Numerical Study of Fluid Flow and Heat Transfer Behaviors

in a Physical Model Similar in Shape to an Actual Glass Melting Furnace

and Its Experimental Verification

Chien-Chih Yen and Weng-Sing Hwang*

Department of Materials Science and Engineering, National Cheng Kung University, Tainan, Taiwan, R. O. China

In this study, a three dimensional numerical model based on the SOLA-VOF method, which incorporates a Quasi-two Phase method toconsider the gas bubbling phenomena, was developed to investigate the fluid flow and heat transfer behaviors in a glass melting furnace. Areduced physical model with heating electrodes and air bubbling devices was also constructed to validate the numerical model. The reducedphysical model was made of an acrylic tank similar in shape to an actual glass melting furnace, but reduced to one-tenth in size. The gas flow ratewas determined at 6:67� 10�7 Nm3/s by the similarity conversions. The electrode temperatures were set between 298K to 373K. The flowtrajectories of tracer particles and temperature field were measured to validate the accuracy and reliability of the numerical model. The resultsshow that the temperature and trajectories of tracer particles predicted by the numerical model were consistent with experimental observations/measurements from the physical model. [doi:10.2320/matertrans.M2010215]

(Received June 24, 2010; Accepted August 4, 2010; Published September 25, 2010)

Keywords: numerical model, glass melting furnace, solution algorithm-volume of fluid, marker-and-cell (MAC), physical model, gas bubbling,

electrode heating

1. Introduction

The quality requirement for glass substrates in liquidcrystal displays (LCD) is very stringent, especially for thealkali-free glass process. The production of glass is a verycomplicated process, which involves a number of physicaland chemical phenomena. However, the quality of glass isdecisively influenced by the fluid flow and heat transferbehaviors of the molten glass in the tank. Therefore,understanding of the fluid flow and heat transfer behaviorsof molten glass is a significant issue. The conventionalapproach to studying the effects of the design and operatingconditions of a glass melting furnace is to employ anempirical method based on the measurements and observa-tions of an actual furnace. However, it is extremely difficultto observe the glass flow patterns and temperature fieldsinside a furnace because of the high temperature environ-ment. Full-scale experiments in an actual furnace are thusvery costly and dangerous. In addition, although theinformation obtained for the molten glass is direct, it is alsoincomplete.

Due to the fast development of computer technology,numerical modeling for the actual glass melting furnaces isbecoming a valuable tool for improving both their design andoperation.1) Viskanta2) reviewed the three-dimensional math-ematical modeling of glass melting furnaces and comparedthe advantages and disadvantages of physical and mathe-matical models. Choudhary3) outlined the significant advan-ces in the mathematical modeling of flow and heat transferphenomena in glass furnaces, describing developments inboth the fundamental/scientific and practical aspects ofmodeling. Ungan et al.4,5) developed a mathematical modelto predict the effects of electric boosting and air bubblingseparately on circulation and heat transfer in a glass-meltingtank. Dzyuzer6) et al. investigated the effect of the profile of

the floor on hydrodynamics and heat exchange in the meltingtank of a glass furnace. The effects of the length and depth ofthe tank on the formation of convection currents and heatexchange in different parts of the tank were established.Schill et al.7) used two methods, coupled and decoupled, tosolve differential equations and discuss various importantphenomena, including heat and mass transfer as well asmelting kinetics for a real glass furnace. However, themathematical models in previous studies were mostlyfocused on traditional glass processes, and few of themconsidered the effects of electrode heating and gas bubblingat the same time. In addition, the validation of the physicalmodels for the mathematical models in previous studies wasdeficient. Therefore, this study mainly focuses on an alkali-free glass furnace that produces glass used in LCD. A threedimensional numerical model based on the SOLA-VOF8)

method was developed to investigate the fluid flow and heattransfer behaviors in the glass tank. This 3-D model can dealwith the effects of electrode heating and gas bubblingsimultaneously. A reduced physical model was also estab-lished according to similarity theory9,10) to validate theaccuracy and reliability of the numerical model.

2. Mathematical Method

2.1 Description of the physical systemIn order to understand the melting process, a schematic

illustration of the furnace for alkali-free glass is shown inFig. 1. Batch materials are fed continuously from the inlet tothe batch zone located between the combustion space andmolten glass zone. Fuel is burned with air or pure oxygen inthe combustion zone to provide heat to the batch blanket forthe fusion of the batch materials and to the glass melt surfaceto obtain a low-viscous melt. Heat from the combustion spacecan be transferred by radiation, convection of the hotcombustion gases, and conduction. Another source of energyto melt the glass batch is an electrode array immersed in the*Corresponding author, E-mail: wshwang@mail.ncku.edu.tw

Materials Transactions, Vol. 51, No. 10 (2010) pp. 1964 to 1972#2010 The Japan Institute of Metals EXPRESS REGULAR ARTICLE

molten zone. Electric boosting is an effective method forincreasing productivity and enhancing glass-melting effi-ciency. By appropriately arranging the electrodes, glass meltcirculation is enhanced as well as lowering the load andtemperature on the combustion space to obtain longersuperstructure life. Heat flux at the batch-glass melt interfaceis also increased, and hence a higher pull rate can beobtained. A higher temperature near the electrodes will causedensity gradients, driving free convection flows in theaffected zone. The convection of mass in the melt is essentialfor mixing and heat transfer, in particular for melts with highthermal resistance. Therefore, all-electric melting furnace is anew tendency to replace the traditional gas combustion glassfurnace in recent years. The bubbling gases move throughbubbling tuyeres mounted on the bottom of the tank, whichenables agitation by bring relatively cold glass melt from thebottom to the surface, and hence the surface temperature ofthe glass melt is decreased. This enhances the circulation inthe molten glass zone.

As described above, the fluid flow and heat transferbehaviors play a significant role in a glass melting furnace.The mathematical model should thus be capable of dealingwith the free surface flow, radiation, heat transfer, andconvection induced by electrode heating and gas bubbling,and the gas-liquid mixture situation. Due to all-electricmelting furnaces is a new development tendency recently,this study mainly focuses on the effects of electrode heatingand gas bubbling. The effects of radiation for glass furnacewere not taken into consideration. As the quality of glass isdecisively influenced by the fluid flow and heat transferbehaviors of the molten glass zone, in this study, a threedimensional numerical model based on the SOLA-VOFmethod, which incorporates a Quasi-two Phase method toconsider the gas bubbling phenomena, was developed toinvestigate the fluid flow and heat transfer behaviors in themolten glass zone. A schematic diagram of the numericalmodel is shown in Fig. 2.

2.2 Governing differential equationsIn order to solve partial differential equations in the

molten glass zone, certain assumptions were made: (1)Molten glass is an incompressible Newtonian fluid; (2)Molten glass enters continuously from the inlets; (3) Theproperties of fluid are constant except for density; (4) Viscousheat dissipation effects are negligible; (5) Fluid flow in thetank is laminar due to the high viscosity and low velocity ofthe fluid. With these characteristics, the energy equation canbe written as:

�lCp

@T

@tþ ~VV � rT

� �¼ kr2T ð1Þ

where �l (kg�m�3) is the density of liquid; Cp (Jg�1 K�1) isthe heat capacity; T (K) is the temperature; t (s) is the time;~VV (m�s�1) is the velocity; k (Wm�1�K�1) is the thermalconductivity. The density variations of the liquid areconsidered by the following equation:

�l ¼ �0½1þ �T ðT � T0Þ� ð2Þ

where �0 (kg�m�3) is the density of liquid at room temper-ature; �T (K

�1) is the coefficient of thermal expansion; T0 (K)is the reference temperature.

The Navier-Stokes equation of momentum is:

�l@ ~VV

@tþ ð ~VV � rÞ ~VV

" #¼ �rPþ �r2 ~VV þ �~gg ð3Þ

where P (kgm�1�s2) is the pressure; � (Pa�s) is the dynamicviscosity; ~gg (m�s�1) is the gravitational acceleration; and �(kg�m�3) is the density of liquid, gas or gas/liquid mixture.If the mesh element is pure liquid, � is equal to �l. If themesh element is pure gas, � is equal to the density of gas. Ifthe mesh element is gas/liquid mixture, � is equal to thedensity of gas/liquid mixture. The density of the gas-liquidmixture was calculated by the weighted average method. Thecontinuity equation (conservation of mass) for incompres-sible flow is:

r � ~VV ¼ 0 ð4Þ

From the law of mass conservation, the volume fraction offluid, F, is governed by the following equation:

@F

@tþ ð ~VV � rÞF ¼ 0 ð5Þ

With the VOF method, a field variable, Fðx; y; z; tÞ, isdesignated to each computational element to indicate thevolume fraction of liquid in that particular cell. When F isequal to 1, it means the cell is full of liquid. When F is equalto 0, it means the cell is full of gas (or empty of liquid). WhenF is between 0 and 1, the element contains both liquid andgas and an interface is then allocated in that particular cell.The F value can thus indicate the domain of fluid flow, andit is a step function.

0.29 m

0.9 m

(b)

(a)

Overflow

Outlet

Electrode

Inlet

Bubbler

Y

X Z

0.15 m

(c)

Fig. 2 Schematic illustrations of the numerical model (a) 3-D view, (b) top

view, (c) side view.

Batch zone

Molten glass zone

Electrode

Bubbler

OverflowOxy-fuel burner Combustion zone

Outlet

Inlet

Fig. 1 A schematic illustration of a melting furnace for alkali-free glass.

Numerical Study of Fluid Flow and Heat Transfer Behaviors and Its Experimental Verification 1965

2.3 Boundary conditionsThe boundary conditions include (1) no-slip condition at

the walls, (2) free surface condition, (3) temperaturecondition. Let un, um1 and um2 denote the normal andtangential velocities to the boundary respectively. Then, ano-slip boundary can be written as:

un ¼ 0

um1 ¼ 0 ð6Þum2 ¼ 0

The approximate boundary conditions on the free surface11)

are

n � � � n ¼ 0

m1 � � � n ¼ 0 ð7Þm2 � � � n ¼ 0

where � ¼ �ij is the stress tensor given by

�ij ¼ �P�ij þ �@ui

@xjþ

@uj

@xi

� �i; j ¼ 1; 2; 3 ð8Þ

and ~nn ¼ ðn1; n2; n3Þ is the local unit normal vector; m1, m2are local tangential vectors; P (kgm�1�s2) is the pressure;and �ij is the Kronecher delta. �ij is equal to 1 as i ¼ j and �ijis equal to 0 as i 6¼ j.The temperature boundary conditions at the interfacesbetween the molten glass and atmosphere in the furnaceas well as furnace walls and ambient environment are asfollows.

�k

h

@T

@n¼ ðT � T1Þ ð9Þ

Subsequently the virtual temperature of the mesh, T� (K),which is close to the free surface mesh or wall mesh in anydirection, can be derived from the equation above and resultsin the differential equation, as follows.

T� ¼

�k

�n�

h

2

�Ti; j;k þ hT1�

k

�nþ

h

2

� ð10Þ

where k (Wm�1�K�1) is the thermal conductivity; h

(Wm�2�K�1) is the heat transfer coefficient; T1 (K) is thetemperature of the furnace atmosphere or ambient temper-ature outside the walls; and �n is the mesh size in x, y or zdirections.

2.4 Treatments for the gas bubblingThe Quasi-two Phase method was used to consider the

rising gas-liquid mixture as a homogenous fluid of variationaldensity. A buoyancy force of gas bubbles was introduced bythe density differences among pure gas, glass-liquid mixture,and pure liquid. Surface tension effects were not yet takeninto consideration. In this study, a spherical gas bubble wasreleased from each of the six tuyeres once every threeseconds, and this frequency was obtained from experimentalobservations. The radius of the released bubble, Rb (m), wasthen calculated by the following equation:

Rb ¼

ffiffiffiffiffiffiffiffiffiffiffiffiffiQb � tb4�=3

3

sð11Þ

where Qb (m3�s�1) is the flow rate of gas bubbles, and tb (s)

is the release time of gas bubbles. As the bubble size issignificantly larger than that of the mesh size, the meshelement specified can then be pure liquid, pure gas, or agas-liquid mixture. The density of the element was thendetermined accordingly. The density of the gas-liquidmixture was calculated by the weighted average method.The gas/liquid interface and the motions of gas bubbles wereconsidered using a marker-and-cell (MAC)12) technique,and the modeling method is shown in Fig. 3. In this study,the virtual markers that were used to deal with gas bubblemixture are referred to as bubble markers. First, the locationof the bubble should be determined, and the radius of thebubble can be calculated by the method mentioned above, asshown in Fig. 3(a). Secondly, the elements covered by thebubble were divided into equal parts, as shown in Fig. 3(b),and virtual bubble markers were then placed at these dividingparts, as shown in Fig. 3(c). Finally, the location of all thebubble markers was checked and those that were outsidethe bubble were eliminated, as shown in Fig. 3(d). The gas/liquid regions can then be obtained. The velocity of a bubblemarker was calculated by the weighted average methodaccording to the nearest eight velocities of elements. Thenew interface and bubble shapes in the next time step canthen be determined. The motion of gas bubbles is shown inFigs. 4(a) to 4(n).

2.5 Treatments for particle tracing of fluidIn order to understand the fluid flow behavior in the glass

furnace, the MAC technique was also used to observe thefluid flow trajectories from inlet to outlet. In this study, thevirtual markers that used to deal with the flow trajectories arereferred to as fluid tracer particles. As the steady state flowfield without gas bubbling or the transient flow field of gasbubbling were obtained for the furnace operation in thenumerical model, the temperatures and the velocities of thefluid flow in all three directions in every grid cell can be

(c) (d)

(b)(a)

Rb

Fig. 3 Method of determining the gas/liquid interface: (a) determine the

location and radius of a bubble, (b) divide the elements into equal parts,

(c) place virtual bubble markers, (d) eliminate markers that are outside the

bubble.

1966 C.-C. Yen and W.-S. Hwang

known. The fluid tracer particles were placed underneaththe inlet as the temperatures and the velocities of the fluidflow were obtained. The fluid tracer particles were thenallowed to flow with the fluid, and the particle flow path canbe traced by the MAC technique.

3. Experimental Method

3.1 Experimental setupA one-tenth-sized physical model with an air bubbling and

electrode heating system, as illustrated in Fig. 5, wasestablished to study the fluid flow and heat transfer behaviorsin the glass furnaces and validate the numerical model. Inorder to observe the flow behaviors, the tank was made oftransparent acrylic, with the dimensions of 0.9m in length,0.29m in width and 0.15m in height. A row of six gas

blowing tuyeres; 0.04m in diameter, was installed at thebottom along the center line of an actual glass furnace. Sincethe physical model is one-tenth the scale of the actualfurnace, the diameter of the tuyere in the physical model is0.004m. Compressed air at room temperature was used as thebottom blown gas. Four rows of electrodes with threeelectrodes on the first three rows and four electrodes on thefourth row were installed on the bottom and connected to aheating control system. Each electrode was 0.0075m indiameter and 0.045m in height, and attached to a thermo-couple. This corresponds to actual electrodes of 0.075m indiameter and 0.45m in height in the actual furnace. Fivethermocouples were installed on the top of the physicalmodel, which could measure the surface or internal temper-ature of the liquid inside. Silicon oil with a viscosity of20 Pa�s was selected to simulate the molten glass. Acrylparticles with a density similar to silicon oil were used astracers. Tracers were inserted at the inlet at steady state, andthe flow behaviors were recorded by a video camera.

3.2 Liquid flow rate conversionDue to the high viscosity of glass melt, the Reynolds

number (Re) is used to convert the fluid flow rate between thephysical model and glass furnace. Applying a Reynoldscriterion between the physical model and glass furnace, thisindicates that

Repm ¼ Regf ð12Þ

Then

Qso � Lpm � �so� � r2pm � �so

¼Qg � Lgf � �g� � r2gf � �g

ð13Þ

Qso can then be calculated in the following manner.

Qso ¼Lgf

Lpm

� �r2pm

r2gf

!�g

�so

� ��so

�g

� �� Qg ð14Þ

where Repm is the Reynolds number of the physical model;Regf is the Reynolds number of the glass furnace; Qso

(m3�s�1) is the flow rate of silicon oil; Qg (m3�s�1) is the flow

rate of molten glass; Lpm (m) is the characteristic length of thephysical model; Lgf (m) is the characteristic length of theglass furnace; �so (kg�m�3) is the density of silicon oil; �g(kg�m�3) is the density of molten glass; rpm (m) is the radiusof the tuyere in the physical model; rgf (m) is the radius ofthe tuyere in the glass furnace; �so (Pa�s) is the viscosity ofsilicon oil and �g (Pa�s) is the viscosity of molten glass.

3.3 Gas flow rate conversionIn order to correlate the gas flow rate between the physical

model and the actual glass furnace, the modified Froudenumber (N 0

Fr)13) was used to convert the gas flow rate.

Applying a modified Froude criterion between the physicalmodel and the actual glass furnace, the following relationshiphas to be obeyed.

ðN 0FrÞpm ¼ ðN 0

FrÞgf ð15Þ

Then,

�airQ2air

�soð�r2pmÞ2 � Lpm � g

¼�O2

Q2O2

�gð�r2gfÞ2 � Lgf � g

ð16Þ

(d)

0.9 sec

(k)

3.0 sec

(m)

3.6 sec

(n)

3.9 sec

(l)

3.3 sec2.7 sec

(j)

2.4 sec

(i)

2.1 sec

(h)

0.3 sec

(b) (a)

0.0 sec 0.6 sec

(c)

1.2 sec

(e)

1.5 sec

(f)

1.8 sec

(g)

Fig. 4 The motion of gas bubbles. (a) Time = 0.0 s; (b) Time = 0.3 s;

(c) Time = 0.6 s; (d) Time = 0.9 s; (e) Time = 1.2 s; (f) Time = 1.5 s;

(g) Time = 1.8 s; (h) Time = 2.1 s; (i) Time = 2.4 s; (j) Time = 2.7 s;

(k) Time = 3.0 s; (l) Time = 3.3 s; (m) Time = 3.6 s; (n) Time = 3.9 s.

Liquid Recycling System

Acrylic model

Electrode Heating System

Bubbling Control System

Liquid Supply System

Video Camera

Temperature Measurement System

Fig. 5 A schematic diagram of the experimental setup.

Numerical Study of Fluid Flow and Heat Transfer Behaviors and Its Experimental Verification 1967

where ðN 0FrÞpm is the modified Froude number of the physical

model; ðN 0FrÞgf is the modified Froude number of the glass

furnace; Qair (Nm3�s�1) is air flow rate in the physical model;QO2

(Nm3�s�1) is the oxygen flow rate in the glass furnace;�O2

(kg�m�3) is the density of oxygen; �air (kg�m�3) is thedensity of air and g (m�s�2) is the gravitational accelerationconstant. Qair can then be calculated in the followingequation.

Qair ¼�O2

�air

� ��so

�g

� �Lpm

Lgf

� �rpm

rgf

� �4" #1=2

QO2ð17Þ

4. Results and Discussion

As the flow field and temperature field were obtained forthe physical and numerical model, fluid and acryl tracerparticles were placed underneath the inlet to observe the fluidflow pattern. For numerical simulations, the computationaldomain is shown in Fig. 2 with the related sizes depicted. Auniform mesh was adopted, and the domain was divided intoa rectangular mesh system of 33� 19� 93.

4.1 Effects of electrode heating4.1.1 Effects of electrode heating on heat transfer

behaviorFor the heat transfer behavior, the 3-D temperature

contours at the electrode temperature of 373K by numericalmodeling for the investigated region shown in Fig. 6(a) areshown in Fig. 6(b). Figure 6(c) is the 2-D sectional viewof Fig. 6(b). The marked positions 1, 2, and 3 in this figureare 0.04m above the bottom. In the physical model, thetemperatures of the silicon oil, which are located in positions1, 2, and 3 as marked in Fig. 6(c), at the electrodetemperature of 373K were also measured. From thenumerical results of Fig. 6(c), the calculated temperatures

at positions 1, 2, and 3 is approximately 343K, 346K and342K. From the measurement of experimental results in thephysical model, the temperature of the silicon oil at positions1, 2, and 3 is 340K, 345K and 342K, respectively. Theseexperimental temperature results are close to the temper-atures calculated from the temperature field by numericalmodeling. The parameters that used in this section are listedin Table 1.4.1.2 Effects of electrode heating on flow behavior

For the effects of electrode heating process condition, theflow fluid behaviors were observed at the electrode temper-atures of 298K and 373K without gas bubbling. From thenumerical model, Fig. 7 shows the 2-D section view of thesteady-state velocity field in the vicinity of the electrodes at298K without heating or bubbling. It can be seen that thevelocity vector in the tank is horizontal toward the outlet.This is believed to be due to the absence of a stirringmechanism, such as free convection induced by electrodeheating or strong forced convection induced by gas bubbling.After the fluid tracer particles were placed underneath theinlet, their flow paths, as shown in Fig. 8, can then beobtained from the steady-state velocity field. Figure 8 showsthe flow paths of fluid tracer particles in the tank. As can beseen from this figure, the flow trajectory of fluid tracerparticles moved horizontally along the free surface to theoutlet, and did not shift much in the y and z directions. Thiscould be due to the absence of a stirring mechanism, asmentioned above. The corresponding experimental observa-

(a)

(b)

321

(c)

2 3 1

Fig. 6 (a) Investigated region in the numerical model; (b) 3-D temperature

contours at the electrode temperature of 373K by numerical modeling;

(c) 2-D section view of (b).

Table 1 The parameters used for simulating the effects of electrode heating

on heat transfer behavior.

Inlet velocity 12:916� 10�4 m�s�1

Outlet velocity 6:458� 10�4 m�s�1

Overflow velocity 6:458� 10�4 m�s�1

Air flow rate 0Nm3�s�1

Thermal conductivity 0.5Wm�1�K�1

Heat capacity 1800 J kg�1�K�1

Heat transfer coefficient

between liquid and air45Wm�2�K�1

Heat transfer coefficient

between liquid and wall1Wm�2�K�1

(a)

(b)

Fig. 7 (a) Investigated region in the numerical model; (b) 2-D section view

of velocity field in the vicinity of the electrodes at 298K.

1968 C.-C. Yen and W.-S. Hwang

tions are shown in Fig. 9, which reveals the flow paths ofacryl tracers in the physical model at 298K without heatingor bubbling. It can be seen that the acryl tracer particles movealong the free surface from inlet to outlet, as shown inFigs. 9(a) to 9(c). Acryl tracer particles did not shift muchin the y and z directions. This is believed to be due to thehigh viscosity of silicon oil and the absence of a stirringmechanism in the physical model. From Figs. 8 and 9, itcan be seen that the simulated results are consistent with theexperimental observations.

With regard to the effects of the electrode heating processcondition, it can be observed that the fluid close to theelectrode would rise upward due to free convection inducedby the heating electrodes. The free convection induced by theheating electrodes would cause small-scale circulations nearcertain electrodes. From the results of the numerical model,Fig. 10 shows the 2-D section view of the steady-statevelocity field in the region between the inlet and the firstrow of electrodes at the electrode temperature of 373K. Ascan be seen from this figure, there was an upward velocityfield near the electrode, and this would drive the nearby flowof fluid upwards to the surface and hinder the forward

velocity from the inlet. Consequently, the fluid in the vicinityof the inlet started to flow downward, and therefore inducedsmall-scale circulation phenomena in this region. Figure 11shows the 2-D section view of the steady-state velocity fieldin the region between the third row of electrodes and thebubblers at the electrode temperature of 373K. It can beseen that there was also an upward velocity field near theelectrode, and this velocity field would drive the nearby flowof fluid upwards to the surface, and cause the fluid in thevicinity of the bubbler to flow backward to the bottom ofthe electrode. Consequently, another small-scale circulation

(a)

(b)

Fig. 8 Schematic illustrations of flow paths of fluid tracers in the numerical

model at 298K without heating and bubbling. (a) Side view; (b) Top view.

(c)

(b)

(a)

Fig. 9 Flow paths of acryl tracers in the physical model at 298K without

heating and bubbling in the vicinity of (a) inlet, (b) bubbling zone,

(c) outlet. (The inserts show the sketches of the investigated regions in

the physical model)

(b)

(a)

Fig. 10 (a) Investigated region in the numerical model; (b) 2-D section

view of the velocity field in the region between the inlet and the first row of

electrodes at the electrode temperature of 373K.

(a)

(b)

Fig. 11 (a) Investigated region in the numerical model; (b) 2-D section

view of the velocity field in the region between the third row of electrodes

and the bubblers at the electrode temperature of 373K.

Numerical Study of Fluid Flow and Heat Transfer Behaviors and Its Experimental Verification 1969

occurs because of the velocity field induced by electrodeheating.

As the steady state flow and temperature field wereobtained, as shown in Figs. 10 and 11, fluid tracer particleswere placed underneath the inlet and allowed to flow with thefluid to obtain the flow pattern in the tank, as shown inFigs. 12 and 13. Figure 12 shows the 3-D flow path of onefluid tracer, which was recorded every 100 seconds in theregion between the inlet and the first row of electrodes at theelectrode temperature of 373K. Figure 13 shows the 3-Dflow path of one fluid tracer, which was recorded every 100seconds in the region between the third row of electrodes andthe bubblers, also at the electrode temperature of 373K. Ascan be seen from these two figures, small-scale circulationswere observed in these two regions due to the free convectioninduced by electrode heating. The corresponding experimen-tal observations are shown in Figs. 14 and 15. Figure 14shows the flow paths of acryl tracers in the region betweeninlet and the first row of electrodes at the electrode temper-ature of 373K. Figure 15 shows the flow paths of acryltracers in the region between the third row of electrodes andthe bubblers at the electrode temperature of 373K. From theexperimental results of the physical model, two small-scalecirculations were also observed near the electrodes, the firstone was in the region between the inlet and the first row ofelectrodes, and the other one was in the region between thethird row of electrodes and the bubblers. As can be seen fromthese two figures, acryl tracer particles close to the electrodeswould rise upward and small-scale circulations occur due tothe free convection induced by the heating electrodes. FromFigs. 12 to 15, it can be seen that the simulated results areconsistent with the experimental observations.

4.2 Effects of gas bubblingWith regard to the effects of gas bubbling, the flow fluid

behavior was observed at the gas flow rate of 6:67�10�7 Nm3/s without electrode heating. From the numericalresults, Fig. 16(b) shows a 2-D section view of the velocityfield in the cross-section of the bubbler near the bubblingzone. As the stirring range in the bubbling zone stabilized, atransient flow field as shown in Fig. 16 was selected as thetime that spherical gas bubble released from each of the sixtuyeres. Fluid tracer particles were then be placed underneath

(a)

(b)

Fig. 12 (a) Investigated region in the numerical model; (b) 3-D Flow path

of a fluid tracer recorded every 100 second in the region between the inlet

and the first row of electrodes at the electrode temperature of 373K.

(a)

(b)

Fig. 13 (a) Investigated region in the numerical model; (b) 3-D flow path

of a fluid tracer recorded every 100 second in the region between the third

row of electrodes and the bubblers at the electrode temperature of 373K.

(a)

(b)

960 sec840 sec780 sec720 sec

660 sec600 sec540 sec480 sec

Fig. 14 (a) Investigated region in the physical model; (b) Flow paths of

acryl tracers in the region between inlet and the first row of electrodes at

the electrode temperature of 373K.

1970 C.-C. Yen and W.-S. Hwang

the inlet and allowed to flow with the fluid to obtain the flowpattern in the tank, as shown in Fig. 17. Figure 17 shows the3-D flow path of a fluid tracer particles which was recordedevery 20 seconds in the region near the bubbling zone, and itcan be seen that there was a long range flow circulation in thisregion. Initially, the fluid tracer particles moved towards thebottom near the third row of electrodes. As the particlestracer approached the bubbler, they rose to the surface andthen some of them moved backwards to the third row ofelectrodes. After several circular flows between the third

row of electrodes and the bubblers, the fluid tracer particlesmoved forward to the fourth row of electrodes at the surfaceand then flowed several times in circles between the fourthrow of electrodes and the bubblers. Some of the fluid tracerparticles moved forward to the fourth row of electrodes first,and then moved backwards to the third row of electrodes. Themoving direction mainly depends on the surface velocityfield of the bubbling zone, as shown in Fig. 16(c). From thisfigure, it can be observed that there were opposing directionsof velocities and these were the influential factor that causedthe fluid tracer particles to move backwards or forward.Specifically, as the particles passed through the bubbling line,they would move forward, but they would move backwardsif they did not pass through the line. The correspondingexperimental observation is shown in Fig. 18.

(a)

(b)

6080 sec5960 sec5900 sec5840 sec

5780 sec5720 sec5660 sec5600 sec

Fig. 15 (a) Investigated region in the physical model; (b) Flow paths of

acryl tracers in the region between the third row of electrodes and bubblers

at the electrode temperature of 373K.

ForwardBackwards

Bubbling Center

(b)

(a)

(c)

Fig. 16 (a) Investigated region in the numerical model; (b) 2-D section

view of the velocity field in the cross-section of the bubbler near the

bubbling zone; (c) 2-D top view of the velocity field in the cross-section of

the bubbling zone by numerical modeling.

(b)

(a)

Fig. 17 (a) Investigated region in the numerical model; (b) 3-D flow path

of a fluid tracer recorded every 20 seconds in the region near the bubbling

zone.

(e)

(d)

(c)

(b)

(a)

Fig. 18 (a) Sketch of the investigated region in the physical model; (b)–(e)

Flow paths of acryl tracer particles at room temperature with gas bubbling.

(The left hand figures are the sketches of the tracers’ positions in the

investigated regions of the physical model)

Numerical Study of Fluid Flow and Heat Transfer Behaviors and Its Experimental Verification 1971

From the experimental results of gas bubbling in thephysical model, a long range flow circulation was alsoobserved near the bubbling zone. This circulation wouldcause some acryl tracer particles to reside inside the bubblingzone for many cycles. From the flow pattern of tracerparticles, the acryl tracers initially moved along the freesurface from the inlet. In the region shown in Fig. 18(a), theythen began to aggregate near the third row of electrodes andmove towards the bottom, as shown in Figs. 18(b)–(c). Asthe tracers approached the bubbler, they rose quickly to thesurface due to fluid current induced by air bubbling, as shownin Fig. 18(d). At the surface some of the acryl tracers movedbackward to the third row of electrodes, and others movedforward to the fourth row of electrodes as shown inFig. 18(e). From Figs. 17 and 18, it can be seen that thesimulated results are consistent with the experimentalobservations.

5. Conclusions

In this study, a numerical model for a glass melting furnacewas developed, and a reduced physical model with heatingelectrodes and air bubbling devices was constructed tovalidate it. The following conclusions are made.(1) With regard to the effects of electrode heating, the

simulated temperatures were close to the temperaturereadings measured in the reduced physical model.

(2) With regard to the effects of electrode heating, twosmall zones of circulation were observed in the vicinityof the electrodes in the numerical model. The first onewas in the region between the inlet and the first row ofelectrodes, and the other one was in the region betweenthe third row of electrodes and the bubblers. Theseresults can be also observed in the reduced physicalmodel.

(3) With regard to the effect of air bubbling, a long rangecirculation was observed between the third and fourthrows of electrodes in the numerical model. Theseresults could be also observed in the reduced physicalmodel.

From the above, it can be found that the results from thenumerical and physical models are similar. Therefore, thenumerical model developed in this study is consideredreliable as a tool to aid the design and operation of a glassmelting furnaces.

Acknowledgments

The authors would like to acknowledge the financialsupported provided by the National Science Council inTaiwan (NSC 98-2221-E-006-066-MY3).

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