near the bottom. The picture of the flow
patterns is clear from Fig. 13. The new development of longitudinal circulations (new unbalanced state) leads to a decrease of the space utilization in the cases with both electrode lengths to the values of 0.26 and 0.27, respectively (compare cases 17 with 15 and 18 with 16 in Table 4). If the entire energy was supplied to the first six electrodes, more apparent longitudinal circulations developed but the space utilization slightly increased with respect to the previous case characterized by 90% of the energy supplied to the first six electrodes (cases 19 and 20 in Table 4). However, the upper forward flow appeared more massive owing to the higher flow rate of the melt. The character of the melt flow is depicted in Fig. 14.
Fig. 7. The character of the longitudinal and transversal melt flow patterns marked by the streamlines of the melt when the melt is heated along the central longitudinal axis of the melting space. The longitudinal section through the space corresponding ¼ or ¾ of the space width (XZ plane) and the transversal section at the distance of 4.6 m from the inner side of the front wall (YZ plane). The arrows → and ← highlight the main directions of the melt flow, the arrow ↓ points at the spring point position. The close-to-bottom input of melt is applied with a melt input temperature of 1420 °C (case 5, Table 2).
Fig. 8. The critical trajectories of sand are projected into planes XY and XZ when sand dissolution is the controlling phenomenon. The close-to-bottom input of melt with the temperature of 1420 °C is applied (case 5, Table 2).
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Fig. 9. The character of the longitudinal and transversal melt flow patterns marked by the streamlines of the melt when the melt is heated along the central longitudinal axis of the melting space. The longitudinal section through the space corresponding ¼ or ¾ of the space width (XZ plane) and the transversal section at the distance of 4.6 m from the inner side of the front wall (YZ plane). The arrows → and ← highlight the main directions of the melt flow. The close-to-bottom input of melt is applied with a melt input temperature of 1445 °C (case 6, Table 2).
5. Discussion of results The input temperature of melt appears a sensitive factor of the melting efficiency because its values, either lower or higher with respect to the average temperature in the space, indicate an unbalanced energetic state [19]. This state leads to the formation of different kinds of longitudinal circulations, shown by Figs. 4, 6, and 9. At lower input temperatures of melt, the forward flow and critical trajectories move along the bottom maintaining a relatively low temperature. The higher glass viscosity slows down the transversal drift of the critical trajectory to the longitudinal axis (see Fig. 5 with the close-to-bottom input), and restricts the effect of the helical-like flow. At the highest input temperature, the critical trajectory then runs in the hot forward flow along the melt level, as Fig. 9 demonstrates. The overall effect of the melt input temperature is quantitatively summarized in Tables 2 and 3, and demonstrated by Figs. 15 and 16. The values of the space utilization related to the relevant controlling phenomenon, mass melting performance (pull rate), and specific heat losses are plotted as functions of the melt input temperature for both types of melt input. When the higher melt input temperatures are gradually set, the increase of the specific melting performance and decrease of the specific heat losses is apparent up to the input temperature of 1420 °C, as well as the rapid worsening of both values at 1445 °C. The presented values of the specific heat losses are nevertheless relatively low owing to the melt level insulation as a necessary boundary condition at modelling.
Naturally, the values should be higher and the decrease should be more significant in a real case. The increasing or decreasing characters of the curves correspond to the above-mentioned longitudinal energy balance in the space. At an input temperature of 1420 °C, the energy in the space is almost balanced and the either uniform or helical flow can be set in the space; both types of flows are characterized by high values of the space utilization and mass melting performance, and by low values of the specific heat losses. At input temperatures lower or higher than the average temperature in the space, the developed longitudinal circulations disturb the above-mentioned beneficial melt flow types. In this work, the helical melt flow was preferred as the more convenient, because it works also under the presence of weak longitudinal circulations. In addition, the establishment of the only uniform flow appears to be very sensible to the character of heating. The almost parallel course of curves of the space utilization and the mass melting performance in both figures shows that the change of the flow character is the principal factor of the increase of the melting performance. This finding is confirmed by the following Fig. 17 where the percentage contributions of the u increase and τDave decrease to the growth of the mass melting performance are depicted for the close-to-bottom input (related to the values at 1320 °C). The steepness of the curve of uD is considerably higher than shows the curve of τD, consequently, the percentage contributions of the melt flow character are always more significant than the relevant contributions of the time-temperature history. Similar results were obtained for the case with a level input.
Fig. 10. The critical trajectories of bubbles are projected into planes XY and XZ when bubble removal is the controlling phenomenon. The close-to-bottom input of melt with the temperature of 1445 °C is applied (case 6, Table 2).
L. Hrbek et al. / Journal of Non-Crystalline Solids 456 (2017) 101–113
109
Table 4 The values of quantities as the space utilization, the melting performance, the specific energy consumption, and other factors are in the space with the level input of melt. The location of the rows of electrodes and the energy distribution are varied. Case no.
t (°C)
Arrangement
u (controlling)
τDave, τFref (s)
τG (s)
_ (kg/s) (t/day) M
HLM (kJ/kg)
1
1320
uD = 0.10
τDave = 2271
22,239
1.3179.7
251.3
2 3 4 5
1320 1320 1420 1320
uF = 0.34 uF = 0.21 uD = 0.39 uF = 0.20
τFref = 1878 τFref = 1879 τDave = 1917 τFref = 1878
5560 9029 4897 9326
5.2449.3 3.2276.5 5.9509.8 3.1267.8
62.9 102.3 56.0 102.3
6
1420
uF = 0.43
τFref = 1878
4380
6.6570.2
56.0
7 8 9
1320 1420 1320
uF = 0.31 uF = 0.52 uF = 0.34
τFref = 1877 τFref = 1878 τFref = 1878
6023 3614 5560
4.8414.7 8.0691.2 5.2449.3
87.6 52.7 62.9
10
1320
uF = 0.29
τFref = 1877
6566
4.4380.2
74.3
11
1320
uF = 0.38
τFref = 1877
4985
5.8501.1
56.4
12
1320
uF = 0.32
τFref = 1879
5896
4.9423.4
66.8
13
1320
uF = 0.42
τFref = 1879
4448
6.5561.6
50.3
14
1320
uF = 0.47
τFref = 1878
3988
7.25626.4
45.9
15
1320
uD = 0.30
τDave = 2085
6962
4.2362.9
78.8
16
1320
uD = 0.40
τDave = 2059
5163
5.6483.4
58.3
17
1320
uD = 0.26
τDave = 2046
7809
3.7319.7
88.4
18
1320
uD = 0.27
τDave = 2078
7608
3.8328.3
85.9
19
1320
uD = 0.29
τDave = 1938
6719
4.3371.5
76.2
20
1320
2 trans. rows of el. (0.3 m), 45% of energy to the first row Electrodes 0.3 m long Electrodes near one sidewall Electrodes near one sidewall 6 el. left side 6el. right side 6 el. left side 6 el. right side Stripping of insulation (0.5h0) Stripping of insulation (0.5h0) 45% of energy to the first 6 el.(0.3 m) 60% of energy to the first 6 el.(0.6 m) 60% of energy to the first 6 el.(0.3 m) 70% of energy to the first 6 el.(0.6 m) 70% of energy to the first 6 el.(0.3 m) 80% of energy to the first 6 el.(0.3 m) 85% of energy to the first 6 el.(0.6 m) 85% of energy to the first 6 el.(0.3 m) 90% of energy to the first 6 el.(0.6 m) 90% of energy to the first 6 el.(0.3 m) 100% of energy to the First 6 el. (0.6 m) 100% of energy to the First 6 el. (0.3 m)
uD = 0.41
τDave = 1903
4663
6.2535.7
52.9
The following Fig. 18 indicates that the helical character of flow intensifies when the melt input temperature increases although the amount of energy for establishment of the helical melt circulations decreased. The average values of the circulation and longitudinal velocities of the melt were read at the distance of 4.6 m from the inner side of the front wall, and their ratio provided a cursory but instructive view on the melt flow character. The increasing ratio vcirc/vlong indicating the melt transversal circularity is apparent in Fig. 18 and was found also for the space with close-to-bottom input. This fact is caused by the slowing down the longitudinal melt circulations when the system approaches the energy balanced state. Thus, both the approach to the uniform
flow and the more distinct helical flow contribute to the higher space utilization when the melt input temperature increases. If the temperatures of the inputting glass and the average temperature in the space are identical, the space utilization keeps high value at all the temperatures, as results from Table 2. The controlling phenomenon fixes at the bubble removal below 1420 °C, because the fining steeply slows with decreasing temperature. The principal effect of temperature on the mass melting performance and specific heat losses may thus be ascribed to the decrease of the reference fining time τFref. This effect is obvious from Fig. 19 where the curve of the relative reference fining time essentially copies the dependence of the relative mass
Fig. 11. The character of the longitudinal and transversal melt flow patterns marked by the streamlines of the melt when the melt is heated along the central longitudinal axis of the melting space. The longitudinal section through the space corresponding ¼ or ¾ of the space width (XZ plane) and the transversal section at the distance of 4.6 m from the inner side of the input front wall (YZ plane). The arrows → and ← highlight the main directions of the melt flow, the arrow ↓ points at the spring point position. The level input of melt with a melt input temperature of 1320 °C. The length of electrodes is 0.3 m; 85% of energy is supplied to the first six electrodes (case 16, Table 4).
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Fig. 12. The critical trajectories of sand are projected into planes XY and XZ when sand dissolution is the controlling phenomenon. The level input of melt with the temperature of 1320 °C is applied. The length of electrodes is 0.3 m; 85% of energy is supplied to the first six electrodes (case 16, Table 4).
performance while the relative space utilization retains an almost constant value. As is obvious from the figures and numerical results, the transversal circulations needed for the achievement of the helical flow are mostly weak with respect to the existing longitudinal flow, and all the factors how to strengthen them should be the centre of interest. In agreement with [19], the horizontal and vertical balancing of energy distribution was examined to slow the existing longitudinal circulations and to promote the transversal ones and, consequently, to achieve higher space utilization. That is why both the 0.6 and 0.3 m long electrodes were applied when the part of Joulean energy supplied to the first electrodes grew from 45% to 90% in this work. The results of these experiments are amassed in cases 2 and 9–19 in Table 4 and the following Fig. 20 represents the modelling experiments with an electrode length of 0.3 m. The shortening of the electrodes to 0.3 m in case 2 brought the maximal developed energy closer to the bottom, caused the increase of the bottom temperature by about 6 °C, and supported the central ascending stream of the melt. This effect led to the apparent increase of the space utilization. Similar growth is indicated by Table 4 when increasing the amount of energy supplied to the first six electrodes. The further explanation of curves in Fig. 20 and in Table 4 corresponds to considerations about a balanced energetic state and relevant flow character. Bubble removal was the controlling phenomenon
at 45–80% of energy supply to the first six electrodes, because the forward flow moved near the bottom. The shift of the amount of energy to the input from 45% to 80% reduced the intensity of the longitudinal circulations which was indicated by the decrease of melt velocities on the level and also near the bottom – the average maximal melt velocity of the forward flow near the bottom decreased by 15.8% and by 19.9% for the electrode lengths 0.3 and 0.6, respectively. The almost uniform flow, obvious from Fig. 11, was observed already at 70% of energy inputted to the first six electrodes. Simultaneously, the already described circularity of the melt increased from 0.754 to 1.03. Consequently, the tendency to both the uniform and the helical flow led to the increase of the space utilization. The contribution of the helical flow to the increase of the space utilization at low amounts of energy at the input can be assessed from the comparison of cases with and without the evoked transversal circulations. The relatively high value of the space utilization of 0.34 resulted in the case with the central longitudinal row of electrodes and 45% of energy localized to the input (helical flow, case 9, Table 4), whereas the relevant case with two transversal rows of electrodes (without helical flow, case 1, Table 4) provided a space utilization value of only 0.1. When the amount of Joulean energy in the input region rises above 80%, the forward melt flow and critical trajectories of particles shifted to the melt level, and the sand dissolution became the controlling phenomenon, as is clear from Fig. 12. The
Fig. 13. The character of the longitudinal and transversal melt flow patterns marked by the streamlines of the melt when the melt is heated along the central longitudinal axis of the melting space. The longitudinal section through the space corresponding ¼ or ¾ of the space width (XZ plane) and the transversal section at the distance of 4.6 m from the inner side of the front wall (YZ plane). The arrows → and ← highlight the main directions of the melt flow, the arrow ↓ points at the spring point position. The level input of melt with a melt input temperature of 1320 °C. The length of electrodes is 0.3 m; 90% of energy is supplied to the first six electrodes (case 18, Table 4).
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Fig. 14. The character of the longitudinal and transversal melt flow patterns marked by the streamlines of the melt when the melt is heated along the central longitudinal axis of the melting space. The longitudinal section through the space corresponding ¼ or ¾ of the space width (XZ plane) and the transversal section at the distance of 4.6 m from the inner side of the front wall (YZ plane). The arrows → and ← highlight the main directions of the melt flow, the arrow ↓ points at the spring point position. The level input of melt with a melt input temperature of 1320 °C. The length of electrodes is 0.3 m; 100% of energy is supplied to the first six electrodes (case 20, Table 4).
transversal circularity of melt decreased by about 10% between 70 and 90% of energy supplied to the input, and the average velocity of the forward melt flow on the level grew by 33% between 85% and 90% of supplied energy. Both were responsible for the decrease of the space utilization. At 90% of energy supply to the input, the overall character of the longitudinal melt flow clearly showed the transition to the flow type with the relatively fast forward flow along the level and development of a backflow near the bottom, as Fig. 13 shows. Consequently, this flow type with developing longitudinal circulations shows lower space utilization. The results are in agreement with the achieved character of the melt flow in a space with a simulated batch blanket [19]. The sudden increase of the space utilization and the relevant growth of the melting performance between 90 and 100% of the transferred Joulean energy appears surprising, as well as the decrease of the specific heat losses. This fact is also obvious from Fig. 20 and from Table 4 (cases 19 and 20). The utilization decrease should rather be expected with further development of the longitudinal circulations. Nevertheless, Fig. 21 helps to explain the opposite behaviour. The curve of the relative space utilization copies the development of the relative mass melting performance well and thus shows the dominating affect of the melt flow character up to 90% of the transferred energy. At 100% of the transferred energy, however, the space utilization and the melting kinetics – represented by the average sand dissolution time – play the almost equivalent role. The reduced values of the average sand dissolution times between 90 and 100% of energy raise the melting performance. As a result, the effect of the developed longitudinal circulations is
weakened and the space utilization then increases. This leads to further increase of the melting performance. The strengthening of the helical flow and its significance for the space utilization at a slightly unbalanced energy distribution was also modelled by stripping a part of the sidewall insulation (cases 7 and 8 in Table 4). As the higher heat losses only very slightly raised the specific heat losses, this step aspires as a usable factor of melt flow control. On the other hand, the electrode arrangements other than the central longitudinal row (cases 3–6 in Table 4) did not prove their efficiency. 6. Conclusion The character of the melt flow can become a valuable factor the significance of which for glass melting may be comparable with the time temperature conditions of the process. This fact is indicated by the theoretical considerations and proved by the results of the mathematical modelling. In agreement with the results achieved by modelling involving simulated batch loading [19], a considerable increase of the melting performance and, consequently, a decrease of the specific heat losses can be achieved under conditions of controlled melt flow. The applied quantity space utilization provides a quantitative evaluation of the melt flow quality with respect to the melting phenomena. The longitudinal distribution of energy supplied to the melting space appears to be the main factor of the flow control. Another important factor sharing in the formation of the melt flow character is the melt flow rate; however, its values are restricted to the accomplishment of all the melting phenomena inside the space. Two final beneficial melt flow characters
Fig. 15. The values of the space utilization of the controlling phenomenon u, mass melting _ and specific heat losses HLM as a function of the melt input temperature performance M, tinput. The space with the close-to-bottom input of melt. The lines serve only as a guide for the eyes.
Fig. 16. The values of the space utilization of the controlling phenomenon u, mass melting _ and specific heat losses HLM as a function of the melt input temperature performance M, tinput. The space with the level input of melt.
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Fig. 17. The percentage contributions of the uD increase and τDave decrease (related to the _ The close-to-bottom values at 1320 °C) to the increase of the mass melting performance M. input of melt.
may be selected: the uniform flow and the helical flow evoked by proper transversal energy distribution. Whereas the uniform flow does not almost tolerate the simultaneous presence of the longitudinal circulation components, the helical flow admits longitudinal circulations of low intensity. That is why the application of the helical flow was the subject of this work aiming at modelling the melting (homogenization) modulus of a segment furnace. The simplest corresponding heating arrangement was realized by the central longitudinal row of electrodes. Both the decreasing difference between the melt input and the average temperature and the substantial supply of energy to the melt input led to balanced horizontal energy distribution, and resulted in an increase of the space utilization as an indicator of melting performance and specific heat losses. The calculated values of the space utilization were considerably higher as compared with the values achieved by simulation of the melt flow in an industrial melting space, which is usually characterized by intensive longitudinal melt circulations. Although the achieved intensity of the transversal circulations was relatively low, the significance of the simulated helical flow was high and was thus proven, as in [19]. The fact that transversal circulations of only a low intensity can be achieved poses a requirement to maintain the horizontal energy distribution near the balanced state. When the melt input
Fig. 18. The space utilization and the ratio of the average value of the transversal circulation melt velocity vcirc to the longitudinal melt velocity vlong as a function of the melt input temperature at the distance of 4.6 m from the inner side of the input front wall. Each velocity was measured in four points of the transversal section through the space. The space with the level input of melt.
Fig. 19. The dependences of the relative values of the space utilization uF/uF0, the mass _ M _ 0 , and the reference bubble removal time τFref0/τFref (its melting performance M= reciprocal value) on the melt input temperature tinput. The values of the quantities were related to the values at 1320 °C. The close-to-bottom input of melt.
temperature was 100 °C lower than the average temperature in the space, the supply of about 70–80% of Joulean energy to the input region of the space corresponded to the approximately balanced state here. The setting up of a helical flow of the described intensity in the modulus can thus facilitate the way to glass melting in a relatively small and efficient two-space melter. When the melt input temperature increases or the relevant energy to the melt input region is supplied to approach the balanced state of energy, the uniform flow gradually takes the beneficial glass melting role. The question of the application of a pure uniform flow therefore remains relevant. The attempts to arrange the energy sources to set the uniform flow by planar heating in [19] led, however, to arising Bernard's circulation flows and to very low values of space utilization. Despite these results, the application of the uniform flow under conditions of very high flow rates and a high portion of energy supplied to the input region of the space seems to be promising. This will also be a subject of subsequent modelling experiments.
_ and specific heat losses HLM as Fig. 20. The space utilization u, mass melting performance M, a function of the part of energy brought to the first six electrodes. The level input of melt, electrodes 0.3 m long.
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References [1] [2] [3] [4] [5] [6] [7] [8] [9] [10] [11]
[12] [13] [14] [15] [16] [17] Fig. 21. The dependences of the relative values of the space utilization uD/uD0, the mass _ M _ 0 , and the average sand dissolution time τDave0/τDave (its melting performance M= reciprocal value) on the amount of energy brought to the first six electrodes. The values of quantities indexed by 0 were related to the values calculated at 1320 °C. A level input of melt.
Acknowledgement This work was financially supported from specific university research (MSMT No. 20-SVV/2016).
[18] [19] [20] [21]
V. Mulholland, US Patent No. 2 068 925 (1937). H.L. Penberthy, US Patent No. 3 268 320 (1966). F.V. Atkeson, US Patent No. 3 305 340 (1967). Y. Takashi, Japan Patent No. S55 116 632 (1980). S. Heurtey, French Patent No. 2 787 784 A1 (2000). M. Polák, L. Němec, J. Non-Cryst. Solids 357 (2011) 3108. P. Cincibusová, L. Němec, Glass Technol.: Eur. J. Glass Sci. Technol. A 53 (2012) 150. L. Němec, P. Cincibusová, Glass Technol.: Eur. J. Glass Sci. Technol. A 53 (2012) 279. M. Polák, L. Němec, J. Non-Cryst. Solids 358 (2012) 1210. P. Cincibusová, L. Němec, Glass Technol.: Eur. J. Glass Sci. Technol. A 56 (2015) 52. G. Aronchik, B.A. Purnode, D. Rue, Proceedings of the 9th International Seminar on Mathematical Modelling of Furnace Design and Operation, Velké Karlovice (CZ), 2007 23–32. G. Villeroy de Galhau, Y. Lefrere, M. Rayer, Demande Internationale de PCT brevet, Numero de Publication International WO (2013/132 184 A1). J.L. Barton, Boletin de la espaňola de ceramica y vidrio, Madrid, 1992 165–184. C.P. Ross, Am. Ceram. Soc. Bull. 83 (2004) 18. D.J. Bender, J.G. Hnat, A.F. Litka, L.W. Donaldson Jr., G.K. Ridderbusch, D.J. Tessari, J.R. Sacks, Glass Ind. 3 (1991) 10. O. Sakamoto, Res. Reports, 59, Asahi Glass Co. Ltd, 2009 55060. L. Němec, M. Polák, P. Cincibusová, M. Jebavá, J. Brada, M. Trochta, J. Kloužek, PCT Application No. PCT/CZ2013/000102. Glass Furnace Model 4.17, Glass Service, Inc., Vsetín, Czech Republic, 2015. M. Jebavá, P. Dyrčíková, L. Němec, J. Non-Cryst. Solids 430 (2015) 52. L. Němec, M. Vernerová, P. Cincibusová, M. Jebavá, J. Kloužek, Ceramics-Silikáty 56 (2012) 367. M. Jebavá, L. Němec, J. Brada, (prepared for publication).